
    7h             -       x   S SK r S SKrS SKJr  S SKJr  S SKJrJr  S SK	J
r
JrJrJr  S SKJr  S SKrS SKJr  S SKJrJrJr  S SKJrJrJrJr  S S	KJr  S S
KJrJ r J!r!  S SKJ"r"J#r#J$r$J%r%J&r&J'r'J(r(J)r)J*r*J+r+J,r,J-r-J.r.  S SK/J0r0J1r1J2r2J3r3J4r4  S SK5J6r6J7r7  S SK8J9r:  S SK;J<r=  \" S5      r>\" S5      r?\R                  R                  rA\R                  R                  SSS5      rD\E" S5      u  rFrGrHS\
\
\?\>4   /\
\?\>4   4   4S jrIS\'4S jrJS rKS rL\I" \AR                  \AR                  /5      \4" 5       SSS\R                  SS4S j5       5       rP\I" \AR                  R                  \AR                  R                  /5      \4" 5       S 5       5       rT\I" \AR                  R                  \AR                  R                  /5      \4" 5       SS .S! j5       5       rUGS'S" jrVS# rWGS(S% jrX\I" \AR                  R                  5      S& 5       rZ\I" \AR                  5      \4" 5       S' 5       5       r[\I" \AR                  R                  \AR                  R                  \AR                  R                  \AR                  R                  /5      \4" S(S)5      S* 5       5       r^\I" \AR                  R                  \AR                  R                  /5      \4" 5       S+ 5       5       r_S, r`GS'S-\S.\a\b   S/\c4S0 jjrd\I" \AR                  R                  \AR                  R                  /5      \4" 5       S1 5       5       rfSrgS.\a\b   4S2 jrh\I" \AR                  R                  \AR                  R                  /5      \4" 5       S3 5       5       rj\I" \AR                  R                  5      SS4.S5 j5       rm\I" \AR                  R                  5      \R                  SSSS6.S7 j5       ro\I" \AR                  R                  \AR                  R                  /5      \4" 5       \R                  SSSS6.S8 j5       5       rq\I" \AR                  R                  \AR                  R                  /5      \4" 5       \R                  SSSS6.S9 j5       5       rt\I" \AR                  R                  \AR                  R                  /5      \4" 5       SSSSS6.S: j5       5       rv\I" \AR                  R                  \AR                  R                  /5      \4" 5       S-\S.\a\b   S;\bS<\b4S= j5       5       rx\I" \AR                  R                  5      GS'S> j5       rzS? r{\I" \AR                  R                  5      S@ 5       r}\I" \AR                  5         GS)SA\SB\SC\SD\\   SE\\   SF\\GR                      4SG jj5       r\I" \AGR                  5       GS*SH\SI\SJ\SF\\GR                      4SK jj5       r\I" \AGR                  5      SLSLSSM.SA\SH\SI\SJ\SF\\GR                      4
SN jj5       r\I" \AGR                  5             GS+SO\R,                  SP\R,                  SD\\   SQ\\   SF\\GR                      SR\cSS\bST\bSU\b4SV jj5       r\I" \AGR                  R                  5      S$SW.S-\S.\bSX\SY\R,                  SZ\S[\cS\4S\ jj5       r\I" \AGR                  R                  5      S$SW.S-\S.\bSX\SY\R,                  SZ\S[\cS\4S] jj5       r\4" 5       \I" \AGR                  R                  5      S^ 5       5       r\I" \AGR                  R                  5      SSSS SSS_.S`\SZ\Sa\\   S)\\   Sb\\   Sc\bSd\cS\4Se jj5       r\I" \AGR                   R                  \AGR                   GR"                  /5      \4" 5       Sf 5       5       r\I" \AGR                   GR&                  5      GS'Sg j5       r\I" \AGR*                  R                  \AGR*                  GR"                  /5      \4" 5       Sh 5       5       r\I" \AGR*                  GR&                  5      GS'Si j5       r\I" \AGR0                  R                  5      Sj 5       r\I" \AGR0                  R                  5      Sk 5       r\I" \AGR6                  R                  5      Sl 5       r\I" \AGR6                  GR:                  5      Sm 5       r\I" \AGR>                  R                  5      Sn 5       r\I" \AGRB                  R                  5      SSSSSSo.Sp j5       r\I" \AGRF                  R                  5      GS,Sq j5       r\I" \AGRH                  R                  5      GS)Sr j5       r\I" \AGRL                  R                  5      GS,Ss j5       r\I" \AGRN                  R                  5      St 5       r\I" \AGRR                  GR:                  5      Su 5       rS-\Sv\4Sw jrS-\Sx\Sy\4Sz jr GS(S{\Sv\S|\c4S} jjrGS-Sx\Sv\S~\4S jjrSx\S\S\cSv\4S jr GS.S\S\SA\S\4S jjrS\4S jr\I" \AGRd                  R                  \AGRd                  GRf                  /5      \4" SS5      GS/Sx\S\S\c4S jj5       5       r\I" \AGRj                  R                  \AGRl                  R                  /5      \4" 5       SA\S\4S j5       5       r\I" \AGRp                  /5      \4" SS5      SA\4S j5       5       rS\S\4S jr\I" \AGRv                  5      \4" 5       S-\Sx\S\cS\4S j5       5       r\I" \AGRx                  5      \4" 5       GS'S-\Sx\S\cS\4S jj5       5       r\I" \AGRz                  5      \4" 5       GS'S-\S\cS\4S jj5       5       r\I" \AGR|                  5      \4" 5       GS'S-\S\cS\4S jj5       5       r\I" \AGR~                  R                  5      GS0Sx\S\cS\c4S jj5       r\I" \AGR                  R                  \AGR                  R                  /5      \4" 5       SA\S\S\4S j5       5       r\I" \AGR                  R                  5      GS'Sx\S\c4S jj5       r\I" \AGR                  R                  \AGR                  R                  /5      \4" SSS5      SSS.S-\S\cS\cS\\\\4   4S jj5       5       r\I" \AGR                  R                  \AGR                  R                  /5      \4" 5       SS.S\S\S\S\cS\4
S jj5       5       r\I" \AGR                  R                  \AGR                  R                  /5      \4" SSS5      S$S.Sx\S\cS\\\\4   4S jj5       5       r\I" \AGR                  R                  \AGR                  R                  /5      \4" SSS5      S$SS.Sx\S\cS\cS\\\\4   4S jj5       5       r\I" \AGR                  R                  \AGR                  R                  /5      \4" 5       S$SS.S\S\S\S\cS\cS\4S jj5       5       r\I" \AGR                  5      \4" SSS5        GS1S\S\S\cS\cS\\\\4   4
S jj5       5       rS\S\\c\c4   4S jr\I" \AGR                  R                  \AGR                  R                  /5      \4" SS5      GS2Sx\S\S\\\4   4S jj5       5       r\I" \AGR                  R                  \AGR                  GR                  /5      \4" SSSS5      Sx\S\\\\\4   4S j5       5       r\I" \AGR                  R                  5         GS3Sx\S\cS\cS\\   4S jj5       rS\S\S\\a\b   \a\b   4   4S jrS\S\Sy\\   S\\\4   4S jrSA\S\S\c4S jr\I" \AGR                  5      S$SSSSSS.Sx\S\S\cS\cS\\   S\\   S\\   S\\   S\\\\\4   4S jj5       r\I" \AGR                  R                  \AGR                  R                  /5      S$SSS.Sx\S\S\cS\cS\cS\\   S\4S jj5       r\I" \AGR                  5      \4" SSS$S9   GS4S-\Sx\S\cS\cS\cS\\\4   4S jj5       5       r\I" \AGR                  R                  5      S 5       r\I" \AGR                  5      \4" 5         GS5SA\S\S\S\cS\cS\4S jj5       5       rS rS r\I" \AGR                  5      \4" 5       S 5       5       r\I" \AGR                  5      \4" 5       S 5       5       rS r\I" \AGR                  5      \4" S5      S 5       5       r\I" \AGR                  5      \4" S5      S 5       5       rS r\I" \AGR                  5      \4" 5       S 5       5       r\I" \AGR                  5      \4" 5       S 5       5       r\I" \AGR                  R                  \AGR                  GR                  \AGR                  R                  \AGR                  GR                  /5      \4" S5      S 5       5       rS r\I" \AGR                  5      \4" 5       S 5       5       r\I" \AGR                  5      \4" 5       S 5       5       r\I" \AGR                  R                  \AGR                  GR                  \AGR                  R                  \AGR                  GR                  /5      \4" S5      S 5       5       r\I" \AGR                  5      \4" 5       GS6S-\S\S\4S jj5       5       Gr \I" \AGR                  5      \4" 5       S\S-\S\S\S\4
S j5       5       Gr\I" \AGR                  R                  \AGR                  R                  /5      \4" S$S9SLSLS.S j5       5       Gr\I" \AGR
                  R                  \AGR
                  R                  /5      \4" 5       SS4.S j5       5       Gr\I" \AGR                  GR                  5      GS7S j5       Gr\I" \AGR
                  GR                  5      GS7S j5       Gr
\I" \AGR                  R                  \AGR                  R                  /5      \4" 5       GS*S j5       5       Gr\I" \AGR                  R                  5        GS0S j5       Gr\I" \AGR                  5      \4" S$S9S 5       5       GrS GrGS8S jGr GS*S\R,                  SB\R,                  S\\a\b   \b4   S\\a\b   \b4   S\\a\b   \b4   S\cS\bS\\\a\b   \b4      4S jjGrS Gr\I" \AGR*                  R                  5      S\R,                  SB\R,                  SD\\R,                     S\\R,                     S\\R,                     S\cS\S\4S j5       Gr\I" \AGR.                  R                  5      S\R,                  SB\R,                  SD\R,                  S\a\b   S\a\b   S\a\b   S\cS\a\b   S\b4S j5       Gr\GR2                  GR4                  (       Ga  \R                  R                  GS SS5      Gr\I" \R                  GR8                  GR:                  R                  5      GS 5       Gr\I" \R                  GR8                  GR>                  R                  5      GS 5       Gr \GR2                  GRB                  (       aO  \R                  R                  GSSS5      Gr"\I" \R                  GRF                  GRH                  5      GS 5       Gr%\R                  R                  GSSS5      Gr&\I" \R                  GRN                  GRP                  R                  5      \I" \R                  GRN                  GRR                  R                  5      GS 5       5       Gr*\I" \R                  GRN                  GRP                  GRV                  5      GS 5       Gr,\I" \R                  GRN                  GRZ                  R                  5      \I" \R                  GRN                  GRZ                  GR\                  5      GS 5       5       Gr/\I" \R                  GRN                  GRZ                  GRV                  5      \I" \R                  GRN                  GRZ                  GR`                  5      GS	 5       5       Gr1\I" \R                  GRN                  GRd                  R                  5      \I" \R                  GRN                  GRf                  R                  5      GS
 5       5       Gr4\R                  R                  GSSS5      Gr5\I" \R                  GRl                  GRn                  5          GS9GS j5       Gr8\I" \R                  GRl                  GRr                  5      GS 5       Gr:GS Gr;\I" \AGRx                  R                  5           GS:GS j5       Gr=GS Gr>\I" \AGR~                  R                  5      GS 5       Gr@\I" \AGR                  5      \4" 5            GS:GS j5       5       GrB\I" \AGR                  5      \4" S5      GS 5       5       GrD\I" \AGR                  R                  5      GS 5       GrF\I" \AGR                  R                  5      GS 5       GrH\I" \AGR                  R                  5      GS 5       GrJ\I" \AGR                  5      \4" S5      GS 5       5       GrLGS\S~\4GS jGrM\I" \AGR                  5      \4" SS)5      GS 5       5       GrO\I" \AGR                  5      \4" S5      GS 5       5       GrQ\I" \AGR                  5      \4" SS)5      GS 5       5       GrS\I" \AGR                  5      \4" S5      GS 5       5       GrU\I" \AGR                  R,                  5      GS*GS  j5       GrW\I" \AGR                  R                  \AGR                  R                  /5      \4" 5       GS! 5       5       GrY\I" \AGR                  R                  \AGR                  R                  /5      \4" 5       SGS".GS#\b4GS$ jj5       5       GrZ\I" \R                  R                  GR                  R                  \R                  R                  GR                  R                  /5      \4" 5       GS% 5       5       Gr[\I" \AGR                  R,                  \AGR                  R,                  /5      GS& 5       Gr^\I" \AGR                  R                  /5      GS' 5       Gr`\I" \AGR                  R                  \AGR                  R                  /5      \4" S$S9SLSLS.GS( j5       5       Grb\I" \AGR                  R,                  /5      GS) 5       Grd\I" \AGR                  R                  \AGR                  R                  /5      SSGS*.GS+ j5       Grg\I" \AGR                  R                  /5      SSGS*.GS, j5       Gri\I" \AGR                  /5      \4" 5       GS- 5       5       Grk\I" \AGR                  /5      GS. 5       Grm\I" \AGR                  /5      GS/ 5       Gro\I" \AGR                  /5      GS0 5       Grq\I" \AGR                  /5      GS1 5       Grs\I" \AGR                  /5      GS2 5       GrtGS3\bGS4\bS\b4GS5 jGruGS6 Grv\I" \AGR                  /5      SD\\   4GS7 j5       Grx\I" \AGR                  /5      GS8 5       Grz\I" \AGR                  /5      GS9 5       Gr|\I" \AGR                  R                  5      GS: 5       Gr~\I" \AGR                  5      \4" 5       GS; 5       5       Gr\I" \AGR                  R                  5            GS;GS< j5       Gr\I" \AGR                  R                  5      GS= 5       GrGS(GS> jGr\I" \AGR                  R                  \AGR                  R                  /5      \4" 5       GS<SGS?.GS@ jj5       5       Gr\I" \AGR                  R                  \AGR                  R                  /5      GSA 5       Gr\I" \AGR                  GR&                  \AGR                  GR                  \AGR                  GR&                  \AGR                  GR                  \AGR                  R                  \AGR                  GR                  /5      \4" S(S)5      GS=GSB j5       5       Gr\I" \AGR                  R                  5      GSC 5       Gr\I" \AGR"                  R                  5      GSD 5       Gr\I" \AGR&                  R                  5      GSE 5       Gr\I" \AGR*                  GR,                  \AGR.                  GR,                  \AGR*                  R,                  \AGR.                  R,                  \AGR0                  R                  \AGR2                  R                  \AGR4                  R                  /5      GSF 5       Gr\I" \AGR8                  GR,                  \AGR:                  GR,                  \AGR8                  R,                  \AGR:                  R,                  /5      GSGSG j5       Gr\I" \AGR>                  R                  \AGR>                  GR@                  /5      GSH 5       GrGSI Gr\I" \AGRF                  R,                  \AGRF                  GR,                  /5      GSJ 5       Gr\I" \AGRJ                  R,                  \AGRJ                  GR,                  /5      GSK 5       Gr\I" \AGRN                  R                  5      GSL 5       Gr\I" \AGRR                  R,                  \AGRR                  GR,                  /5      GSM 5       Gr\I" \AGRV                  R,                  \AGRV                  GR,                  /5      GSN 5       Gr\I" \AGRZ                  R                  5      GSO 5       Gr\I" \AGR^                  R,                  5      \4" 5       GSS\4GSP jj5       5       Gr\I" \AGRb                  /5      \4" 5        GS>GSQ j5       5       Gr\I" \AGRf                  /5       GS>GSR j5       Gr\I" \AGRj                  /5       GS>GSS j5       Gr\I" \AGRn                  R                  \AGRp                  R                  /5      GS'GST j5       Gr\I" \AGRt                  GR,                  5      GSU 5       Gr\I" \AGRx                  R                  5      GSV 5       Gr\I" \AGR|                  5      GSW 5       Gr\I" \AGR                  5      \4" 5       GSX 5       5       Gr\I" \AGR                  5      GSY 5       Gr\I" \AGR                  R                  5      GS'GSZ j5       Gr\I" \AGR                  R                  5      GS[ 5       GrGS,GS\ jGr\I" \AGR                  R                  5      GS] 5       Gr\I" \AGR                  GR                   5      GS^ 5       GrGS_ GrGS` GrGSa GrGSb Gr GS'SA\GSc\bGSd\bGSe\bGSf\bGSg\bGSh\bGSi\bGSj\bGSk\bGSl\bGSm\bGSn\bGSo\bGSp\bGSq\bGSr\bGSs\bGSt\bGSu\bS\GSv\c4,GSw jjGrGSx GrSA\GS\GSc\bGSd\bGSe\bGSf\bGSg\bGSh\bGSi\bGSj\bGSk\bGSl\bGSp\bGSq\bGSr\bGSs\bGSt\bGSu\bS\4&GSy jGrGSz Gr\I" \AGR                  R                  5      GS{ 5       Gr\I" \AGR                  R                  5          GS9GS| j5       Gr\I" \AGR                  R                  5      GS} 5       Gr\I" \AGR                  5      \4" SS)5          GS9GS~ j5       5       Gr\I" \AGR                  5      \4" S5      GS 5       5       GrSA\GS\4GS jGr " GS GS\5      GrSA\GS\GS\b4GS jGr\I" \AGR                  R                  5      GS 5       Gr\I" \AGR                  5      \4" 5       GS 5       5       Gr\I" \AGR                  5      \4" SGS5      GS 5       5       Gr\I" \AGR                  R                  /5      GS 5       Gr\I" \AGR                  R                  5           GS?GS j5       Gr\I" \AGR                  R                  \AGR                  R                  /5      \4" 5       SSSSSGS.GS j5       5       Gr\I" \AGR                  R                  \AGR                  R                  /5      \4" 5       SSSSSGS.GS j5       5       Gr\I" \AGR                  R                  5      GS 5       Gr\I" \AGR                  R                  5      GS 5       Gr\I" \AGR                  R                  5      GS@GS j5       GrGS(S.\bGS\bGS\c4GS jjGrGS GrGS Gr\I" \AGR                  R                  5      GS'GS j5       GrGS'GS jGrGS*GS jGrGS GrGS*GS jGrGSAGS jGr\I" \AGR                  R                  5      GS 5       Gr\I" \AGR                  5      GS 5       Gr\I" \AGR                  GR                   \AGR                  GR                  \AGR                  R                  \AGR                  GR                  /5      \4" 5       GS*GS j5       5       Gr\I" \AGR                  GR                   \AGR                  GR                  \AGR                  R                  \AGR                  GR                  /5      GS*GS j5       Gr\I" \AGR                  /5          GSBGS\GS\GS\GS\GS\cGS\cGS\\   4GS jj5       GrGS\GS\\bGS4   4GS jGr\I" \AGR                  /5          GSBGS\GS\GS\GS\\   GS\cGS\GS\cGS\cGS\\   4GS jj5       Gr
