
    ȅi                   u   % S SK Jr  S SKrS SKrS SKrS SKrS SKrS SKrS SKrS SK	r	S SK
r
S SKrS SKJr  S SKJrJrJrJr  S SKJrJrJrJrJrJrJr  S SKJr  S SKJr  S SKrS SK r S SK!r S SK"r S SK#J$s  J%r&  S SK'J(r(  S S	K)J*r*  S S
K+J,r,  S SK-J.r.  S SK/J0r0  S SK1J2r2J3r3J4r4J5r5J6r6J7r7J8r8J9r9J:r:J;r;J<r<  S SK=J>r>J?r?  S SK@JArAJBrBJCrC  S SKDJErE  S SKFJGrGJHrHJIrIJJrJJKrK  SSKLJMrM  SSKNJOrOJPrPJQrQJRrR  SSKSJTrTJUrU  SSKQJVrVJWrWJXrXJYrYJZrZJ[r[J\r\J]r]J^r^J_r_J`r`JaraJbrbJcrcJdrdJere  SSK$JfrfJgrgJhrhJiriJjrjJkrkJlrlJmrmJnrnJoroJprpJqrq  SSKrJsrsJtrt  \(       a  SSKuJvrv  \" S5      rw\" S5      rx\E" SS/5      ry\R                  " \{5      r|0 r}S\~S '   0 rS!\~S"'   \E\ GR                   GR                     " 5       r\ R                  GR                  r\ R                  GR                  r\ R                  GR
                  r\E\ GR                   GR                     " 5       r\E\ GR                   GR                     " \ GR                  GR                  /5      r\E\ GR                   GR                     " 5       r0 rS#\~S$'   \ R                  GR                  rGSoS% jr    GSpS& jrGSqS' jr    GSrS( jrGSsS) jr    GStS* jr      GSuS+ jr\" \GR(                  \GR*                  \GR,                  \GR.                  \GR0                  \GR2                  \GR4                  \GR6                  \GR8                  \GR:                  \GR<                  \GR>                  \GR@                  \GRB                  /5        \ GRD                  \ GRF                  \ GRH                  \ GRJ                  \ GRL                  \ GRN                  \ GRP                  \ GRR                  \ GRT                  \ GRV                  \ GRT                  \ GRX                  \ GRZ                  S,.rGSvS- jrGSwS. jrGSxS/ jr      GSyS0 jrS1 r      GSzS2 jrGS{S3 jr            GS|S4 jr      GS}S5 jr          GS~S6 jrS7\7GRr                  S7\}4   GSS8 jjrS9 rGSS: jr     GSS; jrGSS< jrGSGSS= jjr\" \ GR                  GR                  SS>9S? 5       r\" \GR                  SS>9GSS@ j5       rS7SA.GSSB jjr\" \GR                  GR                  SS>9GSSC j5       rS7S7SD.GSSE jjr\" \GR                  SS>9GSGSSF jj5       rSSG\7GRr                  S7SSS7S4SH jr\n" SI\7GR                  SSJ9  \" \GR                  SGSSK9GSSL j5       rSM r\" 5          GSSN jr\" \GR                  S7SSK9SO 5       r\" \GR                  S7SSK9SP 5       r\" \GR                  \GR                  \GR                  \GR                  \GR                  /5      SQ 5       r\" \SR5      (       a  \" \GR                  5      " \5        \" \GR                  SS>9GSSS j5       r\" \GR                  SS>9GSST j5       r\" \GR                  /5      GSSU j5       r\" \GR                  5      SV 5       r\" \GR                  5      SW 5       r\" \GR                  5      SX 5       r\" \GR                  5      SY 5       r\" \GR                  GR                  5      SZ 5       r\" \GR                  5      S[ 5       r\" \GR                  SS>9S\ 5       r\" \GR                  SS>9S] 5       r\" \GR                  SS>9S^ 5       r\" \GR                  5      S_ 5       r\" \GR                  SS>9\" \GR                  SS>9\" \GR                  SS>9GSS` j5       5       5       r\" \GR                  SS>9Sa 5       r\" \GR                  SS>9GSSb j5       r\" \GR(                  SS>9GSSc j5       r\" \GR                  SS>9GSSd j5       r\" \GR*                  SS>9GSSe j5       rGSSf jr\" \GR                  SS>9                GSSg j5       rSh r\" \GR                  GR                  5      Si 5       r\" \GR                  GR                  5      Sj 5       r\" \GR                  SS>9SSk.                 GSSl jj5       r\" \GR                  GR                  SS>9              GSSm j5       r\" \GR                  GR                  SS>9SSk.               GSSn jj5       r\" \GR                  GR                  SS>9              GSSo j5       r\" \GR                  GR                  SS>9SSk.               GSSp jj5       r\" \GR                  5      GSSq j5       r\" \GR                  SS>9GSGSSr jj5       r\" \GR                   SS>9GSGSSs jj5       Gr \" \GR                  SS>9GSGSSt jj5       Gr\" \GR                  SS>9Su 5       Gr\" \GR                  SS>9GSSv j5       Gr\" \GR                  SS>9GSSw j5       Gr\" \GR
                  SS>9GSSx j5       Gr\" \GR                  SS>9Sy 5       Gr\" \GR                  SS>9Sz 5       Gr\" \GR                  SS>9S{ 5       GrGSS| jGr	\" \GR                  5      GSS~ j5       Gr
GSS jGr\GR                  S 5       GrGSGSS jjGrGSGSS jjGrGSGSS jjGrGSS jGrS Gr\" \ R                  GR&                  GR(                  SS>9S 5       Gr\" \GR*                  SS>9S 5       Gr\" \GR,                  SS>9S 5       Gr\" \GR.                  GR0                  SS>9S 5       Gr\" \GR4                  5      S 5       Gr\GR6                  " S5      S 5       GrS GrG\" \GR<                  GR                  5      GrG\" \GR<                  GR@                  5      Gr!G\" \GRD                  GR                  5      Gr#G\" \GRD                  GR@                  5      Gr$G\" \GRJ                  5        G\" \ R                  GRL                  GRN                  GR                  5        G\" \ R                  GRL                  GRP                  GR                  5        \" \GR<                  5      S 5       Gr\" \GRD                  5      S 5       Gr"\" \PGRR                  SS>9S 5       Gr*\" \PGRV                  SS>9GSS j5       Gr,\" \PGRZ                  SS>9S 5       Gr.\" \PGR^                  SS>9S 5       Gr0\" \PGRb                  SS>9S S.GSS jj5       Gr2\" \PGRJ                  SS>9S S.         GSS jj5       Gr3GSS jGr4GSS jGr5\" \GRl                  GRn                  SS>9S7S7SSS.             GSS jj5       Gr6\" \GRp                  \7GRr                  S>9S7S7S.       GSS jj5       Gr8S Gr:S Gr;S Gr<S Gr=S Gr>S Gr?S Gr@S GrAG\" \GR                  5        G\" \GR                  5        G\" \GR                  5        G\" \GR                  S7S9  G\" \GR                  GR                  S7S9  G\" \GR                  G\;5        G\" \GR                  S7S9  G\" \GR                  S7S9  \ GR                  GR                  5       (       a  G\" \GR                  S7S9  \ GR                  GR                  5       (       a  G\" \GR                  S7S9  G\" \GR                  5        G\" \GR                  5        G\" \GR                  5        G\" \GR                  GR                  5        G\" \GR                  GR                  5        G\" \GR                  5        G\" \GR                  GR                  5        G\" \GR                  GR                  5        G\" \GR                  GR                  5        G\" \GR                  5        G\" \GR                  S7S9  G\" \GR                  G\:5        G\" \GR4                  G\@5        G\" \GR                  G\:5        G\" \GR                  G\;5        G\" \GR                  G\:5        G\" \GR                  G\;5        G\" \GR                  G\;5        G\" \GR                  G\;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                  G\: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                  G\;5        G\" \GR                  5        G\" \GR                  5        G\" \GR                  G\;5        G\" \GR                  5        G\" \GR                  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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                   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                  GR                  5        G\" \GR4                  GR                  S7S9  G\" \GR6                  G\:5        G\" \ GR8                  GR:                  GR<                  5        G\" \ GR8                  GR:                  GR>                  5        G\" \ GR8                  GR:                  GR@                  5        G\" \GRB                  5        G\" \GRD                  5        G\" \GRF                  G\;5        G\" \GRH                  5        G\" \GRJ                  5        G\" \GRL                  5        G\" \GRN                  5        G\" \GRP                  5        G\" \GRR                  GRT                  5        G\" \GRV                  GR                  G\AS7S9  G\" \GRX                  GR                  G\AS7S9  G\" \GRZ                  GR                  G\AS7S9  G\" \GR\                  GR                  G\AS7S9  G\" \GR^                  GR                  G\AS7S9  G\" \GR`                  GR                  G\AS7S9  G\" \GRb                  GR                  G\AS7S9  G\" \GRd                  GR                  G\AS7S9  G\" \GRf                  GR                  G\AS7S9  G\" \GRh                  GR                  G\AS7S9  G\" \GRj                  GR                  G\A5        G\" \GRl                  GR                  G\A5        G\" \GRn                  GR                  G\A5        G\" \GRp                  GR                  G\A5        G\" \GRr                  5        G\" \GRt                  GRn                  SGS9  G\" \GRv                  GR                  G\;5        \" \GRx                  SS>9GSS j5       Gr\" \GRz                  5      SS.S j5       GrS Gr\" \S5      (       a  \" \GR~                  5      " G\5        \" \GR                  5      S 5       Gr\" \GR                  SS>9GSS j5       Gr\" \GR                  SS>9GSS j5       GrS Gr\" \ GR                  \GR                  /5      SSSS7S.S j5       r\" \ GR                  5      GSS j5       Gr\" \ GR                  5      S 5       Gr\" \GR                  5      S 5       Gr\" \GR                  5      S 5       Gr\" \GR                  5       GSSSS.S jj5       GrS GrS GrS Gr\" \ GR                  \GR                  /5      SSSSSSS.S j5       GrS GrS Gr\" \GR                  5      " G\" G\5      5      GrG\" G\" S5      5      GrG\" G\" S 5      5      GrS Gr\" \GR                  5      SSSSS.S j5       Gr\" \GR                  5      SSSSS.S j5       Gr\" \GR                  5      SSSSS.S j5       Gr\" \GR                  GR                  5      S 5       Gr\" \ GR                  \GR                  /5      S 5       Gr\" \GR                  SS>9GSS j5       Gr\" \GR                  SS>9GSS j5       GrS Gr GSS jGrS GrGSS jGr\" \GR                  SS>9S 5       Gr\" \GR                  SS>9S 5       Gr\" \GR                  SS>9GSS j5       Gr\" \GR                  5      GSS j5       GrS GrS Gr\" \GR                  SS>9GSS j5       Gr\" \PGR                  SS>9GSS j5       GrGSS jGrG\" \GR                  GR                  S7S9GrG\" \GR                  GR                  S7S9Gr\" \GR                  SS>9S 5       Gr\" \GR                  SS>9S 5       Gr\S 5       Gr\" \GR                  SS>9GSS j5       Gr\" \GR                  SS>9GSS j5       GrSSGS.       GSS jjGr\" \GR                  SS>9SS.GSS jj5       Gr\" \GR                  SS>9GSS j5       Gr\" \GR                  SS>9GSS j5       Gr\" \GR                  SS>9GSS j5       Gr\" \GR                  SS>9SGS.GSS jj5       Gr  GS     GSS jjGr\" \GR                  GR                  5      GSGSS jj5       Gr\" \GR                  GR                  5      GSGSS jj5       Gr\" \GR>                  GR                  5       GS   GSS jj5       r\" \GR@                  GR                  5       GS   GSS jj5       r\" \GR                  GR                  5         GS     GSS jj5       Gr\" \GR                  GR                  5         GS     GSS jj5       GrS Gr\" \GR                  GR                  5      S 5       Gr        GSS jGr\" \GR                  SS>9GSS j5       GrGSS jGrGSS jGr GSS jGr GSS jGrSS.S jGrS GrSS.S jGrS Gr\" \GR                  SS>9 GSS j5       Gr          GSS jGr\" \GR                  SS>9S 5       Gr	S Gr
\" \GR6                  SS>9    GSS j5       r\" \GR8                  SS>9    GSS j5       rG\" \GR:                  GR                  S7S9Gr\" \GR:                  SS>9S 5       rGSS jGrGS  GrGS GrGS GrG\" \GR                   GR                  S7S9Gr\" \GR                   5      GS 5       GrG\" \GR$                  GR                  S7S9Gr\" \GR$                  5      GS 5       GrGS Gr\" \GR*                  5      GS 5       Gr\" \GR,                  5      GS 5       GrGS Gr\" \GR0                  GR                  5       GSGS	 j5       GrG\" \GR,                  GR                  S7S9GrG\" \GR4                  GR                  S7S9Gr\" \GR,                  SS>9     GSGS
 j5       r\" \GR4                  SS>9     GSGS j5       GrGS GrG\" \GR.                  GR                  S7S9Gr\" \GR.                  SS>9 GSGS j5       rG\" \GR<                  GR                  S7S9Gr\" \GR<                  SS>9 GSGS j5       GrGS Gr SGS.GS jGr!GSGSGS jjGr"GS Gr#\" \GRH                  5      GSSGS.GS jj5       Gr$GS Gr%GS Gr&GS Gr'GS Gr(\" \GRR                  \GRR                  /5      GSSS7GS.GS jj5       Gr*\" \GRV                  5      GSSS7GS.GS jj5       Gr+GS Gr,\GS 5       Gr-G\" \GR\                  GR^                  S7S9Gr0G\" \GR\                  GRb                  S7S9Gr2G\" \GR\                  GRf                  S7S9Gr4\" \GR\                  SGGS9GS  5       Gr.GSGS! jGr5\" \GRl                  5      GS" 5       Gr6\" \GRn                  SS>9GSGS# j5       Gr7\GS$ 5       Gr8\GS% 5       Gr9\" \GRt                  SGGS9GSGS& j5       Gr;\" \GRx                  /SGGS9GS' 5       Gr<GSGS( jGr=\" \GRt                  /SGGS9GS) 5       Gr>\" \GR~                  \GRt                  GRn                  /SG\7GR                  SK9GS* 5       Gr:\" \GR                  \GR                  /SGGS9GS+ 5       Gr@\" \GR                  \GR                  /5      GSSGS.GS, jj5       GrBG\" \GR                  GR                  5      GrDG\" \GR                  GR                  5      GrFG\" \GR                  GR                  5      GrHG\" \GR                  GR                  5      GrJG\" \GR                  GR                  5      GrL\" \GR                  5      GSGS- j5       GrC\" \GR                  5      GSGS. j5       GrE\" \GR                  5      GS/ 5       GrG\" \GR                  SS>9GSGS0 j5       GrI\" \GR                  SS>9GSGS1 j5       GrK\" \GR                  5      GSSGS.GS2 jj5       GrM\" \GR                  5      GSGS3 j5       GrO\" \GR                  SS>9GSGS4 j5       GrQ\" \GR                  SS>9GSGS5 j5       GrS\" \GR                  5      " G\"" GS65      5        \" \GR                  5      " G\"" GS75      5      GrV\" \GR                  5      " G\"" GS85      5      GrX\" \GR                  5      " G\"" GS9\ GRL                  GS:95      GrZ\" \GR                  5      " G\"" GS;\ GRL                  GS:95      Gr\\" \GR                  SGGS<GS=9Gr]G\" \GR                  GR                  S7S9Gr^\" \GR                  GR                  SS>9SS}S7GS>.GS? j5       Gr_\" \GR                  GR                  SS>9GSGS@ j5       GruGSGSA jGr`GSGSB jGraG\`" \GR                  5      GrbG\a" \GR                  5      GrcG\`" \GR                  5      GrdG\`" \GR                  5      Gre\" \GR                  5      GrfG\a" \GR                  5      GrgG\a" \GR                  5      Grh\" \GR                  5      Gri\" \GR                  SGGSC9GrjG\a" \GR                  5        G\a" \GR                  5        \" \GR                  5      Grm\" \GR                  5      Grn\" \GR                  5      Gro\" \GR                  GSDGSE9Grp\" \GR                  5      Grq\" \GR                  5      Grr\" \GR                  5      GrsG\`" \GR                  5        G\`" \GR                  5      Gru\" \GR                  \7GR                  S>9" G\u5        G\`" \GR                  5        G\`" \GR                  5        G\`" \GR                  5        G\a" \R                  5        \" \GR                  SSG\ GRX                  GSF9Grz\" \GR                  SSG\ GRX                  GSF9Gr{\" \GR                  SSG\ GRX                  GSF9Gr|\" \GR                  SSG\ GRX                  GSF9Gr}\" \GR                  5      Gr~\" \GR                  5      Gr\" \GR                   5      " G\~5        \" \GR                  5      " G\5        \" \GR                  5      Gr\" \GR                  5      GrmG\`" \GR                  5      Gr\" \GR                  5        \" \GR
                  GSGGSE9Gr\" \GR                  5        \" \GR                  \ GRX                  GS:9  \" \GR                  5      " G\5        \" \GR                  \ GRX                  GS:9  \" \GR                  \ GRX                  GS:9  \" \GR                  \ GRX                  GS:9  \" \GR                  \ GRX                  GS:9Gr\" \GR                  \ GRX                  GS:9  \" \GR                  \ GRX                  GS:9  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        SGSHGKGJGrGJGr  GSI GrG\ HR  GrG\" \G\5       H  u  GrGrGr\" G\G\G\G\GSJ9  M     G\" \G\5       H  u  GrGrGr\" G\G\G\G\GSJ9  M     MT     \" \GRL                  GRN                  G\]SGGSC9Gr\" \GRL                  GRb                  G\]SGGSC9Gr\" \GRL                  GRn                  G\]SGGSC9  \" \GRT                  GRN                  G\<5      Gr\" \GRT                  GRn                  G\<5        \" \GRT                  GRb                  G\<5      Gr\" \GRZ                  GRN                  G\j5        \" \GRZ                  GRb                  G\j5        \" \GR\                  GR                  G\5        \" \GR^                  GR                  G\m5        \" \GR`                  GRb                  G\.5        \" \GR`                  GRN                  G\.5        \" \GR`                  GRb                  G\.5        \" \GRd                  GRN                  G\:5      Gr\" \GRd                  GRn                  G\:5        \" \GRd                  GRb                  G\:5      Gr\" \GRj                  G\h5        \" \GRl                  G\b5        \" \GRn                  GRN                  G\~5        \" \GRn                  GRb                  G\~5        \" \GRp                  GRN                  G\5        \" \GRp                  GRb                  G\5        \" \GRr                  GRN                  G\~5        \" \GRr                  GRb                  G\~5        \" \GRt                  GRN                  G\5        \" \GRt                  GRb                  G\5        \" \GRv                  G\5        \" \GRx                  G\5        \" \GRz                  G\5      GrGSK GrG\" \GR                  GRN                  \GRL                  GRN                  G\5        G\" \GR                  GRb                  \GRL                  GRb                  G\5        G\" \GR                  GRN                  \GRT                  GRN                  G\5        G\" \GR                  GRb                  \GRT                  GRb                  G\5        G\" \GR                  GRN                  \GRd                  GRN                  G\5        G\" \GR                  GRb                  \GRd                  GRb                  G\5        G\" \GR                  GR                  \GRz                  GR                  G\5        GSL GrG\" \GR                  G\]5        G\" \GR                  G\n5        G\" \GR                  G\o5        G\" \GR                  G\p5        G\" \GR                  G\q5        G\" \GR                  G\r5        G\" \GR                  G\s5        G\" \GR                  G\<5        G\" \GR                  GRn                  G\:5        G\" \GR                  GR                  G\;5        G\" \GR                  G\z5        G\" \GR                  G\{5        G\" \GR                  G\|5        G\" \GR                  G\}5        G\" \GR                  G\j5        G\" \GR                  G\f5        G\" \GR                  G\g5        \" \GR                  5      " G\n5        \" \GR                  5      " G\o5        \" \GR                  5      " G\q5        \" \GR                  5      " G\r5        \" \GR                  5      " G\s5        G\" \GR                  \GR                  5        G\" \GR                  \GR                  5        G\" \GR                  \GR                  5        G\" \GR                  \GR                  5        G\" \GR                  \GR                  5        \" \GR                  5      GSGSM j5       Gr\" \GR                  GR                  5      GSN 5       Gr\" \GR                  GR                  5      GSO 5       Gr\" \GR                  5      GSP 5       Gr\>GR                  " 5        H  u  GrGr\" \?" G\5      5      " G\5        M      \" \ GR                  5      GSQ 5       Gr\" \GR4                  5      GSR 5       Gr\" \ R                  GR                  GR                  5      GSS 5       Gr\" \ R                  GR                  GR                  5      GST 5       Gr\" \ R                  GR                  GR                  GR                  5      GSU 5       Gr\" \ R                  GR                  GSV5      (       a;  \" \ R                  GR                  GRn                  GR                  5      GSW 5       Gr\" \ R                  GR                  GR                  5      SS.GSX j5       GrS GSYGKGJGr  G\" G\5        \" \,5      GSZ 5       Gr\" \ R                  GR                  GR                  SS>9  GSGS[ j5       Gr\" \ R                  GR                  GR                  SS>9GSGS\ j5       Gr\" \ R                  GR                  GR                  SS>9" \GR                  " G\SGGS]95        \" \ R                  GR                  GR                  SS>9GSGS^ j5       GrGSGS_ jGrS GS`GKGJ Gr   \" G\ SS>9GSa 5       Gr\" \ GR                  GR                  SS>9SGSb.GSGSc jj5       Gr\" \*SS>9    GSGSd j5       Gr\" \ R                  GR
                  GR
                  GR                  5      GSe 5       Gr\" \ R                  GR
                  GR                  GR                  5      GSf 5       Gr\" \ R                  GR                  GR                  SS>9GSg 5       GrSGShGKGJ	Gr	  G\	" 5         \" \PGR                  SS>9GSi 5       Gr
SGSjKNGJGr  \M" G\5        SGSkKNGJGr  G\GR                  " 5         G\GR                  " 5         SGSlKNGJGr  G\GR                   " 5         SGSmKNGJGr  G\GR$                  " 5         \GR&                  GSGSn j5       Grg(      )annotationsN)defaultdict)Callable
CollectionIterableSequence)AnycastOptionalTYPE_CHECKING	TypeGuardTypeVarUnion)	ParamSpec)patch)counters)associative_scan_op)triton_kernel_wrapper_mutation)FakeScriptObject)get_layout_constraint_tag)canonicalize_dimcanonicalize_dimscheckdtype_to_typeelementwise_dtypesELEMENTWISE_TYPE_PROMOTION_KINDget_computation_dtypeis_boolean_dtypeis_float_dtypeis_integer_dtypeNumber)magic_methodsmethod_to_operator)free_unbacked_symbolshas_free_unbacked_symbolsresolve_unbacked_bindings)
OrderedSet)CeilDivFloorDivIdentityModModularIndexing   )import_submodule   )configinductor_primsirtest_operators)decompositionsget_decompositions)BaseView	DtypeView
ExpandViewIndexingConstantIRNode	is_triton
MutableBoxOnlineSoftmaxReductionops_wrapperPermuteView	Pointwise	ReductionSqueezeView	TensorBoxvalidate_irView)ceildivdecode_device
is_dynamicis_gpuis_pointwise_useis_view,needs_fallback_due_to_atomic_add_limitationspad_listlike#register_op_dtype_propagation_rules#register_op_requires_libdevice_fp64sympy_productuse_scatter_fallback)opsV)ReductionType_T_Pztorchvision::roi_alignzaten::index_add8dict[Union[Callable[..., Any], str], Callable[..., Any]]	loweringsz9dict[torch._ops.OpOverload, Optional[Callable[..., Any]]]_maybe_layout_constraintsz2dict[torch._ops.OpOverload, torch._ops.OpOverload]inplaceable_foreach_opsc                     [         R                  R                  R                   H=  n U R                   H*  nUR                  S:X  a  UR
                  [        ;   a  M)      g   M?     g)Ncall_functionTF)rS   graphcurrent_nodeusersoptargetforeach_ops)nodeusers     R/home/james-whalen/.local/lib/python3.13/site-packages/torch/_inductor/lowering.pycur_node_has_non_foreach_usersrf      sI    $$**JJDGG.DKK;4N  +
     c                   [        [        5      nSn[        U 5       H  u  p4[        U[        5      (       d  SnU4n[        U6 (       + =(       d    [        R                  nS nU H4  n[        U[        5      (       d  M  UR                  R                  5       n  O   Uc   S5       eU(       a  Uu  nXU4   R                  X445        M     U$ )NFTz.foreach op should have at least one tensor arg)r   list	enumerate
isinstancer   rH   r0   #combo_kernel_foreach_dynamic_shapesrC   data
get_deviceappend)	arg_pairsoutunpack_argsiargsuse_foreachdevicets           re   group_foreach_argsrx      s     d
CKY'$))K7DD!!OV%O%O 	 A!Y''**,  !S#SS!GT[!"))1)4 (  Jrg   c                    [        U [        R                  R                  5      (       d  g[	        U SS9=n(       a  [        U5      $ U [        ;   a	  [        U    $ g)zHGet layout constraints. Returns None if there are no layout constraints.NF)with_default)rk   torch_ops
OpOverloadr   tag_to_layout_constraintrY   )fnmaybe_layout_tags     re   maybe_layout_constraintsr      sR    b%**//004ReLLL'(899	&&(,,rg   c                   U [         R                  R                  R                  :X  a  [        $ U [         R                  R                  R
                  :X  a  [        $ U [         R                  R                  R                  :X  a  [        $ U [         R                  R                  R                  :X  a  g [        SU  35      e)NzUnknown layout constraint tag: )r{   _CTagneeds_exact_stridesconstrain_to_fake_tensorsneeds_contiguous_stridesrequire_contiguous_stridesneeds_fixed_stride_orderconstrain_to_fx_stridesflexible_layoutAssertionError)tags    re   r~   r~      s     ehhll...((
ehhll333))
ehhll333&&
ehhll***
:3%@
AArg   c                .    U (       d  [        SU 35      eg )Nzinductor does not support NotImplementedErrorcondmsgs     re   
assert_nyir      s    !$>se"DEE rg   c                  ^  [        T [        [        [        [        45      (       a  T  Vs/ s H  n[        U5      PM     sn$ [        T [        R                  R                  5      (       a  [        R                  T 5        g [        T [        R                  R                  5      (       a-  [        R                  U 4S jT R                  5        5       5        g s  snf )Nc              3  <   >#    U  H  n[        TU5      v   M     g 7fN)getattr).0overloadr   s     re   	<genexpr>,add_needs_realized_inputs.<locals>.<genexpr>   s      %
2@hGB!!.   )rk   ri   settupler'   add_needs_realized_inputsr{   r|   r}   needs_realized_inputsaddOpOverloadPacketupdate	overloads)r   xs   ` re   r   r      s     "tS%455689b)!,b99"ejj++,,!!"%
 	 
B

33	4	4$$ %
24,,.%
 	
  :s   Cc                    [        U [        R                  R                  5      (       a*  U R	                  5        H  nU[
        [        X5      '   M     g U[
        U '   g r   )rk   r{   r|   r   r   rY   r   )r   
constraintr   s      re   add_layout_constraintr      sH     "ejj1122H?I%gb&;< ' )3!"%rg   )r   r/   r-                     	   
         c                p    [        U [        5      (       d  U $ U [        ;   d   SU  S35       e[        U    n U $ )Nzid z missing from DTYPE_ID_LOOKUP)rk   intDTYPE_ID_LOOKUPdtypes    re   decode_dtyper     s@    eS!!O#Os5'1N%OO#E"ELrg   c                   [        U [        5      (       a9  [        U R                  5       5      =(       d    [	        U R                  5       5      $ [        U [
        R                  5      (       a  U R                  SL $ [        U [        5      $ NT)	rk   rC   r    	get_dtyper   sympyExpr
is_integerr   r   s    re   is_integer_typer     s^    !Y.Q2B1;;=2QQ	Auzz	"	"||t##!S!!rg   c                ~    [        U [        5      (       a  [        U R                  5       5      $ [        U [        5      $ r   )rk   rC   r   r   boolr   s    re   is_boolean_typer   '  s-    !Y..!T""rg   c                b    SS jnU Vs/ s H
  o2" U5      PM     nn[        USU 06u  pVU$ s  snf )Nc                    [        U [        [        R                  45      (       a  U $ [	        U R                  5       5      n[        R                  " S/U-  U R                  5       S9$ )Nr/   r   )	rk   r!   r   Basiclenget_sizer{   zerosr   )inpdims     re   construct_input+get_promoted_dtype.<locals>.construct_input1  sJ    cFEKK011Jclln%C;;sSy@@rg   type_promotion_kind)r   r	   returnr	   )r   )r   rt   r   arginps_r   s          re   get_promoted_dtyper   .  s?    A -11DSOC DD1!4Q=PQHAL 2s   ,c                R   [        U [        [        45      (       d  U /n O[        U 5      n [        U 5       Hm  n[        U[        R                  R
                  5      (       d  M.  UR                  5        H+  n[        X5      nU[        ;  d  M  U R                  U5        M-     Mo     U $ r   )
rk   ri   r   r{   r|   r   r   r   rX   ro   )aten_fnr   r   other_fns       re   get_overloadsr   >  s}    ge}--)w-7mb%**5566LLN"209,NN8, +  Nrg   c                    [        U [        R                  R                  5      (       a  XR                  ;   $ [        U [        R                  R
                  5      (       a  XR                  5       ;   $ gNF)rk   r{   r|   r   _qualified_op_namer}   name)r`   	namespaces     re   in_namespacer   N  sS     "ejj11221111	B

--	.	.GGI%%rg   c           	     H   [        U R                  [        R                  5      (       a  [	        U R                  5       5      (       a  U $ U R                  5        Vs/ s H,  n[        R                  R                  R                  U5      PM.     nnU R                  5       nUby  UR                  S:X  ai  XA:w  ad  [        U5      S:X  d  [        U5      S:X  aF  US   S:X  a=  [        [        R                  " [        R                  R!                  XS5      5      5      $ U $ s  snf )z:
Copy cpu scalar if doesn't not match with given `device`
cpur   r/   F)rk   rm   r2   ReinterpretViewr%   r   rS   r]   sizevarssize_hint_or_throwrn   typer   rC   
StorageBox
DeviceCopycreate)r   rv   ssize
cur_devices        re   maybe_copy_cpu_scalarr   X  s     affb00115N	

6 6 <=JJLILqAGG//2LDIJOOu$ Y!^D	Q47a<r}}';';A5'QRSSH Js   3Dc           	     ~  ^ ^^^ [        T 5       VVs/ s H  u  pV[        U[        5      (       d  M  UPM      nnnTR                  5        VV	s/ s H  u  p[        U	[        5      (       d  M  UPM      n
nn	U(       d  U
(       d  T T4$ U(       d  U(       Ga:  U(       a  [        R
                  mO{T  Vs/ s H=  n[        U[        [        R                  45      (       d  [        US5      (       d  M;  UPM?     nnUR                  S TR                  5        5       5        [        USU06mU(       a  T US      OTU
S      R                  5       mU H  n[        T U   T5      T U'   M     U
 H  n[        TU   T5      TU'   M     S	UU4S jjnT  Vs/ s H
  o" U5      PM     snm TR                  5        VV	s0 s H  u  pX" U	5      _M     sn	nmU(       GaF  [        [!        ["        R$                  " U 4S jU 5       U4S jU
 5       5      5      6 n[!        US   R'                  5       5      n[)        X~S[+        U5       5       H
  u  pVUT U'   M     [)        X[+        U5      S 5       H
  u  pUTU'   M     [-        [+        T 5      5       HD  n[        T U   [.        R0                  5      (       d  M'  [2        R4                  " T U   U5      T U'   MF     T HD  n[        TU   [.        R0                  5      (       d  M'  [2        R4                  " TU   U5      TU'   MF     T T4$ s  snnf s  sn	nf s  snf s  snf s  sn	nf )
z:
Transforms arguments for broadcasting and type promotion
r   c              3  L   #    U  H  n[        US 5      (       d  M  Uv   M     g7f)r   N)hasattr)r   as     re   r   !transform_args.<locals>.<genexpr>  s     !T_7@S!!_s   $	$r   r   c                   > [        U [        5      (       a  [        U T5      $ [        U [        R                  5      (       a   [        R                  " U R
                  TTS9$ U $ )Nvaluer   rv   )rk   rC   to_dtyper2   Constantr   )r   rv   r   s    re   promotetransform_args.<locals>.promote  sJ    #y))U++C--{{%OO
rg   c              3  .   >#    U  H
  nTU   v   M     g 7fr    )r   rs   rt   s     re   r   r     s     3lT!Wl   c              3  .   >#    U  H
  nTU   v   M     g 7fr   r   )r   kkwargss     re   r   r     s     71VAYr   N)r   r	   r   r	   )rj   rk   rC   itemsr{   r   r!   r   r   r   extendvaluesr   rn   r   broadcast_tensorsri   	itertoolschainr   zipr   ranger2   r   r8   r   )rt   r   	broadcastr   convert_input_to_boolrs   r   args_indicesr   vkwargs_indicesr   promoting_argsr   broadcastedr   rv   r   s   ``              @@re   transform_argsr  l  s    #,D/N/$!Z95MA/LN$*LLNONDAjI6NaNNOV|3 JJE
 Aa&%++!67771g;N    !!!TV]]_!TT&$7E &2Da!vnQ>O7P
*, 	 A+DGV<DG   A-fQi@F1I  	 	 %))Dq
D),2LLN;NDA!WQZ-N;'3l377
 KN++-.2EC4E&FGDADG HC4E4G(HIDAF1I J s4y!A$q'2;;//$++DGT:Q " A&)R[[11&--fQi>q	  <I OO> *;s.   L#L#L)-L)3:L/1L/L49L9c                   ^ [         R                  " T5      SU4S jj5       n[        U 5      n[        R	                  U5        [
        R	                  [        R                  X25      5        U$ )a  
Add a foreach lowering to lowerings dict.

