
    ȅiB             -       D~   S SK r S SKJrJr  S SKJr  S SKJr  S SKJ	r	  S SK
Jr  S SKrS SKJr  S SKJrJrJr  S SKJrJrJrJr  S S	KJr  S S
KJrJr  S SKJrJrJrJ r J!r!J"r"J#r#J$r$J%r%J&r&J'r'J(r(  S SK)J*r*J+r+J,r,J-r-J.r.  S SK/J0r0J1r1  S SK2J3r4  S SK5J6r6J7r7  S SK8J9r:  \	" S5      r;\" S5      r<\Rz                  R|                  r>\R~                  R                  SSS5      rA\B" S5      u  rCrDrES rFS rGS\\\<\;4   /\\<\;4   4   4S jrHS\!4S jrIS rJS rK\H" \>R                  \>R                  /5      \." 5       SSS\R                  SS4S  j5       5       rO\H" \>R                  R                  \>R                  R                  /5      \." 5       S! 5       5       rS\H" \>R                  R                  \>R                  R                  /5      \." 5       S"S#.S$ j5       5       rT\H" \>R                  5      \." 5       S% 5       5       rU\H" \>R                  R                  \>R                  R                  \>R                  R                  \>R                  R                  /5      \." S&S'5      S( 5       5       rX\H" \>R                  R                  \>R                  R                  /5      \." 5       S) 5       5       rYS* rZGS7S+\S,\[\\   S-\]4S. jjr^\H" \>R                  R                  \>R                  R                  /5      \." 5       S/ 5       5       r`SraS,\[\\   4S0 jrb\H" \>R                  R                  \>R                  R                  /5      \." 5       S1 5       5       rd\H" \>R                  R                  5      SS2.S3 j5       rg\H" \>R                  R                  5      \R                  SSSS4.S5 j5       ri\H" \>R                  R                  \>R                  R                  /5      \." 5       \R                  SSSS4.S6 j5       5       rk\H" \>R                  R                  \>R                  R                  /5      \." 5       \R                  SSSS4.S7 j5       5       rn\H" \>R                  R                  \>R                  R                  /5      \." 5       SSSSS4.S8 j5       5       rp\H" \>R                  R                  \>R                  R                  /5      \." 5       S+\S,\[\\   S9\\S:\\4S; j5       5       rr\H" \>R                  R                  5      GS7S< j5       rtS= ru\H" \>R                  R                  5      S> 5       rw\H" \>R                  5         GS8S?\S@\SA\SB\S-  SC\yS-  SD\R                  S-  4SE jj5       r{\H" \>R                  5       GS9SF\SG\SH\SD\R                  S-  4SI jj5       r}\H" \>R                  5      SJSJSSK.S?\SF\SG\SH\SD\R                  S-  4
SL jj5       r\H" \>GR                   5             GS:SM\R$                  SN\R$                  SB\S-  SO\S-  SD\R                  S-  SP\]SQ\\SR\\SS\\4ST jj5       r\H" \>GR                  R                  5      SUSV.S+\S,\\SW\SX\R$                  SY\ySZ\]S\4S[ jj5       r\H" \>GR                  R                  5      SUSV.S+\S,\\SW\SX\R$                  SY\ySZ\]S\4S\ jj5       r\." 5       \H" \>GR                  R                  5      S] 5       5       r\H" \>GR                  R                  5      SSSS SSS^.S_\SY\yS`\S-  S'\S-  Sa\S-  Sb\\Sc\]S\4Sd jj5       r\H" \>GR                  R                  \>GR                  GR                  /5      \." 5       Se 5       5       r\H" \>GR                  GR                  5      GS7Sf j5       r\H" \>GR                  R                  \>GR                  GR                  /5      \." 5       Sg 5       5       r\H" \>GR                  GR                  5      GS7Sh j5       r\H" \>GR$                  R                  5      Si 5       r\H" \>GR$                  R                  5      Sj 5       r\H" \>GR*                  R                  5      Sk 5       r\H" \>GR*                  GR.                  5      Sl 5       r\H" \>GR2                  R                  5      Sm 5       r\H" \>GR6                  R                  5      SSSSSSn.So j5       r\H" \>GR:                  R                  5      GS;Sp j5       r\H" \>GR<                  R                  5      GS8Sq j5       r\H" \>GR@                  R                  5      GS;Sr j5       r\H" \>GRB                  R                  5      Ss 5       r\H" \>GRF                  GR.                  5      St 5       rS+\Su\y4Sv jrS+\Sw\Sx\y4Sy jr GS<Sz\Su\yS{\]4S| jjrGS=Sw\Su\yS}\y4S~ jjrSw\S\S\]Su\y4S jr GS>S\yS\S?\S\y4S jjrS\y4S jr\H" \>GRX                  R                  \>GRX                  GRZ                  /5      \." SS5      GS?Sw\S\yS\]4S jj5       5       r\H" \>GR^                  R                  \>GR`                  R                  /5      \." 5       S?\S\4S j5       5       r\H" \>GRd                  /5      \." SS5      S?\4S j5       5       rS\S\4S jr\H" \>GRj                  5      \." 5       S+\Sw\S\]S\4S j5       5       r\H" \>GRl                  5      \." 5       GS7S+\Sw\S\]S\4S jj5       5       r\H" \>GRn                  5      \." 5       GS7S+\S\]S\4S jj5       5       r\H" \>GRp                  5      \." 5       GS7S+\S\]S\4S jj5       5       r\H" \>GRr                  R                  5      GS@Sw\S\]S\]4S jj5       r\H" \>GRt                  R                  \>GRt                  R                  /5      \." 5       S?\S\S\4S j5       5       r\H" \>GRv                  R                  5      GS7Sw\S\]4S jj5       r\H" \>GRz                  R                  \>GRz                  R                  /5      \." SSS5      SSS.S+\S\]S\]S\\\\4   4S jj5       5       r\H" \>GR                  R                  \>GR                  R                  /5      \." 5       SS.S\S\S\S\]S\4
S jj5       5       r\H" \>GR                  R                  \>GR                  R                  /5      \." SSS5      SUS.Sw\S\]S\\\\4   4S jj5       5       r\H" \>GR                  R                  \>GR                  R                  /5      \." SSS5      SUSS.Sw\S\]S\]S\\\\4   4S jj5       5       r\H" \>GR                  R                  \>GR                  R                  /5      \." 5       SUSS.S\S\S\S\]S\]S\4S jj5       5       r\H" \>GR                  5      \." SSS5        GSAS\S\S\]S\]S\\\\4   4
S jj5       5       rS\yS\\]\]4   4S jr\H" \>GR                  R                  \>GR                  R                  /5      \." SS5      GSBSw\S\yS\\\4   4S jj5       5       r\H" \>GR                  R                  \>GR                  GR                  /5      \." SSSS5      Sw\S\\\\\4   4S j5       5       r\H" \>GR                  R                  5         GSCSw\S\]S\]S\yS-  4S jj5       rS\S\S\\[\\   \[\\   4   4S jrS\S\Sx\yS-  S\\\4   4S jrS?\S\S\]4S jr\H" \>GR                  5      SUSSSSSS.Sw\S\S\]S\]S\S-  S\S-  S\S-  S\S-  S\\\\\4   4S jj5       r\H" \>GR                  R                  \>GR                  R                  /5      SUSSS.Sw\S\S\]S\]S\]S\S-  S\4S jj5       r\H" \>GR                  5      \." SSSUS9   GSDS+\Sw\S\]S\]S\]S\\\4   4S jj5       5       r\H" \>GR                  R                  5      S 5       r\H" \>GR                  5      \." 5         GSES?\S\S\S\]S\]S\4S jj5       5       rS rS r\H" \>GR                  5      \." 5       S 5       5       r\H" \>GR                  5      \." 5       S 5       5       rS r\H" \>GR                  5      \." S5      S 5       5       r\H" \>GR                  5      \." S5      S 5       5       rS r\H" \>GR                  5      \." 5       S 5       5       r\H" \>GR                  5      \." 5       S 5       5       r\H" \>GR                  R                  5      S 5       r\H" \>GR                  R                  \>GR                  GR                  \>GR                  R                  \>GR                  GR                  /5      \." S5      S 5       5       rS r\H" \>GR                  5      \." 5       S 5       5       r\H" \>GR                  5      \." 5       S 5       5       r\H" \>GR                  R                  \>GR                  GR                  \>GR                  R                  \>GR                  GR                  /5      \." S5      S 5       5       r\H" \>GR                  5      \." 5       GSFS+\S\S\4S jj5       5       r\H" \>GR                  5      \." 5       S\S+\S\S\S\4
S j5       5       r\H" \>GR                  R                  \>GR                  R                  /5      \." SUS9SJSJS.S j5       5       Gr \H" \>GR                  R                  \>GR                  R                  /5      \." 5       SS2.S j5       5       Gr\H" \>GR                  GR                  5      GSGS j5       Gr\H" \>GR                  GR
                  5      GSGS j5       Gr\H" \>GR                  R                  \>GR                  R                  /5      \." 5       GS9S j5       5       Gr\H" \>GR                  R                  5        GS@S j5       Gr
\H" \>GR                  5      \." SUS9GS9SD\R                  S-  4S jj5       5       GrS GrGSHS jGr GS9S\R$                  S@\R$                  S\[\\   \\-  S\[\\   \\-  S\[\\   \\-  S\]S\\S\[\\   \\-  S-  4S jjGrS Gr\H" \>GR"                  R                  5      S\R$                  S@\R$                  SB\R$                  S-  S\R$                  S-  S\R$                  S-  S\]S\S\4S j5       Gr\H" \>GR&                  R                  5      S\R$                  S@\R$                  SB\R$                  S\[\\   S\[\\   S\[\\   S\]S\[\\   S\\4S j5       Gr\GR*                  GR,                  (       Ga
  \R~                  R                  GS SS5      Gr\H" \Rz                  GR0                  GR2                  R                  5      GS 5       Gr\H" \Rz                  GR0                  GR6                  R                  5      GS 5       Gr\GR*                  GR:                  (       aO  \R~                  R                  GSSS5      Gr\H" \Rz                  GR>                  GR@                  5      GS 5       Gr!\R~                  R                  GSSS5      Gr"\H" \Rz                  GRF                  GRH                  R                  5      \H" \Rz                  GRF                  GRJ                  R                  5      \H" \Rz                  GRF                  GRJ                  GRL                  5      GS 5       5       5       Gr'\H" \Rz                  GRF                  GRH                  GRP                  5      \H" \Rz                  GRF                  GRH                  GRR                  5      GS 5       5       Gr*\H" \Rz                  GRF                  GRV                  R                  5      \H" \Rz                  GRF                  GRV                  GRL                  5      GS 5       5       Gr,\H" \Rz                  GRF                  GRV                  GRP                  5      \H" \Rz                  GRF                  GRV                  GRR                  5      GS	 5       5       Gr-\H" \Rz                  GRF                  GR\                  R                  5      \H" \Rz                  GRF                  GR^                  R                  5      GS
 5       5       Gr0\R~                  R                  GSSS5      Gr1\H" \Rz                  GRd                  GRf                  5          GSIGS j5       Gr4\H" \Rz                  GRd                  GRj                  5      GS 5       Gr6GS Gr7\H" \>GRp                  R                  5           GSJGS j5       Gr9GS Gr:\H" \>GRv                  R                  5      GS 5       Gr<\H" \>GRz                  5      \." 5            GSJGS j5       5       Gr>\H" \>GR~                  5      \." S5      GS 5       5       Gr@\H" \>GR                  R                  5      GS 5       GrB\H" \>GR                  R                  5      GS 5       GrD\H" \>GR                  R                  5      GS 5       GrF\H" \>GR                  5      \." S5      GS 5       5       GrHGS\S}\y4GS jGrI\H" \>GR                  5      \." SS'5      GS 5       5       GrK\H" \>GR                  5      \." S5      GS 5       5       GrM\H" \>GR                  5      \." SS'5      GS 5       5       GrO\H" \>GR                  5      \." S5      GS 5       5       GrQ\H" \>GR                  R$                  5      GS9GS  j5       GrS\H" \>GR                  R                  \>GR                  R                  /5      \." 5       GS! 5       5       GrU\H" \>GR                  R                  \>GR                  R                  /5      \." 5       S"GS".GS#\\4GS$ jj5       5       GrV\H" \Rz                  R|                  GR                  R                  \Rz                  R|                  GR                  R                  /5      \." 5       GS% 5       5       GrW\H" \>GR                  R$                  \>GR                  R$                  /5      GS& 5       GrZ\H" \>GR                  R                  /5      GS' 5       Gr\\H" \>GR                  R                  \>GR                  R                  /5      \." SUS9SJSJS.GS( j5       5       Gr^\H" \>GR                  R$                  /5      GS) 5       Gr`\H" \>GR                  R                  \>GR                  R                  /5      SSGS*.GS+ j5       Grc\H" \>GR                  R                  /5      SSGS*.GS, j5       Gre\H" \>GR                  /5      \." 5       GS- 5       5       Grg\H" \>GR                  /5      GS. 5       Gri\H" \>GR                  /5      GS/ 5       Grk\H" \>GR                  /5      GS0 5       Grm\H" \>GR                  /5      GS1 5       Gro\H" \>GR                  /5      GS2 5       GrpGS3\\GS4\\S\\4GS5 jGrqGS6 Grr\H" \>GR                  /5      SB\S-  4GS7 j5       Grt\H" \>GR                  /5      GS8 5       Grv\H" \>GR                  /5      GS9 5       Grx\H" \>GR                  R                  5      GS: 5       Grz\H" \>GR                  5      \." 5       GS; 5       5       Gr|\H" \>GR                  R                  5            GSKGS< j5       Gr~\H" \>GR                  R                  5      GS= 5       GrGS<GS> jGr\H" \>GR                  R                  \>GR                  R                  /5      \." 5       GSLSGS?.GS@ jj5       5       Gr\H" \>GR                  R                  \>GR
                  R                  /5      GSA 5       Gr\H" \>GR                  GR                  \>GR                  GR                  \>GR
                  GR                  \>GR
                  GR                  \>GR                  R                  \>GR                  GR                  /5      \." S&S'5      GSMGSB j5       5       Gr\H" \>GR                  R                  5      GSC 5       Gr\H" \>GR                  R                  5      GSD 5       Gr\H" \>GR                  R                  5      GSE 5       Gr\H" \>GR"                  GR$                  \>GR&                  GR$                  \>GR"                  R$                  \>GR&                  R$                  \>GR(                  R                  \>GR*                  R                  \>GR,                  R                  /5      GSF 5       Gr\H" \>GR0                  GR$                  \>GR2                  GR$                  \>GR0                  R$                  \>GR2                  R$                  /5      GSGSG j5       Gr\H" \>GR6                  GR$                  \>GR8                  GR$                  /5      GSGSH j5       Gr\H" \>GR<                  R                  \>GR<                  GR>                  /5      GSI 5       GrGSJ Gr\H" \>GRD                  R$                  \>GRD                  GR$                  /5      GSK 5       Gr\H" \>GRH                  R$                  \>GRH                  GR$                  /5      GSL 5       Gr\H" \>GRL                  R                  5      GSM 5       Gr\H" \>GRP                  R$                  \>GRP                  GR$                  /5      GSN 5       Gr\H" \>GRT                  R$                  \>GRT                  GR$                  /5      GSO 5       Gr\H" \>GRX                  R                  5      GSP 5       Gr\H" \>GR\                  R$                  5      \." 5       GSS\4GSQ jj5       5       Gr\H" \>GR`                  /5      \." 5        GSNGSR j5       5       Gr\H" \>GRd                  /5       GSNGSS j5       Gr\H" \>GRh                  /5       GSNGST j5       Gr\H" \>GRl                  R                  \>GRn                  R                  /5      GS7GSU j5       Gr\H" \>GRr                  GR$                  5      GSV 5       Gr\H" \>GRv                  R                  5      GSW 5       Gr\H" \>GRz                  5      GSX 5       Gr\H" \>GR~                  5      \." 5       GSY 5       5       Gr\H" \>GR                  5      GSZ 5       Gr\H" \>GR                  R                  5      GS7GS[ j5       GrGS;GS\ jGr\H" \>GR                  R                  5      GS] 5       Gr\H" \>GR                  R                  5      GS^ 5       GrGS_ GrGS` GrGSa GrGSb Gr GS7S?\GSc\\GSd\\GSe\\GSf\\GSg\\GSh\\GSi\\GSj\\GSk\\GSl\\GSm\\GSn\\GSo\\GSp\\GSq\\GSr\\GSs\\GSt\\GSu\\S\yGSv\]4,GSw jjGrGSx GrS?\GS\GSc\\GSd\\GSe\\GSf\\GSg\\GSh\\GSi\\GSj\\GSk\\GSl\\GSp\\GSq\\GSr\\GSs\\GSt\\GSu\\S\y4&GSy jGrGSz Gr\H" \>GR                  R                  5      GS{ 5       Gr\H" \>GR                  R                  5          GSIGS| j5       Gr\H" \>GR                  R                  5      GS} 5       Gr\H" \>GR                  5      \." SS'5          GSIGS~ j5       5       Gr\H" \>GR                  5      \." S5      GS 5       5       GrS?\GS\4GS jGr " GS GS\5      GrS?\GS\GS\\4GS jGr\H" \>GR                  R                  5      GS 5       Gr\H" \>GR                  5      \." 5       GS 5       5       Gr\H" \>GR                  5      \." SGS5      GS 5       5       Gr\H" \>GR                  R                  /5      GS 5       Gr\H" \>GR                  R                  5           GSOGS j5       Gr\H" \>GR                  R                  \>GR                  R                  /5      \." 5       SSSSSGS.GS j5       5       Gr\H" \>GR                  R                  \>GR                  R                  /5      \." 5       SSSSSGS.GS j5       5       Gr\H" \>GR                  R                  5      GS 5       Gr\H" \>GR                  R                  5      GSPGS j5       GrGS<S,\\GS\\GS\]4GS jjGrGS GrGS Gr\H" \>GR                  R                  5      GS7GS j5       GrGS7GS jGrGS9GS jGrGS GrGS9GS jGrGSQGS jGr\H" \>GR                  R                  5      GS 5       Gr\H" \>GR                  5      GS 5       Gr\H" \>GR                  GR                  \>GR                  GR                  \>GR                  GR                  \>GR                  GR                  /5      \." 5       GS9GS j5       5       Gr\H" \>GR                   GR                  \>GR                   GR                  \>GR                   GR                  \>GR                   GR                  /5      GS9GS j5       Gr\H" \>GR                  /5          GSRGS\GS\GS\GS\GS\]GS\]GS\S-  4GS jj5       GrGS\GS\\\GS4   4GS jGr\H" \>GR
                  /5          GSRGS\GS\GS\GS\S-  GS\]GS\GS\]GS\]GS\S-  4GS jj5       Gr\H" \>GR                  /5           GSSGS\GS\GS\GS\S-  GS\GS\]GS\]GS\S-  4GS jj5       Gr\H" \>GR                  /5       GS9GS\GS\GS\GS\S\GS\GS\GS\GS\\GS\\GS\GS\]GS\GS\GS\S-  4GS jj5       Gr
\H" \>GR                  /5          GSTGS\GS\GS\GS\GS\]GS\S-  GS\S-  4GS jj5       Gr\H" \>GR                  /5        GS;GS\GS\GS\GS\S\GS\GS\GS\]GS\S-  GS\S-  4GS jj5       Gr\H" \>GR                  /5           GSUGS\GS\GS\GS\S-  GS\GS\]GS\S-  GS\S-  S\\\4   4GS jj5       Gr\H" \>GR"                  /5         GSVGS\GS\GS\GS\S-  GS\]GS\]GS\S-  4GS jj5       Gr\H" \>GR&                  /5        GSWGS\GS\GS\GS\GS\S-  S\GS\GS\GS\GS\GS\[\]   GS\]GS\S-  4GS jj5       Gr\H" \>GR*                  /5       GS9GS\GS\GS\GS\S\GS\GS\GS\GS\GS\GS\GS\\GS\\GS\GS\]GS\S-  4 GS jj5       Gr\H" \>GR.                  /5           GSOGS\GS\GS\GS\S-  GS\S-  GS\\GS\\GS\GS\]GS\]GS\S-  GS\\S-  GS\\S-  GS\S-  GS\S-  4GS jj5       Gr\H" \>GR2                  /5         GS8GS\GS\GS\GS\S\GS\GS\GS\GS\\GS\\GS\GS\]GS\GS\GS\S-  GS\\S-  GS\\S-  4"GS jj5       Gr\H" \>GR6                  /5           GSXGS\GS\GS\SB\S-  GS\S-  GS\S-  GS\\S-  GS\\S-  GS\GS\\GS\]GS\S-  GS\S-  GS\S-  GS\\S-  4GS jj5       Gr\H" \>GR:                  /5         GSQGS\GS\GS\GS\SB\S-  GS\S-  GS\S-  GS\GR<                  GS\GR<                  GS\GS\GS\GS\GS\\GS\]GS\S-  GS\\S-  GS\]4$GS jj5       Gr    GSYS+\R$                  SH\R$                  GS\R$                  GS\R$                  SB\R$                  S-  GS\R$                  S-  SD\R                  S-  GS\]4GS jjGr \H" \>GRB                  R                  /5          GSYS+\R$                  SH\R$                  GS\R$                  GS\R$                  SB\R$                  S-  GS\R$                  S-  SD\R                  S-  GS\]4GS jj5       Gr"     GSZS+\R$                  SH\R$                  GS\[\R$                     GS\[\6   GS\[\R$                     GS\[\6   SB\R$                  S-  SD\R                  S-  GS\[\7   S-  GS\[\7   S-  GS\]4GS jjGr#\H" \>GRH                  R                  /5          GSYS+\R$                  SH\R$                  GS\[\R$                     GS\[\6   GS\[\7   GS\[\R$                     GS\[\6   GS\[\7   SB\R$                  S-  GS\R                  S-  GS\[\\   S-  GS\]4GS jj5       Gr%\H" \>GRL                  GRN                  \>GRL                  GRP                  /5      \." 5       GS<GS j5       5       Gr)\H" \>GRT                  GRN                  5      GS<GS j5       Gr+\H" \>GRX                  R                  \>GRX                  R                  /5      \." 5       GS7SS2.GS jj5       5       Gr-GS Gr.GS Gr/\H" \>GR`                  R                  \>GRb                  R                  /5      GS9GS j5       Gr0\H" \>GRd                  R                  \>GRf                  R                  /5      GS;GS j5       Gr2\H" \>GRh                  R                  \>GRj                  R                  /5        GS;GS\GS\\\\GR<                  -     GS\\\\GR<                  -     GS\S-  GS\S-  4
GS jj5       Gr4\H" \>GRl                  R                  \>GRn                  R                  /5      GS8GS j5       Gr6\H" \>GRp                  R                  \>GRp                  GRr                  \>GRp                  GR                  \>GRp                  GRt                  /5      GS[GS j5       Gr;GS Gr<\H" \>GRz                  R                  5        GS;GS j5       Gr>\H" \>GR~                  R                  5      GS 5       Gr?\H" \>GR                  R                  5      GS 5       Gr@\H" \>GR                  R                  5      GS 5       GrAGS GrBGS GrC\H" \>GR                  R                  \>GR                  R                  /5      GSLGS j5       GrF\H" \>GR                  R                  5      GS\GS j5       GrG\H" \>GR                  R                  5      GS]GS j5       GrI\H" \>GR                  5      \." 5        GS^GS j5       5       GrK\H" \>GR                  R                  \>GR                  GR                  /5      \." S&S'5      GSMGS j5       5       GrM\GR                  GrOGS GrP\H" \>GR                  R                  5      GS 5       GrQ\H" \>GR                  R                  5      GS 5       GrR\H" \>GR                  R                  5      GS 5       GrT\H" \>GR                  R                  5      GS  5       GrU\H" \>GR                  R$                  \>GR                  GR                  /5      \." 5       SSGS.GS j5       5       GrX\H" \>GR                  GR$                  \>GR                  GR                  /5      SSGS.S+\&GS\GS\]GS\]4GS jj5       GrZ\H" \>GR                  /5      \." 5       GS_GS j5       5       Gr\\H" \>GR                  R                  \>GR                  R                  /5        GS;GS j5       Gr_\H" \>GR                  R                  /5        GS;GS	 j5       Gra\H" \>GR                  R                  5      GS
 5       Grb\H" \>GR                  R                  \>GR                  R                  /5      \." 5       GS8GS j5       5       Grc\H" \Rz                  R|                  GR                  5      GS 5       Grd\H" \Rz                  R|                  GR                  5      GS 5       Gre\H" \>GR                  5      \." 5       SSSSGS.GS j5       5       GrgGS Grh\H" \>GR                  5      GS 5       Grj\H" \>GR                  5       GS`GS j5       Grl\H" \>GR                  5       GS`GS j5       Grn\H" \>GR                  5       GS`GS j5       Grp\H" \>GR                  5      \." 5       SSGS.GS j5       5       Grr\H" \>GR                  5      \." 5       GS\\S+\S\4GS j5       5       Grt\H" \>GR                  5      S+\4GS j5       Grv\H" \>GR                  5      \." SUS9S+\S\4GS j5       5       Grw\H" \>GR                  5      \." 5       S+\S\4GS j5       5       GrxGS Gry     GSZGS\GS\GS\R$                  S-  GS\R$                  S-  GS\S-  SB\S-  GS\R$                  S-  SD\R                  S-  GS\]4GS  jjGrz\H" \>GR                  5      \." 5          GS8GS\GS\GS\S-  SB\S-  SD\R                  S-  S\4GS! jj5       5       Gr|\H" \>GR                  /5           GSZGS\R$                  GS\R$                  GS\R$                  GS\R$                  GS\R$                  S-  SB\R$                  S-  GS\R$                  S-  SD\R                  S-  GS\]4GS" jj5       Gr~\H" \>GR                  5      \." 5       GS#\S,\\GS$\]S\4GS% j5       5       Gr\H" \>GR                  5      \." 5       GSGS& j5       5       Gr\H" \>GR                  5      \." 5          GSaS@\S'\GS'\\GS(\]GS)\]S\4GS* jj5       5       Gr\H" \>GR                  R                  5       GSbS&\Sa\[\   GS+\[\\   GS,\4GS- jj5       GrGS. Gr\H" \>GR                  R                  5          GScGS/ j5       GrGS0 GrG\" \>GR                  5        G\" \>GR                  5        G\" \>GR                  5        G\" \>GR                  5        G\" \>GR                  5        G\" \>GR                  5        G\" \>GR                   5        G\" \>GR"                  5        G\" \>GR$                  5        G\" \>GR&                  5        G\" \>GR(                  5        G\" \>GR*                  5        G\" \>GR,                  5        G\" \>GR.                  5        G\" \>GR0                  5        G\" \>GR2                  5        G\" \>GR4                  5        G\" \>GR6                  5        G\" \>GR8                  5        G\" \>GR:                  5        G\" \>GR<                  5        GS1 Gr\H" \>GR@                  5      \." 5       GS2 5       5       Gr\H" \>GRB                  5      \." 5       SJGS3.GS4 j5       5       Gr\H" \>GRD                  5      \." 5       SJGS3.GS5 j5       5       GrG\" \>GR@                  5      GrG\" \>GRB                  5      GrG\" \>GRD                  5      GrS SK/rS SGKrS SGKrGS6 GrG\" 5         g(d      N)CallableSequence)Enum)wraps)TypeVar)	ParamSpec)SymBoolSymFloatTensor)_add_op_to_registry_convert_out_paramsglobal_decomposition_table
meta_table)
OpOverload)_prim_elementwise_meta$ELEMENTWISE_PRIM_TYPE_PROMOTION_KIND)BoolLikecorresponding_complex_dtypecorresponding_real_dtypeelementwise_dtypesELEMENTWISE_TYPE_PROMOTION_KIND	FloatLikeIntLikemake_contiguous_strides_forNumber
NumberTypesuggest_memory_format
TensorLike)_maybe_convert_to_dtype_maybe_resize_out_resize_output_check_safe_copy_outout_wrapper)_broadcast_shapes_maybe_broadcast)_config)ScalingTypeSwizzleType)_pytree_T_PatenIMPLMeta   c                     X-   S-
  U-  $ N    abs     S/home/james-whalen/.local/lib/python3.13/site-packages/torch/_meta_registrations.pyceil_divr8   8   s    EAI!    c                     X-   S-
  U-  U-  $ )z$Rounds up x to nearest multiple of yr2   r3   xys     r7   round_upr>   <   s    UQY1!!r9   returnc                    ^  U 4S jnU$ )Nc                 Z   >^  [        T 5      m U 4S jn[        R                  " UT5        T $ )Nc                 (   > [        [        U T5        g N)r   r   )opfns    r7   register0register_meta.<locals>.wrapper.<locals>.registerE   s    
B3r9   )r   pytree	tree_map_)rE   rF   rD   s   ` r7   wrapperregister_meta.<locals>.wrapperB   s)     $	4 	2&	r9   r3   )rD   rJ   s   ` r7   register_metarL   A   s     Nr9   type_promotionc                     [         R                  " USU 06u  p#U Vs/ s H  n[        XC5      PM     nn[        U6 n[	        US[
        R                  06$ s  snf )Ntype_promotion_kindrM   )utilsr   r   r%   r   r   DEFAULT)rM   args_result_dtyper<   s        r7   elementwise_metarU   N   sp    
 ..	*OA ?CCd#A4dDC T"D "	BJJ  Ds   Ac                     [         R                  [         R                  [         R                  [         R                  [         R
                  [         R                  0nUR                  X 5      $ rC   )torch	complex32halfcfloatfloatcdoubledoubleget)dtypefrom_complexs     r7   toRealValueTypera   b   sC    ekku||L
 E))r9   c                 p   ^ ^ [        [        T /UQ76 5      m[        R                  " TT :H  UU 4S j5        g )Nc                     > ST ST  3$ )Nzoutput with shape z# doesn't match the broadcast shape r3   )broadcasted_shape
self_shapes   r7   <lambda>)check_inplace_broadcast.<locals>.<lambda>o   s    $ZL0STeSfgr9   )tupler$   rW   _check)re   
args_shaperd   s   ` @r7   check_inplace_broadcastrk   k   s0    /
HZHI	LLZ'gr9   Fc	           	        ^ ^^^^	 [        T [        R                  5      (       a)  [        R                  " T R	                  5       S:H  S 5        [        T[        R                  5      (       a)  [        R                  " TR	                  5       S:H  S 5        [        S T TT4 5       5      (       a`  [        R                  " [        R                  " 5       5      m	Tc  T	mOO[        R                  " [        R                  " T5      U	U4S j5        OT=(       d    [        R                  " 5       m[        T[        R                  5      (       d  [        S[        T5       35      e[        R                  " [        T[        5      UU U4S j5        [        T[        5      (       d  [        S[        T5       35      e[        R                  " TS:  S	 5        [        R                  " T4TUS
UUS9$ )Nr   c                      gNz:linspace only supports 0-dimensional start and end tensorsr3   r3   r9   r7   rf   (meta_linspace_logspace.<locals>.<lambda>       Pr9   c                      grn   r3   r3   r9   r7   rf   ro      rp   r9   c              3   B   #    U  H  n[        U[        5      v   M     g 7frC   )
isinstancecomplex).0args     r7   	<genexpr>)meta_linspace_logspace.<locals>.<genexpr>   s     
C/B:c7##/Bs   c                     > ST  ST 3$ )Nzlinspace(): inferred dtype z& can't be safely cast to passed dtype r3   )default_complex_dtyper_   s   r7   rf   ro      s    56K5LLrsxryzr9   zdtype must be torch.dtype, got c                     > S[        T5      R                   S[        T 5      R                   S[        T5      R                   S3$ )Nz4received an invalid combination of arguments - got (, ))type__name__)endstartstepss   r7   rf   ro      sB     u+r$s),,-RU0D0D/EQHr9   zsteps must be IntLike, got c                      g)Nz$number of steps must be non-negativer3   r3   r9   r7   rf   ro      s    %Kr9   metar_   layoutdevice
pin_memoryrequires_grad)rs   rW   r   ri   dimanyrP   r   get_default_dtypeis_complex_dtyper_   AssertionErrorr~   _check_typer   empty)
r   r   r   baser_   r   r   r   r   rz   s
   ``` `    @r7   meta_linspace_logspacer   s   s}    %&&IIK1P	
 #u||$$GGINP	

 
CsE/B
CCC % A A##%!
 =)ELL&&u-z
 2002eU[[))>tE{mLMM 
5'"	H
 eW%%:4;-HII	LL!KL;;	# r9   c                 6  ^ [         R                  " TR                  [         R                  :H  U4S j5        [         R                  " U R                  5       S:H  =(       a    TR                  5       S:g  (       + S 5        U R                  TR                  5      $ )Nc                  "   > ST R                    3$ )Nz2take(): Expected a long tensor for index, but got r_   indexs   r7   rf   meta_take.<locals>.<lambda>   s    DU[[MRr9   r   c                      g)Nz*take(): tried to take from an empty tensorr3   r3   r9   r7   rf   r      s    <r9   )rW   ri   r_   long_check_indexnumel	new_emptyshape)selfr   s    `r7   	meta_taker      sm     
LLuzz!R
 
ZZ\Q55;;=A#56< >>%++&&r9   r   c                b  ^ ^^ T R                   nTR                   n[        R                  " X4:H  S 5        [        R                  " T R                  T5      S:H  =(       a    TR                  T5      S:H  UUU 4S j5        [	        T R
                  TR
                  5      nT R                  U5      $ )Nc                      g)Nz=linalg.cross: inputs must have the same number of dimensions.r3   r3   r9   r7   rf   linalg_cross.<locals>.<lambda>       Or9   r/   c                  V   > ST  STR                  T 5       STR                  T 5       3$ )Nzlinalg.cross: inputs dimension z must have length 3. Got  and size)r   otherr   s   r7   rf   r      s1    -cU 399S>"%

3'8:r9   )ndimrW   ri   r   r$   r   r   )r   r   r   x_dy_d	out_shapes   ```   r7   linalg_crossr      s     ))C
**C	LL
O 
LL		#!4

31 4	
 "$**ekk:I>>)$$r9   c                 x    [        U S5        [        U S5        [        R                  " U [        R                  S9$ )Nzlinalg.matrix_expmemory_format)squareCheckInputscheckFloatingOrComplexrW   
empty_likecontiguous_formatr   s    r7   linalg_matrix_expr      s3     d/04!45D0G0GHHr9   valuesindicesc                 R   [         R                  " U R                  U R                  U R                  S9n[         R                  " U R                  U R                  [         R
                  S9nU R                  5       S:w  a%  U R                  S:w  a  [        XR                  5        X#4$ )Nr   r_   r   )	rW   r   r   r   r_   int64r   r   maybe_wrap_dim)r   r   r   r   s       r7   	cummaxminr      sl    
 [[DKKtzzJFkk$**T[[LGzz|qTYY!^sII&?r9   c                 r    [        XR                  5        [        R                  " U [        R                  S9$ Nr   )r   r   rW   r   r   )r   r   s     r7   logcumsumexpr      s)     3		"D0G0GHHr9   c                V  ^ UR                   n[        U5      nXV-
  n[        [        U5      5      n[        U5       V	s/ s H  n	SPM     n
n	U H  nSX'   M	     / / pU H0  nX   (       d  UR	                  U5        M  UR	                  U5        M2     X-   n[        U5      nUR                  5       mUS U nUR                  U4S jSS9  XUS  -   nUR                  U5      nS/[        UR                  US  5      -   nUR                  U5      nUR                  S5      nUUS'   [        U5      n[        [        U5      5       H  nX#U      UUS-   '   M     U R                  U[        R                  S9  [        U5       V	s/ s H  n	SPM     nn	SnUS-
  nUS:  a1  UU R                  S5      -  UUU   '   UX(U      -  nUS-  nUS:  a  M1  [        Xu5       H   nU R                  SUU-
  -   5      UUU   '   M"     U R                  UUU R                  5       5        U $ s  sn	f s  sn	f )	NFTc                    > TU    $ rC   r3   )r<   self_stridess    r7   rf   _exec_fft.<locals>.<lambda>  s	    <?r9   keyreverser   r   r2   r   )r   lenlistrangeappendstridesortpermuter   reshaper   resize_rW   r   as_strided_storage_offset)outr   	out_sizesr   forwardr   signal_ndim
batch_dimsdim_permuterS   is_transformed_dimdleftright	batch_endtmpinputbatched_sizes
batch_sizebatched_out_sizesiout_stridesbatch_numelr   s                          @r7   	_exec_fftr      s4   99Dc(K#J uT{#K).t5A%5 $  b%!$KKNLLO	 
 ,KD	I;;=L
jy
!CHH*DH9IJ//KLL%E D4JK 899MMM-(EAJ!M!]+3s8_#,V#4!a%  KK!1H1HKI $Dk*k1kK*KQA
q&&1CJJqM&AKN#yQ00	Q q& :$&)jja*n1E&FKN# %OOI{C,>,>,@AJW 6@ +s   H!H&r   r   exclude_lastc                    ^ [        U5      nU R                  5       mUS [        U5      [        U5      -
   R	                  U4S jS9  U$ )Nc                    > TU    $ rC   r3   )r   r   s    r7   rf   _sort_dims.<locals>.<lambda>/  s	    l1or9   )r   )r   r   r   intr   )r   r   r   sorted_dimsr   s       @r7   
_sort_dimsr   +  sL    s)K;;=L6#k"S%667<<% =  r9   c                 
   [         R                  " U R                  R                  5        U(       d  U R	                  5       $ [        X5      nU R                  U R                  5       5      n[        XPU R                  5       XCS9$ )Nr   )	rW   ri   r_   
is_complexcloner   r   r   r   )r   r   normalizationr   r   r   s         r7   meta_fft_c2cr   6  s\     
LL&&'zz|T'K
..