\I" \AGR                  /5           GSCGS\GS\GS\GS\\   GS\GS\cGS\cGS\\   4GS jj5       Gr\I" \AGR                  /5       GS*GS\GS\GS\GS\S\GS\GS\GS\GS\bGS\bGS\GS\cGS\GS\GS\\   4GS jj5       Gr\I" \AGR                  /5          GSDGS\GS\GS\GS\GS\cGS\\   GS\\   4GS jj5       Gr\I" \AGR"                  /5        GS,GS\GS\GS\GS\S\GS\GS\GS\cGS\\   GS\\   4GS jj5       Gr\I" \AGR&                  /5         GSEGS\GS\GS\GS\\   GS\cGS\cGS\\   4GS jj5       Gr\I" \AGR*                  /5        GSFGS\GS\GS\GS\GS\\   S\GS\GS\GS\GS\GS\a\c   GS\cGS\\   4GS jj5       Gr\I" \AGR.                  /5       GS*GS\GS\GS\GS\S\GS\GS\GS\GS\GS\GS\GS\bGS\bGS\GS\cGS\\   4 GS jj5       Gr\I" \AGR2                  /5           GS?GS\GS\GS\GS\\   GS\\   GS\bGS\bGS\GS\cGS\cGS\\   GS\\b   GS\\b   GS\\   GS\\   4GS jj5       Gr\I" \AGR6                  /5         GS)GS\GS\GS\GS\S\GS\GS\GS\GS\bGS\bGS\GS\cGS\GS\GS\\   GS\\b   GS\\b   4"GS jj5       Gr\I" \AGR:                  /5           GSGGS\GS\GS\SD\\   GS\\   GS\\   GS\\b   GS\\b   GS\GS\bGS\cGS\\   GS\\   GS\\   GS\\b   4GS jj5       Gr\I" \AGR>                  /5         GSAGS\GS\GS\GS\SD\\   GS\\   GS\\   GS\GR@                  GS\GR@                  GS\GS\GS\GS\GS\bGS\cGS\\   GS\\b   GS\c4$GS jj5       Gr!\I" \AGRD                  R                  /5          GSHS-\R,                  SJ\R,                  GS\R,                  GS\R,                  SD\\R,                     GS\\R,                     SF\\GR                      GS\c4GS jj5       Gr#\I" \AGRH                  GRJ                  \AGRH                  GRL                  /5      \4" 5       GS(GS j5       5       Gr'\I" \AGRP                  GRJ                  5      GS(GS j5       Gr)\I" \AGRT                  R                  \AGRT                  R                  /5      \4" 5       GS'SS4.GS jj5       5       Gr+GS Gr,GS Gr-\I" \AGR\                  R                  \AGR^                  R                  /5      GS*GS j5       Gr.\I" \AGR`                  R                  \AGRb                  R                  /5      GS,GS j5       Gr0\I" \AGRd                  R                  \AGRf                  R                  /5        GS,GS\GS\\\b\GR@                  4      GS\\\b\GR@                  4      GS\\   GS\\   4
GS jj5       Gr2\I" \AGRh                  R                  \AGRj                  R                  /5      GS)GS j5       Gr4\I" \AGRl                  R                  \AGRl                  GRn                  \AGRl                  GR                  \AGRl                  GRp                  /5      GSIGS j5       Gr9GS Gr:\I" \AGRv                  R                  5        GS,GS j5       Gr<\I" \AGRz                  R                  5      GS 5       Gr=\I" \AGR|                  R                  5      GS 5       Gr>GS Gr?GS Gr@\I" \AGR                  R                  \AGR                  R                  /5      GS<GS j5       GrC\I" \AGR                  R                  5      GSJGS j5       GrD\I" \AGR                  R                  5      GSKGS j5       GrF\I" \AGR                  5      \4" 5        GSLGS j5       5       GrH\I" \AGR                  R                  \AGR                  GR                  /5      \4" S(S)5      GS=GS j5       5       GrJ\GR                  GrLGS GrM\I" \AGR                  R                  5      GS 5       GrN\I" \AGR                  R                  5      GS 5       GrO\I" \AGR                  R                  5      GS 5       GrQ\I" \AGR                  R                  5      GS 5       GrR\I" \AGR                  R,                  \AGR                  GR                  /5      \4" 5       SSGS.GS j5       5       GrU\I" \AGR                  /5      \4" 5       GSMGS j5       5       GrW\I" \AGR                  R                  \AGR                  R                  /5        GS,GS j5       GrZ\I" \AGR                  R                  /5        GS,GS j5       Gr\\I" \AGR                  R                  5      GS 5       Gr]\I" \AGR                  R                  \AGR                  R                  /5      \4" 5       GS)GS j5       5       Gr^\I" \R                  R                  GR                  5      GS 5       Gr_\I" \R                  R                  GR                  5      GS 5       Gr`\I" \AGR                  5      \4" 5       SSSSGS.GS  j5       5       GrbGS Grc\I" \AGR                  5      GS 5       Gre\I" \AGR                  5       GSNGS j5       Grg\I" \AGR                  5       GSNGS j5       Gri\I" \AGR                  5       GSNGS j5       Grk\I" \AGR                  5      \4" 5       SSGS.GS j5       5       Grm\I" \AGR                  5      \4" 5       GS\bS-\S\4GS	 j5       5       Gro\I" \AGR                  5      S-\4GS
 j5       Grq\I" \AGR                  5      \4" S$S9S-\S\4GS j5       5       Grr\I" \AGR                  5      \4" 5       S-\S\4GS j5       5       GrsGS Grt     GSOGS\GS\GS\\R,                     GS\\R,                     GS\\   SD\\   GS\\R,                     SF\\GR                      GS\c4GS jjGru\I" \AGR                  5      \4" 5          GS)GS\GS\GS\\   SD\\   SF\\GR                      S\4GS jj5       5       Grw\I" \AGR                  R                  /5           GSOGS\R,                  GS\R,                  GS\R,                  GS\R,                  GS\\R,                     SD\\R,                     GS\\R,                     SF\\GR                      GS\c4GS jj5       Gry\I" \AGR                  5      \4" 5       GS\S.\bGS\cS\4GS j5       5       Gr{\I" \AGR                  5      \4" 5       GSGS j5       5       Gr}\I" \AGR                  5      \4" 5          GSPSB\S)\GS\bGS\cGS\cS\4GS jj5       5       Gr~\I" \AGR                  R                  5       GSQS(\Sb\a\   GS\a\b   GS\4GS jj5       GrGS GrGS  GrG\" \AGR                  5        G\" \AGR                  5        G\" \AGR
                  5        G\" \AGR                  5        G\" \AGR                  5        G\" \AGR                  5        G\" \AGR                  5        G\" \AGR                  5        G\" \AGR                  5        G\" \AGR                  5        G\" \AGR                  5        G\" \AGR                  5        G\" \AGR                  5        G\" \AGR                   5        G\" \AGR"                  5        G\" \AGR$                  5        G\" \AGR&                  5        G\" \AGR(                  5        G\" \AGR*                  5        G\" \AGR,                  5        G\" \AGR.                  5        GS! Gr\I" \AGR2                  5      \4" 5       GS" 5       5       Gr\I" \AGR4                  5      \4" 5       SLGS#.GS$ j5       5       Gr\I" \AGR6                  5      \4" 5       SLGS#.GS% j5       5       GrG\" \AGR2                  5      GrG\" \AGR4                  5      GrG\" \AGR6                  5      GrS SK5rS SGKrS SGKrGS& GrG\" 5         g(R      N)Sequence)Enum)reducewraps)CallableOptionalTypeVarUnion)	ParamSpec)SymBoolSymFloatTensor)_add_op_to_registry_convert_out_paramsglobal_decomposition_table
meta_table)
OpOverload)_prim_elementwise_meta$ELEMENTWISE_PRIM_TYPE_PROMOTION_KINDview_of)BoolLikecorresponding_complex_dtypecorresponding_real_dtypedefinitely_contiguouselementwise_dtypesELEMENTWISE_TYPE_PROMOTION_KIND	FloatLikeIntLikeis_contiguousmake_contiguous_strides_forNumbersuggest_memory_format
TensorLike)_maybe_convert_to_dtype_maybe_resize_out_resize_output_check_safe_copy_outout_wrapper)_broadcast_shapes_maybe_broadcast)_config)_pytree_T_PatenIMPLMeta   returnc                    ^  U 4S jnU$ )Nc                 Z   >^  [        T 5      m U 4S jn[        R                  " UT5        T $ )Nc                 (   > [        [        U T5        g N)r   r   )opfns    S/var/www/fran/franai/venv/lib/python3.13/site-packages/torch/_meta_registrations.pyregister0register_meta.<locals>.wrapper.<locals>.registerA   s    
B3    )r   pytree	tree_map_)r9   r;   r8   s   ` r:   wrapperregister_meta.<locals>.wrapper>   s)     $	4 	2&	r=    )r8   r@   s   ` r:   register_metarC   =   s     Nr=   type_promotionc                     [         R                  " USU 06u  p#U Vs/ s H  n[        XC5      PM     nn[        U6 n[	        US[
        R                  06$ s  snf )Ntype_promotion_kindrD   )utilsr   r$   r*   r   r   DEFAULT)rD   args_result_dtypexs        r:   elementwise_metarM   J   sp    
 ..	*OA ?CCd#A4dDC T"D "	BJJ  Ds   Ac                     [         R                  [         R                  [         R                  [         R                  [         R
                  [         R                  0nUR                  X 5      $ r7   )torch	complex32halfcfloatfloatcdoubledoubleget)dtypefrom_complexs     r:   toRealValueTyperY   ^   sC    ekku||L
 E))r=   c                 p   ^ ^ [        [        T /UQ76 5      m[        R                  " TT :H  UU 4S j5        g )Nc                     > ST ST  3$ )Nzoutput with shape z# doesn't match the broadcast shape rB   )broadcasted_shape
self_shapes   r:   <lambda>)check_inplace_broadcast.<locals>.<lambda>k   s    $ZL0STeSfgr=   )tupler)   rO   _check)r]   
args_shaper\   s   ` @r:   check_inplace_broadcastrc   g   s0    /
HZHI	LLZ'gr=   Fc	           	        ^ ^^^^	 [        T [        R                  5      (       a)  [        R                  " T R	                  5       S:H  S 5        [        T[        R                  5      (       a)  [        R                  " TR	                  5       S:H  S 5        [        S T TT4 5       5      (       a`  [        R                  " [        R                  " 5       5      m	Tc  T	mOO[        R                  " [        R                  " T5      U	U4S j5        OT=(       d    [        R                  " 5       m[        T[        R                  5      (       d   e[        R                  " [        T[        5      UU U4S j5        [        T[        5      (       d   e[        R                  " TS:  S 5        [        R                  " T4TUSUUS	9$ )
Nr   c                      gNz:linspace only supports 0-dimensional start and end tensorsrB   rB   r=   r:   r^   (meta_linspace_logspace.<locals>.<lambda>       Pr=   c                      grf   rB   rB   r=   r:   r^   rg      rh   r=   c              3   B   #    U  H  n[        U[        5      v   M     g 7fr7   )
isinstancecomplex).0args     r:   	<genexpr>)meta_linspace_logspace.<locals>.<genexpr>   s     
C/B:c7##/Bs   c                     > ST  ST 3$ )Nzlinspace(): inferred dtype z& can't be safely cast to passed dtype rB   )default_complex_dtyperW   s   r:   r^   rg      s    56K5LLrsxryzr=   c                     > S[        T5      R                   S[        T 5      R                   S[        T5      R                   S3$ )Nz4received an invalid combination of arguments - got (, ))type__name__)endstartstepss   r:   r^   rg      sB     u+r$s),,-RU0D0D/EQHr=   c                      g)Nz$number of steps must be non-negativerB   rB   r=   r:   r^   rg      s    %Kr=   metarW   layoutdevice
pin_memoryrequires_grad)rk   rO   r   ra   dimanyrG   r   get_default_dtypeis_complex_dtyperW   _check_typer   empty)
ry   rx   rz   baserW   r   r~   r   r   rr   s
   ``` `    @r:   meta_linspace_logspacer   o   s[    %&&IIK1P	
 #u||$$GGINP	

 
CsE/B
CCC % A A##%!
 =)ELL&&u-z
 2002eU[[)))) 
5'"	H
 eW%%%%	LL!KL;;	# r=   c                 6  ^ [         R                  " TR                  [         R                  :H  U4S j5        [         R                  " U R                  5       S:H  =(       a    TR                  5       S:g  (       + S 5        U R                  TR                  5      $ )Nc                  "   > ST R                    3$ )Nz2take(): Expected a long tensor for index, but got rW   indexs   r:   r^   meta_take.<locals>.<lambda>   s    DU[[MRr=   r   c                      g)Nz*take(): tried to take from an empty tensorrB   rB   r=   r:   r^   r      s    <r=   )rO   ra   rW   long_check_indexnumel	new_emptyshape)selfr   s    `r:   	meta_taker      sm     
LLuzz!R
 
ZZ\Q55;;=A#56< >>%++&&r=   r   c                b  ^ ^^ T R                   nTR                   n[        R                  " X4:H  S 5        [        R                  " T R                  T5      S:H  =(       a    TR                  T5      S:H  UUU 4S j5        [	        T R
                  TR
                  5      nT R                  U5      $ )Nc                      g)Nz=linalg.cross: inputs must have the same number of dimensions.rB   rB   r=   r:   r^   linalg_cross.<locals>.<lambda>       Or=   r2   c                  V   > ST  STR                  T 5       STR                  T 5       3$ )Nzlinalg.cross: inputs dimension z must have length 3. Got  and size)r   otherr   s   r:   r^   r      s1    -cU 399S>"%

3'8:r=   )ndimrO   ra   r   r)   r   r   )r   r   r   x_dy_d	out_shapes   ```   r:   linalg_crossr      s     ))C
**C	LL
O 
LL		#!4

31 4	
 "$**ekk:I>>)$$r=   c                   ^^^ SSK JmJmJn  UU4S jnUU4S jn[	        U 5      S:X  a  S/[	        U5      -  $ [        [        R                  U S5      nU" US:H  5      nU(       a  U" U" X5      5      (       a  U$ S/[	        U5      -  n	U(       aU  [        [	        U5      S-
  SS5       H6  n
U
[	        U5      S-
  :X  a  SX'   M  [        X*S-      S5      XS-      -  X'   M8     U	$ [	        U5      S-
  n
US   nSnSn[        [	        U 5      S-
  SS5       H  nXU   -  nUS:X  d0  U" XS-
     S:g  5      (       d  M'  U" XS-
     X-  :g  5      (       d  M@  U
S:  a^  U" X:  5      (       d  U" X*   S:H  5      (       a=  X-  X'   XU
   -  nU
S-  n
U
S:  a%  U" X:  5      (       a  M)  U" X*   S:H  5      (       a  M=  U" X:g  5      (       a    g US:  d  M  XS-
     nSnSnM     U
S:w  a  g U	$ )Nr   )guard_or_falseguard_or_truesym_eqc                 &   > T(       a  T" U 5      $ U $ r7   rB   )rL   r   size_obliviouss    r:   maybe_guard_or_false-_compute_stride.<locals>.maybe_guard_or_false   s    !!$$r=   c                 &   > T(       a  T" U 5      $ U $ r7   rB   )rL   r   r   s    r:   maybe_guard_or_true,_compute_stride.<locals>.maybe_guard_or_true   s     ##r=      r   )
%torch.fx.experimental.symbolic_shapesr   r   r   lenr   operatormulrangemax)	old_shape
old_stride	new_shaper   r   r   r   r   
zero_numel
new_strideview_dchunk_base_stridetensor_numel
view_numeltensor_dr   r   s      `           @@r:   _compute_strider      s&     9~sS^##8<<A.E%eqj1J*6)+GHHs9~%JC	NQ.B7FY!++%&
" 	1*-q1Jz4JJ "	 8 ^aF"2LJ#i.1,b"5(++q=	Q, 71 <==#a<(L,LL  A+#J$=>>'	(9Q(>??%/%C
"//
! A+#J$=>>'	(9Q(>?? #:#=>>!|$.!|$<! 
/ 60 |r=   c                    ^ SSK Jm  [        U4S jU R                  5        5       5      =(       d?    [        U4S jU R	                  5        5       5      =(       d    [        U4S jU 5       5      $ )Nr   )has_hintc              3   >   >#    U  H  nT" U5      (       + v   M     g 7fr7   rB   rm   sr   s     r:   ro   +_view_has_unbacked_input.<locals>.<genexpr>  s     .XOOX   c              3   >   >#    U  H  nT" U5      (       + v   M     g 7fr7   rB   r   s     r:   ro   r     s     3
18A;
r   c              3   >   >#    U  H  nT" U5      (       + v   M     g 7fr7   rB   r   s     r:   ro   r     s     .18A;r   )r   r   r   r   stride)ar   r   s     @r:   _view_has_unbacked_inputr     sM    > 	.QVVX.. 	/3
33	/...r=   Tc                 ~  ^ ^ SSK JnJn  [        R                  " TSS9m[        R
                  " TT R                  5       5      mT R                  S:X  aV  T nT H<  n[        R                  " US:H  5        [        R                  R                  US5      nM>     UT L a  [        T 5      $ U$ [        T5      S:X  a`  T nT R                   H<  n[        R                  " US:H  5        [        R                  R                  US5      nM>     UT L a  [        T 5      $ U$ [!        ["        R$                  TS5      n[        R                  " T R                  5       U:H  U U4S j5        [        T5      [        T R                  5      :X  a)  U" U" TT R                  5      5      (       a  [        T 5      $ U(       a  ['        T 5      (       a9  O[)        T 5      (       a(  [        R*                  " T5      nT R-                  TU5      $ [/        T R1                  5       T R3                  5       TUS9n	U	b  T R-                  TU	5      $ U(       aO  [        R4                  R6                  R8                  R:                  (       d  [=        T T5      (       a  [?        T TSS	9$ S
T R                   ST R3                  5        ST S3n
[A        U
5      e)Nr   )r   r   F)validater   r   c                  *   > ST R                    ST S3$ )Nz&Could not reshape a tensor with shape  as a tensor with shape !r   r   r   s   r:   r^   %_view_unbacked_meta.<locals>.<lambda>E  s    8	AYZ_Y``abr=   )r   )size_oblivious_enabledz Cannot view a tensor with shape z and strides r   r   )!r   r   r   rG   extract_shape_from_varargs
infer_sizer   r   rO   ra   _refs	unsqueezer   r   r   squeezer   r   r   r   r   r    
as_stridedr   r   r   fxexperimentalr+   backed_size_obliviousr   _view_unbacked_meta
ValueError)r   r   r   r   r   _alengthshape_numelstridesnew_stridesmsgs   ``         r:   r   r   !  s.   L ,,UUCE UAGGI.E 	vv{FLL1%&&r2.B  71:I 5zQggFLL1%$$R,B  71:Iua0K	LL		[ b
 5zS\!nVE1775K&L&Lqz#9Q}Q?O?O33E:||E7++!	!((*e4JK ||E;// %%;;#Au--"1eEJJ,QWWI]188:,Nfglfmmn
oC
S/r=   c                     [         R                  R                  R                  R                  (       d  [        X5      (       a  [        X5      $ [         R                  R                  " U /UQ7SS06$ )N
allow_copyF)	rO   r   r   r+   r   r   r   r   _reshape_view_helperr   s     r:   
_view_metar   e  sW    xx$$::>V	? ? #1,,{{//LELeLLr=   c                 x    [        U S5        [        U S5        [        R                  " U [        R                  S9$ )Nzlinalg.matrix_expmemory_format)squareCheckInputscheckFloatingOrComplexrO   
empty_likecontiguous_formatr   s    r:   linalg_matrix_expr   o  s3     d/04!45D0G0GHHr=   valuesindicesc                 R   [         R                  " U R                  U R                  U R                  S9n[         R                  " U R                  U R                  [         R
                  S9nU R                  5       S:w  a%  U R                  S:w  a  [        XR                  5        X#4$ )Nr   rW   r   )	rO   r   r   r   rW   int64r   r   maybe_wrap_dim)r   r   r   r   s       r:   	cummaxminr   w  sl    
 [[DKKtzzJFkk$**T[[LGzz|qTYY!^sII&?r=   c                 r    [        XR                  5        [        R                  " U [        R                  S9$ Nr   )r   r   rO   r   r   )r   r   s     r:   logcumsumexpr    s)     3		"D0G0GHHr=   c                V  ^ UR                   n[        U5      nXV-
  n[        [        U5      5      n[        U5       V	s/ s H  n	SPM     n
n	U H  nSX'   M	     / / pU H0  nX   (       d  UR	                  U5        M  UR	                  U5        M2     X-   n[        U5      nUR                  5       mUS U nUR                  U4S jSS9  XUS  -   nUR                  U5      nS/[        UR                  US  5      -   nUR                  U5      nUR                  S5      nUUS'   [        U5      n[        [        U5      5       H  nX#U      UUS-   '   M     U R                  U[        R                  S9  [        U5       V	s/ s H  n	SPM     nn	SnUS-
  nUS:  a1  UU R                  S5      -  UUU   '   UX(U      -  nUS-  nUS:  a  M1  [        Xu5       H   nU R                  SUU-
  -   5      UUU   '   M"     U R                  UUU R                  5       5        U $ s  sn	f s  sn	f )	NFTc                    > TU    $ r7   rB   )rL   self_stridess    r:   r^   _exec_fft.<locals>.<lambda>  s	    <?r=   keyreverser   r   r   r   )r   r   listr   appendr   sortpermuter   reshaper   resize_rO   r   as_strided_storage_offset)outr   	out_sizesr   forwardr   signal_ndim
batch_dimsdim_permuterJ   is_transformed_dimdleftright	batch_endtmpinputbatched_sizes
batch_sizebatched_out_sizesiout_stridesbatch_numelr  s                          @r:   	_exec_fftr$    s4   99Dc(K#J uT{#K).t5A%5 $  b%!$KKNLLO	 
 ,KD	I;;=L
jy
!CHH*DH9IJ//KLL%E D4JK 899MMM-(EAJ!M!]+3s8_#,V#4!a%  KK!1H1HKI $Dk*k1kK*KQA
q&&1CJJqM&AKN#yQ00	Q q& :$&)jja*n1E&FKN# %OOI{C,>,>,@AJW 6@ +s   H!H&r   r   exclude_lastc                    ^ [        U5      nU R                  5       mUS [        U5      [        U5      -
   R	                  U4S jS9  U$ )Nc                    > TU    $ r7   rB   )r!  r  s    r:   r^   _sort_dims.<locals>.<lambda>  s	    l1or=   )r  )r	  r   r   intr  )r   r   r%  sorted_dimsr  s       @r:   
_sort_dimsr+    sL    s)K;;=L6#k"S%667<<% =  r=   c                 
   [         R                  " U R                  R                  5        U(       d  U R	                  5       $ [        X5      nU R                  U R                  5       5      n[        XPU R                  5       XCS9$ )Nr  )	rO   ra   rW   
is_complexcloner+  r   r   r$  )r   r   normalizationr  r*  r  s         r:   meta_fft_c2cr1    s\     
LL&&'zz|T'K
..