Arguments:
    aten_fn: torch.ops.aten.* fn we are lowering
    decomp_fn: alternate implementation on our IR
    broadcast: True to apply broadcasting to tensor inputs
    type_promotion_kind: kind of type promotion applied to tensor inputs, `None` means no type promotion
    convert_input_to_bool: some logical ops require inputs are converted to bool
c                 P   > [        U 5      S::  d   eT" U 0 UD6n[        U5        U$ )Nr-   )r   rD   )rt   r   rq   	decomp_fns      re   wrapped+_register_foreach_lowering.<locals>.wrapped  s/    4yA~~((C
rg   )rt   r	   r   r	   r   r	   )	functoolswrapsr   rb   r   rX   dictfromkeys)r   r  r  aten_fnss    `  re   _register_foreach_loweringr    sV     __Y   W%Hx T]]856Nrg   c                   ^ ^^^^ [         R                  " T5      U UUUU4S j5       n[        T 5      m UR                  [        R                  T U5      5        U$ )a  
Add a lowering to lowerings dict

Arguments:
    aten_fn: torch.ops.aten.* fn we are lowering
    decomp_fn: alternate implementation on our IR
    broadcast: True to apply broadcasting to tensor inputs
    type_promotion_kind: kind of type promotion applied to tensor inputs, `None` means no type promotion
    convert_input_to_bool: some logical ops require inputs are converted to bool
c                 v  > [        U 5      n [        U5      nSn[        U 5      S:X  a.  [        U S   [         [        45      (       a  Sn[        U S   5      n [        S T 5       5      (       d  [        S U 5       5      (       a   S5       e[        XTTT5      u  pU(       a  U /n T" U 0 UD6n[        U5        U$ )NFr/   r   Tc              3  X   #    U  H   o[         ;   =(       d    [        US 5      v   M"     g7f)_c10d_functionalN)	fallbacksr   )r   r   s     re   r   6_register_lowering.<locals>.wrapped.<locals>.<genexpr>  s&      
PW"9_DR1C DDPWs   (*c              3  *   #    U  H	  oS :H  v   M     g7f)rq   Nr   r   r   s     re   r   r    s     6v!:v   zout= ops aren't yet supported)	ri   r  r   rk   r   allanyr  rD   )	rt   r   unpackedrq   r   r  r  r  r   s	       re   r  #_register_lowering.<locals>.wrapped  s    t*!%ft9>ja4-@@HQ=D 
PW
 
 
 6v666W8WW6%)%8:O
 6D((C
rg   )r  r  r   r   r  r  )r   r  r  r   r  lowering_dictr  s   `````  re   _register_loweringr'    sO    & __Y   6 G$Gw89Nrg   Fc           	     <    [         R                  " [        U UUUUS9$ )z#
Shim to support decorator syntax.
)r  r   r  r&  )r  partialr'  )r   r  r   r  r&  s        re   register_loweringr*    s)     /3# rg   c                >   [        U5      nU (       a  X:X  a  U$ / n[        R                  " [        U 5      [        U5      [        R
                  R                  S9 GH*  u  p4[        R                  R                  R                  U5      (       a  UR                  U5        MG  [        R                  R                  R                  U5      (       a  UR                  U5        M  [        R                  R                  R                  X45        [        [        R                  " U5      R                  5      [        [        R                  " U5      R                  5      :  a  UR                  U5        GM  UR                  U5        GM-     [        [        U5      5      $ )z
Broadcasting logic based on symbolic shapes.

We give the shapes 0 and 1 concrete values, while all other shapes
are symbolic sympy formulas.
)	fillvalue)r   r  zip_longestreversedr   SOnerS   r]   r   is_size_one_or_falsero   check_equalsr   expandfree_symbols)r   boutputr   ys        re   broadcast_symbolic_shapesr8  $  s    	aAF%%hqk8A;%''++V770033MM!WW22155MM!GG))!/5<<?//03u||A7S7S3TTa a  W &!""rg   c                  ^ Ub
  Ub   S5       eUc  Uc  [         R                  n[        S U  5       5      (       d  U $ [        S U  5       5      (       a2  U=(       d    [	        U SU06mU4S jnU  Vs/ s H
  oC" U5      PM     sn$ [        S U  5       5      n/ nU  GH!  n[        U[        [        45      (       an  UR                  [        R                  " [        R                  " XER                  5       UR                  5       S9[!        UR#                  5       5      5      5        M  [        U[$        R&                  5      (       ad  UR                  [        R                  " [)        XER                  5       UR                  5       S9[!        UR#                  5       5      5      5        GM  UR                  U5        GM$     U$ s  snf )	NzEonly one of override_return_dtype or type_promotion_kind may be givenc              3  l   #    U  H*  n[        U[        R                  [        [        45      v   M,     g 7fr   )rk   r   r   r   floatr   s     re   r   $promote_constants.<locals>.<genexpr>F  s%     HAz!ekk3677   24c              3  l   #    U  H*  n[        U[        [        [        R                  45      v   M,     g 7fr   )rk   r   r;  r   r   r   s     re   r   r<  H  s%     
DV:a#uekk233Vr=  r   c                   > [        U [        R                  5      (       a  [        R                  " U T[        S 5      S9$ [        R                  " U T[        S 5      S9$ )Nindexr   rv   r   )rk   r   r   r2   r9   rG   r   r   r   s    re   
const_func%promote_constants.<locals>.const_funcO  sM    !U[[))**5t1D  {{%d@STTrg   c              3  ~   #    U  H3  n[        U[        [        [        R                  45      (       d  M/  Uv   M5     g 7fr   )rk   rC   r8   r2   r   r   s     re   r   r<  X  s&     WA:a)Z1U#Vaas   .=	=r   r@  )r   DEFAULTr#  r"  r   nextrk   r   r;  ro   r8   r   r2   r   r   get_device_or_errorri   r   r   r   r9   )inputsoverride_return_dtyper   rC  r   exrq   r   s          @re   promote_constantsrL  >  s    (,?,G OG $)<)D=EEHHHH

DV
DDD% 
);*
 !4*
	U (..v!
1v..	WW	WB
Ca#u&&JJ!!KK||~b>T>T>V '	 5;;''JJ!!$||~b>T>T>V '	 JJqM) , J3 /s   3Gc                4   ^ ^^^^^ S S.SUU UUUU4S jjjnU$ )Nalphac           	     .  >^^^^	^
^^ Tb%  [        S T 5       5      (       a  T(       a   eT" T6 $ [        TT5      mT(       a'  U b#  U S:w  a  [        T5      m[        TS   U 5      TS'   OU b   eT Vs/ s H  o"R	                  5       PM     snm
TS   R                  5       mT=(       d    TS   R                  5       mTSS   Hh  n[        U[        R                  5      (       a  M$  [        T5      [        UR                  5       5      :X  a  ML   ST ST SUR                  5        35       e   [        R                  [        R                  4m[        R                  S L=(       a    [!        [        R                  SS 5      S L=(       aa    [        R                  R"                  R$                  S L=(       a4    [        R                  R"                  R$                  R'                  SS	5      m	T	=(       a    TT;   mUUU	UUU
UUU4	S
 jnT(       d_  S nT H=  n[)        UR+                  5       R,                  5      (       d  M-  UR+                  5       n  O   U(       d  TS   R+                  5       nT=(       d    Wn[.        R0                  " UTUTS9$ s  snf )Nc              3  f   #    U  H'  n[        U[        5      =(       a    [        U5      v   M)     g 7fr   rk   r:   r;   )r   r   s     re   r   0make_pointwise.<locals>.inner.<locals>.<genexpr>|  s&      /
BH3JsF#6	#6&   /1r/   r   zndim mismatch  r^   low_precision_pointwise_barrierFc                &  >	 [        U 5      [        T5      :X  d   SU  ST 35       eT[        R                  :X  a  Tb  T" T Vs/ s H
  o" U 5      PM     sn6 $ / n[        T5       Hi  u  p1U" U 5      nTU   R	                  5       nT	(       a1  UT;   a+  [
        R                  " XESS9n[
        R                  " Xe5      nUR                  U5        Mk     T
" U6 nT(       a-  [
        R                  " UTSS9n[
        R                  " UT5      $ U$ s  snf )Nzwrong ndim rV  F)use_compute_types)r   r{   r   rj   r   rR   r   ro   )rA  loadinputs_loaded	inp_indexrq   	inp_dtypedowncastr   emulate_output_castemulate_precision_castsr   rI  loaders	low_pr_fpoverride_fn_when_input_boolrangess          re   inner_fn/make_pointwise.<locals>.inner.<locals>.inner_fn  s   u:V,LE7!F8.LL,

"'B'N2W4UWTT%[W4UVV "'0'9OIu+C &y 1 ; ; =I.9	3I#&<<RW#X!ll8?!((- (: -(&  #||C%PH<<%88
# 5Vs   Drv   r   re  rd  )r#  rL  ri   mulmake_loaderr   r   rk   r2   BaseConstantr   r{   bfloat16float16rS   r]   r   r^   metagetrI   rn   r   r@   r   )rO  rI  r   otherre  rv   rs   r   r_  r`  ra  rb  rd  allow_alphar   override_devicerc  rJ  triton_fallbacks    `     @@@@@@re   innermake_pointwise.<locals>.inner{  sN   &3 /
BH/
 ,
 ,
 #"?"F++"6+@A UaZf U3r
= =,23Fq==?F3##%%>)<)<)>ABZEeR__55V I : At1VHAenn.>-?@A    ^^U]]3	GG4 X6dBX$$))5X $$))--.OQVW	 	  6L%9:L	 	, F!,,.--..\\^F  --/ !*F	
 	
o 4s   4J)rI  rC   r   )r   rJ  rq  rc  rp  rr  rs  s   `````` re   make_pointwiseru  s  s     )- L
 L
\ Lrg   c                $   ^ ^ SS.SUU 4S jjjnU$ )Nr/   rN  c                8  > [        [        R                  R                  R                  5      S:H  =(       d<    [        R                  R                  R
                  [        ;   =(       d
    [        5       nS nU H"  n[        U[        [        45      (       d  M   Un  O   Uc   S5       e/ nU HO  n[        U[        [        45      (       d   UR                  U/[        U5      -  5        M>  UR                  U5        MQ     [        [        U6 5      nS /[        U5      -  nUR                  5        H  u  u  pn
/ nU
 H  u  nnT(       a	  T" USU 06nOT" U6 nXU'   [        R                  R                  U[         R"                  5      (       d  MT  U	(       d  M]  U(       d  Mf  UR%                  5         UR                  UR'                  5       5        M     U(       d  M  [        R                  R)                  U5        M     [+        S U 5       5      (       d   eU$ )Nr   z1at least one input must be a list to a foreach oprO  c              3  (   #    U  H  oS Lv   M
     g 7fr   r   r   s     re   r   8make_foreach_pointwise.<locals>.inner.<locals>.<genexpr>  s     2'QD='   )r   rS   r]   r^   r_   ra   inplace_foreach_opsrf   rk   ri   r   ro   rx   r  r   has_featureBackendFeatureFOREACHrealizeget_operation_nameregister_operation_listr"  )rO  rI  realize_outputsa_list_inputinputbroadcast_inputsgroupsoutputsrv   ru   groupoperation_list
output_indrt   r6  rp  pw_fns                  re   rs  %make_foreach_pointwise.<locals>.inner  s   $$**+q0 0ww##**.AA0-/ 	 E%$//$  ' 	
?	
'
 EedE]33 ''#l2C(CD ''.	  $C)9$:;&3|,,,2LLN(!V5(*N "D66F"D\F&,
# GG''0F0FGG#'NN$"))&*C*C*EF " ~//?1 -;4 2'22222rg   )rI  zlist[list[TensorBox]]r   )r  rp  rs  s   `` re   make_foreach_pointwiser    s    45 6 6p Lrg   c                   ^^ U R                  5       mTT:X  a  U(       a  [        U 5      $ U $ UU4S jn[        UTS9" U 5      $ )Nc                0   > [         R                  " U TTS9$ )N)	src_dtype)rR   r   )r   r   r  s    re   	_to_dtypeto_dtype.<locals>._to_dtype  s    ||Au	::rg   rJ  )r   cloneru  )r   r   copyr  r  s    `  @re   r   r     s@    IEuQx&Q&; )5A!DDrg   r   c                   SSK Jn  UnU R                  nU" U[        R                  S9n[        R
                  " U5         UR                  " U6   SSS5        UR                  nU(       d   e[        U5      nS/[        U5      -  n	UR                  5        H  u  u  pn/ nU Hw  u  nnXU'   [        R                  R                  U
[        R                  5      (       d  M?  U(       d  MH  UR                  5         UR                  UR!                  5       5        My     U(       d  M  [        R                  R#                  U5        M     [%        S U	 5       5      (       d   eU	$ ! , (       d  f       GN= f)a)  
This lowers an invocation of foreach_map
The way this works is that an arbitrary N-arg func is provided by the user, looped over by the
polyfill with the same semantics as a foreach op (a loop applying an n-ary function to n args)
and then traced into a subgraph by dynamo.
This code allows us to inline the subgraph into the main graph lowering using the PontwiseSubgraphLowering.
The graph outputs represent the vertically fused sequence of ops, and then register_operation_list
below registers the buffers as horizontally fuseable in the scheduler.
r/   )PointwiseSubgraphLowering)root_graph_loweringNc              3  (   #    U  H  oS Lv   M
     g 7fr   r   r   s     re   r   _foreach_map.<locals>.<genexpr><  s     .g}grz  )subgraph_loweringr  graph_modulerS   r]   set_graph_handlerrungraph_outputsrx   r   r   r|  r}  r~  r  ro   r  r  r"  )subgraphrt   r   r  rI  gmpw_subgraphsub_outputsr  r  rv   ru   r  r  r  r6  s                   re   _foreach_mapr    s2    =F			B+BAGGLK	
		[	)  
* ++K;,Ffs;''G(.$u$& 
"(Jww""6>+A+ABB{{ %%f&?&?&AB  >GG++N; )7 .g.....N3 
*	)s    E%%
E4c                D   UR                   (       d  U R                  5       R                   (       ag  U R                  5       (       a*  [        XS9n[        R
                  R                  X 5        U$ [        [        R                  R                  SS9" X5      $ [        XSS9$ )Nr   Fadd_to_fallback_setTr  )
is_complexr   r   
empty_liker2   InplaceCopyFallbackr   fallback_handlerprimsconvert_element_typedefaultr   )r   r   dsts      re   _convert_element_typer  @  s~    1;;=33::<< Q,C""))#1J#**22  A4((rg   r  c                  U R                  5       nX1:X  a  U(       a  [        U 5      $ U $ S nU" U5      nU" U5      nXV:w  a)  [        [        R                  R
                  5      " X5      $ [        [        R                  " X5      5      $ )Nc                    U R                   (       a   [        R                  " U 5      R                  $ [        R                  " U 5      R                  $ r   )is_floating_pointr{   finfobitsiinfor   s    re   _get_primitive_bitwidth1to_dtype_bitcast.<locals>._get_primitive_bitwidthU  s5    "";;u%***;;u%***rg   )	r   r  r  atenviewr   rC   r7   r   )r   r   r  x_dtyper  src_bitsdst_bitss          re   to_dtype_bitcastr  P  ss    kkmGuQx&Q&+ 'w/H&u-H		0::))!344rg   c                8   UR                   (       d  U R                  5       R                   (       a`  [        R                  " [        R
                  R                  [        R                  R                  R                  R                  X5      5      $ [        X5      $ r   )r  r   rC   r   r2   ComplexViewr{   rR   r  r  r   r  rB  s     re   _view_dtyper  d  sa    1;;=33NN!!%)).."5"5";";QF
 	
 A%%rg   r  non_blockingc                   [        U5      nU R                  5       U:X  a  U(       a  [        U 5      $ U $ [        R                  " [
        R                  R	                  XU5      5      $ r   )rG   rn   r  rC   r   r2   r   )r   rv   r  r  s       re   	to_devicer  m  sM    6"F||~uQx&Q&BMM00LIJJrg   c                    [        XSUS9$ )NTr  )r  )r   rv   r  s      re   _device_putr  t  s    QTEErg   Tc	                    U=(       d    U R                   n[        U5      n	[        XU5        Ub  [        U5      n[        U	UUUUS9n	[	        U UUUS9" U	5      n	[        [        U5      (       a  [	        [        [        U5      SUS9" U	5        U	$ )z3A pointwise function that maps ops.{name} to inputsN)rJ  rc  rp  rr  )r  r   r  )r   r  )__name__r>   rN   ru  r*  r   r  r   )
r   r   r  r   r  rJ  rc  rp  rr  r   s
             re   register_pointwiser  y  s     #7##D	T	B'#8 #.&12M&N#	
3$?'
B 
/3	

 	

B udE4  $"7	
 		
 Irg   ldexp)r   rJ  )r  r   c                  ^^	 [        S5      mU R                  5       nUR                  5       nUR                  nUR                  (       + =(       a    U[        R                  :g  nU(       a  U(       a  U4S jn[        U5      " X5      $ [        U 5      (       a  [        R                  OUm	U	4S jn[        UT	S9" X5      $ )Nr  c                   > T" X5      $ r   r   )r   nldexp_fns     re   compute_ldexp%ldexp_lowering.<locals>.compute_ldexp  s    A>!rg   c                   > [         R                  " UT5      n[         R                  " ST5      n[         R                  " X25      n[         R                  " X5      $ )Ng       @)rR   r   constantpowrh  )r   r  
n_out_typetwo
pow_result	out_dtypes        re   compute_fallback(ldexp_lowering.<locals>.compute_fallback  s@    a3J,,sI.C1J771))rg   r  )r>   r   r  r{   r   ru  r   float32)
r   r  r  n_dtype
x_is_floatn_is_intr  r  r  r  s
           @@re   ldexp_loweringr    s    7#HkkmGkkmG**J,,,FEJJ1FHh	" m,Q22 &5Q%7%7EMMW		* "+
  	rg   c                 2  ^^ Sn [        S5      mU4S jnU4S jn[        U5      [        U[        R                  S9/mU4S jn[	        [
        R                  5      " U5      n[        [        U 5      (       a  [	        [        [        U 5      SS9" U5        U$ )z2A pointwise function that maps ops.frexp to inputsfrexpc                    > T" U 0 UD6S   $ Nr   r   rt   r   r  s     re   frexp0register_frexp.<locals>.frexp0      d%f%a((rg   c                    > T" U 0 UD6S   $ Nr/   r   r  s     re   frexp1register_frexp.<locals>.frexp1  r  rg   r  c                 0   > TS   " U 0 UD6TS   " U 0 UD64$ Nr   r/   r   )rt   r   pw_fnss     re   r   register_frexp.<locals>.fn  s*    ay$)&)6!9d+Ef+EEErg   Nr  )
r>   ru  r{   int32r*  r  r  r   r  r   )r   r  r  r   r  r  s       @@re   register_frexpr    s    D E)) 	vvU[[AF
F 





B udE4  $	
 	 Irg   c                .    [        XS9n[        X5      nU$ )Nrp  )r  r  )r   pointwise_lowering_fnrp  r   s       re   register_foreach_pointwiser    s    
 
  5	OB	#G	0BIrg   c           
     *   S n[        U[        [        45      (       a  [        U5      " U5      n[        U[        [        45      (       a  [        U5      " U5      nXU/n[	        US   US   [
        R                  S9n[        U5       VVs/ s H  u  pg[        U[        5      (       d  M  UPM      nnn[        U[        U Vs/ s H  odU   PM	     sn6 5       H	  u  pgXtU'   M     [        [        U5      5       H]  n[        XF   [        R                  5      (       d  M&  [        R                   " XF   [#        XHS      R%                  5       5      5      XF'   M_     ['        X5S9" US   [)        US   U5      [)        US   U5      5      $ s  snnf s  snf )Nc                 (    [         R                  " U 6 $ r   )rR   wherert   s    re   r   where.<locals>.fn  s    yy$rg   r/   r-   r  r   r  )rk   r;  r   constant_liker   r   rF  rj   rC   r  r  r  r   r2   r   r8   r   ri   r   ru  r   )	r   r   r5  r   rt   r   rs   r   indicess	            re   r  r    sX     !eS\""!Q!eS\""!QQ<DQa.M.U.UE 't_I_TQ
1i0Hq_GIG.'0J'Qa'0JKLQ M3t9dgr{{++ ''d1:6F6O6O6Q1RSDG  ":Q$q'5)8DGU+C  J0Js   F
,F
Fc                    [        U 5      S:X  a+  [        U S   [        [        45      (       a  [	        U S   6 $ U $ [
        R                  " [        S U  5       S5      n/ nU  Hv  n[        UR                  5       5      =oA:X  a  OC[        U5      [        U5      :w  d   [        S [        XA5       5       5      (       a  [        X15      nUR                  U5        Mx     U$ )Nr/   r   c              3  @   #    U  H  oR                  5       v   M     g 7fr   )r   r   s     re   r   $broadcast_tensors.<locals>.<genexpr>  s     #A&QJJLL&   r   c              3     #    U  HZ  u  p[         R                  R                  R                  U5      [         R                  R                  R                  U5      :g  v   M\     g 7fr   )rS   r]   r   r1  r   r   r5  s      re   r   r     sM      .
 + GG11!4ww44Q78*s   A"A$)r   rk   ri   r   r  r  reducer8  r   r#  r  r3  ro   )rI  ra   r  r   sizess        re   r  r    s    
6{afQi$//$fQi00(//!#A&#A2 F G1::<((E3Z3v;&# .
 E*.
 +
 +

 q!Aq  Nrg   c                    U $ r   r   r   s    re   nopr  *  s    Hrg   
lift_freshc                   [        U [        5      (       d   eUc)  [        [        R                  " U R                  5      5      $ [        U[
        [        R                  45      (       a)  [        R                  R                  R                  U5      O[        S U 5       5      n[        [        U R                  5       5      U5      n[!        [        U[        5      (       d  U4OU5      n/ n[#        U R                  5       5       H`  u  pEXB;   aE  [        R                  R                  R%                  [        R&                  " US5      5      (       a  MO  UR)                  U5        Mb     X0R                  5       :w  a  [+        X5      $ U $ )Nc              3  t   #    U  H.  n[         R                  R                  R                  U5      v   M0     g 7fr   )rS   r]   r   	guard_intr   ds     re   r   squeeze.<locals>.<genexpr><  s(     >#Q177##--a00#s   68r/   )rk   rC   rB   r   rm   r   r   r   rS   r]   r   r  r   r   r   r   r'   rj   guard_or_falseEqro   r  )r   r   dims	new_shaper  r   s         re   squeezer  3  s   a####
{++AFF344 cC,-- 	
""3'>#>> 
 C

-s
3CJsE$:$:sfDDI!**,'	agg..==ehhq!nMMQ (
 "+jjl!:4AArg   c                *    [        [        X5      5      $ r   )r  r  )r   r   s     re   squeeze_copyr  J  s    !!rg   c                    [        X5      n[        U [        5      (       d   e[        U[        5      (       d   eUR                  U l        U $ r   )r  rk   rC   rm   r   r   vals      re   squeeze_r  O  sA    
!/Ca####c9%%%%XXAFHrg   c                    [        U 5      (       a  [        U S[        R                  S9$ [	        S5      n[        U[        R                  S9" U 5      $ )NFr   isinfr  r   	full_liker{   r   r>   ru  r   r   s     re   r  r  X  @    qE44	W	B"EJJ?BBrg   c                    [        U 5      (       a  [        U S[        R                  S9$ [	        S5      n[        U[        R                  S9" U 5      $ )NFr   isnanr  r  r  s     re   r"  r"  `  r   rg   c                p    [        U 5      (       a  [        U 5      $ [        S5      n[        U5      " U 5      $ )Nceilr   r  r>   ru  r  s     re   r$  r$  h  s0    qQx	V	B"a  rg   c                p    [        U 5      (       a  [        U 5      $ [        S5      n[        U5      " U 5      $ )Nfloorr%  r  s     re   r'  r'  p  0    qQx	W	B"a  rg   c                p    [        U 5      (       a  [        U 5      $ [        S5      n[        U5      " U 5      $ )Nroundr%  r  s     re   r*  r*  x  s0    qQx!b!!$$rg   c                p    [        U 5      (       a  [        U 5      $ [        S5      n[        U5      " U 5      $ )Ntruncr%  r  s     re   r,  r,    r(  rg   c                *   [        U /5      u  n [        U [        R                  5      (       a   [        R
                  " U [        U5      5      $ [        U [        5      (       d   e[        U[        [        45      (       d   e[        U R                  5       5      [        U5      :X  a  U $ [        U R                  5       5      (       d  [        R                  R                  R                  [        U R                  5       5      5      nUS:  aT  [        U5      (       dD  U R!                  [        R                  R                  R                  [        U5      5      U-  5        [        [        R
                  " U R"                  [        U5      5      5      $ r  )rL  rk   r2   rj  r8   r   r   rC   ri   r   r$   rS   r]   r   r   rP   
mark_reuserm   )r   r  x_size_products      re   r3  r3    s   aS!DQ!R__%%  E%L11a####edE]++++QZZ\eEl* ..))<<!**,'
 A&;E&B&BLL  33M%4HI!" Z&&qvvuU|<==rg   c                    [        U5      nU H  nSX4'   M	     U n[        U5       H  u  pgUS:w  d  M  [        XV5      nM     [        XQ5      $ NrU  )ri   rj   	unsqueezer3  )r   shapebroadcast_dimensionsr   broadcast_dimensionr	  idxr   s           re   broadcast_in_dimr7    sS    UA3!#  4 	
AA,7!!A  !rg   c                4    [        XR                  5       5      $ r   )r3  r   )r   r7  s     re   	expand_asr9    s    !ZZ\""rg   c                  ^^^ [        U R                  5       5      m[        T5      [        T5      :  aK  [        R                  R
                  /[        T5      [        T5      -
  -  T-   m[        U [        T5      5      n [        T5      [        U R                  5       5      :X  d   e[        U R                  5       5      nSn[        [        T5      5       H  nTU   S:X  a  SnX$   TU   -  X$'   M     U(       a&  [        X R                  5       U R                  5       S9$ [        S [        TT5       5       5      (       a  [        [        X5      5      $ UUU4S jn[        T5      (       d  [        U5      (       d|  [         R"                  R$                  R'                  [)        T5      5      nUS:  aD  U R+                  [         R"                  R$                  R'                  [)        U5      5      U-  5        U R-                  5       m[.        R0                  " U R                  5       U R                  5       U[        U5      S9$ )NFr   Tr   rv   c              3  H   #    U  H  u  pUS :H  =(       d    US :H  v   M     g7fr/   Nr   r  s      re   r   repeat.<locals>.<genexpr>  s$     
A*@$!AFa1f*@s    "c                   > [        U 5      [        T5      :X  d   e[        U 5      n [        [        T5      5       HI  nTU   S:w  d  M  TU   S:X  a  [        R                  R
                  X'   M5  [        X   STU   5      X'   MK     T" U 5      $ r  )r   ri   r  r   r/  Zeror,   )rA  rs   old_sizerepeatsx_loaders     re   re  repeat.<locals>.inner_fn  s}    5zS\)))Us7|$AqzQA;!#$ww||EH.uxHQKHEH % rg   rg  )ri   r   r   r   r/  r0  r  r  emptyr   rn   r"  r  r  r3  r$   rS   r]   r   r   rP   r.  ri  r@   r   )	r   rB  new_sizezero_tensorrs   re  old_size_productrA  rC  s	    `     @@re   repeatrI    s   AJJL!H
7|c(m#GGKK=CL3x=$@AHLDN#w<3qzz|,,,,AJJL!HK3w< 1:?KkGAJ. !
 X[[]1<<>JJ

A#gx*@
AAAVA())	 !**3H3R3R77++>>}X?VWa LL  33M(4KL#$
 }}H||~kkmH~	 rg   c                V    [        [        R                  " U R                  U5      5      $ r   )rC   rE   r   rm   )r   r  s     re   r  r    s     T[[/00rg   c                    [        U [        5      (       d   e[        U[        [        45      (       d   e[        [        R
                  " U R                  [        U5      5      5      $ r   )rk   rC   ri   r   r?   r   rm   )r   r  s     re   permuterL    sL    a####dT5M****[''d<==rg   c                x   SSK JnJn  [        U [        5      (       d   e[        XS5      nU R                  5       U   n[        R                  " U5      n[        U[        R                  5      (       d  US:  d   U5       e US:X  a6  [        R                  R                  R                  X5      (       a  US:X  a  U $ SS jn	Su  pUnU(       a  U	" X(S5      n
U	" X8U5      nU
b  Ub  Xp2SnU(       d3  [	        [        R                   R#                  U R$                  XX4US95      $ U(       d   eU" [        R                  R                  R&                  [        R                  R(                  R*                  S   5      nUc   e[-        U5      S	::  d   U5       eSu  pUR/                  5        H=  u  nnUU" S
5      [0        R2                  " U5      4:X  a  UnM,  UU" S5      4:X  d  M;  UnM?     U
b  Ub   e[        R4                  " UUUUU R                  5       U   5      n[        R                  R7                  U5      Ul        [        R                  R;                  U5        UnU R=                  5       c  U R?                  5         U
b6  Ub   eU RA                  5       RB                  XRE                  5       U   -  -   nO[        RF                  " UUU RA                  5       RB                  U RE                  5       U   U R                  5       U   SS9n[        R                  R7                  U5      Ul        [        R                  R;                  U5        Un[I        U R                  5       5      n[I        U RE                  5       5      nUUU'   UU==   U-  ss'   [K        U UUU5      $ ! [         a     GNf = f)z
Lowers a slice call, creating ExternKernels for the output size & storage offset symbols,
if the indices are unbacked and appropriate semantics aren't known.
If they are known (indices are static/backed/unbacked with info), a SliceView is created.
r   )CallMethodKeyr&   r/   c                   U c  U$ S n[         R                  " U 5      n [         R                  " U5      nU" [         R                  " U S5      5      (       a#  U" [         R                  " X5      5      (       a  U $ U" [         R                  " U S5      5      (       a&  U" [         R                  " X* 5      5      (       a  X-   $ U" [         R
                  " X5      5      (       a  U$ U" [         R                  " X* 5      5      (       a  gg )Nc                T    [         R                  R                  R                  U 5      $ r   )rS   r]   r   r  r   s    re   <lambda>5slice_.<locals>.compute_slice_index.<locals>.<lambda>  s    qww''66q9rg   r   )r   r3  GeLeLtGt)rA  r   r  r   s       re   compute_slice_index#slice_.<locals>.compute_slice_index  s    =N9U#||D!ehhua !!b%)>&?&?L"##588E5+A(B(B<%&&K&''rg   NNFclampunbacked_bindingsr-   r   storage_offsetTr   )&%torch.fx.experimental.symbolic_shapesrN  r&   rk   rC   _validate_dimr   r   r3  r   rS   r]   r   statically_known_leq	TypeErrorr2   	SliceViewr   rm   	shape_envr^   rm  r   r   pytreeSequenceKeyDynamicSliceSizeregister_bufferr   register_operationmaybe_get_layoutr  
get_layoutoffset
get_strideDynamicSelectStorageOffsetri   
as_strided)r   r   startendstepr[  rN  r&   r   rW  start_index	end_indexambiguous_slicer\  sym_sizesym_storagesymkeypathb_sizerF  new_storage_offset	b_storage	new_sizesnew_stridess                           re   slice_r~    s^   
 a####

"C::<D<<DdEJJ''4!89T93QJ  55d@@	H
" (KO)%q9'48	"y'<$3#O LLCUK
 	
 L51	""AGG$8$8$=$=>Q$R ((( !Q&9(99&&H)//1W}V,f.@.@.EFFH'78::K	 2 )"333  	

SF ''))&1FKGGv&H#			"""\\^22[<<>RUCV5VV11LLN!!LLN3JJL
	 00;		""9-(QZZ\"Iq||~&KIcNaK1CDDw  s   ;N+ +
N98N9c                2   S nS n[        U [        5      (       a_  [        U R                  [        R                  5      (       a6  U R                  5       nU R                  nU R                  R                  5       n U R                  5         [        R                  " U 5      (       d  [        SU  S35      e[        R                  " U 5      u  pg[        R                  " U(       a  UOUR                  U(       a  UOUR                  U Vs/ s H  n[        R                  " U5      PM     snU Vs/ s H  n[        R                  " U5      PM     sn[        R                  " U=(       d    S5      5      n	[        [        R                   " XiS95      $ s  snf s  snf )Nzunrealized as_strided(z, ...)r   rm   layout)rk   rC   rm   r2   r6   rn   r   unwrap_viewr  is_storage_and_layoutr   as_storage_and_layoutFixedLayoutrv   r   r3  r   )
r   r   strider]  
new_device	new_dtypestorage
old_layoutr   
new_layouts
             re   rn  rn  s  s$   JI!YJqvvr{{$C$C \\^
GG	FF IIK##A&&!$:1#V"DEE2215G 
j&7&7	J$4$4"&'$Qa$'"()&Qa&)^(q)J R''WHII	 	()s    F- Fc                j    [        U [        5      (       d   e[        XX#5      R                  U l        U $ r   )rk   rC   rn  rm   )r   r   r  r]  s       re   as_strided_r    s.    a####8==AFHrg   c                0    [        XX#5      n[        U5      $ r   )rn  r  )r   r   r  r]  results        re   as_strided_copyr    s    8F=rg   c                  ^ ^^^ / mSnT  H1  nTR                  X"UR                  5       T   -   45        TS   S   nM3     T  Vs/ s H  o3R                  5       PM     snmUU UU4S jn[        T S   R                  5       5      nTS   S   UT'   [        R
                  " T S   R                  5       T S   R                  5       UUS9$ s  snf )Nr   rU  c           	       >^
^ [         R                  " U T   [        R                  5      n/ n/ n[	        [        T5      5       GHH  m
T
S:X  a%  [         R                  " S[        R                  5      O*[         R                  " TT
   S   [        R                  5      n[         R                  " TT
   S   [        R                  5      n[         R                  " X5      n[         R                  " X5      nT
S:X  a  UnO+T
[        T5      S-
  :X  a  UnO[         R                  " Xg5      nUR                  U5        [        U 5      m[        TT   TT
   S   -
  5      TT'   UR                  [         R                  " UU
UU4S jS5      5        GMK     US   n	[	        [        T5      S-
  SS5       H!  m
[         R                  " UT
   UT
   U	5      n	M#     U	$ )Nr   r/   c                    > TT    " T5      $ r   r   )rs   idx_loadinputs_loaderss   re   rQ  1pointwise_cat.<locals>.inner_fn.<locals>.<lambda>  s    N1-h7rg           rU  r-   )rR   
index_exprr{   int64r  r   r  geltand_ro   ri   r*   maskedr  )r6  idx_dimmasksmasked_loadsro  rp  
start_condend_condmasknext_valrs   r  r   rI  r  inputs_rangess             @@re   re  pointwise_cat.<locals>.inner_fn  s   ..S5;;7s6{#A 6 Q,^^M!$4Q$7E 
 ..q!1!!4ekkBC/Jvvg+HAvc&kAo%!xx
5LLCyH %Xc]]15Ea5H%HIHSM