%CS		[JJr9   c                 n    [        U 5      [        :  d!  [        U 5      S:  a  U S   S:X  a
  U S   S:X  a  gg)N   r   r2   FT)r   cufft_max_ndimr   s    r7   use_optimized_cufft_pathr   E  s3    
3x. SX]s1v{s1vQR{r9   c                 |  ^ [         R                  " U R                  R                  5        [	        U R                  5       5      n[	        U5      nUS   nXF   S-  S-   n[	        U5      nXxU'   U(       a  XuU'   [        U 5      S:X  d  [        U 5      S:X  Gax  U R                  U[        R                  " U R                  5      S9n	U n
[        U 5      S:X  a  [        U5      (       a  [        XXQSS9  O[        U5      S:X  a  UOUn[        XX/SS9  [        U5      S:  a.  U R                  U[        R                  " U R                  5      S9n
US S nU(       au  XpU
R                  5       mUR                  U4S	 jSS
9  [        [         [        U5      5      nU[        U5      U-
  S  n[        XXSS9  US [        U5      U-
   nU(       a  Mu  U(       d7  U	R                  U5      XV   :w  a   U
R#                  U[         R$                  S9  U
n	U	$ U R                  U[        R                  " U R                  5      S9$ )Nr   r   r2   cudaxpur   Tr   c                    > TU    $ rC   r3   )r   stridess    r7   rf   meta_fft_r2c.<locals>.<lambda>s  s	    '!*r9   r   r   )rW   ri   r_   is_floating_pointr   r   device_hintr   rP   r   r   r   r   r   r   minr   r   r   )r   r   r   onesidedinput_sizesr   last_dimlast_dim_halfsizeonesided_sizesoutputworking_tensortarget_sizesr   max_dims	last_dimsr   s                  @r7   meta_fft_r2cr  L  s+    
LL--.tyy{#K[!I2wH#-2Q6+&N08/(4F"k$&75&@ U>>tzzJ   
 t&+CC+H+HfidK ),CA9>LflJPTU3x!|!%U%F%Ftzz%R "0 "
 cr(K)7(//1  ,d !  ~s;/?@'K(88(C(EF	Nt **GC,<x,GH + {{8$	(;;&&y@W@W&X' ~~U>>tzzJ  
 	
r9   )	generatorc                D    [        U[        R                  " U /5      5      $ rC   )r    rW   Size)nr  r   s      r7   meta_randpermr    s    S%**aS/22r9   r_   r   r   r   c                .    [         R                  " XX#US9$ Nr  rW   r   )r  r_   r   r   r   s        r7   meta_randperm_defaultr    s     ;;	v r9   c                t   ^ ^ Sm[         R                  " T T:  U U4S j5        [         R                  " XX4US9$ )Nr   c                     > ST ST  3$ Nz:random_ expects 'from' to be less than 'to', but got from=z >= to=r3   highlows   r7   rf   meta_randint.<locals>.<lambda>      LSEQXY]X^_r9   r  rW   ri   r   )r  r   r_   r   r   r   r  s   `     @r7   meta_randintr"    s:     C	LLs
_ ;;&J r9   c                p   ^ ^ [         R                  " TT :  UU 4S j5        [         R                  " X#XEUS9$ )Nc                     > ST ST  3$ r  r3   r  s   r7   rf   "meta_randint_low.<locals>.<lambda>  r   r9   r  r!  )r  r  r   r_   r   r   r   s   ``     r7   meta_randint_lowr&    s5     
LLs
_ ;;&J r9   c                .    [         R                  " XX#US9$ r  r  )r   r_   r   r   r   s        r7   meta_rand_defaultr(    s     ;;&J r9   r   lastdimc                    [         R                  " U R                  R                  5        [	        U 5      S:X  a  [        U R                  5       5      nX4US   '   U R                  U[        U R                  5      S9n[        U5      (       a(  [        UU R                  [         R                  S9UUSS9$ [        U5      S:  a  [        XS S SU5      nOU R                  [         R                  S9n[        XVXAS   /SS9$ U n[        U5      S:  a  US S n[        XUSS9nUSS  n[        UR                  5       5      nX4US   '   U R                  U[        U R                  5      S9n	[        XXASS9$ )	Nr   r   r   r   Fr   r2   r   )rW   ri   r_   r   r  r   r   r   ra   r   r   r   r   r   r   )
r   r   r   r)  r   r	  tempr   c2c_dimsr   s
             r7   meta_fft_c2rr-    s^    
LL&&'4F"%	$#b'	1LM#C((

)@)@
A  3x!|#Dcr(Aw?zz0G0GzHV92wiOO s8a<3BxH NEbc(C&	$#b'nnYodjj.InJYUCCr9   c                 `   SSK Jn  U" U 5      (       d%  [        R                  " U 5      S:X  a  [	        S5      e[        U[        5      (       a`  UR                  X5      nU R                  5       UR                  5       :w  a-  [        R                  R                  X@R                  5       5        U $ )Nr   )free_unbacked_symbolsr2   zQmore than one element of the written-to tensor refers to a single memory location)%torch.fx.experimental.symbolic_shapesr/  rW   _debug_has_internal_overlapRuntimeErrorrs   r   tor   r,   expand_copydefault)r   srcnon_blockingr/  intermediates        r7   
meta_copy_r9    s     L "$''E,M,Md,SWX,X_
 	
 #vvvd199;,++--$$\99;?Kr9   c                     [        U R                  5       5      n[        U R                  5       5      nXR                  5       :  a  SOX!   X1   -  nUR	                  US5        UR	                  X5        X#4$ r1   )r   r   r   r   insert)tensorr   result_sizesresult_strides
new_strides        r7   inferUnsqueezeGeometryr@    sf    &L&--/*NZZ\)|/@>CV/VJQ#*''r9   c                 z    [        XR                  5       S-   5      n[        X5      u  p#U R                  X#5        U $ r1   )r   r   r@  r   )r   r   g_sizes	g_stridess       r7   meta_unsqueeze_rD    s6    
hhj1n
-C/:GW(Kr9   r   weight_metabias_activation_opt	out_dtypec                 N   [        U R                  5      nUbS  UR                  S5      UR                  S5      :w  a/  [        SUR                  S5       SUR                  S5       35      eUR                  S5      U R                  S5      S-  :w  a2  [        SUR                  S5       SU R                  S5      S-   35      eUR                  S5      US'   [	        U R                  5      S:w  a"  [        S	[	        U R                  5       S
35      eSU R                  S5      4nUbM  U R
                  [        R                  :X  a  U[        R                  :X  d  [        SU R
                   SU 35      eU R                  UUc  U R
                  OUS9R                  Xg5      nU$ )Nr   z%output size mismatch: weight.size(0)= != bias.size(0)=r2   r   r   zweight.size(1)=z != input.size(-1)/2=z0we can only handle the squashed input case, got D inputzKout_dtype is only supported for i8i8->i32 linear operator, got input.dtype=, out_dtype=r   )r   r   r   r   r   r_   rW   int8int32r   
as_strided)	r   rE  rF  rG  rH  rI  output_sizestransposed_stridesr	  s	            r7   meta_sparse_structured_linearrS  $  s    $L;;q>TYYq\) 7A7GGXY]YbYbcdYeXfg  {{1~B!++fkk!n--B5::b>TUCUBVW
 	
 {{1~L 5;;1>s5;;?O>PPWX
 	
 UZZ]+uzz)i5;;.F ]^c^i^i]jjv  xA  wB  C  __&.ekkI   j2 
 Mr9   mat1	mat1_metamat2c                 <   [        U R                  5      S:w  a"  [        S[        U R                  5       S35      e[        UR                  5      S:w  a"  [        S[        UR                  5       S35      e[        UR                  5      S:w  a"  [        S[        UR                  5       S35      eU R                  S5      UR                  S5      S-  :w  a2  [        SU R                  S5       S	UR                  S5      S-   35      eU R                  S5      UR                  S5      /nUbM  UR                  [
        R                  :X  a  U[
        R                  :X  d  [        S
UR                   SU 35      eUR                  UUc  UR                  OUS9nU$ )Nr   mat1 must be 2D, got Dmat1_meta must be 2D, got mat2 must be 2D, got r2   r   mat1.size(1)= != mat2.size(0)/2=Jout_dtype is only supported for i8i8->i32 linear operator, got mat2.dtype=rM  r   	r   r   r   r   r_   rW   rN  rO  r   )rT  rU  rV  rI  rQ  r	  s         r7   meta_sparse_structured_mmr`  P  sv    4::!4S_4EQGHH
9??q 9#ioo:N9OqQRR
4::!4S_4EQGHHyy|tyy|a''DIIaL>)<TYYq\A=M<NO
 	
 IIaL$))A,/L

ejj(Y%++-E \]a]g]g\hhtu~t  A  ^^%-djj9  F
 Mr9   r2   )alphabetarI  c                X   [        U R                  5      S:w  a"  [        S[        U R                  5       S35      e[        UR                  5      S:w  a"  [        S[        UR                  5       S35      e[        UR                  5      S:w  a"  [        S[        UR                  5       S35      e[        UR                  5      S:w  a"  [        S[        UR                  5       S35      eU R                  S	5      UR                  S	5      :w  a/  [        S
U R                  S	5       SUR                  S	5       35      eUR                  S5      UR                  S	5      S-  :w  a2  [        SUR                  S5       SUR                  S	5      S-   35      eUR                  S	5      UR                  S5      /nUbM  UR                  [
        R                  :X  a  U[
        R                  :X  d  [        SUR                   SU 35      eUR                  UUc  UR                  OUS9nU$ )Nr2   zKonly input broadcasted to columns of mat1 * mat2 product is supported, got rL  r   rX  rY  rZ  r[  r   zUonly input broadcasted to columns of mat1 * mat2 product is supported, input.size(0)=z != mat1.size(0)=r\  r]  r^  rM  r   r_  )	r   rT  rU  rV  ra  rb  rI  rQ  r	  s	            r7   meta_sparse_structured_addmmrd  p  s    5;;1YZ]^c^i^iZjYkkrs
 	
 4::!4S_4EQGHH
9??q 9#ioo:N9OqQRR
4::!4S_4EQGHHzz!}		!$"ZZ]O+<TYYq\NL
 	
 yy|tyy|a''DIIaL>)<TYYq\A=M<NO
 	
 IIaL$))A,/L

ejj(Y%++-E \]a]g]g\hhtu~t  A  ^^%-djj9  F
 Mr9   compressed_Adense_Bra  transpose_resultalg_idsplit_ksplit_k_modec	           	      X   UR                   [        R                  [        R                  [        R                  [        R
                  [        R                  1;  a  [        SUR                    35      eU R                   UR                   :w  a%  [        SU R                    SUR                    35      e[        UR                  5      S:w  a"  [        S[        UR                  5       S35      eU R                   [        R
                  [        R                  4;   n	U	(       a   UR                  5       (       a  [        S5      eUR                  S5      n
U R                  S	5      nUb4  XR                  S	5      :w  a   [        S
U SUR                  S	5       35      eUbr  U	(       aB  U[        R                  [        R                  [        R                  [        R                  1;   d)  [        SU R                    SUR                    SU S35      eU(       a  X4OX4nUR                  XS9$ )NzA_cslt_sparse_mm only supports fp16, bf16, int8, and fp8e4m3, got z%inputs must have the same dtype, got r   r   z-_cslt_sparse_mm only supports 2d inputs, got rY  z.dense input must be transposed for 8bit dtypesr2   r   zbias size mismatch: m=rK  zout_dtype is not supported for z x z -> z matmul!r   )r_   rW   float32float16bfloat16rN  float8_e4m3fnr   r   r   is_contiguousr   rO  r   )re  rf  rG  ra  rI  rg  rh  ri  rj  is_8bit_input_typer  moutput_shapes                r7   meta__cslt_sparse_mmrt    s    }}

  OPWP]P]_
 	
 W]]*3L4F4F3GuW]]O\
 	
 7==Q;C<N;OqQ
 	
 &++

E<O<O/PP  "" !QRRQA!A		! (+<TYYq\NK  ##	 !1,2D2D1ESW[\e[ffno  .A6A6L\;;r9   T)include_selfr   sourcereduceru  c                H    [         R                  " U [         R                  S9$ r   rW   r   r   r   r   r   rv  rw  ru  s         r7   meta_index_reducer{    s     D0G0GHHr9   c                    U $ rC   r3   rz  s         r7   meta_index_reduce_r}    s	     Kr9   c                     [        U R                  5       5      nU R                  5       S:  a  UR                  5       X1'   U R	                  U5      $ Nr   )r   r   r   r   r   )r   r   r   result_sizes       r7   meta_index_selectr    s>     tyy{#KxxzA~ ;;=>>+&&r9   )lengthsr   offsetsaxisunsafeinitialdatar  r  r  r  c                   ^ ^ Ub  [        S5      eUU 4S jnUb  U" UR                  5      $ Ub+  UR                  S S UR                  S   S-
  4-   n	U" U	5      $ [        S5      e)Nz?segment_reduce(): indices based reduction is not supported yet.c                    > [         R                  " U TR                  TS-   S  -   TR                  S[         R                  S9$ )Nr2   r   r_   r   r   )rW   r   r   r_   r   )lengths_shaper  r  s    r7   segment_reduce_lengths_tensor:meta_segment_reduce.<locals>.segment_reduce_lengths_tensor  s>    {{DJJtaxz22**11	
 	
r9   r   r2   z<segment_reduce(): Either lengths or offsets must be defined.)NotImplementedErrorr   r2  )
r  rw  r  r   r  r  r  r  r  r  s
   `    `    r7   meta_segment_reducer     s|     !M
 	

 ,W]];; cr*gmmB.?!.C-EE,];;
U
VVr9   c                 $    U R                  S5      $ Nr3   r   r   s    r7   meta_maxr  $       >>"r9   c                     [         R                  " U R                  U45      n[        XU5      nU R	                  U5      U R	                  U[
        R                  S94$ Nr   rP   reduction_dimsr   _compute_reduction_shaper   rW   r   r   r   keepdimrs  s       r7   meta_max_dimr  *  P    


tzzC6
2C+Dw?L|$|5::6 r9   c                 $    U R                  S5      $ r  r  r   s    r7   meta_minr  4  r  r9   c                     [         R                  " U R                  U45      n[        XU5      nU R	                  U5      U R	                  U[
        R                  S94$ r  r  r  s       r7   meta_min_dimr  :  r  r9   c                     U R                  5       (       a  [        U R                  5      nO[        U [        R
                  S9u  p![        R                  " XS9$ NrO   r   )r   r   r_   r   r   INT_TO_FLOATrW   r   )r   rT   rS   s      r7   
meta_angler  D  sH    /

;, ? L L
 D55r9   c                     [         R                  " XR                  5       U R                  5        UR	                  [         R
                  " U 5      5      $ rC   )rW   _resize_output_r   r   copy_angle)r   r   s     r7   meta_angle_outr  P  s4    	#yy{DKK899U[[&''r9   c                     g rC   r3   )vals    r7   assert_asyncr  V      
r9   c                     g rC   r3   )r  
assert_msgs     r7   assert_async_metar  [  r  r9   c                     g rC   r3   )ss    r7   
print_metar  `  r  r9   r_   r   r   r   r   c                 ,    [         R                  " SSS9$ )Nr   r   r   r  r  s        r7   make_dep_tokenr  e  s     ;;q((r9   c                 j    SSK Jn  [        U [        [        45      (       a  [        S5      eU" XUS9  g )Nr   )constrain_range'Constraining SymFloat or Symbool is nyir  max)r0  r  rs   r
   r	   
ValueError)r   r  r  r  s       r7   sym_constrain_ranger  q  s0     F$7+,,BCCDs+r9   c                 .    [         R                  XUS9  U$ Nr  )r,   r  r   r  r  	dep_tokens       r7   functional_sym_constrain_ranger  {  s    T4r9   c                 <   SSK Jn  Uc  Uc  [        R                  " U S:  5        g [	        U [
        [        45      (       a  [        S5      e[        U 5      [        L a7  Ub  [        R                  " X:  5        Ub  [        R                  " X:*  5        g U" XUS9  g )Nr   )_constrain_range_for_sizer  r  )
r0  r  rW   ri   rs   r
   r	   r  r~   r   )r   r  r  r  s       r7   sym_constrain_range_for_sizer    s     P
{s{TQY$7+,,BCCDzS?LL%?LL%d5r9   c                 .    [         R                  XUS9  U$ r  )r,   r  r  s       r7   'functional_sym_constrain_range_for_sizer    s    %%d%=r9   c                     U$ rC   r3   )r  r  r  s      r7   functional_assert_async_metar    s    r9   f_namec           	         U R                  5       S:  a  [        U SU R                  5        35      eU R                  S5      U R                  S5      :w  a2  [        U SU R                  S5       SU R                  S5       S35      eg )Nr   z8: The input tensor must have at least 2 dimensions, got r   z5: A must be batches of square matrices, but they are  by 	 matrices)r   r   r   )r   r  s     r7   r   r     s    xxzA~hNtxxzl[
 	
 yy}		"%hKDIIVXM?Z^_c_h_hik_l^mmvw
 	
 &r9   Anamec                   ^ ^^ [         R                  " T R                  TR                  :H  UU 4S j5        [         R                  " T R                  TR                  :H  UU 4S j5        [         R                  " TR	                  S5      TR	                  S5      :H  U4S j5        [         R                  " TR	                  S5      T R	                  S5      :H  UUU 4S j5        g )Nc                  >   > STR                    ST R                    S3$ )Nz:Expected b and A to be on the same device, but found b on z
 and A on 	 instead.r  r  r   s   r7   rf   (linearSolveCheckInputs.<locals>.<lambda>  s     H{{m:ahhZy:r9   c                  >   > STR                    ST R                    S3$ )Nz=Expected b and A to have the same dtype, but found b of type z and A of type r  r   r  s   r7   rf   r    s     Kzzl/!'')=r9   r   r  c                  R   > ST R                  S5       ST R                  S5       S3$ )Nz3A must be batches of square matrices, but they are r  r  r   r  r   r  s   r7   rf   r    s+    FF2J<tAFF2J<yBr9   c                     > ST ST R                  S5       ST R                  S5       STR                  S5       STR                  S5       3
$ )NzIncompatible matrix sizes for z: each A matrix is r   r  z but each b matrix is r  r   )r  r  r   s   r7   rf   r    sM    ,TF 3D$TYYr]O4		"Hr9   )rW   ri   r   r_   r   )r   r  r  s   ```r7   linearSolveCheckInputsr    s    	LLqxx	
 
LL

agg	
 
LL	r
affRj 	
 
LL	r
diim#	
r9   tallow_low_precision_dtypesc                 h  ^^ U R                   m[        R                  " U R                  5       =(       d    U R	                  5       UU4S j5        U(       d\  [        R                  " T[        R
                  [        R                  [        R                  [        R                  4;   UU4S j5        g g )Nc                     > T ST  3$ )Nz<: Expected a floating point or complex tensor as input. Got r3   r_   r  s   r7   rf   (checkFloatingOrComplex.<locals>.<lambda>  s    6(VW\V]^r9   c                     > T ST  3$ )Nz*: Low precision dtypes not supported. Got r3   r  s   r7   rf   r    s    vhHPr9   )	r_   rW   ri   r  r   r[   r]   rZ   r\   )r  r  r  r_   s    ` @r7   r   r     sn    
 GGE	LL	/^ &ekk5<<u}}MMP	
 &r9   arg_namec                 b   ^^ [         R                  " U R                  5       S:  UU4S j5        g )Nr   c                     > T ST  S3$ )Nz: The input tensor z! must have at least 2 dimensions.r3   )r  r  s   r7   rf   checkIsMatrix.<locals>.<lambda>  s    6(-hZ7XYr9   )rW   ri   r   )r  r  r  s    ``r7   checkIsMatrixr    s    	LL	1Yr9   Br   c                   ^ ^^^ [        T T5        [        TT5        [        R                  " T(       a#  T R	                  S5      TR	                  S5      :H  O"T R	                  S5      TR	                  S5      :H  U UUU4S j5        g )Nr  r   c                     > T ST(       a  SOS ST R                  S5       ST R                  S5       STR                  S5       STR                  S5       S	3$ )
Nz2: Incompatible shapes of A and B for the equation zAX = BzXA = Bz (r  r<   r   r   r}   r   )r  r  r  r   s   r7   rf   #checkInputsSolver.<locals>.<lambda>  sV    hHxX.AaffRj\qvvbzl!AFF2J<qJr9   )r   r  rW   ri   r   )r  r  r   r  s   ````r7   checkInputsSolverr    sY    a !V	LL$(r
affRj affRjAFF2J.F	
r9   resultfn_nameresult_namec                 v   ^ ^^^ [         R                  " TR                  TR                  :H  U UUU4S j5        g )Nc            	      L   > T  ST ST STR                    STR                    3	$ )Nz: Expected z5 and input tensors to be on the same device, but got z on z and input on r  )r  r   r  r  s   r7   rf   !checkSameDevice.<locals>.<lambda>  s0    i{;-/dm4nU\\NLr9   )rW   ri   r   )r  r  r   r  s   ````r7   checkSameDevicer    s&     
LL%	
r9   UPLOc                    ^  T R                  5       n[        R                  " [        T 5      S:H  =(       a    US:H  =(       d    US:H  U 4S j5        g )Nr2   ULc                     > ST  3$ )Nz1Expected UPLO argument to be 'L' or 'U', but got r3   )r  s   r7   rf   checkUplo.<locals>.<lambda>  s    CD6Jr9   )upperrW   ri   r   )r  UPLO_uppercases   ` r7   	checkUplor    s<    ZZ\N	LLD	QKNc1J^s5JJr9   eigenvalueseigenvectorsr  	compute_vc                 P   [        U S5        [        U5        [        U R                  5      nU(       a,  U R	                  U5      nUR                  U[        USS95        OU R	                  S/5      nUR                  5         U R	                  U[        U R                  5      S9nXT4$ )Nzlinalg.eighF	row_majorr   r   )
r   r  r   r   r   r   r   popra   r_   )r  r  r  r   vecsvalss         r7   meta__linalg_eighr    s     a'dOME{{5! ;EU ST{{A3	IIK;;uOAGG$<;=D:r9   c                     [        U S5        [        R                  " U R                  5      (       a  U R                  O[        R                  " U R                  5      nU R                  U R                  S S US9$ )Nzlinalg.eigvalsr   r   )r   rP   r   r_   r   r   r   )r   complex_dtypes     r7   meta__linalg_eigvalsr  #  sf     e-. !!%++.. 	..u{{; 
 ??5;;s+=?AAr9   c                    [        U S5        [        R                  " U R                  5      (       a  U R                  O[        R                  " U R                  5      nU R                  U R                  S S US9nU R                  U R                  US9n[        U 5      S:H  nUR                  U R                  [        U R                  US95        X#4$ )Nz
linalg.eigr   r   r   r  )
r   rP   r   r_   r   r   r   r  r   r   )r   r
  r   vectorsis_cudas        r7   meta_linalg_eigr  /  s     e\* !!%++.. 	..u{{; 
 __U[["-]_CFooekko?G% F*G0P ?r9   r6  c                 p    U R                   R                  [        R                  S9R	                  SS5      $ )Nr   r  r   )mTr   rW   r   	transpose)r6  s    r7   cloneBatchedColumnMajorr  A  s*    66<<e&=&=<>HHRPPr9   r  c                     [        U 5      $ rC   )r  )r   r  r  s      r7   _cholesky_solve_helperr  E  s     #4((r9   c                    ^ ^ [         R                  " T R                  S:  U 4S j5        [         R                  " TR                  S:  U4S j5        [        T TS5      u  p4[	        X4U5      $ )Nr   c                  $   > ST R                    S3$ )Nz-b should have at least 2 dimensions, but has  dimensions insteadr   r   s   r7   rf    cholesky_solve.<locals>.<lambda>P  s    ?		{J]^r9   c                  $   > ST R                    S3$ )Nz-u should have at least 2 dimensions, but has r  r  r  s   r7   rf   r  T  s    ?xGZ[r9   cholesky_solve)rW   ri   r   !_linalg_broadcast_batch_dims_namer  )r   r  r  self_broadcastedA_broadcasteds   ``   r7   r  r  K  sd     
LL		Q^ 
LL	![ 'Ha!'# ""25IIr9   c                     U R                  5       S:X  a#  [        R                  " U [        R                  S9$ [	        U S5        [        U 5      $ )Nr   r   cholesky)r   rW   r   legacy_contiguous_formatr   r  r   r  s     r7   r!  r!  \  s@     zz|qE4R4RSSdJ'"4((r9   c                 0    [        U S5        [        U 5      $ )Ncholesky_inverse)r   r  r#  s     r7   r%  r%  e  s     d./"4((r9   check_errorsc                 
   [        U S5        [        U S5        U R                  n[        U5      n[	        US5      nU R                  U5      nUR                  X55        U R                  USUS-
   [        R                  S9nXg4$ )Nzlinalg.choleskyFr   r   r   )	r   r   r   r   r   r   r   rW   rO  )r  r  r&  A_shaper   	L_stridesr  infoss           r7   linalg_cholesky_exr+  m  s|    a*+1/0ggGw<D ,GU;I	GAMM'% KKD1H-U[[KAE8Or9   tauc                 J  ^ ^^ [         R                  " T R                  S:  S 5        [         R                  " T R                  S5      T R                  S5      :  S 5        [         R                  " T R                  S5      TR                  S5      :  S 5        [         R                  " T R                  TR                  -
  S:H  U U4S j5        T R                  S:  a<  T R                  S S nTR                  S S m[         R                  " TU:H  U4S	 j5        [         R                  " TR
                  T R
                  :H  U U4S
 j5        [        STT S5        [         R                  " T R                  [        T R                  SS9T R
                  T R                  S9$ )Nr   c                      g)NzHtorch.linalg.householder_product: input must have at least 2 dimensions.r3   r3   r9   r7   rf   ,linalg_householder_product.<locals>.<lambda>      Zr9   r  r   c                      g)Nzbtorch.linalg.householder_product: input.shape[-2] must be greater than or equal to input.shape[-1]r3   r3   r9   r7   rf   r/    s    tr9   c                      g)Nz`torch.linalg.householder_product: input.shape[-1] must be greater than or equal to tau.shape[-1]r3   r3   r9   r7   rf   r/    s    rr9   r2   c                  <   > STR                    ST R                    3$ )Nzptorch.linalg.householder_product: Expected tau to have one dimension less than input, but got tau.ndim equal to  and input.ndim is equal to r  r   r,  s   r7   rf   r/    "    )),
2Nuzzl\r9   c                     > ST  3$ )Nzltorch.linalg.householder_product: Expected batch dimensions of tau to be equal to input.shape[:-2], but got r3   actual_batch_tau_shapes   r7   rf   r/        66L5MOr9   c                  <   > STR                    ST R                    3$ )Nz,torch.linalg.householder_product: tau dtype z does not match input dtype r   r5  s   r7   rf   r/    s    :399+*5;;-9r9   z torch.linalg.householder_productr,  Fr  r   r   r_   r   )
rW   ri   r   r   r   r_   r  empty_stridedr   r   )r   r,  expected_batch_tau_shaper9  s   `` @r7   linalg_householder_productr?    sK   
 
LL

aZ 
LL

2%**R.(t 
LL

2#((2,&r
 
LL

SXX"	
 zzA~#(;;s#3 !$3B"&>>	
 
LL		U[[ 	
 6UEJ[[*5;;%Hkk||	 r9   c                    [        U S5        [        U SSS9  U R                  U R                  5      nUR	                  U R                  [        U R                  SS95        U R                  U R                  S S [        R                  S9nX#4$ )Nzlinalg.inv_exF)r  r  r  r   r   r   r   r   r   r   rW   rO  )r  r&  r  r*  s       r7   linalg_inv_ex_metarB    so    a)1o%P	AGGAMM!''6qww%PQKKEKKK8E8Or9   LDpivotsinfo)	hermitianr&  rF  c                t   [        U S5        [        U S5        [        R                  " U R                  [        U R                  SS9U R                  U R                  S9nU R                  U R                  S S [        R                  S9nU R                  U R                  S S [        R                  S9nX4U4$ )Nztorch.linalg.ldl_factor_exFr  r<  r   r   r  )
r   r   rW   r=  r   r   r_   r   r   r   )r   rF  r&  rC  rD  rE  s         r7   linalg_ldl_factor_ex_metarH    s     d894!=>			ZZ*4::Gjj{{	
B ^^DJJsO599^=F>>$**Sb/>;Dtr9   )rF  c                j  ^ ^^ [        T S5        [        T S5        [        TT S5        [        R                  " TR
                  S:  U4S j5        T R                  S S n[        R                  " UTR                  :H  U4S j5        [        R                  " [        R                  " TR                  5      U4S j5        [        R                  " T R                  TR                  :H  UU 4S j5        [        TT 5      u  pV[        R                  " U[        USS	9TR                  TR                  S
9$ )Nztorch.linalg.ldl_solver   c                  $   > ST R                    S3$ )NzMtorch.linalg.ldl_solve: Expected B to have at least 2 dimensions, but it has r  r  )r  s   r7   rf   'linalg_ldl_solve_meta.<locals>.<lambda>      &&!46r9   r   c                  $   > ST R                    S3$ )Nzjtorch.linalg.ldl_solve: Expected LD.shape[:-1] and pivots.shape to be the same, but got pivots with shape  insteadr   rD  s   r7   rf   rK        ))/h@r9   c                  "   > ST R                    3$ )Nz<torch.linalg.ldl_solve: Expected pivots to be integers. Got r   rP  s   r7   rf   rK    s    Nv||n]r9   c                  <   > STR                    ST R                    3$ )Nz!torch.linalg.ldl_solve: LD dtype z does not match b dtype r   )r  rC  s   r7   rf   rK    s     3BHH:=UVWV]V]U^_r9   Fr  r<  )r   r   r  rW   ri   r   r   rP   is_integer_dtyper_   _linalg_broadcast_batch_dimsr=  r   r   )rC  rD  r  rF  expected_pivots_shapeB_broadcast_sizerS   s   ```    r7   linalg_ldl_solve_metarX    s     b232781b":;	LL	!	
 HHSbM	LL-	
 
LLv||,] 
LL
AGG_ 7q"=*+;uMggxx	 r9   Pr  )pivotrZ  c                j  ^  [         R                  " T R                  S:  U 4S j5        [        T R                  5      nUS   nUS   n[        X45      nX2S'   U(       a  T R                  U5      nOT R                  S/5      nXRS'   T R                  U5      nXRS'   XBS'   T R                  U5      nXgU4$ )Nr   c                  $   > ST R                    S3$ )Nz@linalg.lu: Expected tensor with 2 or more dimensions. Got size: rN  rO  r  s   r7   rf    linalg_lu_meta.<locals>.<lambda>  s    RSTSZSZR[[cdr9   r  r   r   )rW   ri   r   r   r   r  r   )	r  rZ  sizesrr  r  krY  r  r  s	   `        r7   linalg_lu_metar`    s     
LL	!d
 MEb	Ab	AA	A"IKKKK"I	EA"I"I	EA7Nr9   LU)rZ  r&  c                  ^  [         R                  " T R                  S:  U 4S j5        [        T R                  5      nUS   nUS   n[         R
                  " U[        USS9T R                  T R                  S9nUR                  5         [        XE5      US'   T R                  U[         R                  S9nUR                  5         T R                  U[         R                  S9nXgU4$ )	Nr   c                  $   > ST R                    S3$ )NzFtorch.lu_factor: Expected tensor with 2 or more dimensions. Got size: rN  rO  r  s   r7   rf   *linalg_lu_factor_ex_meta.<locals>.<lambda>(  s    XYZY`Y`Xaaijr9   r  r   Fr  r<  r   )rW   ri   r   r   r   r=  r   r_   r   r  r  r   r   )	r  rZ  r&  r^  rr  r  ra  rD  rE  s	   `        r7   linalg_lu_factor_ex_metare    s     
LL	!j
 MEb	Ab	A			*5EBggxx	
B 
IIKA	E"I[[eii[0F 
IIK;;uEII;.Dtr9   )r   adjointrf  c                
  ^ ^^ [        T S5        [        R                  " T R                  TR                  :H  UU 4S j5        [        R                  " TR                  [        R                  :H  S 5        [        T S5        [        T TUS5        [        R                  " T R                  S5      TR                  S5      :H  S 5        [        R                  " T R                  S S TR                  :H  U4S j5        [        TT 5      u  pV[        R                  " U[        XS(       + S9TR                  TR                  S	9nUR                  5       S
:w  a,  U(       d%  UR                  5       (       a  UR                  5       nU$ )Nztorch.linalg.lu_solvec                  >   > STR                    ST R                    S3$ )NzPlinalg.lu_solve: Expected LU and B to have the same dtype, but found LU of type  and B of type rN  r   )r  ra  s   r7   rf   &linalg_lu_solve_meta.<locals>.<lambda>P  s#    $$&HH:_QWWIXOr9   c                      g)NzElinalg.lu_solve: pivots should be a Tensor of scalar type torch.int32r3   r3   r9   r7   rf   rj  W  s    Wr9   zlinalg.lu_solver   c                      g)NzYlinalg.lu_solve: Number of pivots per batch should be same as the dimension of the matrixr3   r3   r9   r7   rf   rj  _  s    kr9   c                  $   > ST R                    S3$ )Nzclinalg.lu_solve: Expected LU.shape[:-1] and pivots.shape to be the same, but got pivots with shape rN  rO  rP  s   r7   rf   rj  e  rQ  r9   r  r<  r   )r   rW   ri   r_   r   r   r  r   r   rU  r=  r   r   r   r   conj)ra  rD  r  r   rf  rW  rS   r  s   ```     r7   linalg_lu_solve_metaro  B  s-    267	LL
AGG	
 
LL		!W b12b!T#45	LL
v{{2&k 
LL
"%	
 7q"=  *+;xPggxx	F ||~4[[]FMr9   unpack_dataunpack_pivotsc                 6  ^  [         R                  " T R                  S:  U 4S j5        U(       a3  [         R                  " UR                  [         R                  :H  S 5        [        T R                  5      nUS   nUS   n[        XV5      nXTS'   U(       a  T R                  U5      nOT R                  S/5      nU(       a/  XtS'   T R                  U5      n	XtS'   XdS'   T R                  U5      n
O$T R                  S/5      n	T R                  S/5      n
XU
4$ )Nr   c                  $   > ST R                    S3$ )NzFtorch.lu_unpack: Expected tensor with 2 or more dimensions. Got size: rN  rO  )ra  s   r7   rf    lu_unpack_meta.<locals>.<lambda>  s    XY[YaYaXbbjkr9   c                      g)Nztorch.lu_unpack: LU_pivots is expected to be a contiguous tensor of torch.int32 dtype.
Note: this function is intended to be used with the output produced by torch.linalg.lu_factorr3   r3   r9   r7   rf   rt    s    pr9   r  r   r   )	rW   ri   r   r_   rO  r   r   r  r   )ra  rD  rp  rq  r^  rr  r  r_  rY  r  r  s   `          r7   lu_unpack_metarv  {  s     
LL
1k LLEKK'	
 NEb	Ab	AA	A"ILLLL!b	LLb	b	LLLL!LL!7Nr9   modec                    ^  T S:X  a  SnSnX4$ T S:X  a  SnSnX4$ T S:X  a  SnSnX4$ [         R                  " SU 4S j5        WW4$ )NreducedTcompleteFrc                     > ST  S3$ )Nzqr received unrecognized mode 'z=' but expected one of 'reduced' (default), 'r', or 'complete'r3   )rw  s   r7   rf    _parse_qr_mode.<locals>.<lambda>  s    1$ 8N Or9   rW   ri   )rw  	compute_qry  s   `  r7   _parse_qr_moder    s    y	  
		  
	  		
 gr9   QRc                    [        U S5        [        U S5        [        U5      u  p#U R                  S   nU R                  S   n[	        XE5      nU(       aO  [        U R                  5      nU(       a  UOUUS'   U R                  U5      nUR                  U[        USS95        OU R                  S/5      n[        U R                  5      n	U(       d  U(       d  UOUU	S'   U R                  U	5      n
U
R                  U	[        U	SS95        X4$ )Nz	linalg.qrr  r   Fr  r   )	r  r   r  r   r  r   r   r   r   )r  rw  r  reduced_moderr  r  r_  Q_shaper  R_shaper  s              r7   linalg_qr_metar    s     ![!1k*,T2I	A	AA	Aqww-'aQKK 	g:7eTUKK 177mG#9!!GBK	GAMM'6w%PQ4Kr9   sign	logabsdetc                 t   [        U S5        [        U SS5        U R                  nU R                  US S 5      nU R                  US S [	        U R
                  5      S9n[        R                  " U[        US5      U R
                  U R                  S9nU R                  US S [        R                  S9nX#XE4$ )Nzlinalg.slogdetFr  r   r<  r   )r   r   r   r   ra   r_   rW   r=  r   r   rO  )r  r   r  r  ra  rD  s         r7   _linalg_slogdetr    s     a)*1.6GGE;;uSbz"DE#2Joagg.FGI			*5%8ggxx	
B [[s5;;[7FB&&r9   full_matrices
compute_uvdriverc                 b   [        U S5        [        U S5        [        U R                  S S 5      nU R                  S   nU R                  S   n[	        XV5      nU(       a  XEU(       a  UOU/-   nU R                  U5      n	U	R                  U[        USS95        XA(       a  UOUU/-   n
U R                  U
5      n[        U 5      S:H  nUR                  U
[        XS95        O$U R                  S/5      n	U R                  S/5      nU R                  XG/-   [        U R                  5      S9nXU4$ )	Nz
linalg.svdr  r   Fr  r   r   r   )r  r   r   r   r  r   r   r   r  ra   r_   )r  r  r  r  r   rr  r  r_  U_shaper  V_shapeVr  Ss                 r7   _linalg_svd_metar    s    !\"1l+aggcrl#J	A	AA	A11==KK 	g:7eTU]1==KK 
 a.F*	g:7VW KKKK 	
J$OAGG,DEA7Nr9   arg1arg2c                    U R                   S S nUR                   S S n[        X#5      n[        U5      nXPR                  S5      U R                  S5      /-  n[        U5      nXaR                  S5      UR                  S5      /-  nXV4$ )Nr  r   )r   r$   r   r   )r  r  arg1_batch_sizesarg2_batch_sizesexpand_batch_portionarg1_expand_sizearg2_expand_sizes          r7   rU  rU    s    
 zz#2zz#2,-=P012		"66012		"66--r9   c                     U(       a  [        XU5        [        X5      u  p4X0R                  :X  a  U OU R                  U5      nXAR                  :X  a  UOUR                  U5      nXV4$ rC   )r  rU  r   expand)r  r  r  r  r  arg1_broadcastedarg2_broadcasteds          r7   r  r  !  sh     t40)Ed)Q& !JJ.DKK@P4Q  !JJ.DKK@P4Q  --r9   r   c                     U R                   S S nUR                  S:H  =(       d2    U R                  S-
  UR                  :H  =(       a    UR                   U:H  nU$ )Nr   r2   )r   r   )r   r   expected_batched_rhs_shapevector_cases       r7   linalg_solve_is_vector_rhsr  5  sS    !&Sb!1**/ 

Q%**$R8R)R  r9   )r   r&  r  ra  rD  rE  c                  ^ ^ [        T S5        [        R                  " T R                  TR                  :H  U U4S j5        [	        T T5      nU(       a  TR                  S5      OTn	[        T XS5        [        U	T 5      u  p[        R                  " U=(       d    U(       + S 5        U(       a  U
S S OU
n[        R                  " U[        X(       + 5      TR                  TR                  S9nT R                  n[        R                  " U[        US5      T R                  T R                  S9nT R                  US S [        R                  S9nT R                  US S [        R                  S9nXEXg4nXUU4n[        S	 U 5       5      (       aa  [        UU5       HQ  u  nn[!        UUR                  5        UR#                  UR                  UR%                  5       5        ['        UUSS
9  MS     U$ )Nzlinalg.solvec                  >   > ST R                    STR                    S3$ )NzKlinalg.solve: Expected A and B to have the same dtype, but found A of type ri  rN  r   )r  r  s   r7   rf   "_linalg_solve_ex.<locals>.<lambda>L  s     Ywwiqwwix9r9   r   c                      g)Nzlinalg.solve: Vector broadcasting of the left hand side is not supported for left=False. In this case linalg.solve is equivalent to B / A.squeeze(-1)r3   r3   r9   r7   rf   r  W  s    Kr9   r<  Fr   r  c              3   (   #    U  H  oS Lv   M
     g 7frC   r3   )ru   r<   s     r7   rw   #_linalg_solve_ex.<locals>.<genexpr>n  s     
&#QD=#s   )	copy_fromcopy_toexact_dtype)r   rW   ri   r_   r  	unsqueezer  rU  r=  r   r   r   r   rO  allzipr    r   r   r"   )r  r  r   r&  r  ra  rD  rE  r  B_B_broad_shaperS   result_shaperesult_r   LU_pivots_info_r   resr{  os   ``                    r7   _linalg_solve_exr  =  s    1n-	LL	177	
 -Q2K'RQBa>23B:M	LLK	
 *5="%-L!!*<Bggxx	G GGE


*5%8ggxx	C kk%*EKKk8GKKcr
%++K6Ev
$C%
(C

&#
&&&SMDAqa)MM!''188:.QuE " Jr9   )r   unitriangularr   r  r   c                   Uc  U R                  S/5      n[        U[        5      (       d  [        S[	        U5       35      e[        XUS5        [        XS 5      u  pgUR                  SS5      R                  5       =(       a    UR                  5       nU(       a  [        XVR                  5      nU$ [        XVR                  5      (       a=  UR                  UR                  SS5      R                  5        UR                  SS5        U$ )Nr   zout must be TensorLike, got zlinalg.solve_triangularr  r   )r   rs   r   r   r~   r  r  r  rp  is_conjr    r   r!   r   
transpose_)	r  r  r  r   r  r   r  A_avoid_copy_As	            r7   linalg_solve_triangular_metar  x  s     {kk1#c:&&;DI;GHHaD";<.qT:FB<<B'557HBJJLLXX. J  XX..KKR,223NN2r"Jr9   XM)r  r  c                   ^ ^ [         R                  " T R                  S:  U 4S j5        [         R                  " TR                  S:  U4S j5        [        T TS5        TR                  [         R
                  :X  aw  [        T T5      u  pV[         R                  " U[        USS9T R                  T R                  S9n[         R                  " U[        USS9TR                  TR                  S9nXx4$ TR                  [         R                  :X  d  TR                  [         R                  :X  a+  [         R                  " T 5      nT R                  S/5      nXx4$ [         R                  " SS	 5        WW4$ )
Nr   c                  $   > ST R                    S3$ )NzMtorch.triangular_solve: Expected b to have at least 2 dimensions, but it has r  r  r   s   r7   rf   'triangular_solve_meta.<locals>.<lambda>  s    ))$79r9   c                  $   > ST R                    S3$ )NzMtorch.triangular_solve: Expected A to have at least 2 dimensions, but it has r  r  r  s   r7   rf   r    rL  r9   triangular_solveFr  r<  r   c                      g)Nz+triangular_solve: Got an unexpected layout.r3   r3   r9   r7   rf   r    s    $Qr9   )rW   ri   r   r  r   stridedrU  r=  r   r_   r   
sparse_csr
sparse_bsrr   r   )	r   r  r  r  r  self_broadcast_sizeA_broadcast_sizesolutioncloned_coefficients	   ``       r7   triangular_solve_metar    sC    
LL		Q	
 
LL	!	