%CS		[JJr=   c                 n    [        U 5      [        :  d!  [        U 5      S:  a  U S   S:X  a
  U S   S:X  a  gg)N   r   r   FT)r   cufft_max_ndimr   s    r:   use_optimized_cufft_pathr5    s3    
3x. SX]s1v{s1vQR{r=   c                 |  ^ [         R                  " U R                  R                  5        [	        U R                  5       5      n[	        U5      nUS   nXF   S-  S-   n[	        U5      nXxU'   U(       a  XuU'   [        U 5      S:X  d  [        U 5      S:X  Gax  U R                  U[        R                  " U R                  5      S9n	U n
[        U 5      S:X  a  [        U5      (       a  [        XXQSS9  O[        U5      S:X  a  UOUn[        XX/SS9  [        U5      S:  a.  U R                  U[        R                  " U R                  5      S9n
US S nU(       au  XpU
R                  5       mUR                  U4S	 jSS
9  [        [         [        U5      5      nU[        U5      U-
  S  n[        XXSS9  US [        U5      U-
   nU(       a  Mu  U(       d7  U	R                  U5      XV   :w  a   U
R#                  U[         R$                  S9  U
n	U	$ U R                  U[        R                  " U R                  5      S9$ )Nr   r3  r   cudaxpur   Tr-  c                    > TU    $ r7   rB   )r!  r   s    r:   r^   meta_fft_r2c.<locals>.<lambda>  s	    '!*r=   r  r   )rO   ra   rW   is_floating_pointr	  r   device_hintr   rG   r   r5  r$  r   r   r  minr4  r  r   )r   r   r0  onesidedinput_sizesr  last_dimlast_dim_halfsizeonesided_sizesoutputworking_tensortarget_sizesr*  max_dims	last_dimsr   s                  @r:   meta_fft_r2crH    s+    
LL--.tyy{#K[!I2wH#-2Q6+&N08/(4F"k$&75&@ U>>tzzJ   
 t&+CC+H+HfidK ),CA9>LflJPTU3x!|!%U%F%Ftzz%R "0 "
 cr(K)7(//1  ,d !  ~s;/?@'K(88(C(EF	Nt **GC,<x,GH + {{8$	(;;&&y@W@W&X' ~~U>>tzzJ  
 	
r=   )	generatorc                D    [        U[        R                  " U /5      5      $ r7   )r%   rO   Size)nrI  r  s      r:   meta_randpermrM  %  s    S%**aS/22r=   rW   r~   r   r   c                .    [         R                  " XX#US9$ NrN  rO   r   )rL  rW   r~   r   r   s        r:   meta_randperm_defaultrR  *  s     ;;	v r=   c                t   ^ ^ Sm[         R                  " T T:  U U4S j5        [         R                  " XX4US9$ )Nr   c                     > ST ST  3$ Nz:random_ expects 'from' to be less than 'to', but got from=z >= to=rB   highlows   r:   r^   meta_randint.<locals>.<lambda>F      LSEQXY]X^_r=   rN  rO   ra   r   )rW  r   rW   r~   r   r   rX  s   `     @r:   meta_randintr\  8  s:     C	LLs
_ ;;&J r=   c                p   ^ ^ [         R                  " TT :  UU 4S j5        [         R                  " X#XEUS9$ )Nc                     > ST ST  3$ rU  rB   rV  s   r:   r^   "meta_randint_low.<locals>.<lambda>[  rZ  r=   rN  r[  )rX  rW  r   rW   r~   r   r   s   ``     r:   meta_randint_lowr`  M  s5     
LLs
_ ;;&J r=   c                .    [         R                  " XX#US9$ rP  rQ  )r   rW   r~   r   r   s        r:   meta_rand_defaultrb  b  s     ;;&J r=   r0  lastdimc                    [         R                  " U R                  R                  5        [	        U 5      S:X  a  [        U R                  5       5      nX4US   '   U R                  U[        U R                  5      S9n[        U5      (       a(  [        UU R                  [         R                  S9UUSS9$ [        U5      S:  a  [        XS S SU5      nOU R                  [         R                  S9n[        XVXAS   /SS9$ U n[        U5      S:  a  US S n[        XUSS9nUSS  n[        UR                  5       5      nX4US   '   U R                  U[        U R                  5      S9n	[        XXASS9$ )	Nr7  r   r   r   Fr-  r   r   )rO   ra   rW   r.  r<  r	  r   r   rY   r5  r$  r/  r   r   r1  )
r   r   r0  rc  r  rC  tempr  c2c_dimsr  s
             r:   meta_fft_c2rrg  j  s^    
LL&&'4F"%	$#b'	1LM#C((

)@)@
A  3x!|#Dcr(Aw?zz0G0GzHV92wiOO s8a<3BxH NEbc(C&	$#b'nnYodjj.InJYUCCr=   c                 `   SSK Jn  U" U 5      (       d%  [        R                  " U 5      S:X  a  [	        S5      e[        U[        5      (       a`  UR                  X5      nU R                  5       UR                  5       :w  a-  [        R                  R                  X@R                  5       5        U $ )Nr   )free_unbacked_symbolsr   zQmore than one element of the written-to tensor refers to a single memory location)r   ri  rO   _debug_has_internal_overlapRuntimeErrorrk   r   tor   r/   expand_copydefault)r   srcnon_blockingri  intermediates        r:   
meta_copy_rr    s     L "$''E,M,Md,SWX,X_
 	
 #vvvd199;,++--$$\99;?Kr=   c                     [        U R                  5       5      n[        U R                  5       5      nXR                  5       :  a  SOX!   X1   -  nUR	                  US5        UR	                  X5        X#4$ Nr   )r	  r   r   r   insert)tensorr   result_sizesresult_stridesr   s        r:   inferUnsqueezeGeometryry    sf    &L&--/*NZZ\)|/@>CV/VJQ#*''r=   c                 z    [        XR                  5       S-   5      n[        X5      u  p#U R                  X#5        U $ rt  )r   r   ry  r  )r   r   g_sizes	g_stridess       r:   meta_unsqueeze_r}    s6    
hhj1n
-C/:GW(Kr=   r  weight_metabias_activation_opt	out_dtypec                 @   [        U R                  5      nUb+  UR                  S5      UR                  S5      :X  d   S5       eUR                  S5      U R                  S5      S-  :X  d   eUR                  S5      US'   [        U R                  5      S:X  d   S5       eSU R                  S5      4nUb9  U R                  [
        R                  :X  a  U[
        R                  :X  d   S5       eU R                  UUc  U R                  OUS9R                  Xg5      nU$ )	Nr   zoutput size mismatchr   r   r3  z*we can only handle the squashed input case9out_dtype is only supported for i8i8->i32 linear operatorr   )
r	  r   r   r   rW   rO   int8int32r   r   )	r  r~  r  r  r  r  output_sizestransposed_stridesrC  s	            r:   meta_sparse_structured_linearr    s    $L{{1~1-E/EE-;;q>UZZ^a////{{1~L u{{q N"NN UZZ]+{{ejj(Y%++-E 	
G	
E __&.ekkI   j2 
 Mr=   mat1	mat1_metamat2c                    [        U R                  5      S:X  d   e[        UR                  5      S:X  d   e[        UR                  5      S:X  d   eU R                  S5      UR                  S5      S-  :X  d   eU R                  S5      UR                  S5      /nUb9  UR                  [        R
                  :X  a  U[        R                  :X  d   S5       eUR                  UUc  UR                  OUS9nU$ )Nr3  r   r   r  r   r   r   r   rW   rO   r  r  r   )r  r  r  r  r  rC  s         r:   meta_sparse_structured_mmr    s     tzz?ay1$$$tzz?a99Q<499Q<!++++IIaL$))A,/LzzUZZ'I,D 	
G	
D ^^%-djj9  F
 Mr=   r   )alphabetar  c                   [        U R                  5      S:X  d   S5       e[        UR                  5      S:X  d   e[        UR                  5      S:X  d   e[        UR                  5      S:X  d   eU R                  S5      UR                  S5      :X  d   S5       eUR                  S5      UR                  S5      S-  :X  d   eUR                  S5      UR                  S5      /nUb9  UR                  [        R
                  :X  a  U[        R                  :X  d   S5       eUR                  UUc  UR                  OUS9nU$ )Nr   zEonly input broadcasted to columns of mat1 * mat2 product is supportedr3  r   r  r   r  )	r  r  r  r  r  r  r  r  rC  s	            r:   meta_sparse_structured_addmmr    s/    u{{q  O  tzz?ay1$$$tzz?a::a=DIIaL( O( 99Q<499Q<!++++IIaL$))A,/LzzUZZ'I,D 	
G	
D ^^%-djj9  F
 Mr=   compressed_Adense_Br  transpose_resultalg_idsplit_ksplit_k_modec	                    UR                   [        R                  [        R                  [        R                  [        R
                  [        R                  1;   d   S5       eU R                   UR                   :X  d   S5       e[        UR                  5      S:X  d   S5       eU R                   [        R
                  [        R                  4;   n	U	(       a  SOSn
U	(       a  UR                  5       (       a   S5       eUR                  S5      nUR                  S	5      nU R                  5       S
-  X-  -  nUb  XR                  S5      :X  d   eUbP  U	(       aB  U[        R                  [        R                  [        R                  [        R                  1;   d   S5       eU(       a  X4OX4nUR                  XS9$ )Nz;_cslt_sparse_mm only supports fp16, bf16, int8, and fp8e4m3zinputs must have the same dtyper3  z'_cslt_sparse_mm only supports 2d inputs
   	   z.dense input must be transposed for 8bit dtypesr   r      z\out_dtype is not supported for {compressed_A.dtype} x {dense_B.dtype} -> {out_dtype} matmul!r   )rW   rO   float32float16bfloat16r  float8_e4m3fnr   r   r   r   r   r  r   )r  r  r  r  r  r  r  r  r  is_8bit_input_typecompression_factorkrL  moutput_shapes                  r:   meta__cslt_sparse_mmr    s    ==

  E EE  .Q0QQ.w}}"M$MM"%++

E<O<O/PP1q((** 	
<	
* 	QAQA					"(:(>?AIIaL   !iMMNNKK	4
 '
 	
 k	
 
 .A6A6L\;;r=   )include_selfr   sourcer   r  c                H    [         R                  " U [         R                  S9$ r   rO   r   r   r   r   r   r  r   r  s         r:   meta_index_reducer  L  s     D0G0GHHr=   c                    U $ r7   rB   r  s         r:   meta_index_reduce_r  Y  s	     Kr=   c                     [        U R                  5       5      nU R                  5       S:  a  UR                  5       X1'   U R	                  U5      $ Nr   )r	  r   r   r   r   )r   r   r   result_sizes       r:   meta_index_selectr  g  s>     tyy{#KxxzA~ ;;=>>+&&r=   )lengthsr   offsetsaxisunsafeinitialdatar  r  r  r  c                   ^ ^ Ub  [        S5      eUU 4S jnUb  U" UR                  5      $ Ub+  UR                  S S UR                  S   S-
  4-   n	U" U	5      $ [        S5      e)Nz?segment_reduce(): indices based reduction is not supported yet.c                    > [         R                  " U TR                  TS-   S  -   TR                  S[         R                  S9$ )Nr   r|   rW   r   r   )rO   r   r   rW   r   )lengths_shaper  r  s    r:   segment_reduce_lengths_tensor:meta_segment_reduce.<locals>.segment_reduce_lengths_tensor  s>    {{DJJtaxz22**11	
 	
r=   r   r   z<segment_reduce(): Either lengths or offsets must be defined.)NotImplementedErrorr   rk  )
r  r   r  r   r  r  r  r  r  r  s
   `    `    r:   meta_segment_reducer  p  s|     !M
 	

 ,W]];; cr*gmmB.?!.C-EE,];;
U
VVr=   c                 $    U R                  S5      $ NrB   r   r   s    r:   meta_maxr         >>"r=   c                     [         R                  " U R                  U45      n[        XU5      nU R	                  U5      U R	                  U[
        R                  S94$ Nr   rG   reduction_dimsr   _compute_reduction_shaper   rO   r   r   r   keepdimr  s       r:   meta_max_dimr    P    


tzzC6
2C+Dw?L|$|5::6 r=   c                 $    U R                  S5      $ r  r  r   s    r:   meta_minr    r  r=   c                     [         R                  " U R                  U45      n[        XU5      nU R	                  U5      U R	                  U[
        R                  S94$ r  r  r  s       r:   meta_min_dimr    r  r=   c                     U R                  5       (       a  [        U R                  5      nO[        U [        R
                  S9u  p![        R                  " XS9$ NrF   r   )r.  r   rW   r   r   INT_TO_FLOATrO   r   )r   rK   rJ   s      r:   
meta_angler    sH    /

;, ? L L
 D55r=   c                     [         R                  " XR                  5       U R                  5        UR	                  [         R
                  " U 5      5      $ r7   )rO   _resize_output_r   r   copy_angle)r   r  s     r:   meta_angle_outr    s4    	#yy{DKK899U[[&''r=   c                     g r7   rB   )vals    r:   assert_asyncr        
r=   c                     g r7   rB   )r  
assert_msgs     r:   assert_async_metar    r  r=   c                     g r7   rB   )r   s    r:   
print_metar    r  r=   rW   r~   r   r   r   c                 ,    [         R                  " SSS9$ )Nr   r|   r   rQ  r  s        r:   make_dep_tokenr    s     ;;q((r=   c                 j    SSK Jn  [        U [        [        45      (       a  [        S5      eU" XUS9  g )Nr   )constrain_range'Constraining SymFloat or Symbool is nyir=  r   )r   r  rk   r   r   r   )r   r=  r   r  s       r:   sym_constrain_ranger    s0     F$7+,,BCCDs+r=   c                 .    [         R                  XUS9  U$ Nr  )r/   r  r   r=  r   	dep_tokens       r:   functional_sym_constrain_ranger    s    T4r=   c                 6   SSK Jn  Uc  Uc  [        R                  " U 5        g [	        U [
        [        45      (       a  [        S5      e[        U 5      [        L a7  Ub  [        R                  " X:  5        Ub  [        R                  " X:*  5        g U" XUS9  g )Nr   )_constrain_range_for_sizer  r  )r   r  rO   _check_is_sizerk   r   r   r   rv   r)  ra   )r   r=  r   r  s       r:   sym_constrain_range_for_sizer    s     P
{s{T"$7+,,BCCDzS?LL%?LL%d5r=   c                 .    [         R                  XUS9  U$ r  )r/   r  r  s       r:   'functional_sym_constrain_range_for_sizer    s    %%d%=r=   c                     U$ r7   rB   )r  r  r  s      r:   functional_assert_async_metar    s    r=   f_namec                     U R                  5       S:  d
   U S35       eU R                  S5      U R                  S5      :X  d.   U SU R                  S5       SU R                  S5       S35       eg )Nr3  z3: The input tensor must have at least 2 dimensions.r   z5: A must be batches of square matrices, but they are  by 	 matrices)r   r   )r   r  s     r:   r   r     s}    88:? (EF? 99R=DIIbM) (G		RTVZ[_[d[deg[hZiirs)r=   Anamec                   ^ ^^ [         R                  " T R                  TR                  :H  UU 4S j5        [         R                  " T R                  TR                  :H  UU 4S j5        [         R                  " TR	                  S5      TR	                  S5      :H  U4S j5        [         R                  " TR	                  S5      T R	                  S5      :H  UUU 4S j5        g )Nc                  >   > STR                    ST R                    S3$ )Nz:Expected b and A to be on the same device, but found b on z
 and A on 	 instead.r  r  r   s   r:   r^   (linearSolveCheckInputs.<locals>.<lambda>   s     H{{m:ahhZy:r=   c                  >   > STR                    ST R                    S3$ )Nz=Expected b and A to have the same dtype, but found b of type z and A of type r  r   r  s   r:   r^   r  (  s     Kzzl/!'')=r=   r   r  c                  R   > ST R                  S5       ST R                  S5       S3$ )Nz3A must be batches of square matrices, but they are r  r   r   r  r   r  s   r:   r^   r  0  s+    FF2J<tAFF2J<yBr=   c                     > ST ST R                  S5       ST R                  S5       STR                  S5       STR                  S5       3
$ )NzIncompatible matrix sizes for z: each A matrix is r   r   z but each b matrix is r  r   )r  r  r   s   r:   r^   r  8  sM    ,TF 3D$TYYr]O4		"Hr=   )rO   ra   r   rW   r   )r   r  r  s   ```r:   linearSolveCheckInputsr    s    	LLqxx	
 
LL

agg	
 
LL	r
affRj 	
 
LL	r
diim#	
r=   tallow_low_precision_dtypesc                 h  ^^ U R                   m[        R                  " U R                  5       =(       d    U R	                  5       UU4S j5        U(       d\  [        R                  " T[        R
                  [        R                  [        R                  [        R                  4;   UU4S j5        g g )Nc                     > T ST  3$ )Nz<: Expected a floating point or complex tensor as input. Got rB   rW   r  s   r:   r^   (checkFloatingOrComplex.<locals>.<lambda>I  s    6(VW\V]^r=   c                     > T ST  3$ )Nz*: Low precision dtypes not supported. Got rB   r  s   r:   r^   r  N  s    vhHPr=   )	rW   rO   ra   r;  r.  rS   rU   rR   rT   )r  r  r  rW   s    ` @r:   r   r   A  sn    
 GGE	LL	/^ &ekk5<<u}}MMP	
 &r=   arg_namec                 b   ^^ [         R                  " U R                  5       S:  UU4S j5        g )Nr3  c                     > T ST  S3$ )Nz: The input tensor z! must have at least 2 dimensions.rB   )r  r  s   r:   r^   checkIsMatrix.<locals>.<lambda>V  s    6(-hZ7XYr=   )rO   ra   r   )r  r  r  s    ``r:   checkIsMatrixr  S  s    	LL	1Yr=   Br  c                   ^ ^^^ [        T T5        [        TT5        [        R                  " T(       a#  T R	                  S5      TR	                  S5      :H  O"T R	                  S5      TR	                  S5      :H  U UUU4S j5        g )Nr  r   c                     > T ST(       a  SOS ST R                  S5       ST R                  S5       STR                  S5       STR                  S5       S	3$ )
Nz2: Incompatible shapes of A and B for the equation zAX = BzXA = Bz (r  rL   r   r   ru   r   )r  r  r  r  s   r:   r^   #checkInputsSolver.<locals>.<lambda>_  sV    hHxX.AaffRj\qvvbzl!AFF2J<qJr=   )r   r  rO   ra   r   )r  r  r  r  s   ````r:   checkInputsSolverr  Z  sY    a !V	LL$(r
affRj affRjAFF2J.F	
r=   resultfn_nameresult_namec                 v   ^ ^^^ [         R                  " TR                  TR                  :H  U UUU4S j5        g )Nc            	      L   > T  ST ST STR                    STR                    3	$ )Nz: Expected z5 and input tensors to be on the same device, but got z on z and input on r  )r   r  r  r!  s   r:   r^   !checkSameDevice.<locals>.<lambda>o  s0    i{;-/dm4nU\\NLr=   )rO   ra   r   )r   r  r  r!  s   ````r:   checkSameDevicer%  g  s&     
LL%	
r=   UPLOc                    ^  T R                  5       n[        R                  " [        T 5      S:H  =(       a    US:H  =(       d    US:H  U 4S j5        g )Nr   ULc                     > ST  3$ )Nz1Expected UPLO argument to be 'L' or 'U', but got rB   )r&  s   r:   r^   checkUplo.<locals>.<lambda>z  s    CD6Jr=   )upperrO   ra   r   )r&  UPLO_uppercases   ` r:   	checkUplor.  v  s<    ZZ\N	LLD	QKNc1J^s5JJr=   eigenvalueseigenvectorsr)  	compute_vc                 P   [        U S5        [        U5        [        U R                  5      nU(       a,  U R	                  U5      nUR                  U[        USS95        OU R	                  S/5      nUR                  5         U R	                  U[        U R                  5      S9nXT4$ )Nzlinalg.eighF	row_majorr   r   )