75 $D  #Fq("b1AyyaQH 2 rg   rg  )ro   r   ri  ri   r@   r   rn   r   )rI  r   prev_endr   re  rF  r  r  s   ``    @@re   pointwise_catr    s    9;MHh3<<>#3F(FGH $R(  4::6Coo'6:N. .` F1I&&()H!"%b)HSMay##%Qi!!#	 k ;s   C	c           	       ^^^^^^^^	^
 [        TR                  5       5      S:X  d   S5       e[        TR                  5       5      S:X  d   S5       eU R                  5       [        R                  :X  a  [        U [        R                  5      n U R                  5       [        R                  :X  d   SU R                  5        35       eT[        U R                  5       5      :  d!   S[        U R                  5       5       35       eU R                  5       mTR                  5       m	TR                  5       m
UUUUUUU	UU
4	S jn[        R                  " U R                  5       TUU R                  5       S9$ )Nr/   expect scales 1 dimexpect zero_points 1 dim<Expecting input to have dtype torch.float32, but got dtype: Expecting axis to be < c                h  >	 U T
   4nT" U 5      nT" U5      nT" U5      n[        TT[        R                  S9u  pVTR                  [        R                  :w  a%  [        R
                  " U[        R                  5      nTR                  [        R                  :w  a%  [        R
                  " U[        R                  5      n[        R                  " U5      n[        R                  " X'-  5      U-   n[        R                  " U[        R                  " Xh5      5      n	[        R
                  " U	T5      $ Nr   )_create_constantsr{   r  r   rR   r   r  
reciprocalr*  maximumminimum)r6  channel_idxr  scale
zero_pointqminqmax	inv_scaler  clampedaxisr   input_loader	quant_max	quant_minscalesscales_loaderzero_pointszero_points_loaders             re   re  ;quantized_decomposed_quantize_per_channel.<locals>.inner_fn  s    4ylS!k*'4
&y)5==Q
<<5==(LL6E+j%++>JNN5)	ii)*Z7++dCKK$:;||GU++rg   rg  )r   r   r   r{   rk  r   r  ri  r@   r   rn   )r  r  r  r  r  r  r   re  r  r  r  s    `````` @@@re   )quantized_decomposed_quantize_per_channelr    s?    v !Q&=(==&{##%&!+G-GG+ENN*.??- 
FuGXFYZ- #enn&'' 
!#enn&6"7!89' $$&L&&(M$002, ," !~~	 rg   c           	        ^ ^ T R                  5         [        T [        R                  5      m U U4S jn[        R
                  " T R                  5       T R                  5       U[        T R                  5       5      S9nUR                  5         U$ )Nc                   > [         R                  R                  5          [        R                  " TR                  5       " U 5      T5      sS S S 5        $ ! , (       d  f       g = fr   )r2   ComputedBufferforce_realizerR   device_assert_asyncri  )rA  r   r   s    re   re  _assert_async.<locals>.inner_fn  s?    ,,.**4+;+;+=e+DcJ /..s   +A
A#rg  )
r  r   r{   r   r@   r   rn   r   ri   r   )r   r   re  assertion_ops   ``  re   _assert_asyncr    sm    LLND%**%DK ## nnDMMO$	L rg   c                    [        X5      $ r   r  r   s     re   lower_assert_asyncr  '      ##rg   c                    [        X5      $ r   r  r   s     re   lower_assert_functional_asyncr  ,  r  rg   )r  c               ~  ^^^^^	^
^ [        TR                  5       5      S:X  d   S5       e[        TR                  5       5      S:X  d   S5       eU R                  5       U:X  d   SU SU R                  5        35       eT[        U R                  5       5      :  d!   S[        U R                  5       5       35       eTc  [        R                  mU R                  5       m	TR                  5       m
TR                  5       mUU	UUU
UU4S jn[        R                  " U R                  5       TUU R                  5       S9$ )	Nr/   r  r  Expecting input to have dtype , but got dtype: r  c                  > U T   4nT" U 5      nT
" U5      nT" U5      nT	R                   [        R                  :w  a%  [        R                  " U[        R                  5      nTR                   [        R                  :w  a%  [        R                  " U[        R                  5      n[        R
                  " [        R                  " U[        R                  5      U5      U-  n[        R                  " UT5      nU$ r   )r   r{   r  rR   r   sub)r6  r  r  r  r  r  r  r  r  r  r  r  r  s         re   re  =quantized_decomposed_dequantize_per_channel.<locals>.inner_fnO  s    4ylS!k*'4
<<5==(LL6E-j%--@Jggcll5%--8*EMll3	*
rg   rg  	r   r   r   r{   r  ri  r@   r   rn   )r  r  r  r  r  r  r   r  re  r  r  r  s    ```   ` @@@re   +quantized_decomposed_dequantize_per_channelr  1  s-    v !Q&=(==&{##%&!+G-GG+??% 
(/@AR@ST% #enn&'' 
!#enn&6"7!89' MM	$$&L&&(M$002  !~~	 rg   c                  ^^^^ U R                  5       [        R                  :X  a  [        U [        R                  5      n U R                  5       [        R                  :X  d   SU R                  5        35       eU R                  5       mUUUU4S jn[        R                  " U R                  5       T[        R                  " U[        U5      [        U5      S9U R                  5       S9$ )Nr  c                @  > T
" U 5      n[        SU-  U[        R                  S9u  pB[        R                  " X4-  5      U-   n[        TT[        R                  S9u  pg[        R
                  " [        R                  " XV5      U5      n[        R                  " UT	5      $ )N      ?r   )r  r{   r  rR   r*  r  r  r   )r6  r  r  r  r  r  r  r  r  r   r  r  r  s            re   re  Bquantized_decomposed_quantize_per_tensor_default.<locals>.inner_fny  s    S! 1%K5==!
	 ii)*Z7&y)5==Q
++ckk#4d;||GU++rg   r  r  rg  )r   r{   rk  r   r  ri  r@   r   rn   r  r)  r;  r   r   )r  r  r  r  r  r   re  r  s      ``` @re   0quantized_decomposed_quantize_per_tensor_defaultr  f  s     ENN*.??- 
FuGXFYZ- $$&L, , !""E%LS_
 ~~ rg   c               j  ^^ U R                  5       U:X  d   SU SU R                  5        35       eTc  [        R                  mU R                  5       mUU4S jn[        R
                  " U R                  5       T[        R                  " U[        U5      [        U5      S9U R                  5       S9$ )Nr  r  c                   > T" U 5      n[        X[        R                  S9u  p[        R                  " [        R
                  " U[        R                  5      U5      U-  n[        R
                  " UT5      nU$ r  )r  r{   r  rR   r  r   )r6  r  r  r  r  r  r  s        re   re  Dquantized_decomposed_dequantize_per_tensor_default.<locals>.inner_fn  sY    S!-eu}}Uggcll5%--8*EMll3	*
rg   r  rg  )r   r{   r  ri  r@   r   rn   r  r)  r;  r   r   )	r  r  r  r  r  r   r  re  r  s	         ` @re   2quantized_decomposed_dequantize_per_tensor_defaultr    s     ??% 
(/@AR@ST% MM	$$&L !""E%LS_
 ~~ rg   c                >  ^^^^^^^^	 U R                  5       [        R                  :X  a  [        U [        R                  5      n U R                  5       [        R                  :X  d   SU R                  5        35       e[        TR                  5       5      S:X  d;  [        TR                  5       5      S:X  a  TR                  5       S   S:X  d   S5       e[        TR                  5       5      S:X  d;  [        TR                  5       5      S:X  a  TR                  5       S   S:X  d   S5       eU R                  5       mTR                  5       mTR                  5       m	UUUUUUUU	4S jn[        R                  " U R                  5       TUU R                  5       S9$ )Nr  r   r/   expect scale as scalar tensor"expect zero_point as scalar tensorc                  > T	" U 5      nT" [        TR                  5       5      S:X  a  SOS5      nT" [        TR                  5       5      S:X  a  SOS5      nTR                  [        R                  :w  a%  [
        R                  " U[        R                  5      nTR                  [        R                  :w  a%  [
        R                  " U[        R                  5      n[
        R                  " U[
        R                  " U5      -  5      U-   n[        TT
[        R                  S9u  pV[
        R                  " [
        R                  " XE5      U5      n[
        R                  " UT5      $ )Nr/   r   r   r   )r   r   r   r{   r  rR   r   r*  r  r  r  r  )r6  r  _scale_zero_pointr  r  r  r  r   r  r  r  r  scale_loaderr  zero_point_loaders           re   re  Aquantized_decomposed_quantize_per_tensor_tensor.<locals>.inner_fn  s    S!c%..*:&;q&@dbI'ENN4D0E0JPRS;;%--'\\&%--8Fu}},,,{EMMBKiiv 667+E&y)5==Q
++ckk#4d;||GU++rg   rg  )r   r{   rk  r   r  r   r   ri  r@   r   rn   )
r  r  r  r  r  r   re  r  r  r  s
    ````` @@@re   /quantized_decomposed_quantize_per_tensor_tensorr    sf    ENN*.??- 
FuGXFYZ- u~~ A%ENN"u~~'7':a'?'&'  z""$%*J!"a'J,?,?,A!,D,I,+,  $$&L$$&L"..0, , !~~	 rg   c                 ^^^^^	^
 [        TR                  5       5      S:X  d;  [        TR                  5       5      S:X  a  TR                  5       S   S:X  d   S5       e[        TR                  5       5      S:X  d;  [        TR                  5       5      S:X  a  TR                  5       S   S:X  d   S5       eU R                  5       U:X  d   SU SU R                  5        35       eTc  [        R                  mU R                  5       mTR                  5       m	TR                  5       m
UUUU	UU
4S jn[        R                  " U R                  5       TUU R                  5       S9$ )	Nr   r/   r  r  r  r  c                h  > T" U 5      nT" [        TR                  5       5      S:X  a  SOS5      nT
" [        TR                  5       5      S:X  a  SOS5      nTR                  [        R                  :w  a%  [
        R                  " U[        R                  5      nT	R                  [        R                  :w  a%  [
        R                  " U[        R                  5      n[
        R                  " [
        R                  " U[        R                  5      U5      U-  n[
        R                  " UT5      nU$ )Nr/   r  r   )r   r   r   r{   r  rR   r   r  )r6  r  r  r  r  r  r  r  r  r  r  s        re   re  Cquantized_decomposed_dequantize_per_tensor_tensor.<locals>.inner_fn  s    S!c%..*:&;q&@dbI'ENN4D0E0JPRS;;%--'\\&%--8Fu}},,,{EMMBKggcll5%--8+FOll3	*
rg   rg  r  )r  r  r  r  r  r   r  re  r  r  r  s    ``   ` @@@re   1quantized_decomposed_dequantize_per_tensor_tensorr    sU    u~~ A%ENN"u~~'7':a'?'&'  z""$%*J!"a'J,?,?,A!,D,I,+,  ??% 
(/@AR@ST% MM	$$&L$$&L"..0
 
 !~~	 rg   c                |  ^^^^^^^ U S   R                  5       R                  S:H  nU(       a  [        S U  5       5      (       au  U  H  nUR                  5         M     [        S U  5       5      (       a  [	        [
        R                  /U Q76 u  p[        [
        R                  R                  5      " X5      $ [        U 5      S:X  a  [        U S   5      $ [        U S   US5      n[        U S[        R                  06nU  Vs/ s H  n[        Xe5      PM     n nSS jmS mUUU4S	 jm[!        U4S
 jU  5       5      nSUU4S jjm["        R$                  (       a  ['        X5      $ U(       a(  [)        [*        R,                  R/                  X5      5      $ UU4S jmSnSmSS jm[        U 5      U::  d8  [        U 5      ["        R0                  ::  a  [        UU4S jU  5       5      (       a  [        U4S j[2        R4                  R6                   5       5      n	[!        U4S jU  5       5      =(       a    U	n
[        U4S jU  5       5      =(       a    [!        U4S jU  5       5      (       + nU
(       d  U(       a  U(       d  ['        X5      $ [)        [*        R,                  R/                  X5      5      $ s  snf )Nr   r   c              3     #    U  H5  oR                  5       [        R                  [        R                  4;   v   M7     g 7fr   )r   r{   int8uint8r   r  s     re   r   cat.<locals>.<genexpr>  s*      DJ5ejj%++66Fs   =?c              3  Z   #    U  H!  n[        UR                  5       5      S :H  v   M#     g7f)r   N)r   r   r  s     re   r   r     s!     >ves5>>#$)vs   )+r/   r   c                $   [        U [        5      (       aO  [        U R                  [        R                  5      (       a  U R                  R                  5       $ U R                  $ [        U [        R                  5      (       a  U R                  $ U $ r   )rk   rC   rm   r2   r6   r  r   r   s    re   unwrap_tensorcat.<locals>.unwrap_tensor-  s_    a##!&&"++..vv))++vva''66Mrg   c                    [        U [        R                  5      =(       a$    [        U R                  [        R                  5      $ r   )rk   r2   r  rm   rA   )rw   s    re   is_reductioncat.<locals>.is_reduction9  s)    !R../TJqvvr||4TTrg   c                  > [        U [        [        R                  45      (       a  T" T" U 5      5      $ T" U 5      =(       dD    [        U [        R                  5      =(       a#    [        U4S jU R                  5        5       5      $ )Nc              3  n   >#    U  H*  nT" [         R                  R                  U5      5      v   M,     g 7fr   )rS   r]   
get_buffer)r   readcan_fuse_reductions     re   r   2cat.<locals>.can_fuse_reduction.<locals>.<genexpr>B  s/      .D #177#5#5d#;<<.s   25)rk   rC   r2   r   r@   r#  get_read_names)rw   r  r  r  s    re   r  cat.<locals>.can_fuse_reduction<  sk    a)R]]344%mA&677O !R\\*  ,,. 	
rg   c              3  4   >#    U  H  nT" U5      v   M     g 7fr   r   r   rw   r  s     re   r   r  I  s     B6a.q116   c                X  > [         R                  " U 5      (       a;  [         R                  " U SS9u  p[         R                  R	                  U5      (       + $ [        U [        [         R                  45      (       a  T" T" U 5      5      $ [        U [         R                  5      (       a  gg)NF)freezeT)	r2   r  r  ConcatKernelcan_realize_into_without_copyrk   rC   r   r@   )r   r  r   should_lower_cat_inputr  s      re   r  #cat.<locals>.should_lower_cat_inputK  s     ##A&&11!EBJGDDWMMMa)R]]344)-*:;;a&&rg   c                `  > [        U [        [        R                  45      (       a  T" T" U 5      5      $ [        U [        R                  5      (       d  gU R                  5       R                  nU R                  5        H+  nUT" [        R                  R                  U5      5      -  nM-     U$ r  )rk   rC   r2   r   r@   inner_fn_opcountnum_opsr  rS   r]   r  )r   countr  op_countr  s      re   r  cat.<locals>.op_countb  s    a)R]]344M!,-- !R\\**""$,,$$&DXagg00677E ' rg   r   r-   c                p    U [         R                  R                  [         R                  R                  4;   $ r   )r  catr  constant_pad_ndr`   s    re   additional_pointwise_ops%cat.<locals>.additional_pointwise_opsw  s(    dhh&&(<(<(D(DEEErg   c              3  :   >#    U  H  nT" U5      T:*  v   M     g 7fr   r   )r   rw   MAX_SIMPLE_OP_COUNTr  s     re   r   r  |  s     CFq22F   c              3  <   >#    U  H  n[        UT5      v   M     g 7fr   )rJ   )r   user  s     re   r   r  ~  s#      
+ S":;;+r   c              3  4   >#    U  H  nT" U5      v   M     g 7fr   r   r   r   r  s     re   r   r    s     >v&s++vr  c              3  4   >#    U  H  nT" U5      v   M     g 7fr   r   r$  s     re   r   r    s      "
39C"3''6r  c              3  4   >#    U  H  nT" U5      v   M     g 7fr   r   r
  s     re   r   r    s     <V(++Vr  )r   zUnion[TensorBox, ir.StorageBox]r   	ir.IRNoder   r   r`   torch._ops.OpOverload)rn   r   r"  r  require_channels_lastr  r  r  r  r   r  r_  r   r   rF  r   r#  r0   force_pointwise_catr  rC   r2   r  r   max_pointwise_cat_inputsrS   r^   r_   )rI  r   
cpu_devicer  r   r   r   fusable_reductionMAX_COMPLEX_POINTWISE_CATpointwise_usesfuse_pointwise_usehorizontal_fuse_catr  r  r  r  r  r  r  s               @@@@@@@re   r  r    sD   %%',,5Jc DJ  
 EMMO >v>>>-dhh@@IF 0 01&>>
6{aVAY
q	3
*C	%D%L%LE /55fshs"fF5
U

 B6BB  !!V)) //<==$ !"F 6{//	V77	7CFCCC 
~~++
 
 >v>>Q> 	 " "
39"
 
 =<V<<< 	 "5>O --R__++F899K 6s   J9c                  ^^^
^^ U R                  5       m[        T5      m[        TTS9m[        TTS9m[        TT:g  UU4S j5        [        R
                  R                  R                  [        R                  " US5      5      nU(       a\  [        R
                  R                  R                  [        R
                  R                  R                  TT   U-   TT   5      S5      nO[[        R
                  R                  R                  [        R
                  R                  R                  TT   TT   U-
  5      S5      nSm
U(       a  U* S4m
OSU4m
[        T5       VVs/ s H  u  pgUTT4;  d  M  UPM     nnnUR                  U5        U
UUUU4S jn	[        [        R                   R#                  XU	5      5      $ s  snnf )N)r6  rankc                    > ST  ST 3$ )Nz(diagonal dimensions cannot be identical z, r   )dim1dim2s   re   rQ  diagonal.<locals>.<lambda>  s     HbQUPVWrg   r   )r   r   c                   > U S   nS/[        T	5      -  nSn[        T5       H2  nUT:X  a  UTS   -   X$'   M  UT:X  a  UTS   -   X$'   M'  X   X$'   US-  nM4     U[        T	5      S-
  :X  d   eU$ )NrU  r   r/   r-   )r   r  )
r6  diag_idxoriginal_idxcur_dimr  base_idxr7  r8  num_dimsoriginal_shapes
        re   	reindexerdiagonal.<locals>.reindexer  s    r7sS00xADy"*Xa["8d"*Xa["8"%,1 ! #n-1111rg   )r   r   r   r   rS   r]   r   evaluate_exprr   rU  evaluate_maxevaluate_minrj   ro   rC   r2   GenericViewr   )r  rk  r7  r8  offset_negative	diag_sizers   r   r  rA  r>  r?  r@  s     ``      @@@re   diagonalrI    s   ^^%N>"H84D84D	W gg&&44UXXfa5HIOGG$$11GG))t$v-~d/C 	
	 GG$$11GG))t$nT&:V&C 	
	 HGQ<v;$^4N441$8MQ4EN	LL   R^^**5CDD' Os   &G8Gc                ,    [        [        XX#5      5      $ r   )r  rI  )r  rk  r7  r8  s       re   diagonal_copyrK    s    %455rg   c                J    [        U 5      n[        XRX45      n[        Xa5        U$ r   )r  rI  	mutate_to)r  srcrk  r7  r8  r6  ra   s          re   diagonal_scatterrO    s$    5\Ffd1FfMrg   c           	     l   [         R                  " U5      n[         R                  " U R                  5       U   5      nS n[        R                  R
                  R                  [         R                  " US5      5      (       a  X#-   nOE[        R                  R
                  R                  [         R                  " US5      5      (       a  UnUb  [        U5      (       ab  U R                  5         U R                  5       nU R                  5       nU R                  5       R                  Xa   U-  -   nXQ	 Xa	 [        XXg5      $ [        XXDS-   SS9n[!        X5      $ [#        [        R                  R
                  R$                  [        R                  R&                  R(                  S   5      n	U	c   e[+        U	5      S:X  d   U	5       e[-        [/        U	R1                  5       5      5      u  pU R                  5         U R                  5       nU R                  5       nU
n[2        R4                  " U
UU R                  5       R                  Xa   U R                  5       U   SS9n[        R                  R7                  U5      Ul        [        R                  R;                  U5        XQ	 Xa	 [        XXg5      $ )Nr   r/   FrZ  r\  )r   r3  r   rS   r]   r   r  rU  rS  r%   r  rl  rj  rk  rn  r~  r  r&   rc  r^   rm  r   rG  iterr   r2   rm  rg  r   rh  )r   r   r6  r   actual_indexrF  
new_striderz  slice_resultr\  unbacked_offset_symr   buffers                re   selectrW    s.   
,,s
C<<

S)*DLww&&uxxQ'788z	
			(	(#q)9	:	:$S)) IIKzz|HJ!"!6!6<9W!Wa:JJ "!,q8HPUVL<-- 2	""AGG$8$8$=$=>Q$R ((( !Q&9(99&!$'8'>'>'@"AB IIKzz|HJ,**		

SF ''))&1FKGGv&a:BBrg   c                n   [        XS5      nUn[        U[        [        45      (       d^  U R	                  5       U   n[
        R                  R                  R                  [        XA-   S-
  U5      5      nU/U-  nXES-
  U-  -
  US'   / nSnU H#  nXx-   n	UR                  [        XXySS95        U	nM%     U$ )Nr   r/   rU  FrZ  )r_  rk   ri   r   r   rS   r]   r   r  r)   ro   r~  )
r   r  r   sizes_x_sizechunksr  ro  r   rp  s
             re   splitr\    s    

"CF edE]++c"!!++HV^a5G,OP6!zU22r
 FEl 	fQUu=>  Mrg   c                    [        XU5      $ r   )r\  )r   r  r   s      re   split_with_sizesr^  3  s    3rg   c                    [        XS5      n[        R                  R                  R	                  U R                  5       U   5      n[        U5       Vs/ s H  n[        XU5      PM     nnU$ s  snf r  )r_  rS   r]   r   r  r   r  rW  )r   r   rZ  rs   r  s        re   unbindr`  8  s\    

"CWW''

S(9:F).v7AfQQF7M 8s   A.c                6  ^^ U R                  5       n[        U5      n[        XQ5      mUS:X  a  [        [	        U S5      USS9$ UT   n[
        R                  R                  nUR                  X&5        UR                  ST5        [        Xb-
  T5      S-   nUR                  U5      S:  a,  U R                  UR                  [        X-  U5      5      5        / US T QUPUTS-   S  QUPn	UU4S jn
[        [        R                   R#                  X	U
5      5      $ )Nr   F)rp  r[  r/   c                D   > U S   U T   T-  -   n/ U S T QUPU TS-   S Q7$ )NrU  r/   r   )r6  dim_idxr   rq  s     re   rA  unfold.<locals>.reindexerV  s?    b'CHtO+8Tc8G8c#'B&788rg   )r   r   r   r~  r2  rS   r]   r   	check_leqcheck_ltr)   r   r.  r(   rC   r2   rF  r   )r   	dimensionr   rq  r  ndimdim_sizer   new_dim_sizeout_sizerA  r   s      `       @re   unfoldrl  @  s   JJLEu:D
4
+Cqyi1o4u==SzHwwHt&aHOT2Q6L""8,q0	''0CX(NO	
 EtDlDU379-=DtDH9 R^^**1	BCCrg   c                    [        XS5      n[        U R                  5       5      nUR                  U[        R
                  R                  5        [        X5      $ r  )r_  ri   r   insertr   r/  r0  r  )r   r   r  s      re   r2  r2  ]  sA    

"CQZZ\"IS%''++&rg   c                    [        X5      n[        U [        5      (       d   e[        U[        5      (       d   eUR                  U l        U $ r   )r2  rk   rC   rm   r  s      re   
unsqueeze_rp  e  sB    
A
Ca####c9%%%%XXAFHrg   c                   [         R                  R                  R                  R	                  [
        R                  " U5      5      n[        U R                  5       5      nUS:  a  XU-   -  nSUs=::  a	  X2-   :  d   e   eU$ r  )	rS   r]   r   rc  rC  r   sympifyr   r   )r   r   rk  rh  s       re   r_  r_  n  sn    
''


$
$
2
25==3E
FCqzz|D
Qwf}#dm#####Jrg   rU  c                    [        XS5      n[        R                  R                  R	                  U R                  5       U   5      S-  n[        XSUSS9n[        XX"S-  SS9n[        U[        U5      5      $ )Nr   r-   FrZ  )	r_  rS   r]   r   r  r   r~  rh  sigmoid)r   r   new_lenr   r5  s        re   glurv  w  sk    

"Cgg((c):;q@Gqq'/Aqw!59Aq'!*rg   c                Z   ^  U(       a  [         R                  T 5        U 4S jnSUl        U$ )Nc                 |   > S n[         R                  " U[        R                  R                  " T/U Q70 UD65      $ )Nc                p    [        U [        R                  5      (       a  [        R                  " U 5      $ U $ r   rk   r2   r:   rC   r   r   s    re   wrap_tensors7fallback_handler.<locals>.handler.<locals>.wrap_tensors  (    *4Q		*B*B9##A&IIrg   )rd  tree_mapr2   FallbackKernelr   )rt   r   r{  kernels      re   handler!fallback_handler.<locals>.handler  s<    	J "++226KDKFK
 	
rg   T)r  r   _is_fallback_handler)r  r  r  s   `  re   r  r    s&    f
 $(G Nrg   c                 0    [         R                  " S5        g )NzjTorchinductor does not support code generation for complex operators. Performance may be worse than eager.)warningswarnr   rg   re   _warn_complex_not_supportedr    s    MMtrg   c                   U R                  5       (       a  [        5         gU R                  (       a  gU R                  (       a  gU R                  [
        R                  :X  Ga  U(       d  g[        UR                  [
        R                  R                  5      =(       as    UR                  [        R                  R                  [        R                  R                  [        R                  R                  [        R                   R                  4;   =(       dJ    [        UR                  [
        R                  R                  5      =(       a    [#        UR                  5      (       + $ g)z0Do not support reading or writing to this tensorTF)r  r  is_meta	is_sparser   r{   float8_e8m0fnurk   ra   r|   r}   r  r  r  r  r  
_scaled_mmrK   )rw   rc   s     re   unsupported_input_tensorr    s    ||~~#%yy{{ww%&&&
 t{{EJJ$9$9: 		  

""''	Y 4;;

(=(=>W74;;CW

 
	
 rg   c                L   [         R                  R                  [        R                  R
                  R                  R                  4nUb&  UR                  U;   a  U R                  5       (       a  g[        X5      (       a  gU R                  =(       a    [        R                  $ )z2Do not support writing tensor but can read from itFT)r  r  r   r{   rR   r  r  r  ra   r  r  is_cpur0   disable_cpp_codegen)rw   rc   supported_complex_viewss      re   unsupported_output_tensorr    sr     					,,44 DKK+BBq||~~((882222rg   c                ^  ^  T R                   [        R                  R                  L a  gT R                  S:X  a  gT R                   [        R
                  R                  L a  gU 4S jn[        R                  " T R                  0 T R                  D6 H  nU" USS9(       d  M    g   U" T SS9$ )NFplaceholderc                  > [        U [        R                  R                  5      (       d  gSU R                  ;  a  g[
        R                  " U R                  S   5       H]  n[        U[        R                  R                  5      (       d  M.  U(       a  [        UT5      (       a    gMJ  [        UT5      (       d  M]    g   g)NFr  T)rk   r{   fxNoderm  rd  tree_leaves_subclasses
FakeTensorr  r  )inp_out_node	is_outputrm  rc   s      re   check_skip_conditionCfallback_node_due_to_unsupported_type.<locals>.check_skip_condition  s    ,66)))&&|'8'8'?@DdE$5$5$@$@AA,T488 9 ,D$77 A rg   )r  T)
ra   r  view_as_complexr  r`   lift_fresh_copyrd  arg_tree_leavesrt   r   )rc   allow_cpu_inputsr  r   s   `   re   %fallback_node_due_to_unsupported_typer    s    {{d**222ww- {{d**222* %%tyy@DKK@u55 A  55rg   c                  ^ U [         ;  d  U(       d
   SU  35       eU(       a  [        [        R                  " S5      5      (       a  [	        U /5      (       a  [
        R                  (       a(  U [        R                  R                  R                  ;   ds  U(       dl  [        R                  R
                  R                  (       a4  S[        R                  R
                  l        [        R                  S5        [        SU  S35      eU4S jn[!        U [        R"                  R$                  5      (       a+  U R'                  5        H  n[)        X5      nU" U5        M     g [!        U [        R"                  R*                  [        R"                  R,                  45      (       a	  U" U 5        g [/        SU  S	[1        U 5       35      e)
Nz*both a fallback and a decomp for same op: CIFznA make_fallback error occurred in suppress_errors config, and suppress_errors is being disabled to surface it.zmake_fallback(a.  ): a decomposition exists, we should switch to it. To fix this error, either add a decomposition to core_aten_decompositions (preferred) or inductor_decompositions, and delete the corresponding `make_fallback` line. Get help from the inductor team if unsure, don't pick arbitrarily to unblock yourself.c                j   > [        U 5        Tb  [        U T5        [        U S S9" [        U 5      5      $ Nr  )r   r   r*  r  )op_overloadlayout_constraints    re   register_fallback(make_fallback.<locals>.register_fallback	  s8    !+.(!+/@A $G[)
 	
rg   zUnsupported fallback z with type )r4   r   osgetenvr5   r0   fallback_randomr{   _decompdecompositions_for_rngextra_random_decomps_dynamosuppress_errorslogwarningr   rk   r|   r   r   r   r}   HigherOrderOperatorRuntimeErrorr   )r`   r  r  override_decompr  olr  s    `     re   make_fallbackr    sV   ^# 
4RD96 	4!!t$$ ""emm::OOO ==//38EMM  0KKH RD !f f
 	

 "ejj1122,,.B!"/Kk* ! 
B..