 4$67xx5== 0LTST0U-&&$./BeT**;;	
 #00!./?5Q''88	
 '' 
U%%	%U5E5E)E##D)!^^QC0 '' 	UQR'''r9   c                 ^   [        U S5        [        U S5        U R                  U R                  S S 5      nU R                  U R                  5      nUR	                  U R                  [        U R                  SS95        U R                  U R                  S S [        R                  S9nXU4$ )Nz
linalg.detr  Fr  r   r   rA  )r  detra  rD  s       r7   _linalg_det_metar    s    a&1l+
++aggcrl
#C	
QWW	BNN17775QR[["U[[[9FF?r9   c                 X  ^ ^^^^^ [         R                  " T R                  S:  S 5        [         R                  " TR                  S:  S 5        U(       a  SOSm[         R                  " TR                  T   TR                  S   :  U4S j5        [         R                  " TR                  T   T R                  S   :H  U4S j5        [         R                  " TR                  S   T R                  S   :*  S 5        [         R                  " T R                  TR                  -
  S	:H  U U4S
 j5        [         R                  " T R                  TR                  :H  U U4S j5        T R                  S:  ai  T R                  S S nTR                  S S m[         R                  " TU:H  U4S j5        TR                  S S m[         R                  " TU:H  U4S j5        [         R                  " TR                  T R                  :H  U U4S j5        [         R                  " TR                  T R                  :H  U U4S j5        [        STT S5        [        STT S5        [         R                  " TR                  [        TR                  SS9TR                  TR                  S9$ )Nr   c                      g)Nz3torch.ormqr: input must have at least 2 dimensions.r3   r3   r9   r7   rf   ormqr.<locals>.<lambda>      !Vr9   c                      g)Nz3torch.ormqr: other must have at least 2 dimensions.r3   r3   r9   r7   rf   r    r  r9   r  r   c                     > ST  S3$ )Ntorch.ormqr: other.shape[z0] must be greater than or equal to tau.shape[-1]r3   left_size_conditions   r7   rf   r    s    +,?+@@pqr9   c                     > ST  S3$ )Nr  z"] must be equal to input.shape[-2]r3   r  s   r7   rf   r    s    +,?+@@bcr9   c                      g)NzHtorch.ormqr: tau.shape[-1] must be less than or equal to input.shape[-1]r3   r3   r9   r7   rf   r    r0  r9   r2   c                  <   > STR                    ST R                    3$ )Nz[torch.ormqr: Expected tau to have one dimension less than input, but got tau.ndim equal to r4  r  r5  s   r7   rf   r    r6  r9   c                  <   > STR                    ST R                    3$ )Nzhtorch.ormqr: Expected other to have the same number of dimensions as input, but got other.ndim equal to r4  r  r   r   s   r7   rf   r    s&    ++0::,6RSXS]S]R^`r9   c                     > ST  3$ )NzWtorch.ormqr: Expected batch dimensions of tau to be equal to input.shape[:-2], but got r3   r8  s   r7   rf   r    r:  r9   c                     > ST  3$ )NzYtorch.ormqr: Expected batch dimensions of other to be equal to input.shape[:-2], but got r3   )actual_batch_other_shapes   r7   rf   r    s    66N5OQr9   c                  <   > ST R                    STR                    3$ )NzPtorch.ormqr: Expected input and tau to have the same dtype, but input has dtype z and tau has dtype r   r5  s   r7   rf   r    s"    ##(;;-/B399+Or9   c                  <   > ST R                    STR                    3$ )NzRtorch.ormqr: Expected input and other to have the same dtype, but input has dtype z and other has dtype r   r  s   r7   rf   r    s"    ##(;;-/DU[[MSr9   ztorch.ormqrr,  r   Fr  r<  )	rW   ri   r   r   r_   r  r=  r   r   )	r   r,  r   r   r  expected_batch_shaper  r9  r  s	   ```   @@@r7   ormqrr    s    
LL

aV 
LL

aV !%""	LL'(CIIbM9q 
LL'(EKKO;c
 
LL		"R(Z
 
LL

SXX"	
 
LL

ejj 	
 zzA~${{3B/!$3B"&::	
 $);;s#3 $(<<	
 
LL		U[[ 	
 
LLu{{"	
 M3u5M5%9[[*5;;%Hkk||	 r9   c                  ^ ^^ [         R                  " [        T5      ST-  :H  UU4S j5        T R                  nUTS-   :H  nUnU(       + nU(       a1  [	        SU5       H   nU=(       a    T R                  U5      S:g  nM"     O/[	        U5       H   nU=(       a    T R                  U5      S:g  nM"     [         R                  " U=(       d    UUU 4S j5        g )Nr   c                  ,   > SST -   S[        T5       3$ )Nzpadding size is expected to be r   z, but got: r   )r   paddings   r7   rf   ,_padding_check_valid_input.<locals>.<lambda>1  s    1!c'+c'l^Tr9   r2   r   c                  :   > ST S-    ST S-    STR                    3$ )N	Expected r2   zD or r   zcD (batch mode) tensor with possibly 0 batch size and other non-zero dimensions for input, but got: rO  )r   r   s   r7   rf   r  F  s-    aycAgY /AAFOr9   )rW   ri   r   r   r   r   )r   r  r   	input_dimis_batch_modevalid_batch_modevalid_non_batch_moder   s   ```     r7   _padding_check_valid_inputr  .  s    	LLGCT
 

I#'*M$,,q)$A/FEJJqMQ4F % y!A#7#NEJJqMQ<N  " 
LL00	
r9   c                  ^ ^^^^	^
 SnSmSnT R                   S:X  a  T R                  S5      nTS-  mUS-  n[        T USS9  Uu  m	m
T R                  U5      nT R                  T5      mTT	-   T
-   mU(       a-  [        R                  " T	T:  =(       a    T
T:  UU U	U
4S j5        [        R                  " TS:  UU4S j5        T R                   S:X  a  T R                  UT45      $ T R                  XET45      $ )Nr   r2   r/   r   c                  4   > ST ST ST  STR                    3$ NzcArgument #4: Padding size should be less than the corresponding input dimension, but got: padding (r|   ) at dimension 
 of input rO  dim_wr   pad_lpad_rs   r7   rf   _pad1d_common.<locals>.<lambda>b  -    %%*G2eWOE7*UZU`U`Tacr9   c                     > ST  ST 3$ )Nz
input (W: z%) is too small. Calculated output W: r3   )input_woutput_ws   r7   rf   r  j  s    *WI%J8*Ur9   r   )r   r   r  rW   ri   r   )r   r  is_reflection	dim_planenbatchnplaner  r  r  r  r  s   `     @@@@@r7   _pad1d_commonr  M  s    IEFzzQA
Q	ug15LE5ZZ	"FjjG&HGO/	
 
LLAU
 zzQ1229::r9   c                     [        XSS9$ NTr  )r  r   r  s     r7   meta_reflection_pad1dr  s       t<<r9   c                    ^  [         R                  " T R                  [         R                  :g  U 4S j5        [	        T USS9$ )Nc                  @   > ST R                   R                  5        S3$ )Nz)"replication_pad1d" not implemented for ''r_   __str__r   s   r7   rf   (meta_replication_pad1d.<locals>.<lambda>~      =ekk>Q>Q>S=TTUXr9   Fr  )rW   ri   r_   boolr  r  s   ` r7   meta_replication_pad1dr  y  5     
LLuzz!X u==r9   c                  ^ ^^^^^ SmU(       d$  [         R                  " [        U5      S:H  S 5        TR                  S:X  a  TS-  mUu  mmTR	                  T5      nUT-   T-   mU(       a-  [         R                  " TU:  =(       a    TU:  UUUU4S j5        [         R                  " TT R	                  T5      :H  UU U4S j5        TR                  TR                  5      $ )Nr2   r   c                      g)Nz padding size is expected to be 2r3   r3   r9   r7   rf   (_pad1d_backward_common.<locals>.<lambda>  s    0Rr9   r/   c                  4   > ST ST ST  STR                    3$ r  rO  r  s   r7   rf   r    r   r9   c                  2   > ST STR                  T 5       3$ Nz(grad_output width unexpected. Expected: , Got: r   r  grad_outputr  s   r7   rf   r         :8*GKL\L\]bLcKder9   )rW   ri   r   r   r   r   r   )	r"  r   r  r  r  r  r  r  r  s	   ``   @@@@r7   _pad1d_backward_commonr$    s    ES\Q&(RSzzQ
LE5jjG&HGO/	
 
LLK$$U++e
 ??5;;''r9   
grad_inputc                     [        XUSS9$ r
  r$  r"  r   r  s      r7   meta_reflection_pad1d_backwardr)    s     "+gTRRr9   c                     [        XUSS9$ )NFr  r'  r(  s      r7   meta_replication_pad1d_backwardr+    s     "+gUSSr9   c                  ^ ^^^	^
^^^^^^ SmSmSnSn[        T USS9  T R                  nUS:X  a   T R                  S5      nTS-  mTS-  mUS-  nUu  mmmmT R                  U5      nT R                  T5      m	T R                  T5      m
T	T-   T-   mT
T-   T-   mU(       aZ  [        R                  " TT
:  =(       a    TT
:  UU UU4S j5        [        R                  " TT	:  =(       a    TT	:  UU UU4S j5        [        R                  " TS:  =(       d    TS:  U	U
UU4S j5        T R                  S	:X  a  T R                  UTT45      $ T R                  XFTT45      $ )
Nr   r2   r   r      c                  4   > ST ST ST  STR                    3$ r  rO  r  s   r7   rf   _pad2d_common.<locals>.<lambda>  r   r9   c                  4   > ST ST ST  STR                    3$ NzcArgument #6: Padding size should be less than the corresponding input dimension, but got: padding (r|   r  r  rO  dim_hr   pad_bpad_ts   r7   rf   r/    r   r9   c                      > ST  ST ST ST 3$ )Nz
input (H:  W: z%) is too small. Calculated output H: r3   )input_hr  output_hr  s   r7   rf   r/    s%    	gY /$$,:T(=r9   r/   r  r   r   rW   ri   r   )r   r  r  
dim_slicesr  r   r  r3  r  r8  r  r9  r  r4  r  r  r5  s   `      @@@@@@@@@@r7   _pad2d_commonr<    sS   EEJFug15::DqyA

a
!(E5%ZZ
#FjjGjjG&H&HGO/	
 	GO/	
 
LLA&Q	
 zzQ(;<<(CDDr9   c                     [        XSS9$ r
  )r<  r  s     r7   meta_reflection_pad2dr>    r  r9   c                    ^  [         R                  " T R                  [         R                  :g  U 4S j5        [	        T USS9$ )Nc                  @   > ST R                   R                  5        S3$ )Nz)"replication_pad2d" not implemented for 'r  r  r  s   r7   rf   (meta_replication_pad2d.<locals>.<lambda>  r  r9   Fr  )rW   ri   r_   r  r<  r  s   ` r7   meta_replication_pad2drB    r  r9   c                 `    [         R                  " U5      n[         R                  " U5      nXV4$ rC   rW   r   )grad_wsaved_vsaved_gsaved_normsr   grad_vgrad_gs          r7   meta_weight_norm_backwardrK    s,     g&Fg&F>r9   c                   ^ ^^^^ SmSmSnUR                   nUR                  5       S:X  a  TS-  mTS-  mUS-  nUu  pVpxUT   n	UT   n
X-   U-   mX-   U-   m[        R                  " TT R	                  T5      :H  UU U4S j5        [        R                  " TT R	                  T5      :H  UU U4S j5        UR                  UR                   5      $ )Nr   r2   r   r-  c                  2   > ST STR                  T 5       3$ r  r   r!  s   r7   rf   %meta_pad2d_backward.<locals>.<lambda>  r#  r9   c                  2   > ST STR                  T 5       3$ Nz)grad_output height unexpected. Expected: r   r   r3  r"  r9  s   r7   rf   rN         ;H:W[M]M]^cMdLefr9   )r   r   rW   ri   r   r   )r"  r   r  r  re   r  r  r5  r4  r8  r  r3  r  r9  r  s   `          @@@@r7   meta_pad2d_backwardrS    s     EEIJxxzQ

Q	!(E%GG&H&H	LLK$$U++e 
LLK$$U++f >>$**%%r9   c          	      ~  ^ ^^^	^
^^^^^^^^^^^ Sm	SmSmSn[        T USS9  T R                  S:H  nU(       a%  T R                  S5      nT	S-  m	TS-  mTS-  mUS-  nUu  mmmmmmT R                  U5      nT R                  T5      m
T R                  T5      mT R                  T	5      mT
T-   T-   mTT-   T-   mTT-   T-   mU(       a  [        R                  " TT:  =(       a    TT:  U	U UU4S j5        [        R                  " TT:  =(       a    TT:  UU UU4S j5        [        R                  " TT
:  =(       a    TT
:  UU UU4S	 j5        [        R                  " TS:  =(       d    TS:  =(       d    TS:  U
UUUUU4S
 j5        U(       a  T R                  WUTTT45      $ T R                  UTTT45      $ )Nr/   r   r2   r   r      c                  4   > ST ST ST  STR                    3$ r  rO  r  s   r7   rf   _pad3d_common.<locals>.<lambda>>  r   r9   c                  4   > ST ST ST  STR                    3$ r1  rO  r2  s   r7   rf   rW  E  r   r9   c                  4   > ST ST ST  STR                    3$ )NzcArgument #8: Padding size should be less than the corresponding input dimension, but got: padding (r|   r  r  rO  )dim_dr   pad_bkpad_fs   r7   rf   rW  L  s-    %%*G2fX_UG:V[VaVaUbdr9   c                  ,   > ST  ST ST ST ST ST 3$ )Nz
input (D:  H: r7  z%) is too small. Calculated output D: r3   )input_dr8  r  output_dr9  r  s   r7   rf   rW  T  s2    	gYd7) <$$,:T(4zKr9   r:  )r   r  r  r  
batch_moder  r  rZ  r3  r  r_  r8  r  r`  r9  r  r4  r[  r\  r  r  r5  s   `      @@@@@@@@@@@@@@@r7   _pad3d_commonrb  !  s   EEEIug15qJA


Q	07-E5%vZZ	"FjjGjjGjjG'H&H&HGO/	
 	GO/	
 	GO0 0	
 
LLA7Q7(a-	
 	
 (HMNN(HEFFr9   c                     [        XSS9$ r
  )rb  r  s     r7   meta_reflection_pad3drd  `  r  r9   c                    ^  [         R                  " T R                  [         R                  :g  U 4S j5        [	        T USS9$ )Nc                  @   > ST R                   R                  5        S3$ )Nz)"replication_pad3d" not implemented for 'r  r  r  s   r7   rf   (meta_replication_pad3d.<locals>.<lambda>k  r  r9   Fr  )rW   ri   r_   r  rb  r  s   ` r7   meta_replication_pad3drh  f  r  r9   c                 \  ^ ^^^^^^ [         R                  " [        U5      S:H  S 5        UR                  S::  a  [	        SUR                   35      eT R                  UR                  :w  a%  [	        ST R                   SUR                   35      eSmSmSmUR                  S	:X  a  TS-  mTS-  mTS-  mUu  p4pVpxUR                  T5      n	UR                  T5      n
UR                  T5      nX-   U-   mX-   U-   mX-   U-   m[         R                  " TT R                  T5      :H  UU U4S
 j5        [         R                  " TT R                  T5      :H  UU U4S j5        [         R                  " TT R                  T5      :H  UU U4S j5        UR                  UR                  5      $ )N   c                      g)Nz padding size is expected to be 6r3   r3   r9   r7   rf   %meta_pad3d_backward.<locals>.<lambda>z  s    ,Nr9   r/   zinput.ndim must be > 3, got z,grad_output.ndim must equal input.ndim, got  != r   r2   rU  c                  2   > ST STR                  T 5       3$ r  r   r!  s   r7   rf   rl    r#  r9   c                  2   > ST STR                  T 5       3$ rP  r   rQ  s   r7   rf   rl    rR  r9   c                  2   > ST STR                  T 5       3$ )Nz(grad_output depth unexpected. Expected: r   r   )rZ  r"  r`  s   r7   rf   rl    r#  r9   )rW   ri   r   r   r   r   r   r   )r"  r   r  r  r  r5  r4  r\  r[  r_  r8  r  rZ  r3  r  r`  r9  r  s   `           @@@@@@r7   meta_pad3d_backwardrq  p  s    
LLW"$NOzzQ;EJJ<HII5::%:;;K;K:LDQVQ[Q[P\]
 	
 EEEzzQ


07-E%jjGjjGjjG'H&H&H	LLK$$U++e 
LLK$$U++f 
LLK$$U++e
 ??5;;''r9   pc                 @   [         R                  " U R                  5       S 5        U R                  S5      nUS::  a-  U R	                  S/5      R                  [         R                  S9$ U R	                  X"S-
  -  S-  45      R                  [         R                  S9$ )Nc                      g)Nz(_pdist_forward requires contiguous inputr3   r3   r9   r7   rf   %meta__pdist_forward.<locals>.<lambda>  s    &Pr9   r   r2   r   r   )rW   ri   rp  r   r   r3  r"  )r   rr  r  s      r7   meta__pdist_forwardrv    s     
LLP 			!AAv~~qc"%%E4R4R%SS~~qE{a/125588 6 
 	
r9   gradpdistc                     [         R                  " UR                  5       S 5        [         R                  " UR                  5       S 5        [         R                  " U[         R                  S9$ )Nc                      g)Nz._pdist_backward requires self to be contiguousr3   r3   r9   r7   rf   &meta__pdist_backward.<locals>.<lambda>  s    &Vr9   c                      g)Nz/_pdist_backward requires pdist to be contiguousr3   r3   r9   r7   rf   r{    s    'Xr9   r   )rW   ri   rp  r   r"  )rw  r   rr  rx  s       r7   meta__pdist_backwardr}    sW     
LLV 
LLX D0N0NOOr9   )rb  ra  c          
      b  ^ ^^^^^ SSK JnJn  TR                  S5      nTR                  S5      nTR                  S5      n	U" [        R
                  " U" T R                  XxU	45      5      5      (       a  T R                  XxU	45      m [        R                  " TR                  5       S:H  S 5        [        R                  " TR                  5       S:H  S 5        [        R                  (       dN  [        R                  " T R                  TR                  s=:H  =(       a    TR                  :H  Os  UUU 4S j5        TR                  n
TR                  mU
S   mU
S   m[        R                  " TS   T:H  =(       a    TS   T:H  UUU4S	 j5        T R                  T R                  5       5      $ )
Nr   )guard_or_truesym_eqr2   r   r/   c                      gNzbatch1 must be a 3D tensorr3   r3   r9   r7   rf   meta_baddbmm.<locals>.<lambda>      ,Hr9   c                      gNzbatch2 must be a 3D tensorr3   r3   r9   r7   rf   r    r  r9   c                  V   > STR                    ST R                    STR                    3$ )Nz+Input dtypes must be the same, got: input: z
, batch1: z
, batch2: r   )batch1batch2r   s   r7   rf   r    s.    A$**ZX^XdXdWeeopvp|p|o}~r9   c            	      .   > ST ST ST S    ST S    S3	$ Nz@Expected size for first two dimensions of batch2 tensor to be: [r|   z] but got: [r   r2   ].r3   batch2_sizesbscontraction_sizes   r7   rf   r    s5    t2&'|LO3DB|TUFWWY[r9   )r0  r  r  r   rW   sym_notr   r  ri   r   
exp_config&skip_dtype_check_in_meta_registrationsr_   r   )r   r  r  rb  ra  r  r  dim1dim2dim3batch1_sizesr  r  r  s   ```        @@@r7   meta_baddbmmr    s9    L;;q>D;;q>D;;q>DU]]6$**t46H#IJKK{{D-.	LL"$HI	LL"$HI<<JJ&,,66&,,6~	
 <<L<<L	aB#A	LLQ2E,q/5E"E	
 >>$))+&&r9   c                H    [         R                  " U [         R                  S9$ r   ry  r   r  s     r7   meta_bernoullir    s     D0G0GHHr9   c                     U $ rC   r3   r   rr  r  s      r7   meta_bernoulli_r        Kr9   c                 H    [         R                  " U [         R                  S9$ r   ry  r  s      r7   meta_bernoulli_pr    s     D0G0GHHr9   c                 .    [         R                  " U 5      $ rC   rD  r  s     r7   meta_poissonr         D!!r9   c                     [         R                  " XR                  5       :  S 5        [         R                  " U [         R                  S9n[         R                  " U 5      U4$ )Nc                      g)NzJError in fused_moving_avg_obs_fake_quant_cpu: ch_axis must be < self.dim()r3   r3   r9   r7   rf   6meta__fused_moving_avg_obs_fq_helper.<locals>.<lambda>	      \r9   r   )rW   ri   r   r   r  )r   observer_onfake_quant_onrunning_minrunning_maxscale
zero_pointaveraging_const	quant_min	quant_maxch_axisper_row_fake_quantsymmetric_quantmasks                 r7   $meta__fused_moving_avg_obs_fq_helperr    sM      
LL((*\ D

3DT"D))r9   c                 \  ^^^^ [         R                  " U R                  5       S:H  S 5        [         R                  " UR                  5       S:H  S 5        U R                  u  mmUR                  u  mm[         R                  " TT:H  UUUU4S j5        Ubr  [         R                  " X R                  :H  =(       dG    U[         R
                  :H  =(       a-    U R                  [         R                  [         R                  4;   S 5        Uc  U R                  OUnU R                  TT4US9$ )Nr   c                      g)Nza must be 2Dr3   r3   r9   r7   rf   meta_mm.<locals>.<lambda>	      ~r9   c                      g)Nzb must be 2Dr3   r3   r9   r7   rf   r  	  r  r9   c            	      "   > ST ST  ST ST S3	$ )Nz/a and b must have same reduction dim, but got [r|   z] X [r  r3   )M1M2NrY  s   r7   rf   r  	  s&    A!Brd%PRtSUVWUXXZ[r9   c                      g)NzFout_dtype must be the same as input dtype or fp32 for fp16/bf16 inputsr3   r3   r9   r7   rf   r   	  s    \r9   r   )	rW   ri   r   r   r_   rl  rm  rn  r   )r5   r6   rI  rT   r  r  r  rY  s       @@@@r7   meta_mmr  	  s     
LLA56	LLA56GGEArGGEB	LL
b[   U]]* ?GGu~~>>\	
 (/177YL;;1v\;22r9   c                    ^ ^ U(       a)  [        UU 4S j[        T R                  5       5       5      $ [        R                  " T R
                  T5      $ )Nc              3   P   >#    U  H  oT;  a  TR                   U   OS v   M     g7f)r2   NrO  )ru   r   dimsr   s     r7   rw   +_compute_reduction_shape.<locals>.<genexpr>(	  s$     UDTqtmTZZ]:DTs   #&)rh   r   r   rP   compute_reduction_output_shaper   )r   r  r  s   `` r7   r  r  &	  s7    UE$))DTUUU//

DAAr9   c                 :   [        U [        R                  R                  5      (       a  U R                  R
                  $ [        U S5      (       aK  [        U R                  S5      (       a0  U R                  R
                  S:w  a  U R                  R
                  $ g)Nr   r~   r   r   )rs   rW   _subclasses
FakeTensorfake_devicer~   hasattrr   )r<  s    r7   r  r  1	  sp    &%++6677!!&&&!!FMM6**MM&(}}!!!r9   input_tensorr   r  dilationis_transposedgroupsoutput_paddingc                 r  ^^ S[         S[         S[         S[         S[         S[         4S jnS[         S[         S[         S[         S[         S[         S[         4S	 jn	UR                  S
S  n
U R                  S
S  mU(       a  XaR                  S   -  nO=UR                  S   nUR                  S   U-  U R                  S   :w  a  [        S5      eU R                  S   U/m[        U[        5      (       a  U/[        T5      -  nO![        U5      S:X  a  US   /[        T5      -  n[        U[        5      (       a  U/[        T5      -  nO![        U5      S:X  a  US   /[        T5      -  n[        U[        5      (       a  U/[        T5      -  nO![        U5      S:X  a  US   /[        T5      -  nS nU(       aI  [        U[        5      (       a  U/[        T5      -  nO$[        U5      S:X  a  US   /[        T5      -  nOUn[        [        T5      5       H[  nU(       a+  TR                  U	" TU   X=   XM   X   X-   X   5      5        M5  TR                  U" TU   X=   XM   X   X-   5      5        M]     SSKJ	n  [        R                  " U" TS
S   Vs/ s H  oS:  PM	     sn6 UU4S j5        T$ s  snf )Nlnrr  r   r_  r  r?   c                 4    U SU-  -   X#S-
  -  -
  S-
  U-  S-   $ )aE  
Formula to apply to calculate the length of some dimension of the output

See: https://pytorch.org/docs/stable/generated/torch.nn.Conv2d.html

Args:
    ln: length of the dimension
    p: padding in that dim
    d: dilation in that dim
    k: kernel size in that dim
    s: stride in that dim
Returns:
    The output length
r   r2   r3   )r  rr  r   r_  r  s        r7   _formula+calc_conv_nd_return_shape.<locals>._formulaH	  s,     QU
Qa%[(1,2Q66r9   rD   c                 :    U S-
  U-  SU-  -
  X#S-
  -  -   U-   S-   $ )a  
Formula to apply to calculate the length of some dimension of the output
if transposed convolution is used.
See: https://pytorch.org/docs/stable/generated/torch.nn.ConvTranspose2d.html

Args:
    ln: length of the dimension
    p: padding in that dim
    d: dilation in that dim
    k: kernel size in that dim
    s: stride in that dim
    op: output padding in that dim

Returns:
    The output length
r2   r   r3   )r  rr  r   r_  r  rD   s         r7   _formula_transposed6calc_conv_nd_return_shape.<locals>._formula_transposedY	  s0    " Q!|a!e#aq5k1B6::r9   r   r2   r   zInvalid channel dimensions)sym_orc                  .   > S[        T 5       STSS   S3$ )NzGiven input size per channel: z&. Calculated output size per channel: r   z. Output size is too small)r   )r  	ret_shapes   r7   rf   +calc_conv_nd_return_shape.<locals>.<lambda>	  s(    0d =//8}o >#$r9   )r   r   r2  rs   r   r   r   r   r0  r  rW   ri   )r  rE  r   r  r  r  r  r  r  r  kernel_sizeout_channelsoutput_padding_listr   r  r<   r  r  s                   @@r7   calc_conv_nd_return_shaper  >	  s   7S 7S 7S 7S 7S 7S 7"; ; ; ; ; ; ;QT ;& ,,qr"Kab!DQ/||A<<?V#|'9'9!'<<;<<##A&5I&'""CI%	V	)s4y('7##)c$i'	W	1:,T*(G$$:D	)	X!	QK=3t9,,0ng..#1"2SY"> A%#1!#4"5D	"A"03t9#GJ KNI'* a'*hk;>69U% , =	LL	!".1Q./	$  /s   J4c                 b    [         R                  R                  U 5      [         R                  :H  $ rC   rW   _prims_commonr   channels_lasttens    r7   is_channels_lastr  	  s$    44S9U=P=PPPr9   running_meanrunning_vartrainingexponential_average_factorepsilonc                 z  ^  T R                   nUb  UR                   OUR                   n	Ub  UR                   OUR                   n
U 4S jnT R                  U5      R                  U" 5       S9nU(       a#  T R                  U	5      nT R                  U
5      nO"T R                  S5      nT R                  S5      nXU4$ )Nc                     > [        T 5      (       a  [        R                  $ T R                  [        R                  S9(       a  [        R                  $ [        R                  $ r   )r  rW   r  rp  r   )r  s   r7   pick_memory_format2meta_miopen_batch_norm.<locals>.pick_memory_format	  sI    L))&&&%%E4K4K%L***&&&r9   r   r   )r   r   r3  )r  rE  rG  r  r  r  r  r  r   save_mean_shapesave_var_shaper  r   	save_meansave_vars   `              r7   meta_miopen_batch_normr  	  s     ""I -9,Dl((&,,O*5*A[&&v||N' 
 
 
+
.
.=O=Q
.
RC **?;	)).9 **40	))$/8##r9   c	           
          [        U UUUUUUU(       a  UOS 5      n	Sn
SnU R                  U
5      S:X  a  SX'   U R                  U	5      nU$ Nr2   r   )r  r   r   )r  rE  rG  r   r  r  r  r  r  	shape_outinput_channels_dimoutput_channels_dimr   s                r7   	meta_convr  	  si     *'T	I +,1)*	&

 
 
+CJr9   mkldnnc
           
          [        XXCUSU/ 5      n
U R                  U
5      n[        R                  nU R	                  5       S:X  a  [        R
                  nUR                  US9nU$ )NFrU  r   )r  r   rW   r  r   channels_last_3dr3  )r  rE  rG  r  r   r  r  attrscalars	algorithmr  r   out_memory_formats                r7   meta_mkldnn_convolution_defaultr  
  sl     .&8UFB
	 $$Y/!//" % 6 6ff#4f5
r9   c                 b    U R                  / U R                  S S QUR                  S   P75      $ Nr   r   r   r   )r  rE  rG  r   r  r  s         r7   meta_linear_pointwise_defaultr  
  s5     %%&Q(:(:3B(?&Qa&QRRr9   mklc                 b    U R                  / U R                  S S QUR                  S   P75      $ r  r  )r  packed_weightorig_weightrG  r   s        r7   meta_mkl_linearr  %
  s:    ))@,$$Sb)@;+<+<Q+?@ r9   onednnc           
      
   [        U UUUU	SU
S 5      nUc  U R                  nU[        R                  [        R                  [        R
                  [        R                  [        R                  4;  a  [        SU 35      eU R                  UUS9n[        U5      S;  a  [        S[        U5       S35      e[        R                  [        R                  [        R                  S.[        U5         nUR                  US9nU$ )NFOoutput_dtype must be one of float32, bfloat16, uint8, int8, float8_e4m3fn, got r   )r/   r-  rU  z3Expect output to be 3d/4d/5d for conv1d/2d/3d, got r   r   )r  r_   rW   rl  rn  uint8rN  ro  r   r   r   r   r  r  r3  )r<   x_scalex_zpww_scalew_zprG  r   r  r  r  output_scaleoutput_zero_pointoutput_dtyper   r  r  r  r   formats                       r7   meta_qconv_pointwiser  /
  s   , .	
	 77LMMNNKKJJ 
 
 !abnaop  kk)<k8y>* Ec)nEUUVW  &&""%%
 i.	