r   r.  r	  r   r   r  r    poprY   rW   )r  r&  r1  r   vecsvalss         r:   meta__linalg_eighr8  ~  s     a'dOME{{5! ;EU ST{{A3	IIK;;uOAGG$<;=D:r=   c                     [        U S5        [        R                  " U R                  5      (       a  U R                  O[        R                  " U R                  5      nU R                  U R                  S S US9$ )Nzlinalg.eigvalsr   r   r   rG   r   rW   r   r   r   )r  complex_dtypes     r:   meta__linalg_eigvalsr<    sf     e-. !!%++.. 	..u{{; 
 ??5;;s+=?AAr=   c                 0   [        U S5        [        R                  " U R                  5      (       a  U R                  O[        R                  " U R                  5      nU R                  U R                  S S US9nU R                  U R                  US9nX#4$ )Nz
linalg.eigr   r   r:  )r  r;  r   vectorss       r:   meta_linalg_eigr?    s     e\* !!%++.. 	..u{{; 
 __U[["-]_CFooekko?G?r=   ro  c                 p    U R                   R                  [        R                  S9R	                  SS5      $ )Nr   r  r   )mTr/  rO   r   	transpose)ro  s    r:   cloneBatchedColumnMajorrC    s*    66<<e&=&=<>HHRPPr=   r,  c                     [        U 5      $ r7   )rC  )r   r  r,  s      r:   _cholesky_solve_helperrE    s     #4((r=   c                    ^ ^ [         R                  " T R                  S:  U 4S j5        [         R                  " TR                  S:  U4S j5        [        T TS5      u  p4[	        X4U5      $ )Nr3  c                  $   > ST R                    S3$ )Nz-b should have at least 2 dimensions, but has  dimensions insteadr   r   s   r:   r^    cholesky_solve.<locals>.<lambda>  s    ?		{J]^r=   c                  $   > ST R                    S3$ )Nz-u should have at least 2 dimensions, but has rH  rI  r  s   r:   r^   rJ    s    ?xGZ[r=   cholesky_solve)rO   ra   r   !_linalg_broadcast_batch_dims_namerE  )r   r  r,  self_broadcastedA_broadcasteds   ``   r:   rL  rL    sd     
LL		Q^ 
LL	![ 'Ha!'# ""25IIr=   c                     U R                  5       S:X  a#  [        R                  " U [        R                  S9$ [	        U S5        [        U 5      $ )Nr   r   cholesky)r   rO   r   legacy_contiguous_formatr   rC  r   r,  s     r:   rQ  rQ    s@     zz|qE4R4RSSdJ'"4((r=   c                 0    [        U S5        [        U 5      $ )Ncholesky_inverse)r   rC  rS  s     r:   rU  rU    s     d./"4((r=   check_errorsc                 
   [        U S5        [        U S5        U R                  n[        U5      n[	        US5      nU R                  U5      nUR                  X55        U R                  USUS-
   [        R                  S9nXg4$ )Nzlinalg.choleskyFr   r3  r   )	r   r   r   r   r    r   r  rO   r  )r  r,  rV  A_shaper   	L_stridesr)  infoss           r:   linalg_cholesky_exr[    s|    a*+1/0ggGw<D ,GU;I	GAMM'% KKD1H-U[[KAE8Or=   tauc                 J  ^ ^^ [         R                  " T R                  S:  S 5        [         R                  " T R                  S5      T R                  S5      :  S 5        [         R                  " T R                  S5      TR                  S5      :  S 5        [         R                  " T R                  TR                  -
  S:H  U U4S j5        T R                  S:  a<  T R                  S S nTR                  S S m[         R                  " TU:H  U4S	 j5        [         R                  " TR
                  T R
                  :H  U U4S
 j5        [        STT S5        [         R                  " T R                  [        T R                  SS9T R
                  T R                  S9$ )Nr3  c                      g)NzHtorch.linalg.householder_product: input must have at least 2 dimensions.rB   rB   r=   r:   r^   ,linalg_householder_product.<locals>.<lambda>      Zr=   r  r   c                      g)Nzbtorch.linalg.householder_product: input.shape[-2] must be greater than or equal to input.shape[-1]rB   rB   r=   r:   r^   r_    s    tr=   c                      g)Nz`torch.linalg.householder_product: input.shape[-1] must be greater than or equal to tau.shape[-1]rB   rB   r=   r:   r^   r_    s    rr=   r   c                  <   > STR                    ST R                    3$ )Nzptorch.linalg.householder_product: Expected tau to have one dimension less than input, but got tau.ndim equal to  and input.ndim is equal to rI  r  r\  s   r:   r^   r_    "    )),
2Nuzzl\r=   c                     > ST  3$ )Nzltorch.linalg.householder_product: Expected batch dimensions of tau to be equal to input.shape[:-2], but got rB   actual_batch_tau_shapes   r:   r^   r_        66L5MOr=   c                  <   > STR                    ST R                    3$ )Nz,torch.linalg.householder_product: tau dtype z does not match input dtype r   re  s   r:   r^   r_    s    :399+*5;;-9r=   z torch.linalg.householder_productr\  Fr3  r   r   rW   r   )
rO   ra   r   r   r   rW   r%  empty_stridedr    r   )r  r\  expected_batch_tau_shaperi  s   `` @r:   linalg_householder_productro    sK   
 
LL

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

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

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

SXX"	
 zzA~#(;;s#3 !$3B"&>>	
 
LL		U[[ 	
 6UEJ[[*5;;%Hkk||	 r=   c                    [        U S5        [        U SSS9  U R                  U R                  5      nUR	                  U R                  [        U R                  SS95        U R                  U R                  S S [        R                  S9nX#4$ )Nzlinalg.inv_exF)r  r3  r  r   r   r   r   r   r  r    rO   r  )r  rV  r)  rZ  s       r:   linalg_inv_ex_metarr    so    a)1o%P	AGGAMM!''6qww%PQKKEKKK8E8Or=   LDpivotsinfo)	hermitianrV  rv  c                t   [        U S5        [        U S5        [        R                  " U R                  [        U R                  SS9U R                  U R                  S9nU R                  U R                  S S [        R                  S9nU R                  U R                  S S [        R                  S9nX4U4$ )Nztorch.linalg.ldl_factor_exFr3  rl  r   r   r  )
r   r   rO   rm  r   r    rW   r   r   r)  )r   rv  rV  rs  rt  ru  s         r:   linalg_ldl_factor_ex_metarx  +  s     d894!=>			ZZ*4::Gjj{{	
B ^^DJJsO599^=F>>$**Sb/>;Dtr=   )rv  c                j  ^ ^^ [        T S5        [        T S5        [        TT S5        [        R                  " TR
                  S:  U4S j5        T R                  S S n[        R                  " UTR                  :H  U4S j5        [        R                  " [        R                  " TR                  5      U4S j5        [        R                  " T R                  TR                  :H  UU 4S j5        [        TT 5      u  pV[        R                  " U[        USS	9TR                  TR                  S
9$ )Nztorch.linalg.ldl_solver3  c                  $   > ST R                    S3$ )NzMtorch.linalg.ldl_solve: Expected B to have at least 2 dimensions, but it has rH  rI  )r  s   r:   r^   'linalg_ldl_solve_meta.<locals>.<lambda>N      &&!46r=   r   c                  $   > ST R                    S3$ )Nzjtorch.linalg.ldl_solve: Expected LD.shape[:-1] and pivots.shape to be the same, but got pivots with shape  insteadr   rt  s   r:   r^   r{  V      ))/h@r=   c                  "   > ST R                    3$ )Nz<torch.linalg.ldl_solve: Expected pivots to be integers. Got r   r  s   r:   r^   r{  ]  s    Nv||n]r=   c                  <   > STR                    ST R                    3$ )Nz!torch.linalg.ldl_solve: LD dtype z does not match b dtype r   )r  rs  s   r:   r^   r{  a  s     3BHH:=UVWV]V]U^_r=   Fr3  rl  )r   r   r  rO   ra   r   r   rG   is_integer_dtyperW   _linalg_broadcast_batch_dimsrm  r    r   )rs  rt  r  rv  expected_pivots_shapeB_broadcast_sizerJ   s   ```    r:   linalg_ldl_solve_metar  @  s     b232781b":;	LL	!	
 HHSbM	LL-	
 
LLv||,] 
LL
AGG_ 7q"=*+;uMggxx	 r=   Pr(  )pivotr  c                j  ^  [         R                  " T R                  S:  U 4S j5        [        T R                  5      nUS   nUS   n[        X45      nX2S'   U(       a  T R                  U5      nOT R                  S/5      nXRS'   T R                  U5      nXRS'   XBS'   T R                  U5      nXgU4$ )Nr3  c                  $   > ST R                    S3$ )Nz@linalg.lu: Expected tensor with 2 or more dimensions. Got size: r~  r   r  s   r:   r^    linalg_lu_meta.<locals>.<lambda>q  s    RSTSZSZR[[cdr=   r  r   r   )rO   ra   r   r	  r   r=  r   )	r  r  sizesr  rL  r  r  r)  r(  s	   `        r:   linalg_lu_metar  l  s     
LL	!d
 MEb	Ab	AA	A"IKKKK"I	EA"I"I	EA7Nr=   LU)r  rV  c                  ^  [         R                  " T R                  S:  U 4S j5        [        T R                  5      nUS   nUS   n[         R
                  " U[        USS9T R                  T R                  S9nUR                  5         [        XE5      US'   T R                  U[         R                  S9nUR                  5         T R                  U[         R                  S9nXgU4$ )	Nr3  c                  $   > ST R                    S3$ )NzFtorch.lu_factor: Expected tensor with 2 or more dimensions. Got size: r~  r   r  s   r:   r^   *linalg_lu_factor_ex_meta.<locals>.<lambda>  s    XYZY`Y`Xaaijr=   r  r   Fr3  rl  r   )rO   ra   r   r	  r   rm  r    rW   r   r5  r=  r   r)  )	r  r  rV  r  r  rL  r  rt  ru  s	   `        r:   linalg_lu_factor_ex_metar    s     
LL	!j
 MEb	Ab	A			*5EBggxx	
B 
IIKA	E"I[[eii[0F 
IIK;;uEII;.Dtr=   )r  adjointr  c                
  ^ ^^ [        T S5        [        R                  " T R                  TR                  :H  UU 4S j5        [        R                  " TR                  [        R                  :H  S 5        [        T S5        [        T TUS5        [        R                  " T R                  S5      TR                  S5      :H  S 5        [        R                  " T R                  S S TR                  :H  U4S j5        [        TT 5      u  pV[        R                  " U[        XS(       + S9TR                  TR                  S	9nUR                  5       S
:w  a,  U(       d%  UR                  5       (       a  UR                  5       nU$ )Nztorch.linalg.lu_solvec                  >   > STR                    ST R                    S3$ )NzPlinalg.lu_solve: Expected LU and B to have the same dtype, but found LU of type  and B of type r~  r   )r  r  s   r:   r^   &linalg_lu_solve_meta.<locals>.<lambda>  s#    $$&HH:_QWWIXOr=   c                      g)NzElinalg.lu_solve: pivots should be a Tensor of scalar type torch.int32rB   rB   r=   r:   r^   r    s    Wr=   zlinalg.lu_solver   c                      g)NzYlinalg.lu_solve: Number of pivots per batch should be same as the dimension of the matrixrB   rB   r=   r:   r^   r    s    kr=   c                  $   > ST R                    S3$ )Nzclinalg.lu_solve: Expected LU.shape[:-1] and pivots.shape to be the same, but got pivots with shape r~  r   r  s   r:   r^   r    r  r=   r3  rl  r   )r   rO   ra   rW   r)  r   r  r   r   r  rm  r    r   r   r.  conj)r  rt  r  r  r  r  rJ   r  s   ```     r:   linalg_lu_solve_metar    s-    267	LL
AGG	
 
LL		!W b12b!T#45	LL
v{{2&k 
LL
"%	
 7q"=  *+;xPggxx	F ||~4[[]FMr=   unpack_dataunpack_pivotsc                 6  ^  [         R                  " T R                  S:  U 4S j5        U(       a3  [         R                  " UR                  [         R                  :H  S 5        [        T R                  5      nUS   nUS   n[        XV5      nXTS'   U(       a  T R                  U5      nOT R                  S/5      nU(       a/  XtS'   T R                  U5      n	XtS'   XdS'   T R                  U5      n
O$T R                  S/5      n	T R                  S/5      n
XU
4$ )Nr3  c                  $   > ST R                    S3$ )NzFtorch.lu_unpack: Expected tensor with 2 or more dimensions. Got size: r~  r   )r  s   r:   r^    lu_unpack_meta.<locals>.<lambda>  s    XY[YaYaXbbjkr=   c                      g)Nztorch.lu_unpack: LU_pivots is expected to be a contiguous tensor of torch.int32 dtype.
Note: this function is intended to be used with the output produced by torch.linalg.lu_factorrB   rB   r=   r:   r^   r    s    pr=   r  r   r   )	rO   ra   r   rW   r  r	  r   r=  r   )r  rt  r  r  r  r  rL  r  r  r)  r(  s   `          r:   lu_unpack_metar    s     
LL
1k LLEKK'	
 NEb	Ab	AA	A"ILLLL!b	LLb	b	LLLL!LL!7Nr=   modec                    ^  T S:X  a  SnSnX4$ T S:X  a  SnSnX4$ T S:X  a  SnSnX4$ [         R                  " SU 4S j5        WW4$ )NreducedTcompleteFrc                     > ST  S3$ )Nzqr received unrecognized mode 'z=' but expected one of 'reduced' (default), 'r', or 'complete'rB   )r  s   r:   r^    _parse_qr_mode.<locals>.<lambda>  s    1$ 8N Or=   rO   ra   )r  	compute_qr  s   `  r:   _parse_qr_moder    s    y	  
		  
	  		
 gr=   QRc                    [        U S5        [        U S5        [        U5      u  p#U R                  S   nU R                  S   n[	        XE5      nU(       aO  [        U R                  5      nU(       a  UOUUS'   U R                  U5      nUR                  U[        USS95        OU R                  S/5      n[        U R                  5      n	U(       d  U(       d  UOUU	S'   U R                  U	5      n
U
R                  U	[        U	SS95        X4$ )Nz	linalg.qrr  r   Fr3  r   )	r  r   r  r   r=  r	  r   r  r    )r  r  r  reduced_moder  rL  r  Q_shaper  R_shaper  s              r:   linalg_qr_metar  $  s     ![!1k*,T2I	A	AA	Aqww-'aQKK 	g:7eTUKK 177mG#9!!GBK	GAMM'6w%PQ4Kr=   sign	logabsdetc                 t   [        U S5        [        U SS5        U R                  nU R                  US S 5      nU R                  US S [	        U R
                  5      S9n[        R                  " U[        US5      U R
                  U R                  S9nU R                  US S [        R                  S9nX#XE4$ )Nzlinalg.slogdetFr  r   rl  r   )r   r   r   r   rY   rW   rO   rm  r    r   r  )r  r   r  r  r  rt  s         r:   _linalg_slogdetr  @  s     a)*1.6GGE;;uSbz"DE#2Joagg.FGI			*5%8ggxx	
B [[s5;;[7FB&&r=   full_matrices
compute_uvdriverc                 b   [        U S5        [        U S5        [        U R                  S S 5      nU R                  S   nU R                  S   n[	        XV5      nU(       a  XEU(       a  UOU/-   nU R                  U5      n	U	R                  U[        USS95        XA(       a  UOUU/-   n
U R                  U
5      n[        U 5      S:H  nUR                  U
[        XS95        O$U R                  S/5      n	U R                  S/5      nU R                  XG/-   [        U R                  5      S9nXU4$ )	Nz
linalg.svdr  r   Fr3  r7  r   r   )r  r   r	  r   r=  r   r  r    r<  rY   rW   )r  r  r  r  r  r  rL  r  U_shaper(  V_shapeVis_cudaSs                 r:   _linalg_svd_metar  T  s    !\"1l+aggcrl#J	A	AA	A11==KK 	g:7eTU]1==KK 
 a.F*	g:7VW KKKK 	
J$OAGG,DEA7Nr=   arg1arg2c                    U R                   S S nUR                   S S n[        X#5      n[        U5      nXPR                  S5      U R                  S5      /-  n[        U5      nXaR                  S5      UR                  S5      /-  nXV4$ )Nr  r   )r   r)   r	  r   )r  r  arg1_batch_sizesarg2_batch_sizesexpand_batch_portionarg1_expand_sizearg2_expand_sizes          r:   r  r  z  s    
 zz#2zz#2,-=P012		"66012		"66--r=   c                     U(       a  [        XU5        [        X5      u  p4X0R                  :X  a  U OU R                  U5      nXAR                  :X  a  UOUR                  U5      nXV4$ r7   )r  r  r   expand)r  r  r  r  r  arg1_broadcastedarg2_broadcasteds          r:   rM  rM    sh     t40)Ed)Q& !JJ.DKK@P4Q  !JJ.DKK@P4Q  --r=   r   c                     U R                   S S nUR                  S:H  =(       d2    U R                  S-
  UR                  :H  =(       a    UR                   U:H  nU$ )Nr   r   )r   r   )r  r   expected_batched_rhs_shapevector_cases       r:   linalg_solve_is_vector_rhsr    sS    !&Sb!1**/ 

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

&#
&&&SMDAqa)MM!''188:.QuE " Jr=   )r  unitriangularr  r  r  c                   Uc  U R                  S/5      n[        U[        5      (       d   e[        XUS5        [	        XS 5      u  pgUR                  SS5      R                  5       =(       a    UR                  5       nU(       a  [        XVR                  5      nU$ [        XVR                  5      (       a=  UR                  UR                  SS5      R                  5        UR                  SS5        U$ )Nr   zlinalg.solve_triangularr  r   )r   rk   r#   r  rM  rB  r   is_conjr%   r   r&   r  
transpose_)	r  r  r,  r  r  r  r  A_avoid_copy_As	            r:   linalg_solve_triangular_metar    s     {kk1#c:&&&&aD";<.qT:FB<<B'557HBJJLLXX. J  XX..KKR,223NN2r"Jr=   XM)r  rB  c                   ^ ^ [         R                  " T R                  S:  U 4S j5        [         R                  " TR                  S:  U4S j5        [        T TS5        TR                  [         R
                  :X  aw  [        T T5      u  pV[         R                  " U[        USS9T R                  T R                  S9n[         R                  " U[        USS9TR                  TR                  S9nXx4$ TR                  [         R                  :X  d  TR                  [         R                  :X  a+  [         R                  " T 5      nT R                  S/5      nXx4$ [         R                  " SS	 5        WW4$ )
Nr3  c                  $   > ST R                    S3$ )NzMtorch.triangular_solve: Expected b to have at least 2 dimensions, but it has rH  rI  r   s   r:   r^   'triangular_solve_meta.<locals>.<lambda>  s    ))$79r=   c                  $   > ST R                    S3$ )NzMtorch.triangular_solve: Expected A to have at least 2 dimensions, but it has rH  rI  r  s   r:   r^   r    r|  r=   triangular_solveFr3  rl  r   c                      g)Nz+triangular_solve: Got an unexpected layout.rB   rB   r=   r:   r^   r  (  s    $Qr=   )rO   ra   r   r  r~   stridedr  rm  r    rW   r   
sparse_csr
sparse_bsrr   r   )	r   r  r,  rB  r  self_broadcast_sizeA_broadcast_sizesolutioncloned_coefficients	   ``       r:   triangular_solve_metar     sC    
LL		Q	
 
LL	!	