0N0NO	P	P"22$k$r(LMMrg   c                P    SnU  H  nX-  nM	     [        U[        R                  S9$ )z
TorchInductor offset calculation differs from PyTorch eager offset
calculation for random ops (tl.rand vs torch.rand). In future, we should
strive for same impl for tl.rand and torch.rand.
r/   r   tensorr{   r  )r3  numelr   s      re   philox_rand_offsetr  &	  s+     E	 %u{{++rg   c                @  ^^	^
^ [         R                  " UTU [         R                  R                  U 5      5      R	                  5       m
UR                  5       mUR                  5       m	UU	U
U4S jn[        R                  " UTU[        U 5      S9n[        U 5      nXx4$ )Nc                  > [         R                  " T" / 5      [        R                  5      n[         R                  " T" / 5      [        R                  5      n[         R                  " [         R
                  " T" U 5      [        R                  5      U5      n[         R                  " UU5      n[         R                  " UT5      $ r   )rR   r   r{   r  r   r  rand)	rA  seed_index_exproffset_index_exprrand_index_exprr  r   offset_loader
random_posseed_loaders	        re   re  philox_rand.<locals>.inner_fn?	  s     ,,{2DLLr):EKKH''NN:e,ekk:<M
 
 ||FE**rg   rg  )
r2   r  FlexibleLayoutcontiguous_stridesmake_indexerri  r@   r   ri   r  )r   seedrk  r  rv   r   re  random_values_nodeoffset_noder  r  r  s        `   @@@re   philox_randr  2	  s     
,,T2	
 ln  ""$K&&(M+ + #))Dz	 %T*K**rg   c           	         [         R                  (       a\  [        R                  " [        R
                  [        R                  R                  [        R                  R                  XU5      5      $ [        S5      e)Nz&should be handled in replace_random.py)r0   r  rd  r~  rC   r   r2   r  r  native_dropoutr  r   )r   ptrains      re   r  r  Y	  sW    $$T%8%8%@%@!N
 	

 EFFrg   c                   [         R                  (       d/  U R                  5       [        R                  " S5      :X  d   S5       eU R                  5         [        U5      S:X  d  [        US   [        5      (       a  [        R                  R                  O[        R                  R                  n[        R                  " X /UQ76   U $ )Nr   Tthis should be handled in decomps unless config.fallback_random or the device is CPUr   )r0   r  rn   r{   rv   r  r   rk   r;  r  
bernoulli_Tensorr2   InplaceBernoulliFallback)r   rt   r  s      re   r  r  d	  s    !!Q\\^u||E7J%J ^J IIK t9>ZQ77 	__## 
 66Hrg   c                    [         R                  (       d/  U R                  5       [        R                  " S5      :X  d   S5       e[        [        U 5      /UQ76 $ )Nr   r  )r0   r  rn   r{   rv   r  r  )r   rt   s     re   bernoulli_pr  s	  sG    !!Q\\^u||E7J%J ^J eAh&&&rg   c                    [         er   r   )r   s    re   _foobarr  |	  s    
rg   c                .    [         R                  S5        g )Nz1using triton random, expect difference from eager)r  info)salts    re   _warn_triton_randomr  	  s    HH@Arg   c                 J    [        [        R                  R                  5        g r   )r  rS   r]   creation_timer   rg   re   warn_triton_randomr  	  s    --.rg   c                     UR                  S5      b  [        U 0 UD6$ [        R                  (       a  UR	                  SS 5        [        U 0 UD6$ [        S5      eN	generatorz-should have been handled in replace_random.py)rn  fallback_rand_generatorr0   r  popfallback_rand_defaultr   rt   r   s     re   r  r  	  sT    zz+*&777			

;%$d5f55
H
IIrg   c                     UR                  S5      b  [        U 0 UD6$ [        R                  (       a  UR	                  SS 5        [        U 0 UD6$ [        S5      er  )rn  fallback_randn_generatorr0   r  r  fallback_randn_defaultr   r  s     re   randnr  	  sT    zz+*'888			

;%%t6v66
H
IIrg   c                l    [         R                  " U5      n[         R                  R                  X5      $ r   )r2   get_stride_orderExternKernelrequire_stride_order)input_tensorr  stride_orders      re   inductor_force_stride_orderr  	  s'    &&v.L??//KKrg   c                    [        S5      e)Nz.should be handled in fuse_seed_creation_pass()r  )rv   s    re   inductor_seedr  	  s    
I
JJrg   c                ~    [        5         [        R                  " [        R                  " U [        U5      5      5      $ r   )r  rC   r   r2   RandomSeedsrG   )r  rv   s     re   inductor_seedsr  	  s)    BNN5-2GHIIrg   c                z   ^ ^ UU 4S jn[         R                  " T R                  5       T R                  5       U/ S9$ )Nc                N   > [         R                  " TR                  5       T5      $ r   )rR   	load_seedget_name)r   rA  seedss    re   re  &inductor_lookup_seed.<locals>.inner_fn	  s    }}U^^-u55rg   rg  )r@   r   rn   r   )r  rA  re  s   `` re   inductor_lookup_seedr  	  s9    6 !oo	 rg   rk  c                 ^^^	 [         R                  (       a   eTS;   d   e/ U Qn [        R                  nUR	                  5       n[
        R                  " XTU [
        R                  R                  U 5      US9R                  5       mUR                  5       m	UUU	4S jn[        R                  " UUU/ U QS9nUR                  5         U$ )N)r  r  r  c                   > [        [        T5      " T" / 5      [        R                  " T" U 5      [        R                  5      5      $ r   )r   rR   r  r{   r  )rA  moder  r  s    re   re  !inductor_random.<locals>.inner_fn	  s5    sD!ONN:e,ekk:
 	
rg   rg  )r0   r  r{   r  rH  r2   r  r  r  r  ri  r@   r   r  )
r   r  r  rk  r   rv   re  r  r  r  s
     `     @@re   inductor_randomr	  	  s    %%%%$$$$T7DMME%%'FtR..AA$GPVln  ""$K
 w	F NNMrg   c               h  ^ ^^^	 [         R                  (       a   e/ UQn[        R                  nUR	                  5       n[
        R                  " XeU[
        R                  R                  U5      US9R                  5       mUR                  5       m	UU UU	4S jn[        R                  " UUU/ UQS9$ )Nr  c           	        > [         R                  " T" / 5      [         R                  " T" U 5      [        R                  5      [         R                  " T[        R
                  5      [         R                  " T[        R
                  5      5      $ r   )rR   	randint64r  r{   r  r  )rA  highlowr  r  s    re   re  "inductor_randint.<locals>.inner_fn	  sV    }}ONN:e,ekk:NN3,NN4-	
 	
rg   rg  )r0   r  r{   r  rH  r2   r  r  r  r  ri  r@   r   )
r  r  r   r  rk  r   rv   re  r  r  s
   ``      @@re   inductor_randintr  	  s     %%%%T7DKKE%%'FtR..AA$GPVln  ""$K
 
 w	 rg   c                    U R                  5       nU R                  5       n[        S [        X5       5       5      US   -   nU R	                  5       US   UUS   4$ )Nc              3  6   #    U  H  u  pUS -
  U-  v   M     g7fr=  r   )r   r   sts      re   r   %_boundaries_helper.<locals>.<genexpr>
  s     A/@eaa!er\/@s   rU  )r   rl  sumr  r   )tbr   r  
max_offsets       re   _boundaries_helperr  
  s\    
 ;;=D]]_FAs4/@AAF2JNJ
Rr
	 rg   c                H    U R                  5       U R                  5       S   4$ r1  )r   rl  r  s    re   _sorter_helperr  
  s    ;;="--/"---rg   	out_int32rightsidesorterc          	     p  ^ ^^^
^ S nU" T 5      (       a  U" U5      (       a  Tb8  U" T5      (       d+  [        [        R                  R                  SS9" T UUTUTS9$ Ub  US:X  a  SmU(       a  [        R
                  O[        R                  m
UR                  5       mT R                  5         Tb  TR                  5         [        T R                  5       5      S:X  a  U
UU UU4S jnO
U
UU UU4S	 jnUR                  5       n[        R                  " UT
UUR                  S
9n	U	R                  5         U	$ )Nc                ^    [         R                  R                  U [        R                  5      $ r   )rS   r]   r|  r}  	BUCKETIZEr  s    re   rQ  searchsorted.<locals>.<lambda>
  s    AGG$7$7
N$$%rg   Fr  r  r  Tr/   c           
        > T" U 5      n[         R                  " U[        T5      STTTc  S O
[        T5      Tc  S S9$ SS9$ )Nr   r   sorter_indicesrR   	bucketizer  r  )r6  r  index_dtyper  sorted_sequencer   values_loaders     re   re  searchsorted.<locals>.inner_fnD
  sV    $C=="?3%~t>&3I'-~t  <= rg   c                   >^  T" T 5      nSU U4S jjn[         R                  " U[        T5      U" T5      TTTc  S O
[        T5      Tc  S S9$ U" T5      S9$ )Nc                   > U R                  5       n[        R                  " [        R                  " [
        R                  S [        US S TS S 5       5       5      T5      $ )Nc              3  .   #    U  H  u  pX-  v   M     g 7fr   r   )r   r   rs   s      re   r   Nsearchsorted.<locals>.inner_fn.<locals>.get_flattened_index.<locals>.<genexpr>[
  s     &U9Tqu9T   rU  )rl  rR   r  r  r  operatorr   r  )r  stridesr6  r*  s     re   get_flattened_index;searchsorted.<locals>.inner_fn.<locals>.get_flattened_indexW
  sU    --/~~$$ &UWSb\3sPR89T&U  	 rg   r&  )r  rC   r(  )r6  r  r5  r*  r  r+  r   r,  s   `  re   re  r-  R
  sm    $C  =="?3#O4%~t>&3I'-~t  <Ov;V rg   rg  )r  r  searchsortedr  r{   r  r  ri  r  r   r   rn   r@   r   r3  )r+  selfr  r  r  r   validate_bucketizere  rv   r  r*  r,  s   `  ` `    @@re   r7  r7  
  s    //!$'''9&'A'A 1 1 8 8eT
 	
 DGO!*%++K$$&M 
?##%&!+
	 
		 	0 __Fzz	F NNMrg   r  r  c                 ^^^^ [        TR                  5       5      S:X  d   e[        R                  R	                  U [
        R                  5      (       a3  [        R                  R	                  T[
        R                  5      (       d)  [        [        R                  R                  SS9" U TUTS9$ TR                  5         U R                  5       nU R                  5       mU(       a  [        R                  O[        R                   mUUUU4S jn["        R$                  " UTUU R                  5       S9nUR                  5         U$ )Nr/   Fr  r:  c                ^   > T" U 5      n[         R                  " U[        T5      STT5      nU$ r  )rR   r)  r  )rA  r  r  
boundariesr*  r  r  s      re   re  bucketize.<locals>.inner_fn
  s6    5!--z*
 rg   rg  )r   r   rS   r]   r|  r}  r#  r  r  r)  r  r  rn   ri  r{   r  r  r@   r   )	r  r=  r  r  rv   re  r  r*  r  s	    ` `   @@re   r)  r)  w
  s     z""$%*** 	
E>#;#;<<GG
N,D,DEE 5 55Q:%
 	
 F$$&L!*%++K
 
 ~~	F NNMrg   c                    [         R                  " [        R                  [        R                  R
                  X45      u  pX4$ r   )rd  tree_map_onlyr2   r:   r  require_stride1r   rt   r   s      re   require_denserC  
  s5    ''
		2??22TNLD <rg   c                    [         R                  " [        R                  [        R                  R
                  X45      u  pX4$ r   )rd  r@  r2   r:   r  require_contiguousrB  s      re   rE  rE  
  s5    ''
		2??55~LD <rg   c                    [         R                  " [        R                  [        R                  R
                  X45      u  pX4$ r   )rd  r@  r2   r:   r  r   rB  s      re   r   r   
  s7     ''
		2??==~LD <rg   c                    [         R                  " [        R                  [        R                  R
                  X45      u  pX4$ r   )rd  r@  r2   r:   r  r+  rB  s      re   r+  r+  
  s5    ''
		2??884.LD <rg   c           	     \   Uc  U $ [        U[        5      (       a  U $ [        U [        R                  5      (       at  UR	                  5        Vs/ s H:  n[        U[
        R                  5      (       a  UR                  R                  OUPM<     nn[        R                  R                  X5      $ [        U [        5      (       a!  U  Vs0 s H  oD[        X   X   5      _M     sn$ [        U [        [        45      (       a!  [        U 5      " S [!        X5       5       5      $ U $ s  snf s  snf )Nc              3  <   #    U  H  u  p[        X5      v   M     g 7fr   constrain_to_fake_tensor)r   r   f_as      re   r   +constrain_to_fake_tensor.<locals>.<genexpr>
  s      
=O!$Q,,=O   )rk   r   r2   r:   r  r{   SymIntrc   exprr  require_exact_stridesr  rK  r   ri   r   r  )r   fake_argr   meta_stride_exprkeys        re   rK  rK  
  s   
(,--
#ryy!!GOGX
GX!:a66AFFKKA=GX 	 
 44SKK#tRUVRU3-chFFRUVV	C%	'	'Cy 
=@=O
 
 	
 J

 Ws   AD$	D)c           
         [        S [        X5       5       5      n UR                  5        VVs0 s H  u  pEU[        XSU   5      _M     nnnX4$ s  snnf )Nc              3  <   #    U  H  u  p[        X5      v   M     g 7fr   rJ  )r   r   rR  s      re   r   ,constrain_to_fake_tensors.<locals>.<genexpr>
  s!      1MC 	!//1rN  )r   r  r   rK  )rt   r   	fake_argsfake_kwargsr   r	  s         re   r   r   
  s[      1 D JPXa)!^<<FX< Ys   Ac           
        ^ U4S jm[        U4S j[        XR                  5       5       5      nUR                  5        VVs0 s H  u  p4UT" X@R                  U   5      _M     nnnX4$ s  snnf )Nc           	       > [        U [        R                  5      (       as  [        R                  " UR                  S   R                  5       [        R                  R                  R                  5      n[        R                  R                  X5      $ [        U [        5      (       a  U  Vs0 s H  o3T" X   X   5      _M     sn$ U $ s  snf Nr  )rk   r2   r:   r  rm  r  rS   r]   r   rc  r  r  r  )r   fx_argr  rT  apply_constraints       re   r^  1constrain_to_fx_strides.<locals>.apply_constraint
  s    c299%%..E"))+QWW-=-=-G-GL ??77JJc4  LOPCS)#(FK@@CPP
 Qs   -C	c              3  8   >#    U  H  u  pT" X5      v   M     g 7fr   r   )r   r   r]  r^  s      re   r   *constrain_to_fx_strides.<locals>.<genexpr>
  s       9P+#%%9Ps   )r   r  rt   r   r   fx_nodert   r   r   r	  r^  s        @re   r   r   
  sl      9<T<<9P D EKLLNSNDAa!!^^A%677NFS< Ts   "A+c                   ^ ^ U 4S jm[        U4S j[        [        UT R                  5      5       5       5      nUR	                  5        VVs0 s H  u  p4UT" SUT R
                  U   5      _M     nnnX4$ s  snnf )Nc           
       >^ [        U[        R                  5      (       d  U$ UR                  S   nUR	                  5        Vs/ s H:  n[        U[
        R                  5      (       a  UR                  R                  OUPM<     nn[        R                  R                  R                  n[        R                  " UR	                  5       U5      nU(       a=  US   S:w  a4  [        [        [!        [#        UR%                  5       5      5      5      5      nTR&                  [(        R*                  R,                  :X  a  U S;   a  [#        U5      S:X  d   eSnUR.                  (       d  [        R0                  R3                  X5      $ SmTR&                  [
        R4                  R(                  R6                  R,                  :H  =(       a    U S:H  n[        U[8        5      (       d   e[#        UR%                  5       5      S	;  a  U$ [        R:                  " UT5      n	U	(       a4  [        R<                  " [        R0                  R?                  U5      U5      $ [        U[        5      (       aL  URA                  5       b;  U	(       a4  [        R<                  " [        R0                  R?                  U5      U5      $ U(       Ga  [        UR%                  5       5      n
/ nURA                  5       n[!        [#        UR%                  5       5      S
-
  5       H}  n[        R                  R                  RC                  X]   S5      (       d8  Uc  M9  [        R                  R                  RC                  X   S5      (       d  Ml  URE                  U5        M     S/[#        U
5      -  nS
US'   S
n[!        [#        U
5      S-
  SS5       H  nXS
-      S:w  a
  XUS
-      -  nX;   a=  [        R                  R                  RC                  XS
-      T-  S5      (       a  SX'   MZ  [        R                  R                  RC                  UT-  S5      (       d  [G        UT5      T-  nXU'   M     [        R0                  RI                  X5      $ U	(       a4  [        R<                  " [        R0                  R?                  U5      U5      $ [        U[        5      (       aL  URA                  5       b;  U	(       a4  [        R<                  " [        R0                  R?                  U5      U5      $ U4S jn[        URJ                  [        RL                  5      (       a\  U" U5      (       dO  U" URO                  5       5      (       a4  [        R<                  " [        R0                  R?                  U5      U5      $ [        R0                  R3                  X5      $ s  snf )Nr  rU  r   )r   r   r   )r   r/   r-   r   r   r   r   r   r/   r-   c                   > [         R                  R                  R                  [        R
                  " [        U R                  5       S   T5      S5      5      $ )NrU  r   )rS   r]   r   r  r   r  r+   r   )r   	ALIGNMENTs    re   
is_aligned=sdpa_constraint.<locals>.apply_constraint.<locals>.is_aligneds  s@    77##22QZZ\"-y91= rg   )(rk   r2   r:   rm  r  r{   rO  rc   rP  rS   r]   r   rc  r  ri   r.  r  r   r   ra   r  0_scaled_dot_product_efficient_attention_backwardr  is_cudar  r  rR   '_scaled_dot_product_efficient_attentionrC   is_aligned_realized_tensortry_match_insignificant_stridesrealize_inputmaybe_get_stridestatically_known_equalsro   rF   rQ  rm   r6   r  )r6  r   r]  meta_valr   rS  rc  r  effn_attn_fwd_biasis_aligned_tensorrk  expanded_dimsmaybe_striders   out_stridesr  ri  rh  rc  s                    @re   r^  )sdpa_constraint.<locals>.apply_constraint  s   #ryy))J;;u%GOGX
GX!:a66AFFKKA=GX 	 
 GG$$..	**8??+<iHL,1s3<<>/B)C DEL NNDDLLMv|$)))
 (L??77JJ 	 NNyy~~EEMMN q 	 #y))))s||~f,J99#yI55--c24D 
 sF##$$&2!55--c24D  CLLN+HM //1L3s||~.2377##;;<L<OQRSS ,((@@RSTT!((+ 4 $X.KKOF3x=1,b"51u%*#q1uo5F %ww''??#E*Y6  *+ ww''??@RTUVV$VY7)CF!'A! 6$ ??88JJ55--c24D 
 sF##$$&2!55--c24D 	
 chh,,c??coo/00==55c:<L  33CFFo
s   AWc              3  @   >#    U  H  u  nu  p#T" XU5      v   M     g 7fr   r   )r   r6  r   r]  r^  s       re   r   "sdpa_constraint.<locals>.<genexpr>  s)      "DC# 	6**"Ds   rU  )r   rj   r  rt   r   r   rb  s   `    @re   sdpa_constraintr|     sz    |G|  "+Cgll,C"D D IOWa!"a):;;FW< Xs   $A8)r  )r  c                   [        U[        R                  5      (       d&  [        XR	                  5       U R                  5       S9nUnU R                  5       UR                  5       :w  a  [        X0R                  5       5      nU R	                  5       UR	                  5       :w  a  [        X0R	                  5       5      nU R                  5       UR                  5       :w  a$  [        X0R                  5       5      n[        U5      $ [        U5      $ Nr;  )rk   r2   r:   r  r   rn   r  r   r   r3  r  )r8  rN  r  r   rq   s        re   r  r  f  s    c299%%S 09JKACNN,,a*+~~3==?*Q()}}#,,.(Q(Sz8Org   )memory_formatc          	         [         R                  " U R                  5       U R                  5       U R	                  5       [        U R                  5       5      S9$ Nrg  )r@   r   rn   r   ri  ri   r   )r   r  s     re   r  r  v  s@     ||~kkmAJJL!	 rg   c                "   / n[        U [        5      (       a  [        U R                  [        R                  5      (       a  U R                  n [        U [        R                  5      (       aL  UR                  U R                  5       5        U R                  n [        U [        R                  5      (       a  ML  [        U 5      n [        U 5      n U(       a:  U R                  n US S S2    H  n[        R                  " XS9n M     [        U 5      n U $ )NrU  r  )rk   rC   rm   r2   r   ro   rj  r  )r   reinterpret_view_layoutsr  s      re   clone_preserve_reinterpret_viewr    s    !!YJqvvr7I7I$J$JFFB..//$++ALLN;A B..// aLaAFF.tt4F""9A 5aLHrg   r  c               Z   ^^^ UUU4S jn[         R                  " [        U5      TUU /S9$ )Nc                @   > [         R                  " TU S   -  T-   TS9$ )Nr   r   rR   r  )rA  r   ro  rq  s    re   r   iota.<locals>.fn  s!    ~~dU1Xo5UCCrg   rg  )r@   r   rG   )lengthro  rq  r   rv   requires_gradr   s    ```   re   iotar    s1    D V$x	 rg   c           	       ^^^^ [        XR                  5       5      nU R                  5       m[        U TS5      m[        R
                  R                  R                  [        R                  " TS5      5      (       a  TU R                  5       T   -   mOo[        R
                  R                  R                  [        R                  " TS5      5      (       a  O+[        [        R                  R                  5      " XTT5      $ [        R
                  R                  R!                  ST5        [        R
                  R                  R#                  TU R                  5       T   5        [%        ['        UT5      U R                  5       5      nUR                  5       mUUUU4S jn[(        R*                  " U R-                  5       U R                  5       U[/        U R                  5       5      S9$ )Nr   c           	       > [         R                  " [         R                  " [         R                  " U T   [        R
                  5      [         R                  " T[        R
                  5      5      T" U 5      T" U 5      5      $ r   )rR   r  eqr  r{   r  )r6  r   rA  
src_loaderrC  s    re   re   select_scatter.<locals>.inner_fn  sX    yyFFs3x5uekk2 sOSM
 	
rg   rg  )r   r   ri  r_  rS   r]   r   r  r   rU  r   rS  r  r  select_scatterr  re  rf  r3  r2  r@   r   rn   ri   )r   rN  r   rA  re  r  rC  s     `` @@re   r  r    sX   
3
&C}}H
3
"Cww&&uxxq'9::

S))	
			(	(%);	<	<   3 3 ; ;<QS%PPGGq%(GGeQZZ\#%67
3$ajjl
3C"J
 
 ||~kkmAJJL!	 rg   c           	     6  ^ ^^^^^^	^
 [        UT R                  5       5      nT R                  5       m
[        T TS5      mT R	                  5       T   m[
        R                  R                  T TTT5      u  mm[        T R	                  5       5      n[        TT-
  TS-
  -   T5      UT'   [        X5      nUR                  5       m	UUUU	UUU U
4S jn[        R                  " T R                  5       T R                  5       U[        T R	                  5       5      S9$ )Nr   r/   c                V  >^ T	S:X  a  TT:X  a  T
S:X  a  T" U 5      $ [         R                  " U T   [        R                  5      n[	        U 5      m[        U T   T	-
  T
5      TT'   / nT	S:w  a]  UR                  [         R                  " U[         R                  " [        R                  " T	5      [        R                  5      5      5        TT:w  a]  UR                  [         R                  " U[         R                  " [        R                  " T5      [        R                  5      5      5        T
S:w  a}  UR                  [         R                  " [         R                  " [        U T   T	-
  ST
5      [        R                  5      [         R                  " S[        R                  5      5      5        U(       d   e[        R                  " [         R                   U5      n[         R"                  " UUU4S j[%        T5      (       a  SOS5      n[         R&                  " UUT" U 5      5      $ )Nr   r/   c                    > T" T 5      $ r   r   )src_idxr  s   re   rQ  1slice_scatter.<locals>.inner_fn.<locals>.<lambda>  s
    Jw'rg   r  )rR   r  r{   r  ri   r)   ro   r  r   r3  r  r  r,   r  r  r  r  r  r   r  )r6  r  r  src_valr  r   ri  rp  r  ro  rq  r   rC  s       @re   re  slice_scatter.<locals>.inner_fn  s   A:#/daic?"..S5;;7s)C5 0$7A:KKNN5<<#6D (?KKNN5<<#4ekkB 19KKNN'C5(8!TBEKK LLEKK0	 t$/**' ##A

 yySM
 	
rg   rg  )r   r   ri  r_  r   r2   rb  normalize_start_endri   r)   r3  r@   r   rn   )r   rN  r   ro  rp  rq  src_sizere  ri  r  rC  s   ` ````  @@@re   slice_scatterr    s    
3
&C}}H
3
"Czz|C H 11!S%EJE3AJJL!HS5[D1H5t<HSM

C"J,
 ,
\ ||~kkmAJJL!	 rg   c                v    [        U [        [        45      (       a  [        U 5      S:  a  [	        U S   5      $ U $ r  )rk   ri   r   r   _unwrapr   s    re   r  r    s0    !dE]##A
qt}Hrg   r   rv   r  
pin_memoryc               :  ^ ^ [        US [        R                  4;   SU 35        [        U(       + S5        [        [	        T 5      [
        5      (       a  T=(       d    [        R                  mOT=(       d    [        R                  " 5       m/ n[        T [        R                  5      (       a  U U4S jnO[        T [        [
        45      (       a  U U4S jnO[        T 5      S:X  d-  [        T S   [        [
        45      (       aE  [        T 5      S::  a6  UR                  [        R                  " [        T 5      5      5        U U4S jnO3[        R                  R!                  [        R"                  " T TUS95      $ [$        R&                  " [)        U5      TUUS	9$ )
Nlayout=r  c                2   > [         R                  " TT5      $ r   r  rA  rm   r   s    re   re  tensor.<locals>.inner_fn+  s    >>$..rg   c                2   > [         R                  " TT5      $ r   rR   r  r  s    re   re  r  0  s    <<e,,rg   r   r   c                   >^ ^ UUUU 4S jm[        T5      S:X  a  [        R                  " ST5      $ T" S[        T5      5      $ )Nc           	     n  > X:  d   eX-
  S:X  a  [         R                  " TU    T5      $ X-
  S-  U -   n[         R                  " [         R                  " [         R                  " TS   [
        R                  5      [         R                  " U[
        R                  5      5      T" X5      T" X!5      5      $ )Nr/   r-   r   )rR   r  r  r  r  r{   r  )ro  rp  midbinary_searchrm   r   rA  s      re   r  /tensor.<locals>.inner_fn.<locals>.binary_search8  s    {"{;!#<<UU;;{q(50yyFFuQx=S%++6 "%-!#+ rg   r   )r   rR   r  )rA  r  rm   r   s   `@re   re  r  7  s<      4yA~||Au-- CI..rg   r;  rg  )r   r{   stridedrk   r  r   r  get_default_dtyper   r   r;  r   ro   IntegerrS   r]   add_tensor_constantr  r@   r   rG   )rm   r   rv   r  r  rd  re  s   ``     re   r  r    s+   v$..'&0BC:~|,'$-%%$2002!F$$$	/ 
D5#,	'	'	- 
Ta:d1gs|<<TaemmCI./	/( ww**LLU6:
 	
 V$	 rg   c                |    [        U [        5      (       a  Ub  [        X5      n Ub  [        X5      n U $ [	        XUS9$ r~  )rk   rC   r   r  r  )rm   r   rv   s      re   	as_tensorr  W  sA    $	""D(DT*D$F33rg   c                2    [        U [        R                  S9$ r  r  )rm   s    re   long_tensorr  b  s    $ekk**rg   c                   [        [        R                  R                  R                  [        R                  R
                  R                  S   5      nUc   e[        U5      S:X  d   U5       e[        [        UR                  5       5      5      u  p#[        R                  " X#U 5      n[        R                  R                  U5      Ul        [        R                  R                  U5        [        R                  R
                  R                  S   n[!        U["        R$                  ["        R&                  ["        R(                  45      (       a  UR*                  R,                  $ [.        R0                  " U5      $ )Nr\  r/   r  )r&   rS   r]   r   rc  r^   rm  r   rG  rQ  r   r2   DynamicScalarrg  r   rh  rk   r{   rO  SymFloatSymBoolrc   rP  r   rr  )rm   r\  binding_symrx  rV  r  s         re   _local_scalar_denser  g  s    2	""AGG$8$8$=$=>Q$R ((( !Q&9(99&   %6%<%<%> ?@KkD9F''))&1FKGGv& ''


#
#E
*C#ennemmDEExx}}}}S!!rg   c                    g r   r   )rm   r   s     re   _assert_scalarr    s     rg   )rv   r  c                   g r   r   )r   r   r  r   rv   r  s         re   _assert_tensor_metadatar    s     rg   c                  ^^^ U m[        U [        [        45      (       d  [        TS5      (       a  TR                  m[        T[        [        45      (       a  UU4S jnO\[        T[
        R                  5      (       a  UU4S jnO5[        TR                  5       5      S:X  d   eTR                  5       mU4S jn[        R                  " UTU[        U5      S9$ )Nr   c                2   > [         R                  " TT5      $ r   r  rA  r   r   s    re   re  _full.<locals>.inner_fn  s    <<u--rg   c                2   > [         R                  " TT5      $ r   r  r  s    re   re  r    s    >>%//rg   r   c                   > T" / 5      $ r   r   )rA  value_loaders    re   re  r    s    ##rg   rg  )rk   r   r;  r   r   r   r   r   r   ri  r@   r   ri   )
fill_valuerv   r   r   re  r   r  s     `  @@re   _fullr    s    Ej3,//GE74K4K%#u&&	. 
E5;;	'	'	0 5>>#$)))((*	$ Dz	 rg   c                8    [        [        U5      5      " U 40 UD6$ r   create_tensor_liketensor_constructor)r   r  r   s      re   r  r    s    0<=aJ6JJrg   c                &   ^  S S S S SS S.U 4S jjnU$ )NF)namesr   rv   r  r  r  c                0  > [        U S L S5        [        US [        R                  4;   SU 35        [        U(       + S5        [        U5      nU=(       d    [        R                  " 5       n[        U5      S:X  a;  [        US   [        [        [        R                  45      (       a  [        US   5      nU H$  n[        U[        R                  5      (       d  M$   e   U Vs/ s H  n[        R                  " U5      PM     nn[        TX!U5      $ s  snf )Nnamed tensorsr  r  r/   r   )r   r{   r  rG   r  r   rk   ri   r   SizerO  r   r3  r  )	r  r   rv   r  r  r  r   r   r  s	           re   rs  !tensor_constructor.<locals>.inner  s     	5D=/26dEMM22gfX4FGz><0v&2002t9>ja4

2KLLa>D A!!U\\2222 )-.AQ.Z55 /s   $ Dr   )r  rs  s   ` re   r  r    s(     6 6. Lrg   )r  r   r  rv   r  r  c           	         [        U S L S5        [        U5      n[        U5      S:X  a;  [        US   [        [
        [        R                  45      (       a  [        US   5      n[        US XX4S9$ )Nr  r/   r   r   r  rv   r  )	r   rG   r   rk   ri   r   r{   r  empty_strided)r  r   r  rv   r  r  r   s          re   rE  rE    se     u}o.6"F
4yA~*T!WtUEJJ.GHHT!W~d%v rg   c                $   ^  SSSSSS.U 4S jjnU$ )zR
Shim to convert X_like(...) into X(...).  For example zeros_like() into zeros().
NF)r   rv   r  r  r  c                 > [        U(       + S5        [        US [        R                  4;   SU 35        Uc  U R                  5       nO[	        U5      nU=(       d    U R                  5       n[        U R                  5       5      nT" XaX#US9$ )Nr  r  r  )r   r{   r  r   r   rn   ri   r   )r   r   rv   r  r  r  r   creation_fns          re   _constant_like*create_tensor_like.<locals>._constant_like  s~     	z><06dEMM22gfX4FG=KKME 'E)1<<>AJJL!f

 	
rg   r   )r  r  s   ` re   r  r    s#     duTX
 
 rg   c                *    [        [        U 5      5      $ r   r  )r  s    re   r  r    s    0<==rg   c                "   ^  S S S S S.U 4S jjnU$ )Nr  c                 > [        U[        [        45      (       d   e[        U(       + S5        [        US [        R
                  4;   SU 35        [        U5      =(       d    U R                  5       nU=(       d    U R                  5       nU Vs/ s H  n[        R                  " U5      PM     nn[        T[        U5      X!5      $ s  snf )Nr  r  )rk   ri   r   r   r{   r  r   r   rn   r   r  r  rG   )r   r   r   r  rv   r  r   r  s          re   _new_constant#new_constant.<locals>._new_constant  s     $u....z><06dEMM22gfX4FGU#4q{{})1<<>*./$Qa $/Zv!6DD 0s    C	r   )r  r  s   ` re   new_constantr    s     tDT
E 
E rg   r  c          	     |    Uc  U R                  5       nUc  U R                  5       n[        US UU[        U5      US9$ Nr  r   rn   r  rG   )r   r   r   r  rv   r  s         re   	new_emptyr  &  sF    }~V$ rg   c                  [        U [        [        45      (       d   e[        U[        [        [        S 5      45      (       d   e[	        U(       + S5        [	        US [
        R                  4;   SU 35        [        U5      =(       d    [
        R                  " 5       nU=(       d     [
        R                  " S5      R                  n[        U5      n[        SXBU S9nUR                  5         UR                  R                  n[        R                   " UR                  S/[#        U 5      -  S9Ul        [        U[$        R&                  5      (       d   eU  Vs/ s H  n[(        R*                  " U5      PM     n nU(       a'  U Vs/ s H  n[(        R*                  " U5      PM     snO[$        R,                  R/                  U 5      n[$        R0                  " UUU US9Ul        U$ s  snf s  snf )Nr  r  r  r   )r  rv   r   r   )rd  )rv   r   r   r  )rk   ri   r   r   r   r{   r  r   r  r  rv   rG   r  r  rm   dataclassesreplacer   r2   r  r   r3  r  r  r  r  )	r   r  r   r  rv   r  	pointwiserV  r   s	            re   r  r  6  s    dT5M****ftUDJ78888:~|,v$..'&0BC<5#:#:#<E/u||C(//F6"F6TJI^^  F%%fkk1#D	/JFKfb//0000%)*TELLOTD*  #))&Qa&)11$7 
 NN	FM  +)s    G' G,c          	     |    Uc  U R                  5       nUc  U R                  5       n[        UUUU[        U5      US9$ r  r  )r   r   r  r   r  rv   r  s          re   new_empty_stridedr  W  sH     }~V$ rg   c                   U Vs/ s H,  n[         R                  R                  R                  U5      PM.     nn[	        [        [        U5      5      UR                  S9n[        R                  R                  X5      $ s  snf )N)rT  )rS   r]   r   r   sortedr  r   __getitem__r2   r  r  )r   r  r   r  s       re   copy_stridedr  i  sa    >DEfagg11!4fFE%F,&2D2DEL??//@@ Fs   3A?c                X    UR                  S5      c   S5       e[        U5      " U 40 UD6$ )Nr   z(dtype should be handled by decomposition)rn  r  )r   r  r   s      re   fullr  p  s2    ::g*V,VV*j)$9&99rg   c                  ^^^^ [        U [        5      (       d   eUR                  5       S:X  a  [        XR	                  5       5      $ U R	                  5       m[        T5      S:H  n[        U TU5      mU(       a  [        U S/5      n S/mU R                  5       mUR                  5       mUUUU4S jn[        R                  " U R                  5       U R                  5       UUR	                  5       S9$ )Nr   r/   c                   > [        U 5      n [        R                  " T" U 5      TT   5      n[        U 5      S:X  a  U/n OXT'   T" U 5      $ r  )ri   rR   indirect_indexingr   )r6  
gather_idxr   index_loaderr   rC  s     re   r   gather.<locals>.fn  sJ    3i**<+<d3iH
s8q=,C!H}rg   rg  )rk   rC   	get_numelr  r   r   r_  r3  ri  r@   r   rn   r   )	r   r   rA  sparse_gradrk  r   r  r   rC  s	    `    @@@re   gatherr  v  s     a####ANN,--::<DY!^F
3
'C1qcNs}}H$$&L  ||~kkm~~	 rg   c                V  ^^^^	^
 U(       a+  [        [        R                  R                  5      " XX#U5      $ U(       a   e[	        U [
        5      (       d   e[	        U[
        5      (       d   eS[        UR                  5       5      ;   d   eU R                  5       m	UR                  5       m[        UR                  5       5      mU R                  5       m
/ UR                  5       QT
SS  QmUUUU	U
4S jn[        R                  " U R                  5       U R                  5       UTS9$ )Nr   r/   c                   > [        U 5      [        T5      :X  d   U  ST 35       eT" U S T 5      n[        R                  " UTS   5      // U TS  Q-   nT" U5      $ )Nz != r   )r   rR   r  )r6  	var_index
weight_idxindices_loaderindices_ndimrF  weight_loaderweight_sizes      re   r   embedding.<locals>.fn  s{    3x3x=(@SEhZ*@@("3}#56	++I{1~FG K
K
 

 Z((rg   rg  )r  r  	embeddingr  rk   rC   strr   ri  r   r   r@   r   rn   )weightr  padding_idxscale_grad_by_freqsparser   r  r  rF  r  r  s         @@@@@re   r  r    s    6 67[f
 	