 ff6f*
r9   c                 0    US:w  a  [        SU S35      eU$ )Nsumz#binary_op_name must be 'sum', got 'r  r   )r<   r  r  r  r  r  accumrG  r   r  r  r  r  r  r  accum_scaleaccum_zero_pointbinary_op_namera  unary_op_nameunary_op_argsunary_op_algorithms                         r7   meta_qconv2d_pointwise_binaryr&  h
  s-    4 U" 5n5EQG  r9   c                 0   [        U R                  5      nUR                  S   US'   U	[        R                  [        R                  [        R
                  [        R                  [        R                  4;  a  [        SU	 35      eU R                  XS9nU$ )Nr2   r   zOoutput_dtype must be one of float32, bfloat16, int8, uint8, float8_e4m3fn, got r   )
r   r   rW   rl  rn  rN  r  ro  r   r   )r<   r  r  r  r  r  rG  r  r  r  post_op_namepost_op_argspost_op_algorithmrs  r   s                  r7   meta_qlinear_pointwiser+  
  s    " AGG}771:RMMNNJJKK 
 
 !abnaop  kk,k;
r9   c                 B   US:X  a  U$ [        U R                  5      nUR                  S   US'   U
[        R                  [        R                  [        R
                  [        R                  [        R                  4;  a  [        SU
 35      eU R                  UU
S9nU$ )Nr  r2   r   r  r   )
r   r   rW   rl  rn  r  rN  ro  r   r   )r<   r  r  r  r  r  x_2rG  r  r  r  x2_scalex2_zpr"  ra  r#  r$  r%  rs  r   s                       r7   meta_qlinear_pointwise_binaryr0  
  s    , U"JAGG}771:RMMNNKKJJ 
 
 !abnaop  kk,lk;
r9   c                 v    [        U R                  5      nUR                  S   US'   U R                  U5      nU$ )Nr2   r   )r   r   r   )r<   r  rG  rs  r   s        r7   meta_linear_dynamic_fp16r2  
  s6     AGG}771:Rkk,'
r9   	quantizedr  r2   c                 "   [        XX#XE5      u  nnnU R                  5       S:X  a  U R                  S5      OSn	[        R                  n
U R                  5       S:X  a  XgU/nOXXx/n[        R
                  " UU R                  U R                  U
S9$ Nr-  r2   r/   r  )#max_pool2d_checks_and_compute_shaper   r   rW   r  r   r_   r   r   r  r   r  r  	ceil_modenInputPlaneoutputHeightoutputWidthr  r   r   s               r7   meta_quantized_max_pool2dr>  
  s     0
		
 $)99;!#3B++99;!{;DCD{{++<<'	
 	
r9   c                   ^ ^^^ [         R                  " T R                  5       S:H  U 4S j5        [         R                  " TR                  5       S:H  U4S j5        [         R                  " T R                  [         R                  [         R
                  [         R                  4;   U 4S j5        [         R                  " TR                  [         R                  :H  U4S j5        [         R                  " TR                  [         R                  :H  U4S j5        [         R                  " TR                  T R                  :H  U4S j5        T R                  T R                  S5      TR                  S5      T R                  S	9$ )
Nr   c                  ,   > ST R                  5        S3$ )Nzx must be a 2D tensor, got rY  r   r<   s   r7   rf   /meta_int4mm_packed_weight_cpu.<locals>.<lambda>      -H	QR+Sr9   c                  ,   > ST R                  5        S3$ )Nzw must be a 2D tensor, got rY  r   r  s   r7   rf   rB    rC  r9   c                  "   > ST R                    3$ Nz#expected x to be f32/f16/bf16, got r   rA  s   r7   rf   rB    s    9!''Cr9   c                  "   > ST R                    3$ Nzexpected w to be uint8, got r   rE  s   r7   rf   rB    s    .J177),Tr9   c                  "   > ST R                    3$ )Nz q_group_size must be int64, got r   )q_group_sizes   r7   rf   rB    s    6|7I7I6JKr9   c                  "   > ST R                    3$ )Nz5q_scale_and_zeros must have the same dtype as x, got r   )q_scale_and_zeross   r7   rf   rB    s    KL]LcLcKder9   r   r   )rW   ri   r   r_   rl  rm  rn  r  r   r   r   r<   r  rK  rM  s   ````r7   meta_int4mm_packed_weight_cpurO  
  s    QUUW\#STQUUW\#STGGu}}ennEEC	
 	GGu{{"$T	
 	%++-K	
 	##qww.e	
 {{166!9affQiqww{??r9   c                    ^ ^^^ [         R                  " T R                  5       T:H  =(       a    T R                  T   T:H  UUUU 4S j5        g )Nc                  j   > ST  ST ST S3STR                  5        ST STR                  T    3-   $ )NzExpected a tensor of dimension z and tensor.size[z] == r|   zbut got : dimension z] = r   r   )r   dim_sizer   r<  s   r7   rf    check_dim_size.<locals>.<lambda>  sN    1#6GzQVW[V\\^_ .?zfll[cNdMe
fgr9   )rW   ri   r   r   )r<  r   rS  r   s   ````r7   check_dim_sizerU    s6    	LL

>X 6$ >	gr9   c                   ^  S nU" SU5      u  p[         R                  " [        U5      S;   S 5        [         R                  " T R                  [         R                  [         R
                  [         R                  [         R                  4;  U 4S j5        [        U5      S:X  a  XpO$[        U5      S:X  a
  US   US   pOU" SU5      u  pU" S	U5      u  p[         R                  " US L =(       d    US:g  S
 5        T R                  5       S:X  a  T R                  S5      OSnT R                  S5      nT R                  S5      nT R                  S5      n[        UXU
SU5      n[        UXUSU5      n[        R                  " T 5      n[        T UU	U
UUUSSUUUUUU5        T R                  5       S:X  a  UUU/nOXUU/n[         R                  " UT R                  T R                  US9$ )Nc                    ^  [         R                  " [        U5      S;   U 4S j5        US   n[        U5      S:X  a  UOUS   nX#4$ )Nr2   r   c                     > ST  S3$ )Nzavg_pool2d: 4 must either be a single int, or a tuple of two intsr3   r  s   r7   rf   1meta_avg_pool2d.<locals>.unpack.<locals>.<lambda>+      l4&(\]r9   r   r2   rW   ri   r   r  r  HWs   `   r7   unpackmeta_avg_pool2d.<locals>.unpack(  E    H]	
 FSQACFtr9   r  r   r2   r   c                      gNzOavg_pool2d: stride must either be omitted, a single int, or a tuple of two intsr3   r3   r9   r7   rf   !meta_avg_pool2d.<locals>.<lambda>4      ar9   c                  @   > ST R                   R                  5        S3$ )Nz""avg_pool2d" not implemented for 'r  r  r  s   r7   rf   rh  8      6u{{7J7J7L6MQQr9   r   r2   r   r  c                      gNzdivisor must be not zeror3   r3   r9   r7   rf   rh  E      *r9   r-  r7  r  r   r/   r  )rW   ri   r   r_   r  uint16uint32uint64r   r   pooling_output_shaperP   r   pool2d_shape_checkr   r   )r   r  r   r  r:  count_include_paddivisor_overriderb  kHkWdHdWpadHpadWr  r;  inputHeight
inputWidthr<  r=  r   r   s   `                     r7   meta_avg_pool2dr    s    M;/FB	LLFy a 
LLEKKu||U\\RRQ 6{aB	V	F1IB&)	7+JD	LLD 9$4$9*
  %yy{a/UZZ^QF**R.K**R.KBJ'Rr1iPL&z2RINK//6M



		$ yy{a\;7\;?;;kk||#	 r9   c                     [        U UUUUUUSSU	U
UUUU5        U R                  5       nU	n[        XUS-
  U5        [        XUS-
  U5        [        XUS-
  U5        g )Nr2   r/   r   )rt  r   rU  )r   
gradOutputr  rw  rx  ry  rz  r{  r|  r;  r}  r~  r<  r=  
mem_formatr   nOutputPlanes                    r7   avg_pool2d_backward_shape_checkr  p  s{    " 



		$ 99;DL:TAX|<:TAX|<:TAX{;r9   c                    [         R                  " [        U5      S:H  =(       d    [        U5      S:H  S 5        US   n[        U5      S:X  a  UOUS   n	[         R                  " [        U5      S:H  =(       d#    [        U5      S:H  =(       d    [        U5      S:H  S 5        [        U5      S:X  a  UOUS   n
[        U5      S:X  a  U	O[        U5      S:X  a  U
OUS   n[         R                  " [        U5      S:H  =(       d    [        U5      S:H  S 5        US   n[        U5      S:X  a  UOUS   n[         R                  " US L =(       d    US:g  S 5        UR                  nUR	                  5       S:X  a  US	   OSnUS
   nUS   nUS   n[        UXU
SU5      n[        UXUSU5      n[        R                  " U5      n[        UU UUU	U
UUUUUUUUU5        [         R                  " UUR                  UR                  US9$ )Nr2   r   c                      g)NzKavg_pool2d: kernel_size must either be a single int, or a tuple of two intsr3   r3   r9   r7   rf   *meta_avg_pool2d_backward.<locals>.<lambda>  s    ]r9   r   c                      grg  r3   r3   r9   r7   rf   r    ri  r9   c                      g)NzGavg_pool2d: padding must either be a single int, or a tuple of two intsr3   r3   r9   r7   rf   r    s    Yr9   c                      grm  r3   r3   r9   r7   rf   r    rn  r9   r-  r7  ro  r  r   r  )rW   ri   r   r   r   rs  rP   r   r  r   r_   r   )gradOutput_r   r  r   r  r:  ru  rv  rw  rx  ry  rz  r{  r|  
input_sizer  r;  r}  r~  r<  r=  r  s                         r7   meta_avg_pool2d_backwardr    s    
LLKA6[!1Q!6] 
QB;1$+a.B	LLFq@CK1,@Fq0@a 6{aVAYB6{a3v;!+;RB	LLG.S\Q.Y 1:Dw<1$4'!*D	LLD 9$4$9*
 J$yy{a/Z^QFR.KR.KBJ'Rr1iPL&z2RINK,,U3J#



$ ;;kk|| 	 r9   c                 n  ^  [         R                  " [        U5      S;   S 5        US   n[        U5      S:X  a  UOUS   n[        U5      S:X  a  UOUS   n	[         R                  " U(       + =(       d    [        U5      S;   S 5        [         R                  " T R                  [         R                  [         R
                  [         R                  [         R                  4;  U 4S j5        U(       d  UOUS   n
U(       d  UO[        U5      S:X  a  U
OUS   nU(       d  U	O[        U5      S:X  a  U
OUS   n[         R                  " [        U5      S;   S 5        US   n[        U5      S:X  a  UOUS   n[        U5      S:X  a  UOUS   n[         R                  " T R                  S	;   S
 5        [         R                  " U(       + =(       d    US:g  S 5        T R                  S5      nT R                  S5      nT R                  S5      nT R                  S5      nT R                  S5      n[        UX}U
SU5      n[        UXUSU5      n[        UXUSU5      n[        T UUUU	U
UUUUUSSSUUUUUUSSS9  T R                  S:X  a  T R                  UUUU45      $ T R                  UUUUU45      $ )Nr2   r/   c                      gNzFavg_pool3d: kernel_size must be a single int, or a tuple of three intsr3   r3   r9   r7   rf   !meta_avg_pool3d.<locals>.<lambda>      Xr9   r   r2   r   c                      gNzJavg_pool3d: stride must be omitted, a single int, or a tuple of three intsr3   r3   r9   r7   rf   r    r  r9   c                  @   > ST R                   R                  5        S3$ )Nz""avg_pool3d" not implemented for 'r  r  r  s   r7   rf   r    rk  r9   c                      gNzBavg_pool3d: padding must be a single int, or a tuple of three intsr3   r3   r9   r7   rf   r        Tr9   r-  rU  c                      gNz9non-empty 4D or 5D (batch mode) tensor expected for inputr3   r3   r9   r7   rf   r        Kr9   c                      grm  r3   r3   r9   r7   rf   r    rn  r9   r7  ro  r  r   zavg_pool3d()T)check_input_sizer-  )rW   ri   r   r_   r  rp  rq  rr  r   r   rs  pool3d_shape_checkr   )r   r  r   r  r:  ru  rv  kTrw  rx  dTry  rz  padTr{  r|  r  nslicesitimeiheightiwidthotimeoheightowidths   `                       r7   meta_avg_pool3dr    s    
LLKF"X 
QB;1$+a.B;1$+a.B	LL
+c&kV+\ 
LLEKKu||U\\RRQ vayBc&kQ&6F1IBc&kQ&6F1IB	LLGT 1:Dw<1$4'!*Dw<1$4'!*D	LL

fK
 
LL5 0A 5*
 ZZ]FjjnGJJrNEjjnGZZ^F "aCE"7Bb!YGG!&"B9EF





			-2 zzQ@AAHIIr9   c                 B   [         R                  " [        U5      S;   S 5        US   n[        U5      S:X  a  UOUS   n	[        U5      S:X  a  UOUS   n
[         R                  " U(       + =(       d    [        U5      S;   S 5        U(       d  UOUS   nU(       d  U	O[        U5      S:X  a  UOUS   nU(       d  U
O[        U5      S:X  a  UOUS   n[         R                  " [        U5      S;   S 5        US   n[        U5      S:X  a  UOUS   n[        U5      S:X  a  UOUS   n[         R                  " UR                  S;   S	 5        [         R                  " U(       + =(       d    US:g  S
 5        UR	                  S5      nUR	                  S5      nUR	                  S5      nUR	                  S5      n[        UXUSU5      n[        UXUSU5      n[        UU
UUSU5      n[        UU UUU	U
UUUUUUUUUUUUS5        UR                  UR                  5      $ )Nr  c                      gr  r3   r3   r9   r7   rf   *meta_avg_pool3d_backward.<locals>.<lambda>M  r  r9   r   r2   r   c                      gr  r3   r3   r9   r7   rf   r  U  r  r9   c                      gr  r3   r3   r9   r7   rf   r  ]  r  r9   r  c                      gr  r3   r3   r9   r7   rf   r  e  r  r9   c                      grm  r3   r3   r9   r7   rf   r  j  rn  r9   r7  ro  r  r   zavg_pool3d_backward())	rW   ri   r   r   r   rs  avg_pool3d_backward_shape_checkr   r   )r"  r   r  r   r  r:  ru  rv  r  rw  rx  r  ry  rz  r  r{  r|  r  r  r  r  otime_for_shape_checkoheight_for_shape_checkowidth_for_shape_checks                           r7   meta_avg_pool3d_backwardr  ?  s    
LLKF"X 
QB;1$+a.B;1$+a.B	LL
+c&kV+\ vayBc&kQ&6F1IBc&kQ&6F1IB	LLGT 1:Dw<1$4'!*Dw<1$4'!*D	LL

fK
 
LL5 0A 5*
 jjnGJJrNEjjnGZZ^F0"aS27Bb!YW1&"dB9U#





', ??5;;''r9   c                 8  ^  [         R                  " T R                  S:H  =(       d    T R                  S:H  U 4S j5        T R                  S S [	        U5      -   n[
        R                  " T 5      n[         R                  " UT R                  T R                  US9$ )Nr/   r-  c                  "   > ST R                    3$ )Nz"Expected 3D or 4D tensor, but got rO  r   s   r7   rf   *meta_adaptive_avg_pool2d.<locals>.<lambda>      4TZZLAr9   r  r  )
rW   ri   r   r   rh   rP   r   r   r_   r   )r   output_sizers  r   s   `   r7   meta_adaptive_avg_pool2dr    s|    	LL		Q($))q.A ::cr?U;%77L//5M ;;jj{{#	 r9   c                    ^  [         R                  " T R                  S:H  =(       d    T R                  S:H  U 4S j5        T R                  T R                  S S [        U5      -   5      $ )Nr-  rU  c                  "   > ST R                    3$ )Nz"Expected 4D or 5D tensor, but got rO  r   s   r7   rf   *meta_adaptive_avg_pool3d.<locals>.<lambda>  r  r9   ro  )rW   ri   r   r   r   rh   )r   r  s   ` r7   meta_adaptive_avg_pool3dr    sO    	LL		Q($))q.A >>$**Sb/E+,>>??r9   c                   ^ ^^ T R                   n[        SU5       H1  m[        R                  " T R	                  T5      S:  U U4S j5        M3     [        R                  " US:H  =(       d    US:H  U4S j5        [        R                  " TR
                  T R
                  :H  U U4S j5        [        R                  n[        T5      (       a  [        R                  nTR                  TR                  5      R                  US9$ )	Nr2   r   c                  *   > ST R                    ST S3$ )Nz{adaptive_avg_pool2d_backward(): Expected grad_output to have non-zero                       size for non-batch dimensions,  with dimension  being emptyrO  )grad_outr   s   r7   rf   4meta__adaptive_avg_pool2d_backward.<locals>.<lambda>  s$     66>nn5EEUVWUXXdfr9   r/   r-  c                  "   > ST R                    3$ )NzBadaptive_avg_pool2d_backward(): Expected 3D or 4D tensor, but got rO  r   s   r7   rf   r    s    TUYU_U_T`ar9   c                  <   > STR                    ST R                    3$ Nexpected dtype z! for `grad_output` but got dtype r   )r  r   s   r7   rf   r    s    /$**-Nx~~N^_r9   r   )r   r   rW   ri   r   r_   r   r  r  r   r   r3  )r  r   r   r   r   s   ``  @r7   "meta__adaptive_avg_pool2d_backwardr    s    ==D1d^MM!q f	
  
LL	TQYa 
LL

hnn$_ ++M++>>$**%((}(EEr9   c                 `    [        U S5        [        R                  " U[        R                  S9$ )Nadaptive_avg_pool3d_backwardr   )!_adaptive_pool_empty_output_checkrW   r   r"  r"  r   s     r7   "meta__adaptive_avg_pool3d_backwardr    s(     &k3QRD0N0NOOr9   r"  c                    ^ ^^ T R                   n[        SU5       H2  m[        R                  " T R	                  T5      S:  UU U4S j5        M4     g )Nr2   r   c                  .   > T  STR                    ST S3$ )Nzc(): Expected grad_output to have non-zero size for non-batch dimensions, but grad_output has sizes r  r  rO  )r  r"  r   s   r7   rf   3_adaptive_pool_empty_output_check.<locals>.<lambda>  s*    * --8->->,??OPQsR^`r9   )r   r   rW   ri   r   )r"  r  r   r   s   `` @r7   r  r    sB    D1d^Q!#	
 r9   c                   ^ ^ T R                   n[        R                  " US;   U 4S j5        [        SU5       H1  m[        R                  " T R	                  T5      S:  UU 4S j5        M3     [        R                  " [        U5      S:H  S 5        SnSnSnT R                   S:X  a  T R	                  S5      nUS-  nT R	                  US-
  5      nUu  pgT R                   S	:X  a6  XVU4nT R                  U5      n	T R                  U[        R                  S
9n
X4$ XEXg4n[        R                  " T 5      nT R                  U5      R                  US9n	T R                  U[        R                  S
9R                  US9n
X4$ )Nr/   r-  c                  "   > ST R                    3$ )Nz:adaptive_max_pool2d(): Expected 3D or 4D tensor, but got: rO  r  s   r7   rf   *meta_adaptive_max_pool2d.<locals>.<lambda>      LU[[MZr9   r2   r   c                  *   > STR                    ST  S3$ )Nzjadaptive_max_pool2d(): Expected input to have non-zero size for non-batch dimensions, but input has sizes r  r  rO  r   r   s   r7   rf   r         '',{{m3CA3lTr9   r   c                      g)NzCadaptive_max_pool2d(): internal error: output_size.size() must be 2r3   r3   r9   r7   rf   r        Ur9   r-  r/   r   r   )r   rW   ri   r   r   r   r   r   rP   r   r3  )r   r  r   dimHsizeBsizeDosizeHosizeWr   r   r   r   r   s   `           @r7   meta_adaptive_max_pool2dr    sk    ::D	LLZ 1d^JJqMA	
  
LLKAU
 DEEzzQ

1	JJtax E NFzzQF+	ooi(//)5;;/?|62	33E:ooi(++-+H//)5;;/?BB' C 
 |r9   c                 T  ^ ^ T R                   n[        R                  " US;   U 4S j5        [        T S5        [        R                  " TR                  T R                  :H  U U4S j5        [
        R                  " T5      nTR                  TR                  5      R                  US9$ )Nr  c                  "   > ST R                    3$ )NzKadaptive_max_pooling2d_backward(): Expected 3D or 4D grad_output, but got: rO  r"  s   r7   rf   3meta_adaptive_max_pool2d_backward.<locals>.<lambda>
  s    ]^i^o^o]pqr9   adaptive_max_pool2d_backwardc                  <   > STR                    ST R                    3$ r  r   )r"  r   s   r7   rf   r    s    /%++.OP[PaPaObcr9   r   )
r   rW   ri   r  r_   rP   r   r   r   r3  )r"  r   r   r   r   s   ``   r7   !meta_adaptive_max_pool2d_backwardr    s     D	LLq
 &k3QR	LL{(((c
 //6M??5;;'***GGr9   c                   ^ ^ T R                   n[        R                  " US;   U 4S j5        [        SU5       H1  m[        R                  " T R	                  T5      S:  UU 4S j5        M3     [        R                  " [        U5      S:H  S 5        SnSnSnUS:X  a  T R	                  S5      nUS-  nT R	                  U5      nUu  pgnUS	:X  a  XVXx4n	OXEXgU4n	T R                  U	5      n
T R                  U	[        R                  S
9nX4$ )Nr  c                  "   > ST R                    3$ )Nz:adaptive_max_pool3d(): Expected 4D or 5D tensor, but got: rO  r  s   r7   rf   *meta_adaptive_max_pool3d.<locals>.<lambda>  r  r9   r2   r   c                  *   > STR                    ST  S3$ )Nzjadaptive_max_pool3d(): Expected input to have non-zero size for non-batch dimensions, but input has sizes r  r  rO  r  s   r7   rf   r  #  r  r9   r/   c                      g)NzCadaptive_max_pool3d(): internal error: output_size.size() must be 3r3   r3   r9   r7   rf   r  +  r  r9   rU  r-  r   )r   rW   ri   r   r   r   r   r   )r   r  r   dimDr  r  osizeTr  r  r   r   r   r   s   `           @r7   meta_adaptive_max_pool3dr    s    ::D	LLZ 1d^JJqMA	
  
LLKAU
 DEEqy

1	JJtE(FFqyF3	66:	
//)
$Cooiu{{o;G<r9   c                 P    [        U S5        UR                  UR                  5      $ )Nadaptive_max_pool3d_backward)r  r   r   )r"  r   r   s      r7   !meta_adaptive_max_pool3d_backwardr  D  s"     &k3QR??5;;''r9   c                 @    Uc  [        S5      eU R                  U5      $ )Nz:cannot repeat_interleave a meta tensor without output_size)r2  r   )repeatsr  s     r7   meta_repeat_interleave_Tensorr  K  s%    WXX[))r9   c                    U R                   R                  (       d  [        SU R                    35      eUR                   R                  (       d  [        SUR                    35      e[        U R	                  [        U R                   5      5      UR	                  [        UR                   5      5      [        R                  S9nU$ )Nz!real must be floating point, got z!imag must be floating point, got rM   )r_   r  r   rU   r3  r   r   rQ   )realimagr  s      r7   meta_complexr  R  s     ::''@MNN::''@MNN+DJJ78+DJJ786>>F
 Mr9   )
fill_valuer  c                    [        U 5      S;   a-  U R                  XR                  5       4[        R                  S9$ [        R
                  " XR                  5       4SU4[        R                  U R                  S9$ )N)cpur   r   r2   r_   r   )r  r   r   rW   r   r=  r   )r   r   r  s      r7   nonzero_staticr  a  se     4N*~~tXXZ0

~CC""88:I**;;	
 	
r9   c                    [         R                  " [        R                  S 5        [         R                  " U R                  5       U R                  5       4SU R                  5       4[         R                  U R                  S9$ )Nc                      g)NaY  The register_meta function for torch.nonzero() raises unimplemented by default, as a correct data-independent implementation does not exist. This implementation returns a fake value, assuming all elements of the tensor are non-zero. To enable this registration, please set 'torch.fx.experimental._config.meta_nonzero_assume_all_nonzero' to True.r3   r3   r9   r7   rf   nonzero.<locals>.<lambda>u  s     Sr9   r2   r  )	rW   _check_not_implementedr  meta_nonzero_assume_all_nonzeror=  r   r   r   r   r   s    r7   nonzeror	  p  sf     
  22	S 	txxz"	
DJJLjj{{	 r9   c           
      n	  ^ ^^^^^^^^ [         R                  " [        T5      S 5        / n[        T5       GH  u  mmTGbr  [         R                  " TR                  [         R
                  [         R                  [         R                  [         R                  4;   S 5        TR                  [         R                  [         R                  4;   a  TR                  5       n[        U5      m[         R                  " TTR                  -   T R                  :*  U 4S j5        [        TR                  5       Hc  m[         R                  " TR                  T   T R                  TT-      :H  UUUUU 4S j5        UR                  UR                  ST5      5        Me     GMi  UR                  T5        GM}  UR                  T5        GM     Um[         R                  " [        T5      T R                  :*  UU 4S j5        SS KJn  [%        UR&                  " T6 5      m[        T5      T R                  :  a,  TR                  S 5        [        T5      T R                  :  a  M,  SnSnT H&  mUS:X  a	  Tb  SnM  M  US:X  a	  Tc  S	nM  M!  Tc  M&    O   S
nU(       d  / n/ n[        T5       H-  u  mmTc  M  UR                  T5        UR                  T5        M/     [        T5       H-  u  mmTb  M  UR                  T5        UR                  T5        M/     T R)                  U5      m Um/ m/ m/ m[        T5       He  u  n	mTcG  T(       a   TR                  T R                  U	   5        M0  TR                  T R                  U	   5        MP  [%        TR                  5      mMg     UUU4S jn
T R+                  TT-   T-   5      nSSKJn  U" T R1                  5       S:H  5      (       a  U$ U
" T 5      n[2        R4                  " U5      u  p[%        U5      [%        [        [        U5      5      5      :w  a  [2        R6                  " UR                  U5      n[2        R8                  " U5      n[2        R6                  " U[2        R:                  " U5      5      nUR=                  UR?                  5       U5      nU$ )Nc                      g)Nz#at least one index must be providedr3   r3   r9   r7   rf   #meta_index_Tensor.<locals>.<lambda>  s    (Mr9   c                      g)Nz?tensors used as indices must be long, int, byte or bool tensorsr3   r3   r9   r7   rf   r    s    Yr9   c                  "   > ST R                    3$ )N)too many indices for tensor of dimension r  r   s   r7   rf   r    s    G		{Sr9   c            	      N   > STR                    ST  STR                    STT-    3$ )NzThe shape of the mask 
 at index z0 does not match the shape of the indexed tensor rO  )r   r   jr_  r   s   r7   rf   r    s:    "8ZPQs SJJN**U_`ade`e_f!hr9   r2   c                  <   > STR                    S[        T 5       S3$ )Nr  z (got r}   )r   r   )r   r   s   r7   rf   r    s    ;DII;fSQX\NZ[\r9   r   Fr   Tc                    > TT-   T-   n[        U R                  5       5      nS/[        T5      -  U[        T5      [        U R                  5      [        T5      -
  & U R	                  X5      $ )z9
This follows restride_src in TensorAdvancedIndexing.cpp
r   )r   r   r   r   rP  )r   r   r   after_shapebefore_shapereplacement_shapes      r7   _restride_src(meta_index_Tensor.<locals>._restride_src  sm     00;>t{{}%KL#PSQ
 K
L!C

Oc+6F$FG u..r9   guard_or_false) rW   ri   r  	enumerater_   r   r   rN  r	  r   r   r   r   r   r   selecttorch._refs_refsr   r%   r   r   r0  r  r   rP   3compute_elementwise_output_logical_to_physical_perm
apply_permr   invert_permrP  r   )r   r   r  r	  refsstatehas_contiguous_subspacer  transposed_indicesr   r  r   r  restrided_selfpermrS   
perm_shaper?  r  r  r   r   r  r_  r  s   ``                @@@@@@@r7   meta_index_Tensorr*    s   	LLg MN #%Fg&5LL

EIIuzz5::NNY {{uzz5::66--/K""

Ndii/S uzz*A&&A$**QU*;;h h
 MM'..A"67 + e$MM% / '0 G	LLG		!\
 4(('23G
g,
"t g,
" E#A:  !aZ}     #'
 #!'*HAu A"))%0 + "'*HAu}A"))%0 + ||D!$ !LK#%(
U= ""4::c?3##DJJsO4 $U[[ 1 )
/ ..(99KG
HCDdjjla'((

 #4(NGGWGD DzT%D	*++%%cii6
66zB
%%j%2C2CD2IJ
nnSXXZ4Jr9   c                 J   S nS nS nS nU
S   (       a4  U" X5      nU R                  UR                  5       5      R                  US9nU
S   (       a4  U" X5      nU R                  UR                  5       5      R                  US9nU
S   (       a  U R                  U5      nXU4$ )Nc                 .   [        U 5      n[        U5      nU[        R                  :X  d  U[        R                  :X  a  [        R                  $ U[        R                  :X  d  U[        R                  :X  a  [        R                  $ [        R                  $ rC   )r   rW   r  r  r   )t1t2fmt1fmt2s       r7   _conv_memory_format6meta_convolution_backward.<locals>._conv_memory_format$  sr     %R($R(5&&&$%2E2E*E&&&5)))TU5K5K-K)))&&&r9   r   r   r2   r   )r   r   r3  )grad_output_input_weight_bias_sizes_optr   r  r  
transposedr  r  output_maskbackend_grad_inputbackend_grad_weightbackend_grad_biasr1  r   s                   r7   meta_convolution_backwardr<    s      	' 1~+LB)33FKKMBEE' F 
 1~+FA*44W\\^DGG' H 
 1~(22>B5FGGr9   c                  ^^ TR                  S5      nTR                  S5      nU R                  XV45      n [        R                  " TR	                  5       S:H  S 5        [        R                  " TR	                  5       S:H  S 5        [        R                  " TR                  S5      TR                  S5      :H  UU4S j5        [        R                  " TR                  S5      TR                  S5      :H  UU4S j5        [        R                  " U R                  S5      U:H  =(       a    U R                  S5      U:H  S	 5        U R                  U R                  5       5      $ )
Nr2   r   r/   c                      gr  r3   r3   r9   r7   rf   meta_addbmm.<locals>.<lambda>E  r  r9   c                      gr  r3   r3   r9   r7   rf   r?  F  r  r9   r   c                  P   > ST R                  S5       STR                  S5       3$ )Nz8batch1 and batch2 must have same number of batches, got r   r   r   r  r  s   r7   rf   r?  I  s,    J6;;WX>JZZ_`f`k`klm`n_opr9   c            
         > ST R                  S5       ST R                  S5       STR                  S5       STR                  S5       S3	$ )Nz#Incompatible matrix sizes for bmm (r2   r<   r   r   r}   r   rB  s   r7   rf   r?  M  sL    1&++a.1A6;;q>BR S;;q>"!FKKN#316r9   c                      g)Nz.self tensor does not match matmul output shaper3   r3   r9   r7   rf   r?  T  s    @r9   )r   r  rW   ri   r   r   )r   r  r  rb  ra  r  r  s    ``    r7   meta_addbmmrE  ?  s     ;;q>D;;q>D;;|$D	LL"$HI	LL"$HI	LLA&++a.(p 
LLA&++a.(	
 
LL		!51!5@ >>$))+&&r9   c                 @    U R                  U R                  5       5      $ rC   r   r   )r   r  kwargss      r7   meta_randint_likerI  Y  s    >>$))+&&r9   )
grad_scale	found_infc       	         p   ^ XX#XE4 H,  m[         R                  " [        T[        5      U4S j5        M.     g )Nc                      > S[        T 5       3$ Nz'exponent must be a tensor list but got r~   ls   r7   rf   #meta__fused_adam_.<locals>.<lambda>t      =d1gYGr9   rW   ri   rs   r   )r   gradsexp_avgsexp_avg_sqsmax_exp_avg_sqsstate_stepslrbeta1beta2weight_decayepsamsgradmaximizerJ  rK  rQ  s                  @r7   meta__fused_adam_ra  ^  s0    & 8/Oq$G	
 Pr9   c       	            ^ XX#XE4 H,  m[         R                  " [        T[        5      U4S j5        M.     S nU" U 5      U" U5      U" U5      U" U5      U" U5      4$ )Nc                      > S[        T 5       3$ rN  rO  rP  s   r7   rf   "meta__fused_adam.<locals>.<lambda>  rS  r9   c                 Z    U  Vs/ s H  n[         R                  " U5      PM     sn$ s  snf rC   rD  )tensor_listr  s     r7   empty_like_list)meta__fused_adam.<locals>.empty_like_list  s%    -89[  #[999s    (rT  )r   rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  rJ  rK  rg  rQ  s                   @r7   meta__fused_adamri  x  si    & 8/Oq$G	
 P: 	!$( r9   c                 t  ^ ^ [         R                  " T R                  5       S:H  S 5        [         R                  " TR                  5       S:H  S 5        [         R                  " T R                  [         R                  L U 4S j5        [         R                  " TR                  [         R                  L U4S j5        [         R                  " T R                  S5      TR                  S5      :H  U U4S j5        T R                  T R                  S5      TR                  S5      4[         R                  S	9$ )
Nr   c                      g)Nza must be a 2D tensorr3   r3   r9   r7   rf   meta__int_mm.<locals>.<lambda>      '>r9   c                      g)Nzb must be a 2D tensorr3   r3   r9   r7   rf   rl    rm  r9   c                  "   > ST R                    3$ )Nzexpected self to be int8, got r   )r5   s   r7   rf   rl        0	:r9   c                  "   > ST R                    3$ )Nzexpected mat2 to be int8, got r   )r6   s   r7   rf   rl    rp  r9   r2   r   c            
         > ST R                  S5       ST R                  S5       STR                  S5       STR                  S5       S3	$ )Nz'Incompatible matrix sizes for _int_mm (r   r<   r2   r   r}   r   r4   s   r7   rf   rl    sH    5affQi[!&&) M66!9+Qqvvayk,r9   r   )rW   ri   r   r_   rN  r   r   rO  r4   s   ``r7   meta__int_mmrs    s     
LLA>?	LLA>?	LL	5::: 
LL	5::: 
LL	q	QVVAY	
 ;;q	166!9-U[[;AAr9   c                 d  ^  [         R                  " T R                  5       S:H  S 5        [         R                  " T R                  [         R                  L U 4S j5        T R                  S5      nT R                  S5      S-  nT R                  US-  X1S-  -  SUS-  4[         R                  S	9$ )
Nr   c                      gNzw must be a 2D tensorr3   r3   r9   r7   rf   2meta__convert_weight_to_int4pack.<locals>.<lambda>  rm  r9   c                  "   > ST R                    3$ rI  r   rE  s   r7   rf   rw        .qwwi8r9   r   r2             r   )rW   ri   r   r_   r  r   r   rO  r  inner_k_tilesr  r_  s   `   r7    meta__convert_weight_to_int4packr    s    	LLA>?	LL	5;;8 	
q	A	q	AA;;F"$%Q		
 kk   r9   c                 H  ^  [         R                  " T R                  5       S:H  S 5        [         R                  " T R                  [         R                  L U 4S j5        T R                  S5      nT R                  S5      nT R                  X#S-  4[         R                  S9$ )Nr   c                      grv  r3   r3   r9   r7   rf   :meta__convert_weight_to_int4pack_for_cpu.<locals>.<lambda>  rm  r9   c                  "   > ST R                    3$ Nzexpected w to be int32, got r   rE  s   r7   rf   r    ry  r9   r   r2   r   )rW   ri   r   r_   rO  r   r   r  r}  s   `   r7   (meta__convert_weight_to_int4pack_for_cpur    s}    	LLA>?	LL	5;;8 	
q	A	q	A;;	
Fkk   r9   c                   ^ ^^ [         R                  " T R                  5       S:H  S 5        TR                  R                  S:X  a  SOSm[         R                  " TR                  5       T:H  U4S j5        [         R                  " T R
                  [         R                  [         R                  [         R                  4;   U 4S j5        [         R                  " TR
                  [         R                  L U4S j5        TR                  R                  S:X  a  TR                  S5      OTR                  S5      S	-  nT R                  T R                  S5      UT R
                  S
9$ )Nr   c                      gNzx must be a 2D tensorr3   r3   r9   r7   rf   *meta__weight_int4pack_mm.<locals>.<lambda>  rm  r9   r   r-  c                     > ST  S3$ )Nzw must be a zD tensorr3   )expected_dims   r7   rf   r    s    Lh2Wr9   c                  "   > ST R                    3$ rG  r   rA  s   r7   rf   r        5aggY?r9   c                  "   > ST R                    3$ r  r   rE  s   r7   rf   r    ry  r9   r   rz  r   )rW   ri   r   r  r~   r_   rl  rm  rn  rO  r   r   )r<   r  rK  rM  dim_nr  s   ``   @r7   meta__weight_int4pack_mmr    s    	LLA>?**e31L	LLL(*WX	LL	EMM5==%..AA? 
LL	5;;8 ++u4AFF1I!&&)a-E;;qvvay%qww;77r9   c                 0  ^ ^ [         R                  " T R                  5       S:H  S 5        [         R                  " TR                  5       S:H  S 5        [         R                  " T R                  [         R                  [         R
                  [         R                  4;   U 4S j5        [         R                  " TR                  [         R                  L U4S j5        T R                  T R                  S5      TR                  S5      T R                  S9$ )Nr   c                      gr  r3   r3   r9   r7   rf   2meta__weight_int4pack_mm_for_cpu.<locals>.<lambda>  rm  r9   c                      grv  r3   r3   r9   r7   rf   r    rm  r9   c                  "   > ST R                    3$ rG  r   rA  s   r7   rf   r    r  r9   c                  "   > ST R                    3$ rI  r   rE  s   r7   rf   r    ry  r9   r   r   )
rW   ri   r   r_   rl  rm  rn  r  r   r   rN  s   ``  r7    meta__weight_int4pack_mm_for_cpur        	LLA>?	LLA>?	LL	EMM5==%..AA? 
LL	5;;8 ;;qvvay!&&)177;;;r9   c                 0  ^ ^ [         R                  " T R                  5       S:H  S 5        [         R                  " TR                  5       S:H  S 5        [         R                  " T R                  [         R                  [         R
                  [         R                  4;   U 4S j5        [         R                  " TR                  [         R                  L U4S j5        T R                  T R                  S5      TR                  S5      T R                  S9$ )Nr   c                      gr  r3   r3   r9   r7   rf   ;_weight_int4pack_mm_with_scales_and_zeros.<locals>.<lambda>  rm  r9   c                      grv  r3   r3   r9   r7   rf   r    rm  r9   c                  "   > ST R                    3$ rG  r   rA  s   r7   rf   r    r  r9   c                  "   > ST R                    3$ r  r   rE  s   r7   rf   r    ry  r9   r   r   )
rW   ri   r   r_   rl  rm  rn  rO  r   r   )r<   r  rK  qScaleqZeross   ``   r7   )_weight_int4pack_mm_with_scales_and_zerosr    r  r9   r5   r6   c                     X-   S-
  U-  U-  $ r1   r3   r4   s     r7   kai_roundupr    s    UQY1!!r9   c                   ^	^
^^^^^^^^^ U S:X  a{  X2:X  a(  SnSnSnSmSmSmS mUUUU4S jmU4S jnU" XXEU5      $ US-  S	:X  aD  X#-  S	:X  a;  SnSnSnSmSmSmSm	U	UU4S
 jnU	U
UUUUU4S jmS m
U	4S jmU	4S jmU" XXEXc5      $ g g g )Nr-  rz  r{  r   c                 4    [        X-  S5      n[        X5      $ )Nr-  r  )r_  krsrkr_sr_roundedup4s       r7   kai_k_roundedup3get_kai_packed_weight_size.<locals>.kai_k_roundedup  s     $/rw#: "177r9   c                 f   > T" XU5      nUS-  S:w  a  [        SU 35      eUUS-  T-   T-   T-   -  $ )Nr   r   zk_internal must be even, got r  )	r_  nrr  r  
k_internalr  kai_num_bytes_biaskai_num_bytes_multiplier_rhskai_num_bytes_sum_rhss	        r7   9kai_get_rhs_packed_stride_rhs_pack_nxk_qsi4cxp_qsu4cxs1s0]get_kai_packed_weight_size.<locals>.kai_get_rhs_packed_stride_rhs_pack_nxk_qsi4cxp_qsu4cxs1s0  s^     -QB7
Nq((+H)UVV1_23+, )) r9   c                 8   > [        X5      U-  nUT" XX45      -  $ rC   r  )r  r_  r  r  r  num_rowsr  s         r7   7kai_get_rhs_packed_size_rhs_pack_nxk_qsi4cxp_qsu4cxs1s0[get_kai_packed_weight_size.<locals>.kai_get_rhs_packed_size_rhs_pack_nxk_qsi4cxp_qsu4cxs1s0+  s0     'q-3 Orr9   r|  r   c                    > XS-  S:w  a  [        SU SU S35      eUT	-  S:w  a  [        SU ST	 S35      eUT-  S:w  a  [        SU ST S35      e[        X5      U-  nUT" XX4U5      -  $ Nr   bl (z) must be divisible by kr (r}   znr (z+) must be divisible by kai_nr_multiple_of (+) must be divisible by kai_bl_multiple_of (r   r  )
r  r_  r  r  r  blr  kai_bl_multiple_of;kai_get_rhs_packed_stride_rhs_pack_nxk_qsi4c32p_qsu4c32s1s0kai_nr_multiple_ofs
          r7   9kai_get_rhs_packed_size_rhs_pack_nxk_qsi4c32p_qsu4c32s1s0]get_kai_packed_weight_size.<locals>.kai_get_rhs_packed_size_rhs_pack_nxk_qsi4c32p_qsu4c32s1s0C  s     G>(4t3NrdRS)TUU++1(rd"MN`Maabc  ++1(rd"MN`Maabc  'q-3 Qrrr9   c                    > XB-  S:w  a  [        SU SU S35      eUT
-  S:w  a  [        SU ST
 S35      eUT-  S:w  a  [        SU ST S35      eT	" 5       nT" X5      nT" XE5      nUXv-  T-   T-   -  $ r  r  )r_  r  r  r  r  num_bytes_multiplier_rhsnum_blocks_per_rownum_bytes_per_blockr  #kai_get_bf16_datatype_size_in_bytesr  kai_num_blocks_per_rowr  kai_num_bytes_per_blockr  s           r7   r  _get_kai_packed_weight_size.<locals>.kai_get_rhs_packed_stride_rhs_pack_nxk_qsi4c32p_qsu4c32s1s0Z  s     G>(4t3NrdRS)TUU++1(rd"MN`Maabc  ++1(rd"MN`Maabc 
 ,O+P(%;A%B"&='# (=+,() r9   c                      g)Nr   r3   r3   r9   r7   r  Gget_kai_packed_weight_size.<locals>.kai_get_bf16_datatype_size_in_bytesw  s    r9   c                 V   > UT-  S:w  a  [        SU ST S35      e[        X5      U-  $ )Nr   r  r  r}   r  )r_  r  r  s     r7   r  :get_kai_packed_weight_size.<locals>.kai_num_blocks_per_rowz  sF    ++1(rd"MN`Maabc  #1)R//r9   c                 J   > U T-  S:w  a  [        SU  ST S35      eU S-  U-   $ )Nr   r  r  r}   r   r  )r  r  r  s     r7   r  ;get_kai_packed_weight_size.<locals>.kai_num_bytes_per_block  sF    ++1(rd"MN`Maabc  a#;;;r9   r3   )n_bitsr  K	groupsizekai_nrkai_krkai_srr  r  r  r  r  r  r  r  r  r  r  r  r  s            @@@@@@@@@@@r7   get_kai_packed_weight_sizer  
  s    {>FFF$%!+,(!"8 
 Kff  ^q Q]a%7FFF$%!!"!"!#. :0< Mff ] &8 _ r9   c                   ^  [         R                  " T R                  [         R                  L U 4S j5        [         R                  R
                  R                  5       (       a  X4:X  a  UR                  [         R                  :X  d4  X4:  ac  US-  S:X  aZ  XC-  S:X  aR  UR                  [         R                  :X  a4  [        SXTU5      nT R                  [        U5      [         R                  S9$ T R                  5       UR                  5       -   nUb  XbR                  5       -  nT R                  U[         R                  S9$ )Nc                  "   > ST R                    3$ rI  r   )weightss   r7   rf   2meta__dyn_quant_pack_4bit_weight.<locals>.<lambda>  s    .w}}o>r9   r|  r   r-  r   )rW   ri   r_   r  backendskleidiaiis_availabler[   rn  r  r   r   r   )r  scales_zerosrG  
block_sizein_featuresout_featurespacked_weight_sizes   `      r7    meta__dyn_quant_pack_4bit_weightr    s    
LL$> ~~++--		"|'9'9U[['H$R1$(A-""enn4 8|*
   %7!8 LL <+=+=+??jjl*/u{{CCr9   c                   ^ ^^ [         R                  " T R                  5       S:H  S 5        [         R                  " T R                  [         R                  :H  =(       d)    T R                  [         R
                  :H  =(       a    TT:H  UUU 4S j5        T R                  S5      nT R                  XTT R                  S9$ )Nr   c                      g)Nzinput must be a 2D tensorr3   r3   r9   r7   rf   -meta__dyn_quant_matmul_4bit.<locals>.<lambda>  s    )Dr9   c                  .   > STR                    ST  ST 3$ )NzPexpected input to be f32 or bf16 (bf16 requires block_size == in_features), got z with block_size=z and in_features=r   )r  r  inps   r7   rf   r    s%    99+.zl:KK=Zr9   r   r   )rW   ri   r   r_   rl  rn  r   r   )r  packed_weightsr  r  r  r  s   ` ``  r7   meta__dyn_quant_matmul_4bitr    s     
LLa!DE	LL	emm	# 	GII'EJ+,E	
 	A==		=::r9   c                 0  ^ ^ [         R                  " T R                  5       S:H  S 5        [         R                  " T R                  [         R                  [         R
                  [         R                  4;   U 4S j5        [         R                  " TR                  5       S:H  S 5        [         R                  " TR                  [         R                  L U4S j5        T R                  T R                  S5      TR                  S5      T R                  S9$ )Nr   c                      gr  r3   r3   r9   r7   rf   *meta__weight_int8pack_mm.<locals>.<lambda>  rm  r9   c                  "   > ST R                    3$ rG  r   rA  s   r7   rf   r    r  r9   c                      grv  r3   r3   r9   r7   rf   r    rm  r9   c                  "   > ST R                    3$ )Nzexpected w to be int8, got r   rE  s   r7   rf   r    s    -aggY7r9   r   r   )
rW   ri   r   r_   rl  rm  rn  rN  r   r   )r<   r  q_scaless   `` r7   meta__weight_int8pack_mmr    s    	LLA>?	LL	EMM5==%..AA? 