 4$67xx5== 0LTST0U-&&$./BeT**;;	
 #00!./?5Q''88	
 '' 
U%%	%U5E5E)E##D)!^^QC0 '' 	UQR'''r=   c                 ^   [        U S5        [        U S5        U R                  U R                  S S 5      nU R                  U R                  5      nUR	                  U R                  [        U R                  SS95        U R                  U R                  S S [        R                  S9nXU4$ )Nz
linalg.detr  Fr3  r   r   rq  )r  detr  rt  s       r:   _linalg_det_metar  -  s    a&1l+
++aggcrl
#C	
QWW	BNN17775QR[["U[[[9FF?r=   c                 X  ^ ^^^^^ [         R                  " T R                  S:  S 5        [         R                  " TR                  S:  S 5        U(       a  SOSm[         R                  " TR                  T   TR                  S   :  U4S j5        [         R                  " TR                  T   T R                  S   :H  U4S j5        [         R                  " TR                  S   T R                  S   :*  S 5        [         R                  " T R                  TR                  -
  S	:H  U U4S
 j5        [         R                  " T R                  TR                  :H  U U4S j5        T R                  S:  ai  T R                  S S nTR                  S S m[         R                  " TU:H  U4S j5        TR                  S S m[         R                  " TU:H  U4S j5        [         R                  " TR                  T R                  :H  U U4S j5        [         R                  " TR                  T R                  :H  U U4S j5        [        STT S5        [        STT S5        [         R                  " TR                  [        TR                  SS9TR                  TR                  S9$ )Nr3  c                      g)Nz3torch.ormqr: input must have at least 2 dimensions.rB   rB   r=   r:   r^   ormqr.<locals>.<lambda>E      !Vr=   c                      g)Nz3torch.ormqr: other must have at least 2 dimensions.rB   rB   r=   r:   r^   r  H  r  r=   r  r   c                     > ST  S3$ )Ntorch.ormqr: other.shape[z0] must be greater than or equal to tau.shape[-1]rB   left_size_conditions   r:   r^   r  N  s    +,?+@@pqr=   c                     > ST  S3$ )Nr
  z"] must be equal to input.shape[-2]rB   r  s   r:   r^   r  R  s    +,?+@@bcr=   c                      g)NzHtorch.ormqr: tau.shape[-1] must be less than or equal to input.shape[-1]rB   rB   r=   r:   r^   r  W  r`  r=   r   c                  <   > STR                    ST R                    3$ )Nz[torch.ormqr: Expected tau to have one dimension less than input, but got tau.ndim equal to rd  rI  re  s   r:   r^   r  \  rf  r=   c                  <   > STR                    ST R                    3$ )Nzhtorch.ormqr: Expected other to have the same number of dimensions as input, but got other.ndim equal to rd  rI  r  r   s   r:   r^   r  c  s&    ++0::,6RSXS]S]R^`r=   c                     > ST  3$ )NzWtorch.ormqr: Expected batch dimensions of tau to be equal to input.shape[:-2], but got rB   rh  s   r:   r^   r  n  rj  r=   c                     > ST  3$ )NzYtorch.ormqr: Expected batch dimensions of other to be equal to input.shape[:-2], but got rB   )actual_batch_other_shapes   r:   r^   r  w  s    66N5OQr=   c                  <   > ST R                    STR                    3$ )NzPtorch.ormqr: Expected input and tau to have the same dtype, but input has dtype z and tau has dtype r   re  s   r:   r^   r    s"    ##(;;-/B399+Or=   c                  <   > ST R                    STR                    3$ )NzRtorch.ormqr: Expected input and other to have the same dtype, but input has dtype z and other has dtype r   r  s   r:   r^   r    s"    ##(;;-/DU[[MSr=   ztorch.ormqrr\  r   Fr3  rl  )	rO   ra   r   r   rW   r%  rm  r    r   )	r  r\  r   r  rB  expected_batch_shaper  ri  r  s	   ```   @@@r:   ormqrr  ;  s    
LL

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

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

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

ejj 	
 zzA~${{3B/!$3B"&::	
 $);;s#3 $(<<	
 
LL		U[[ 	
 
LLu{{"	
 M3u5M5%9[[*5;;%Hkk||	 r=   c                  ^ ^^ [         R                  " [        T5      ST-  :H  UU4S j5        T R                  nUTS-   :H  nUnU(       + nU(       a1  [	        SU5       H   nU=(       a    T R                  U5      S:g  nM"     O0[	        SU5       H   nU=(       a    T R                  U5      S:g  nM"     [         R                  " U=(       d    UUU 4S j5        g )Nr3  c                  ,   > SST -   S[        T5       3$ )Nzpadding size is expected to be r3  z, but got: r   )r   paddings   r:   r^   ,_padding_check_valid_input.<locals>.<lambda>  s    1!c'+c'l^Tr=   r   r   c                  :   > ST S-    ST S-    STR                    3$ )N	Expected r   zD or r3  zcD (batch mode) tensor with possibly 0 batch size and other non-zero dimensions for input, but got: r   )r   r  s   r:   r^   r    s-    aycAgY /AAFOr=   )rO   ra   r   r   r   r   )r  r  r   	input_dimis_batch_modevalid_batch_modevalid_non_batch_moder  s   ```     r:   _padding_check_valid_inputr$    s    	LLGCT
 

I#'*M$,,q)$A/FEJJqMQ4F % q)$A#7#NEJJqMQ<N  % 
LL00	
r=   c                  ^ ^^^^	^
 SnSmSnT R                   S:X  a  T R                  S5      nTS-  mUS-  n[        T USS9  Uu  m	m
T R                  U5      nT R                  T5      mTT	-   T
-   mU(       a-  [        R                  " T	T:  =(       a    T
T:  UU U	U
4S j5        [        R                  " TS:  UU4S j5        T R                   S:X  a  T R                  UT45      $ T R                  XET45      $ )Nr   r   r2   r   c                  4   > ST ST ST  STR                    3$ NzcArgument #4: Padding size should be less than the corresponding input dimension, but got: padding (rt   ) at dimension 
 of input r   dim_wr  pad_lpad_rs   r:   r^   _pad1d_common.<locals>.<lambda>  -    %%*G2eWOE7*UZU`U`Tacr=   c                     > ST  ST 3$ )Nz
input (W: z%) is too small. Calculated output W: rB   )input_woutput_ws   r:   r^   r.    s    *WI%J8*Ur=   r3  )r   r   r$  rO   ra   r   )r  r  is_reflection	dim_planenbatchnplaner+  r1  r2  r,  r-  s   `     @@@@@r:   _pad1d_commonr7    s    IEFzzQA
Q	ug15LE5ZZ	"FjjG&HGO/	
 
LLAU
 zzQ1229::r=   c                     [        XSS9$ NTr3  )r7  r  r  s     r:   meta_reflection_pad1dr<         t<<r=   c                    ^  [         R                  " T R                  [         R                  :g  U 4S j5        [	        T USS9$ )Nc                  @   > ST R                   R                  5        S3$ )Nz)"replication_pad1d" not implemented for ''rW   __str__r  s   r:   r^   (meta_replication_pad1d.<locals>.<lambda>      =ekk>Q>Q>S=TTUXr=   Fr:  )rO   ra   rW   boolr7  r;  s   ` r:   meta_replication_pad1drG    5     
LLuzz!X u==r=   c                  ^ ^^^^^ SmU(       d$  [         R                  " [        U5      S:H  S 5        TR                  S:X  a  TS-  mUu  mmTR	                  T5      nUT-   T-   mU(       a-  [         R                  " TU:  =(       a    TU:  UUUU4S j5        [         R                  " TT R	                  T5      :H  UU U4S j5        TR                  TR                  5      $ )Nr   r3  c                      g)Nz padding size is expected to be 2rB   rB   r=   r:   r^   (_pad1d_backward_common.<locals>.<lambda>  s    0Rr=   r2   c                  4   > ST ST ST  STR                    3$ r'  r   r*  s   r:   r^   rK    r/  r=   c                  2   > ST STR                  T 5       3$ Nz(grad_output width unexpected. Expected: , Got: r   r+  grad_outputr2  s   r:   r^   rK         :8*GKL\L\]bLcKder=   rO   ra   r   r   r   r   r   )	rQ  r  r  r3  r1  r+  r2  r,  r-  s	   ``   @@@@r:   _pad1d_backward_commonrT    s    ES\Q&(RSzzQ
LE5jjG&HGO/	
 
LLK$$U++e
 ??5;;''r=   
grad_inputc                     [        XUSS9$ r9  rT  rQ  r  r  s      r:   meta_reflection_pad1d_backwardrY  
  s     "+gTRRr=   c                     [        XUSS9$ )NFr:  rW  rX  s      r:   meta_replication_pad1d_backwardr[    s     "+gUSSr=   c                  ^ ^^^	^
^^^^^^ SmSmSnSn[        T USS9  T R                  nUS:X  a   T R                  S5      nTS-  mTS-  mUS-  nUu  mmmmT R                  U5      nT R                  T5      m	T R                  T5      m
T	T-   T-   mT
T-   T-   mU(       aZ  [        R                  " TT
:  =(       a    TT
:  UU UU4S j5        [        R                  " TT	:  =(       a    TT	:  UU UU4S j5        [        R                  " TS:  =(       d    TS:  U	U
UU4S j5        T R                  S	:X  a  T R                  UTT45      $ T R                  XFTT45      $ )
Nr3  r   r   r      c                  4   > ST ST ST  STR                    3$ r'  r   r*  s   r:   r^   _pad2d_common.<locals>.<lambda>0  r/  r=   c                  4   > ST ST ST  STR                    3$ NzcArgument #6: Padding size should be less than the corresponding input dimension, but got: padding (rt   r(  r)  r   dim_hr  pad_bpad_ts   r:   r^   r_  7  r/  r=   c                      > ST  ST ST ST 3$ )Nz
input (H:  W: z%) is too small. Calculated output H: rB   )input_hr1  output_hr2  s   r:   r^   r_  ?  s%    	gY /$$,:T(=r=   r2   r$  r   r   rO   ra   r   )r  r  r3  
dim_slicesr5  r   r6  rc  r+  rh  r1  ri  r2  rd  r,  r-  re  s   `      @@@@@@@@@@r:   _pad2d_commonrl    sS   EEJFug15::DqyA

a
!(E5%ZZ
#FjjGjjG&H&HGO/	
 	GO/	
 
LLA&Q	
 zzQ(;<<(CDDr=   c                     [        XSS9$ r9  )rl  r;  s     r:   meta_reflection_pad2drn  K  r=  r=   c                    ^  [         R                  " T R                  [         R                  :g  U 4S j5        [	        T USS9$ )Nc                  @   > ST R                   R                  5        S3$ )Nz)"replication_pad2d" not implemented for 'r@  rA  rC  s   r:   r^   (meta_replication_pad2d.<locals>.<lambda>V  rE  r=   Fr:  )rO   ra   rW   rF  rl  r;  s   ` r:   meta_replication_pad2drr  Q  rH  r=   c                   ^ ^^^^ SmSmSnUR                   nUR                  5       S:X  a  TS-  mTS-  mUS-  nUu  pVpxUT   n	UT   n
X-   U-   mX-   U-   m[        R                  " TT R	                  T5      :H  UU U4S j5        [        R                  " TT R	                  T5      :H  UU U4S j5        UR                  UR                   5      $ )Nr3  r   r   r]  c                  2   > ST STR                  T 5       3$ rN  r   rP  s   r:   r^   %meta_pad2d_backward.<locals>.<lambda>x  rR  r=   c                  2   > ST STR                  T 5       3$ Nz)grad_output height unexpected. Expected: rO  r   rc  rQ  ri  s   r:   r^   ru  |       ;H:W[M]M]^cMdLefr=   )r   r   rO   ra   r   r   )rQ  r   r  r4  r]   r,  r-  re  rd  rh  r1  rc  r+  ri  r2  s   `          @@@@r:   meta_pad2d_backwardrz  [  s     EEIJxxzQ

Q	!(E%GG&H&H	LLK$$U++e 
LLK$$U++f >>$**%%r=   c          	      ~  ^ ^^^	^
^^^^^^^^^^^ Sm	SmSmSn[        T USS9  T R                  S:H  nU(       a%  T R                  S5      nT	S-  m	TS-  mTS-  mUS-  nUu  mmmmmmT R                  U5      nT R                  T5      m
T R                  T5      mT R                  T	5      mT
T-   T-   mTT-   T-   mTT-   T-   mU(       a  [        R                  " TT:  =(       a    TT:  U	U UU4S j5        [        R                  " TT:  =(       a    TT:  UU UU4S j5        [        R                  " TT
:  =(       a    TT
:  UU UU4S	 j5        [        R                  " TS:  =(       d    TS:  =(       d    TS:  U
UUUUU4S
 j5        U(       a  T R                  WUTTT45      $ T R                  UTTT45      $ )Nr2   r3  r   r   r      c                  4   > ST ST ST  STR                    3$ r'  r   r*  s   r:   r^   _pad3d_common.<locals>.<lambda>  r/  r=   c                  4   > ST ST ST  STR                    3$ ra  r   rb  s   r:   r^   r~    r/  r=   c                  4   > ST ST ST  STR                    3$ )NzcArgument #8: Padding size should be less than the corresponding input dimension, but got: padding (rt   r(  r)  r   )dim_dr  pad_bkpad_fs   r:   r^   r~    s-    %%*G2fX_UG:V[VaVaUbdr=   c                  ,   > ST  ST ST ST ST ST 3$ )Nz
input (D:  H: rg  z%) is too small. Calculated output D: rB   )input_drh  r1  output_dri  r2  s   r:   r^   r~    s2    	gYd7) <$$,:T(4zKr=   rj  )r  r  r3  r4  
batch_moder5  r6  r  rc  r+  r  rh  r1  r  ri  r2  rd  r  r  r,  r-  re  s   `      @@@@@@@@@@@@@@@r:   _pad3d_commonr    s   EEEIug15qJA


Q	07-E5%vZZ	"FjjGjjGjjG'H&H&HGO/	
 	GO/	
 	GO0 0	
 
LLA7Q7(a-	
 	
 (HMNN(HEFFr=   c                     [        XSS9$ r9  )r  r;  s     r:   meta_reflection_pad3dr    r=  r=   c                    ^  [         R                  " T R                  [         R                  :g  U 4S j5        [	        T USS9$ )Nc                  @   > ST R                   R                  5        S3$ )Nz)"replication_pad3d" not implemented for 'r@  rA  rC  s   r:   r^   (meta_replication_pad3d.<locals>.<lambda>  rE  r=   Fr:  )rO   ra   rW   rF  r  r;  s   ` r:   meta_replication_pad3dr    rH  r=   c                   ^ ^^^^^^ [         R                  " [        U5      S:H  S 5        UR                  S:  d   eT R                  UR                  :X  d   eSmSmSmUR                  S:X  a  TS-  mTS-  mTS-  mUu  p4pVpxUR	                  T5      n	UR	                  T5      n
UR	                  T5      nX-   U-   mX-   U-   mX-   U-   m[         R                  " TT R	                  T5      :H  UU U4S j5        [         R                  " TT R	                  T5      :H  UU U4S j5        [         R                  " TT R	                  T5      :H  UU U4S	 j5        UR                  UR                  5      $ )
N   c                      g)Nz padding size is expected to be 6rB   rB   r=   r:   r^   %meta_pad3d_backward.<locals>.<lambda>  s    ,Nr=   r2   r3  r   r|  c                  2   > ST STR                  T 5       3$ rN  r   rP  s   r:   r^   r    rR  r=   c                  2   > ST STR                  T 5       3$ rw  r   rx  s   r:   r^   r    ry  r=   c                  2   > ST STR                  T 5       3$ )Nz(grad_output depth unexpected. Expected: rO  r   )r  rQ  r  s   r:   r^   r    rR  r=   rS  )rQ  r  r  r,  r-  re  rd  r  r  r  rh  r1  r  rc  r+  r  ri  r2  s   `           @@@@@@r:   meta_pad3d_backwardr    sS    
LLW"$NO::>>uzz)))EEEzzQ


07-E%jjGjjGjjG'H&H&H	LLK$$U++e 
LLK$$U++f 
LLK$$U++e
 ??5;;''r=   pc                 @   [         R                  " U R                  5       S 5        U R                  S5      nUS::  a-  U R	                  S/5      R                  [         R                  S9$ U R	                  X"S-
  -  S-  45      R                  [         R                  S9$ )Nc                      g)Nz(_pdist_forward requires contiguous inputrB   rB   r=   r:   r^   %meta__pdist_forward.<locals>.<lambda>	  s    &Pr=   r   r   r   r3  )rO   ra   r   r   r   rl  rR  )r   r  rL  s      r:   meta__pdist_forwardr   	  s     
LLP 			!AAv~~qc"%%E4R4R%SS~~qE{a/125588 6 
 	
r=   gradpdistc                     [         R                  " UR                  5       S 5        [         R                  " UR                  5       S 5        [         R                  " U[         R                  S9$ )Nc                      g)Nz._pdist_backward requires self to be contiguousrB   rB   r=   r:   r^   &meta__pdist_backward.<locals>.<lambda>	  s    &Vr=   c                      g)Nz/_pdist_backward requires pdist to be contiguousrB   rB   r=   r:   r^   r  	  s    'Xr=   r   )rO   ra   r   r   rR  )r  r   r  r  s       r:   meta__pdist_backwardr  	  sW     
LLV 
LLX D0N0NOOr=   )r  r  c          
      b  ^ ^^^^^ SSK JnJn  TR                  S5      nTR                  S5      nTR                  S5      n	U" [        R
                  " U" T R                  XxU	45      5      5      (       a  T R                  XxU	45      m [        R                  " TR                  5       S:H  S 5        [        R                  " TR                  5       S:H  S 5        [        R                  (       dN  [        R                  " T R                  TR                  s=:H  =(       a    TR                  :H  Os  UUU 4S j5        TR                  n
TR                  mU
S   mU
S   m[        R                  " TS   T:H  =(       a    TS   T:H  UUU4S	 j5        T R                  T R                  5       5      $ )
Nr   )r   r   r   r3  r2   c                      gNzbatch1 must be a 3D tensorrB   rB   r=   r:   r^   meta_baddbmm.<locals>.<lambda>%	      ,Hr=   c                      gNzbatch2 must be a 3D tensorrB   rB   r=   r:   r^   r  &	  r  r=   c                  V   > STR                    ST R                    STR                    3$ )Nz+Input dtypes must be the same, got: input: z
, batch1: z
, batch2: r   )batch1batch2r   s   r:   r^   r  *	  s.    A$**ZX^XdXdWeeopvp|p|o}~r=   c            	      .   > ST ST ST S    ST S    S3	$ Nz@Expected size for first two dimensions of batch2 tensor to be: [rt   z] but got: [r   r   ].rB   batch2_sizesbscontraction_sizes   r:   r^   r  2	  s5    t2&'|LO3DB|TUFWWY[r=   )r   r   r   r   rO   sym_notr   r  ra   r   
exp_config&skip_dtype_check_in_meta_registrationsrW   r   )r   r  r  r  r  r   r   dim1dim2dim3batch1_sizesr  r  r  s   ```        @@@r:   meta_baddbmmr  	  s9    L;;q>D;;q>D;;q>DU]]6$**t46H#IJKK{{D-.	LL"$HI	LL"$HI<<JJ&,,66&,,6~	
 <<L<<L	aB#A	LLQ2E,q/5E"E	
 >>$))+&&r=   c                H    [         R                  " U [         R                  S9$ r   r  r   rI  s     r:   meta_bernoullir  :	  s     D0G0GHHr=   c                     U $ r7   rB   r   r  rI  s      r:   meta_bernoulli_r  A	      Kr=   c                 H    [         R                  " U [         R                  S9$ r   r  r  s      r:   meta_bernoulli_pr  F	  s     D0G0GHHr=   c                 .    [         R                  " U 5      $ r7   rO   r   r  s     r:   meta_poissonr  L	       D!!r=   c                     [         R                  " XR                  5       :  S 5        [         R                  " U [         R                  S9n[         R                  " U 5      U4$ )Nc                      g)NzJError in fused_moving_avg_obs_fake_quant_cpu: ch_axis must be < self.dim()rB   rB   r=   r:   r^   6meta__fused_moving_avg_obs_fq_helper.<locals>.<lambda>d	      \r=   r   )rO   ra   r   r   rF  )r   observer_onfake_quant_onrunning_minrunning_maxscale