 :fi((((gy))))C))+,,,,&&(M((*Nw'')*L//#K6!!#6k!"o6H) )   " 	 rg   c           
     L   [        S U  5       5      (       d-   SU  Vs/ s H  o"c  M  UR                  5       PM     sn 35       e[        S U  5       5      (       a  [        S5      e[	        U 5       VVs/ s H  u  p#[        U[        5      (       d  M  UPM      nnn[        U5      S:  d   S5       eS /[        U 5      -  n[        U[        U Vs/ s H  o U   PM	     sn6 5       H(  u  p#UR                  5       U:w  a  [        S5      eX5U'   M*     XT4$ s  snf s  snnf s  snf )Nc              3     #    U  HY  nUc  M  UR                  5       [        R                  [        R                  [        R                  [        R
                  4;   v   M[     g 7fr   )r   r{   r  r  r   r  r   rs   s     re   r   .check_and_broadcast_indices.<locals>.<genexpr>  sA      A 	M%++u{{EJJLLs   A#AA#z)indices must be int64, byte or bool. Got c              3     #    U  H:  oc  M  UR                  5       [        R                  [        R                  4;   v   M<     g 7fr   )r   r{   r   r  r	  s     re   r   r
    s.      <Cq2%**ekk22Gs
   A8AzFallback for bool indicesr   z"requires at least 1 non-None indexz.Fallback when indices is on a different device)r"  r   r#  r   rj   rk   rC   r   r  r  rn   )r  rv   rs   r   
valid_idxsnew_indicess         re   check_and_broadcast_indicesr    s2       
 4G4eGq]Q[[]G4e3fg   <C   ""=>> )' 2O 2jI6N! 2JOz?QD DD&3w<'KJ 1
3S
1AJ
3S TU <<>V#%&VWWA V ""# 5f P 4Ts   DD5DDD!c	           
     l  ^^^^^^^^^^ Sm[         R                  " T5       H  u  pX-
  S:w  d  M  SmM     [        T5       VVs/ s H  u  pUb  M
  X   PM     snnm/ TQU [        T5      [        T5      -   S  QmTS   nT(       a  TT-   mOTS U T-   TUS  -   mUUUUUUUUUU4
S jnTU4$ s  snnf )NFr/   Tr   c                  >
 [        U 5      [        T5      :X  d   e[        T5      [        T
5      :X  d   e[        T5      n/ nTS   nT(       a  SOUnSn[        TS   S-   5       H|  nXd:X  a  XQ-  nTU   c+  U[        U 5      :  d   eUR                  X   5        US-  nM=  TU   nUc   eT
U   nUR                  [        R                  " U" XXA-    5      UT	TS95        M~     / UQXS  QnTc  U$ T" U5      $ )Nr   rU  r/   r   wrap_neg)r   r  ro   rR   r  )r6  r5  	new_indexfirst_tensor_indexstart_offsetnext_idxrs   loaderr   r   indexed_sizer  indices_loadersnon_consecutive_tensorsoutput_sizetensor_indicestensor_sizer  rC  s            re   r   *index_output_size_and_inner_fn.<locals>.fn  s=   3x3{++++?#s<'8888;	+A.3q9K~b)A-.A  qz!#c(***  /A(+)))#A  ))s,2EFG#!)	 /&

^
	 %,yE(92EErg   )r  pairwiserj   r   )rZ  r  r  r  r  r  rC  r   r  previouscurrentrs   r  r  r   r  r  s    ````````      @@re   index_output_size_and_inner_fnr"    s    $ $&//?"&*# @ ,5W+=M+=969+=MKSKS&[)9C<O)O)Q"RSK'*!K/ ++,,-./ 	 F  FD ?_ Ns   	B0B0c                    [        XU5      u  p4n[        R                  " U R                  5       U R	                  5       UUS9$ r  )index_impl_helperr@   r   rn   r   )r   r  r   r  re  r   s         re   
index_implr%     s>    0UCK1||~kkm	 rg   c                  ^^ [        U[        [        45      (       d   eU R                  5       m[	        XR                  5       5      u  p[        U5      S:  d   S5       eU Vs/ s H  oUb  UR                  5       OS PM     nn[        XS      R                  5       5      nU R                  5       n[        [        U5      5       Vs/ s H  oQU   c  M
  X   PM     n	nU(       a  SU	;   a  SU;  a  [        S5      e[        [        U5      5       Vs/ s H  oXU   PM	     n	n[        UUUUUU	S UUS9	u  n
mUU4S jnXT4$ s  snf s  snf s  snf )Nr   z Must have at least one valid idxz0index is out of bounds for dimension with size 0r  c                    > T" T" U 5      5      $ r   r   )r6  index_inner_fnrC  s    re   re  #index_impl_helper.<locals>.inner_fnJ  s    s+,,rg   )rk   ri   r   ri  r  rn   r   r   r  
IndexErrorr"  )r   r  r   r  r  rs   r  r  rZ  r  r  re  r(  rC  s               @@re   r$  r$  +  sL   ge}----}}H9'<<>RG~"F$FF"KRS7a-q}}TA7OS wa01::<=KZZ\F',S\':U':!ajIFI':LUl"q';KLL',S\':;':!1I':L;"@
#K- .009 T V <s   %E		EEEc                     [        XSS9$ ! [         a;    U R                  5         [        [        R
                  R                  SS9" X5      s $ f = f)NTr   Fr  )r%  r   r  r  r  rA  r  r   r  s     re   rA  rA  P  sM    
!D11 
			

 1 1uM
 	

s   	 AAAc                    [        XSS9$ )NFr,  )r%  r-  s     re   _unsafe_indexr/  \  s    a..rg   c           	     .    [        [        U 5      XUSSS9$ )NTFr   may_realizeindex_put_impl_r  r   r  r   
accumulates       re   	index_putr7  i  s    a':Tu rg   c           	     .    [        [        U 5      XUSSS9$ )NFr1  r3  r5  s       re   _unsafe_index_putr9  p  s    a':U rg   c                    UR                  5       U R                  5       :w  a  [        X R                  5       5      nU(       a  [        X5      n[        U [	        US   X 5      5      $ r  )rn   r  r   rM  r  )r8  r  r   r6  s       re   index_put_as_masked_fillr;  w  sP    T__..%!23D T5U9::rg   c                   SSK Jn  [        [        R                  [
        R                  R                  R                  R                  5      n[
        R                  R                  n[        R                  (       dQ  UbN  U" U5      (       aA  SnUR                  R                  SS 5      =n(       a  U SU 3nU[
        R                  l        [        R                   " XPXU5        U $ )Nr/   ),_fx_node_is_input_dependent_cudagraph_unsafezLindex_put_ fallback with boolean indexing is not compatible with CUDA graphsstack_trace Found from : 
 )utilsr=  r   r  
index_put_rS   r]   r^   ra   _overloadnamer0   graph_partitionrm  rn  disable_cudagraphs_reasonr2   IndexPutFallback)	r8  r  r   r6  r=  r  rc  r   r>  s	            re   index_put_fallbackrF    s    C$//177+?+?+F+F+T+TUK
 gg""G""8AA\!,,**=$??;?E*;-8C,/)7JGKrg   c           	         [        XX#SSS9$ )NTr1  r4  r8  r  r   r6  s       re   rA  rA    s    v4 rg   c           	         [        XX#SSS9$ )NFTr1  rH  rI  s       re   _unsafe_index_put_rK    s    vD rg   c                  ^ U(       aU  S m[         R                  " U 5      UR                  5       ;   a*  [        U4S jU 5       5      (       d  UR	                  5         UR                  5       S:X  a  [        U5      S:X  a  US   R                  5       [        R                  [        R                  4;   a_  US   n[        [        UR                  5       5      [        U R                  5       5      5       H  n[        US5      nM     [        X/X#5      $ [        R                  " 5       (       a  [!        XX#5      $ U HH  nUc  M  UR                  5       [        R                  [        R                  4;   d  M<  [!        XX#5      s  $    U R                  5       n	[        U	5      n
U(       aQ  [#        U R                  5       5      (       a3  U
S:X  a  [%        U S/5      n [!        XX#5      n U
S:X  a  [%        U / 5      n U $ ['        X R                  5       5      n [)        XR+                  5       5      u  pU Vs/ s H  ob  UR/                  5       OS PM     nn[1        U [2        5      (       d   eU R	                  5         U
S:X  a  [%        U S/5      n [5        XS      R                  5       5      n[        [        U5      5       Vs/ s H  oU   PM	     nn[7        U	UUUUUS US9u  nn[9        UU5      nU R+                  5       nUc   e[         R:                  " UU R                  5       UR/                  5       UUU(       a  SOS S9n[         R<                  " S [         R>                  " U 5      US	9n[@        RB                  RE                  U5      Ul#        [@        RB                  RI                  U5        U
S:X  a  [%        U / 5      n U $ ! [,         a    [!        XX#5      s $ f = fs  snf s  snf )
Nc                $   [        U [        5      (       a  [        U R                  [        R                  5      (       a  U R                  R                  5       n [        U [        R                  5      =(       a    [        U R                  [        R                  5      =(       al    [        U R                  SS 5      =(       aN    U R                  R                  R                  [        R                  R                  R                  R                  L $ g)Nrc  F)rk   rC   rm   r2   r6   r  r   r  r   rc  ra   r{   rR   r  randpermr  )indices    re   indice_slice_from_randperm3index_put_impl_.<locals>.indice_slice_from_randperm  s     &),,FKK1U1U002vr}}5 V"6;;@VY=V ++22eiinn6M6M6U6UU	 rg   c              3  4   >#    U  H  nT" U5      v   M     g 7fr   r   )r   rO  rP  s     re   r   "index_put_impl_.<locals>.<genexpr>  s      H
=D6&v..Wr  r/   r   rU  r,  
atomic_addrv   r   re  rd  output_indexerscatter_moder   r  rm   )%r2   try_get_namer  r"  r  r  r   r   r{   r   r  r  r   r2  r;  $are_deterministic_algorithms_enabledrF  rL   r  r   r  rn   r   ri  rk   rC   ri   r"  r3  Scatterr  MutationLayoutSHOULDREMOVErS   r]   rg  r   rh  )r8  r  r   r6  r   r2  r  r   rA  rZ  x_ndimr  rs   r  r  r  expected_vals_sizere  rv   scatterrV  rP  s                        @re   r4  r4    sq   	 ??4 F$9$9$;;C H
=DH
 E
 E
 NN 	aLAAJ  "uzz5;;&??qzs4==?+S-ABAT2&D C'ffII 1133!$DD !2uzz5;;6O!O%dVHH  ]]_F[FB4>>CSTTQ;qc?D!$DQ;b>Dfnn./FE"=__&#
 LSS7a-q}}TA7OSdI&&&&LLN {D1# wa01::<=K',S\':;':!1I':L;#A	$  F./F __Fjjnn##%!%/\TG ,,T2F
 ''))&1FKGGv&{D"~Ke  E!$DDE T <s   O 5O"O'OOr  c                   ^^^^^	 [        XSSS9u  pEmTR                  5       mU R                  5       m	UUUUU	4S jn[        R                  " U R	                  5       U R                  5       UUS9$ )NFr  c                   >^  TR                   [        R                  :w  a,  [        R                  " T" T 5      [        R                  5      nOT" T 5      n[        R
                  " UUU U4S jT5      $ )Nc                     > T" T " T5      5      $ r   r   )_unsafe_index_fnr6  self_loaders   re   rQ  8_unsafe_masked_index.<locals>.inner_fn.<locals>.<lambda>1  s    K8H8M,Nrg   )r   r{   r   rR   r   r  )r6  mask_valrc  fillr  mask_loaderrd  s   ` re   re  &_unsafe_masked_index.<locals>.inner_fn,  sK    ::#||K$4ejjAH"3'Hzz($NPTUUrg   rg  )r$  ri  r@   r   rn   r   )
r8  r  r  rg  rd  r   re  rc  rh  rd  s
    ` `   @@@re   _unsafe_masked_indexrj  $  ss    "3UU#F ""$K""$KV V  nn	 rg   c           	         [        XS5      nU R                  5       n[        [        U5      5       Vs/ s H%  nX&   (       a  [	        X&   XV   * XV   S-
  5      OS PM'     nn[        XUSS9$ s  snf )Nr   r/   T)r6  )r  r   r  r   r[  r9  )r   r  r  r   masked_valuer3  rs   clamped_indicess           re   #_unsafe_masked_index_put_accumulatern  ;  sx    q)LJJLE s7|$$A 7>jgj58)UX\2dJ$   Q$OOs   ,A,c                X    [         R                  " U[         R                  " X 5      5      $ r   )rR   r  r  r   minmaxs      re   r[  r[  H  s    ;;sCKK/00rg   c                J    [        U 5      n[        XRX45      n[        Xa5        U$ r   )r  rn  copy_)r8  rN  r   r  r]  r6  output_views          re   as_strided_scatterrv  M  s$    4[FV6BK	+Mrg   c                0    [        [        U 5      XU40 UD6$ r   )scatter_r  )r   r   rA  rN  r   s        re   r_  r_  U  s    E!Hc#888rg   r  include_selfc               T   [        U[        5      n[        U UUR                  5       [	        [
        R                  U(       a  UR                  5       O
[        U5      5      U(       a  UR                  5       R                  OSU5      (       a  [        R                  " U UUUUUUS9  U$ g )Nznot implry  )rk   rC   rQ   r   r
   r{   r   r   rn   r2   ScatterFallback)r  r8  r   rA  rN  r  rz  src_is_tensors           re   scatter_fallbackr~  Z  s     sI.MU[[]#--/S	J!.J  	%	
 rg   r  c          	         US;   d   eUcV  [        [        R                  [        R                  R
                  R                  R                  5      n[        XPXX4S9nUb  U$ US:X  a  SnOUS:X  a  Sn[        XX#U5      $ )N)Nr   multiplyr  r   r  r  prod)
r   r  rx  rS   r]   r^   ra   rB  r~  scatter_reduce_)r8  r   rA  rN  r  r  fallback_results          re   rx  rx  |  s    ....~dmmQWW-A-A-H-H-V-VW*s3
 &""	:	4e&99rg   c                .    [        [        U 5      XU5      $ r   )scatter_add_r  r   r   rA  rN  s       re   scatter_addr    s    a#c22rg   c                    [        XX#S5      $ )Nr  )r  r  s       re   r  r    s    15u55rg   c                0    [        [        U 5      XX440 UD6$ r   )r  r  )r   r   rA  rN  reduction_typer   s         re   scatter_reducer    s    58SOOOrg   )rz  c          
       ^ ^^^^ US;   d   e[        [        R                  R                  5       5      S:X  a"  S[        R                  R                  5       ;   d   S5       e[	        T[
        5      (       a  [        T T5      m[        [        R                  R                  T TUTUUS9nU(       a  U$ [	        T [        5      (       d   eS[        UR                  5       5      ;   d   e[        T R                  5       5      nUS:X  a  [        T S/5      m [	        T[        5      (       a*  [        TR                  5       5      S:X  a  [        TS/5      m[	        U[        5      (       a*  [        UR                  5       5      S:X  a  [        US/5      nUR                  5       S:X  a  T $ [        T T5      mT R!                  5         UR#                  5       m[	        T[        5      (       a  TR#                  5       OS mUUU 4S jnU UU4S	 jn	S
 n
T R%                  5       nUc   eU(       d  [&        R(                  " UT R                  5       U 4S jUR                  5       US S9n[&        R*                  " S [&        R,                  " T 5      US9n[.        R0                  R3                  U5      Ul        [.        R0                  R7                  U5        [&        R(                  " UT R                  5       U	UR                  5       UU
" U5      S9n[&        R*                  " S [&        R,                  " T 5      US9n[.        R0                  R3                  U5      Ul        [.        R0                  R7                  U5        US:X  a  [        T / 5      m T $ )N)Nr  r  meanamaxaminr/   r  zKaten.scatter_reduce_.two is not the unique overload of aten.scatter_reduce_ry  r   r   c                   > TR                  5       n[        U5      n[        U 5      n[        R                  " T" U 5      US:X  a  SOUT   SS9UT'   U$ )Nr   r/   F)r  )r   r   ri   rR   r  )r6  r3  rh  indirect_idxr   r  r8  s       re   rV  'scatter_reduce_.<locals>.output_indexer  sU    5zCy11DAIq5:
S rg   c                l   > T(       a  T" U 5      $ [         R                  " TTR                  5       5      $ r   rR   r  r   )r6  r8  rN  r  s    re   r   scatter_reduce_.<locals>.fn  s*    c?" <<T^^%566rg   c                    U S:X  a  gU b   eg )Nr  rT  r   r  s    re   backend_reduce_str+scatter_reduce_.<locals>.backend_reduce_str  s    U? >!>rg   c                N   > [         R                  " STR                  5       5      $ r  r  )rA  r8  s    re   rQ  !scatter_reduce_.<locals>.<lambda>  s    3<<4>>3C#Drg   rU  rX  )r   r  r  r   rk   r!   r  r~  r  rC   r  r   r   r  r  r_  r  ri  rn   r2   r[  r  r\  rS   r]   rg  r   rh  )r8  r   rA  rN  r  rz  r  rh  rV  r   r  rv   zero_outrV  r_  r  r  s   `` `           @@re   r  r    s   BBBBD  **,-2T))3355U UU	6 #vc"&  !O dI&&&&C)****t}}DqyD1##y!!c#,,.&9Q&>3n%##ENN,<(=(BUQC A
c
"CLLN$$&L&0i&@&@"dJ7 __F::.."D>>#)
 ""006

 gg--f5	""6*
 jjnn~~%'/G ,,T2F
 ''))&1FKGGv&qyD"~Krg   c                d  ^^^^^^ U R                  5         U R                  5       mU R                  5       T* S  mU R                  5       S T*  nT Vs/ s H,  n[        R                  R
                  R                  U5      PM.     snm[        U5      T:X  d   eUn[        TU5       VVs/ s H	  u  phXh-  PM     snnm[        U5       H  u  piU	c  M
  SU	-  TU'   M     U4S jmUUUUU4S jn
[        R                  " U R                  5       U R                  5       U
/ UQUQS9$ s  snf s  snnf )Nr  c                  > [         R                  " U [        R                  5      n T(       a:  [         R                  " U [         R
                  " S[        R                  5      5      n [         R                  " U [         R
                  " U[        R                  5      5      n [         R                  " U [        R                  5      n [         R                  " XSS9$ )N      ?Fr,  )
rR   r  r{   r  r   r  rh  r   r  r  )r   r  r   exacts      re   scale_fn$upsample_nearestnd.<locals>.scale_fn'  s     NN1emm,3<<U]];<AGGAs||E5==9:LLEKK($$QE::rg   c                   > U T* S  nU S T*  nT
" / UQ[        UTT5       VVVs/ s H  u  p4nT	" X4U5      PM     snnnQ5      $ s  snnnf r   )r  )r6  r   r5  rs   r   r   i_sizes
inv_scalesr  r  rC  s         re   r   upsample_nearestnd.<locals>.fn2  s_    H!HWaW#aW:UV:UJA$8A$':UVW
 	
Vs   Arg  )realize_hintri  r   rS   r]   r   r  r   r  rj   r@   r   rn   r   )r   r  scales_xr  r  batchrs   o_sizesor  r   r  r  r  rC  s      ``      @@@@re   upsample_nearestndr    s    NN}}HjjlA23GJJL1"E6=>gqww))!,g>Gx=AG$'$9:$9DA!%$9:Jh'%KJqM (	;
 
 ||~kkm!!!	 9 ?
 ;s   3D'+D,c                    [        XU4SS9$ )Nr/   r  r  r   r  r  s      re   upsample_nearest1dr  A  s    avi1==rg   c                    [        XU4SSS9$ )Nr/   Tr  r  r  r  s      re   _upsample_nearest_exact1dr  F  s    avi1DIIrg   c                    [        XX#4SS9$ )Nr-   r  r  r   r  scales_hscales_ws       re   upsample_nearest2dr  K  s     ax.BaHHrg   c                    [        XX#4SSS9$ )Nr-   Tr  r  r  s       re   _upsample_nearest_exact2dr  R  s     ax.BatTTrg   c                    [        XX#U4SS9$ )Nr   r  r  r   r  scales_dr  r  s        re   upsample_nearest3dr  Y  s     ax8.LPQRRrg   c                    [        XX#U4SSS9$ )Nr   Tr  r  r  s        re   _upsample_nearest_exact3dr  d  s     	X6!4 rg   c                .   ^  [        U 4S jU 5       5      $ )Nc              3  R   >#    U  H  n[         R                  " UT5      v   M     g 7fr   r  )r   r   r   s     re   r   $_create_constants.<locals>.<genexpr>r  s     6Aa''s   $')r   )r   rt   s   ` re   r  r  q  s    6666rg   c                   ^^^ U R                  5       mU R                  5       mUUU4S jn[        R                  " U R	                  5       U R                  5       UTS9$ )Nc                   > [        U 5      n [        U 5      [        T5      :X  d   eT H  nTU   S-
  X   -
  X'   M     T" U 5      $ r  )ri   r   )r6  r   r  r  rC  s     re   r  rev.<locals>.loader{  sN    3i3x3u:%%%Cc
Q#(2CH  }rg   rg  )ri  r   r@   r   rn   r   )r   r  r  r  rC  s    ` @@re   revr  u  sM     }}HJJLE ||~kkm	 rg   c                   S nU" 5       (       a  g[        U5      S:w  d  [        U R                  5       5      S:w  a  gU R                  5         [        U [        R
                  5      (       a  [        U R                  [        R                  5      (       a  [        U R                  R                  [        R                  5      (       dH  [        R                  (       aX  [        U R                  R                  [        R                  5      (       a%  U R                  R                  R                  (       d  gU R                  5         [        R                  " U 5      u  pEUR                  nUS   S:w  a  gUS   S:w  d  US   S:w  d	  US   S:w  a  gUS   nUS:X  a  gUS   nUR                   S   n	XU-   :  a  gU R                  R                  R                  n
UR                   S   UR                   S   U-   /nU["        R$                  R&                  U
'   [)        U UUR                  UR*                  5      n[-        USXU-   SS	9n[/        X5        [0        S
   S==   S-  ss'   U$ )z
This optimization changes the semantics of padding from 'clone'
style to 'view' style.

Thanks to functionalization, this change can still maintain numerical
correctness.
c                    [         R                  R                  n U c  g[        U R                  5      n[        U5      S:X  aF  US   R                  [        R                  R                  [        R                  R                  4;   a  gg)z
Conservatively check if padding can be fused with downstream op.
1. if the downstream op is a sum, then there is little benefit to
   do inplace padding
2. if the downstream op is a matmul, doing inplace padding can
   save membw.
Tr/   r   F)rS   r]   r^   r   r_   r   ra   r  mmr  addmm)r^   r_   s     re   _padding_can_be_fused6inplace_constant_pad_nd.<locals>._padding_can_be_fused  sk     ww++l(()u:?uQxGGOOJJ3
  
 rg   Nr   r-   r/   r   r   F)r   ro  rp  r[  inductorinplace_padding)r   r   r  rk   r2   rC   rm   r   r  r0   can_inplace_pad_graph_inputInputBufferr   freeze_layoutr  r  r   rS   r]   buffer_to_padded_sizern  rk  r~  fill_r   )r   paddingr  r  r   r  r4  npadstride0rowsizebufnamepadded_size	resized_xsliced_xs                 re   inplace_constant_pad_ndr    s   (  7|qC

-2
 IIK
 q",,''!&&"--00qvv{{B$5$56622qvv{{BNN;; vv{{OO((+IAmmGqzQqzQ'!*/WQZ1_1:DqyajGkk!nG4ffkkG;;q>6;;q>D#89K-8AGG!!'*		I iQgT>QVWH	(Z*+q0+rg   c                  ^^^^^^^ [        U5      S-  S:X  d   e[        S U 5       5      (       a  [        U 5      $ [        R                  (       a  [        XT5      nU(       a  U$ U R                  5       n[        [        [        [        US S S2   USS S2   5      5      5      5      m[        U5      [        T5      -
  m/ mT H?  u  pVTR                  [        R                  R                  R                  U5      U45        MA     [        US T 5      n/ m[        TUTS  5       HC  u  u  pn
TR                  U
5        UR                  [        R                   " X-   U	-   5      5        ME     [        U5      [        U5      :X  d   e[#        U R%                  5       5      " T5      mUUUUU4S jmUUU4S jnU R'                  5       m[(        R*                  " U R-                  5       U R%                  5       UUS9$ )Nr-   r   c              3  *   #    U  H	  oS :H  v   M     g7fr   Nr   r   r  s     re   r   "constant_pad_nd.<locals>.<genexpr>  s     
#7a67r!  r/   c                N  >^  / n[        T T	S  TT5       HL  u  nu  p4nUS:w  a  UR                  [        US5      5        US:w  d  M2  UR                  [        X%5      5        MN     [        R
                  " [        R                  U5      n[        R                  " UU U
4S jT5      $ )Nr   c                    > T" T 5      $ r   r   )rA  rC  s   re   rQ  /constant_pad_nd.<locals>.mask.<locals>.<lambda>  s	    rg   )	r  ro   range_mask_lowrange_mask_highr  r  rR   r  r  )rA  r  r6  r  r  r  boundsr  
mask_sizesr  rC  s   `     re   r  constant_pad_nd.<locals>.mask  s    (+E!"Ivz(J$C#faxN323qyOC89	 )K
 $/zz$ 7DDrg   c                   > [        U S T 5      n[        U TS  T5       H  u  nu  p4UR                  X#-
  5        M     [        U5      [        U 5      :X  d   eT" U5      $ r   )ri   r  ro   r   )rA  r  r6  r  _highbounds_precompr  r  s        re   	offset_fn"constant_pad_nd.<locals>.offset_fn  sa    rO	!$U12Y!?C#SY' "@9~U+++Irg   rg  )r   r"  r  r0   r  r  r   ri   r.  r  ro   rS   r]   r   lookup_precomputed_sizer   r3  r   r   ri  r@   r   rn   )r   r  r  rq   r  lhr  r  r  r   r  r  r  r  r  r  rC  s     `         @@@@@@re   r  r    s   L1"""

#7
###Qx%a*=J JJLE(4GCaCL'!$Q$- @ABCFE
S[ A 68Nqww//GGJANO  uRay/KJ qr3T$5<<
T(9:; 4 {s5z)))q{{}-j9JE E }}H||~kkm	 rg   c                    [         R                  " [         R                  " U [        R                  5      [         R                  " [
        R                  " U5      [        R                  5      5      $ r   )rR   r  r  r{   r  r   r  )rs   r  s     re   r  r  "  s@    66q%++&u}}S)5;;7 rg   c                    [         R                  " [         R                  " U [        R                  5      [         R                  " U[        R                  5      5      $ r   )rR   r  r  r{   r  )rs   r  s     re   r  r  )  s7    66q%++&tU[[) rg   c                T    [         R                  " [        X5      [        X5      5      $ r   )rR   r  r  r  )rs   r  r  s      re   
range_maskr  0  s#    88q  rg   c                   ^ ^^^^^^^ T R                  5       T* S  mT R                  5       mT=(       d    S/T-  mUUUUUUU U4S jnU$ )Nr   c                h  >^^ U S T*  mU T* S  m[         R                  " [        R                  [	        T5       Vs/ s H   n[        TU   TU   T
U   -   T
U   * 5      PM"     sn5      nT	(       a   [        R                  " UUUUUU4S jT5      $ [        R                  " UUUU4S jT5      $ s  snf )Nc                 .   > [        TTT S9" / TQTQ5      $ )Nr   )constant_boundary_condition)r   ihpad_fill_valueprefixr   s   re   rQ  ;constant_boundary_condition.<locals>.load.<locals>.<lambda>K  s    3A~3O"fNrNrg   c                    > T" / TQT Q5      $ r   r   )r  r  rC  s   re   rQ  r   Q  s    (>V>b>*Brg   )r  r  rR   r  r  r  r  )rA  rs   r  r  r  r   r  r  r  r  	padding_hr   rC  s      @@re   rZ  )constant_boundary_condition.<locals>.load?  s    uC45\HHLQRUJWJqZ1qtil2Yq\MBJW
  JJ  
	
 D"BJO
	
 Xs   'B/
)r   ri  )	r   r  r  r  r   rZ  r  r  rC  s	   ````` @@@re   r  r  7  sE     	


cTUA}}H$A39I
 
* Krg   dilationc                  Uc  S/[        U5      -  n[        U SXA   -  -   Xa   X!   S-
  -  -
  X1   S-
  -   X1   5      nU(       Ga  [        U SXA   -  -   Xa   X!   S-
  -  -
  SX1   S-
  -  -   X1   5      n[        R                  R                  R                  US-
  X1   -  U -
  XA   -
  5      S:  a<  US-  n[        R                  R                  R                  SXU   -  U -
  XA   -
  5        [        R                  R                  R                  Xx-
  5      S:X  a.  [        R                  R                  R                  Xx5        SnXu4$ UnXu4$ )Nr/   r-   r   F)r   r)   rS   r]   r   	size_hintre  r2  )	r   rs   kernel_sizer  r  	ceil_moder  x_outx_alts	            re   pooling_sizer  W  si   3W%	A
NX[KNQ,>??69q=Q	E
 '*nk[^a/01 69q=!" I
 77%%uqyFI&=&AGJ&NOSTTQJEGG&&q%)*;a*?'**LM77%%em49GG))%7I  Erg   c               l    [        X5      n [        R                  " [        R                  U 5      nUS:  $ )N   )rM   r  r  r3  rh  )r  n_dimwindow_sizes      re   %should_fallback_max_pool_with_indicesr  u  s-    {2K""8<<=Krg   assert_fallbackc                  US:X  a  S/U-  nUS:X  a  S/U-  nU(       d  Un[        X5      n[        X%5      n[        X55      n[        XE5      n[        U [        5      (       d   e[        U5      U:X  d   e[        U5      U:X  d   e[        U5      U:X  d   e[        U5      U:X  d   e[        U R	                  5       5      US-   US-   4;   d   e[        XS9nUb  Xv:X  d   eXX4U4$ )Nr   r/   r-   r  )rM   rk   rC   r   r   r  )r   r  r  r  r  r  r  use_fallbacks           re   max_pool_checksr  {  s    !|#+1}3;{2K&(F7*GH,Ha####{u$$$v;%w<5   x=E!!!qzz|EAI 66668RL"...<??rg   c               &  ^^^^^ U R                  5         U R                  S T*  nU R                  T* S  n[        [        T5       V	s/ s H  n	[	        X   XTTUTS9PM     sn	6 u  pU R
                  nU[        R                  L a  SO;UR                  (       a  [        S5      O[        R                  " U5      R                  n[        U5      [        U
5      -   n[        T5      (       d'  [        U5      (       d  [        S T 5       5      (       a  [        XTS9mOU R                  5       mUUUUU4S jn[         R"                  " SU U R%                  5       UUUUUS9n[         R"                  " S	U U R%                  5       [        R&                  UUUUS9n[)        UR*                  R*                  [         5      (       a  UR-                  5         [)        UR*                  R*                  [         5      (       a  UR-                  5         UU4$ s  sn	f )
Nr  F-infc              3  *   #    U  H	  oS :  v   M     g7fr=  r   r  s     re   r   )_max_pool_with_offsets.<locals>.<genexpr>  s     ,EHqUHr!  r  c                   > U S T*  nU T* S  n[        T5       Vs/ s H  nX4   T	U   -  X   TU   -  -   TU   -
  PM      nnT
" / UQUQ5      $ s  snf r   r  )r6  reduction_idxr  bhrs   r  r  r  r  r  rC  s         re   fn_inner(_max_pool_with_offsets.<locals>.fn_inner  s    Wuf%\ 5\
! UVAY=#3hqk#ABWQZO! 	 
 &2''	
s   %Arr  r  
input_noderv   	dst_dtyper  re  rd  reduction_rangesargmax)r  r3  r  r  r  r   r{   r   r  r;  r  rq  ri   r#  r  ri  rA   r   rn   r  rk   rm   r  )r   r  r  r  r  r	  r  r  dhwr  dhw_outr   	min_valuerF  r   r  offsetsrC  s     ``` `          @re   _max_pool_with_offsetsr+    s    NNGGGeVE
''5&'
C
 5\	

 " X "	

G GGE EJJ 	$66eFmEKK<N<R<R  E{T']*H
7||s9~~,EH,E)E)E.qG==?( ( ||~$	F ||~++$	G &++""I..',,##Y//7?s

s   Hc                    [        U5      n[        U UUUUUSS9u  pp4n[        R                  " SS9   [	        U UUUUUUS9u  pU[        U	[        R                  5      4sS S S 5        $ ! , (       d  f       g = f)NFr  r  unroll_reductions_thresholdr  )r   r  r0   r   r+  r   r{   r  )
r   r  r  r  r  r	  r  r   r  r*  s
             re   !_low_memory_max_pool_with_offsetsr/    s     E 1@	1-KA 
"	50
 x44 
6	5	5s   -A**
A8c                R  ^^^^^^ [        T5      mU R                  5       m[        R                  " [        R
                  " [        R                  T5      5      mUUUUUU4S jn[        R                  " U R                  5       [        R                  UU R                  5       S9nU$ )Nc                   > T	" U 5      n[         R                  " UT
5      n[        R                  " UT5      nT" X5      n[         R                  " [        R
                  " UTT* S  5      [        R                  5      $ r   )rR   r  r1   _flattened_index_to_ndr  _flatten_indexr{   r  )r6  rk  offset_sympyr  idhwincrements_to_index
input_sizer  r  offsets_loaderr  s        re   offsets_to_indices4_pool_offsets_to_indices.<locals>.offsets_to_indices  sk    $,,V[A&==lKX"36~~))$
E670CDekk
 	
rg   rg  )r   ri  r   rr  r  r  r3  rh  r@   r   rn   r{   r  r   )	r*  r  r7  r6  r9  r  r  r8  r  s	    ```  @@@re   _pool_offsets_to_indicesr;    s     E((*N--	 0 0{ KLK
 
 !!#kk#!	G Nrg   c                J   ^^^^ [        U5      mUUUU4S jn[        XX&5      $ )Nc                   > U T* S  n[        T5       Vs/ s H  nX#   TU   -  X   TU   -  -   TU   -
  PM      sn$ s  snf r   r  )r6  r  r  rs   r  r  r  r  s       re   r6  D_low_memory_max_pool_offsets_to_indices.<locals>.increments_to_index.  s`    %\ 5\
! UVAY=#3hqk#ABWQZO!
 	
 
s   %=)r   r;  )r*  r  r7  r  r  r  r6  r  s      ``` @re   '_low_memory_max_pool_offsets_to_indicesr?  %  s-     E
 
 $j rg   c           
     ~    [        XX#XFS9u  pp4n[        XX#XEUS9u  p[        U	UU R                  U* S  UUU5      n
X4$ )Nr  )r  r+  r?  r3  )r   r  r  r  r  r	  r  r   rq   r*  r  s              re   _max_pool_with_indicesrA  :  si     1@	1-KA *	ELC 6	G <rg   c           
         [        XX#XESS9$ Nr-   r  rA  r   r  r  r  r  r	  s         re   max_pool2d_with_indicesrF  X       "	A rg   c           
         [        XX#XESS9$ Nr   r  rD  rE  s         re   max_pool3d_with_indicesrJ  g  rG  rg   c                n  ^^^^^^^^^^^ TS:X  a  SS/mUS:X  a  SS/nT(       d  Tm[        U[        5      (       d   e[        T5      S:X  d   e[        T5      S:X  d   e[        T5      S:X  d   e[        U5      S:X  d   e[        UR                  5       5      S;   d   eU R	                  5         U R                  5       n[        U[        5      (       a  [        UR                  R                  [        5      (       a  UR                  R                  n	U	R                  5       n
U
c   e[        R                  " S [        R                  " U
U	R                  5       U	R                  5       S9U	S9nUR                  5         UR                  5       nOUR                  5       nUS L=(       a    US   S:H  =(       d    US L=(       a    US   S:H  n[        S U 5       5      (       a  [!        XTTTXVU5      $ UR                  5       Gt pmU R                  5       Gt nmmUR#                  5       mU R#                  5       m[%        UR                  5       5      n['        UU4S j[)        TS   S-  5       5       5      m['        UU4S	 j[)        TS   S-  5       5       5      mTT-  nUS
:  a  [!        XTTTXVU5      $ UR                  5       mUUUUUUUUUUU4S jn[        R*                  " U R                  5       U R                  5       UUS9nU(       a  [        R,                  R/                  U5      $ U$ )Nr   r/   r-   rf  )rv   r   r   rX  c              3  *   #    U  H	  oS :g  v   M     g7fr=  r   r  s     re   r   3max_pool2d_with_indices_backward.<locals>.<genexpr>  s     
$8a68r!  c              3     >#    U  H>  n[        [        UTS    5      [        S [        UTS    -
  TS    5      5      -
  S5      v   M@     g7fr   r/   Nrr  r)   r   r  r  r  s     re   r   rM    O      *A 	HQq	"SHQQ5GPQ,S%TTVWXX*   AA	c              3     >#    U  H>  n[        [        UTS    5      [        S[        UTS    -
  TS    5      5      -
  S 5      v   M@     g7fr/   r   NrP  r   wr  r  s     re   r   rM    rR  rS  r  c                  > U Gt pn[         R                  " UT-  U-   [        R                  5      nUTS   -   nUTS   -   n[         R                  " [	        UTS   -
  TS   -   TS   5      [        R                  5      n[         R                  " [	        UTS   -
  TS   -   TS   5      [        R                  5      n[         R                  " [	        UTS   5      S-   [        R                  5      n[         R                  " [	        UTS   5      S-   [        R                  5      n[         R
                  " U[         R                  " S[        R                  5      5      n[         R
                  " U[         R                  " S[        R                  5      5      n[         R                  " U[         R                  " T[        R                  5      5      n[         R                  " U[         R                  " T[        R                  5      5      nS n	[        T5       GHD  n
[        T5       GH0  n[         R                  " U[         R                  " U
[        R                  5      5      n[         R                  " U[         R                  " U[        R                  5      5      n/ UQ[         R                  " [         R                  " U[         R                  " U[         R                  " S[        R                  5      5      5      TS   SS9P[         R                  " [         R                  " U[         R                  " U[         R                  " S[        R                  5      5      5      TS   SS9PnT" U5      nT" U5      n[         R                  " X5      nU	c>  [         R                  " UU[         R                  " S[        R                  5      5      n	GM  [         R                  " [         R                  " [         R                   " X5      [         R                   " X5      5      U5      n[         R                  " U[         R                  " U	U5      U	5      n	GM3     GMG     U	c   eU	$ )Nr   r/   Fr,  rU  r  )rR   r  r{   r  r)   r  r  r  r  r   r  r  r  r  r  r  r  )r6  r  r  rW  
index_testphstartpwstartphendpwendgradientph_pw_phpw
grad_indexindex_actual	grad_partr   r  grad_loaderh_window_sizer  indices_sizer  r  pooled_heightpooled_widthr  w_window_sizewidths                      re   r   ,max_pool2d_with_indices_backward.<locals>.fn  s+   A^^AIM5;;?