LLA>?	LL	5::7 ;;qvvay!&&)177;;;r9   c                   ^ ^^ [         R                  " T R                  5       S:  U 4S j5        [         R                  " TR                  5       S:  U4S j5        [         R                  " T R                  S5      TR                  S5      :H  U U4S j5        [         R                  " [        R
                  " T R                  5      U 4S j5        [         R                  " [        R
                  " TR                  5      U4S j5        [         R                  " US:  S	 5        [         R                  " TS
;   U4S j5        T R                  S5      nTR                  S5      nT R                  S S nTR                  S S n[        [         R                  " Xg5      5      nUR                  XE/5        T R                  U5      $ )Nr   c                  ,   > ST R                  5        S3$ )Nz1cdist only supports at least 2D tensors, X1 got: rY  r   x1s   r7   rf   $meta_cdist_forward.<locals>.<lambda>      CBFFH:QOr9   c                  ,   > ST R                  5        S3$ )Nz1cdist only supports at least 2D tensors, X2 got: rY  r   x2s   r7   rf   r    r  r9   r   c                  P   > ST R                  S5       STR                  S5       3$ )Nz4X1 and X2 must have the same number of columns. X1: r   z X2: r   )r  r  s   r7   rf   r    s*    Frwwr{mSXY[Y`Y`acYdXefr9   c                  "   > ST R                    3$ )Nz3cdist only supports floating-point dtypes, X1 got: r   r  s   r7   rf   r        EbhhZPr9   c                  "   > ST R                    3$ )Nz3cdist only supports floating-point dtypes, X2 got: r   r  s   r7   rf   r    r  r9   r   c                      g)Nz)cdist only supports non-negative p valuesr3   r3   r9   r7   rf   r    s    !Lr9   )Nr   r2   r   c                     > ST  3$ )Nz(possible modes: None, 0, 1, 2, but was: r3   )compute_modes   r7   rf   r    s    :<.Ir9   r  )rW   ri   r   r   rP   is_float_dtyper_   r   r   broadcast_shapesextendr   )	r  r  rr  r  r1r2batch_tensor1batch_tensor2rs  s	   `` `     r7   meta_cdist_forwardr    sF   	LL
AO 
LL
AO 
LL
rwwr{"f 
LLRXX&P 
LLRXX&P 
LLaLM	LL'I 
B	BHHSbMMHHSbMM..}LML!<<%%r9   c                 <   UR                   S   nUR                   S   nUR                   S   nUR                   S S nUR                   S S n	[        [        R                  " X5      5      n
U
R	                  5       nUR                  Xe/5        [        R                  " U
5      nUS:X  d  US:X  d  US:X  d  US:X  a  [        R                  " U5      $ U[        UR                   5      :w  a  UR                  U5      n[        R                  " U[        R                  S9$ )Nr   r  r   r   )r   r   rW   r  copyr  mathprod
zeros_liker  r   r   )rw  r  r  rr  cdistc1r  r  r	  r
  r  tensor1_expand_sizebatch_products                r7   meta_cdist_backwardr    s     
"B	"B	"BHHSbMMHHSbMM 6 6} TU.335x(II23M	Qw"'R1W(:##d288n,YY*+Be.E.EFFr9   c	                 Z  ^ ^^^^^ [         R                  " TR                  [         R                  [         R                  4;   U4S j5        [         R                  " TR                  [         R                  [         R                  4;   U4S j5        [         R                  " [
        R                  " T R                  5      U 4S j5        TR                  S5      n	U(       a   [         R                  " U	S:  S 5        U	S-  n	T R                  U	T R                  S5      5      n
Tb  [         R                  " U[        :H  S 5        [         R                  " TR                  S:H  U4S j5        [         R                  " TR                  5       TR                  5       :H  UU4S	 j5        U4S
 jmS mUU4S jn[        T5      S:w  a}  TR                  TR                  S5      5      nTR                  TR                  5       5      nU[        :X  a"  TR                  U	T R                  S5      5      nOTR                  S5      nOU" T TX5      nU[        [        4;   d  U(       d!  TR                  TR                  S5      5      nOTR                  S5      nTR                  U	5      nTR                  S   nU[        :X  aG  U(       a   [         R                  " US:  S 5        US-  nTR                  UT R                  S   5      nOTR                  UR                  5       5      nXX4$ )Nc                  "   > ST R                    3$ )Nz(expected indices to be long or int, got r   )r   s   r7   rf   $meta_embedding_bag.<locals>.<lambda>      :7==/Jr9   c                  "   > ST R                    3$ )Nz(expected offsets to be long or int, got r   )r  s   r7   rf   r    r  r9   c                  "   > ST R                    3$ )Nz/expected weight to be floating point type, got r   )rE  s   r7   rf   r    s    A&,,Pr9   r   r2   c                      gNz1include_last_offset: numBags should be at least 1r3   r3   r9   r7   rf   r  $  s    Gr9   c                      g)Nz@embedding_bag: per_sample_weights only supported with mode='sum'r3   r3   r9   r7   rf   r  -  s    Vr9   c                  $   > ST R                    S3$ )Nz1expected per_sample_weights to be 1D tensor, got rY  r  )per_sample_weightss   r7   rf   r  1  s    GHZH_H_G``abr9   c                  N   > STR                  5        ST R                  5        S3$ )Nz%expected per_sample_weights.numel() (z$ to be the same as indices.numel() (r}   r   )r   r   s   r7   rf   r  5  s/    78J8P8P8R7S T66=mmo5FaIr9   c                 L   > T" XU5      =(       a    UR                  S5      S:H  $ Nr   r2   r   )r6  r  r	  padding_idxis_fast_path_index_selects       r7   is_fast_path_index_select_scale;meta_embedding_bag.<locals>.is_fast_path_index_select_scale;  s&    %c;?XELLQROWXDX	
r9   c                    U R                   [        R                  :H  =(       d    U R                   [        R                  :H  =(       a;    U R	                  S5      S:H  =(       a     UR	                  S5      S:H  =(       a    US:  $ r  )r_   rW   r[   rY   r   )r6  r	  r&  s      r7   r'  5meta_embedding_bag.<locals>.is_fast_path_index_select@  sb    YY%++%@ejj)@  

1" a A%  a		
r9   c                 .   > Ub	  T" XX#5      $ T" XU5      $ rC   r3   )r6  r  r	  r&  r'  r(  s       r7   is_fast_path(meta_embedding_bag.<locals>.is_fast_pathH  s#    23vSS,S+FFr9   r  c                      gr  r3   r3   r9   r7   rf   r  b  s    Or9   )rW   ri   r_   r   r   rP   r  r   r   MODE_SUMr   r   r  MODE_MAX	MODE_MEANr   )rE  r   r  scale_grad_by_freqrw  sparser   include_last_offsetr&  num_bagsr	  r-  
offset2bagbag_sizemax_indicesfast_path_sumnumBagsr'  r(  s   ```   `          @@r7   meta_embedding_bagr<    sw    
LL%**eii00J 
LL%**eii00J 
LLV\\*P
 ||AHMG	
 	AhA7F%HV	
 	##q(b	
 	$$&'--/9	



G 7u$&&w||A7
$$W\\^48!++Hfkk!nEK!++A.K$V-?UIx(( **7<<?;J **1-J$$X.--"8"qLO 1!++GV\\!_EK!++HMMO<Kx44r9   c                     [        XU/UQ76 u  pEpg[        U5      S:X  a  UR                  UR                  5       5      nXEXg4$ )Nr  )r<  r  r   r   )rE  r   r  rR   r	  r7  r8  r9  s           r7   meta_embedding_bag_forward_onlyr>  k  sN    0B1#'1-F 7u$$$W\\^4x44r9   c                     U(       a  U$ U R                   R                  (       d  U R                   R                  (       a  U R                   $ U(       a  [        R                  $ U R                   $ rC   )r_   r  r   rW   r   )r   r_   promote_int_to_longs      r7   _get_reduction_dtyperA  u  sD    {{$$(>(>{{	zz;;r9   r   c                    [        XSS9n[        R                  " U R                  U5      n[	        XU5      nU R                  XTS9$ )NT)r@  r   )rA  rP   r  r   r  r   )r   r  r  r_   r  rs  s         r7   meta_nansumrC    sC     ($OLT2D+EAL??<?<<r9   c           	          [         R                  " U R                  [        [	        U R                  5       5      5      5      nU R                  U5      $ rC   )rP   r  r   rh   r   r   r   )r   rs  s     r7   meta_medianrE    s<    77U5-.L ??<((r9   c                    [        U 5      S:X  a  [        R                  " S5        [        R                  " U R                  U45      n[        XU5      nU R                  U5      U R                  U[        R                  S94$ )Nr   zmedian CUDA with indices outputr   )	r  rP   alert_not_deterministicr  r   r  r   rW   r   )r   r   r  rs  s       r7   meta_median_mode_dimrH    sn     5V#%%&GH


u{{SF
3C+E@L%EJJ7 r9   c                     U $ rC   r3   r   s    r7   meta_logical_not_rJ    r  r9   c                   ^^ [         R                  " [        U5      U R                  5       :  S 5        [	        U5       H%  u  mm[         R                  " TS:  UU4S j5        M'     [        U5      U R                  5       -
  nSU-  [        U R                  5      -   n[        [        U5      5       Vs/ s H  oCU   X   -  PM     nnU R                  U5      $ s  snf )Nc                      g)NzZNumber of dimensions of repeat dims can not be smaller than number of dimensions of tensorr3   r3   r9   r7   rf   meta_repeat.<locals>.<lambda>  s    lr9   r   c                     > ST ST  3$ )Nz"Repeats cannot be negative, found r  r3   )r   reps   r7   rf   rM    s    8ZsKr9   r4  )	rW   ri   r   r   r  rh   r   r   r   )r   r  num_new_dimensionspadded_sizer   target_sizerO  s       ` @r7   meta_repeatrS    s    	LLG
"l G$31HK	
 % W
2++eDJJ.??K8=c'l8KL8K1q>GJ.8KKL>>+&& Ms   6Cc                     U $ rC   r3   r   s    r7   
meta_zero_rU    r  r9   c                     [        U[        R                  5      (       a   [        U R                  UR                  5        U $ rC   )rs   rW   r   rk   r   r   r   s     r7   meta_binop_inplacerX    s,     %&&

EKK8Kr9   c                 *   S nS nS nU" U 5      (       a  U" U5      (       a  [        S5      eU" U 5      (       a  U" U5      (       d  [        S5      e[        U[        R                  5      (       a   [	        U R
                  UR
                  5        U $ )a  
Some checks for inplace ops.
Checks for promotion rules for some dtypes.
int.add/sub_(float) and bool.add/sub_(others) are rejected.
Promoting in these in-place operations would require reallocating
and copying over elements, hence not allowed.
Checks for alpha param.
c                     [        U [        5      (       a   [        R                  " U R                  5      $ [        U [
        5      $ rC   )rs   r   rP   rT  r_   r   rv   s    r7   is_integeric.meta_binop_inplace_alpha.<locals>.is_integeric  s1    c:&&))#))44c7++r9   c                     [        U [        5      (       a   [        R                  " U R                  5      $ [        U [
        5      $ rC   )rs   r   rP   r  r_   r   r[  s    r7   
is_floatic,meta_binop_inplace_alpha.<locals>.is_floatic  s1    c:&&''		22c9--r9   c                     [        U [        5      (       a   [        R                  " U R                  5      $ [        U [
        5      $ rC   )rs   r   rP   is_boolean_dtyper_   r   r[  s    r7   is_booleanic.meta_binop_inplace_alpha.<locals>.is_booleanic  s1    c:&&))#))44c8,,r9   z]Promotion of int.add/sub_(float) in in-place ops are not possible due to element size change.z_Promotion of book.add/sub_(others) in in-place ops are not possible due to element size change.)r2  rs   rW   r   rk   r   )r   r   ra  r\  r_  rc  s         r7   meta_binop_inplace_alphare    s    $,.- Dj//k
 	

 D,u"5"5m
 	
 %&&

EKK8Kr9   c                 2    [        X[        R                  S9$ Nr  rU   r   rQ   r   r   ra  s      r7   meta_binop_alpharj    s     $C$K$K r9   c                 2    [        U [        R                  S9$ rg  rh  )r   rH  s     r7   
meta_roundrl    s    <DD r9   c                   ^ ^^ [         R                  " [        R                  " TR                  5      U U4S j5        [        T[         R                  5      (       a;  [         R                  " [        R                  " TR                  5      U U4S j5        g [         R                  " [        T[        5      U U4S j5        g )Nc                  &   > T  STR                    3$ )Nz7: Expected input tensor to have an integral dtype. Got r   )r  r   s   r7   rf   #shift_dtype_check.<locals>.<lambda>#  s    7)RSWS]S]R^_r9   c                  &   > T  STR                    3$ )Nz6: Expected shift value to have an integral dtype. Got r   r  r  s   r7   rf   ro  (  s    wiUVYV_V_U`ar9   c                     > T  ST 3$ )Nz): Expected shift value to be an int. Got r3   rq  s   r7   rf   ro  -  s    wiHNr9   )rW   ri   rP   rT  r_   rs   r   r   )r  r   r  s   ```r7   shift_dtype_checkrs     ss    	LLtzz*_ #u||$$""399-a	

 	sG$N	
r9   c                 J    [        SX5        [        X[        R                  S9$ )Nrshiftr  rs  rU   r   rQ   rW  s     r7   meta_rshiftsrw  1  %    h,$C$K$K r9   c                 J    [        SX5        [        X[        R                  S9$ )Nlshiftr  rv  rW  s     r7   meta_lshiftsr{  9  rx  r9   c                 8    U R                  U R                  5      $ rC   r  r   s    r7   	meta_zeror}  A  s    >>$**%%r9   c                     U $ rC   r3   r   r  s     r7   
meta_fill_r  F  r  r9   c                 .    [         R                  " U 5      $ rC   rD  r  s     r7   	meta_fillr  K      D!!r9   c                     U $ rC   r3   r   s    r7   
meta_relu_r  P  r  r9   c                 2    [        X[        R                  S9$ rg  rh  ri  s      r7   meta__add_relur  U  s     $C$K$K r9   c                 .    [         R                  " U 5      $ rC   rD  r   noiselowerr  r  r  s         r7   meta_rrelu_with_noiser  ]  s    
 D!!r9   c                 Z    [         R                  " U 5      [         R                  " U5      4$ rC   rD  r  s         r7    meta_rrelu_with_noise_functionalr  e  s%     D!5#3#3E#:::r9   c                     U $ rC   r3   )r   r  r  r  r  s        r7   meta_rrelu_with_noise_r  l  s	     Kr9   c                 .    [         R                  " U 5      $ rC   rD  r   r   r   
accumulates       r7   meta_index_putr  s  r  r9   c                 F    [        U R                  UR                  5        U $ rC   rk   r   )r   r  values      r7   meta_masked_fill_r  x  s    DJJ

3Kr9   c                     U R                  U R                  5       5      R                  [        R                  " U 5      S9nU$ r   )r   r   r3  rP   r   )r   r  r  masked_scales       r7   meta__masked_scaler  ~  s<    >>$))+.1111$7 2 L r9   c                    ^ ^ [         R                  " UR                  [         R                  [         R                  4;   S 5        [         R                  " T R                  TR                  :H  U U4S j5        T $ )Nc                      g)NzMask must be bool or uint8r3   r3   r9   r7   rf   &meta_masked_scatter_.<locals>.<lambda>  s    9Ur9   c                  <   > ST R                    STR                    3$ )NzEmasked_scatter: expected self and source to have same dtypes but got r   r   )r   rv  s   r7   rf   r    s      **U6<<.:r9   )rW   ri   r_   r  r  )r   r  rv  s   ` `r7   meta_masked_scatter_r    sU    	LL

uzz5;;//1U 
LL

fll"	:
 Kr9   c                 z    [        X5      u  p[        R                  " U [        R                  S9n[	        X1U5      $ r   )r%   rW   r   r   r  )r   r  rv  r	  s       r7   meta_masked_scatterr    s5     "$-JDd%2I2IJFf55r9   c                 $    U R                  U5      $ rC   r  )r   r  r^  s      r7   meta_masked_scatter_backwardr    s    >>%  r9   c                     U $ rC   r3   r  s       r7   meta_index_put_r    r  r9   c           	        ^^^^^ SSK JnJn  [        R                  " U R                  5       S:H  S 5        [        R                  " UR                  5       S:H  S 5        U R                  5       nUR                  5       mUS   mUS   mUS   nTS   n	TX4m[        R                  " U" U" TS   T5      U" TS   T5      5      UUU4S j5        U(       a  U R                  [        R                  :H  =(       d    U R                  [        R                  :H  =(       a    U[        R                  :H  n
[        R                  " X@R                  :H  =(       d    U
S	 5        UR                  T5      R                  U5      nOUR                  T5      nU(       d]  TbZ  [        R                  " TR                  5       S:H  S
 5        [        R                  " U" TR                  5       T5      UU4S j5        U$ )Nr   )sym_andr  r/   c                      gr  r3   r3   r9   r7   rf   )common_meta_baddbmm_bmm.<locals>.<lambda>  r  r9   c                      gr  r3   r3   r9   r7   rf   r    r  r9   r   r2   c            	      .   > ST ST ST S    ST S    S3	$ r  r3   r  s   r7   rf   r    s3    RSURV
l<?*;2l1o=NbRr9   c                      g)Nzfout_dtype only supported for torch.float32 output with float16/bfloat16 inputs or same as input dtypesr3   r3   r9   r7   rf   r    s    |r9   c                      g)Nzself must be a 3D tensorr3   r3   r9   r7   rf   r    s    6Pr9   c                  0   > ST  STR                  5        3$ )Nz*Expected an input tensor shape with shape z but got shape: r   )r  self_baddbmms   r7   rf   r    s    @M]^j^o^o^q]rsr9   )r0  r  r  rW   ri   r   r   r_   rm  rn  rl  r   r3  )r  r  is_bmmr  rI  r  r  r  res_rowsres_colssupported_out_dtyper	  r  r  r  r  s      `        @@@@r7   common_meta_baddbmm_bmmr    s   E	LL"$HI	LL"$HI;;=L;;=L	aB#AAHAHx*K	LL|A+VLOEU-VW	R
 LLEMM)KV\\U^^-K)5==( 	 	%<)<|	
 !!+.11)< !!+.l.\%%'1,.PQ<$$&4s	

 Mr9   c                     [        XS5      $ )NTr  )r   rV  s     r7   meta_bmmr    s    "4t44r9   c                     [        XSUS9$ )NT)rI  r  )r   rV  rI  s      r7   meta_bmm_dtyper    s    "4tyIIr9   c                 h    X-  nX-  nUS:w  a#  [        US:  5      [        US:  5      :w  a  US-  nU$ r$  )r  )r<   r=   qr{  s       r7   div_rtnr    s>    	A	A 	Av4A;$q1u+-	QHr9   c                     [        U U-   U-   XQS-
  -  -
  S-
  U(       a  US-
  OS-   U5      S-   nU(       a  US-
  U-  X-   :  a  US-  nU$ r  )r  )	inputSize
kernelSizer  r  r   r  r:  
outputSizes           r7   pooling_output_shape_pad_lrr    s     	 q.)* 	
 'vzA/ 	
 		  Nf$	(99!OJr9   c           	         ^^^ [         R                  " US:g  S 5        [         R                  " TS:  U4S j5        [         R                  " TTS-
  T-  S-   S-  :*  UUU4S j5        [        U TTTUTU5      $ )Nr   c                      g)Nzstride should not be zeror3   r3   r9   r7   rf   &pooling_output_shape.<locals>.<lambda>   s    &Ar9   c                     > ST  3$ )Nz'pad must be non-negative, but got pad: r3   pads   r7   rf   r    s    %LSE#Rr9   r2   r   c                     > ST ST ST  3$ )NzApad should be at most half of effective kernel size, but got pad=z, kernel_size=z and dilation=r3   )r  r  r  s   r7   rf   r    s"    OPSu U%,nXJ@r9   )rW   ri   r  )r  r  r  r   r  r:  s    `` ` r7   rs  rs    ss    	LL1AB	LLRS	LLa8+a/A55	
 ':sC9 r9   c           	        ^ ^^^^^^^^^	^
^^^^ T R                  5       nT	m[        R                  " TS:  =(       a    TS:  UU4S j5        [        R                  " TS:  =(       a    TS:  UU4S j5        [        R                  " TS:  =(       a    TS:  UU4S j5        T R                  S5      S:g  =(       a    T R                  S5      S:g  nU[        R                  :X  aC  [        R                  " US:H  =(       a    U=(       a    T R                  S5      S:g  U 4S	 j5        Or[        R                  " US:H  =(       a    T R                  S5      S:g  =(       a    U=(       d)    US:H  =(       a    U=(       a    T R                  S5      S:g  U 4S
 j5        [        R                  " TS-  T:  =(       a    TS-  T:  UUUU4S j5        [        R                  " TS:  =(       a    TS:  U
UU	UUU4S j5        g )Nr   c                     > ST  ST 3$ )Nz5kernel size should be greater than zero, but got kH: , kW: r3   )rw  rx  s   r7   rf   $pool2d_shape_check.<locals>.<lambda>$  s    Gt6RTQUVr9   c                     > ST  ST 3$ )Nz0stride should be greater than zero, but got dH: , dW: r3   )ry  rz  s   r7   rf   r  (  s    B2$fRDQr9   c                     > ST  ST 3$ )Nz9dilation should be greater than zero, but got dilationH: , dilationW: r3   )	dilationH	dilationWs   r7   rf   r  ,  s    KI;Vcdmcnor9   r2   r   r-  r/   c                  *   > ST R                  5        3$ )NzExpected 4D (batch mode) tensor expected for input with channels_last layout with optional 0 dim batch size for input, but got: r   r  s   r7   rf   r  4  s     CCH::<.Rr9   c                  *   > ST R                  5        3$ )NzYExpected 3D or 4D (batch mode) tensor with optional 0 dim batch size for input, but got: r   r  s   r7   rf   r  ;  s    opupzpzp|o}~r9   c                      > ST ST ST ST  3$ )NzKpad should be smaller than or equal to half of kernel size, but got padW = z	, padH = z, kW = z, kH = r3   )rw  rx  r{  r|  s   r7   rf   r  @  s$     ygbT>r9   c                  .   > ST ST  ST ST ST ST S3$ NzGiven input size: (r<   z). Calculated output size: (z). Output size is too smallr3   )r}  r~  r;  r  r<  r=  s   r7   rf   r  F  s8    %k]!K=* N$$0><.+ O##r9   )r   rW   ri   r   r  )r   rw  rx  ry  rz  r{  r|  r  r  r;  r}  r~  r<  r=  r   r   
valid_dimsr  s   ``````````````   @r7   rt  rt    s   " 99;DL	LL
Q26V 
LL
Q26Q 
LLA')a-o
 A!#:

1(:J+++AI;*;A!);R	
 	QY<5::a=A-<* A	?j?UZZ]a-?~	
 
LL
a4+B!GtO	> 
LLq.\Q.	# 	#r9   r  r  rw  rx  r  ry  rz  pTpHpW	dilationTr  r  r  r  r  r  r  r  r  c           
        ^ ^^^^^^^^^	^
^^^^^^^^^^^ T R                   n[        R                  " TS:  =(       a    TS:  =(       a    TS:  UUU4S j5        [        R                  " TS:  =(       a    TS:  =(       a    TS:  UUU4S j5        [        R                  " TS:  =(       a    TS:  =(       a    TS:  UUU4S j5        [        R                  " US;   UU 4S j5        [        U5       H@  mUS:X  a  TS:X  a  M  [        R                  " T R	                  T5      S:  UUU 4S j5        MB     U(       a;  [        R                  " TT:  =(       a    TT:  =(       a    TT:  UUUUUU4S	 j5        [        R                  " TS
-  T:  =(       a    TS
-  T
:  =(       a    TS
-  T	:  UUUU	UU
4S j5        [        R                  " TS:  =(       a    TS:  =(       a    TS:  UUUUUUU4S j5        g )Nr   c                     > ST ST  ST 3$ )Nz5kernel size should be greater than zero, but got kT: z, kH: r  r3   )rw  r  rx  s   r7   rf   $pool3d_shape_check.<locals>.<lambda>h  s    $fRDrd,r9   c                     > ST ST  ST 3$ )Nz0stride should be greater than zero, but got dT: z, dH: r  r3   )ry  r  rz  s   r7   rf   r  o  s    >rd&FSURVWr9   c                     > ST ST  ST 3$ )Nz9dilation should be greater than zero, but got dilationT: z, dilationH: r  r3   )r  r  r  s   r7   rf   r  u  s    #M)M)Vr9   r  c                  &   > T  STR                    3$ )Nz/: Expected 4D or 5D tensor for input, but got: rO  )r  r   s   r7   rf   r  }  s    7)J5;;-Xr9   rU  c                  L   > T  STR                    STR                  T5       S3$ )NzZ: Expected input's non-batch dimensions to have positive length, but input has a shape of z and non-batch dimension z has length zero!)r   r   )r  r   r   s   r7   rf   r    s.    ) --2[[M+EJJqM?:KMr9   c                  .   > ST ST  ST ST ST ST S3$ )Nzinput image (T: r^  r7  z ) smaller than kernel size (kT:  kH:  kW: r}   r3   )r  r  r  rw  r  rx  s   r7   rf   r    s4    "5'gYd6( C$$&4uRDbT<r9   r   c                  ,   > ST ST ST  ST ST ST 3$ )NzHpad should be smaller than or equal to half of kernel size, but got kT: r  r  z padT: z padW: z padH: r3   )rw  r  rx  r  r  r  s   r7   rf   r    s1    $eB4uRDt72$gbTKr9   r2   c                  :   > ST ST ST  ST ST ST ST ST S3$ r  r3   )r  r  r  r  r  r  r  s   r7   rf   r    sD    !'!E7!G9AfX F((/y%'!F8 L'(r9   )r   rW   ri   r   r   )r   r  r  rw  rx  r  ry  rz  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r   s   `````````````````````  @r7   r  r  L  s   0 ::D	LL
Q$26$b1f	
 
LL
Q$26$b1f	
 
LLA9)a-9IM	
 
LLX
 4[19aJJqMA	
	  RK:GrM:fl 	
 
LL
Q"6a26"q&B,	
 	
 
LL
3v{3w!|	
 	
r9   c                 j   U R                   n[        U UUUUUUU	U
UUUUUUUUUUUU5        [        UUUS-
  U5        [        UUUS-
  U5        [        UUUS-
  U5        [        UUUS-
  U5        [        UUUS-
  U5        [        UUUS-
  U5        [        UUUS-
  U5        [        UUUS-
  U5        g )Nr-  r/   r   r2   r   r  rU  )r   r"  r   r  r  rw  rx  r  ry  rz  r  r  r  r  r  r  r  r  r  r  r  r  r  r   s                           r7   max_pool3d_backward_shape_checkr    s    2 ::D








+0 ;dQh8;dQh6;dQh8;dQh77D$(G47D$(E27D$(G47D$(F3r9   c                     U R                   n[        U UUUUUUUU	U
USSSUUUUUUUS5        [        UUUS-
  U5        [        UUUS-
  U5        [        UUUS-
  U5        [        UUUS-
  U5        g )Nr2   Tr-  r/   r   r  )r   r"  r  r  rw  rx  r  ry  rz  r  r  r  r  r  r  r  r  r  r  r   s                       r7   r  r    s    * ::D








			-2 ;dQh8;dQh6;dQh8;dQh7r9   c                    S nU" SU5      u  px[         R                  " [        U5      S;   S 5        [        U5      S:X  a  XxpOU" SU5      u  pU" SU5      u  pU" SU5      u  pU R                  S	5      nU R                  S
5      nU R                  S5      n[        R
                  " U 5      nU[         R                  :X  a*  [         R                  " U R                  5       S:H  S 5        OVU[         R                  :X  a*  [         R                  " U R                  5       S;   S 5        O[         R                  " SS 5        [        UX{XU5      n[        UXXU5      n[        U UUU	U
UUUUUUUUUU5        UUU4$ )Nc                    ^  [         R                  " [        U5      S;   U 4S j5        US   n[        U5      S:X  a  UOUS   nX#4$ )NrX  c                     > ST  S3$ )Nzmax_pool2d: rZ  r3   r[  s   r7   rf   Emax_pool2d_checks_and_compute_shape.<locals>.unpack.<locals>.<lambda>(  r]  r9   r   r2   r^  r_  s   `   r7   rb  3max_pool2d_checks_and_compute_shape.<locals>.unpack%  rd  r9   r  re  c                      g)NzOmax_pool2d: stride must either be omitted, a single int, or a tuple of two intsr3   r3   r9   r7   rf   5max_pool2d_checks_and_compute_shape.<locals>.<lambda>2  ri  r9   r   r   r  r  ro  r  r   r-  c                      g)NzMnon-empty 4D (batch mode) tensor expected for input with channels_last layoutr3   r3   r9   r7   rf   r  C  s    cr9   r  c                      g)Nz9non-empty 3D or 4D (batch mode) tensor expected for inputr3   r3   r9   r7   rf   r  H      Or9   Fc                      g)NzAUnsupported memory format. Supports only ChannelsLast, Contiguousr3   r3   r9   r7   rf   r  M  s    Wr9   )rW   ri   r   r   rP   r   r  r   r   rs  rt  )r   r  r   r  r  r:  rb  rw  rx  ry  rz  r{  r|  r  r  r;  r}  r~  r   r<  r=  s                        r7   r8  r8    sy    M;/FB	LLFy a 6{aB&)	7+JD!*h7I**R.K**R.KBJ//6M+++IIK1c	
 
%11	1IIK6!O	

 	W	

 (RriXL&z2RIVK



$ k11r9   c                 |  ^ ^^^^^ [        TX#XEU5      u  nmm[        R                  " TR                  T R                  :H  U U4S j5        UmTR                  mUUUU4S jn	U	" T 5        U	" U5        [
        R                  " T5      n
[        R                  " TR                  TR                  TR                  U
S9$ )Nc                  <   > STR                    ST R                    3$ )NzExpected dtype z  for `gradOutput` but got dtype r   r  s   r7   rf   7meta_max_pool2d_with_indices_backward.<locals>.<lambda>}  s    /$**-MkN_N_M`ar9   c                 l   > [        U TTS-
  T5        [        U TTS-
  T5        [        U TTS-
  T5        g )Nr/   r   r2   )rU  )r  r  r   r<  r=  s    r7   _check_dim_size>meta_max_pool2d_with_indices_backward.<locals>._check_dim_size  s9    q$q,7q$q,7q$q+6r9   r  )
r8  rW   ri   r_   r   rP   r   r   r   r   )r"  r   r  r   r  r  r:  r   r;  r  r   r  r   r<  r=  s   ``         @@@@r7   %meta_max_pool2d_with_indices_backwardr  h  s     	,k7i		
 
LL

k'''a
 L99D7 7
 K G//5M;;

jj{{#	 r9   c                    [        XX#XE5      u  nnnU R                  5       S:X  a  U R                  S5      OSn	[        R                  " U 5      n
U R                  5       S:X  a  XgU/nOXXx/n[
        R                  " UU R                  U R                  U
S9[
        R                  " U[
        R                  U R                  U
S94$ r6  )
r8  r   r   rP   r   rW   r   r_   r   r   r9  s               r7   meta_max_pool2d_with_indicesr    s     	,FX		
  %yy{a/UZZ^QF//6Myy{a;7\?++<<'		
 	++<<'		
 r9   c                   ^ ^^^
^^ [         R                  " T R                  S;   U 4S j5        T R                  n[        US-
  U5       H1  m
[         R                  " T R	                  T
5      S:  U
U 4S j5        M3     [         R                  " [        T5      S:H  S 5        [         R                  " [        U5      S:H  S 5        T R	                  S	5      nT R	                  S
5      mT R	                  S5      mUS:X  a  T R	                  S5      nOSn[         R                  " T R                  TR                  :H  S 5        [         R                  " TR                  S:H  U4S j5        TR	                  S5      nTR	                  S5      nTR	                  S5      m
[         R                  " Xv:  S 5        [         R                  " X:H  S 5        [         R                  " T
S:H  U
4S j5        [         R                  " US   TS   -   S-
  T:*  UU4S j5        [         R                  " US   TS   -   S-
  T:*  UU4S j5        T R                  5       S:X  a  XeUS   US   /n	O
XRS   US   /n	[         R                  " U	T R                  T R                  S9[         R                  " U	[         R                  T R                  S94$ )Nr  c                  "   > ST R                    3$ )Nz:fractional_max_pool2d: Expected 3D or 4D tensor, but got: r  r   s   r7   rf   ,meta_fractional_max_pool2d.<locals>.<lambda>  s    LTYYKXr9   r/   r   c                  2   > STR                  5        ST  S3$ )Nz_fractional_max_pool2d: Expected input to have non-zero  size for non-batch dimensions, but got r  z emptyr   )r   r   s   r7   rf   r    s%     77;yy{mCSTUSVV\^r9   r   c                      g)NzNfractional_max_pool2d: kernel_size musteither be a single int or tuple of Intsr3   r3   r9   r7   rf   r         2r9   c                      g)NzOfractional_max_pool2d: output_size must either be a single int or tuple of Intsr3   r3   r9   r7   rf   r    r  r9   ro  r  r   r-  r2   c                      g)Nz6Expect _random_samples to have the same dtype as inputr3   r3   r9   r7   rf   r    s    Hr9   c                  "   > ST R                    3$ )Nz1Expect _random samples to have 3 dimensions got, r  )random_sampless   r7   rf   r    s    CNDWDWCXYr9   c                      g)Nz=Expect _random_samples.size(0) no less then input batch size.r3   r3   r9   r7   rf   r    r   r9   c                      g)Nz<Expect _random_samples.size(1) equals to input channel size.r3   r3   r9   r7   rf   r        Nr9   c                     > ST  S3$ )Nz/Expect _random_samples.size(2) equals to 2 got .r3   )r   s   r7   rf   r    s    #RSTRUUV!Wr9   c                     > STS    ST  3$ )Nz%fractional_max_pool2d: kernel height r   z' is too large relative to input height r3   )input_heightr  s   r7   rf   r    s    7A7GGno{n|}r9   c                     > STS    ST  3$ )Nz$fractional_max_pool2d: kernel width r2   z& is too large relative to input width r3   )input_widthr  s   r7   rf   r    s    6{1~6FFlmxlyzr9   r  )rW   ri   r   r   r   r   r_   r   r   r   r   )r   r  r  r  r   input_channelsinput_batchr  cr   r   r  r  s   `` `      @@@r7   meta_fractional_max_pool2dr    sf   	LL		VX 99D4!8T"IIaL1^	
 # 
LLKA	2
 
LLKA	2 YYr]N99R=L))B-Kqyiil	LL

n***H 
LLq Y
 	AAAAAA	LL	O 
LL	N 
LLaWX	LLAQ'!+|;} 
LLAQ'!+{:z
 xxzQ[^[^LAA? 	**;;	

 	++;;	
 r9   c                 H   [         R                  " [        U5      S;   S 5        US   n[        U5      S:X  a  UOUS   n[        U5      S:X  a  UOUS   n[         R                  " U(       + =(       d    [        U5      S;   S 5        U(       d  UOUS   n	U(       d  UO[        U5      S:X  a  U	OUS   n
U(       d  UO[        U5      S:X  a  U	OUS   n[         R                  " [        U5      S;   S 5        US   n[        U5      S:X  a  UOUS   n[        U5      S:X  a  UOUS   n[         R                  " [        U5      S;   S 5        US   n[        U5      S:X  a  UOUS   n[        U5      S:X  a  UOUS   n[         R                  " U R                  S	;   S
 5        U R                  S:X  a  U R	                  S5      OSnU R	                  S5      nU R	                  S5      nU R	                  S5      nU R	                  S5      n[        UXlXU5      n[        UX}U
UU5      n[        UXUUU5      n[        U UUUUU	U
UUUUUUUUUUUUUS5        U R                  S:H  =(       a'    [        R                  " U 5      [         R                  :H  nU R                  S:X  a  UUUU4nOUUUUU4nU R                  U5      nU R                  U[         R                  S9nU(       a:  UR                  [         R                  S9nUR                  [         R                  S9nUU4$ )Nr  c                      gNzMmax_pool3d: kernel_size must either be a single int, or a tuple of three intsr3   r3   r9   r7   rf   .meta_max_pool3d_with_indices.<locals>.<lambda>      _r9   r   r2   r   c                      gNzQmax_pool3d: stride must either be omitted, a single int, or a tuple of three intsr3   r3   r9   r7   rf   r  $      cr9   c                      gNzImax_pool3d: padding must either be a single int, or a tuple of three intsr3   r3   r9   r7   rf   r  ,      [r9   c                      gNzJmax_pool3d: dilation must be either a single int, or a tuple of three intsr3   r3   r9   r7   rf   r  4  r  r9   r  c                      gr  r3   r3   r9   r7   rf   r  <  r  r9   rU  r7  ro  r  r   zmax_pool3d_with_indices()r-  r   r   )rW   ri   r   r   r   rs  r  rP   r   r  r   r   r3  )r   r  r   r  r  r:  r  rw  rx  r  ry  rz  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r   r   s                                 r7   meta_max_pool3d_with_indicesr(    s    
LLKF"_ 
QB;1$+a.B;1$+a.B	LL
+c&kV+c vayBc&kQ&6F1IBc&kQ&6F1IB	LLG[ 
B7|q gajB7|q gajB	LLH\ I ]a/	Xa[I ]a/	Xa[I	LL

fK
  %zzQUZZ^AFjjnGJJrNEjjnGZZ^F yIE"7BB	9MG!&""iKF








#+4 	

aXE77>%BXBXX  zzQeWf5	WeWf=	
//)
$Cooiu{{o;Gff5#9#9f:**5+A+A*B<r9   c                 r   [         R                  " [        U5      S;   S 5        US   n[        U5      S:X  a  UOUS   n	[        U5      S:X  a  UOUS   n
[         R                  " U(       + =(       d    [        U5      S;   S 5        U(       d  UOUS   nU(       d  U	O[        U5      S:X  a  UOUS   nU(       d  U
O[        U5      S:X  a  UOUS   n[         R                  " [        U5      S;   S 5        US   n[        U5      S:X  a  UOUS   n[        U5      S:X  a  UOUS   n[         R                  " [        U5      S;   S 5        US   n[        U5      S:X  a  UOUS   n[        U5      S:X  a  UOUS   n[         R                  " UR                  S	;   S
 5        UR	                  S5      nUR	                  S5      nUR	                  S5      nUR	                  S5      nU R	                  S5      nU R	                  S5      nU R	                  S5      n[        UU UUUU	U
UUUUUUUUUUUUUUUS5        UR                  S:H  =(       a'    [        R                  " U5      [         R                  :H  nUR                  UR                  5      nU(       a  UR                  [         R                  S9nU$ )Nr  c                      gr  r3   r3   r9   r7   rf   7meta_max_pool3d_with_indices_backward.<locals>.<lambda>  r  r9   r   r2   r   c                      gr  r3   r3   r9   r7   rf   r+    r   r9   c                      gr"  r3   r3   r9   r7   rf   r+    r#  r9   c                      gr%  r3   r3   r9   r7   rf   r+    r  r9   r  c                      gr  r3   r3   r9   r7   rf   r+    r  r9   r7  ro  r  r   z"max_pool3d_with_indices_backward()rU  r   )rW   ri   r   r   r   r  rP   r   r  r   r   r3  )r"  r   r  r   r  r  r:  r   r  rw  rx  r  ry  rz  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r%  s                                r7   %meta_max_pool3d_with_indices_backwardr0  t  s    
LLKF"_ 
QB;1$+a.B;1$+a.B	LL
+c&kV+c vayBc&kQ&6F1IBc&kQ&6F1IB	LLG[ 
B7|q gajB7|q gajB	LLH\ I ]a/	Xa[I ]a/	Xa[I	LL

fK
 jjnGJJrNEjjnGZZ^FR Er"Gb!F#








,/8 	

aXE77>%BXBXX  -J]]1G1G]H
r9   gridc                   ^ ^^ [         R                  " T R                  TR                  :H  UU 4S j5        [         R                  " T R                  [         R                  :H  =(       a    TR                  [         R                  :H  UU 4S j5        [         R                  " T R
                  S   TR
                  S   :H  UU 4S j5        [         R                  " TR
                  S   T R                  S-
  :H  UU 4S j5        [        ST R                  5       H/  m[         R                  " T R
                  T   S:  UU 4S j5        M1     g )	Nc                  <   > STR                    ST R                    3$ )NzNgrid_sampler(): expected input and grid to be on same device, but input is on z and grid is on r  r1  r   s   r7   rf   +check_grid_sampler_common.<locals>.<lambda>  s"    \\N"24;;-Ar9   c                  <   > STR                    ST R                    3$ )NzTgrid_sampler(): expected input and grid to have torch.strided layout, but input has z and grid has )r   r4  s   r7   rf   r5    s!    nT[[MCr9   r   c                  <   > STR                    ST R                    3$ )NzZgrid_sampler(): expected grid and input to have same batch size, but got input with sizes  and grid with sizes rO  r4  s   r7   rf   r5    s"      %},A$**Or9   r   r   c                  B   > STR                   S-
   ST R                   3$ )Nz+grid_sampler(): expected grid to have size r   z, in last dimension, but got grid with sizes )r   r   r4  s   r7   rf   r5    s'    9%**q.9I J226**?r9   c                  *   > STR                    ST  S3$ )NzYgrid_sampler(): expected input to have non-empty spatial dimensions, but input has sizes r  r  rO  r  s   r7   rf   r5    r  r9   )rW   ri   r   r   r  r   r   r   )r   r1  r   s   ``@r7   check_grid_sampler_commonr;    s    	LL#	
 
LL%F$++*F	
 
LLA$**Q-'	
 
LL

2%**q.(	
 1ejj!KKNQ	
 "r9   c                        \ rS rSrSrSrSrSrg)GridSamplerInterpolationi  r   r2   r   r3   N)r   
__module____qualname____firstlineno__BILINEARNEARESTBICUBIC__static_attributes__r3   r9   r7   r=  r=    s    HGGr9   r=  interpolation_modec                 6  ^ ^ [         R                  " T R                  S:H  =(       a    T R                  TR                  :H  UU 4S j5        [         R                  " T R                  S:H  =(       a    U[        R                  R
                  :H  (       + S 5        g )NrU  c                  <   > STR                    ST R                    3$ )Nzdgrid_sampler(): expected 5D input and grid with same number of dimensions, but got input with sizes r8  rO  r4  s   r7   rf   'check_grid_sampler_3d.<locals>.<lambda>  s!    449KK=#DJJ<1r9   c                      g)Nz<grid_sampler(): bicubic interpolation only supports 4D inputr3   r3   r9   r7   rf   rH    r  r9   )rW   ri   r   r=  rC  r  )r   r1  rE  s   `` r7   check_grid_sampler_3drJ    sp    	LL

a3EJJ$))3	
 
LLJJ!O M"&>&F&F&L&LL	
 	Or9   c                     US   nU(       a$  [         R                  " U[         R                  S9nOS n[         R                  " U[         R                  S9n	X4$ Nr   r   )rW   r  r   r   
r"  r   r1  rE  padding_modealign_cornersr8  input_requires_gradr%  	grad_grids
             r7   grid_sampler_2d_backward_metarR    sO     &a.%%e5;R;RS

  U5L5LMI""r9   c                     [        X5        [        XU5        U R                  S   nU R                  S   nUR                  S   nUR                  S   nUR                  S   n	U R                  XVXxU	45      $ )Nr   r2   r   r/   )r;  rJ  r   r   )
r   r1  rE  rN  rO  r  Cout_Dout_Hout_Ws
             r7   grid_sampler_3drX  (  sn     e*%'9:AAAAJJqMEJJqMEJJqME??A%677r9   rQ  c                     [        X5        [        XU5        US   nU(       a$  [        R                  " U[        R                  S9nOS n[        R
                  " U[        R                  S9n	X4$ rL  )r;  rJ  rW   r  r"  r   rM  s
             r7   grid_sampler_3d_backwardrZ  ;  sg     e*%'9:%a.%%!?!?

 
  U5S5STI  r9   c                     UR                  S5      nU(       d  [        R                  " U5      nXCS'   [        R                  " U /UQ70 UD6$ )Nr_   )r^   rP   	get_dtyperW   r   )r   r  rR   rH  r_   s        r7   fullr]  S  sA    JJwE
+7O;;t-d-f--r9   c           	      V   U[         R                  :X  a  [         R                  " US L S 5        [         R                  " SUc  U R                  OUUUc  U R
                  OUUS9nU R                  (       a>  UR                  U R                  5       U R                  5       U R                  5       5        O/UR                  U R                  5       U R                  5       S5        UR                  S5        U$ [        R                  R                  U UUUUUS9nUR!                  S5        U$ )Nc                      g)Nz9memory format option is only supported by strided tensorsr3   r3   r9   r7   rf   zeros_like.<locals>.<lambda>j  r  r9   r   r  Tr  )rW   
sparse_coori   r   r_   r   	is_sparsesparse_resize_and_clear_r   
sparse_dim	dense_dimr   _coalesced_r,   r   r5  fill_)r   r_   r   r   r   r   r  s          r7   r  r  ^  s     !!!T!O	

 kk %$**5"(.4;;f!
 >>((		T__.0@ ((dhhj!D

//
!
!# " C IIaLJr9   r   c                    Uc  [         R                  " 5       nUc  [         R                  " 5       nUc  [         R                  n[         R                  " XX#US9$ r  rW   r   get_default_devicer  r   r   r_   r   r   r   r   s         r7   	meta_onesrl    P     }'')~))+~;;&J r9   c                    Uc  [         R                  " 5       nUc  [         R                  " 5       nUc  [         R                  n[         R                  " XX#US9$ r  ri  rk  s         r7   
meta_zerosro    rm  r9   c                 .    [         R                  " U 5      $ rC   rP   clone_preserve_strides)r   r6  r   r   s       r7   meta_select_scatterrs        ''--r9   c                 .    [         R                  " U 5      $ rC   rq  )r   r6  r   r   r   steps         r7   meta_slice_scatterrw    rt  r9   dim_post_exprwrap_scalarc           	          US::  a  U(       d  [        SU S35      eSnU* nUS-
  nX:  d  X:  a  [        SU  SU SU S35      eU S:  a  X-  n U $ )	Nr   zdim_post_expr=z <= 0 but wrap_scalar is Falser2   zdim z out of bounds (r|   r}   r  )r   rx  ry  r  r  s        r7   r   r     s}      /MN  .C
!