zero_pointaveraging_const	quant_min	quant_maxch_axisper_row_fake_quantsymmetric_quantmasks                 r:   $meta__fused_moving_avg_obs_fq_helperr  R	  sM      
LL((*\ D

3DT"D))r=   c                 P  ^^^^ [         R                  " U R                  5       S:H  S 5        [         R                  " UR                  5       S:H  S 5        U R                  u  mmUR                  u  mm[         R                  " TT:H  UUUU4S j5        U R	                  TT5      $ )Nr3  c                      g)Nza must be 2DrB   rB   r=   r:   r^   meta_mm.<locals>.<lambda>m	      ~r=   c                      g)Nzb must be 2DrB   rB   r=   r:   r^   r  n	  r  r=   c            	      "   > ST ST  ST ST S3	$ )Nz/a and b must have same reduction dim, but got [rt   z] X [r  rB   )M1M2Nr  s   r:   r^   r  s	  s&    A!Brd%PRtSUVWUXXZ[r=   )rO   ra   r   r   r   )r   br  r  r  r  s     @@@@r:   meta_mmr  j	  sz     
LLA56	LLA56GGEArGGEB	LL
b[ ;;q!r=   c                    ^ ^ U(       a)  [        UU 4S j[        T R                  5       5       5      $ [        R                  " T R
                  T5      $ )Nc              3   P   >#    U  H  oT;  a  TR                   U   OS v   M     g7f)r   Nr   )rm   r!  dimsr   s     r:   ro   +_compute_reduction_shape.<locals>.<genexpr>z	  s$     UDTqtmTZZ]:DTs   #&)r`   r   r   rG   compute_reduction_output_shaper   )r   r  r  s   `` r:   r  r  x	  s7    UE$))DTUUU//

DAAr=   c                 :   [        U [        R                  R                  5      (       a  U R                  R
                  $ [        U S5      (       aK  [        U R                  S5      (       a0  U R                  R
                  S:w  a  U R                  R
                  $ g)Nr   rv   r|   r7  )rk   rO   _subclasses
FakeTensorfake_devicerv   hasattrr   )rv  s    r:   r<  r<  	  sp    &%++6677!!&&&!!FMM6**MM&(}}!!!r=   input_tensorr   r  dilationis_transposedgroupsoutput_paddingc                 P  ^^ S[         S[         S[         S[         S[         S[         4S jnS[         S[         S[         S[         S[         S[         S[         4S	 jn	UR                  S
S  n
U R                  S
S  mU(       a  XaR                  S   -  nO=UR                  S   nUR                  S   U-  U R                  S   :w  a  [        S5      eU R                  S   U/m[        U[        5      (       a  U/[        T5      -  nO![        U5      S:X  a  US   /[        T5      -  n[        U[        5      (       a  U/[        T5      -  nO![        U5      S:X  a  US   /[        T5      -  n[        U[        5      (       a  U/[        T5      -  nO![        U5      S:X  a  US   /[        T5      -  nS nU(       aI  [        U[        5      (       a  U/[        T5      -  nO$[        U5      S:X  a  US   /[        T5      -  nOUn[        [        T5      5       H[  nU(       a+  TR                  U	" TU   X=   XM   X   X-   X   5      5        M5  TR                  U" TU   X=   XM   X   X-   5      5        M]     [        R                  " [        S TS
S   5       5      UU4S j5        T$ )Nlnr  r  r  r   r3   c                 4    U SU-  -   X#S-
  -  -
  S-
  U-  S-   $ )aE  
Formula to apply to calculate the length of some dimension of the output

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

Args:
    ln: length of the dimension
    p: padding in that dim
    d: dilation in that dim
    k: kernel size in that dim
    s: stride in that dim
Returns:
    The output length
r3  r   rB   )r  r  r  r  r   s        r:   _formula+calc_conv_nd_return_shape.<locals>._formula	  s,     QU
Qa%[(1,2Q66r=   r8   c                 :    U S-
  U-  SU-  -
  X#S-
  -  -   U-   S-   $ )a  
Formula to apply to calculate the length of some dimension of the output
if transposed convolution is used.
See: https://pytorch.org/docs/stable/generated/torch.nn.ConvTranspose2d.html

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

Returns:
    The output length
r   r3  rB   )r  r  r  r  r   r8   s         r:   _formula_transposed6calc_conv_nd_return_shape.<locals>._formula_transposed	  s0    " Q!|a!e#aq5k1B6::r=   r3  r   r   zInvalid channel dimensionsc              3   *   #    U  H	  oS :  v   M     g7fr   NrB   r  s     r:   ro   ,calc_conv_nd_return_shape.<locals>.<genexpr>	  s     )=aE=   c                  .   > S[        T 5       STSS   S3$ )NzGiven input size per channel: z&. Calculated output size per channel: r3  z. Output size is too small)r	  )r  	ret_shapes   r:   r^   +calc_conv_nd_return_shape.<locals>.<lambda>	  s(    0d =//8}o >#$r=   )r)  r   rk  rk   r   r   r   r
  rO   ra   r   )r  r~  r   r  r  r  r  r  r  r  kernel_sizeout_channelsoutput_padding_listr!  r  r  s                 @@r:   calc_conv_nd_return_shaper  	  s   7S 7S 7S 7S 7S 7S 7"; ; ; ; ; ; ;QT ;& ,,qr"Kab!DQ/||A<<?V#|'9'9!'<<;<<##A&5I&'""CI%	V	)s4y('7##)c$i'	W	1:,T*(G$$:D	)	X!	QK=3t9,/3ng..#1"2SY"> A%#1!#4"5D	"A"03t9#GJKNI'*	 a'*hk;>69U $ 
LL)9QR=))	$ r=   c                 b    [         R                  R                  U 5      [         R                  :H  $ r7   rO   _prims_commonr"   channels_lasttens    r:   is_channels_lastr  	  s$    44S9U=P=PPPr=   running_meanrunning_vartrainingexponential_average_factorepsilonc                 z  ^  T R                   nUb  UR                   OUR                   n	Ub  UR                   OUR                   n
U 4S jnT R                  U5      R                  U" 5       S9nU(       a#  T R                  U	5      nT R                  U
5      nO"T R                  S5      nT R                  S5      nXU4$ )Nc                     > [        T 5      (       a  [        R                  $ T R                  [        R                  S9(       a  [        R                  $ [        R                  $ r   )r  rO   r  r   r   )r  s   r:   pick_memory_format2meta_miopen_batch_norm.<locals>.pick_memory_format
  sI    L))&&&%%E4K4K%L***&&&r=   r   r   )r   r   rl  )r  r~  r  r  r  r  r  r  r   save_mean_shapesave_var_shaper  r  	save_meansave_vars   `              r:   meta_miopen_batch_normr   
  s     ""I -9,Dl((&,,O*5*A[&&v||N' 
 
 
+
.
.=O=Q
.
RC **?;	)).9 **40	))$/8##r=   c	           
         ^ ^ U U4S jn	[        T TUUUUUU(       a  UOS 5      n
SnSnT R                  U5      S:X  a  SX'   T R                  U
5      nUR                  U	" 5       S9nU$ )Nc                    > [        T 5      S:X  a1  [        T 5      (       d  [        T5      (       a  [        R                  $ O [        T 5      (       a  [        R                  $ T R	                  [        R
                  S9(       a  [        R
                  $ T R	                  [        R                  S9(       a  [        R                  $ g Nr7  r   )r<  r  rO   r  r   r   preserve_format)r  r~  s   r:   r  %meta_conv.<locals>.pick_memory_format2
  s    |$.--1A&1I1I*** 2J  --***%%E4K4K%L***''e6K6K'L((( Mr=   r   r   r   )r  r   r   rl  )r  r~  r  r   r  r  r  r  r  r  	shape_outinput_channels_dimoutput_channels_dimr  s   ``            r:   	meta_convr'  &
  s    
) *'T	I +,1)*	&

 
 
+C
&&13&
4CJr=   mkldnnc
           
          [        XXCUSU/ 5      n
U R                  U
5      n[        R                  nU R	                  5       S:X  a  [        R
                  nUR                  US9nU$ )NFr|  r   )r  r   rO   r  r   channels_last_3drl  )r  r~  r  r  r   r  r  attrscalars	algorithmr$  r  out_memory_formats                r:   meta_mkldnn_convolution_defaultr/  X
  sl     .&8UFB
	 $$Y/!//" % 6 6ff#4f5
r=   c                 b    U R                  / U R                  S S QUR                  S   P75      $ Nr   r   r   r   )r  r~  r  r+  r,  r-  s         r:   meta_linear_pointwise_defaultr3  o
  s5     %%&Q(:(:3B(?&Qa&QRRr=   mklc                 b    U R                  / U R                  S S QUR                  S   P75      $ r1  r2  )r  packed_weightorig_weightr  r  s        r:   meta_mkl_linearr8  z
  s:    ))@,$$Sb)@;+<+<Q+?@ r=   onednnc           
      z   [        U UUUU	SU
S 5      nU[        R                  [        R                  [        R                  [        R
                  4;   d   eU R                  UUS9n[        U5      S;   d   S5       e[        U5      S:X  a  [        R                  O[        R                  nUR                  US9nU$ )NFr   r2   r]  zonly conv1d/2d are supportedr]  r   )r  rO   r  r  uint8r  r   r   r  r   rl  )rL   x_scalex_zpww_scalew_zpr  r   r  r  r  output_scaleoutput_zero_pointoutput_dtyper+  r,  r-  r$  r  formats                       r:   meta_qconv_pointwiserF  
  s    * .	
	 u~~u{{EJJWWWWkk)<k89~'G)GG'(+I!(;$$AXAXff6f*
r=   c                     US:X  d   eU$ )NsumrB   )rL   r=  r>  r?  r@  rA  accumr  r   r  r  r  rB  rC  rD  accum_scaleaccum_zero_pointbinary_op_namer  unary_op_nameunary_op_argsunary_op_algorithms                         r:   meta_qconv2d_pointwise_binaryrP  
  s    2 &&&r=   c                     [        U R                  5      nUR                  S   US'   U	[        R                  [        R                  [        R
                  [        R                  4;   d   eU R                  XS9nU$ )Nr   r   r   )r	  r   rO   r  r  r  r<  r   )rL   r=  r>  r?  r@  rA  r  rB  rC  rD  post_op_namepost_op_argspost_op_algorithmr  r  s                  r:   meta_qlinear_pointwiserU  
  s_    " AGG}771:Ru~~uzz5;;WWWWkk,k;
r=   c                    US:X  a  U$ [        U R                  5      nUR                  S   US'   U
[        R                  [        R                  [        R
                  [        R                  4;   d   eU R                  UU
S9nU$ )NrH  r   r   r   )r	  r   rO   r  r  r<  r  r   )rL   r=  r>  r?  r@  rA  x_2r  rB  rC  rD  x2_scalex2_zprL  r  rM  rN  rO  r  r  s                       r:   meta_qlinear_pointwise_binaryrZ  
  sn    , U"JAGG}771:Ru~~u{{EJJWWWWkk,lk;
r=   c                 v    [        U R                  5      nUR                  S   US'   U R                  U5      nU$ )Nr   r   )r	  r   r   )rL   r?  r  r  r  s        r:   meta_linear_dynamic_fp16r\  
  s6     AGG}771:Rkk,'
r=   	quantizedr  r   c                 "   [        XX#XE5      u  nnnU R                  5       S:X  a  U R                  S5      OSn	[        R                  n
U R                  5       S:X  a  XgU/nOXXx/n[        R
                  " UU R                  U R                  U
S9$ Nr]  r   r2   r  )#max_pool2d_checks_and_compute_shaper   r   rO   r  r   rW   r   r  r  r   r  r  	ceil_modenInputPlaneoutputHeightoutputWidthr5  r   r   s               r:   meta_quantized_max_pool2drh    s     0
		
 $)99;!#3B++99;!{;DCD{{++<<'	
 	
r=   c                    [         R                  " U R                  5       S:H  SU R                  5        S35        [         R                  " UR                  5       S:H  SUR                  5        S35        [         R                  " U R                  [         R                  [         R
                  [         R                  4;   SU R                   35        [         R                  " UR                  [         R                  :H  SUR                   35        [         R                  " UR                  [         R                  :H  SUR                   35        [         R                  " UR                  U R                  :H  SUR                   35        U R                  U R                  S	5      UR                  S	5      U R                  S
9$ )Nr3  zx must be a 2D tensor, got Dzw must be a 2D tensor, got #expected x to be f32/f16/bf16, got expected w to be uint8, got z q_group_size must be int64, got z5q_scale_and_zeros must have the same dtype as x, got r   r   )rO   ra   r   rW   r  r  r  r<  r   r   r   rL   r?  q_group_sizeq_scale_and_zeross       r:   meta_int4mm_packed_weight_cpurp  +  s@   QUUW\%@	#KLQUUW\%@	#KLGGu}}ennEE1!'';	
 	QWW+/KAGG9-UV%++-.|/A/A.BC	
 	##qww.CDUD[D[C\]	
 {{166!9affQiqww{??r=   c                    ^ ^^^ [         R                  " T R                  5       T:H  =(       a    T R                  T   T:H  UUUU 4S j5        g )Nc                  j   > ST  ST ST S3STR                  5        ST STR                  T    3-   $ )NzExpected a tensor of dimension z and tensor.size[z] == rt   zbut got : dimension z] = r   r   )r   dim_sizer   rv  s   r:   r^    check_dim_size.<locals>.<lambda>C  sN    1#6GzQVW[V\\^_ .?zfll[cNdMe
fgr=   )rO   ra   r   r   )rv  r   rt  r   s   ````r:   check_dim_sizerv  @  s6    	LL

>X 6$ >	gr=   c                   ^  S nU" SU5      u  p[         R                  " [        U5      S;   S 5        [         R                  " T R                  [         R                  [         R
                  [         R                  [         R                  4;  U 4S j5        [        U5      S:X  a  XpO$[        U5      S:X  a
  US   US   pOU" SU5      u  pU" S	U5      u  p[         R                  " US L =(       d    US:g  S
 5        T R                  5       S:X  a  T R                  S5      OSnT R                  S5      nT R                  S5      nT R                  S5      n[        UXU
SU5      n[        UXUSU5      n[        R                  " T 5      n[        T UU	U
UUUSSUUUUUU5        T R                  5       S:X  a  UUU/nOXUU/n[         R                  " UT R                  T R                  US9$ )Nc                    ^  [         R                  " [        U5      S;   U 4S j5        US   n[        U5      S:X  a  UOUS   nX#4$ )Nr   r3  c                     > ST  S3$ )Nzavg_pool2d: 4 must either be a single int, or a tuple of two intsrB   r  s   r:   r^   1meta_avg_pool2d.<locals>.unpack.<locals>.<lambda>U      l4&(\]r=   r   r   rO   ra   r   r  r  HWs   `   r:   unpackmeta_avg_pool2d.<locals>.unpackR  E    H]	
 FSQACFtr=   r  r   r   r3  c                      gNzOavg_pool2d: stride must either be omitted, a single int, or a tuple of two intsrB   rB   r=   r:   r^   !meta_avg_pool2d.<locals>.<lambda>^      ar=   c                  @   > ST R                   R                  5        S3$ )Nz""avg_pool2d" not implemented for 'r@  rA  rC  s   r:   r^   r  b      6u{{7J7J7L6MQQr=   r   r   r   r  c                      gNzdivisor must be not zerorB   rB   r=   r:   r^   r  o      *r=   r]  ra  r  r   r2   r  )rO   ra   r   rW   r<  uint16uint32uint64r   r   pooling_output_shaperG   r"   pool2d_shape_checkr   r   )r  r  r   r  rd  count_include_paddivisor_overrider  kHkWdHdWpadHpadWr5  re  inputHeight
inputWidthrf  rg  r   r   s   `                     r:   meta_avg_pool2dr  H  s    M;/FB	LLFy a 
LLEKKu||U\\RRQ 6{aB	V	F1IB&)	7+JD	LLD 9$4$9*
  %yy{a/UZZ^QF**R.K**R.KBJ'Rr1iPL&z2RINK//6M



		$ yy{a\;7\;?;;kk||#	 r=   c                     [        U UUUUUUSSU	U
UUUU5        U R                  5       nU	n[        XUS-
  U5        [        XUS-
  U5        [        XUS-
  U5        g )Nr   r2   r3  )r  r   rv  )r  
gradOutputr5  r  r  r  r  r  r  re  r  r  rf  rg  
mem_formatr   nOutputPlanes                    r:   avg_pool2d_backward_shape_checkr    s{    " 



		$ 99;DL:TAX|<:TAX|<:TAX{;r=   c                    [         R                  " [        U5      S:H  =(       d    [        U5      S:H  S 5        US   n[        U5      S:X  a  UOUS   n	[         R                  " [        U5      S:H  =(       d#    [        U5      S:H  =(       d    [        U5      S:H  S 5        [        U5      S:X  a  UOUS   n
[        U5      S:X  a  U	O[        U5      S:X  a  U
OUS   n[         R                  " [        U5      S:H  =(       d    [        U5      S:H  S 5        US   n[        U5      S:X  a  UOUS   n[         R                  " US L =(       d    US:g  S 5        UR                  nUR	                  5       S:X  a  US	   OSnUS
   nUS   nUS   n[        UXU
SU5      n[        UXUSU5      n[        R                  " U5      n[        UU UUU	U
UUUUUUUUU5        [         R                  " UUR                  UR                  US9$ )Nr   r3  c                      g)NzKavg_pool2d: kernel_size must either be a single int, or a tuple of two intsrB   rB   r=   r:   r^   *meta_avg_pool2d_backward.<locals>.<lambda>  s    ]r=   r   c                      gr  rB   rB   r=   r:   r^   r    r  r=   c                      g)NzGavg_pool2d: padding must either be a single int, or a tuple of two intsrB   rB   r=   r:   r^   r    s    Yr=   c                      gr  rB   rB   r=   r:   r^   r    r  r=   r]  ra  r  r  r   r  )rO   ra   r   r   r   r  rG   r"   r  r   rW   r   )gradOutput_r  r  r   r  rd  r  r  r  r  r  r  r  r  
input_sizer5  re  r  r  rf  rg  r  s                         r:   meta_avg_pool2d_backwardr    s    
LLKA6[!1Q!6] 
QB;1$+a.B	LLFq@CK1,@Fq0@a 6{aVAYB6{a3v;!+;RB	LLG.S\Q.Y 1:Dw<1$4'!*D	LLD 9$4$9*
 J$yy{a/Z^QFR.KR.KBJ'Rr1iPL&z2RINK,,U3J#

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$ ;;kk|| 	 r=   c                 n  ^  [         R                  " [        U5      S;   S 5        US   n[        U5      S:X  a  UOUS   n[        U5      S:X  a  UOUS   n	[         R                  " U(       + =(       d    [        U5      S;   S 5        [         R                  " T R                  [         R                  [         R
                  [         R                  [         R                  4;  U 4S j5        U(       d  UOUS   n
U(       d  UO[        U5      S:X  a  U
OUS   nU(       d  U	O[        U5      S:X  a  U
OUS   n[         R                  " [        U5      S;   S 5        US   n[        U5      S:X  a  UOUS   n[        U5      S:X  a  UOUS   n[         R                  " T R                  S	;   S
 5        [         R                  " U(       + =(       d    US:g  S 5        T R                  S5      nT R                  S5      nT R                  S5      nT R                  S5      nT R                  S5      n[        UX}U
SU5      n[        UXUSU5      n[        UXUSU5      n[        T UUUU	U
UUUUUSSSUUUUUUSSS9  T R                  S:X  a  T R                  UUUU45      $ T R                  UUUUU45      $ )Nr   r2   c                      gNzFavg_pool3d: kernel_size must be a single int, or a tuple of three intsrB   rB   r=   r:   r^   !meta_avg_pool3d.<locals>.<lambda>      Xr=   r   r   r3  c                      gNzJavg_pool3d: stride must be omitted, a single int, or a tuple of three intsrB   rB   r=   r:   r^   r  $  r  r=   c                  @   > ST R                   R                  5        S3$ )Nz""avg_pool3d" not implemented for 'r@  rA  rC  s   r:   r^   r  (  r  r=   c                      gNzBavg_pool3d: padding must be a single int, or a tuple of three intsrB   rB   r=   r:   r^   r  0      Tr=   r]  r|  c                      gNz9non-empty 4D or 5D (batch mode) tensor expected for inputrB   rB   r=   r:   r^   r  8      Kr=   c                      gr  rB   rB   r=   r:   r^   r  =  r  r=   ra  r  r  r   zavg_pool3d()T)check_input_sizer]  )rO   ra   r   rW   r<  r  r  r  r   r   r  pool3d_shape_checkr   )r  r  r   r  rd  r  r  kTr  r  dTr  r  padTr  r  r5  nslicesitimeiheightiwidthotimeoheightowidths   `                       r:   meta_avg_pool3dr    s    