N
N..QQ'&)3VAY?
 ..QQ'&)3VAY?
 x6!9595;;Gx6!9595;;G++gs||Au{{'CD++gs||Au{{'CDE3>>-#MNE3>>,#LM'C]+WWWcll3&DEWWWcll3&DE))Bs||Au{{7S(TU$R(# ))Bs||Au{{7S(TU$R(#
  .j9'
3	|8#"yyy#,,sEMM*J H 88FF2-FF2- D  #yyswwx/KXVHE , (H ###rg   rg  )rk   rC   r   r   r  rq  rm   r@   rn   r2   r  r  r   decide_layoutrl  r#  )fallback_max_pool2d_with_indices_backwardri  ri   rr  r  r   r  r+  )grad_outputr   r  r  r  r  r	  r  	gO_striderm   rv   x_bufferx_strideis_channels_last_batch_heightr   rF  r  r   rq   rg  rh  r  ri  rj  rk  rl  rm  s     ```                @@@@@@@@re    max_pool2d_with_indices_backwardrx  {  s    !|a&1}q6a####{q   v;!w<1x=Aqzz|&&& ,,.I!YJqvv{{I$F$Fvv{{"!!!$$$$nn&]]_
 
 	 &&(%%' ,A!1A 3)A,!"3  
$8
$$$8K(w
 	
  jjlVe&1&:&:&<#Q|((*N))+KAJJL!H {1~)* M  {1~)* M
  -/KR8K(w
 	
 ##%L9 9v 

%%'##%	C 44S99
rg   c                8   ^^ U R                  5       mUU4S jnU$ )Nc           
       >^ ^^^	^
 Uu  mm	Uu  mm
Uu  pE[         R                  " [         R                  " [         R                  " TT-   [        R
                  5      [         R                  " U[        R
                  5      5      [         R                  " [         R                  " T
T	-   [        R
                  5      [         R                  " U[        R
                  5      5      5      n[         R                  " UUUU	U U
U4S jT5      $ )Nc                 ,   > T" / TQT T-   PTT-   P5      $ r   r   )h_start_indexr  iwr  w_start_indexrC  s   re   rQ  3pad_adaptive_loader.<locals>.load.<locals>.<lambda>"  s$    HNvN}r'9N=2;MNOrg   )rR   r  r  r  r{   r  r  )r  
incrementsstart_indicesend_indicesh_end_indexw_end_indexr  r|  r  r}  r~  pad_valrC  s   `      @@@@re   rZ  !pad_adaptive_loader.<locals>.load  s    B'4$}#. xxFF}r15;;?{EKK8 FF}r15;;?{EKK8	
 zzOO
 	
rg   ri  )r   r  rZ  rC  s    ` @re   pad_adaptive_loaderr    s    }}H
, Krg   c                    [         R                  " XUS9n[         R                  " XUS9n[         R                  " XUS9n[         R                  " XUS9n	XgX4$ )N)out_diminp_dim)r  r)  )
rr  rs  h_inw_inh_outw_outr|  r  r~  r  s
             re    compute_indices_adaptive_poolingr  )  sU    %%k$OM##IdKK%%k$OM##IdKK}AArg   c                \   ^^^^^^ Uu  pgUu  p[        XXgX5      u  mmmmUUUUUU4S jn
U
$ )Nc                   > U Gt p#nT" U5      nT" U5      nT" U5      nT" U5      nS n	[         R                  " [        TS   5      [        TS   5      5       H"  u  pU" UX/XW/Xh/5      nU	c  Un	M  T" X5      n	M$     U	$ r  )r  productr  )r6  r  r  r  bwr|  r  r~  r  r  r  r}  r  h_end_index_fnh_start_index_fnkernel_maxes
pooling_fnw_end_index_fnw_start_index_fns                re   r    _adaptive_pooling_fn.<locals>.fnB  s    R(,$R((,$R(''l1o(>lSTo@VWFB.*	C ~#C0 X rg   r  )rr  rs  r  in_sizes	out_sizesr  r  r  r  r  r   r  r  r  r  s     `  `     @@@@re   _adaptive_pooling_fnr  3  sF     JDLE 	)E	
 . Irg   c                d   ^^^
^^^^ Uu  nmUu  px[        XUTXx5      u  mm
mmU
UUUUUU4S jn	U	$ )Nc                  > U Gt p#nT" U5      nT" U5      nT" U5      nT" U5      nS n	S n
[         R                  " [        TS   5      [        TS   5      5       H  u  pU" UX/XW/Xh/5      n[        R                  " X[-   T-  U-   U-   [
        R                  5      nU
c  Un
O+[        R                  " [        R                  " X5      X5      n
U	c  Un	M{  T" X5      n	M     U
$ r  )	r  r  r  rR   r  r{   r  r  gt)r6  r  r  r  r  r|  r  r~  r  maxvalmaxindexr  r}  r  rA  r  r  r  r  r  r  r  s                  re   r   )_adaptive_pooling_fn_with_idx.<locals>.fnk  s    R(,$R((,$R(''l1o(>lSTo@VWFB.*	C NN#t+m;b@%++E  99SVVC%8%J~#C0) X, rg   r  )rr  rs  r  r  r  r  r  r  r  r   r  r  r  r  r  s     `  `    @@@@@re   _adaptive_pooling_fn_with_idxr  \  sK     JD$LE 	)dE	
! !F Irg   c           	     &  ^ ^^ T R                  5       [        R                  :X  a  [        S5      e[	        T [
        5      (       d   e[        U5      S:X  d   eT R                  5         T R                  5       Gt p#n[        R                  R                  R                  U5      n[        R                  R                  R                  U5      nUu  pVX5:X  a  XF:X  a  [        T 5      $ US:X  d  US:X  a/  / UQUPUPn[        UT R                  5       T R                  5       S9$ X5-  S:X  a*  XF-  S:X  a"  [!        X55      [!        XF5      /n[#        T U5      $ [%        X5-   S-
  U5      n	[%        XF-   S-
  U5      n
['        U5      XV/-   nT R                  5       nX-  nUS:  a  [)        T U5      $ S nS n[+        UUX/X4/XV/[,        R.                  S	9m[1        [3        T 5      5      mUUU 4S
 jn[4        R6                  " T R                  5       UUUS9nU$ )Nz0'adaptive_avg_pool2d' not implemented for 'Long'r-   r   r;  r/   r  c                    [        X-  U5      $ r   r)   rA  r  r  s      re   rr  )_adaptive_avg_pool2d.<locals>.start_index      733rg   c                2    [        U S-   U-  U-   S-
  U5      $ r  r  r  s      re   rs  '_adaptive_avg_pool2d.<locals>.end_index  "    g-7!;WEErg   rr  rs  r  r  r  r  c                `   > [         R                  " T" U [        T5      5      T" U T5      5      $ r   )rR   truedivr  )r6  fn_sumones_loaderr   s    re   r    _adaptive_avg_pool2d.<locals>.fn  s-    {{3+A./[1I
 	
rg   rg  )r   r{   r  r  rk   rC   r   r  r   rS   r]   r   r  r  rE  rn   r)   
avg_pool2drF   ri   fallback_adaptive_avg_pool2dr  rR   r   r  	ones_liker@   r   )r   r  r  r  r  r  r  o_sizer  h_kernel_maxw_kernel_maxrF  r   r  rr  rs  r   rvr  r  s   `                 @@re   _adaptive_avg_pool2dr    s   {{}#MNNa####{q   NNU$77%%d+D77%%d+DLE }QxzUaZ'5'%''V1;;=HH|qT\Q.,ht.CD![))DL1,u5LDL1,u5LE{e^+HKKME-KR+A{;;4F ""1.77F &il3K

 
		||~	
B Irg   c           	       ^ ^^ T R                  5       [        R                  :X  a  [        S5      e[	        T [
        5      (       d   e[        U5      S:X  d   eT R                  5         T R                  5       Gt p#n[        R                  R                  R                  U5      n[        R                  R                  R                  U5      nUu  pVUS:X  d  US:X  aV  / UQUPUPn[        UT R                  5       T R                  5       S9[        U[        R                  T R                  5       S94$ X5-  S:X  a  XF-  S:X  a  [        e[!        X5-   S-
  U5      n[!        XF-   S-
  U5      n	[#        U5      XV/-   n
T R                  5       nX-  nUS:  a  [%        T U5      $ S nS n['        UUX/X4/XV/[(        R*                  S	9m[-        UUX/X4/XV/[(        R*                  S	9mUU 4S
 jnUU 4S jn[.        R0                  " T R                  5       UUU
S9n[.        R0                  " T R                  5       [        R                  UU
S9nUU4$ )Nz,adaptive_max_pool2d not implemented for Longr-   r   r;  r/   r  c                    [        X-  U5      $ r   r  r  s      re   rr  (adaptive_max_pool2d.<locals>.start_index  r  rg   c                2    [        U S-   U-  U-   S-
  U5      $ r  r  r  s      re   rs  &adaptive_max_pool2d.<locals>.end_index	  r  rg   r  c           	     <   > T" U [        T[        S5      5      5      $ Nr  r  r;  )r6  inner_func_max_valr   s    re   inner_fn_max_val-adaptive_max_pool2d.<locals>.inner_fn_max_val      !#':1eFm'LMMrg   c           	     <   > T" U [        T[        S5      5      5      $ r  r  )r6  inner_func_max_idxr   s    re   inner_fn_max_idx-adaptive_max_pool2d.<locals>.inner_fn_max_idx!  r  rg   rg  )r   r{   r  r  rk   rC   r   r  r   rS   r]   r   r  rE  rn   
ValueErrorrF   ri   fallback_adaptive_max_pool2dr  rR   r  r  r@   r   )r   r  r  r  r  r  r  r  r  r  rF  r   r  rr  rs  r  r  r  rir  r  s   `                  @@re   adaptive_max_pool2dr    s3   {{}#IJJa####{q   NNU$77%%d+D77%%d+DLEzUaZ'5'%''V1;;=H%%++allnK
 
 	
 |qT\Q.DL1,u5LDL1,u5LE{e^+HKKME-KR+A{;;4F ."1.;; 7"1.;;NN 
		||~!	
B 
		||~kk!	
B r6Mrg   c                j   ^ ^^^^^^ TT   mTT   mTT   mT R                  5       mUUUUUU U4S jnU$ )Nc                |  > TR                  5       n[        U5      S:X  a]  [        U 5      S:X  a  T" SU S   TS-
  T
-
  /5      nOK[        U 5      S:  a  T" U S   U S   TS-
  T
-
  /5      nO$T" SSTS-
  T
-
  /5      nOT" / U QTS-
  T
-
  P5      n[        R                  " UTR	                  5       5      n[        R                  " TT-
  [
        R                  5      n[        R                  " TS-
  [
        R                  5      n[        R                  " [        R                  " U[
        R                  5      [        R                  " U[
        R                  5      5      n[        R                  " [        R                  " US5      SU5      n[        R                  " XC-   U-  5      [        R                  " X7-  5      -
  n[        R                  " U[
        R                  5      n[        R                  " XF5      n	[        R                  " [        R                  " XU5      [        R                   " T5      5      $ )Nr   r/   r   r-   )r   r   rR   r  r   r{   r  r  r   float64r  r  r,  r  r  r   rr  )r  rs   samples_shapesamplei_exprdiffout_sz_exprrO  seq_ir  r   in_sz	kernel_szndimsout_szsamplessamples_loaders             re   rZ  )_fractional_pooling_offsets.<locals>.load9  s     ((*}"6{a (F1Iuqy3(GHV! (F1Iuqy3(OP (Auqy3(?@ $$>f$>eai#o$>?F7#4#4#67~~ei/=nnVaZ=LLu}}-s||K/W
 		#&&a0!U;		6?e34syy7PPUEKK0vvf*$$SYYtD%A5==QVCWXXrg   r  )r  r  r  r  r   r  rZ  r  s   `````` @re   _fractional_pooling_offsetsr  3  s@    C[F#JE#I((*N!Y !YF Krg   c                    [        XX#SS9$ rC  _fractional_max_poolr   r  r  random_sampless       re   fractional_max_pool2dr  _      STUUrg   c                    [        XX#SS9$ rI  r  r  s       re   fractional_max_pool3dr  d  r  rg   c                  ^^^^ U R                  5         U R                  S T*  U R                  T* S  pe[        R                  " SS9   [	        T5       Vs/ s H  n[        UUUUTUS9PM     snmU R                  5       mUUU4S jnUU4S jm[        U5      [        U5      -   n	U R                  5       n
[        R                  " SU U R                  5       U
U
UU	US9n[        R                  " SU U R                  5       [        R                  U
UU	US9n[        U[        5      (       d   U5       e[        UR                   R                   [        5      (       a  UR#                  5         [        U[        5      (       d   U5       e[        UR                   R                   [        5      (       a  UR#                  5         [%        XU R                  T5      nX4sS S S 5        $ s  snf ! , (       d  f       g = f)	Nr  r-  )r  r  r  r  r  r   c                4   > U S T*  nT" / UQT" X5      Q5      $ r   r   )r6  r  r  r6  r  rC  s      re   r   &_fractional_max_pool.<locals>.fn_inner|  s,    5&\FOfO':3'NOPPrg   c                   > U S T*  nU T* S  n[        T5       Vs/ s H  nTU   " X#U   5      X   -   PM     sn$ s  snf r   r  )r6  r  r  bdhwr  dhw_index_fnr  s        re   r6  1_fractional_max_pool.<locals>.increments_to_index  s]    5&\Fvw<D u%A QQ0=3CC%  s   ;rr  r"  r&  )r  r3  r0   r   r  r  ri  ri   r   rA   r   rn   r{   r  rk   rC   rm   r  r;  )r   r  r  r  r  r  inp_dhwr  r   rF  r   r  r*  r  r  r6  rC  s       `         @@@re   r  r  i  s   NNWWWuf%qwwvw'77	"	5 5\

 " (&"% "

 ==?	Q	 ;k!22!! <<>(	
 ""#<<>kk(	
 &),,4f4,fkk&&	22NN'9--6w6-gll''33OO*!''+>
 { 
6	5

 
6	5s   G)G$.E,G)$G))
G7c           	     `  ^ ^^ T R                  5         T R                  5       Gt pVn[        R                  R                  R                  U5      n[        R                  R                  R                  U5      nUGt pXn	Xh-  S:X  a'  Xy-  S:X  a  [        T [        Xh5      [        Xy5      /SS9$ [        Xh5      n
[        Xy5      nS mU4S jn[        TUX/Xg/X/[        R                  S9mUU 4S jn[        R                  " T R                  5       T R                  5       U[!        U5      S9nU$ )	Nr   r/   )divisor_overridec                F    [        X-  [        R                  " U5      5      $ r   )r(   r   rr  r  s      re   rr  0upsample_nearest2d_backward.<locals>.start_index  s    ug(>??rg   c                   > T" U S-   X5      $ r  r   )rA  r  r  rr  s      re   rs  .upsample_nearest2d_backward.<locals>.end_index  s    EAI99rg   r  c                (   > T" U [        T5      5      $ r   )r  )r6  r  r   s    re   r   'upsample_nearest2d_backward.<locals>.fn  s    c.q122rg   rg  )r  r   rS   r]   r   r  r  r)   rF   r  rR   r   r@   r   rn   r   ri   )r   r  r7  r  r  rv  inp_hinp_wout_hout_wr  r  rs  r   r  r  rr  s   `              @@re   upsample_nearest2d_backwardr     s    NNJJLVEGG&&u-EGG&&u-E 'VE}emq0&(>?RS
 	
 5(L5(L@: ""1.77F3 
		||~kkmJ
B Irg   c                "    [        U UUUUUUSS9$ )Nr-   r  _avg_poolndr   r  r  r  r	  count_include_padr  s          re   r  r    )     		 	rg   c                "    [        U UUUUUUSS9$ )Nr   r  r  r  s          re   
avg_pool3dr    r  rg   c                  ^^^^^^^^^^^ T(       d  TmT(       d  S/T-  m[        TT5      m[        TT5      m[        TT5      m[        U [        5      (       d   e[        T5      T:X  d   e[        T5      T:X  d   e[        T5      T:X  d   e[        U R	                  5       5      TS-   TS-   4;   d   eU R                  5         U R	                  5       S T*  nU R	                  5       T* S  m[        [        T5       V	s/ s H  n	[        TU	   U	TTTU5      PM     sn	6 u  p[        T5      (       d  [        U5      (       a  [        U STS9mSnOU R                  5       mSn[        U5      [        U
5      -   nU R                  5       m[        R                  " [         R"                  T5      nUS:  a6  TS:X  a  [$        nOTS	:X  a  [&        nO[)        S
T 35      eU" U TTTUTU5      $ UUUU4S jmU(       a  U(       a5  U(       a  UOUmTR*                  (       a  ST-  mUUUU4S jnOUUUU4S jnOUUUUUUUUU4	S jn[,        R.                  " U R1                  5       TUUS9nU$ s  sn	f )Nr   r/   r-   r  r  TFr  r   zUnknown dim: c           	     f  > U S T	*  nU T	* S  nS n[         R                  " [        T	5       Vs/ s H  n[        T
U   5      PM     sn6  HZ  n[        T	5       Vs/ s H  oSU   TU   -  Xe   -   TU   -
  PM     nnU" / UQUQ5      nUc  UnMD  [        R                  " X5      nM\     U$ s  snf s  snf r   )r  r  r  rR   r   )r6  r  r  r5  totalrs   r  r   r  r   r  r  r  s            re   r  _avg_poolnd.<locals>.fn_sumT  s    UsdJ##U3Z%PZeKN&;Z%PQBBG*M*QQ4&)#be+gaj8*CM6C)C}+ R  &QMs   B)B.c                j   > [         R                  " T" U T5      [         R                  " TT5      5      $ r   )rR   rh  r  )r6  r   r  r  rC  s    re   r   _avg_poolnd.<locals>.fnf  s&    wwvc84cll5%6PQQrg   c                j   > [         R                  " T" U T5      [         R                  " TT5      5      $ r   )rR   truncdivr  )r6  divisorr   r  rC  s    re   r   r  k  s'    ||F3$93<<QV;WXXrg   c                h  >	 U T	* S  n/ n[        T	5       H  nX   TU   -  TU   -
  n[        R                  " UTU   -   TU   TU   -   5      nT(       d1  [        R                  " US5      n[        R                  " UTU   5      n[        R
                  " XT-
  [        R                  5      nUR                  U5        M     [        R                  " [        R                  U5      nT
R                  (       a  [        R                  " T" U T5      U5      $ [        R                  " T" U T5      U5      $ r  )r  r   MinMaxrR   r  r{   r  ro   r  r  rh  r  r  r  )r6  r  divide_factorsrs   hstarthendfactordivide_factorr  r   r   r  r  r  r  r  rC  s           re   r   r  q  s    cTUBN3Z*WQZ7yy+a.!8!A$:KL("YYvq1F 99T1Q40Du{{C%%f-   &,,SWWnEM&&{{6#x#8-HH<<sH 5}EErg   rg  )rM   rk   rC   r   r   r  r  r  r  r#  r  ri  ri   r   r  r  r3  rh  fallback_avg_pool2dfallback_avg_pool3dr  r  r@   r   rn   )r   r  r  r  r	  r  r  r   r  rs   r  
ceil_modeshad_paddingrF  r  fallbackr   r  r  r   r  r  r  rC  s    ``` ` `          @@@@@@re   r  r    sc    #){C0K&#&F7C(Ga####{s"""v;#w<3qzz|q#' 2222NNJJL3$E	

cTUA 3Z

 1q+vw	J

E 7||s:.q#3?==?E{T%[(HKKME""8<<=KR!8*HAX*H}SE233
 	
  *&6"K""KER R
Y Y	F 	F$ 
		||~	
B Iu

s   I-c                (  ^^^^^^^^^^^^^^ Tb  TS:w  d   S5       eT(       d  TmT(       d  SS/m[        U [        5      (       d   e[        U[        5      (       d   e[        T5      S:X  d   e[        T5      S:X  d   e[        T5      S:X  d   e[        UR                  5       5      S;   d   eU R	                  5         UR                  5       Gt nmm[        TSTTTU5      u  p[        TSTTTU5      u  pU R                  5       mTS   =(       d    TS   =(       d    U
=(       d    UmU R                  5       Gt nmm[        UR                  5       5      nUR                  5       n[        UU4S j[        TS   S-  5       5       5      m[        UU4S j[        TS   S-  5       5       5      mTT-  nUS:  a  [        U UTTTUTT5      $ UUUUU4S	 jmUUUUUUUUUUUU4S
 jn[        R                  " U R                  5       UUUS9nU$ )Nr   divisor must be not zeror-   rf  r/   c              3     >#    U  H>  n[        [        UTS    5      [        S [        UTS    -
  TS    5      5      -
  S5      v   M@     g7frO  rP  rQ  s     re   r   &avg_pool2d_backward.<locals>.<genexpr>  rR  rS  c              3     >#    U  H>  n[        [        UTS    5      [        S[        UTS    -
  TS    5      5      -
  S 5      v   M@     g7frU  rP  rV  s     re   r   r"    rR  rS  r  c           	     n  > [         R                  " TS   [        R                  5      n[         R                  " TS   [        R                  5      n[         R                  " TS   [        R                  5      n[         R                  " TS   [        R                  5      n[         R                  " TS   [        R                  5      n[         R                  " TS   [        R                  5      n[         R                  " [         R
                  " X5      U5      n[         R                  " [         R
                  " X5      U5      n	[         R                  " [         R                  " X5      [         R                  " [         R                  " T[        R                  5      U5      5      n
[         R                  " [         R                  " X5      [         R                  " [         R                  " T[        R                  5      U5      5      n[         R                  " U[         R                  " S[        R                  5      5      n[         R                  " U	[         R                  " S[        R                  5      5      n	[         R                  " U
[         R                  " T[        R                  5      5      n
[         R                  " U[         R                  " T[        R                  5      5      n[         R
                  " [         R                  " X5      [         R                  " X5      5      nU$ )zc
This computes the scaling factor that we will divide an element
by when `count_include_pad=False`
r   r/   )
rR   r  r{   r  r  rh  r  r   r  r  )rb  rc  stride_hstride_wpad_hpad_wkernel_hkernel_wr  wstartr  wendr  heightr  r  r  rm  s                re   !compute_pool_size_without_padding>avg_pool2d_backward.<locals>.compute_pool_size_without_padding  s   
 <<q	5;;7<<q	5;;7WQZ5WQZ5<<A<<<A<.6.6{{GGF%GGCNN65;;7?
 {{GGF%GGCNN5%++6>
 VS\\!U[[%ABVS\\!U[[%AB{{4!DE{{4u{{!CD 5swwt7LMrg   c                  > U Gt pnUTS   -   nUTS   -   n[         R                  " [        UTS   -
  TS   -   TS   5      [        R                  5      n[         R                  " [        UTS   -
  TS   -   TS   5      [        R                  5      n[         R                  " [        UTS   5      S-   [        R                  5      n[         R                  " [        UTS   5      S-   [        R                  5      n[         R
                  " U[         R                  " S[        R                  5      5      n[         R
                  " U[         R                  " S[        R                  5      5      n[         R                  " U[         R                  " T[        R                  5      5      n[         R                  " U[         R                  " T[        R                  5      5      nS n[        T5       GHD  n	[        T5       GH0  n
[         R                  " U[         R                  " U	[        R                  5      5      n[         R                  " U[         R                  " U
[        R                  5      5      nTb  TnO"T(       d  T(       d  TS   TS   -  nOT" X5      n[         R                  " T" / UQ[         R                  " [         R                  " U[         R                  " U[         R                  " S[        R                  5      5      5      TSS9P[         R                  " [         R                  " U[         R                  " U[         R                  " S[        R                  5      5      5      TSS9P5      U5      n[         R                  " [         R                  " X5      [         R                  " X5      5      nUc=  [         R                  " X[         R                  " S[        R                   5      5      nGM  [         R                  " U[         R                  " X5      U5      nGM3     GMG     Uc   eU$ )Nr   r/   Fr,  r  )rR   r  r)   r{   r  r  r  r  r  r   r  r  r  r  r  r  r  )r6  r  r  rW  r[  r\  r]  r^  r_  r`  ra  rb  rc  r  partr  r.  r  r  rg  rh  r  r  r  rj  rk  r  rl  s                   re   r   avg_pool2d_backward.<locals>.fn  s   A
N
N..QQ'&)3VAY?
 ..QQ'&)3VAY?
 x6!9595;;Gx6!9595;;G++gs||Au{{'CD++gs||Au{{'CDE3>>-#MNE3>>,#LM'C]+WWWcll3&DEWWWcll3&DE#/,E&k'N[^;E=bEE{{#11 #$&s||Au{{7S(T!" !.&+  11 #$&s||Au{{7S(T!" !-&+& ). xxFF2%FF2% #"yyS\\#u}}5UVH"yyswwx/FQHS , (V ###rg   rg  )rk   rC   r   r   r  r  ri  ri   r   rr  r  fallback_avg_pool2d_backwardr@   r   rn   )rq  r   r  r  r  r	  r  r  r   _h_out
ceil_mode1_w_out
ceil_mode2rF  r   r  r   r  r.  rg  rh  r  r-  rj  rk  rl  rm  s     ``` ``          @@@@@@@@@re   avg_pool2d_backwardr8    s"    #'71'<X>XX<a&k9----a####{q   v;!w<1qzz|&&&

Q%;F &eQVWiXF))+K!*F
FjFJK&1&:&:&<#Q|AJJL!HKKME {1~)* M  {1~)* M
  -/KR+	
 		
 8? ? ?B 
		%%'	
B Irg   c                  ^^^^^^^^^^^^^^^^^  Tb  TS:w  d   S5       eT(       d  TmT(       d  / SQm[        U [        5      (       d   e[        U[        5      (       d   e[        T5      S:X  d   e[        T5      S:X  d   e[        T5      S:X  d   e[        UR                  5       5      S;   d   eU R	                  5         UR                  5       Gt nmmm [        TSTTTU5      u  p[        TSTTTU5      u  p[        T STTTU5      u  pU R                  5       m[        T5      =(       d    U
=(       d    U=(       d    UmU R                  5       Gt nmmm[        UR                  5       5      nUR                  5       nUU4S j[        S5       5       u  mmmTT-  T-  nUS	:  a  [        U UTTTUTT5      $ UUUUUU 4S
 jmUUUUUUUUUUUUUU4S jn[        R                  " U R                  5       UUUS9nU$ )Nr   r   )r   r   r   r   )r   r   r/   r-   c              3  r   >^#    U  H+  m[        UUU4S  j[        TT   S-  5       5       5      v   M-     g7f)c           
   3  z   >#    U  H0  n[        UTT   -  [        S UTT   -
  TT   -  5      -
  S5      v   M2     g7frO  )rr  )r   r  rs   r  r  s     re   r   0avg_pool3d_backward.<locals>.<genexpr>.<genexpr>k  sH      
. VAYQ[^);q	(I!JJANN.s   8;r-   N)rr  r  )r   rs   r  r  s    @re   r   &avg_pool3d_backward.<locals>.<genexpr>j  sA      3
 A	 	 
;q>A-.
 	
 	
 s   37}   c           	       > S T 5       u  p4nS T 5       u  pgnS T 5       u  pnS [        XU/X4U/XgU/5       5       u  pnS [        XU/XU/TTT/XgU/5       5       u  nnnS XU4 5       u  pnS [        UUU/TTT/5       5       u  nnn[        R                  " [        R                  " [        R                  " X5      [        R                  " UU5      5      [        R                  " UU5      5      nU$ )Nc              3  l   #    U  H*  n[         R                  " U[        R                  5      v   M,     g 7fr   rR   r  r{   r  )r   r   s     re   r   Qavg_pool3d_backward.<locals>.compute_pool_size_without_padding.<locals>.<genexpr>  s"     'UfQ(D(Dfr=  c              3  l   #    U  H*  n[         R                  " U[        R                  5      v   M,     g 7fr   rA  r  s     re   r   rB    s"     MWs||Au{{;;Wr=  c              3  l   #    U  H*  n[         R                  " U[        R                  5      v   M,     g 7fr   rA  )r   r   s     re   r   rB    s%      (
2=QCLLEKK((+r=  c              3  ~   #    U  H3  u  pn[         R                  " [         R                  " X5      U5      v   M5     g 7fr   )rR   r  rh  )r   r  r   pads       re   r   rB    s5      "
	c GGCGGAM3''s   ;=c           
   3     #    U  Hk  u  pp4[         R                  " [         R                  " X5      [         R                  " [         R                  " U[        R
                  5      U5      5      v   Mm     g 7fr   )rR   r  r   r  r{   r  )r   ro  r   r   rF  s        re   r   rB    sV      

'"# KK!3773>>#u{{+KS#Q 's   A3A5c              3     #    U  H?  n[         R                  " U[         R                  " S [        R                  5      5      v   MA     g7fr  rR   r  r  r{   r  )r   ro  s     re   r   rB    s4      "
1 KKs||Au{{;<<1   AA	c              3     #    U  HA  u  p[         R                  " U[         R                  " U[        R                  5      5      v   MC     g 7fr   rR   r  r  r{   r  )r   rp  r   s      re   r   rB    s6      
K KKS^^C=>>K   A	A)r  rR   rh  r  )pdrb  rc  stride_dr%  r&  pad_dr'  r(  kernel_dr)  r*  dstartr  r+  dendr  r,  r  depthr-  r  r  r  rm  s                      re   r.  >avg_pool3d_backward.<locals>.compute_pool_size_without_padding  s.   'Uf'U$HMWMe(
2=(
$H"
 x8<uU>S"


 '*(X.&u%	'	

dD"
 &1"

tT 2UFE4JK
dD GGCGGD)3774+@A3774QWCX
 rg   c                R  > U Gt pp4S [        X#U/T5       5       u  p#nS [        X#U/TT!5       5       u  pVnS [        X#U/T!5       5       u  pn
S XVU4 5       u  pVnS [        XU
/TTT /5       5       u  pn
S n[        T5       GH  n[        T5       GH  n[        T"5       GHo  nS [        XVU/XU/5       5       u  nnnTb  TnO*T(       d  T(       d  TS   TS   -  TS	   -  nO
T" UUU5      n[        R                  " T" / UQ[        R                  " [        R
                  " U[        R                  " U[        R                  " S[        R                  5      5      5      TS
S9P[        R                  " [        R
                  " U[        R                  " U	[        R                  " S[        R                  5      5      5      TS
S9P[        R                  " [        R
                  " U[        R                  " U
[        R                  " S[        R                  5      5      5      T S
S9P5      U5      n[        R                  " [        R                  " [        R                  " X5      [        R                  " UU	5      5      [        R                  " UU
5      5      nUc>  [        R                  " UU[        R                  " S[        R                  5      5      nGMB  [        R                  " U[        R                  " UU5      U5      nGMr     GM     GM     Uc   eU$ )Nc              3  .   #    U  H  u  pX-   v   M     g 7fr   r   )r   r	  rF  s      re   r   2avg_pool3d_backward.<locals>.fn.<locals>.<genexpr>  s     A)@vq17)@r2  c              3     #    U  H<  u  pn[         R                  " [        X-
  U-   U5      [        R                  5      v   M>     g 7fr   rR   r  r)   r{   r  )r   r	  r   r   s       re   r   rX    s:      %
>a NN8AEAIq15;;??>s   AAc              3     #    U  H8  u  p[         R                  " [        X5      S -   [        R                  5      v   M:     g7fr=  rZ  )r   r	  r   s      re   r   rX    s4      
. NN8A>A-u{{;;.s   A Ac              3     #    U  H?  n[         R                  " U[         R                  " S [        R                  5      5      v   MA     g7fr  rI  )r   pstarts     re   r   rX    s4      %
5 KKQ <==5rJ  c              3     #    U  HA  u  p[         R                  " U[         R                  " U[        R                  5      5      v   MC     g 7fr   rL  )r   pend
pooled_dims      re   r   rX    s;      
%  KKcnnZEFF%rM  c              3     #    U  HA  u  p[         R                  " U[         R                  " U[        R                  5      5      v   MC     g 7fr   )rR   r   r  r{   r  )r   r]  p_s      re   r   rX    s:      "+JF R(EFF+rM  r   r/   r-   Fr,  r  )r  r  rR   r  r  r  r  r  r{   r  r  r  r  r  r   )#r6  r  r  r  rW  pdstartr[  r\  pdendr]  r^  r_  pd_r`  ra  rN  rb  rc  r  r1  r  r.  r  d_window_sizer  rg  rh  r  r  r  pooled_depthrj  rk  r  rl  s#                        re   r   avg_pool3d_backward.<locals>.fn  s   AAaAY)@Aa%
ay+v>%
!'