C
yCItC5(8RuAFGG
QwJr9   c                 L    U R                  5       S:X  a  S$ U R                  U   $ r$  rR  )r  r   s     r7   ensure_nonempty_sizer|    s!    11.!''#,.r9   c                 F  ^ ^^^ [        T R                  5       S5      n[        TR                  5       S5      n[        R                  " X4:H  S 5        [	        U5       H@  mTT:w  d  M  [        R                  " [        TT5      [        T T5      :*  UUUU 4S j5        MB     g )Nr2   c                      g)NzDIndex tensor must have the same number of dimensions as input tensorr3   r3   r9   r7   rf   $gather_shape_check.<locals>.<lambda>  s    Vr9   c                  N   > ST STR                    3STR                    ST  3-   $ )Nz!Size does not match at dimension z expected index  to be no larger than self  apart from dimension rO  )r   r   r   r   s   r7   rf   r    s5    ;A3>Nu{{m\/

|;QRUQVWXr9   )r  r   rW   ri   r   r|  )r   r   r   	self_dims
index_dimsr   s   ```  @r7   gather_shape_checkr    s}    DHHJ"IUYY[!$J	LLV 98LL$UA.2FtQ2OOX r9   c                   ^ SSK Jn  [        XR                  5       5      nU" TR	                  5       S:H  5      nU(       df  [
        R                  " TR                  [
        R                  :H  =(       d    TR                  [
        R                  :H  U4S j5        [        XT5        U R                  TR                  5      $ )Nr   r  c                  "   > ST R                    3$ )Nz8gather(): Expected dtype int32/int64 for index, but got r   r   s   r7   rf   meta_gather.<locals>.<lambda>  s    Nu{{m\r9   )r0  r  r   r   r   rW   ri   r_   r   r   r  r   r   )r   r   r   sparse_gradr  wrapped_dimis_index_emptys     `    r7   meta_gatherr    s~    D hhj1K#EKKMQ$67NKK5::%A		)A\	
 	4e4>>%++&&r9   c                     U(       a<  U S:X  a  gU S:X  a  gU S:X  a  gU S:X  a  gU S	:X  a  g
[         R                  " SS 5        g U S:X  a  gU S:X  a  g[         R                  " SS 5        g )Nr  
REDUCE_ADDr  REDUCE_MULTIPLYmeanREDUCE_MEANamaxREDUCE_MAXIMUMaminREDUCE_MINIMUMFc                      g)Nz=reduce argument must be either sum, prod, mean, amax or amin.r3   r3   r9   r7   rf   #get_operator_enum.<locals>.<lambda>  s    Sr9   addmultiplyc                      g)Nz/reduce argument must be either add or multiply.r3   r3   r9   r7   rf   r    s    $Ur9   r~  )reduce_use_new_optionss     r7   get_operator_enumr    s{    e$ ##S	
 	e
"$UUVr9   c                 n  ^  SSK Jn  U" UR                  5       S:g  5      (       aZ  [        R                  " UR
                  [        R                  :H  =(       d    UR
                  [        R                  :H  U 4S j5        Ub3  [        R                  " UR
                  UR
                  :H  U 4S j5        g g )Nr   )r  c                     > T  S3$ )Nz((): Expected dtype int32/int64 for indexr3   method_names   r7   rf   ,scatter_gather_dtype_check.<locals>.<lambda>  s    {m#KLr9   c                     > T  S3$ )Nz0(): Expected self.dtype to be equal to src.dtyper3   r  s   r7   rf   r    s    {m#STr9   )r0  r  r   rW   ri   r_   r   r   )r  r   r   src_optr  s   `    r7   scatter_gather_dtype_checkr    sy    CU[[]a'((KK5::%A		)AL	

 JJ'--'T	
 r9   c                     [        U S5      $ r1   )r  r   s    r7   ensure_nonempty_dimr  "  s    sA;r9   c                 .  ^ ^^^ SSK Jn  U" TR                  5       S:H  5      (       a  g [        R                  " [        T R                  5       5      [        TR                  5       5      :H  S 5        Sn[        T R                  5       5      n[        U5       H+  n[        TU5      nUT:X  a  M  U[        T U5      :  d  M)  Sn  O   U(       d5  Tb2  [        U5       H#  n[        TU5      nU[        TU5      :  d  M!  Sn  O   Tbm  [        R                  " [        T R                  5       5      [        TR                  5       5      :H  S 5        [        R                  " U(       + UUU U4S j5        g [        R                  " U(       + UUU 4S j5        g )	Nr   r  c                      gNzCIndex tensor must have the same number of dimensions as self tensorr3   r3   r9   r7   rf   %scatter_shape_check.<locals>.<lambda>.  r  r9   FTc                      gr  r3   r3   r9   r7   rf   r  H  s    Yr9   c                  b   > STR                    STR                    3ST  STR                    3-   $ )NExpected index r  r  z and to be no larger than src rO  )r   r   r   r  s   r7   rf   r  L  s6    oekk]2Mdjj\Z&se+I'--YZr9   c                  H   > STR                    STR                    3ST  3-   $ )Nr  r  r  rO  )r   r   r   s   r7   rf   r  R  s*    oekk]2Mdjj\Z&se,-r9   )	r0  r  r   rW   ri   r  r   r   r|  )	r   r   r   r  r  is_wrong_shaper  r   index_d_sizes	   ````     r7   scatter_shape_checkr  '  sI   Dekkmq())	LLDHHJ'+>uyy{+KKU
 N#DHHJ/I 9+E158.tQ77!N  g1y!A/q9L27A>>!%	 " 
+/B599;/OOY	
 	Z	
 	-	
r9   c                     [        XR                  5       5      n[        SXU5        [        XX#5        Ub  [	        XE5        g g )Nscatter)r   r   r  r  r  )r   r   r   r6  r  r  r  s          r7   scatter_meta_implr  X  s;     hhj1Ky$s;56'3 r9   c                 R    [        XX#S5        U R                  U R                  5      $ Nr  r  r   r   r   r   r   r6  s       r7   meta_scatter_addr  a  s!    dU3>>$**%%r9   c                      [        XX#S5        U $ r  r  r  s       r7   meta_scatter_add_r  g  s    dU3Kr9   c                     [        U[        R                  5      (       a  UOS n[        XX%U5        U R	                  U R
                  5      $ rC   )rs   rW   r   r  r   r   r   r   r   src_or_valuerw  r6  s         r7   meta_scatterr  m  s:     %\5<<@@,dCdV4>>$**%%r9   c                 f    [        U[        R                  5      (       a  UOS n[        XX%U5        U $ rC   )rs   rW   r   r  r  s         r7   meta_scatter_r  |  s,     %\5<<@@,dCdV4Kr9   queryr   r  	dropout_p	is_causalreturn_debug_maskr  c           	      4   U R                  S5      nU R                  S5      nU R                  S5      n	U R                  S5      n
UR                  S5      n[        R                  " U 5      n[        R                  " XxU	4[        R                  U R
                  S9nU(       a`  U
S:  a  SOSn[        R                  " X-  5      nUS::  a  SnOUS::  a  Sn[        R                  " XxX4U R                  U R
                  S9nO*[        R                  " SU R                  U R
                  S9n[        R                  R                  (       a#  [        R                  R                  5       (       d  [        U 5      S	:X  aI  [        R                  " S
[        R                  SS9n[        R                  " S
[        R                  SS9nOH[        R                  " S[        R                  SS9n[        R                  " S
[        R                  SS9nUUS S U	UUUU4	$ )Nr   r2   r   r/   r  @         r   r3   r   )r   rW   r   r   r[   r   r  ceilr_   versionhipr   r  r  r   rr  )r  r   r  r  r  r  r  r   	num_headsmax_seqlen_batch_qhead_dimmax_seqlen_batch_k	attention	logsumexpblocksize_cmax_seqlen_k
debug_maskseedoffsets                      r7   (meta__scaled_dot_product_flash_attentionr    s    AJ

1IAzz!}H!  'I	 23kk||I %]cyy!3!AB$L3&L[[$6E++<<

 [[%++ellK
 }}UZZ4466+e:LPU:U{{2UZZ?Ruzz&A{{Aell6BRu||FC 	
 
r9   	res_shape.c                   ^  [        T R                  5      U:X  a  [        R                  " T 5      nU$ [	        / SQU 4S jSS9nU Vs/ s H  oAU   PM	     nn[        [        U5      5       Vs/ s H  ocR                  U5      PM     nn[        R                  " UT R                  T R                  S9R                  U5      nU$ s  snf s  snf )N)r   r2   r   r/   c                 *   > TR                  5       U    $ rC   r%  )idxr  s    r7   rf   ,alloc_with_matching_layout.<locals>.<lambda>  s    %,,.*=r9   Tr   r  )rh   r   rW   r   sortedr   r   r   r   r_   r   r   )r  r  r  	dim_orderr  permuted_shaper   final_permutes   `       r7   alloc_with_matching_layoutr    s     U[[Y&u% J =t
	 5>>ISC.I>5:3y>5JK5J+5JKkk%++ell

'-
  	 J ?Ks   C.C
	attn_biascompute_log_sumexpc	           	         U R                  S5      n	U R                  S5      n
U R                  S5      nUR                  S5      nUR                  S5      nXX4n[        X5      n[        R                  " XUS4[        R                  U R
                  S9n[        R                  " S[        R                  SS9n[        R                  " S[        R                  SS9nUUS S UUUUS 4	$ Nr   r2   r   r   r  r3   r   r   r  rW   r   r[   r   r   )r  r   r  r  r  r  r  r  r  r  r`  S_QS_KVD_Vr  r  
logsum_expr  r  s                      r7   (meta__scaled_dot_product_cudnn_attentionr    s     	

1A

1A
**Q-C88A;D
**R.Cs I
$U
6C	
sAkk||J ;;rF;D[[5::f=F 	
 
r9   c           	         U R                  S5      nU R                  S5      n	U R                  S5      n
UR                  S5      nUR                  S5      nXX4n[        X5      n[        R                  " XU
4[        R                  U R
                  S9n[        R                  " S[        R                  SS9n[        R                  " S[        R                  SS9nUUS S U
UUUS 4	$ r  r  )r  r   r  r  r  r  r  r  r  H_Qr  r  r  r  r  r  r  r  s                     r7   5meta__scaled_dot_product_fused_attention_overrideabler  	  s     	

1A
**Q-C
**Q-C88A;D
**R.C"I
$U
6C	
kk||J ;;rF;D[[5::f=F 	
 
r9   r  r  	cum_seq_q	cum_seq_kmax_qmax_kphilox_seedphilox_offsetc                     [         R                  " U5      n[         R                  " U5      n[         R                  " U5      nUUU4$ rC   rD  )r  r  r   r  r   r  r  r  r  r  r  r  r  r  r  grad_qgrad_krI  s                     r7   'meta__scaled_dot_product_flash_backwardr  4  sA    , e$Fc"Fe$F66!!r9   	attn_maskc                    U R                  S5      nU R                  S5      nU R                  S5      n	[        R                  " U 5      n
[        R                  " UU	U4[        R                  U R
                  S9R                  SS5      nU
U4$ )Nr   r2   r   r  )r   rW   r   r   r[   r   r  )r  r   r  r  r  r  r  r   r  r  r  r  s               r7   0meta__scaled_dot_product_flash_attention_for_cpur  P  s     AJ

1IA  'I	

 kk|| i1o  	 r9   c
                 `   [         R                  " UR                  5       SUR                  UR                  S9n
[         R                  " UR                  5       SUR                  UR                  S9n[         R                  " UR                  5       SUR                  UR                  S9nXU4$ )Nr   r   r2   r/   r  )rW   empty_permutedr   r_   r   )r  r  r   r  r   r  r  r  r  r  r  r  rI  s                r7   9meta__scaled_dot_product_flash_attention_for_cpu_backwardr  r  s    & !!

kk||	F !!
iizz	F !!

kk||	F 6!!r9   dropout_maskc                   ^ ^^^^^^^ S nU" T 5      u  mmU" U5      u  pU" U5      u  pTR                   u  mmmmU	R                   u  pmn
UUUUUU U4S jnUUUUU4S jnTS:  d  UT:  a  TS:  a  U" 5       $ U" 5       $ )Nc                 p   U R                  5       S:X  a  U R                  S5      S4$ U R                  5       S:  ax  Sn[        U R                  5       S-
  5       H  nXR                  U   -  nM     U R	                  XR                  S5      U R                  S5      U R                  S5      5      S4$ U S	4$ )
Nr/   r   Tr-  r2   ro  r  r   F)r   r  r   r   viewr   )r<   r   r   s      r7   	ensure_4dBmeta__scaled_dot_product_attention_math_for_mps.<locals>.ensure_4d  s    557a<;;q>4''UUWq[J1557Q;'ggaj(
 (66*ffRj!&&*affRjI4OOe8Or9   c                  j  > TR                  TR                  5      n T	(       a  U R                  T5      n TR                  TTTT45      nT	(       aa  TR                  5       S:X  a  UR	                  S5      nX4$ [        TR                  S S 5      UR                  SS -   nUR                  U5      nX4$ )Nr/   r   ro  r2   r-  )r   r   view_asr   squeezer   r  )
r   attnr   r   max_seq_lengthnum_headq_q_sizer  
unsqueezeds
      r7   sdpa_vector_fast_mpsMmeta__scaled_dot_product_attention_math_for_mps.<locals>.sdpa_vector_fast_mps  s    ll288$++e$C||Z6>JKyy{a||A y U[["-.Aa@yy'yr9   c                  p   > Sn TR                  TR                  5      nTR                  TTTU T45      nX4$ )Nr|  r  )blocksr   r8  r   	head_sizer  r  r  s      r7   sdpa_vector_2pass_mpsNmeta__scaled_dot_product_attention_math_for_mps.<locals>.sdpa_vector_2pass_mps  s<    ll288$||Z669$UV  r9   i   i   rO  )r  r   r  r  r  r  r  r  r  k_rS   v_k_sizer  r  r   r  r  r  r  r  r  s   `              @@@@@@@r7   /meta__scaled_dot_product_attention_math_for_mpsr    s    	 u%NB
cNEBeEB.0hh+J&)#%88 A~q ! ! 	$FVO$8N$&&#%%r9   c           	      R   U R                  SS5      n UR                  SS5      nUR                  SS5      nU R                  S5      nU R                  S5      n	U R                  S5      n
UR                  S5      n[        R                  " XXU R                  U R
                  S9n[        R                  R                  (       a0  [        R                  R                  5       (       a   U(       a  U	OSnO%U(       a  [        R                  " U	S-  5      S-  OSn[        R                  " XU4[        R                  U R
                  S9nUR                  SS5      n[        R                  " S[        R                  S	S9n[        R                  " S[        R                  S	S9nXUU4$ )
Nr2   r   r   r  r   r  r|  r3   r   )r  r   rW   r   r_   r   r  r  r   r  r  r  r[   r   )r  r   r  r  r  r  r  r  r  r  r  Kvr  logsumexp_dimr  r  r  s                    r7   ,meta__scaled_dot_product_efficient_attentionr     s?    OOAq!E
--1
COOAq!E

1A

1A

2I	BB
++aIU\\
RC}}UZZ4466	 0Q2D		!b&)B.!	
}%kk||J --1
C ;;rF;D[[5::f=FD&((r9   grad_input_maskc                    UR                  S5      nUR                  S5      nUR                  S5      nUR                  S5      nUR                  S5      nUR                  S5      n[        R                  " XUU4SUR                  UR                  S9n[        R                  " XUU4SUR                  UR                  S9n[        R                  " XUU4SUR                  UR                  S9nS nUb  U
S   (       ax  UR                  S5      nUS-  S:X  a  UO
US-   US-  -
  n[        UR                  5       5      nUUS'   [        R                  " UUR                  UR                  S9nUS	S U24   nUUUU4$ )
Nr   r2   r   r/   r   r  r   r{  .)r   rW   r  r_   r   r   r   )r  r  r   r  r  r   r  r  r  r  r!  r  r  r   r  r  r  
head_dim_vr  r  r  rI  	grad_biaslastDimlastDimAligned	new_sizess                             r7   +meta__scaled_dot_product_efficient_backwardr(    su   ( AJ

1IJJqMEzz!}HAJHHQKE!!	x0kk||	F !!	x0iizz	F !!	z2kk||	F I!3..$$+bLA$57R<'TV,;V)*	&	"KKY__Y5E5E
	 c8G8m,	669,,r9   c                     [         R                  " U5      n[         R                  " U5      n[         R                  " U5      nUUU4$ rC   rD  )r  r  r   r  r   r  r  r  r  r  r  r  r  r  r  r  r  r  rI  s                      r7   'meta__scaled_dot_product_cudnn_backwardr*  ;  sA    . e$Fc"Fe$F66!!r9   window_size_leftwindow_size_right	seqused_kalibi_slopesc                    Uc  U R                  S5      OUR                  5       S-
  nUc  U R                  S5      OUnUc  UR                  S5      OUnU R                  S5      nU R                  S5      n[        R                  " U 5      nUc2  [        R                  " UUU4[        R
                  U R                  S9nOAU R                  S5      n[        R                  " UU4[        R
                  U R                  S9nU	(       ac  US:  a  SOSn[        R                  " UU-  5      nUS::  a  SnOUS::  a  Sn[        R                  " UUUU4U R                  U R                  S9nO*[        R                  " SU R                  U R                  S9nS	u  nn[        R                  R                  (       al  [        R                  R                  5       (       aI  [        R                  " S
[        R                  SS9n[        R                  " S
[        R                  SS9nOH[        R                  " S[        R                  SS9n[        R                  " S
[        R                  SS9nUUUUU4$ )Nr   r2   r  r   r  r  r  r  NNr3   r   r   )r   r   rW   r   r   r[   r   r  r  r_   r  r  r   r  r   rr  )r  r   r  r  r  r  r  r  r  r  r  r+  r,  r-  r.  r   r  r  r  r  r  r  total_qr  r  r  r  r  s                               r7   meta__flash_attention_forwardr2  X  s   4 #,"3A9JQ9NJ*3*;A(1(9!u

2Izz"~H   'IKK$67++<<
	 **Q-KK ELL
	 %]cyy!3k!AB$L3&L[[$6E++<<

 [[%++ellK
 LD&}}UZZ4466{{2UZZ?Ruzz&A{{Aell6BRu||FC r9   c                     [         R                  " U5      n[         R                  " U5      n[         R                  " U5      nUUU4$ rC   rD  )r  r  r   r  r   r  r  r  r  r  r  r  r  r  r  r+  r,  
grad_querygrad_key
grad_values                       r7   meta__flash_attention_backwardr7    sA    0 !!%(J$H!!%(Jx++r9   cu_seqlens_qcu_seqlens_kmax_seqlen_qr  custom_mask_typecausal_diagonalseqlen_kwindow_sizec           	         U R                  S5      nU R                  S5      nUR                  S5      nU R                  S5      nUR                  S5      n[        R                  " UUUUU R                  U R                  S9nUb  UR                  S5      S-
  OUnUnUb  Uc  [        S5      eUnUb  UOUnU
(       a  [        R                  " US-  5      S-  OSn[        R                  " UUU4[        R                  U R                  S9n[        R                  " S[        R                  S	S9n[        R                  " S[        R                  S	S9nUUUUUU4$ )
Nr   r2   r  r   r  z;max_seqlen_q must not be None when cu_seqlens_q is providedr|  r3   r   )
r   rW   r   r_   r   r   r  r  r[   r   )r  r   r  rG  r8  r9  r:  r  r  r;  r  r  r<  r=  r>  r  r  r  r  r  r  logsumexp_batch_dimactual_max_seqlen_qactual_max_seqlen_kr  r  r  r  s                               r7   !meta__efficient_attention_forwardrC    sE   , 	

1A

1AA

2I	BB
++aIrU\\
RC7C7O,++A.2VW M  +*6*B,4F		%*+b0A  	i7kk||J ;;rF;D[[5::f=F
D&*=?RRRr9   bias_requires_gradnum_splits_keyshared_storage_dqdkdvc                    U(       a  [         R                  " UR                  S   UR                  S   :H  S 5        [         R                  " UR                  S   UR                  S   :H  S 5        [         R                  " / UR                  SS QSPUR                  S   PUR                  S   P7UR                  UR
                  S9nUR                  S	S5      nUR                  S	S5      nUR                  S	S
5      nOB[         R                  " U5      n[         R                  " U5      n[         R                  " U5      nUby  UR                  S5      nUS-  S:X  a  UO
US-   US-  -
  n[        UR                  5       5      nUUS'   [         R                  " UUR                  UR
                  S9nUSS U24   nO[         R                  " SUR
                  S9nUUUU4$ )Nr2   c                      g)Nz,seqlen must match for `shared_storage_dqdkdvr3   r3   r9   r7   rf   4meta__efficient_attention_backward.<locals>.<lambda>  s    Br9   r/   c                      g)Nz3embedding dim must match for `shared_storage_dqdkdvr3   r3   r9   r7   rf   rI        Ir9   r   r  r   r  ro  r   r{  .r3   r  )
rW   ri   r   r   r_   r   r  r   r   r   )r  r  r   r  rG  r8  r9  r:  r  r  r  r  r  r;  rD  r  rE  rF  chunkr4  r5  r6  r%  r&  r'  r$  s                             r7   "meta__efficient_attention_backwardrM    s   2 KKNciil*B	
 	KKNciil*I	
 Eekk!BEEEKKOEU[[_E++<<

 \\"a(
<<A&\\"a(
%%e,
##C(%%e,
))B-$+bLA$57R<'TV,;V%	&	"KK	DKKP	c8G8m,	KK5<<8	xY66r9   scale_ascale_bscale_resultuse_fast_accumc                   ^ ^^^^^^^^ S n[         R                  " T R                  5       S:H  =(       a    TR                  5       S:H  UU 4S j5        [         R                  " U" T R                  5      =(       a    U" TR                  5      UU 4S j5        [	        T 5      S:X  d  [	        T 5      S:X  Ga  S n	S n
S	 n[         R                  " U	" T R                  5       5      =(       d    U" T 5      U 4S
 j5        [         R                  " U
" TR                  5       5      =(       d    U" T5      U4S j5        [         R                  " T R                  S5      S-  S:H  U 4S j5        [         R                  " TR                  S5      S-  S:H  =(       a    TR                  S5      S-  S:H  U4S j5        T R                  u  mmTR                  S5      mTR                  [         R                  :H  =(       a    TR                  [         R                  :H  =(       dA    TR                  [         R                  :H  =(       a    TR                  [         R                  :H  nTR                  5       S:X  am  TR                  5       S:X  aY  [         R                  " TR                  [         R                  :H  =(       a    TR                  [         R                  :H  S 5        GOU(       a  TR                  [         R                  :X  a  SnTS-  mOSnSn[        TU5      n[        US5      S-  nU[        TU5      -  U-  mU[        TU5      -  U-  mTR                  5       T:X  ab  TR                  5       T:X  aN  [         R                  " TR                  5       S 5        [         R                  " TR                  5       S 5        GO[         R                  " SUUUU4S j5        GO[         R                  " TR                  [         R                  :H  =(       a    TR                  [         R                  :H  S 5        [         R                  " TR                  5       S:H  =(       a    TR                  5       S:H  UU4S j5        TR                  S5      T:X  a~  TR                  S5      S:X  ai  TR                  S5      S:X  aT  TR                  S5      T:X  a?  [         R                  " TR                  5       =(       a    TR                  5       S 5        GO\TR                  S5      T:X  aX  TR                  S5      TR                  S5      s=:X  a  [        TS5      :X  a#  O  O TR                  S5      [        TS5      :X  a  OTR                  S5      T:X  aN  TR                  S5      TR                  S5      s=:X  a  [        TS5      :X  a  O  OTR                  S5      T:X  a  OTR                  S5      [        TS5      :X  aN  TR                  S5      TR                  S5      s=:X  a  [        TS5      :X  a  O  OTR                  S5      T:X  a  O[         R                  " SUUUUU4S j5        Ub  UOT R                  n[         R                  " T R                  S5      TR                  S5      UT R                  S9$ )Nc                     U [         R                  [         R                  [         R                  [         R                  [         R
                  4;   $ rC   rW   ro  float8_e5m2float8_e4m3fnuzfloat8_e5m2fnuzfloat4_e2m1fn_x2r   s    r7   is_fp8_or_fp4_type2_check_scaled_mm_sizes.<locals>.is_fp8_or_fp4_typeD  A    !!!!""
 
 	
r9   r   c                  L   > STR                  5        ST R                  5        3$ Nz%Inputs must be 2D but got self.dim()=z and mat2.dim()=r   rV  r   s   r7   rf   (_check_scaled_mm_sizes.<locals>.<lambda>O  %    7
|CSTXT\T\T^S_`r9   c                  <   > STR                    ST R                    3$ Nz?Expected both inputs to be fp8 or fp4 types but got self.dtype=z and mat2.dtype=r   r^  s   r7   rf   r_  S  $    QRVR\R\Q]]mnrnxnxmyzr9   r   r   c                 6    U S   U S   :  =(       a    U S   S:H  $ r$  r3   r%  s    r7   is_row_major,_check_scaled_mm_sizes.<locals>.is_row_majorX  "    !9vay(;VAY!^;r9   c                 0    U S   S:H  =(       a    U S   S:  $ r$  r3   r%  s    r7   is_col_major,_check_scaled_mm_sizes.<locals>.is_col_major[      !9>3fQi!m3r9   c                 `    U R                  S5      S:H  =(       d    U R                  S5      S:H  $ r$  r   	tensor_2ds    r7   has_zero_dim,_check_scaled_mm_sizes.<locals>.has_zero_dim^  )    >>!$)CY^^A->!-CCr9   c                  *   > ST R                  5        3$ Nz#self must be row_major, got stride r%  r   s   r7   rf   r_  c      9$++-Ir9   c                  *   > ST R                  5        3$ Nz#mat2 must be col_major, got stride r%  rV  s   r7   rf   r_  g  rt  r9   r2   r{  r   c                  ,   > ST R                  S5       3$ NzBExpected self.size(1) to be divisible by 16, but got self.size(1)=r2   r   r   s   r7   rf   r_  k      XY]YbYbcdYeXfgr9   c                  "   > ST R                    3$ Nz?Expected both dimensions of mat2 to be divisible by 16 but got rO  rw  s   r7   rf   r_  o      UVZV`V`Uabr9   c                      g)NzNFor tensorwise scaling, both scale_a and scale_b must be float (fp32) tensors.r3   r3   r9   r7   rf   r_    s    hr9   r|  r  r-  c                      g)Nzscale_a must be contiguousr3   r3   r9   r7   rf   r_        8r9   c                      g)Nzscale_b must be contiguousr3   r3   r9   r7   rf   r_    r  r9   Fc            	      Z   > ST  STR                  5        ST STR                  5        S3	$ )NzTInvalid blockwise scaling configuration. For blockwise scaling, scale_a should have  elements, got z, scale_b should have r  r"  )expected_a_sizeexpected_b_sizerN  rO  s   r7   rf   r_    sC    FFUEVVefmfsfsfuev w//>.?w}}N__`br9   c                      g)NzKFor rowwise scaling, both scale_a and scale_b must be float (fp32) tensors.r3   r3   r9   r7   rf   r_    s    er9   c                  P   > ST R                  5       < STR                  5       < 3$ )NzLFor non-tensorwise scaling, scale tensors must be 2D, but got scale_a.dim()=z and scale_b.dim()=r   rN  rO  s   r7   rf   r_    s*    gY`YdYdYfXhh|nunynyn{m}~r9   c                      g)Nz@Both scale_a and scale_b must be contiguous for rowwise scaling.r3   r3   r9   r7   rf   r_    s    ^r9   c                    > ST ST ST S[        T S5       S3	S[        T S5       S[        TS5       ST S[        T S5       S3	-   S[        T S5       ST S	[        TS5       S[        T S5       S3	-   S[        T S5       ST S
TR                  S5       STR                  S5       STR                  S5       STR                  S5       S3-   $ )N}Invalid scaling configuration. For tensorwise scaling, both scales should be scalar. For rowwise scaling, scale_a should be (, 1), scale_b should be (1, >). For (BlockWise1x128, BlockWise128x128), scale_a should be (r|   r  ), scale_b should be (<). For (BlockWise1x128, BlockWise1x128), scale_a should be (z>). For (BlockWise128x128, BlockWise1x128), scale_a should be (). Got scale_a.size()=(r   r2   ) and scale_b.size()=(r}   r8   r   )_krr  r  rN  rO  s   r7   rf   r_    sG   CCD#Eabcad eVVWUXXZ[cdfhk[lZmmpr 0S0A/B"XaQTEUDV WTTUSVVXYabdfiYjXkknp	p 0S0A/B"QC HVV^_`beVfUggijrsuwzj{i||AA 0S0A/B"QC H//6||A.?r',,q/AR S//6||A.?r',,q/ARRSU
Ur9   r  )rW   ri   r   r_   r  r   r   r   float8_e8m0fnuro  r   rl  r8   rp  r   r   )r   rV  rN  rO  rG  rP  rI  rQ  rY  re  ri  ro  is_blockwise_scalingblock_size_kblock_size_mnnum_k_blockspadded_num_k_blocks
_out_dtyper  r  r  rr  r  s   ````              @@@@@r7   _check_scaled_mm_sizesr  :  s   
 
LL
a+DHHJ!O` 
LL4::&I+=djj+Iz
 4F"k$&75&@	<	4	D 	'=<+=I	
 	'=<+=I	
 	IIaL2"g	
 	IIaL2"=tyy|b'8A'=b	
 

2IIaL !5!55 :MMU%9%99
 !4!44 9MMU%8%88 	 ==?aGMMOq$8LL.Q7==EMM3Qh " }} 3 33  "!V!M#B5L"*<";a"? M ::=PP  M ::=PP 
 ?2MMO6))+8 ))+8
  LL.Q7==EMM3Qe
 LL"9w{{}'9~ Q1$LLOq(LLOq(LLOq( ))+G0E0E0G^
 Q1$LLOw||AK(2s:KKLLOx3'77 Q1$LLOw||AK(2s:KKLLOq( Q8As#33LLOw||AK(2s:KKLLOq(   " (3J;;tyy|TYYq\DKKXXr9   c           
          [        XX#XEXg5      $ rC   )r  )r   rV  rN  rO  rG  rP  rI  rQ  s           r7   meta_scaled_mmr    s     "Gd) r9   scale_recipe_ascale_recipe_b	swizzle_a	swizzle_bc           
        ^ ^^^^^	^^^^ ^!^"^#^$^% S nS n[         R                  " T R                  5       S:H  =(       a    TR                  5       S:H  UU 4S j5        [         R                  " U" T R                  5      =(       a    U" TR                  5      UU 4S j5        T R                  S   mT R                  S   mTR                  S   m U" T R                  5      (       a  U" TR                  5      (       a  SnTU-  mU Vs/ s H  n[        U5      PM     nnU Vs/ s H  n[        U5      PM     nnT(       a  T Vs/ s H  n[        U5      PM     snmO[        R                  /mT	(       a  T	 Vs/ s H  n[        U5      PM     snm	O[        R                  /m	[        T 5      S:X  d  [        T 5      S	:X  GaU  S
 nS nS n[         R                  " U" T R                  5       5      =(       d    U" T 5      U 4S j5        [         R                  " U" TR                  5       5      =(       d    U" T5      U4S j5        [         R                  " T R                  S5      S-  S:H  U 4S j5        [         R                  " TR                  S5      S-  S:H  =(       a    TR                  S5      S-  S:H  U4S j5        S[        [
           S[        [
           4S jnS[        [
           S[        [
           4S jnS[        [
           S[        [
           4S jnS[        [
           S[        [
           4S jnS[        [
           S[        [
           4S jnS[        [
           S[        [
           4S jnS[        [
           S[        [
           4S jnU" X55      (       a  [         R                  " TS   R                  5       S:H  =(       ad    TS   R                  5       S:H  =(       aG    TS   R                  [         R                  :H  =(       a     TS   R                  [         R                  :H  S 5        G	OU" X55      (       a  [         R                  " TS   R                  S   T:H  =(       a    TS   R                  5       T:H  =(       ad    TS   R                  [         R                  :H  =(       a=    TS   R                  5       T :H  =(       a     TS   R                  [         R                  :H  UUUU 4S j5        G	OU" X55      (       Ga  TS   R                  [         R                  :H  =(       a     TS   R                  [         R                  :H  nTS   m$T$R                  S   T:H  =(       a    T$R                  S   TS-  :H  =(       ac    T$R                  S5      S:H  =(       aH    T$R                  S5      T:H  =(       d-    T$R                  S   S:H  =(       a    T$R                  S5      S:H  nTS   m%T%R                  S   T :H  =(       a    T%R                  S   TS-  :H  =(       ac    T%R                  S5      S:H  =(       aH    T%R                  S5      T :H  =(       d-    T%R                  S   S:H  =(       a    T%R                  S5      S:H  n[         R                  " U=(       a    U=(       a    UUUU U$U%4S j5        GOIU" X55      (       Ga  TS   R                  [         R                  :H  =(       a     TS   R                  [         R                  :H  n[        TS-  S5      mTS   m$T$R                  S   T:H  =(       a    T$R                  S   TS-  :H  =(       ac    T$R                  S5      S:H  =(       aH    T$R                  S5      T:H  =(       d-    T$R                  S   S:H  =(       a    T$R                  S5      S:H  nTS   m%T%R                  S   T :H  =(       a    T%R                  S   TS-  :H  =(       ac    T%R                  S5      S:H  =(       aH    T%R                  S5      T :H  =(       d-    T%R                  S   S:H  =(       a    T%R                  S5      S:H  n[         R                  " U=(       a    U=(       a    UUUUU U$U%4S  j5        GOwU" X55      (       Ga  TS   R                  [         R                  :H  =(       a     TS   R                  [         R                  :H  n[        TS-  S5      mTS   m$T$R                  S   T:H  =(       a    T$R                  S   TS-  :H  =(       ac    T$R                  S5      S:H  =(       aH    T$R                  S5      T:H  =(       d-    T$R                  S   S:H  =(       a    T$R                  S5      S:H  nTS   m%T%R                  S   T:H  =(       a    T%R                  S   T S-  :H  =(       ac    T%R                  S5      S:H  =(       aH    T%R                  S5      T:H  =(       d-    T%R                  S   S:H  =(       a    T%R                  S5      S:H  n[         R                  " U=(       a    U=(       a    UUUUU U$U%4S! j5        GOU" X55      (       Ga  [         R                  R                   (       ac  [#        T R                  S   S"5      T R                  S   -  m![#        T R                  S   S"5      T R                  S   -  m"[        R                  m#O[        T R                  S   S5      [        [#        T R                  S   S"5      S5      -  m![        TR                  S   S5      [        [#        T R                  S   S"5      S5      -  m"[        R$                  m#[         R                  " TS   R                  5       T!:H  =(       a    TS   R                  [         R&                  :H  =(       a[    TS   R                  5       T":H  =(       a>    TS   R                  [         R&                  :H  =(       a    TS   T#:H  =(       a    T	S   T#:H  U!U"U#UUUU	4S# j5        GOU" X55      (       Ga  [        TS5      [        [#        TS5      S5      -  m![        T S5      [        [#        TS5      S5      -  m"[        R$                  m#[         R                  " TS   R                  5       T!:H  =(       Ga
    TS   R                  [         R(                  :H  =(       a    TS   R                  5       S:H  =(       a    TS   R                  [         R                  :H  =(       a    TS   R                  5       T":H  =(       a    TS   R                  [         R(                  :H  =(       a[    TS   R                  5       S:H  =(       a>    TS   R                  [         R                  :H  =(       a    TS   T#:H  =(       a    T	S   T#:H  U!U"U#UUUU	4S$ j5        O[         R                  " S%UUU UU4S& j5        Ub  UOT R                  n[         R*                  " TT UT R,                  S'9$ s  snf s  snf s  snf s  snf )(Nc                     U [         R                  [         R                  [         R                  [         R                  [         R
                  4;   $ rC   rT  r   s    r7   rY  5_check_scaled_mm_sizes_v2.<locals>.is_fp8_or_fp4_type  r[  r9   c                 (    U [         R                  :H  $ rC   )rW   rX  r   s    r7   is_fp4_type._check_scaled_mm_sizes_v2.<locals>.is_fp4_type  s    ....r9   r   c                  L   > STR                  5        ST R                  5        3$ r]  r   r^  s   r7   rf   +_check_scaled_mm_sizes_v2.<locals>.<lambda>"  r`  r9   c                  <   > STR                    ST R                    3$ rb  r   r^  s   r7   rf   r  &  rc  r9   r   r2   r   r   c                 6    U S   U S   :  =(       a    U S   S:H  $ r$  r3   r%  s    r7   re  /_check_scaled_mm_sizes_v2.<locals>.is_row_majorG  rg  r9   c                 0    U S   S:H  =(       a    U S   S:  $ r$  r3   r%  s    r7   ri  /_check_scaled_mm_sizes_v2.<locals>.is_col_majorJ  rk  r9   c                 `    U R                  S5      S:H  =(       d    U R                  S5      S:H  $ r$  r   rm  s    r7   ro  /_check_scaled_mm_sizes_v2.<locals>.has_zero_dimM  rq  r9   c                  *   > ST R                  5        3$ rs  r%  r   s   r7   rf   r  R  rt  r9   c                  *   > ST R                  5        3$ rv  r%  rw  s   r7   rf   r  V  rt  r9   r{  c                  ,   > ST R                  S5       3$ ry  r   r   s   r7   rf   r  Z  rz  r9   c                  "   > ST R                    3$ r|  rO  rw  s   r7   rf   r  ^  r}  r9   recipe_arecipe_bc                     [        U 5      S:H  =(       aH    [        U5      S:H  =(       a3    U S   [        R                  :H  =(       a    US   [        R                  :H  $ r  )r   r'   
TensorWiser  r  s     r7   is_tensorwise0_check_scaled_mm_sizes_v2.<locals>.is_tensorwisea  sT    H" :MQ&:QK;#9#99: QK;#9#99	r9   c                     [        U 5      S:H  =(       aH    [        U5      S:H  =(       a3    U S   [        R                  :H  =(       a    US   [        R                  :H  $ r  )r   r'   RowWiser  s     r7   
is_rowwise-_check_scaled_mm_sizes_v2.<locals>.is_rowwisei  sT    H" 7MQ&7QK;#6#667 QK;#6#66	r9   c                     [        U 5      S:H  =(       aH    [        U5      S:H  =(       a3    U S   [        R                  :H  =(       a    US   [        R                  :H  $ r  )r   r'   BlockWise1x32r  s     r7   is_mx(_check_scaled_mm_sizes_v2.<locals>.is_mxq  sT    H" =MQ&=QK;#<#<<= QK;#<#<<	r9   c                 0   [        U 5      S:H  =(       a    [        U5      S:H  =(       am    U S   [        R                  :H  =(       aP    U S   [        R                  :H  =(       a3    US   [        R                  :H  =(       a    US   [        R                  :H  $ )Nr   r   r2   )r   r'   BlockWise1x16r  r  s     r7   is_nv(_check_scaled_mm_sizes_v2.<locals>.is_nvy  s    H" :MQ&:QK;#<#<<: QK;#9#99: QK;#<#<<	:
 QK;#9#99r9   c                     [        U 5      S:H  =(       aH    [        U5      S:H  =(       a3    U S   [        R                  :H  =(       a    US   [        R                  :H  $ r  )r   r'   BlockWise1x128r  s     r7   is_1x128_1x1281_check_scaled_mm_sizes_v2.<locals>.is_1x128_1x128  sT    H" >MQ&>QK;#=#==> QK;#=#==	r9   c                     [        U 5      S:H  =(       aH    [        U5      S:H  =(       a3    U S   [        R                  :H  =(       a    US   [        R                  :H  $ r  )r   r'   r  BlockWise128x128r  s     r7   is_1x128_128x1283_check_scaled_mm_sizes_v2.<locals>.is_1x128_128x128  sW    H" @MQ&@QK;#=#==@ QK;#?#??	r9   c                     [        U 5      S:H  =(       aH    [        U5      S:H  =(       a3    U S   [        R                  :H  =(       a    US   [        R                  :H  $ r  )r   r'   r  r  r  s     r7   is_128x128_1x1283_check_scaled_mm_sizes_v2.<locals>.is_128x128_1x128  sT    H" >MQ&>QK;#?#??> QK;#=#==	r9   c                      g)Nz\For Tensorwise scaling, both scale_a and scale_b must be single element float (fp32) tensorsr3   r3   r9   r7   rf   r    s    vr9   c            	         > STR                   S    STS   R                  5        ST R                   S    STS   R                  5        S3	$ )Nz'For Rowwise scaling, scale_a must have r   z elements (got: z), and scale_b must have r2   r}   )r   r   )rV  rN  rO  r   s   r7   rf   r    s\    =djjm_L\]def]g]m]m]o\p q//3zz!}o=MgVWjN^N^N`Maabdr9   r  c                     > ST ST S-   STR                    ST STR                   ST ST S-   STR                    ST STR                   S3$ )Nz>For 1x128 x 1x128 blockwise scaling, scale a must have shape [r|   r  ] (got: ) and stride [1, )scale b must have shape [r}   r   r   )r  r  r  sasbs   r7   rf   r    sy    001s"Q#XJhrxxjPabcaddlmomvmvlw x001s"Q#XJhrxxjPabcaddlmomvmvlwwxzr9   r-  c                     > ST STS-   STR                    ST STR                   ST ST S-   STR                    ST STR                   S3$ )Nz]For 128x128 x 1x128 blockwise scaling, L4 = {round_up(K / 128, 4)}, scale a must have shape [r|   r  r  r  r  r}   r  r  L4r  r  r  r  s   r7   rf   r    sy    002t2a3hZxzQbcebffnoqoxoxny z001s"Q#XJhrxxjPabcaddlmomvmvlwwxzr9   c                     > ST ST S-   STR                    ST STR                   ST STS-   STR                    ST STR                   S3$ )Nz]For 1x128 x 128x128 blockwise scaling, L4 = {round_up(K / 128, 4)}, scale a must have shape [r|   r  r  r  r  r}   r  r  s   r7   rf   r    sy    001s"Q#XJhrxxjPabcaddlmomvmvlw x002t2a3hZxzQbcebffnoqoxoxnyyz|r9   r|  c                     > ST  STS   R                  5        ST STS   R                  5        S[        R                   STS   R                   STS   R                   ST S	TS    STS    S
3$ )Nz!for MX scaling scale_a must have  (got: r   ) and scale_b must have z). Scales must have types z (for self: 	, mat_b: z) Must have swizzle type  (got self: r}   )r   rW   r  r_   expected_scale_a_elemsexpected_scale_b_elemsexpected_swizzlerN  rO  r  r  s   r7   rf   r  #  s    78N7OwW^_`WaWgWgWiVj k--C,DGGTUJL\L\L^K_ `""'"6"6!7|GAJDTDTCUU^_fgh_i_o_o^p q..>-?|IVWL>Ybclmncobppqsr9   c                     > ST  STS   R                  5        ST STS   R                  5        ST STS    STS    S3$ )	Nz!for NV scaling scale_a must have r  r   r  z). Must have swizzle type r  r  r}   r"  r  s   r7   rf   r  9  sq    78N7OwW^_`WaWgWgWiVj k--C,DGGTUJL\L\L^K_ `$$4#5\)A,yYbcdYeXffgir9   Fc                  b  > ST ST ST S[        T S5       S3	S[        T S5       S[        TS5       ST S[        T S5       S3	-   S[        T S5       ST S	TS
   R                  S
5       STS
   R                  S5       STS
   R                  S
5       STS
   R                  S5       S3-   $ )Nr  r  r  r|   r  r  r  r  r  r   r2   r  r}   r  )r  r  r  rN  rO  s   r7   rf   r  B  s   ??@cA]^_]` aRRSQTTVW_`acfWgVhhkm ,HQ,<+=RC@P?Q RPPQsRTU]^_adUeTffik	k ,HQ,<+=Rs C++21:??1+=*>bQRAS@T U++21:??1+=*>bQRAS@TTUWWr9   r  )rW   ri   r   r_   r   r'   r(   
NO_SWIZZLEr  r   r   r   r   rl  r>   r  r  r8   SWIZZLE_32_4_4r  ro  r   r   )&r   rV  rN  r  rO  r  rG  rI  r  r  rQ  rY  r  K_packed_multipliersire  ri  ro  r  r  r  r  r  r  r  types_ok
scale_a_ok
scale_b_okr  r  r  r  r  r  r  r  r  r  s&   ``` `   ``                   @@@@@@@@@r7   _check_scaled_mm_sizes_v2r    s(   
/ 
LL
a+DHHJ!O` 
LL4::&I+=djj+Iz 	

1A

1A

1A 4::;tzz#:#:	  0>?"k"oN?0>?"k"oN?/89y[_y9	 ""
	 /89y[_y9	 ""
	 4F"k$&75&@	<	4	D 	'=<+=I	
 	'=<+=I	
 	IIaL2"g	
 	IIaL2"=tyy|b'8A'=b	

	D$5 	kAR 		k!2 	d;>O 		D- 	k9J 		D- 	k9J 		T+%6 	${BS 		tK'8 	DDU 		tK'8 	DDU 	 88LL
  "a' 6AJ$$&!+6AJ$$56 AJ$$5v 77LL
  #q( 6AJ$$&!+6AJ$$56 AJ$$&!+6 AJ$$5
 N;;
 
  EMM1Wgaj6F6F%--6W  Bq  THHQK18+TIIaLA%T YYq\Q&R288A;!+;+Q		!PQ@Q	  Bq  THHQK18+TIIaLA%T YYq\Q&R288A;!+;+Q		!PQ@Q	  LL6Z6J  n== 
  EMM1Wgaj6F6F%--6W  !c'1%BBr! UHHQK18+UIIaLA%U YYq\R'SBHHQK1,<,R1QRAR	  Bq  THHQK18+TIIaLA%T YYq\Q&R288A;!+;+Q		!PQ@Q	  LL6Z6J  n== 
  EMM1Wgaj6F6F%--6W  !c'1%BBq  THHQK18+TIIaLA%T YYq\Q&R288A;!+;+Q		!PQ@Q	  Br! UHHQK18+UIIaLA%U YYq\R'SBHHQK1,<,R1QRAR	  LL6Z6J  >22}}  )1$**Q-)DtzzRS})T&)1$**Q-)DtzzRS})T&#.#9#9 )1$**Q-)ETZZ]B/I *& *2$**Q-)ETZZ]B/I *& $/#=#= LL
  "&<< 5AJ$$(<(<<5AJ$$&*@@5 AJ$$(<(<<5 aL$44	5
 aL$44  >22%-a%5!RRS8T%T"%-a%5!RRS8T%T"*99LL
  "&<< 	5 	5AJ$$(;(;;	5AJ$$&!+	5 AJ$$5	5 AJ$$&*@@		5
 AJ$$(;(;;	5 AJ$$&!+	5 AJ$$5	5 aL$44	5 aL$44 $ LL
 
 (3J;;q!:dkkBBw @? : :s   y
#yy:yr  contraction_dimsc                 (    [        U UUUUUUU	UUUS9$ )N)rG  rI  r  r  rQ  )r  )r   rV  rN  r  r  rO  r  r  rG  r  r  rQ  s               r7   meta_scaled_mm_v2r  S  s2     %% r9   c           	      P    [        XX#USS9  U R                  U R                  5      $ NT)r  r  r   r   r   r6  rw  ru  s         r7   meta_scatter_reduce_twor  q  s%     dVTJ>>$**%%r9   c           	          [        XX#USS9  U $ r  r  r  s         r7   meta_scatter_reduce__twor  x  s    dVTJKr9   c                |  ^  [         R                  " ST R                  5       s=:  =(       a    S:*  Os  U 4S j5        T R                  5       S:X  a.  [         R                  " U[         R                  T R
                  S9$ [         R                  " T R                  S5      U[         R                  T R
                  S9$ )Nr   r   c                  *   > ST R                  5        3$ )NzAThe probability distributions dimensions must be 1 or 2, but got r   r  s   r7   rf   "meta_multinomial.<locals>.<lambda>  s    STYT]T]T_S`ar9   r2   r  )rW   ri   r   r   r   r   r   )r   num_samplesreplacementr  s   `   r7   meta_multinomialr	  ~  s     
LL	EIIK1a yy{a{{;ejjNN;;

1{%**U\\ r9   c                 $    SnU  H  nX-  nM	     U$ r1   r3   )vsr{  vs      r7   multiply_integersr	    s    	A	 Hr9   c                 ^  ^ ^^^ [         R                  " [        T5      T:H  UU4S j5        TS-   m[         R                  " [        T 5      T:H  UU 4S j5        [         R                  " [        S T SS   5       5      =(       a    [        S T 5       5      U U4S j5        T S S u  p4X4/TQ7$ )Nc                  &   > ST  S[        T5       3$ )Nz%It is expected output_size equals to , but got size r  )num_spatial_dimsr  s   r7   rf   'upsample_common_check.<locals>.<lambda>  s    78H7IY\]hYiXjkr9   r   c                  &   > ST  S[        T5       3$ )Nz$It is expected input_size equals to r		  r  )expected_input_dimsr  s   r7   rf   r	    s    67J6K?[^_i[jZklr9   c              3   *   #    U  H	  oS :  v   M     g7fr   Nr3   ru   r  s     r7   rw   (upsample_common_check.<locals>.<genexpr>  s     *>aE>   c              3   *   #    U  H	  oS :  v   M     g7fr	  r3   r	  s     r7   rw   r	    s     2N+Qq5+r	  c                     > ST  ST 3$ )NzDInput and output sizes should be greater than 0, but got input size z and output size r3   )r  r  s   r7   rf   r	    s      \!2;-Ar9   )rW   ri   r   r  )r  r  r
	  r  channelsr	  s   ```  @r7   upsample_common_checkr	    s    	LLK,,k +Q.	LLJ..l
 
LL*:ab>**Ns2N+2N/N	A ""1~F+{++r9   c                 8  ^  [         R                  " T R                  5       S:g  =(       d    [        T R	                  5       SS  5      U 4S j5        [        T R	                  5       USS9nT R                  U5      R                  [        R                  " T 5      S9$ )Nr   r2   c                  *   > ST R                  5        3$ )Nz>Non-empty 3D data tensor expected but got a tensor with sizes r   r  s   r7   rf   $upsample_nearest1d.<locals>.<lambda>      PQVQ[Q[Q]P^_r9   r
	  r   
rW   ri   r   r	  r   r	  r   r3  rP   r   )r   r  scalesfull_output_sizes   `   r7   upsample_nearest1dr	         
LLA/

QR0@A_ -

kA ??+,//11%8 0  r9   c                   ^  [         R                  " T R                  5       S:g  =(       d    [        T R	                  5       SS  5      U 4S j5        [        T R	                  5       USS9nT R                  U5      n[        R                  " T 5      nT R                  u  px  nT R                  R                  S:X  a  US:  a  [         R                  nUR                  US9nU$ )	Nr   r2   c                  *   > ST R                  5        3$ Nz>Non-empty 4D data tensor expected but got a tensor with sizes r   r  s   r7   rf   $upsample_nearest2d.<locals>.<lambda>  r	  r9   r   r	  r   r-  r   )rW   ri   r   r	  r   r	  r   rP   r   r   r   r~   r   
contiguous)	r   r  scales_hscales_wr	  r	  r   rS   
n_channelss	   `        r7   upsample_nearest2dr)	    s     
LLA/

QR0@A_ -

kA __-.F //6M  ++A1a||F"zA~//];FMr9   r  r  r&	  r'	  c                 X  ^ ^^ [        X!SS9m[        R                  " T R                  S:H  U 4S j5        [	        S5       H5  m[        R                  " T R                  T5      TT   :H  UU U4S j5        M7     T R                  U5      R                  [        R                  " T 5      S9$ )Nr   r	  r-  c                  "   > ST R                    3$ NzFExpected grad_output to be a tensor of dimension 4 but got: dimension r  r  s   r7   rf   -upsample_nearest2d_backward.<locals>.<lambda>      XYdYiYiXjkr9   c            
      D   > ST ST T    ST STR                  T5       3$ )NzCExpected grad_output to have the same shape as output; output.size() = z but got grad_output.size(r   r	  r"  r   s   r7   rf   r-	    s9      !s$'7':&;,QCtK4D4DQ4G3HJr9   r   )
r	  rW   ri   r   r   r   r   r3  rP   r   )r"  r  r  r&	  r'	  r	  r   s   `    @@r7   upsample_nearest2d_backwardr2	    s     -! 