LLKF"X 
QB;1$+a.B;1$+a.B	LL
+c&kV+\ 
LLEKKu||U\\RRQ vayBc&kQ&6F1IBc&kQ&6F1IB	LLGT 1:Dw<1$4'!*Dw<1$4'!*D	LL

fK
 
LL5 0A 5*
 ZZ]FjjnGJJrNEjjnGZZ^F "aCE"7Bb!YGG!&"B9EF

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			-2 zzQ@AAHIIr=   c                 B   [         R                  " [        U5      S;   S 5        US   n[        U5      S:X  a  UOUS   n	[        U5      S:X  a  UOUS   n
[         R                  " U(       + =(       d    [        U5      S;   S 5        U(       d  UOUS   nU(       d  U	O[        U5      S:X  a  UOUS   nU(       d  U
O[        U5      S:X  a  UOUS   n[         R                  " [        U5      S;   S 5        US   n[        U5      S:X  a  UOUS   n[        U5      S:X  a  UOUS   n[         R                  " UR                  S;   S	 5        [         R                  " U(       + =(       d    US:g  S
 5        UR	                  S5      nUR	                  S5      nUR	                  S5      nUR	                  S5      n[        UXUSU5      n[        UXUSU5      n[        UU
UUSU5      n[        UU UUU	U
UUUUUUUUUUUUS5        UR                  UR                  5      $ )Nr  c                      gr  rB   rB   r=   r:   r^   *meta_avg_pool3d_backward.<locals>.<lambda>w  r  r=   r   r   r3  c                      gr  rB   rB   r=   r:   r^   r    r  r=   c                      gr  rB   rB   r=   r:   r^   r    r  r=   r  c                      gr  rB   rB   r=   r:   r^   r    r  r=   c                      gr  rB   rB   r=   r:   r^   r    r  r=   ra  r  r  r   zavg_pool3d_backward())	rO   ra   r   r   r   r  avg_pool3d_backward_shape_checkr   r   )rQ  r  r  r   r  rd  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  otime_for_shape_checkoheight_for_shape_checkowidth_for_shape_checks                           r:   meta_avg_pool3d_backwardr  i  s    
LLKF"X 
QB;1$+a.B;1$+a.B	LL
+c&kV+\ vayBc&kQ&6F1IBc&kQ&6F1IB	LLGT 1:Dw<1$4'!*Dw<1$4'!*D	LL

fK
 
LL5 0A 5*
 jjnGJJrNEjjnGZZ^F0"aS27Bb!YW1&"dB9U#

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', ??5;;''r=   c                 8  ^  [         R                  " T R                  S:H  =(       d    T R                  S:H  U 4S j5        T R                  S S [	        U5      -   n[
        R                  " T 5      n[         R                  " UT R                  T R                  US9$ )Nr2   r]  c                  "   > ST R                    3$ )Nz"Expected 3D or 4D tensor, but got r   r   s   r:   r^   *meta_adaptive_avg_pool2d.<locals>.<lambda>      4TZZLAr=   r  r  )
rO   ra   r   r   r`   rG   r"   r   rW   r   )r   output_sizer  r   s   `   r:   meta_adaptive_avg_pool2dr    s|    	LL		Q($))q.A ::cr?U;%77L//5M ;;jj{{#	 r=   c                    ^  [         R                  " T R                  S:H  =(       d    T R                  S:H  U 4S j5        T R                  T R                  S S [        U5      -   5      $ )Nr]  r|  c                  "   > ST R                    3$ )Nz"Expected 4D or 5D tensor, but got r   r   s   r:   r^   *meta_adaptive_avg_pool3d.<locals>.<lambda>  r  r=   r  )rO   ra   r   r   r   r`   )r   r  s   ` r:   meta_adaptive_avg_pool3dr    sO    	LL		Q($))q.A >>$**Sb/E+,>>??r=   c                   ^ ^^ T R                   n[        SU5       H1  m[        R                  " T R	                  T5      S:  U U4S j5        M3     [        R                  " US:H  =(       d    US:H  U4S j5        [        R                  " TR
                  T R
                  :H  U U4S j5        [        R                  n[        T5      (       a  [        R                  nTR                  TR                  5      R                  US9$ )	Nr   r   c                  *   > ST R                    ST S3$ )Nz{adaptive_avg_pool2d_backward(): Expected grad_output to have non-zero                       size for non-batch dimensions,  with dimension  being emptyr   )grad_outr!  s   r:   r^   4meta__adaptive_avg_pool2d_backward.<locals>.<lambda>  s$     66>nn5EEUVWUXXdfr=   r2   r]  c                  "   > ST R                    3$ )NzBadaptive_avg_pool2d_backward(): Expected 3D or 4D tensor, but got r   r   s   r:   r^   r    s    TUYU_U_T`ar=   c                  <   > STR                    ST R                    3$ Nexpected dtype z! for `grad_output` but got dtype r   )r  r   s   r:   r^   r    s    /$**-Nx~~N^_r=   r   )r   r   rO   ra   r   rW   r   r  r  r   r   rl  )r  r   r   r   r!  s   ``  @r:   "meta__adaptive_avg_pool2d_backwardr    s    ==D1d^MM!q f	
  
LL	TQYa 
LL

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

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

1	JJtE(FFqyF3	66:	
//)
$Cooiu{{o;G<r=   c                 P    [        U S5        UR                  UR                  5      $ )Nadaptive_max_pool3d_backward)r  r   r   )rQ  r  r   s      r:   !meta_adaptive_max_pool3d_backwardr  n  s"     &k3QR??5;;''r=   c                 @    Uc  [        S5      eU R                  U5      $ )Nz:cannot repeat_interleave a meta tensor without output_size)rk  r   )repeatsr  s     r:   meta_repeat_interleave_Tensorr  u  s%    WXX[))r=   c                     U R                   R                  (       d   eUR                   R                  (       d   e[        U R                  UR                  5      nU R	                  U[        U R                   5      S9$ r  )rW   r;  r)   r   r   r   )realimagr   s      r:   meta_complexr  |  s[     ::''''::''''!$**djj9I>>)+Ftzz+R>SSr=   )
fill_valuer  c                \    U R                  XR                  5       4[        R                  S9$ r  )r   r   rO   r   )r   r   r  s      r:   nonzero_staticr     s$     >>4,EJJ>??r=   c                    [         R                  " [        R                  S 5        [         R                  " U R                  5       U R                  5       4SU R                  5       4[         R                  U R                  S9$ )Nc                      g)NaY  The register_meta function for torch.nonzero() raises unimplemented by default, as a correct data-independent implementation does not exist. This implementation returns a fake value, assuming all elements of the tensor are non-zero. To enable this registration, please set 'torch.fx.experimental._config.meta_nonzero_assume_all_nonzero' to True.rB   rB   r=   r:   r^   nonzero.<locals>.<lambda>  s     Sr=   r   rW   r   )	rO   _check_not_implementedr  meta_nonzero_assume_all_nonzerorm  r   r   r   r   r   s    r:   nonzeror'    sf     
  22	S 	txxz"	
DJJLjj{{	 r=   c           
      j	  ^ ^^^^^^^^ [         R                  " [        T5      S 5        / n[        T5       GH  u  mmTGbr  [         R                  " TR                  [         R
                  [         R                  [         R                  [         R                  4;   S 5        TR                  [         R                  [         R                  4;   a  TR                  5       n[        U5      m[         R                  " TTR                  -   T R                  :*  U 4S j5        [        TR                  5       Hc  m[         R                  " TR                  T   T R                  TT-      :H  UUUUU 4S j5        UR                  UR                  ST5      5        Me     GMi  UR                  T5        GM}  UR                  T5        GM     Um[         R                  " [        T5      T R                  :*  UU 4S j5        SS KJn  [%        UR&                  " T6 5      m[        T5      T R                  :  a,  TR                  S 5        [        T5      T R                  :  a  M,  SnSnT H&  mUS:X  a	  Tb  SnM  M  US:X  a	  Tc  S	nM  M!  Tc  M&    O   S
nU(       d  / n/ n[        T5       H-  u  mmTc  M  UR                  T5        UR                  T5        M/     [        T5       H-  u  mmTb  M  UR                  T5        UR                  T5        M/     T R)                  U5      m Um/ m/ m/ m[        T5       He  u  n	mTcG  T(       a   TR                  T R                  U	   5        M0  TR                  T R                  U	   5        MP  [%        TR                  5      mMg     UUU4S jn
T R+                  TT-   T-   5      nSSKJn  U" T R1                  5       S:H  5      (       a  U$ U
" T 5      n[2        R4                  " U5      n[%        U5      [%        [        [        U5      5      5      :w  a  [2        R6                  " UR                  U5      n[2        R8                  " U5      n[2        R6                  " U[2        R:                  " U5      5      nUR=                  UR?                  5       U5      nU$ )Nc                      g)Nz#at least one index must be providedrB   rB   r=   r:   r^   #meta_index_Tensor.<locals>.<lambda>  s    (Mr=   c                      g)Nz?tensors used as indices must be long, int, byte or bool tensorsrB   rB   r=   r:   r^   r*    s    Yr=   c                  "   > ST R                    3$ )N)too many indices for tensor of dimension rI  r   s   r:   r^   r*    s    G		{Sr=   c            	      N   > STR                    ST  STR                    STT-    3$ )NzThe shape of the mask 
 at index z0 does not match the shape of the indexed tensor r   )r!  r   jr  r   s   r:   r^   r*    s:    "8ZPQs SJJN**U_`ade`e_f!hr=   r   c                  <   > STR                    S[        T 5       S3$ )Nr-  z (got ru   )r   r   )r   r   s   r:   r^   r*    s    ;DII;fSQX\NZ[\r=   r   Fr3  Tc                    > TT-   T-   n[        U R                  5       5      nS/[        T5      -  U[        T5      [        U R                  5      [        T5      -
  & U R	                  X5      $ )z9
This follows restride_src in TensorAdvancedIndexing.cpp
r   )r	  r   r   r   r   )r   r   r   after_shapebefore_shapereplacement_shapes      r:   _restride_src(meta_index_Tensor.<locals>._restride_src   sm     00;>t{{}%KL#PSQ
 K
L!C

Oc+6F$FG u..r=   guard_size_oblivious) rO   ra   rF  	enumeraterW   r   r)  r  r'  r   r   r   r   r   r
  selecttorch._refsr   r	  r*   r  r   r   r9  r   rG   3compute_elementwise_output_logical_to_physical_perm
apply_permr    invert_permr   r   )r   r   r  r'  refsstatehas_contiguous_subspacer  transposed_indicesr   r6  r  r9  restrided_selfperm
perm_shaper   r3  r4  r!  r   r0  r  r5  s   ``               @@@@@@@r:   meta_index_TensorrG    s   	LLg MN &(Fg&5LL

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

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

 #4(NDD^TD DzT%D	*++%%cii6
66zB
%%j%2C2CD2IJ
nnSXXZ4Jr=   c                     S nS nS nU
S   (       a  U R                  UR                  5       5      nU
S   (       a  U R                  UR                  5       5      nU
S   (       a  U R                  U5      nXU4$ )Nr   r   r3  r   r   )grad_output_input_weight_bias_sizes_optr   r  r  
transposedr  r  output_maskbackend_grad_inputbackend_grad_weightbackend_grad_biass                 r:   meta_convolution_backwardrS  !  sv      1~)33FKKMB1~*44W\\^D1~(22>B5FGGr=   c                  ^^ TR                  S5      nTR                  S5      nU R                  XV45      n [        R                  " TR	                  5       S:H  S 5        [        R                  " TR	                  5       S:H  S 5        [        R                  " TR                  S5      TR                  S5      :H  UU4S j5        [        R                  " TR                  S5      TR                  S5      :H  UU4S j5        [        R                  " U R                  S5      U:H  =(       a    U R                  S5      U:H  S	 5        U R                  U R                  5       5      $ )
Nr   r3  r2   c                      gr  rB   rB   r=   r:   r^   meta_addbmm.<locals>.<lambda>E  r  r=   c                      gr  rB   rB   r=   r:   r^   rV  F  r  r=   r   c                  P   > ST R                  S5       STR                  S5       3$ )Nz8batch1 and batch2 must have same number of batches, got r   r   r   r  r  s   r:   r^   rV  I  s,    J6;;WX>JZZ_`f`k`klm`n_opr=   c            
         > ST R                  S5       ST R                  S5       STR                  S5       STR                  S5       S3	$ )Nz#Incompatible matrix sizes for bmm (r   rL   r3  r   ru   r   rY  s   r:   r^   rV  M  sL    1&++a.1A6;;q>BR S;;q>"!FKKN#316r=   c                      g)Nz.self tensor does not match matmul output shaperB   rB   r=   r:   r^   rV  T  s    @r=   )r   r  rO   ra   r   r   )r   r  r  r  r  r  r  s    ``    r:   meta_addbmmr\  ?  s     ;;q>D;;q>D;;|$D	LL"$HI	LL"$HI	LLA&++a.(p 
LLA&++a.(	
 
LL		!51!5@ >>$))+&&r=   c                 @    U R                  U R                  5       5      $ r7   rI  )r   rW  kwargss      r:   meta_randint_liker_  Y  s    >>$))+&&r=   )
grad_scale	found_infc       	         p   ^ XX#XE4 H,  m[         R                  " [        T[        5      U4S j5        M.     g )Nc                      > S[        T 5       3$ Nz'exponent must be a tensor list but got rv   ls   r:   r^   #meta__fused_adam_.<locals>.<lambda>t      =d1gYGr=   rO   ra   rk   r	  )r   gradsexp_avgsexp_avg_sqsmax_exp_avg_sqsstate_stepslrbeta1beta2weight_decayepsamsgradmaximizer`  ra  rg  s                  @r:   meta__fused_adam_rw  ^  s0    & 8/Oq$G	
 Pr=   c       	            ^ XX#XE4 H,  m[         R                  " [        T[        5      U4S j5        M.     S nU" U 5      U" U5      U" U5      U" U5      U" U5      4$ )Nc                      > S[        T 5       3$ rd  re  rf  s   r:   r^   "meta__fused_adam.<locals>.<lambda>  ri  r=   c                 Z    U  Vs/ s H  n[         R                  " U5      PM     sn$ s  snf r7   r  )tensor_listr  s     r:   empty_like_list)meta__fused_adam.<locals>.empty_like_list  s%    -89[  #[999s    (rj  )r   rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  r`  ra  r}  rg  s                   @r:   meta__fused_adamr  x  si    & 8/Oq$G	
 P: 	!$( r=   c                 t  ^ ^ [         R                  " T R                  5       S:H  S 5        [         R                  " TR                  5       S:H  S 5        [         R                  " T R                  [         R                  L U 4S j5        [         R                  " TR                  [         R                  L U4S j5        [         R                  " T R                  S5      TR                  S5      :H  U U4S j5        T R                  T R                  S5      TR                  S5      4[         R                  S	9$ )
Nr3  c                      g)Nza must be a 2D tensorrB   rB   r=   r:   r^   meta__int_mm.<locals>.<lambda>      '>r=   c                      g)Nzb must be a 2D tensorrB   rB   r=   r:   r^   r    r  r=   c                  "   > ST R                    3$ )Nzexpected self to be int8, got r   )r   s   r:   r^   r        0	:r=   c                  "   > ST R                    3$ )Nzexpected mat2 to be int8, got r   )r  s   r:   r^   r    r  r=   r   r   c            
         > ST R                  S5       ST R                  S5       STR                  S5       STR                  S5       S3	$ )Nz'Incompatible matrix sizes for _int_mm (r   rL   r   r   ru   r   r   r  s   r:   r^   r    sH    5affQi[!&&) M66!9+Qqvvayk,r=   r   )rO   ra   r   rW   r  r   r   r  r  s   ``r:   meta__int_mmr    s     
LLA>?	LLA>?	LL	5::: 
LL	5::: 
LL	q	QVVAY	
 ;;q	166!9-U[[;AAr=   c                 d  ^  [         R                  " T R                  5       S:H  S 5        [         R                  " T R                  [         R                  L U 4S j5        T R                  S5      nT R                  S5      S-  nT R                  US-  X1S-  -  SUS-  4[         R                  S	9$ )
Nr3  c                      gNzw must be a 2D tensorrB   rB   r=   r:   r^   2meta__convert_weight_to_int4pack.<locals>.<lambda>  r  r=   c                  "   > ST R                    3$ Nrl  r   r?  s   r:   r^   r        .qwwi8r=   r   r      r      r   )rO   ra   r   rW   r<  r   r   r  r?  inner_k_tilesrL  r  s   `   r:    meta__convert_weight_to_int4packr    s    	LLA>?	LL	5;;8 	
q	A	q	AA;;F"$%Q		
 kk   r=   c                 H  ^  [         R                  " T R                  5       S:H  S 5        [         R                  " T R                  [         R                  L U 4S j5        T R                  S5      nT R                  S5      nT R                  X#S-  4[         R                  S9$ )Nr3  c                      gr  rB   rB   r=   r:   r^   :meta__convert_weight_to_int4pack_for_cpu.<locals>.<lambda>  r  r=   c                  "   > ST R                    3$ Nzexpected w to be int32, got r   r  s   r:   r^   r    r  r=   r   r   r   )rO   ra   r   rW   r  r   r   r<  r  s   `   r:   (meta__convert_weight_to_int4pack_for_cpur    s}    	LLA>?	LL	5;;8 	
q	A	q	A;;	
Fkk   r=   c                 6  ^ ^ [         R                  " T R                  5       S:H  S 5        [         R                  " TR                  5       S:H  S 5        [         R                  " T R                  [         R                  [         R
                  [         R                  4;   U 4S j5        [         R                  " TR                  [         R                  L U4S j5        T R                  T R                  S5      TR                  S5      S-  T R                  S	9$ )
Nr3  c                      gNzx must be a 2D tensorrB   rB   r=   r:   r^   *meta__weight_int4pack_mm.<locals>.<lambda>  r  r=   r]  c                      g)Nzw must be a 4D tensorrB   rB   r=   r:   r^   r    r  r=   c                  "   > ST R                    3$ Nrk  r   rL   s   r:   r^   r        5aggY?r=   c                  "   > ST R                    3$ r  r   r  s   r:   r^   r    r  r=   r   r  r   
rO   ra   r   rW   r  r  r  r  r   r   rm  s   ``  r:   meta__weight_int4pack_mmr    s    	LLA>?	LLA>?	LL	EMM5==%..AA? 