Q1Iv.
e
%
"W5%
!'
$'u%m\'R%
e 'C]+ /C"*-$w7#C+"JBB (3 0*+ +AQ ?+a. P A"b" M;;#!' # 5 5$'KK(*CGGE3<<5;;;W,X%& %1*/!" !$ 5 5$'KK(*CGGE3<<5;;;W,X%& %2*/!"  !$ 5 5$'KK(*CGGE3<<5;;;W,X%& %1*/!"!4 7D< 88!2CFF2u4EFr5)D  '#&99 $S%--(H$ $'99T3778T3JH#Um 0 , (r ###rg   rg  )rk   rC   r   r   r  r  ri  r#  ri   r   r  fallback_avg_pool3d_backwardr@   r   rn   )!rq  r   r  r  r  r	  r  r  rv  _d_outceil_mode_dr4  ceil_mode_hr6  ceil_mode_wr   rF  r   r  r   r  r.  rf  rT  rg  rh  r  r-  rg  rj  rk  rl  rm  s!     ``` ``             @@@@@@@@@@@@re   avg_pool3d_backwardrn  =  s    #'71'<X>XX<k9----a####{q   v;!w<1qzz|&&&$%JJL!VUFE&q+vw	F ';F 'q+vw	F ))+Kg,K+KKK4?4H4H4J1Qm\AJJL!HKKME3
 q3/M=-  -/-?KS+	
 		
# #JU U Un 
		%%'	
B Irg   c                F   U R                  5       n[        U[        5      (       a  U/nOU(       d  [        [	        U5      5      n[	        U5      S:X  a  [        U5      S;   d
   SU 35       e/ $ [        U5      n[        [	        U5      5       Hg  nX   S:  a'  X==   [	        U5      (       a  [	        U5      OS-  ss'   SX   s=::  a  [	        U5      :  a  ML  O  [	        U5      S:X  a
  X   S:X  a  Mg   e   [	        [        U5      5      [	        U5      :X  d   S5       eU$ )Nr   )r   r  rU  zinvalid axis: r/   zreduction axis not unique)r   rk   r   r  r   r   ri   r'   )r   r  r   rs   s       re   _validate_reduction_axisrq    s    ::<D$vSY
4yA~T{//H>$1HH/	:D3t97Q;GCIIs4y14GDG'c$i'CINtw!|LL  z$ CI-J/JJ-Krg   )r  c          	       ^^^^^^^ Ub  [        X5      n U R                  5       m[        [           " [	        X5      5      n/ n/ m/ m/ m[        [        T5      5       HT  nXq;   a'  TR                  U5        TR                  TU   5        M/  TR                  U5        UR                  TU   5        MV     SmUS;   Ga  [        T5      S:  a  [        U 5      (       a  [        U R                  [        5      (       a  SmO[        U R                  [        R                  5      (       d\  [        U R                  [        R                  5      (       ao  [        U R                  R                  [        R                  5      (       a<  U R!                  5       nUR#                  5       =(       d    UR%                  5       (       + mUUUUUUU4S jn	T(       a1  ['        T5      n
T H  n[(        R*                  R,                  X'   M!     OUn
U R/                  5       m[1        U R3                  5       U=(       d    U R5                  5       U R5                  5       U	U
TS9$ )NF)r&  argminr/   Tc                  > [        U5      [        T5      :X  d   eT
(       a.  [        U 5      [        T5      :X  d   eT Vs/ s H  o U   PM	     n n[        U 5      [        T5      :X  d   eS /[        U 5      [        U5      -   -  n[        R                  " [        TU 5      [        TU5      5       H	  u  pEXSU'   M     T	" U5      nT(       a{  U Vs/ s H  n[        R
                  " U5      PM     nnUS   n[        S[        U5      5       H  nUTU   -  Xr   -   nM     U[        R                  " U[        R                  5      4$ U$ s  snf s  snf r  )r   r  r  r  r   r3  r  rR   r  r{   r  )rA  reduction_indexrs   r  r6  varr   rindex
linear_idxinner_loaderkeepdimskept_idxreduced_idxreduced_sizesshould_compute_logical_indexr   s            re   r  %_make_reduction_inner.<locals>.loader<  s:   ?#s;'7777u:T***'/0x!1XxE05zS]***Fc%j3+??@	!% #k?"C
HC !cN
 Y' (/>?!ell1oF?  J1c&k*'-*::VYF
 + 3>>*ekkBCC+ 1 @s   E
 E)rv   r$  r  re  rd  r%  )r   r   r'   r   rq  r  r   ro   r;   rk   rm   r?   r2   r   r   Bufferrj  is_transposedis_contiguousri   r   r/  r0  ri  r  rn   r   )r   r  rz  r   rJ  r  
kept_sizesrs   r  r  rF  ry  r{  r|  r}  r~  r   s     `        @@@@@@re   _make_reduction_innerr    s    Q::<Dc?3A<=DJHMK3t99q!  a)OOAd1g&  $) .."aLLaffk**+/( 2 233qvvr}}--*QVV[["))2T2T\\^F$$&Df.B.B.D*D ) 6 :A''++HK  ==?L||~'81;;=++-& rg   c                $   ^ ^ SS S.UU 4S jjjnU$ )Nr   c          	        > [        U UUUTTS9n[        R                  " STU S.UD6n[        UR                  R                  [        5      (       a  UR                  5         U$ )N)r  rz  r   rJ  r  )r  r#  r   )r  rA   r   rk   rm   r  )r   r  rz  r   r   r  rJ  r  s         re   rs  make_reduction.<locals>.innerj  sj    &"7)
 !!XAXQWXKK
 
 NNrg   r   r   )r  rJ  rs  s   `` re   make_reductionr  i  s    T  " Lrg   c                   Ub  [        X5      n [        X5      n[        U R                  5       U R	                  5       4U R                  5       4U R                  5       US9$ )N)rv   dtypes	inner_fnsr   r  )r   r_  r  rn   r   ri  r   )r   r  r   s      re   _make_scan_innerr  ~  sV    Q!D||~==?$ZZ\ rg   r   c                 ^ Ub  [        X5      n U R                  5       m[        X5      nU R                  5       nU[        R
                  [        R                  4;   a  [        U [        R                  5      n [        XU5      n[        U4S jU 5       5      n[        R                  " X`R                  5       U R                  5       S9n[        R                  " U[        UR                  5       5      5      n[        [!        XV5      U5      $ )Nc              3  .   >#    U  H
  nTU   v   M     g 7fr   r   r   rs   r   s     re   r   mean.<locals>.<genexpr>       04a$q'4r   r@  )r   r   rq  r   r{   rl  rk  r;  sum_rP   r2   r9   rn   r8   r   ri   div)r   r  keepdimr   output_dtype
sum_resultdenomr   s          @re   r  r    s    Q::<D#A,D;;=Lu~~66Q$aw'J0400Ee;;=XEeT**=*=*?%@AEC
*L99rg   c                F  ^
 Uc  SnU R                  5       m
[        X5      n[        XSS9nU(       a  UR                  5         [	        [        X5      5      n[        XaU5      n[        U
4S jU 5       5      nU(       a  [        R                  " X-
  S5      n[        R                  " XR                  5       U R                  5       S9n[        R                  " U[!        UR                  5       5      5      n[#        Xx5      n	U(       d  U	4$ U(       a  UO
[%        XQ5      nX4$ )Nr/   T)r  c              3  .   >#    U  H
  nTU   v   M     g 7fr   r   r  s     re   r    var_mean_sum_.<locals>.<genexpr>  r  r   r   r@  )r   rq  r  r  squarer  r  rP   r   r  r2   r9   r   rn   r8   r   ri   r  r  )r   r  
correctionr  return_meanx_meandiffsr  r  x_varr   s             @re   var_mean_sum_r    s    
::<D#A,D!4(F3q>"Ee7+J0400E		%,a0e;;=XEeT**=*=*?%@AE
"ExVGF$9F=rg   c                    [        X5      n[        XUS S S9nUS   n[        US   5      n[        U[        R
                  5      =(       a1    [        U5      [        R                  :  =(       a    [        U5      S:g  $ )Nr  rz  r   rJ  rd  r%  r/   )	rq  r  rP   rk   r   r  r   r0   r.  )r   r  r  r   rd  reduction_numels         re   use_two_step_variancer    sx    #A,D"	wd$F HF#F+=$>?O?EMM2 	' 6#E#EE	'&!Q&rg   c                 ^^^^^ Tc  Sm[        XUS S S9nUR                  S5      nUR                  S5        UR                  S5        [        R                  R                  " SU4SU R                  5       S.UD6u  pxn	UR                  5         U R                  5       mU R                  5       m[        X5      n[        U4S jU 5       5      mS	 mUUUU4S
 jn
[        U
5      " U5      nU(       a  UR                  5         X4$ U4$ )Nr/   r  re  r$  r  welford_reduce)r  r  r   c              3  .   >#    U  H
  nTU   v   M     g 7fr   r   r  s     re   r   $var_mean_welford_.<locals>.<genexpr>  s     1Dq47Dr   c                   [        U [        R                  5      (       aK  U R                  (       d:  [        R
                  " [        R                  " U [        R                  5      U5      $ [        R                  " X5      $ r   )
rk   r   r   	is_numberrR   r   r  r{   r  r  rB  s     re   get_constant_or_index_expr5var_mean_welford_.<locals>.get_constant_or_index_expr  sH    a$$Q[[<<q%++ >FF||A%%rg   c                   > T" TT5      nT" TT5      n[         R                  " ST5      nU [         R                  " X2U-
  5      -  $ r  )rR   r  r  )rm   cNzeror  r   r  rnumels       re   r  #var_mean_welford_.<locals>.scale_fn  sC    &z59&vu5||Au%ckk$A...rg   r   )r  r  r2   WelfordReductionr   r   r  r   rq  rP   ru  )r   r  r  r  r  r   r  r  m2r   r  rv  r   r  r  r   s     `         @@@@re   var_mean_welford_r    s    
"	wd$F ZZ
#F
JJ{
JJ{%%,, )'kkm 	KDa JJLKKME::<D#A,D1D11F&
/ / 
"2
&Cy6Mrg   c                  ^ U R                  5       m[        T5      n[        XSS9n [        U UUUUS9n[	        XUS9(       a  [        S0 UD6O
[        S0 UD6n[        U4S jU 5       5      nU(       d  US   $ U$ )NFr  )r   r  r  r  r  )r  r  c              3  :   >#    U  H  n[        UTS S9v   M     g7f)Fr  N)r   )r   r   r  s     re   r   #var_mean_helper_.<locals>.<genexpr>  s     Fv!8Ayu5vr   r   r   )r   r   r   r  r  r  r  r   )	r   r  r  r  r  compute_dtyper   r6  r  s	           @re   var_mean_helper_r    s    I))4M.A
F !w? 	(( 
 FvFFF'6!93V3rg   )r  r  c                   [        XX#SS9$ )NFr  r  r  r  r  r   r  r  r  s       re   var_r    s    	% rg   c                   [        XX#SS9$ )NTr  r  r  s       re   var_meanr    s    	$ rg   c                (   US:  a"  [        [        R                  " U 5      U* U5      $ US:X  a  [        R                  " SU5      $ US:X  a  U $ [        XS-  U5      n[        R                  " X35      nUS-  S:X  a  [        R                  " X05      nU$ )Nr   r/   r-   )pow_recursiverR   r  r  rh  )r   r7  r   r  s       re   r  r    s    1uS^^A.E::Av||Au%%Av11fe,FWWV$F	A!|#Mrg   c                .    [         R                  " X5      $ r   )rR   r  r   r5  s     re   
pow_nativer  #  s    771=rg   )r  c                  ^ ^^ [        T[        5      (       a*  TR                  5       (       a  [        T [	        T5      5      $ [        T[        5      (       a  TS:X  a  [        T 5      $ [        T[        5      (       a  TS:X  a  [        T 5      $ [        S T T4 5       5      n[        U5      n[        T[        5      =(       a*    STs=:  =(       a    S:  Os  =(       d    U=(       a    TS:  nU(       aY  T R                  5       mU UU4S jn[        R                  " T R                  5       T R                  5       UT R                  5       S9$ [        T [        5      (       aA  T S:X  a  [!        TS5      $ T S	:X  a)  [#        TR                  5       5      (       a  [%        T5      $ U(       aN  [        T [        5      (       a  ['        T T5      $ [        T[        5      (       a  [)        T T5      $ [+        T T5      $ [-        T T5      $ )
Nr  r/   c              3     #    U  H6  n[        U[        R                  5      (       d  M$  UR                  5       v   M8     g 7fr   )rk   r2   rC   r   r   s     re   r   pow.<locals>.<genexpr>;  s'     N1*Q2Ms
   #A A i    r   c                F   > [        T" U 5      TTR                  5       5      $ r   )r  r   )r6  r   r5  r  s    re   r   pow.<locals>.fnE  s     a??rg   rg  r-   )rk   r;  r   r  r   sqrtr  rG  r    ri  r@   r   rn   r   r   r!   r  r   exp2fallback_pow_scalarfallback_pow_tensor_scalarfallback_pow_tensor_tensorr  )r   r5  r   is_integer_powembed_exponentr   r  s   ``    @re   r  r  1  s   !U1c!f~	Au		!s(Aw	As		QQx NANNE%e,N  3' a"32AF  	@ <<>++-::<	
 	
 !V6Q?"6nQ[[]337Na  &q!,,6""-a33-a33arg   c                f   [        U [        5      (       a  U R                  nOU n[        U[        5      (       a  UR                  n[        U[        R                  5      (       d  [
        R                  " U R                  5       U R                  5       UR                  5       U R                  5       S9n[        U[        [        45      (       d   eUR                  n[        U[        R                  5      (       d   e[        U[        R                  5      (       av  UR                  5       (       da  UR                  5       (       dL  [        UR                  [        R                  5      (       d#  UR!                  5         UR                  Ul        U $ [        R"                  R%                  XUS9  U $ )Nrg  unsafe_alias)rk   rC   rm   r2   r   r@   r   rn   r   ri  r   r6   r<   is_input_bufferis_module_buffer	NopKernelr  r\  realize_into)changedr  r  changed_datarc   s        re   rM  rM  b  sC   '9%%||#y!!hhc2==))%%'##%__&##%	
 $: 67777ii#r}}----,..$$&&((**l''66 	HH!!.. /  Nrg   c                ,    [        U [        X5      5      $ r   )rM  r  )r   r  s     re   r  r    s    Q	!011rg   c                    XL a  U $ [        XR                  5       5      n[        XR                  5       5      n[	        XR                  5       5      n[        X5      $ r   r  rn   r   r   r3  r   rM  )r  rN  r  s      re   rt  rt    sH    
z

C)
*C
3
(C
lln
%CSrg   c                .    [         R                  " X5      $ r   )rR   floordivr  s     re   r  r        <<rg   c                .    [         R                  " X5      $ r   )rR   r  r  s     re   r  r    r  rg   c                t   [        U 5      =(       a    [        U5      n[        U 5      =(       a    [        U5      nUS:X  a4  U(       a   S5       eU(       a  [        X5      $ [        [	        X5      5      $ US:X  a4  U(       a   S5       eU(       a  [        X5      $ [        [	        X5      5      $ [	        X5      $ )Nr'  z5floordiv operands can not be boolean at the same timer,  z5truncdiv operands can not be boolean at the same time)r   r   r  r'  r  r  r,  )r   r5  rounding_modeboth_integerboth_booleans        re   div_moder    s    "1%</!*<L"1%</!*<L X!XX!-x~C5Q3CCX!XX!-x~C5Q3CCq9rg   c                    [        U 5      =(       a    [        U5      nU(       a  [        X5      $ [        [        R                  R
                  5      n[        U5      " X5      $ r   )r   logical_andr>   r  rh  r  ru  )r   r5  	both_boolr   s       re   rh  rh    sH    "9q'9I1  **+b!!''rg   c                   [        U [        R                  5      (       a  [        U R                  5      $ [        U [        R
                  5      (       a  [        U R                  5       5      $ [        U [        R                  5      (       a  U $ [        U [        R                  5      (       d  g[        R                  R                  R                  U R                  5       5      n[        R                  " U5         [         R"                  " [        R$                  SS5         U R&                  " U R)                  5       6 nSSS5        SSS5        [        W[        R                  R*                  R,                  5      (       d   e[        UR.                  [        R                  5      (       a  UR.                  $ g! , (       d  f       N= f! , (       d  f       N= f)z:Try convert an arbitrary IR node into an ir.Constant valueNallow_indexingT)rk   r2   r<   get_constant_valuerm   r6   r  r   Loopsr{   	_inductorops_handlerExtractConstantsHandlerrn   rS   set_ops_handlerr   objectr  re  inner_fn_argsvirtualizedOpsValuer   )r   r  rq   s      re   r  r    s1   
 !R]]##!!&&))!R[[!!!!--/22!R[[!! a""oo))AA!,,.QG	'"R&&(8$?jj!//+, 	@ 	#
 c5??66??@@@@#))R[[))yy 	@? 	#"s$   ;'G"F; G;
G		G
Gc                v   [        S X4 5       5      nU(       a  [        X5      $ [        U5      =nbs  U R                  5       R                  S:w  aU  UR
                  S:X  a+  [        R                  " [        S5      UR
                  5      nOSUR
                  -  n[        X5      $ S n[        U5      " X5      $ )Nc              3  \   #    U  H"  n[        U5      =(       d    [        U5      v   M$     g 7fr   )r   r   r   s     re   r   div_prim.<locals>.<genexpr>  s"     O1oa(>OA,>>s   *,r   r   infr  c                 (    [         R                  " U 6 $ r   )rR   r  r  s    re   r   div_prim.<locals>.fn  s    {{D!!rg   )r"  r  r  rn   r   r   mathcopysignr;  rh  ru  )r   r5  is_integralr  r  r   s         re   div_primr    s    OOOK~ &a((5!,,.:M:MQV:V ==AuU|W]]CJw}},J1!!" "a##rg   c                N    [        X4[        R                  S9u  p[        X5      $ r  )rL  r   INT_TO_FLOATr  r  s     re   r  r    s*     	
$C$P$PDA A>rg   c                z    [        U 5      =(       d    [        U 5      nU(       a  S nOS n[        U5      " X5      $ )Nc                .    [         R                  " X5      $ r   )rR   modr  s     re   r   fmod.<locals>.fn  s    771= rg   c                .    [         R                  " X5      $ r   )rR   fmodr  s     re   r   r  
  s    88A>!rg   )r   r   ru  )r   r5  r  r   s       re   r
  r
    s5    !!$:(:K	!
	" "a##rg   c                   [        U R                  5       5      (       d  [        U R                  5       5      (       a  Uc  [        R                  n[        SUS9nU" XX#S9$ )Nr  r  r   r    r   r   r{   r  r  r   r  rz  r   r   s        re   r  r    sM     	''+;AKKM+J+J
-	U	;Bax--rg   c                   [        U R                  5       5      (       d  [        U R                  5       5      (       a  Uc  [        R                  n[        U R                  5       5      S:X  a+  US;   d   eU=(       d    U R                  5       n[        XSS9$ S n[        XUS9n[        R                  R                  " S	0 UDSU0D6u  nUc
  [        XUS9$ U$ )
Nr   r   rU  Tr  c                @    U u  nUu  n[         R                  " X#5      4$ r   )rR   r   a_tupleb_tupler   r5  s       re   
combine_fncumsum.<locals>.combine_fn.  !    rg   r  r   r  r   r   r   )r    r   r   r{   r  r   r   r   r  r2   Scanr   fallback_cumsumr   r  r   r  r   r  s         re   cumsumr  "  s     	''+;AKKM+J+J
-
1::<Aw&t,, 
 a%8F??J?IV~q%88Mrg   c                   [        U R                  5       5      (       d  [        U R                  5       5      (       a  Uc  [        R                  n[        U R                  5       5      S:X  a+  US;   d   eU=(       d    U R                  5       n[        XSS9$ S n[        XUS9n[        R                  R                  " S	0 UDSU0D6u  nUc
  [        XUS9$ U$ )
Nr   r  Tr  c                @    U u  nUu  n[         R                  " X#5      4$ r   )rR   rh  r  s       re   r  cumprod.<locals>.combine_fnF  r  rg   r  r  r  r   )r    r   r   r{   r  r   r   r   r  r2   r  r   fallback_cumprodr  s         re   cumprodr!  :  s     	''+;AKKM+J+J
-
1::<Aw&t,, 
 a%8F??J?IV~599Mrg   c                   S nU R                  5       n[        U R                  5       5      S:X  a  US;   d   e[        U 5      $ [	        XUS9n[
        R                  R                  " S0 UDSU0D6u  nUc	  [        XS9$ U$ )Nc           	     .   U u  nUu  n[         R                  " X#5      n[         R                  " X#5      nXE:g  [         R                  " U5      ) -  n[         R                  " U[         R
                  " [         R                  " XE-
  5      5      U-   U5      4$ r   )rR   r  r  r  r  log1pexp)r  r  r   r5  min_vmax_vr  s          re   log_add_exp_helper(logcumsumexp.<locals>.log_add_exp_helperT  ss    A!A!CIIe$4#45		$		#''%-*@ AE I1MOOrg   r   r  r  r  r  r   )	r   r   r   r  r  r2   r  r   fallback_logcumsumexp)r   r   r(  r   r   r  s         re   logcumsumexpr+  R  s{    P KKME
1::<Ag~~Qxa7FGG4FGIV~$Q00Mrg   c                  ^ [        U R                  5       5      S:X  a+  TS;   d   e[        U 5      [        U [        R
                  S94$ U R                  5       n[        R                  " SUSS9n[        U TUS9nU[        R
                  4US'   U R                  5       U4S	 j4US
'   [        R                  R                  " S0 UDSU0D6u  pVUc
  [        U TS9$ XV4$ )Nr   r  r   r&  Fr   arg_break_ties_leftr  r  c                T   > [         R                  " U T   [        R                  5      $ r   rR   r  r{   r  r6  r  s    re   rQ  cummax.<locals>.<lambda>w      CNN3t9ekk:rg   r  r  r  r   )r   r   r  r  r{   r  r   r2   get_reduction_combine_fnr  ri  r  r   fallback_cummaxr   r  r   r  r   r   r  s    `     re   cummaxr7  h      
1::<AwQxAU[[999KKME,,5J ad%8Fu{{+F8	:F; ggnnEvE*EOF~qd++?rg   c                  ^ [        U R                  5       5      S:X  a+  TS;   d   e[        U 5      [        U [        R
                  S94$ U R                  5       n[        R                  " SUSS9n[        U TUS9nU[        R
                  4US'   U R                  5       U4S	 j4US
'   [        R                  R                  " S0 UDSU0D6u  pVUc
  [        U TS9$ XV4$ )Nr   r  r   rs  Fr-  r  r  c                T   > [         R                  " U T   [        R                  5      $ r   r0  r1  s    re   rQ  cummin.<locals>.<lambda>  r3  rg   r  r  r  r   )r   r   r  r  r{   r  r   r2   r4  r  ri  r  r   fallback_cumminr6  s    `     re   cumminr=    r8  rg   c                   [        U R                  5       5      (       d  [        U R                  5       5      (       a  Uc  [        R                  n[        SUS9nU" XX#S9$ )Nr  r  r   r  r  s        re   r  r    sM     	''+;AKKM+J+J
-	e	<Bax--rg   c                V    [        U [        R                  5      n [        S5      " XUS9$ )Nr#  r  rz  )r   r{   r   r  r   r   r  s      re   
reduce_anyrB    s$    EJJA% w??rg   c                F    Ub  [        XUS9[        XUS94$ [        U S US9$ Nr@  )reduce_amaxreduce_argmaxrA  s      re   
reduce_maxrG    6    
g6!8
 	

 qtg66rg   c                F    Ub  [        XUS9[        XUS94$ [        U S US9$ rD  )reduce_aminreduce_argminrA  s      re   
reduce_minrL    rH  rg   xor_sumrr  rq  r&  r  rs  
logical_or)rp  rc  stabler   
descendingc          
        Uc  SnU R                  5       nU R                  5       n[        [        U5      U5      n[        U5      S:X  a'  [	        U 5      [        SU[        R                  U5      4$ [        U5      (       a  XB   OSn[        R                  R                  R                  U[        R                  " [        R                  5      R                  5      (       d
  [        XX#S9$ [!        USS[        R                  USS9nS/[        U5      -  n[        U5      (       a  XhU'   [#        Xx5      n[%        Xt5      n[&        R(                  R+                  UU R,                  UR,                  4U R/                  5       UR/                  5       4UUUUS9u  pU	c
  [        XX#S9$ Uc   eU	[1        U[        R                  5      4$ )NFr   r/   rO  )ro  rq  r   rv   r  )rv   r  r  r   r  rP  rQ  )r   rn   r   r   r  r  r{   r  rS   r]   r   statically_known_ltr  int16rr  sort_fallbackr  r  r3  r2   Sortr   r   ri  r   )
r   rP  r   rQ  r3  rv   ri  r  
view_shaper   s
             re   sort_stablerX    s   ~JJLE\\^F
3u:s
+C
5zQQxq&%++u=== ZZuzQH77//%++ekk:R:V:VWWQ3NNVSXG s5z!J
5zz"37'GW$Gggnn'==?G$7$7$9: % OF ~Q3NN8GU[[111rg   c                    [        U SXS9$ )NFrO  )rX  )r   r   rQ  s      re   sortrZ    s    qCGGrg   c                6    [        U U[        R                  US9$ )Nr   r   rr  )r  r   r  )r`   r   rr  s      re   register_pointwise_numericr]    s!    
;HH'	 rg   c                \    [        U R                  5        [        U [        R                  S9$ r  )rO   r  r  r   r  r  s    re    register_pointwise_numeric_ldf64r_    s'    '4
;HH rg   r  logical_not)rc  )r   r  rJ  identity)r}  pointwise_overrides_datac              #  V  ^#    [         U   m[        U TR                  S 5      nUc  g U4S jn[        U[        R
                  R                  5      (       a:  UR                  5        H%  n[        X$5      nUTR                  U" U5      4v   M'     g UTR                  U" U5      4v   g 7f)Nc                6   > TR                   c  [        U 5      $ g r   )tritonr  )r`   rm   s    re   make_triton_fallback6_get_pointwise_overrides.<locals>.make_triton_fallbackq  s    ;;#B'' rg   )	rb  r   r   rk   r{   r|   r   r   r   )nsr   r`   rf  olnamer  rm   s         @re   _get_pointwise_overridesrj  k  s     #D)D	TYY	%B	z( "ejj1122llnF$Bd..0DR0HHH % $**,@,DDDs   B&B)r\  c                d   ^ U [         U'   [        R                  U 5        U4S jn[        X5        g )Nc            	     ~   > T" U 0 UD6n/ n[        U S   U5       H  u  pEUR                  [        XESS95        M      U$ )Nr   Tr  )r  ro   rM  )rt   r   resultsmut_resultsr   r  outplace_ops         re   r   $register_foreach_inplace.<locals>.fn  sK    t.v.tAw0KCy4HI 1 rg   )rZ   r{  r   r  )aten_opoutplace_aten_opro  r   s     ` re   register_foreach_inplacers    s,    07,-G$ w+rg   c                .   ^ [        U S S9U4S j5       nU$ )Nr  c                 j   > T" U 0 UD6n[        X S   R                  5       5      n[        U S   U5      $ r  )r   r   rM  )rt   r   r  ro  s      re   r   register_inplace.<locals>.fn  s:    d-f-&q'"3"3"56a&))rg   )r*  )rq  ro  r   s    ` re   register_inplacerw    s#    wD9* :*
 Irg   c                    g r   r   rp  s      re   sym_constrain_rangery  	      rg   c                    [         R                  R                  R                  S   n[	        U[
        R                  5      (       a  UR                  R                  $ [        U5      $ r\  
rS   r]   r^   rm  rk   r{   rO  rc   rP  r   r   r   r  s      re   ru  ru    D    
''


#
#E
*C#u||$$xx}}3xrg   c                    [         R                  R                  R                  S   n[	        U[
        R                  5      (       a  UR                  R                  $ [        U5      $ r\  r|  r}  s      re   
sym_strider    r~  rg   c                "    U R                  5       $ r   )r  r   s    re   	sym_numelr     s    ;;=rg   c                (    [         R                  " U 6 $ r   )r   Addr  s    re   sym_sumr  )  s    99drg   c                    [        S5      e)NzHelpful for debuggingr   )r8  rt   r   s      re   foobarr  .  s    
5
66rg   c                8    U R                  5         [        U 5      $ r   )r  r  r   s    re   _realizer  3  s    IIK8Org   c                R    U R                  5         [        R                  " X5        U $ r   )r  r2   ResizeStorageBytes)variablerF  s     re   resize_storage_bytes_r  9  s!    (-Org   c                    U R                  5         UR                  5         [        R                  " [        R                  " X5      5      $ r   )r  rC   r   r2   SetSourceTensorKernel)r8  source_tensors     re   set__source_tensorr  @  s3    LLNB44TIJJrg   rt  c                    XL a  U $ [        XR                  5       5      n[        XR                  5       5      n[	        XR                  5       5      n[        X5      $ r   r  )r  rN  s     re   
fsdp_copy_r  I  sH    :J^^-.sMMO,S,,.)""rg   c                 ^	^
^^ [        U [        5      (       d   e[        U[        [        45      (       d   eUc  [        R
                  nU[        R                  :X  a  [        SU 35      eU[        R                  :X  a  [        U5      S:X  d   eU[        R                  :X  a  [        U5      S:X  d   eU R                  5       m
U R                  5       nU R                  5       n[        U R                  [        R                   5      (       a  U R                  R#                  5       U l        [        R$                  " 5       (       ay  [        R&                  R(                  R*                  (       aP  [-        U5      (       a  [/        S5      mO6[1        U5      (       a!  [        R2                  " U5      R4                  mOSmOSm[6        R8                  R:                  R=                  T
S5      (       a  [?        UTX4S9$ [A        U T
/S	/5      nURC                  5       m	[        RD                  RG                  X5      n[        RH                  " XCX5      RK                  5       mU	U
UU4S
 jn[L        RN                  " XCU[        U5      S9nU$ )Nzunsupported memory format: r   r   nanTr  r   r;  r/   c                  >^ T" U 5      m[         R                  " T[        R                  5      n[         R                  " T[        R                  5      n[         R                  " X5      n[         R
                  " UUU4S jT5      $ )Nc                    > T" T /5      $ r   r   )
flat_indexflat_loaders   re   rQ  *resize.<locals>.inner_fn.<locals>.<lambda>  s    ZL(Arg   )rR   r  r{   r  r  r  )	r6  flat_index_exprlimitr  r  r  	old_numelout_indexeruninitialized_vals	       @re   re  resize.<locals>.inner_fn  sX     %
..U[[Ay%++6vvo-zz$ ACTUUrg   rg  )(rk   rC   ri   r   r{   contiguous_formatpreserve_formatr  channels_lastr   channels_last_3dr  r   rH  rm   r2   r6   r  rZ  r@  deterministicfill_uninitialized_memoryr   r;  r    r  rr  rS   r]   r   rr  r  rn  ri  r   stride_ordered_for_memory_formatr  r  r@   r   )r   r   r  r   rv   x_flat
out_stridere  rq   r  r  r  r  s            @@@@re   resizer  T  s
   a####dT5M****//---8HII+++4yA~~...4yA~~IKKME""$F!&&"++&&##% 	2244KK%%??%   %ee$$ %E 2 6 6 $  ww//	1==D+5HH		
 	
F $$&K""CCDXJ..ANNPKV V 

Xd4jC Jrg   )auto_functionalizedc                    SSK Jn  UR                  U5      n[        R                  " U UU0 UEUES9  UR                  5        VVs0 s H  u  px[        U[        5      (       d  M  Xx_M      snn$ s  snnf )Nr   )kernel_side_table)
kernel_idxgridtma_descriptor_metadatakernel_args)*torch._higher_order_ops.triton_kernel_wrapr  get_constant_argsr2   UserDefinedTritonKernelr   rk   rC   )	r  constant_args_idxr  r  r   r  constant_argsrT  r  s	            re   triton_kernel_wrap_r    sl     M%778IJM 7/v//	 &,\\^R^z#y7QHCH^RRRs   A/%A/c                n   [        S U /UQ 5       5      (       aY  Sn[        R                  R                  R                  R                  SS 5      =n(       a  U SU 3nU[        R                  l        [        R                  R                  XX#5      n[        [        [        R                  U5      5      $ )Nc              3  f   #    U  H'  n[        U[        5      =(       a    [        U5      v   M)     g 7fr   rR  r   s     re   r   cond.<locals>.<genexpr>  s%     
M;La:a 1Yq\1;LrT  z"control flow operator: torch.cond.r>  r?  )r#  rS   r]   r^   rm  rn  rD  r2   Conditionalr   ri   maprC   )predtrue_fnfalse_fnoperandsr   r>  r  s          re   r   r     s     
MD;L8;L
MMM2''..3377tLL;LE*;-8C,/)^^""4(EFI$$f-..rg   c                   [         R                  (       dr  [        S X#-    5       5      (       aY  Sn[        R                  R
                  R                  R                  SS 5      =n(       a  U SU 3nU[        R                  l        [        R                  R                  XX#U5      n[        U[        5      (       d   e[        [        [        R                  R                   U5      5      $ )Nc              3  f   #    U  H'  n[        U[        5      =(       a    [        U5      v   M)     g 7fr   rR  r   s     re   r   while_loop.<locals>.<genexpr>  s*      *3A 	1f.)A,.3rT  z(control flow operator: torch.while_loop.r>  r?  )r0   rC  r#  rS   r]   r^   rm  rn  rD  r2   	WhileLoopr   rk   r   ri   r  _maybe_wrap_as_tensor_box)cond_fnbody_fncarried_inputsadditional_inputsstack_outputr   r>  r  s           re   
while_loopr    s     !!c *3* ' ' 9''..3377tLL;LE*;-8C,/)\\  .\F fh''''BLL::FCDDrg   )r  c                    [         R                  R                  " U /UQ76 n[        [	        [
        R                  U5      5      $ r   )r2   InvokeSubgraphr   ri   r  rC   )subgraph_fn
identifierr  r  s       re   invoke_subgraphr    s5    %%k=H=FI$$f-..rg   c                f   Sn[        U R                  R                  5       GHb  u  p4UR                  S:X  aA  U[        R                  R
                  ;  d   eX   [        R                  R
                  U'   MW  UR                  S:X  a\  [        R                  R                  U5      u  pV[        R                  R                  R                  [        R                  XEU5      nM  U[        R                  R
                  ;  d   e[        R                  R                  n U[        R                  l        [        R                  R                  U5      [        R                  R
                  U'   U[        R                  l        GMe     Uc  [        S5      eU$ ! U[        R                  l        f = f)a  Process nodes from a FX graph by executing them through V.graph.