LLAk 1XQ#3A#66	
    ,//11+> 0  r9   c                 8  ^  [         R                  " T R                  5       S:g  =(       d    [        T R	                  5       SS  5      U 4S j5        [        T R	                  5       USS9nT R                  U5      R                  [        R                  " T 5      S9$ )Nr   r2   c                  *   > ST R                  5        3$ )Nz>Non-empty 5D data tensor expected but got a tensor with sizes r   r  s   r7   rf   $upsample_nearest3d.<locals>.<lambda>  r	  r9   r/   r	  r   r	  )r   r  scales_dr&	  r'	  r	  s   `     r7   upsample_nearest3dr7	    r 	  r9   c                    [         R                  " U 5      [         R                  " U [         R                  S9pvUb  Ub  [        U[        5      (       d  [        S[        U5       35      e[        U[        5      (       d  [        S[        U5       35      eUR                  nUR                  5       n	[        XH5      n[        XX5      nUR                  X5        UR                  X5        [        XdS9  [        XuS9  XE4$ Xg4$ )Nr   zvalues must be TensorLike, got z indices must be TensorLike, got )r  r  )rW   r   r   rs   r   r   r~   r   r   r    r   r"   )
r   stabler   
descendingr   r   r	  r   r   
out_strides
             r7   	meta_sortr<	    s     D!5#3#3D#Lqg1&*-- #B4<.!QRR':.. #CDM?!STT GG	XXZ
"65#G791I2344Kr9   c           	      >  ^ ^^^^^^^ [         R                  " T R                  S:H  U 4S j5        [         R                  " T R                  TR                  :H  UU 4S j5        T R	                  S5      mTb  [         R                  " TR                  S:H  U4S j5        [         R                  " TR                  5       T:H  UU4S j5        [         R                  " TR                  TR                  :H  UU4S j5        [         R                  " TR                  S:H  U4S j5        T R	                  S	5      T-  T-  m[         R                  " TR                  5       T:H  UUUU U4S
 j5        [         R                  " [        U 4S jTTTT4 5       5      S 5        g )Nr   c                  "   > T R                    S3$ Nz != 2r  )input_gatess   r7   rf   %rnn_cell_checkSizes.<locals>.<lambda>*      ;3C3C2DE0Jr9   c                  :   > TR                    ST R                    3$ Nrm  rO  )hidden_gatesr@	  s   r7   rf   rA	  -  s    ;$$%T,*<*<)=>r9   r2   c                  "   > T R                    S3$ )Nz != 1r  )
input_biass   r7   rf   rA	  1  s    joo5Fe3Lr9   c                  .   > TR                  5        ST  3$ rD	  r"  )
gates_sizerG	  s   r7   rf   rA	  4  s    z'')*$zl;r9   c                  :   > TR                    ST R                    3$ rD	  rO  )hidden_biasrG	  s   r7   rf   rA	  8  s    z''([->->,?@r9   c                  "   > T R                    S3$ r?	  r  )prev_hiddens   r7   rf   rA	  :  rB	  r9   r   c            
      `   > TR                  5        STR                  S5       ST ST ST  S3
$ )Nrm  r   z * z // z (aka r}   )r   r   )expected_prev_hidden_numelfactorrI	  r@	  rM	  s   r7   rf   rA	  >  s@    ;$$&'tK,<,<Q,?+@J<tTZS[[ab|a}}~r9   c              3   V   >#    U  H  nUR                   TR                   :H  v   M      g 7frC   r  )ru   r<   r@	  s     r7   rw   &rnn_cell_checkSizes.<locals>.<genexpr>A  s'      
I HH***Is   &)c                      g)Nz%expected all inputs to be same devicer3   r3   r9   r7   rf   rA	  E  s    7r9   )rW   ri   r   r   r   r   r  )r@	  rE	  rG	  rK	  rP	  rM	  rO	  rI	  s   ``````@@r7   rnn_cell_checkSizesrT	  "  sC    
LL!!Q&(JK	LL\///> !!!$JZ__)+LM*,;	
 	 1 11@	
 
LL!!Q&(JK!,!1!1!!4z!AV!K	LL99 
LL 
"J[I
 	
 	8r9   c                     [        XX4SU5        [        R                  " U [        R                  S9n[        R                  " U[        R                  S9n[        R                  " U[        R                  S9nXgU4$ )Nr-  r   )rT	  rW   r   r   )r@	  rE	  cxrG	  rK	  	workspacehycys           r7   _thnn_fused_lstm_cell_metarZ	  I  se     :ArR  E<S<STI			"E,C,C	DB			"E,C,C	DBIr9   c                    [        U5      S:g  nU(       a   [        U5      nUS   nU R                  S   nOLU
(       a  U R                  S   OU R                  S   nU
(       a  U R                  S   OU R                  S   nSnU(       a  SOSnUS:w  a  UOUnU(       a  UUU-  /nOU
(       a  UUUU-  /OUUUU-  /nU R                  U5      nU	U-  UU/nUc   [        R                  " SU R
                  S9nOUR                  U5      nUR                  U	U-  UU/5      nU(       a  SOSnU R                  U[        R                  S9nUUUUU4$ )Nr   r2   r   r   r  r   )r   r   r   rW   r   r   r  )r   rE  weight_stride0
weight_bufhxrV	  rw  hidden_size	proj_size
num_layersbatch_firstdropouttrainbidirectionalbatch_sizesdropout_stateis_input_packed
seq_length
mini_batchbatch_sizes_sumnum_directionsout_sizer   r	  
cell_shaperY	  rX	  reserve_shapereserves                                r7   
_cudnn_rnnrq	  X  sS   & +&!+O%
 ^
++a.'2U[[^A
'2U[[^A
'QQN%NyH$h&?@	  X%>?j(^*CD 	
 __Y'F~-z;GJ	z[[5<<0\\*%	zN2JI	JB AAMoom5;;o?G2r7J..r9   c                     SnU H+  nUR                  5       S:  d  M  XR                  5       -  nM-     U R                  U45      n[        U UUUUUUUSUUU	U
UUU5      $ r  )r   r   rq	  )r   rE  r\	  r^	  rV	  rw  r_	  ra	  rb	  rc	  rd	  re	  rf	  rg	  total_weight_elemsr  r]	  s                    r7   
miopen_rnnrt	    s    & 779q='')+  "4!67J

	! r9   c                 >   U(       a  U R                   S   OU R                   S   nU(       a  U R                   S   OU R                   S   nU
nU(       a  UUU/OUUU/nU R                  U5      nUc   [        R                  " SU R                  S9nOUR                  UR                   5      nUc   [        R                  " SU R                  S9nOUR                  UR                   5      n[        R                  " SU R                  [        R
                  S9nUUUU4$ )Nr2   r   r  r   )r   r   rW   r   r   r  )r   w0w1w2w3hx_cx_r   rf	  rw  r_	  ra	  
has_biasesre	  rb	  rd	  ri	  rj	  output_chanelsr   r	  rX	  rY	  rW	  s                           r7   mkldnn_rnn_layerr~	    s    & $/QEKKNJ#.QEKKNJ N  
Z0*n5 
 __Y'F
{[[5<<0]]399%
{[[5<<0]]399%Aell%++FI2r9$$r9   c                    ^^ U R                   S:X  a,  [        R                  " TS:H  =(       d    TS:H  UU4S j5        g [        R                  " U R                  T5      S:g  UU4S j5        g )Nr   r   c                     > T ST  3$ )Nz4: Expected reduction dim -1 or 0 for scalar but got r3   r   r  s   r7   rf   'zero_numel_check_dims.<locals>.<lambda>  s    wiSTWSXYr9   c                     > T ST  S3$ )Nz: Expected reduction dim z to have non-zero size.r3   r	  s   r7   rf   r	    s    wi8=TUr9   )r   rW   r   r   )r   r   r  s    ``r7   zero_numel_check_dimsr	    sR    yyA~1H!r	Y	

 	IIcNaU	
r9   c                    ^  Ub&  [        X!R                  5       5      n[        XT 5        g [        R                  " UR                  5       S:g  U 4S j5        g )Nr   c                     > T  S3$ )Nz@: Expected reduction dim to be specified for input.numel() == 0.r3   r[  s   r7   rf   %check_argmax_argmin.<locals>.<lambda>  s    tf\]r9   )r   r   r	  rW   ri   r   )r  r   r   s   `  r7   check_argmax_argminr	    s?    
S((*-d.JJLA]	
r9   c                     [        SX5        [        R                  " U R                  Ub  U4OS 5      n[	        XU5      nU R                  U[        R                  S9$ )Nargmaxr   )r	  rP   r  r   r  r   rW   r   )r   r   r  r  r   s        r7   argmax_argmin_metar	    sM    $,

coSF4PD$T9E>>%u{{>33r9   c                 v    U[         R                  :X  a  [         R                  n[         R                  " SXX4S9$ )Nr3   r  )rW   jaggedr  r   )r  r_   r   r   r   s        r7   scalar_tensorr	    s1    
 ;;
%v r9   c                    [        X R                  5       SS9nU R                  5       S:X  a  SOU R                  U5      n[        R                  " US:  5        [        R                  " X:*  S 5        [        U R                  5      n[        U5      S:  a  XU'   U R                  U5      U R                  U[        R                  S94$ )NTry  r   r2   c                      g)Nzk not in range for dimensionr3   r3   r9   r7   rf   topk_meta.<locals>.<lambda>  s    )Gr9   r   )
r   r   r   rW   ri   r   r   r   r   r   )r   r_  r   largestr  	sliceSizetopKSizes          r7   	topk_metar	    s     hhjd
;CXXZ1_$))C.I	LLa	LL!GHDJJH
8}q>>(#T^^HEKK^%PPPr9   c                     Uc  Uc  [        S5      eUR                  5       nU R                  5       n	[        R                  " UU	R                  U	R
                  U	R                  S9$ )Nz;segment_reduce(): Either lengths or offsets must be defined)r_   r   r   )r   r%	  rW   r   r_   r   r   )
rw  r	  r  rw  r  r  r  r  data_contiggrad_contigs
             r7   meta__segment_reduce_backwardr	     sh    
 7?I
 	
 //#K//#K!!!!	 r9   c                   ^ SSK Jn  [        TU R                  5       SS9mU R                  5       S:  a  U R	                  T5      OSn[
        R                  " U" US:  X:*  5      U4S j5        [        U R                  S T U R                  TS-   S  -   5      nU(       a&  U R                  5       S:  a  UR                  TS5        U R                  U5      U R                  U[
        R                  S94$ )Nr   )r  Tr	  r2   c                     > ST  3$ )Nz9kthvalue(): selected number k out of range for dimension r3   r   s   r7   rf   kthvalue_meta.<locals>.<lambda><  s    KC5Qr9   r   )r0  r  r   r   r   rW   ri   r   r   r;  r   r   )r   r_  r   r  r  dimSizer   s     `    r7   kthvalue_metar	  3  s     >
dhhjd
;C $
QdiinAG	LLQ%Q
 DS!DJJsQwy$99:E488:>S!>>% $..ekk."JJJr9   c                    U b  U OUn[         R                  " UR                  5       S:H  S 5        UR                  5       nU b)  [         R                  " U R                  5       U:H  S 5        Ub)  [         R                  " UR                  5       U:H  S 5        [         R                  " UR                  5       U:H  S 5        [         R                  " UR                  5       U:H  S 5        [         R                  " UR                  5       S:H  S 5        [         R                  " UR	                  5       US   US	   -  S
-  :H  S 5        g )Nr   c                      gN r3   r3   r9   r7   rf   (checkLSTMBackwardSizes.<locals>.<lambda>K  s    "r9   c                      gr	  r3   r3   r9   r7   rf   r	  N      r9   c                      gr	  r3   r3   r9   r7   rf   r	  P  r	  r9   c                      gr	  r3   r3   r9   r7   rf   r	  Q      r9   c                      gr	  r3   r3   r9   r7   rf   r	  R  r	  r9   c                      gr	  r3   r3   r9   r7   rf   r	  S  s    rr9   r   r2   r-  c                      gr	  r3   r3   r9   r7   rf   r	  T  s    Rr9   )rW   ri   r   r   r   )grad_hygrad_cyrV	  rY	  rW	  defined_gradexp_sizes          r7   checkLSTMBackwardSizesr	  I  s    %17wL	LL!!#q(*5  "HW\\^x/<W\\^x/<	LLh&
3	LLh&
3	LLA%z2	LL"hqkHQK&?!&CCZPr9   c                     U c  Uc  g[        XX#U5        [        R                  " U[        S9n[        R                  " U[        S9nU(       a  UR	                  SSS9OS nXgU4$ )NNNNr   r   F)r  )r	  rW   r   legacy_contiguous_memory_formatr  )	r	  r	  rV	  rY	  rW	  has_bias
grad_gatesgrad_cxr$  s	            r7   #_thnn_fused_lstm_cell_backward_implr	  X  sf    7?7RY?!!!@J r1PQG4<
q%0$I	))r9   c                 2   S nS nS nUS   (       a  UR                  U R                  5       5      nUS   (       d
  US   (       aQ  UR                  UR                  S5      U R                  S5      45      nUR                  UR                  S5      5      nXEU4$ )Nr   r2   r   r   rG  )r4  r3  r5  r8  r%  grad_weightr$  s          r7   linear_backwardr	  f  s    JKI1~!++FKKM:
1~Q",,l.?.?.CV[[QS_-UV **<+<+<R+@A	Y//r9   c                   ^ ^ [        T R                  5      S:  a  T R                  S   X-  -  S:X  d  [        ST R                   SU 35      eS mUU 4S jnT R                  S   X-  -  nT R                  S   U-  nT R                  S	   U-  n/ T R                  S S QUPUPUP7nT R                  U5      nUR	                  U" 5       S
9nU$ )Nr   ro  r   z'Invalid input shape for pixel_shuffle: z with upscale_factor = c                 b    [         R                  R                  U 5      [         R                  :H  $ rC   r  r  s    r7   r  ,meta_pixel_shuffle.<locals>.is_channels_last|  s$    ""88=ATATTTr9   c                  F  > T " T5      (       a/  [        T5      S:X  a  [        R                  $ [        R                  $ TR	                  [        R                  S9(       a  [        R                  $ TR	                  [        R
                  S9(       a  [        R
                  $ g )Nr   r   )r  rW   r   r  rp  preserve_format)r  r   s   r7   r  .meta_pixel_shuffle.<locals>.pick_memory_format  s    D!!4 F*...***e.E.EF***e.C.CD((( Er9   r  r   r   )r   r   r   r   r3  )	r   upscale_factorr  rT  HrWrr   r   r  s	   `       @r7   meta_pixel_shuffler	  s  s     	DJJ!

2.2Q RVW W5djj\AXYgXhi
 	
U	) 	

2>:;A	B.	(B	B.	(B-$**Sb/-1-b-"-I
..
#C
&&13&
4CJr9   c                 X   U R                  U R                  5      nUR                  UR                  5      nUR                  UR                  5      nUR                  UR                  5      nUR                  UR                  5      nUR                  UR                  5      nUUUUUUU4$ rC   r  )r   weight0weight1weight2weight3rz	  cx_tmpr	  hy_cy_grad_output_r_optgrad_hy_r_optgrad_cy_r_optr   rw  r_	  ra	  r|	  rd	  re	  rf	  rb	  rW	  diff_xdiff_hxdiff_cxdiff_w1diff_w2diff_bs                                r7   mkldnn_rnn_layer_backwardr	    s    4 __U[[)FmmCII&Gv||,G.G.Gw}}-F7GVVWgEEr9   )	out_int32r   c                    [         R                  " U U(       a  [         R                  O[         R                  [         R                  S9$ )Nr_   r   )rW   r   rO  r   r   r   
boundariesr	  r   s       r7   meta_bucketizer	    s2     &ekkEKK-- r9   r	  r	  r   c                p    UR                  SU(       a  [        R                  S9$ [        R                  S9$ )Nr3   r   )r   rW   rO  r   r	  s       r7   meta_bucketize_scalarr	    s>     
&ekk    ,1KK    r9   c                   ^ ^^^^ Sm[        T 5      S:X  a)  [        R                  " T R                  5       U 4S j5        [        T 5      S:X  a+  T R                  5       (       a  [        R
                  " S5        [        R                  " [        T[        5      UU4S j5        [        R                  " TS:  UU4S j5        [        R                  " [        T[        5      UU4S	 j5        [        R                  " [        T[        5      UU4S
 j5        [        R                  " TT:  U4S j5        [        R                  " TT R                  T R                  S9$ )Nzhistc()r  c                  $   > ST R                    S3$ )Nz%"histogram_cpu" not implemented for 'r  r   r  s   r7   rf   meta_histc.<locals>.<lambda>  s    =ekk]!Lr9   r   z%_histc_cuda with floating point inputc                  $   > T S[        T 5       3$ )Nz#: argument 'bins' must be int, not rO  binsr  s   r7   rf   r	    s    7)>tDzlKr9   r   c                     > T ST  3$ )Nz: bins must be > 0, but got r3   r	  s   r7   rf   r	    s    gY.J4&#Qr9   c                  $   > T  S[        T5       3$ )Nz%: argument 'min' must be Number, not rO  )r  r  s   r7   rf   r	        7)@cLr9   c                  $   > T  S[        T5       3$ )Nz%: argument 'max' must be Number, not rO  )r  r  s   r7   rf   r	    r	  r9   c                     > T  S3$ )Nz: max must be larger than minr3   )r  s   r7   rf   r	    s    y0M%Nr9   r   )r  rW   ri   r  rP   rG  rs   r   r   r   r   r_   )r   r	  r  r  r  s   ````@r7   
meta_histcr	    s     G5U"##%L	
 5V#(?(?(A(A%%&MN	LL4!K 
LLQR	LL3L 
LL3L 
LLNO;;tELLDDr9   c                 F  ^  [        T R                  5       USS9n[        R                  " T R	                  5       S:g  =(       d#    [        S T R                  5       SS   5       5      U 4S j5        T R                  U5      R                  [        R                  " T 5      S9$ )Nr   r	  r   c              3   *   #    U  H	  oS :  v   M     g7fr	  r3   )ru   r   s     r7   rw   ,meta_upsample_bimode2d_aa.<locals>.<genexpr>  s     !H7Gt(7Gr	  r2   c                  *   > ST R                  5        3$ r#	  r   r  s   r7   rf   +meta_upsample_bimode2d_aa.<locals>.<lambda>  r	  r9   r   )
r	  r   rW   ri   r   r  r   r3  rP   r   )r   r  rO  r&	  r'	  r	  s   `     r7   meta_upsample_bimode2d_aar	    s     -

kA 
LLHc!Huzz|AB7G!HH_ ??+,//11%8 0  r9   c                 T  ^ ^^ [        X!SS9m[        R                  " T R                  S:H  U 4S j5        [	        S5       H3  m[        R                  " T R
                  T   TT   :H  UU U4S j5        M5     T R                  U5      R                  [        R                  " T 5      S9$ )Nr   r	  r-  c                  "   > ST R                    3$ r,	  r  r  s   r7   rf   4meta_upsample_bimode2d_aa_backward.<locals>.<lambda>  r.	  r9   c            
      D   > ST ST T    ST STR                  T5       3$ )NzD
Expected grad_output to have the same shape as output; output.size(r0	  z
but got grad_output_size(r   r1	  s   r7   rf   r	    s>     DDE3dK[\]K^J_ `D!1!1!!4 59r9   r   )
r	  rW   ri   r   r   r   r   r3  rP   r   )r"  r  r  rO  r&	  r'	  r	  r   s   `     @@r7   "meta_upsample_bimode2d_aa_backwardr	    s     -! 
LLAk 1Xa $4Q$779	
    ,//11+> 0  r9   c                 X   [         R                  " UR                  5       S:H  S 5        [         R                  " UR                  5       S:H  S 5        [         R                  " UR                  R                  S 5        [         R                  " UR                  R                  S 5        g )Nr2   c                      g)Nz%found_inf must be a 1-element tensor.r3   r3   r9   r7   rf   <_amp_foreach_non_finite_check_and_unscale_.<locals>.<lambda>!      (Or9   c                      g)Nz%inv_scale must be a 1-element tensor.r3   r3   r9   r7   rf   r	  $  r	  r9   c                      g)Nz!found_inf must be a float tensor.r3   r3   r9   r7   rf   r	  (      3r9   c                      g)Nz!inv_scale must be a float tensor.r3   r3   r9   r7   rf   r	  ,  r	  r9   )rW   ri   r   r_   r  )r   rK  	inv_scales      r7   *_amp_foreach_non_finite_check_and_unscale_r 
    s|    	LLQ O 
LLQ O 
LL))3 
LL))3r9   c                 .    [         R                  " U 5      $ rC   rD  )r   nanposinfneginfs       r7   
nan_to_numr
  1  r  r9   c                    U R                   [        R                  [        R                  [        R                  [        R
                  1;   a  [        SU R                    S35      eU R                  n[        X5      n[        X#5      nX:X  a  U $ [        U R                  5       5      n[        U R                  5       5      nXR   XQ   sXQ'   XR'   XB   XA   sXA'   XB'   U R                  XE5        U $ )Nz>torch.transpose_: in-place transposition is not supported for z layout)r   rW   r  
sparse_cscr  
sparse_bscr   r   r   r   r   r   r   )r   dim0r  ndimsr   r   s         r7   r  r  7  s    {{	  LT[[MY`a
 	
 IIE$&D$&D|		D$++- F!'v|FL&,!ZDJ
T"Kr9   c                 2   U R                   nU R                  (       a?  U R                  5       nU R                  5       nUS::  a  US:X  d  [	        SU SU S35      eO#U R                  5       S:  a  [	        SU S35      e[        U SUS:  a  S5      $ S5      $ )	Nr   r   zEt_ expects a tensor with <= 2 sparse and 0 dense dimensions, but got z sparse and z dense dimensionsz6t_ expects a tensor with <= 2 dimensions, but self is rY  r2   )r   rb  rd  re  r   r   r  )r   r

  rd  re  s       r7   t_r
  U  s    IIE~~__&
NN$	aIN %,l9+=NP  %3 88:> HqQ  dAEAIq55155r9   )r	  r   sidesorterc                  ^ ^^ [         R                  " [        T R                  5      S:*  =(       d    T R                  S S TR                  S S :H  UU 4S j5        [         R                  " TS L =(       d    T R                  TR                  :H  U U4S j5        [         R                  " US:g  =(       d    U(       + S 5        U(       a  [         R                  O[         R
                  n[        T[         R                  5      (       a$  [         R                  " TU[         R                  S9$ [         R                  " SUT R                  S	9$ )
Nr2   r   c                  `   > S[        TR                  5       S[        T R                  5       3$ )Nztorch.searchsorted(): boundaries tensor should be 1 dimension or the first N-1 dimensions of boundaries tensor and input value tensor must match, but we got boundaries tensor z and input value tensor r   r   )r   sorted_sequences   r7   rf   #meta_searchsorted.<locals>.<lambda>z  s3    3378M8M3N2O P""&tzz"2!35r9   c                  n   > S[        T R                  5       STb  [        TR                  5       3$ /  3$ )Nz[torch.searchsorted(): boundary and sorter must have the same size, but got boundary tensor z and got sorter tensor r
  )r
  r
  s   r7   rf   r
    sB    ##'(=(=#>"??V%+%7tFLL!@B=?@Br9   r   c                      g)Nzetorch.searchsorted(): side and right can't be set to opposites, got side of left while right was Truer3   r3   r9   r7   rf   r
    s     $r9   r	  r3   r  )rW   ri   r   r   rO  r   rs   r   r   r   r   r   )r
  r   r	  r   r
  r
  r_   s   ``   ` r7   meta_searchsortedr
  j  s     
LLO!!"a' 	9  "%CR8	
	 
LL$?///6<<?	
 
LL#e)	$ %EKK%++E$%%U-D-D
 	
 {{2U?3I3IJJr9   c                    ^  [         R                  " T [         R                  [         R                  [         R                  4;  U 4S j5        g )Nc                     > ST  3$ )Nz/Unsupported input type encountered for isin(): r3   r   s   r7   rf   3_check_for_unsupported_isin_dtype.<locals>.<lambda>  s    A%Ir9   )rW   ri   r  
complex128	complex64r   s   `r7   !_check_for_unsupported_isin_dtyper
    s/    	LLejj%"2"2EOODDIr9   c                 H    U R                  X R                  S5      45      nU$ )Nr   rG  )r"  r   num_weightsr&  r3  r	  s         r7   meta_embedding_dense_backwardr
    s(     ''6F6Fr6J(KLKr9   c                 t    U	(       a  [         R                  U UUUUUUUU
U5
      $ [        U UUUUUUUU
U5
      $ rC   )r,   _embedding_bag_sparse_backward!meta_embedding_bag_dense_backward)rw  r   r  r7  r8  maximum_indicesr
  r3  rw  r4  r   r&  s               r7   meta_embedding_bag_backwardr$
    se     22
 	
 1
 	
r9   c
                 X  ^  [         R                  " T R                  [         R                  [         R                  [         R
                  [         R                  4;   U 4S j5        U[        :X  a  [         R                  " US L5        T R                  UT R                  S5      45      n
U
$ )Nc                  "   > ST R                    3$ )Nz$Unsupported input type encountered: r   )rw  s   r7   rf   3meta_embedding_bag_dense_backward.<locals>.<lambda>  s    6tzzlCr9   r2   )
rW   ri   r_   rm  rn  rl  float64r1  r   r   )rw  r   r7  r8  r#
  r
  r3  rw  r   r&  index_grad_weights   `          r7   r"
  r"
    sv     
LL

u}}ennemmU]]SSC x_D01TYYq\'BCr9   c                    U R                  S5      n[        R                  " U[        :H  S 5        [        R                  " U R	                  5       S:H  5        [        R                  " UR	                  5       S:H  5        UR                  S5      n[        R                  " UR	                  5       S:H  5        [        R                  " UR                  S5      U:H  5        U R                  U45      n	U	$ )Nr2   c                      g)NzHembedding_bag_backward: per_sample_weights only supported for mode='sum'r3   r3   r9   r7   rf   @meta_embedding_bag_per_sample_weights_backward.<locals>.<lambda>  r0  r9   r   r   )r   rW   ri   r0  r   r   )
rw  rE  r   r  r7  rw  r&  embedding_featuresr 	  r	  s
             r7   .meta_embedding_bag_per_sample_weights_backwardr.
    s     1	LLZ 
LLq!	LL!#$,,q/K	LL"#	LLQ#556^^[N+FMr9   )assume_uniqueinvertc                   [         R                  " [        U [        5      =(       d    [        U[        5      S 5        [        U [        5      (       d  [         R                  " XR
                  S9n [        U[        5      (       d  [         R                  " XR
                  S9n[        U R                  5        [        UR                  5        [         R                  " U [         R                  S9$ )Nc                      g)Nz<At least one of elements and test_elements must be a Tensor.r3   r3   r9   r7   rf   meta_isin.<locals>.<lambda>  r  r9   r  r   )
rW   ri   rs   r   r<  r   r
  r_   r   r  )elementstest_elementsr/
  r0
  s       r7   	meta_isinr6
  	  s     
LL8V$I
=&(IN h''<<1E1EFmV,,]??K%hnn5%m&9&9:HEJJ77r9   r  c                     [         R                  " U S:  S 5        [        U[        R                  S9u  p#[         R
                  " XS9$ )Nr   c                      g)Nz,polygamma(n, x) does not support negative n.r3   r3   r9   r7   rf    meta_polygamma.<locals>.<lambda>  s    !Or9   r  r   )rW   ri   r   r   r  r   )r  r   rS   rT   s       r7   meta_polygammar:
    sB     
LLaOP(;HHOA D55r9   c                     [        S5      e)Nz.Tensor.item() cannot be called on meta tensors)r2  r   s    r7   meta_local_scalar_denser<
  &  s    
G
HHr9   c                 .    [         R                  " U 5      $ rC   rD  r   s    r7   silur>
  +  r  r9   c                 ^    [        U [        R                  S9u  p[        R                  " XS9$ r  )r   r   r  rW   r   )r   rS   rT   s      r7   sigmoidr@
  1  s/     );HHOA D55r9   c                 |   U R                  5       S:H  nUR                  5       S:H  nU(       a  U(       a4  UR                  S5      U R                  S5      UR                  S5      /nGO*[        R                  " UR                  S5      UR                  S5      :H  S 5        U R                  S5      UR                  S5      /nOU(       a\  [        R                  " UR                  S5      U R                  S5      :H  S 5        U R                  S5      UR                  S5      /nOk[        R                  " U R                  S5      UR                  S5      :H  S 5        U R                  S5      U R                  S5      UR                  S5      /nU=(       d    U R                  n[        R
                  R                  (       aV  SUR                  -  nUS   U-   S-
  U-  U-  nXE:X  a  US   U-  US/n	OUS/n	[        R                  " XiX0R                  S	9n
U
$ [        R                  " XcU R                  S	9n
U
$ )
Nr   r   r2   c                      gNz matrix batch sizes have to matchr3   r3   r9   r7   rf   2_create_grouped_mm_output_tensor.<locals>.<lambda>D      6Xr9   r   c                      grC
  r3   r3   r9   r7   rf   rD
  J  rE
  r9   c                      g)Nzbatched dimension has to matchr3   r3   r9   r7   rf   rD
  P  s    6Vr9   r{  r  )r   r   rW   ri   r_   r  r   itemsizer=  r   r   )rT  rV  offsrI  
mat1_is_2d
mat2_is_2drm	  	alignmentsize_paddedr;	  r   s              r7    _create_grouped_mm_output_tensorrN
  ;  s   qJqJ		!diilDIIaLAHLL		!		!,.X 		!diim4HLL		!		!,.X 		!diil3H LL		!		!,.V 		!diilDIIbMBH'TZZI}}),,,	|i/!3	AIM#"1+3[!DJ%q)J!!	++

 J kk(DKKHJr9   mat_amat_brI
  c	                   ^ ^^^^^ [         R                  " TS L TS L :H  S 5        TS L=(       a    TS Ln	U	(       a  [         R                  R                  (       a  [         R                  O[         R
                  n
[         R                  " T R                  U
:H  =(       a    TR                  U
:H  U U4S j5        O[[         R                  " T R                  [         R                  :H  =(       a    TR                  [         R                  :H  U U4S j5        [         R                  " T R                  5       S;   =(       a    TR                  5       S;   U U4S j5        T R                  5       S:H  nTR                  5       S:H  nU(       a  U(       d9  [         R                  " T R                  S5      TR                  S5      :H  S	 5        U	(       aH  S
 nS n[         R                  " U" T 5      U 4S j5        [         R                  " U" T5      U4S j5        S nU" ST 5        U" ST5        TGbD  TGb@  [         R                  " TR                  [         R                  :H  =(       a    TR                  [         R                  :H  =(       dA    TR                  [         R                  :H  =(       a    TR                  [         R                  :H  UU4S j5        TR                  [         R                  :H  =(       a    TR                  [         R                  :H  mSU4S jjnTb  U(       a  U(       a  TR                  S   OSnU" STT SU5        U" STTSU5        [         R                  " US L S 5        U(       d  U(       a  [         R                  " TS LU U4S j5        Tbb  [         R                  " TR                  5       S:H  U4S j5        [         R                  " TR                  [         R                  :H  U4S j5        O[         R                  " TS L S 5        [         R                  " US L S 5        [         R                  " US L =(       d    U[         R                  :H  S 5        [        T TTU5      $ )Nc                      g)Nz,Either both scale factors are given, or noner3   r3   r9   r7   rf   )_meta_grouped_mm_common.<locals>.<lambda>r  s    >r9   c                  >   > ST R                    STR                    S3$ )Nz5Expected inputs of E4M3 FP8 type but got mat_a.dtype= and mat_b.dtype=r  r   rO
  rP
  s   r7   rf   rS
  ~  s#    KEKK=Xijojujuivvwxr9   c                  >   > ST R                    STR                    S3$ )Nz1Expected inputs of BF16 type but got mat_a.dtype=rU
  r  r   rV
  s   r7   rf   rS
    s#    G}Tefkfqfqerrstr9   )r   r/   c                  L   > ST R                  5        STR                  5        3$ )Nz3Multiplicands must be 2D or 3D but got mat_a.dim()=z and mat_b.dim()=r   rV
  s   r7   rf   rS
    s%    Eeiik]Rcdidmdmdocpqr9   r   r   r  c                      g)Nz3contraction dimension of mat_a and mat_b must matchr3   r3   r9   r7   rf   rS
    rK  r9   c                 P    U R                  5       nUS   S:  =(       a    US   S:H  $ Nr  r2   r   r%  mat
mat_strides     r7   re  -_meta_grouped_mm_common.<locals>.is_row_major  s*    Jb>A%=*R.A*==r9   c                 P    U R                  5       nUS   S:H  =(       a    US   S:  $ r[
  r%  r\
  s     r7   ri  -_meta_grouped_mm_common.<locals>.is_col_major  s*    Jb>Q&=:b>A+==r9   c                  0   > ST R                  5       SS   3$ )NzNExpected mat_a tensor to be row major in the last two dimensions, got strides r  r%  )rO
  s   r7   rf   rS
    s!    dejeqeqestvtwexdyzr9   c                  0   > ST R                  5       SS   3$ )NzQExpected mat_b tensor to be column major in the last two dimensions, got strides r  r%  )rP
  s   r7   rf   rS
    s!    ghmhththvwywzh{g|}r9   c                   ^ ^^^ TR                  5       S-
  mSTR                  5       -  nTR                  5       mTTS-
     S:X  aJ  TT   [        STR                  TS-
     5      :  a'  [
        R                  " TT   U-  S:H  UU U4S j5        g TT   S:X  aM  TTS-
     [        STR                  T   5      :  a*  [
        R                  " TTS-
     U-  S:H  UU U4S j5        g [
        R                  " SUU4S j5        g )Nr2   r{  r   c                  "   > ST ST  STT     S3$ )Nr   stride along % dim to be multiple of 16 bytes, got r  r3   end_dimmat_namer^
  s   r7   rf   F_meta_grouped_mm_common.<locals>.check_valid_strides.<locals>.<lambda>  s'    )H:^G9Dijtu|j}i~~  Ar9   c                  .   > ST ST S-
   STT S-
      S3$ )Nr  rf
  r2   rg
  r  r3   rh
  s   r7   rf   rk
    sI    )H:^GaK=Hmnx  zA  DE  zE  oF  nG  GH  Ir9   Fc                  *   > ST ST R                    S3$ )NzInvalid strides/sizes, got z for strides and z for sizes.rO  r\
  s   r7   rf   rk
    s    5j\ARSVS\S\R]]hir9   )r   element_sizer   r  r   rW   ri   )rj
  r]
  rL
  ri
  r^
  s   `` @@r7   check_valid_strides4_meta_grouped_mm_common.<locals>.check_valid_strides  s    '')a-#**,,	ZZ\
gk"a'Jw,?3syy1%D
 -
 LL7#i/14 A  A%*Wq[*ASsyy!F
 +
 LL7Q;')3q8 I
 LLir9   rO
  rP
  c                  >   > ST R                    STR                    S3$ )NzhFor FP8 scales must both be float32, or for MXFP8 both scales must be float8_e8m0fnu. Got scale_a.dtype=z and scale_b.dtype=r  r   r  s   r7   rf   rS
    sR    ~  @G  @M  @M  N  Na  bi  bo  bo  ap  pq  rr9   r2   c                    >^ ^^^^^^	^
 TR                  5       S:X  a  [        R                  " TR                  5       U 4S j5        T(       a=  [        R                  " TR                  5       TR                  5       :H  UUU 4S j5        g [        R                  " TR                  5       S:H  UU 4S j5        [        R                  " TR                  S   TR                  T   T-  :H  UUUU U4S j5        g [        R                  " TR                  S5      S:H  U 4S	 j5        [        R                  " TR                  S   TR                  S   :H  UUU 4S
 j5        T(       a  [        R                  " TR                  TR                  S-
  :H  UUU 4S j5        TR                  u  mpVSn[        XW-  S5      m	[        US5      m
[        R                  " TR                  S   T:H  =(       a    TR                  S   T	T
-  :H  UU	U
UU4S j5        g [        R                  " TR                  5       S:H  UU 4S j5        [        R                  " TR                  S   TR                  ST-      :H  UUU U4S j5        g )Nr   c                     > ST  S3$ )Nr  z to be contiguous.r3   
scale_names   r7   rf   >_meta_grouped_mm_common.<locals>.check_scale.<locals>.<lambda>  s    i
|3EFr9   c                  B   > ST ST R                    STR                    3$ )NzKFor MXFP8, scale must have same number of dimensions as target tensor, but  has mat.ndim= and scale.ndim=r  r]
  r  ru
  s   r7   rf   rv
    sX    "mnxmy  zH  IL  IQ  IQ  HR  Rb  ch  cm  cm  bn  !or9   r2   c                  2   > ST ST R                  5        S3$ )Nr  z to be 1D tensor, but got 	D tensor.r   r  ru
  s   r7   rf   rv
    !    )J<7QRWR[R[R]Q^^g hr9   r   c                  V   > ST ST R                   T   T-   STR                   S    S3$ )Nr  z	 to have r  r   z
 elements.rO  )r]
  r  scale_multiplierru
  
scaled_dims   r7   rf   rv
    sU    )J<y:AVYiAi@jjyz  {F  {F  GH  {I  zJ  JT  !Ur9   r   c                     > ST  S3$ )Nr  z( to be contiguous in the last dimension.r3   rt
  s   r7   rf   rv
    s    i
|3[\r9   c                  P   > ST ST R                   S    STR                   S    S3$ )Nr  z batch dimension to be r   , got r  rO  rz
  s   r7   rf   rv
    s4    i
|3J399UV<.X^_d_j_jkl_m^nnopr9   c                  B   > ST ST R                    STR                    3$ )Nz0For MXFP8, 3d tensor should have 2d scales, but rx
  ry
  r  rz
  s   r7   rf   rv
    sD    "RS]R^^lmpmumulv  wG  HM  HR  HR  GS  !Tr9   r|  r-  r  c                  N   > STR                    ST  STT-   STR                    3$ )NzFor MXFP8, expected mat.shape=z to have scale shape of (,z), but got rO  )G	blocked_K	blocked_Nr]
  r  s   r7   rf   rv
      sO    "@Kdefdgghiru~i~h  @K  LQ  LW  LW  KX  !Yr9   c                  2   > ST ST R                  5        S3$ )Nr  z to be 2D tensor, but got r|
  r   r}
  s   r7   rf   rv
     r~
  r9   c                  V   > ST ST R                   ST-       STR                   S    S3$ )Nr  z non-batch dimension to be r2   r
  r  rO  )r]
  r  ru
  r
  s   r7   rf   rv
  	   sR    )J<7RSVS\S\]^ak]kSlRmmstytt  AB  uC  tD  DE  !Fr9   )r   rW   ri   rp  r   r   r   r>   )ru
  r  r]
  r
  r
  r  r  r  r
  r
  r
  is_mxfp8s   `````   @@@r7   check_scale,_meta_grouped_mm_common.<locals>.check_scale  s   wwyA~'')F LL		swwy0 o
 LL		q(h LLA#))J*?BR*RR U  U
 LL$)\ KKNciil2p LL

chhl2 T "iiGAq!#J ( ;I (C 0ILLA!+WA)iBW0W Y  Y
 LL		q(h LLA#))A
N*CC Fr9   r   rN  rO  c                      g)Nz:Scale result tensor provided, but it is not supported yet.r3   r3   r9   r7   rf   rS
     rp   r9   c                  N   > ST R                  5        STR                  5        S3$ )Nz/Offsets tensor not provided, but is needed for zD/zD multiplicand layouts.r   rV
  s   r7   rf   rS
     s(    Eeiik]RTUZU^U^U`Taaxyr9   c                  ,   > ST R                  5        S3$ )Nz.Offsets tensor must be 1D, but got offs.dim()=r  r   rI
  s   r7   rf   rS
     s    HTUVr9   c                  $   > ST R                    S3$ )Nz7Offsets tensor must be integer (int32) tensor, but got r  r   r
  s   r7   rf   rS
  #   s    QRVR\R\Q]]^_r9   c                      g)NzJOffsets tensor provided, but is not needed for 3D/3D multiplicand layouts.r3   r3   r9   r7   rf   rS
  (   s    `r9   c                      g)Nz2Bias tensor provided, but it is not supported yet.r3   r3   r9   r7   rf   rS
  -   s    Dr9   c                      g)Nz4If output dtype provided, it must be torch.bfloat16.r3   r3   r9   r7   rf   rS
  2   s    Fr9   r4  )rW   ri   r  r  rV  ro  r_   rn  r   r   rl  r  r   rO  rN
  )rO
  rP
  rN  rO  rI
  rG  rP  rI  rQ  scaled	fp8_dtypemat_a_is_2dmat_b_is_2dre  ri  ro
  r
  r
  r
  s   `````             @r7   _meta_grouped_mm_commonr
  e  s]    
LL	Dgo.> D 8WD%8F -2]]->->E))EDWDW	KK9$A	)Ax	

 	KK5>>)KekkU^^.Kt	

 
LL		v7%))+"7q
 ))+"K))+"KkJJrNejjn,I	

 	>	> 	z	
 	}	

0 ''w2]]emm+N0N !5!55 :MMU%9%99 r	
 MMU111 6!5!55 	
:	z "-++DJJqMST 	 	Iwq2BCIwq2BCD P	

 ky	
 LL
aV LL

ekk)_
 	DL`	

 
LLD
 
LLT8Y%..8F
 ,E5$	JJr9   c                 "    [        U US S UUS US9$ )N)rN  rO  rI
  rG  rP  rI  )r
  )rO
  rP
  rI
  rG  rI  s        r7   meta_grouped_mmr
  8   s)     #	 	r9   c	                 V    U=(       d    [         R                  n[        U UUUUUUUUS9	$ )N)rN  rO  rI
  rG  rP  rI  rQ  )rW   rn  r
  )	rO
  rP
  rN  rO  rI
  rG  rP  rI  rQ  s	            r7   meta_scaled_grouped_mmr
  M   s:     +U^^I"!%
 
r9   r<   half_to_floatc                 \   U(       aG  U R                   [        R                  [        R                  4;  a  [	        SU R                    S35      e[
        R                  " U [
        R                  R                  S9u  p4U(       d  UOUn[        R                  " X[        R                  S9nU$ )Nz%half_to_float is True but x.dtype is z, expected half or bfloat16r  r	  )r_   rW   rY   rn  r   rP   r   r   rQ   r   r   )r<   r   r
  computation_dtyperT   r  s         r7   softmaxr
  i   s     775::u~~66 7y@[\  ',&>&>	uDDLL'# (5<:KL


1@W@W
XCJr9   c           	        ^^^^	^
^ [         R                  " [        T5      S-  S:H  U4S j5        U R                  m[        T5      m
[        T5      S-  nT
U-
  m	[         R                  " T
U:  U
U4S j5        [	        S T 5       5      (       a  U n[        T	T
5       Hx  mST
T-
  S-
  -  mTT   S:  a*  UR                  TTT   * UR                  T   TT   -   5      nTTS-      S:  d  MO  UR                  TSUR                  T   TTS-      -   5      nMz     UR                  5       $ [        TS T	 5      n[        U5       Ha  m[        T5      TS-   S-  -
  mTT	T-      TT   -   TTS-      -   n[         R                  " US:  UUU	UU4S j5        UR                  U5        Mc     [         R                  " UU R                  U R                  U R                  [        U 5      S9$ )	Nr   r   c                      > S[        T 5       3$ )Nz1Length of pad must be even but instead it equals r  r  s   r7   rf   '_constant_pad_nd_meta.<locals>.<lambda>   s    CCH:Nr9   c                  (   > S[        T5       ST  S3$ )Nz`Length of pad should be no more than twice the number of dimensions of the input. Pad length is z while the input has z dimensions.r  )l_inpr  s   r7   rf   r
     s      225c(;P'r9   c              3   n   #    U  H+  n[        U[        R                  5      =(       a    US :*  v   M-     g7fr	  )rs   rP   IntWithoutSymInt)ru   rr  s     r7   rw   (_constant_pad_nd_meta.<locals>.<genexpr>   s)     
IS:a//0;Q!V;Ss   35r2   c            	      F   > STTT -       STT    STTS-       STT -    S3	$ )NzThe input size z, plus negative padding r   r2   zG resulted in a negative output size, which is invalid. Check dimension z of your input.r3   )r   r  l_diffr  pad_idxs   r7   rf   r
     sE    ok&1*&=%>>V7|nE#gk"2!3 4117!OMr9   )r_   r   r   r   )rW   ri   r   r   r  r   narrowr   r   r   r   r_   r   r   r   )r   r  r  l_padc_input	new_shapenew_dimr   r  r
  r
  r
  s    `     @@@@@r7   _constant_pad_nd_metar
  {   s    
LLC1N
 ++KEHMEU]F	LL	 
IS
IIIvu%A519q=)G7|a!..G}gmmA&6W&E 7Q;!#!..Aw}}Q/?#gPQkBR/RS & }}[&)*I5\c(q1uk*fqj)CL83w{;KKqLM M	
 	!  ;;kk||))+E2 r9   r&  r3  r4  c                 B   U R                  5       S:w  a  [        SU R                  5        S35      eU R                  nUR                  nUR                  S:X  a  US   4nO%UR                  S:X  a  US   US   4nO
/ UQUS   P7nU R                  nU R                  XxS9$ )Nr   z'weight' must be 2-D, got z-Dr   r2   r   )r   r   r   r   r_   r   )	rE  r   r&  r3  r4  weight_shapeindices_shaper   rI  s	            r7   	embeddingr
     s     zz|q9&**,rJKK<<LMMM||q&21o%7			"1%|A7	5m5\!_5	II77r9   max_lengthspadding_valuec                    [        U5      S:w  a  [        S[        U5       S35      e[        U5      S:w  a  [        S[        U5       S35      eUS   R                  S   S-
  nUS   nXE/U R                  SS  Q7nU R                  U5      $ )Nr2   z&Only one jagged dim is supported, got z offsetsz max_lengthsr   )r   r   r   r   )r   r  r
  r
  r  r  rs  s          r7   $meta__jagged_to_padded_dense_forwardr
     s     7|q4S\N(K
 	
 ;14S5E4FlS
 	
 	
aAAA,6<<+,LL))r9   c                 B    [        U 5      [        5       S 5       5       nU$ )Nc                 2    [        U [        R                  S9$ rg  rU   r   r  rA  s    r7   _f)_create_unary_float_meta_func.<locals>._f   s      =JJ
 	
r9   rL   r#   funcr
  s     r7   _create_unary_float_meta_funcr
     *    4]
  

 Ir9   c                 (   U R                   (       d"  UR                   (       d  UR                   (       a  [        S5      eU R                  5       S:X  a,  U R                  U R                  5      U R                  S5      4$ U R                  S5      nU R                  S5      nUR                  S5      nU R                  XU5      nU
(       a4  U(       a  U R                  XU5      nUU4$ U R                  XX5      n UU4$ U R                  S5      nUU4$ )NzP_native_multi_head_attention fake implementation does not support nested tensorsr   r2   )	is_nestedr  r   r   r   r   )r  r   r  	embed_dimr  
qkv_weightqkv_biasproj_weight	proj_biasr  need_weightsaverage_attn_weights	mask_typer  T
output_dimr	  attn_weightss                     r7    native_multi_head_attention_faker
     s      #--5??!^
 	
 {{},eooa.@AA

1A

1A !!!$J__Q:.F !??13L L!!	 !??1=L L!! q)L!!r9   c                 B    [        U 5      [        5       S 5       5       nU$ )Nc                 2    [        X[        R                  S9$ rg  r
  r;   s     r7   r
  *_create_binary_float_meta_func.<locals>._f!!  s      !@!M!M
 	
r9   r
  r
  s     r7   _create_binary_float_meta_funcr
   !  r
  r9   c                    ^  [        T 5      U 4S j5       nT R                   S3nX!l        [        [        [        U5      5      " U5      nU$ )Nc                 `   > T" U /UQ70 UD6n[        U R                  UR                  5        U $ rC   r  )r   rR   rH  r   rE   s       r7   _fn#_register_inplace_meta.<locals>._fnE!  s.    '''

CII6r9   rS   )r   r   rL   getattrr,   )rE   r
  inplace_names   `  r7   _register_inplace_metar
  D!  sK    
2Y 
 kk]!$LL
l3
4S
9CJr9   c                 z  ^ ^^ [         R                  " T R                  TR                  :H  UU 4S j5        T T/n[        T[        5      (       aT  TR
                  S:w  a3  [         R                  " T R                  TR                  :H  U U4S j5        UR                  T5        [        US[        R                  06$ )Nc                  <   > STR                    ST R                    3$ )Nr  z for `end`, but got dtype r   )r   r   s   r7   rf   lerp.<locals>.<lambda>W!  s    /%++.HTr9   r   c                  <   > ST R                    STR                    3$ )Nr  z for `weight`, but got dtype r   )r   rE  s   r7   rf   r
  ^!  s    /%++6STZT`T`Sabr9   rM   )
rW   ri   r_   rs   r   r   r   rU   r   rQ   )r   r   rE  rR   s   ``` r7   lerpr
  R!  s     
LLsyy T 3<D&*%%;;!LLv||+b 	F	=EE r9   )r  c                4    [        XU[        R                  S9$ rg  rh  r   tensor1tensor2r  s       r7   addcmulr
  f!  s     0O0W0W r9   c                    [         R                  " [        R                  " UR                  5      =(       a     [        R                  " UR                  5      (       + S 5        [        XU[        R                  S9$ )Nc                      g)N)zFInteger division with addcdiv is no longer supported, and in a future zErelease addcdiv will perform a true division of tensor1 and tensor2. z4The historic addcdiv behavior can be implemented as zA(input + value * torch.trunc(tensor1 / tensor2)).to(input.dtype) zfor integer inputs and as z6(input + value * tensor1 / tensor2) for float inputs. z?The future addcdiv behavior is just the latter implementation: z4(input + value * tensor1 / tensor2), for all dtypes.r3   r3   r9   r7   rf   addcdiv.<locals>.<lambda>v!  s     	
r9   r  )rW   ri   rP   rT  r_   rU   r   rQ   r
  s       r7   addcdivr
  n!  s`     
LL""7==1 6&&w}}5	
		
  0O0W0W r9   c                  ,   0 n S H"  n[         U   nU H  nX0;  d  M
  X#   X'   M     M$     U R                  5        GH  u  pE[        U[        R                  R
                  5      (       a  M1  [        U[        5      (       d  [        S[        U5       35      eUR                  [        R                  R                  R                  5      " U5        [        R                  R                  UR                  5       S5      (       a  U[         S   ;   a  [        U S35      eM  UR                   (       a  M  UR                  5       S;   a  GM  SUR                  5       ;   a  ["        R%                  XE5        GM<  SUR                  5       ;   a  [&        R%                  XE5        GMh  S	UR                  5       ;   a  [(        R%                  XE5        GM  S
UR                  5       ;   a  [*        R%                  XE5        GM  [,        R%                  XE5        GM     g )N)r   post_autogradpre_autogradz$op_overload must be OpOverload, got CompositeImplicitAutogradr   z is a CompositeImplicitAutograd op, we shouldn't register meta function for it. Instead, we should let the decomposition run and write meta kernels for the base operators.>   aten::cloneaten::copy_aten::rot90aten::_to_copyaten::empty_stridedaten::constant_pad_ndaten::as_strided_scatterzmkldnn::zmkl::zonednn::zquantized::)r   itemsrs   rW   _opsHigherOrderOperatorr   r   r~   py_impl_CDispatchKeyr.   %_dispatch_has_kernel_for_dispatch_keyr  r2  is_view2_meta_lib_dont_use_me_use_register_meta_for_mkldnnimpl/_meta_lib_dont_use_me_use_register_meta_for_mkl2_meta_lib_dont_use_me_use_register_meta_for_onednn5_meta_lib_dont_use_me_use_register_meta_for_quantized'_meta_lib_dont_use_me_use_register_meta)activate_meta_tabletypregistryopoop_overloadrE   s         r7   activate_metar  !  s    9-c2C-+3=#(  9 /446
 k5::#A#ABB+z22 6tK7H6IJ  	EHH00556r:8899 ;
 
 8@@""m $; ;  A    	 [--//BGGXK,,..?DD[U{//11BGGX+"2"2"44EJJ 8<<[Ms 7r9   )Fr	  rC   )NNNFr   r2   r   r0  )Tr  )r  )r  T)FF)TT)ry  )FTN)TFF)TF)r   )g      ?N)r?   str)r3   r  r4  F)r3   r  FTN)Fr   FNFr   )NF)r   F)g      ?gUUUUUU?FN)NNNNN)r   NNr2   )NNF)        FFN)Nr  FFN)r  FNN)Nr  FNN)r  FN)FN)FNNNN)NNNF)NNNNF)Nr   FNN)NNNN)r   TT)NNr   N)d   r   r   )r   )r   FF)r  )NTTN(  r  collections.abcr   r   enumr   	functoolsr   typingr   typing_extensionsr   rW   torch._prims_commonr  rP   r	   r
   r   torch._decompr   r   r   r   
torch._opsr   torch._primsr   r   r   r   r   r   r   r   r   r   r   r   r   r   torch._prims_common.wrappersr   r    r!   r"   r#   r  r$   r%   torch.fx.experimentalr&   r  torch.nn.functionalr'   r(   torch.utilsr)   rH   r*   r+   opsr,   libraryLibraryr  r   r0  r2  r1  r8   r>   rL   rU   ra   rk   linspacelogspacer  r   taker5  r   r   r   r   cummaxcumminr   r   r   r   r   r  r   _fft_c2cr   r   r   _fft_r2cr  randpermgenerator_outr  r   r  randintr"  r  low_outr&  randr(  _fft_c2rr-  r  r9  r@  
unsqueeze_rD  _sparse_semi_structured_linearr  r_   rS  _sparse_semi_structured_mmr`  _sparse_semi_structured_addmmrd  _cslt_sparse_mmrt  index_reducer{  index_reduce_r}  index_selectr  segment_reducer  r  	unary_outr  r   r  r  r  r  r  r  r  _assert_asyncr  msgr  _printr  _make_dep_tokenr  r  _functional_sym_constrain_ranger  r  (_functional_sym_constrain_range_for_sizer  _functional_assert_asyncr  r   r  r   r  r  r  r  _linalg_eighr  r  _linalg_eigvalslinalg_eigvalsr  
linalg_eigr  r  r  r  r!  r%  r+  r?  linalg_inv_exrB  linalg_ldl_factor_exrh   rH  linalg_ldl_solverX  	linalg_lur`  linalg_lu_factor_exre  linalg_lu_solvero  	lu_unpackrv  r  	linalg_qrr  r  r  _linalg_svdr  rU  r  r  r  linalg_solve_triangularr  r  r  _linalg_detr  r  r  r  reflection_pad1dr  replication_pad1dr  r$  reflection_pad1d_backwardr)  replication_pad1d_backwardr+  r<  reflection_pad2dr>  replication_pad2drB  _weight_norm_interface_backwardrK  reflection_pad2d_backwardr%  replication_pad2d_backwardrS  rb  reflection_pad3drd  replication_pad3drh  reflection_pad3d_backwardreplication_pad3d_backwardrq  _pdist_forwardr[   rv  _pdist_backwardr}  baddbmmr  	bernoullir  
bernoulli_r  rr  r  poissonr  _fused_moving_avg_obs_fq_helperr  mmr  r  r  r  r  miopen_batch_normr  convolutionr  r
  _has_mkldnnr  r  _convolution_pointwiser  _linear_pointwiser  has_mklr  r	  _mkl_linearr  r  r  qconv2d_pointwiseqconv_pointwiser<  r  binarybinary_tensorr&  qlinear_pointwiser+  r0  linear_dynamic_fp16linear_relu_dynamic_fp16r2  r  r3  
max_pool2dr>  int4mm_packed_weight_cpurO  rU  
avg_pool2dr  r  avg_pool2d_backwardr  
avg_pool3dr  avg_pool3d_backwardr  _adaptive_avg_pool2dr  _adaptive_avg_pool3dr  _adaptive_avg_pool2d_backwardr  _adaptive_avg_pool3d_backwardr  r  adaptive_max_pool2dr  r  r  adaptive_max_pool3dr  r  r  repeat_interleaver  rt   r  r  r	  r   _unsafe_indexr*  convolution_backwardr<  addbmmrE  randint_likerI  _fused_adam__fused_adamw_ra  _fused_adamri  _int_mmrs  _convert_weight_to_int4packr  #_convert_weight_to_int4pack_for_cpur  _weight_int4pack_mmr  _weight_int4pack_mm_for_cpur  r  r  r  _dyn_quant_pack_4bit_weightr  _dyn_quant_matmul_4bitr  _weight_int8pack_mmr  _cdist_forwardr  _cdist_backwardr  _embedding_bagr<  _embedding_bag_forward_onlyr>  rA  nansumrC  median	nanmedianrE  
dim_valuesrw  r   rH  logical_not_rJ  repeatrS  zero_rU  mul_Scalardiv_logical_and_logical_or_logical_xor_rX  add_sub_re  r  subrj  rounddecimalsrl  rs  
__rshift__rw  
__lshift__r{  zeror}  rg  r  fillr  relu_r  	_add_relur  rrelu_with_noiser  rrelu_with_noise_functionalr  rrelu_with_noise_r  	index_put_unsafe_index_putr  masked_fill_r  _masked_scaler  masked_scatter_r  masked_scatterr  masked_scatter_backwardr  
index_put_r  r  bmmr  r  r  r  rs  rt  r  r  r  r8   max_pool2d_with_indices_backwardr  max_pool2d_with_indicesr  fractional_max_pool2dr  max_pool3d_with_indicesr(   max_pool3d_with_indices_backwardr0  r;  r=  rJ  grid_sampler_2d_backwardrR  rX  rZ  r]  r  onesrl  zerosro  select_scatterrs  slice_scatterrw  r   r|  r  gatherr  r  r  r  r  r  scatter_addr  scatter_add_r  r  r6  r  rw  value_reducer  scatter_r  #_scaled_dot_product_flash_attentionr  r  #_scaled_dot_product_cudnn_attentionr  0_scaled_dot_product_fused_attention_overrideabler  ,_scaled_dot_product_flash_attention_backwardr  +_scaled_dot_product_flash_attention_for_cpur  4_scaled_dot_product_flash_attention_for_cpu_backwardr  *_scaled_dot_product_attention_math_for_mpsr  '_scaled_dot_product_efficient_attentionr   0_scaled_dot_product_efficient_attention_backwardr(  ,_scaled_dot_product_cudnn_attention_backwardr*  _flash_attention_forwardr2  _flash_attention_backwardr7  _efficient_attention_forwardrC  _efficient_attention_backwardSymIntrM  r  
_scaled_mmr  r  _scaled_mm_v2r  scatter_reducetwotwo_outr  scatter_reduce_r  multinomialr	  r	  r	  r	  _upsample_nearest_exact1dr)	  _upsample_nearest_exact2dr2	  "_upsample_nearest_exact2d_backwardr7	  _upsample_nearest_exact3dr   r9	  values_stabler<	  rT	  _thnn_fused_lstm_cellrZ	  rq	  rt	  r~	  r	  r	  r	  argminr	  r	  topkr	  _segment_reduce_backwardr	  kthvaluer	  r   r	  r	  r	  r	  pixel_shuffler	  r	  	bucketize
Tensor_outr	  
Scalar_outr	  histcr	  _upsample_bilinear2d_aa_upsample_bicubic2d_aar	   _upsample_bilinear2d_aa_backwardr	  r 
  r
  r  r
  searchsortedr
  r
  embedding_dense_backwardr
  _embedding_bag_backwardr$
  _embedding_bag_dense_backwardr"
  *_embedding_bag_per_sample_weights_backwardr.
  isinr6
  	polygammar:
  _local_scalar_denser<
  r>
  r@
  rN
  r
  _grouped_mmr
  _scaled_grouped_mmr
  _softmaxr
  constant_pad_ndr
  r
  _jagged_to_padded_dense_forwardr
  r
  _native_multi_head_attentionr
  r
  special_airy_aispecial_bessel_y0special_bessel_y1special_modified_bessel_i0special_modified_bessel_i1special_modified_bessel_k0special_modified_bessel_k1!special_scaled_modified_bessel_k0!special_scaled_modified_bessel_k1special_chebyshev_polynomial_tspecial_chebyshev_polynomial_uspecial_chebyshev_polynomial_vspecial_chebyshev_polynomial_w&special_shifted_chebyshev_polynomial_t&special_shifted_chebyshev_polynomial_u&special_shifted_chebyshev_polynomial_v&special_shifted_chebyshev_polynomial_wspecial_hermite_polynomial_hspecial_hermite_polynomial_hespecial_laguerre_polynomial_lspecial_legendre_polynomial_pr
  r
  r
  r
  lerp_addcmul_addcdiv_torch._refs.nn.functionaltorch._refs.specialr  r3   r9   r7   <module>r     sK    .    '  # + +  " U     < 7 8 ) T]t_yy~~*/--*?*?PV*W ' %a )X"

8BF#3"4hr2v6F"FG 
3(* t}}-.
 

==7  /7t 		!!499==12'  3' !!))4+<+<+@+@AB%' %  C%$ t%%&I  'I 	[[$++//4;;+>+>P Xy! " !!))4+<+<+@+@ABI  CI3lV $s) 4  %%t}}'8'89:K  ;K $s)  %%t}}'8'89:8
  ;8
v t}}**+"& 3 ,3 t}}$$% **
 &
 $$dll&6&678
 **  9&   $,,"6"678 **  9& 		!!499==12%)$tPT   3 %%t}}'8'89:$Dv $DDI $Dc $DC $D  ;$DN tzz!!" #0	( t&&' ( t223
 "&$(((( ( 4-	(
 4Z( {{T!( 4(V t../
 %)	
  {{T!	 0> t112 	
$())
) ) 	) {{T!) 3)X t##$ $(";<,,;<\\;< 4-;< D=	;<
 {{T!;< ;< ;< ;< ;< %;<| t  (() 	I
	I		I 	I LL		I
 	I 	I 	I *	I t!!))* 	
			 	 LL		
 	 	 	 +	 t  (()' * ' t""**+
 "!! W
 W W d]	 W
 d] W d] W  W  W  W , WF   $(("4"456  7 txx||    $(("4"456  7 txx||  tzz!!"6 #6 tzz~~( (
 t!!))* + t!!%%& ' t{{""# $ t##++, ) -) t''//0, 1, t33;;< =
 t008896 :6& t<<DDE F
 t,,001 2

F 
C 
   F  #  N (,


 !%
$V S C 
 
F 
$ 
 
"  	  	C  !!))4+<+<+H+HIJ]N+ s T  , K" $$,,d.A.A.E.EFGB B6 B  HB  !]N+6  , " Q QF Q t**+) )F )4 )F )  ,) t""#J JF J4 JF J  $J t}})6 )$ )6 )  ) t$$%)6 )$ )6 )  &) t&&../&  T  0" 	$$,,d.M.M.Q.QR .f .6 .f . .d t!!))*&   + ))1143L3L3P3PQRT8V$ 	
  	
 666!" % S& %%--t/D/D/H/HIJ ''' '
 ' '  K'T &&(:(:;<S#s/3 f  fff>T8U   =4 ((00$2J2J2N2NOPT8V$ 	  	
 666!" % QD $$,,d.B.B.F.FGH 444 4
 4 4 4  I4n t~~S#s 	$$$ $ 	$
 666!"$  $P tTz!2 * &&(:(:;<S#f C ffn8M   =4 $$,,d.B.B.G.GHIV[$1'v '%(F"G ' 2 J'$ t''(  	""" " $J	" )"J.
.
. 49d3i .".
.
. *. 66>	.(f V   t$$%
   777 	7
 7 TM7 	7 TM7 4-7 6666)*7 &7t ,,44d6R6R6V6VWX  	
   
$  Y4 t$$%S#4( +(
+(+( +( 	+(
 +( 66>+( ) &+(^ t''(
 )
 tzz
 WW	W W 	W
 W W  Wt>#;L t$$%=  &= t%%&>  '>(< t--.\S  /S t../\T  0T2Ej t$$%=  &= t%%&>  '> ((00 &&..&&11''//''22	 \& &:<G~ t$$%=  &= t%%&>  '> &&..&&11''//''22	 \(( ((V t""#

f 

 

v 

  $

 t##$Pv PV P Pf PQW P  %P $$dll&6&678/0 '  9': &&(:(:;<&* I  =I
 t$$% & t~~ I !I
 $$dll&6&678"  9" t33;;< * =*. tww3U[[4/ 3  3,B
* .2s,,sLLs IOs #Y_	s
 3i#os s s IOd*slQ t%%--."$,,"$LL"$ ,,
"$ ,,%	"$
 $"$ "$ !&"$ "$ /"$J t''(,,LL ,, I	
 #Y 3i  I  )> 	889>9N9N&&:6 599##::BBC D, 599##55==>S ?S
 xx:?--:O:O66;
7 
uyy}}00	1	 
2	
 :?9N9N&&:6 599##55==>599##33;;<599##33::;4 < = ?4l 599##55<<=599##55CCD E >< 599##55==>599##55<<= > ?> 599##55<<=599##55CCD$ E >$L 599##77??@599##<<DDE	 F A	 =BMM<Q<QVV=9 599&&112 
 3
8 599&&??@@ A@, t&&' M (Mb(<X t''//0E 1EP t UJ   UJp t''(\K(  )K(\ t((001 2" t((001@ 2@ t1199:F ;F, t112\P  3P
	
6 	
S 	
 t''(UI+  )+\ t001\H  2H$ t''(UI'  )'T t001\(  2(
 t%%,,-* .* $$dll&6&678
  9
 ##++T-@-@-D-DEF46 

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
  G

 		&&..		0F0F0J0JKL  M" 

!!4#5#5#<#<=>@ ?@F ))11234H 44Hn ##T[[__56./q '  7'0 !!(()*' +' !!))4+=+=+E+EFG  !
 H
2   (()*  !! +!H ~B  B* 0012 3& 889: ; (()*8 +8  0012< 3< >>?@< A<"3 "3 "3 "@F 0012D!'$D 3D4 ++,-; .;( (()*< +< t""**+ & , &F t##$G  %G* t""**+
 	
`5 ,`5F t//7785 95
 ##T[[__56=$ =  7= ##T^^%;%;<=) >) !!					 Xy! "	 t  (() * t{{""#' $'& tzz!!" # 								!!  !!

 									**Z  

""DJJ$7$789 :
" &&(>(>?@ A &&(>(>?@ A tyy  !& "& 

!!4::#4#456 7 		  $))"2"234" 5" tzz!!" # t~~$$%F   & %%&'RV"  (" 0012RV; 3; &&'(KO ) &&(>(>(F(FGH" I" t  ''( )
 t!!))* + t##$	 %	 t""#6  $6 t++,! -! t&&' ((V txx 5 !5 txx~~J J6;h #-YYY 	Y 		Y
 	Y 	Y 	Y 	Y 	Y 	Y 	Y Y Y Y Y  !Y" #Y$ %Y& 'Y( )Y* +Y, -Yx;4|383838 38 		38
 	38 	38 	38 	38 	38 	38 	38 	38 38 38 38  !38" #38$ %38& '38lI2X t44<<=( >(V t++334 # 5#L t))112Q 3Qh t++,UI _  -_D t445\\  6\~%
V %
6 %
Pt  v 3 $ t,,445# 6#$ t##$8  %8" t,,-\;'! ( .!, 		!!"#. $. t&&' ) ()X 		!!499==12   3( 

""DJJNN34   5( t""**+. ,. t!!))*. +.
 C d  /
  t{{""#' $'6
 
-
b4 t''(& )&
 t  ! "
 !!	 & & ""	 889:
 #<<	< < 	<
 < < 4<< ;<~S#X& 889: #((	( ( }	(
 ( ( ( ( 4<( ;(V EEFG
  $#''	' ' }	'
 ' ' ' 4<' H'T 99( """ 
" 	"
 
" " " " " " " " " " 4<"
". 88 #	  	
  } 4<
: AA  $!"!"!" 
!" 	!"
 
!" !" !" !" }!" 4<!"
!"H ??@A
  $"&3&3&	3& 3& }	3&
 3& 3& 4-3& 4<3& 66>3& B3&l <<=> ))))	)) )) }	))
 )) )) 4<)) ?))X ==" 4-4-4- 
4- 	4-
 }4- 
4- 4- 4- 4- 4- $Z4- 4- 4<4-
4-n 99* !""" 
" 	"
 
" " " " " " " " " " "  4<!"
"0 %%  #'$(#"&HH	H H }	H
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HV &&( #'$(#,,, 
, 	,
 
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47 	47
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,,zY
,,zY \\zY \\	zY
 ,,
zY ,,%zY {{T!zY zYz ''() !%(,$( 
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 ,,% {{T!  *, !%$(*.*. IC
,,IC
,,IC %,,IC %	IC
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IC {{T!IC K 4'IC K 4'IC ICX
 ""**+, !%'+)- 
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,, %,, %	
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 ++$ 3i$&  -: ##'')<)<)D)DEF&  G&
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   (($*:*:*>*>?@	 	  A	,* 	$$d&D&D&L&LM

 	$$d&D&D&L&LM. ((00//77 "!#,- u||+, dl	
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
 									*$N t))112
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Q "
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	-K  "-K` t,,- . t++, '
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 ,,
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-" :-"` d22 3 d44 5 d44 5 d== > d== > d== > d== > dDD E dDD E tBB C tBB C tBB C tBB C tJJ K tJJ K tJJ K tJJ K t@@ A tAA B tAA B tAA B tyy  $ t||./    t||./   , 	tyy)!$,,/!$,,/
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