This is a common pattern for executing a subgraph's nodes:
- Placeholder nodes are mapped to the provided args
- Output nodes return their result
- Other nodes are executed via V.graph.run_node

Nr  r6  zNo output node found in graph)rj   r]   nodesr`   rS   envfetch_args_kwargs_from_envr{   r  Interpreterr6  r^   run_noder  )r  rt   r6  rs   rc   output_argsr   saved_current_nodes           re   process_subgraph_nodesr    s0    F\//55677m#qww{{*** $AGGKKWW "#''"D"DT"JKXX))00$VTFqww{{***!"!5!5:'+$$%GG$4$4T$:D!'9$! 7$ ~:;;M (:$s    AFF0)control_depsc                   / nU  HI  n[        U[        5      (       d  M  UR                  5         UR                  UR	                  5       5        MK     [
        R                  R                  R                  nSn[        U5      U-   [        U5      :X  d   e[        [
        R                  R                  5      n[        UR                  R                  R                  SS95      [        U5      :X  d   e[        UR                  [        U5      5      nUb  U (       d   e[
        R                  R                  US  HI  n	U H@  n
U	R                  nUc   e[
        R                  R                   U   R#                  U
5        MB     MK     U$ )a;  
Lower control_deps_op by ensuring dependencies are realized and tracking them.

The control_deps_op HOP makes dependencies explicit in the graph. During lowering:
1. Realize all additional dependencies to ensure they're computed
2. Execute the target operation normally
3. Track the dependencies for the scheduler
r-   r  r  N)rk   r:   r  ro   r   rS   r]   r^   rt   r   
operationsr  
find_nodesr  ri   operation_nameadditional_buffer_depsr   )additional_depsr  rt   	dep_namesdeporiginal_args
arg_offsetoperation_lenr6  r`   dep_nameop_names               re   control_deps_op_loweringr    sF    I#v&&(  GG((--MJt9z!S%7777**+M{''--88M8JKsSWyXXX $K$<$<d4jIF/11 gg  0!H''G&&&GG**7377A " 1 Mrg   )schemec               
   S n[         R                  R                  R                  R	                  SS 5      nUc   e[        U R                  R                  R                  5       GH  u  pVUR                  S:X  a!  X%   [         R                  R                  U'   M7  UR                  S:X  Ga  [         R                  R                  U5      u  px[        R                  " XxR                  5       5       H  n	U	R                  5         UR                  (       a7  [         R                  R                   R#                  U	R%                  5       5        [         R                  R&                  R#                  U	R%                  5       5        M     [(        R*                  R,                  R/                  [         R                  XgU5      nGM_  [         R                  R1                  U5      [         R                  R                  U'   GM     U$ )Nquant_optionsr  r6  )rS   r]   r^   rm  rn  rj   r  r  r`   r  r  r  r  r   r  codegen_low_precisionlow_precision_codegen_opsr   r  invoke_quant_opsr{   r  r  r6  r  )
r  r  r  r6  r  rs   rc   rt   r   r	  s
             re   invoke_quant_tracerr  5  sW   FGG((--11/4HM$$$[55;;AAB77m# (AGGKKWW 77==dCLD__T==?;		 66GG5599!:N:N:PQ((,,Q-A-A-CD < XX))00$fMF ! 0 0 6AGGKK% C( Mrg   c                  ^
 SSK JnJn  [        U5      S:  a  [	        S5      e[
        R                  " X5       Vs/ s H&  nU" UR                  5       UR                  5       S9PM(     nnU" X5      m
U
4S jn[        US   SS S9n[        S U 5       5      US	'   [        S
 U 5       5      US'   [        R                  R                  " SUSS.UD6n	U	S   c  [	        S5      eU	$ s  snf )Nr/   )InputDescriptorlower_pointwise_subgraphr   zSUnable to generate code for associative_scan op, because there are lifted argumentsr;  c                h   > T" / [         R                  " U 5      Q[         R                  " U5      Q76 $ r   )rd  r  )lhsrhslowered_combine_fns     re   wrapped_combine_fn,associative_scan.<locals>.wrapped_combine_fnc  s6    ! 
$
$
 	
rg   r  c              3  @   #    U  H  oR                  5       v   M     g 7fr   )r   r   s     re   r   #associative_scan.<locals>.<genexpr>j  s     7Bq[[]]Br  r  c              3  @   #    U  H  oR                  5       v   M     g 7fr   r  r   s     re   r   r  k  s     <Ar  r  F)r  can_fallback_to_atenz/Unable to generate code for associative_scan opr   )r  r  r  r   r  r  r  r   rn   r  r   r2   r  r   )r  xsr  r  r  r   subgraph_inputsr  r   r  r  s             @re   associative_scanr 	  R  s     M
!a
 	
 ((A 	akkmALLNC(   2*N
 be!48F7B77F8<<<F;WW^^ %" F
 ayLMMM-s   -C'c                    g r   r   )tokenss    re   _sink_tokensr	  v  rz  rg   c                     g r   r   r   rg   re   _make_tokenr	  {  rz  rg   c                   SSK JnJn  U" U5      nUc  U[        R                  R
                  R                  L a  SSKJnJ	n  UR                  5       n	U	(       a  U	R                  R                  [        R                  R
                  R                  5      n
U
(       aW  [        X5      (       d   eU
R                  US   5      nU(       a*  [        U5      S:X  d   S5       e[!        [#        U5      5      n[        [$        R&                  R(                  5      nU[*        ;   a-  [*        U   " U0 UD6n[,        R.                  " [0        S U5        O<S n[,        R2                  " U[4        R6                  R8                  " U/UQ70 UD65      n[        [$        R&                  R(                  US 5      S:  d   S	U S
35       eU(       a  [$        R&                  R:                  R=                  U5      n[$        R&                  R(                  US  H^  nS Ul        U(       d  M  URA                  5       n[$        R&                  RB                  U   RE                  URA                  5       5        M`     W[$        R&                  R:                  U'    S n[,        R2                  " UX#45      u  nnU" UUU5      n[        URR                  5      S:X  a  X4$ [        URR                  5      S:X  a  X4$ U /UQ7$ ! [F         aU  n[I        U5      n[J        RM                  SUU5        [        U[N        [P        45      (       a  U /UQ7s SnA$ X4s SnA$ SnAff = f)zs
We lower the operator directly, and then we add StarDep dependencies to all
the newly created nodes in the graph.
r   )_get_effect_get_schemaN)InvokeSubgraphCacheTracingContextr/   zMultiple effects NYIc                "    U R                  5       $ r   )r  r  s    re   rQ  with_effects.<locals>.<lambda>  s
    !))+rg   c                p    [        U [        R                  5      (       a  [        R                  " U 5      $ U $ r   rz  r   s    re   r{  "with_effects.<locals>.wrap_tensors  r}  rg   zCNo operation nodes were generated when lowering effectful operator .c                     gr   r   r   rg   re   rQ  r	    s    drg   c                f   [        U [        R                  5      (       a  U R                  5       $ [        U [        5      (       aU   U R
                  n[        US5      (       a5  [        UR
                  S5      (       a  UR
                  R                  5       $ U $ U $ ! [        [        4 a     U $ f = f)Nrm   get_example)
rk   r2   TorchBindObject	get_valuerC   rm   r   r	  AttributeErrorr   )r   r  s     re   convert_ir_to_value)with_effects.<locals>.convert_ir_to_value  s    !R//00{{}$Ay))ffGw//Gm5 5  '||7799 H	 '(;< s   AB B0/B0z5Failed to get schema for %s: %s. Assuming list output)*torch._higher_order_ops.effectsr	  r	  r{   rR   higher_orderr  torch._guardsr		  r
	  try_gethop_dispatch_set_cache	get_cacherk   get_effectsr   rG  rQ  rS   r]   r  rX   rd  r@  rC   r~  r2   r  r   effectful_opsrn  has_side_effectsr   additional_star_depsr   r  r  r  r  r   ri   returns)tokenr`   rt   r   r	  r	  effect_typer		  r
	  tracing_ctxinvoke_subgraph_cacheeffectsr  r  r{  prev_effect_buffernew_opr  r	  schema_argsschema_kwargsschemae	error_msgs                           re   with_effectsr/	    s    I b/KrUYY%;%;%K%KKE$,,.$/$F$F$P$P		&&66%! %!"7MMMM/;;DGDw<1,D.DD,"&tG}"5K **+M 
Y2//Y(=vF	J "++222GGG
 qww!!-.12Q6 
MbTQRS6 WW2266{Cgg((8F&2F#!! //+,,W599:L:U:U:WX 9  	
k* #	$ &,__$&
"] Rm< 6>>a	V^^		!  #F	CR	
 fudm,,#F##?"#s+   (K3 3
M=AM?MMMM)register_comm_loweringsc                h   [        XSSSS9nUS   n[        R                  R                  R	                  [        U5      5      n[        R                  R                  " S0 UDSUS.D6u  pVUS:X  a\  [        R                  R                  R                  U[        R                  5      (       a  [        R                  " SU SUS	.UD6u  pxXx4$ [        R                  " [         R"                  " S
5      5        [%        XSS9n	[&        [(        R*                     " [-        X	5      5      n
[/        XSS9nX4$ )zf
Lowering inductor_prims.prepare_softmax_online to compute max/sum in one pass if no split is needed.
TNr  r%  online_softmax_reduce)r  r  r/   r-   )r#  
num_outputreduction_hintz
            Online softmax is disabled on the fly since Inductor decides to
            split the reduction. Cut an issue to PyTorch if this is an
            important use case and you want to speed it up with online
            softmax.
            )rz  r   )r  rS   r]   r   simplifyrP   r2   rA   
num_splitsstatically_known_geqr0   r.  r=   r   r  r  textwrapdedentrE  rX   r  r%  r  r  )r   r   r   r%  r  hint	num_split
max_tensor
sum_tensorr  r%  xsums               re   prepare_softmax_onliner?	    s*   
 #	d$dF 01WW&&}5E'FGFll-- 
.OD A~!''**??22  "8!>!> "
Qt"
?E"

 %% 	OO		
 1D1!#a,/Ct,zrg   )r  )quantized_lowerings)mkldnn_lowerings)jagged_loweringsc              #  v  #    [        U [        R                  R                  5      (       d   S5       e[        R                  U 5      n [        U 5      " [        U 5      5        Sv   U(       a
  U[        U '   g[        R                  U 5        g! U(       a
  U[        U '   f [        R                  U 5        f = f7f)zR
A context manager to force fallback an op. Used in unit test
for FallbackKernel.
z+Only OpOverload to make the clean up easierN)	rk   r{   r|   r}   rX   rn  r*  r  r  )r`   old_handlers     re   force_fallbackrE	  9  s      b%**//00 50 --#K".r23'IbMMM" 'IbMMM"s   AB9	B ''B9(B66B9r(  )rp   zIterable[Any]r   z4defaultdict[tuple[Any, bool], list[tuple[int, Any]]])r   Callable[..., Any]r   zOptional[Callable[..., Any]])r   ztorch._C.Tagr   z(Optional[Callable[..., tuple[Any, Any]]])r   r   r   r  r   None)r   zUnion[Collection[Union[torch._ops.OpOverload, torch._ops.OpOverloadPacket]], torch._ops.OpOverload, torch._ops.OpOverloadPacket]r   zOptional[list[Any]])r   z9Union[torch._ops.OpOverloadPacket, torch._ops.OpOverload]r   zCallable[..., tuple[Any, Any]]r   rG	  )r   zUnion[int, torch.dtype]r   torch.dtype)r   r	   r   z,TypeGuard[Union[TensorBox, sympy.Expr, int]])r   r	   r   z!TypeGuard[Union[TensorBox, bool]])rt   r	   r   r   r   rH	  )r`   z>Union[Any, torch._ops.OpOverloadPacket, torch._ops.OpOverload]r   r  r   r   )r   rC   rv   torch.devicer   rC   )rt   	list[Any]r   zdict[str, Any]r  r   r   )Optional[ELEMENTWISE_TYPE_PROMOTION_KIND]r  r   r   z tuple[list[Any], dict[str, Any]])r   r*  r  rF	  r   rF	  )
r  rF	  r  r   r   rK	  r  r   r&  rW   )r   rK	  r   z.Callable[[Callable[_P, _T]], Callable[_P, _T]]rY  )NNNFN)F)r   rC   r   rH	  r  r   )r   rC   r   rH	  )r   rC   rv   rI	  )r   rC   r  rC   r   )r   rC   r  zSequence[sympy.Expr]r   rC   )r   r   l            r/   Tr  )r  rC   r  rC   r  rC   r  r   r  r   r  r   r   rH	  r   rC   )r  rC   r  rC   r  rC   r  r   r  r   r  r   r   rH	  r  Optional[torch.dtype]r   rC   )r  rC   r  r;  r  r   r  r   r  r   r   rH	  r   rC   )r  rC   r  r;  r  r   r  r   r  r   r   rH	  r  rL	  r   rC   )r  rC   r  rC   r  rC   r  r   r  r   r   rH	  r   rC   )r  rC   r  rC   r  rC   r  r   r  r   r   rH	  r  rL	  r   rC   )r   r   r/   )rk  r   r7  r   r8  r   rp  )T)rw   ztorch.Tensor)rc   ztorch.fx.Node)NTF)rv   rI	  )r   	list[int]r  rC   r  r  rk  r   )
r  r   r  r   r   rM	  r  rC   rk  r   )r  rC   r   z.tuple[str, sympy.Expr, sympy.Expr, sympy.Expr])r  rC   r   ztuple[str, sympy.Expr])r+  rC   r8  rC   r  r   r  r   r  Optional[str]r   Optional[TensorBox]r   rC   )r  rC   r=  rC   r  r   r  r   )r   r   rA  r   )r   NNr/   )NNN)rU  FF)r   r   )r  r*  r   r   r  rN	  rz  r   )r   r   r  rN	  )r   r   rz  r   )r-   F)r  ztuple[Optional[float], ...]r  r   r  r   )r  Optional[float])r  rP	  r  rP	  )r  rP	  r  rP	  r  rP	  )r   rC   r  zSequence[int]r  r;  r   rO	  )rs   
sympy.Exprr  zUnion[sympy.Expr, int])rs   rQ	  r  rQ	  )rs   rQ	  r  rQ	  r  rQ	  )Nr  N)
r*  rC   r  "Sequence[Union[int, torch.SymInt]]r7  rR	  r6  zxCallable[[Sequence[Union[int, torch.SymInt]], Sequence[Union[int, torch.SymInt]]], torch._inductor.virtualized.OpsValue]r   rC   )Nr   r/   F)r  )NNNN)r   r   FTN)r  rT   r   )r   r'  r   zOptional[ir.Constant])rU  F)r`   ztorch._ops.OpOverloadPacket)r   z3list[Union[ir.TensorBox, ir.ShapeAsConstantBuffer]])r  ir.Subgraphr  r  )r  ztorch.fx.GraphModulert   rJ	  )r  rS	  )r  rS	  r  ztuple[torch.Tensor]r)  (  
__future__r   
contextlibr  r  r  loggingr  r3  r  r8	  r  collectionsr   collections.abcr   r   r   r   typingr	   r
   r   r   r   r   r   typing_extensionsr   unittest.mockr   r   r{   $torch.ao.quantization.fx._decomposedtorch.fxtorch.utils._pytreer@  _pytreerd  torch._dynamo.utilsr   (torch._higher_order_ops.associative_scanr   r  r   "torch._library.fake_class_registryr   torch._library.utilsr   torch._prims_commonr   r   r   r   r   r   r   r   r   r    r!   torch.fx.experimental.sym_noder"   r#   r^  r$   r%   r&   torch.utils._ordered_setr'   torch.utils._sympy.functionsr(   r)   r*   r+   r,   _dynamo.utilsr.    r0   r1   r2   r3   decompositionr4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   rF   rG   rH   rI   rJ   rK   rL   rM   rN   rO   rP   rQ   r  rR   rS   r  rT   rU   rV   FALLBACK_ALLOW_LIST	getLoggerr  r  rX   __annotations__rY   r|   r}   r  r  tr_c10dr  r   _higher_order_opsr  rb   r{  rZ   quantized_decomposedrf   rx   r   r~   r   r   r   rn  r  r  r8  bmmconvolutionconvolution_backwardrF  rJ  rx  r  r  r  _int_mmr  r  rT  r  r  rl  r  r  	complex32	complex64r   rk  r   r   r   r   r   r   r   r   r  r  r'  rF  r*  r8  rL  ru  r  r   r  r  r  r  r   r  r  
device_putr  r  r  r  r  r  r  r  r  aliasdetachdetach_liftview_ofr  r   r	  r  r  r  r  r"  r$  r'  r*  r  r,  r3  r7  r9  rI  _unsafe_viewreshaperL  slicer~  r  r  quantize_per_channelr  r  r   r  _functional_assert_asyncr  dequantize_per_channelr  quantize_per_tensorr  dequantize_per_tensorr  r  r  r  r  rI  rK  rO  rW  r\  r^  r`  rl  r2  rp  r_  rv  r  cacher  r  r  r  r  r  rngprimsr  r  r  	bernoullir  r  r  	lru_cacher  r  r  r  r  r  r  r  r  randintstreamsrecord_event
wait_eventforce_stride_orderr  r  r  r  r  lookup_seedr  randomr	  r  r  r  r7  r  r)  	NO_OPMATHrC  rE  r   r+  rK  r   r   r|  _adaptive_avg_pool3dadaptive_max_pool3d*_scaled_dot_product_attention_math_for_mpsuniformexponential_pdist_forwardsoft_margin_loss_backward_fused_rms_normxpuis_availableembedding_dense_backwardmtia_is_compilednative_layer_norm_cdist_forward_cdist_backward
_trilinearsegment_reduce_segment_reduce_backwardhistc	histogrambin_ct_histogramdd_bin_edges_histogramdd_from_bin_ctsaddbmm_addmm_activation_grouped_mm
_cudnn_rnn_cudnn_rnn_backward
miopen_rnnmiopen_rnn_backward_embedding_bag_embedding_bag_forward_only_embedding_bag_backward*_embedding_bag_per_sample_weights_backward_fused_moving_avg_obs_fq_helper*_fused_moving_avg_obs_fq_helper_functional max_pool3d_with_indices_backward_adaptive_avg_pool2d_backward_adaptive_avg_pool3d_backwardadaptive_max_pool2d_backwardadaptive_max_pool3d_backwardfractional_max_pool2d_backwardfractional_max_pool3d_backwardreplication_pad1d_backwardreplication_pad2d_backwardupsample_linear1d_backwardupsample_bicubic2d_backwardupsample_trilinear3d_backwardgrid_sampler_2d_backward_pdist_backwardrZ  rP  kthvaluetopkr  median	nanmedianrN  resize_
resize_as__linalg_detlinalg_householder_productlinalg_inv_exlinalg_ldl_factor_exlinalg_ldl_solve	linalg_lulinalg_lu_factor_exlinalg_lu_solvelinalg_matrix_exp	linalg_qr_linalg_slogdet_linalg_solve_exlinalg_solve_triangular_linalg_svd	lu_unpackormqr_linalg_check_errorslinalg_pinvatol_rtol_tensor_linalg_eightriangular_solvelinalg_cholesky_excholesky_inversecholesky_solvegeqrf_fft_r2cnonzerogcd_thnn_fused_lstm_cell_prims	rng_primsrun_and_save_rng_staterun_with_rng_stategraphsafe_run_with_rng_statemasked_scattermasked_scatter_backwardr  angle_efficientzerotensor(_sparse_coo_tensor_with_dims_and_tensors	to_sparse
_to_sparser   r  rm  rk  #_scaled_dot_product_flash_attention,_scaled_dot_product_flash_attention_backward#_scaled_dot_product_cudnn_attention,_scaled_dot_product_cudnn_attention_backward+_scaled_dot_product_flash_attention_for_cpu4_scaled_dot_product_flash_attention_for_cpu_backward0_scaled_dot_product_fused_attention_overrideable9_scaled_dot_product_fused_attention_overrideable_backward_flash_attention_forward_flash_attention_backward_efficient_attention_forward_efficient_attention_backwardindex_reducerepeat_interleave_weight_norm_interface_backwardr  r  r  r  r  r  r  r  scalar_tensorr  
LongTensorr  r  r  r  r  r  r  rE  r  r  r  r  
zeros_liker  r  r  r  r  r  r  r  r  r"  r%  r$  rA  r/  r7  r9  r;  rF  rA  rK  r4  rj  fallback__unsafe_masked_indexrn  ,fallback__unsafe_masked_index_put_accumulater[  rv  r_  r~  rx  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r+  r/  r;  r?  rA  rp  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r3  rn  ri  rq  r  r  r  r  r  r  r  r  rv  r  r  r  r  r  Tensor_Tensorr  Scalarr  Tensor_Scalarr  rM  r  rt  r  r  r  r  rh  r  r  true_divider
  r  r  r  r  r!  r   r+  r*  r7  r5  r=  r<  r  r#  rB  rr  rG  rq  rL  rM  r  rE  r  rJ  r&  rF  rs  rK  r   rU  rX  r]  r_  rsqrtr%  r  expm1relurt  r  r  r  cossinabsbitwise_andbitwise_left_shiftbitwise_not
bitwise_orbitwise_right_shiftbitwise_xorlgammaerfspecial_erfr$  tantanhr  r`  rN  logical_xorr  r  	clamp_min	clamp_maxnegr  	remaindersignsignbit	_neg_viewler  r  r  r  necoshsinhacosacoshasinasinhatan2atanatanhr   erfcerfinvhypotlog10log2	nextaftercodegen.commonr}  rb  rj  r   r`   r   rr  _foreach_addListforeach_add_listforeach_add_scalar_foreach_mulforeach_mul_listforeach_mul_scalar_foreach_sub_foreach_neg_foreach_abs_foreach_powScalarAndTensor_foreach_divforeach_div_listforeach_div_scalar_foreach_sqrt_foreach_rsqrt_foreach_maximum_foreach_minimum_foreach_clamp_min_foreach_clamp_max_foreach_reciprocal_foreach_sign_foreach_copyforeach_copyrs  _foreach_add__foreach_mul__foreach_div__foreach_copy_rw  add_bitwise_and_bitwise_left_shift_bitwise_not_bitwise_or_bitwise_right_shift_bitwise_xor_mul_div_Tensor_modelogical_and_logical_not_logical_or_logical_xor_sub_relu_sigmoid___and__
__lshift____or__
__rshift____xor____iand____ilshift____ior____irshift____ixor__ry  ru  r   r  r  r   methodfuncr  r  _inductor_testr  r  r  r  set_source_Tensorr  fsdpr  r  *torch._higher_order_ops.auto_functionalizer  r  r	  r   r  while_loop_stack_outputr)  r  r  .torch._inductor.fx_passes.control_dependenciesr  r  invoke_quantr  r 	  r	  r	  r/	  comm_loweringr0	  r?	  r  r@	  register_quantized_opsregister_woq_mm_opsrA	  register_onednn_fusion_opsrB	  register_jagged_opscontextmanagerrE	  r   rg   re   <module>r~
     s8   "        	   # D D P P P '    +  $ $ ( H U ? :    M 
 0  - 8 8 =    $      * T]t_ !   !FH	C H     uzz,,-/	yy~~
))

		"5::#8#89; ../
))*
 !!6!679 NP K Pyy55 90B	B-BF
	 &3A3.3 
3   !!$$$$--&&, {{zz{{{{{{}}}}}}

."#%D  FSV	(O
OO O C	O
  O &Od"/A62!2 2 C	2
  2 L2n  	(// 4,#42n  $Vr9xE E 5**77TR) S)X 5--4H) I) @E 5 5( 499??=& >& ;@e K K 5##>F ?F 
7?? $*Z $7DD 4::4H I>>    4::DI J0 4))UPTU V. DJJT\\499emmTU V 4doo&s+ 4<<T:B ;B, 4$$$?" @" DMM?# $ 4::C C 4::C C 499! ! 4::! ! 4::%%&% '% 4::! ! 4;;D9> :>4 5))tD
 E
 4>>t<# =# 4;;1  1h 4$$$?499$74<<T:1 ; 8 @1 4<<T:> ;> 4::48uE 9uEp 4??=J >J8 4##> ? 4''TB C
BJ '<<RVW/// / 	/
 / / / / X/d$ 4%%))*$ +$ 400445$ 6$ //T (,/// / 	/
 / / / %/ //d ,,44$!!! ! 	!
 ! ! !!H ..66D (,!!! ! 	!
 ! ! %! !!H ,,33*** * 	*
 * * **Z ..554 (,,,, , 	,
 , , %, ,,^ 488y: y:x 4==d;3E <3El 4%%4@6 A6 4((dC D 4;;D9=C :=C@ 4::48 94 4((dC  D  4;;D9 : 4;;D9D :D8 4>>t< = 4??= > 488 $   D
3 
3%6 %6P/Nd	, 599%%11tL#+ M#+L 4&&DAG BG 4??= > 4>>##>' ?' 4<<  ! QB B/
 )):):; *499+>+>? )$***<*<= +DJJ,@,@A  dll  eii,,44 5 eii**22 3 499J J 4::J J >44$OL PL
 >&&DAK BK >''TBJ CJ
 >--4H	 I	 >((dCRS  D6 >))tDLM	(09FI E8 . 4$$++F
 "&^^
^ 	^
 ^ ^  ^ ^ G^B NN(G(Q(Q 777 	7
 77t&$FT d'' ( d&& ' d== > dll ' d&&U 3 d!!#5 6 d,,5 9 d"" /99%%E 	::U
 d!! " d"" # doo  d!!)) * d++33 4 djj  dnn## $ d))11 2 d,,44 5 dkk  d$$5 1 d . d'')@ A doo} - d&&(: ; doo} - d&&(: ; d!!#5 6 d..0B C d** + d== > d== > d22 3 d== > d33 4 d00- @ d00 1 d// 0 d// 0 d11 2 d11 2 d-- . d-- . d-- . d..0B C d00 1 d++ , d""$6 7 dii  dii  dmm  dii  dii  dkk  dnn  dmm  dll  doo  d  d-- . d   ! d'' ( d## $ dnn  d&& ' d"" # d$$ % dnn  d"" # d## $ d** + d  dnn  djj  d'' ( d// 0 d   d## $ d%% & d## $ d!! " djj  dmm  dll"" # dhhU + d((- 8 ell$$;; < ell$$77 8 ell$$AA B
 d!! " d** + d""$6 7 djj  d'' ( d;; < dnn  doo  djj  0088	
 99AA	
 ,,44	
 55==	
 ,,44	
 55==	
 44<<	
 ==EE	
 99AA	
 BBJJ	
 d++33_ E d,,44o F d//77 I d0088/ J d   d$$++T B d22::<N O
 499$7 8 4::"  * 4"##d**+E2 5:: ( 4&&DA  B F 4%%4@A AAH ELL$"4"456tDU 5 75p 5??#4 $4 5##$+ %+ 4++,)" -)"X 4&&' ( 4//0%)59$ 1<K8 EKK,- 
 .$.> t/0B50IJ
1!45	 21 56
  4>>" $T$4  # 4%%&Td '@ 4))*"4 +" 5%%--.A /A EJJ		*+: ,:
 4;;D9! :!H 4>>t< =B#F FR"1J 4::48
 9
 4%%4@/ A/ 4>>t< = 4))* +;. 4??= > >44$O Ptn !1%%5!  0@,,44%0 ,
 4,,$G H, 4;;QUV	P W	P 1 1 4**E F 4<<T:9 ;9 !& 
  D 4==d;DH : <:" 4##>3 ?3 4$$$?6 @6 4&&DAP BP 4''TBPT q Cqp , *, 	,
 ,^ 4**223> 4> 41199:J ;J 4**223RVI-I@OI 4I 41199:RVU-U@OU ;U 4**223 !% $ $S S 	S
 S 4S 41199: !% $ $	 	 		
 	 ;	7 599$$% &*\\(\6;\\~ 4''TB4 C4n :>@ MQ < JN@:HV 5::PTU 5 V5D3 3	 > 	11t$< 4//TJ 
 K
 4//TJ 
 K
 -=))11- ) 488dSN TNb8B&R2j  0%%5  
 4,,-B .BJ  0$$%  
 4++,N -Nb)X 4--.V /V 4--.V /VAH 433;;<BF. =.b 'OO  'OO 
 4??=  >* 4??=  >*wt  0$$%  
 4++F b GbJ  0$$%  
 4++F D GDN& HLO Od * 499:t : : 4 (V4( DHHeii()T5  * 4==!u  "   .HH  'txxER -HH 
 488t,- --`"J 4::2 2 4::48 9     488t, - DHH:.( /(@ EII;$/$ 0$. 	txx'7DD

 DIIuzz*d;$ <$  DHHeii(). . *. #4;;#6#67#DLL$8$89 ():):)B)BC "4;;#6#67"4;;#6#67 4;;  . 4<<  !. 4$$% &* 4;;D9 :, 4;;D9 :, 499. . . 488@ @
 48867 77 48867 77 %--  	!: ;		*>%+@A		*>%+@A!$++.85;;? "$++.85;;? HH$L !!1!1uM 499##>!re $2 ?$2N 499$$$?H @H 	#4::.&txx0!$)),"4::.$))$
*4<<
8'		2	DKK	(t4   *   *" !1!12'(?(?@  -  0
()A)AB  !1!12 4;; ' * *I*V*V 4:: & 488 $ 499 %   * **	 !**	  OO**	
 !**	 T\\
*
T\\
* $.. !' * $.. !' *""'8
 4>> "$))L 499  4<<uzz B $.. !# & 477%** = 477%** = 477%** =uzzB 477%** = 477%** = 499 % 499 % 499 % 4:: & 499 % 4:: & 4:: & 499 % 4:: & 4== ) 499 % 4;; ' 4:: & 4:: & 499 % 4>> * D DE$ %D4Ld50 	 3+		
5 5Mt50 	 3+		
5 %, .CT  0ct  4,,33Sd K-d.?.?.D.DcJ  4,,33S 9/0A0A0H0H#N  4,,113 7 4,,33S 9 4,,44c : 4,,44c : 4,,33S 9 4,,113 7 4,,<<c B-d.?.?.D.DcJ  4,,33S 9/0A0A0H0H#N  4--t 4 4.. 6 40055w ? 40077 A 40055w ? 40077 A 42277 A 422997 C 42277 A 422997 C 433Z @ 4--t 4)$*<*<dC, T..335E t00779K T..335E t00779K T..335E t00779K !3!3!;!;\
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 599))99tT/ U/
 H H G <T:+ ;+\ 5**77TRDH   S8 &DA  4G  B F 599??//778 9 599??..667 8 599))66DQc  Rc L 3 2   >88dS1 T1j     ! !  * * ,  ' ' )    + + -    $ $ &  rg   