LL	5;;8 ;;qvvay!&&)a-qww;??r=   c                 0  ^ ^ [         R                  " T R                  5       S:H  S 5        [         R                  " TR                  5       S:H  S 5        [         R                  " T R                  [         R                  [         R
                  [         R                  4;   U 4S j5        [         R                  " TR                  [         R                  L U4S j5        T R                  T R                  S5      TR                  S5      T R                  S9$ )Nr3  c                      gr  rB   rB   r=   r:   r^   2meta__weight_int4pack_mm_for_cpu.<locals>.<lambda>  r  r=   c                      gr  rB   rB   r=   r:   r^   r    r  r=   c                  "   > ST R                    3$ r  r   r  s   r:   r^   r    r  r=   c                  "   > ST R                    3$ r  r   r  s   r:   r^   r    r  r=   r   r   )
rO   ra   r   rW   r  r  r  r<  r   r   rm  s   ``  r:    meta__weight_int4pack_mm_for_cpur        	LLA>?	LLA>?	LL	EMM5==%..AA? 
LL	5;;8 ;;qvvay!&&)177;;;r=   c                 0  ^ ^ [         R                  " T R                  5       S:H  S 5        [         R                  " TR                  5       S:H  S 5        [         R                  " T R                  [         R                  [         R
                  [         R                  4;   U 4S j5        [         R                  " TR                  [         R                  L U4S j5        T R                  T R                  S5      TR                  S5      T R                  S9$ )Nr3  c                      gr  rB   rB   r=   r:   r^   ;_weight_int4pack_mm_with_scales_and_zeros.<locals>.<lambda>  r  r=   c                      gr  rB   rB   r=   r:   r^   r    r  r=   c                  "   > ST R                    3$ r  r   r  s   r:   r^   r    r  r=   c                  "   > ST R                    3$ r  r   r  s   r:   r^   r    r  r=   r   r   r  )rL   r?  rn  qScaleqZeross   ``   r:   )_weight_int4pack_mm_with_scales_and_zerosr    r  r=   r   r  c                     X-   S-
  U-  U-  $ rt  rB   r  s     r:   kai_roundupr    s    UQY1!!r=   c                   ^	^
^^^^^^^^^ U S:X  a{  X2:X  a(  SnSnSnSmSmSmS mUUUU4S jmU4S jnU" XXEU5      $ US-  S	:X  aD  X#-  S	:X  a;  SnSnSnSmSmSmSm	U	UU4S
 jnU	U
UUUUU4S jmS m
U	4S jmU	4S jmU" XXEXc5      $ g g g )Nr]  r  r  r3  c                 4    [        X-  S5      n[        X5      $ )Nr]  r  )r  krsrkr_sr_roundedup4s       r:   kai_k_roundedup3get_kai_packed_weight_size.<locals>.kai_k_roundedup  s     $/rw#: "177r=   c                 X   > T" XU5      nUS-  S:X  d   S5       eUUS-  T-   T-   T-   -  $ )Nr3  r   zk_internal must be evenrB   )	r  nrr  r  
k_internalr  kai_num_bytes_biaskai_num_bytes_multiplier_rhskai_num_bytes_sum_rhss	        r:   9kai_get_rhs_packed_stride_rhs_pack_nxk_qsi4cxp_qsu4cxs1s0]get_kai_packed_weight_size.<locals>.kai_get_rhs_packed_stride_rhs_pack_nxk_qsi4cxp_qsu4cxs1s0  sW     -QB7
"Q1,G.GG,1_23+, )) r=   c                 8   > [        X5      U-  nUT" XX45      -  $ r7   r  )rL  r  r  r  r  num_rowsr  s         r:   7kai_get_rhs_packed_size_rhs_pack_nxk_qsi4cxp_qsu4cxs1s0[get_kai_packed_weight_size.<locals>.kai_get_rhs_packed_size_rhs_pack_nxk_qsi4cxp_qsu4cxs1s0'  s0     'q-3 Orr=   r  r   c                 z   > XS-  S:X  d   eUT	-  S:X  d   eUT-  S:X  d   e[        X5      U-  nUT" XX4U5      -  $ r  r  )
rL  r  r  r  r  blr  kai_bl_multiple_of;kai_get_rhs_packed_stride_rhs_pack_nxk_qsi4c32p_qsu4c32s1s0kai_nr_multiple_ofs
          r:   9kai_get_rhs_packed_size_rhs_pack_nxk_qsi4c32p_qsu4c32s1s0]get_kai_packed_weight_size.<locals>.kai_get_rhs_packed_size_rhs_pack_nxk_qsi4c32p_qsu4c32s1s0?  sh     A~%~//A555//A555&q-3 Qrrr=   c                    > XB-  S:X  d   eUT
-  S:X  d   eUT-  S:X  d   eT	" 5       nT" X5      nT" XE5      nUXv-  T-   T-   -  $ r  rB   )r  r  r  r  r  num_bytes_multiplier_rhsnum_blocks_per_rownum_bytes_per_blockr  #kai_get_bf16_datatype_size_in_bytesr  kai_num_blocks_per_rowr  kai_num_bytes_per_blockr  s           r:   r  _get_kai_packed_weight_size.<locals>.kai_get_rhs_packed_stride_rhs_pack_nxk_qsi4c32p_qsu4c32s1s0O  s     A~%~//A555//A555 ,O+P(%;A%B"&='# (=+,() r=   c                      g)Nr3  rB   rB   r=   r:   r  Gget_kai_packed_weight_size.<locals>.kai_get_bf16_datatype_size_in_bytese  s    r=   c                 6   > UT-  S:X  d   e[        X5      U-  $ r  r  )r  r  r  s     r:   r  :get_kai_packed_weight_size.<locals>.kai_num_blocks_per_rowh  s'    //A555"1)R//r=   c                 *   > U T-  S:X  d   eU S-  U-   $ )Nr   r3  rB   )r  r  r  s     r:   r  ;get_kai_packed_weight_size.<locals>.kai_num_bytes_per_blockl  s'    //A555a#;;;r=   rB   )n_bitsr  K	groupsizekai_nrkai_krkai_srr  r  r  r  r  r  r  r  r  r  r  r  r  s            @@@@@@@@@@@r:   get_kai_packed_weight_sizer    s    {>FFF$%!+,(!"8 
 Kff  ^q Q]a%7FFF$%!!"!"!#  ,0< Mff u &8 [ r=   c                 \  ^  [         R                  " T R                  [         R                  L U 4S j5        [         R                  R
                  R                  5       (       a  X4:X  a  UR                  [         R                  :X  d4  X4:  ac  US-  S:X  aZ  XC-  S:X  aR  UR                  [         R                  :X  a4  [        SXTU5      nT R                  [        U5      [         R                  S9$ T R                  5       UR                  5       -   nT R                  U[         R                  S9$ )Nc                  "   > ST R                    3$ r  r   )weightss   r:   r^   2meta__dyn_quant_pack_4bit_weight.<locals>.<lambda>{  s    .w}}o>r=   r  r   r]  r   )rO   ra   rW   r<  backendskleidiaiis_availablerS   r  r  r   r)  r   )r  scales_zerosr  
block_sizein_featuresout_featurespacked_weight_sizes   `      r:    meta__dyn_quant_pack_4bit_weightr  u  s     
LL$> ~~++--		"|'9'9U[['H$R1$(A-""enn4 8|*
   %7!8 LL <+=+=+??/u{{CCr=   c                   ^  [         R                  " T R                  5       S:H  S 5        [         R                  " T R                  [         R                  4;   U 4S j5        T R                  S5      nT R                  XTT R                  S9$ )Nr3  c                      g)Nzinput must be a 2D tensorrB   rB   r=   r:   r^   -meta__dyn_quant_matmul_4bit.<locals>.<lambda>  s    )Dr=   c                  "   > ST R                    3$ )Nzexpected input to be f32, got r   )inps   r:   r^   r    s    0<r=   r   r   )rO   ra   r   rW   r  r   r   )r  packed_weightsr  r  r  r  s   `     r:   meta__dyn_quant_matmul_4bitr     se     
LLa!DE	LL		emm_$< 	A==		=::r=   c                 0  ^ ^ [         R                  " T R                  5       S:H  S 5        [         R                  " T R                  [         R                  [         R
                  [         R                  4;   U 4S j5        [         R                  " TR                  5       S:H  S 5        [         R                  " TR                  [         R                  L U4S j5        T R                  T R                  S5      TR                  S5      T R                  S9$ )Nr3  c                      gr  rB   rB   r=   r:   r^   *meta__weight_int8pack_mm.<locals>.<lambda>  r  r=   c                  "   > ST R                    3$ r  r   r  s   r:   r^   r    r  r=   c                      gr  rB   rB   r=   r:   r^   r    r  r=   c                  "   > ST R                    3$ )Nzexpected w to be int8, got r   r  s   r:   r^   r    s    -aggY7r=   r   r   )
rO   ra   r   rW   r  r  r  r  r   r   )rL   r?  q_scaless   `` r:   meta__weight_int8pack_mmr    s    	LLA>?	LL	EMM5==%..AA? 
LLA>?	LL	5::7 ;;qvvay!&&)177;;;r=   c                   ^ ^^ [         R                  " T R                  5       S:  U 4S j5        [         R                  " TR                  5       S:  U4S j5        [         R                  " T R                  S5      TR                  S5      :H  U U4S j5        [         R                  " [        R
                  " T R                  5      S 5        [         R                  " [        R
                  " TR                  5      S 5        [         R                  " US:  S	 5        [         R                  " TS
;   U4S j5        T R                  S5      nTR                  S5      nT R                  S S nTR                  S S n[        [         R                  " Xg5      5      nUR                  XE/5        T R                  U5      $ )Nr3  c                  ,   > ST R                  5        S3$ )Nz1cdist only supports at least 2D tensors, X1 got: rj  r   )x1s   r:   r^   $meta_cdist_forward.<locals>.<lambda>      CBFFH:QOr=   c                  ,   > ST R                  5        S3$ )Nz1cdist only supports at least 2D tensors, X2 got: rj  r   )x2s   r:   r^   r    r  r=   r   c                  P   > ST R                  S5       STR                  S5       3$ )Nz4X1 and X2 must have the same number of columns. X1: r   z X2: r   )r  r  s   r:   r^   r    s*    Frwwr{mSXY[Y`Y`acYdXefr=   c                      g)Nz=cdist only supports floating-point dtypes, X1 got: {x1.dtype}rB   rB   r=   r:   r^   r    r   r=   c                      g)Nz=cdist only supports floating-point dtypes, X2 got: {x2.dtype}rB   rB   r=   r:   r^   r    r   r=   r   c                      g)Nz)cdist only supports non-negative p valuesrB   rB   r=   r:   r^   r    s    !Lr=   Nr   r3  c                     > ST  3$ )Nz%possible modes: None, 1, 2, but was: rB   )compute_modes   r:   r^   r    s    7~Fr=   r  )rO   ra   r   r   rG   is_float_dtyperW   r   r	  broadcast_shapesextendr   )	r  r  r  r  r1r2batch_tensor1batch_tensor2r  s	   `` `     r:   meta_cdist_forwardr    sF   	LL
AO 
LL
AO 
LL
rwwr{"f 
LLRXX&O 
LLRXX&O 
LLaLM	LL$F 
B	BHHSbMMHHSbMM..}LML!<<%%r=   c                 <   UR                   S   nUR                   S   nUR                   S   nUR                   S S nUR                   S S n	[        [        R                  " X5      5      n
U
R	                  5       nUR                  Xe/5        [        R                  " U
5      nUS:X  d  US:X  d  US:X  d  US:X  a  [        R                  " U5      $ U[        UR                   5      :w  a  UR                  U5      n[        R                  " U[        R                  S9$ )Nr   r  r   r   )r   r	  rO   r  copyr  mathprod
zeros_liker  r   r   )r  r  r  r  cdistc1r  r  r  r  r  tensor1_expand_sizebatch_products                r:   meta_cdist_backwardr(    s     
"B	"B	"BHHSbMMHHSbMM 6 6} TU.335x(II23M	Qw"'R1W(:##d288n,YY*+Be.E.EFFr=   c	                 Z  ^ ^^^^^ [         R                  " TR                  [         R                  [         R                  4;   U4S j5        [         R                  " TR                  [         R                  [         R                  4;   U4S j5        [         R                  " [
        R                  " T R                  5      U 4S j5        TR                  S5      n	U(       a   [         R                  " U	S:  S 5        U	S-  n	T R                  U	T R                  S5      5      n
Tb  [         R                  " U[        :H  S 5        [         R                  " TR                  S:H  U4S j5        [         R                  " TR                  5       TR                  5       :H  UU4S	 j5        U4S
 jmS mUU4S jn[        T5      S:w  a}  TR                  TR                  S5      5      nTR                  TR                  5       5      nU[        :X  a"  TR                  U	T R                  S5      5      nOTR                  S5      nOU" T TX5      nU[        [        4;   d  U(       d!  TR                  TR                  S5      5      nOTR                  S5      nTR                  U	5      nTR                  S   nU[        :X  aG  U(       a   [         R                  " US:  S 5        US-  nTR                  UT R                  S   5      nOTR                  UR                  5       5      nXX4$ )Nc                  "   > ST R                    3$ )Nz(expected indices to be long or int, got r   )r   s   r:   r^   $meta_embedding_bag.<locals>.<lambda>      :7==/Jr=   c                  "   > ST R                    3$ )Nz(expected offsets to be long or int, got r   )r  s   r:   r^   r+    r,  r=   c                  "   > ST R                    3$ )Nz/expected weight to be floating point type, got r   )r~  s   r:   r^   r+    s    A&,,Pr=   r   r   c                      gNz1include_last_offset: numBags should be at least 1rB   rB   r=   r:   r^   r+    s    Gr=   c                      g)Nz@embedding_bag: per_sample_weights only supported with mode='sum'rB   rB   r=   r:   r^   r+    s    Vr=   c                  $   > ST R                    S3$ )Nz1expected per_sample_weights to be 1D tensor, got rj  rI  )per_sample_weightss   r:   r^   r+    s    GHZH_H_G``abr=   c                  N   > STR                  5        ST R                  5        S3$ )Nz%expected per_sample_weights.numel() (z$ to be the same as indices.numel() (ru   r   )r   r3  s   r:   r^   r+    s/    78J8P8P8R7S T66=mmo5FaIr=   c                 L   > T" XU5      =(       a    UR                  S5      S:H  $ Nr   r   r   )ro  r  rC  padding_idxis_fast_path_index_selects       r:   is_fast_path_index_select_scale;meta_embedding_bag.<locals>.is_fast_path_index_select_scale  s&    %c;?XELLQROWXDX	
r=   c                    U R                   [        R                  :H  =(       d    U R                   [        R                  :H  =(       a;    U R	                  S5      S:H  =(       a     UR	                  S5      S:H  =(       a    US:  $ Nr   r   )rW   rO   rS   rQ   r   )ro  rC  r9  s      r:   r:  5meta_embedding_bag.<locals>.is_fast_path_index_select"  sb    YY%++%@ejj)@  

1" a A%  a		
r=   c                 .   > Ub	  T" XX#5      $ T" XU5      $ r7   rB   )ro  r  rC  r9  r:  r;  s       r:   is_fast_path(meta_embedding_bag.<locals>.is_fast_path*  s#    23vSS,S+FFr=   cpuc                      gr0  rB   rB   r=   r:   r^   r+  D  s    Or=   )rO   ra   rW   r   r)  rG   r  r   r   MODE_SUMr   r   r<  MODE_MAX	MODE_MEANr   )r~  r   r  scale_grad_by_freqr  sparser3  include_last_offsetr9  num_bagsrC  rA  
offset2bagbag_sizemax_indicesfast_path_sumnumBagsr:  r;  s   ```   `          @@r:   meta_embedding_bagrQ    sw    
LL%**eii00J 
LL%**eii00J 
LLV\\*P
 ||AHMG	
 	AhA7F%HV	
 	##q(b	
 	$$&'--/9	



G 7u$&&w||A7
$$W\\^48!++Hfkk!nEK!++A.K$V-?UIx(( **7<<?;J **1-J$$X.--"8"qLO 1!++GV\\!_EK!++HMMO<Kx44r=   c                     [        XU/UQ76 u  pEpg[        U5      S:X  a  UR                  UR                  5       5      nXEXg4$ )NrC  )rQ  r<  r   r   )r~  r   r  rI   rC  rL  rM  rN  s           r:   meta_embedding_bag_forward_onlyrS  M  sN    0B1#'1-F 7u$$$W\\^4x44r=   c                     U(       a  U$ U R                   R                  (       d  U R                   R                  (       a  U R                   $ U(       a  [        R                  $ U R                   $ r7   )rW   r;  r.  rO   r   )r  rW   promote_int_to_longs      r:   _get_reduction_dtyperV  W  sD    {{$$(>(>{{	zz;;r=   r   c                    [        XSS9n[        R                  " U R                  U5      n[	        XU5      nU R                  XTS9$ )NT)rU  r   )rV  rG   r  r   r  r   )r  r  r  rW   rD  r  s         r:   meta_nansumrX  d  sC     ($OLT2D+EAL??<?<<r=   c           	          [         R                  " U R                  [        [	        U R                  5       5      5      5      nU R                  U5      $ r7   )rG   r  r   r`   r   r   r   )r  r  s     r:   meta_medianrZ  m  s<    77U5-.L ??<((r=   c                    [        U 5      S:X  a  [        R                  " S5        [        R                  " U R                  U45      n[        XU5      nU R                  U5      U R                  U[        R                  S94$ )Nr7  zmedian CUDA with indices outputr   )	r<  rG   alert_not_deterministicr  r   r  r   rO   r   )r  r   r  r  s       r:   meta_median_mode_dimr]  u  sn     5V#%%&GH


u{{SF
3C+E@L%EJJ7 r=   c                     U $ r7   rB   r   s    r:   meta_logical_not_r_    r  r=   c                   ^^ [         R                  " [        U5      U R                  5       :  S 5        [	        U5       H%  u  mm[         R                  " TS:  UU4S j5        M'     [        U5      U R                  5       -
  nSU-  [        U R                  5      -   n[        [        U5      5       Vs/ s H  oCU   X   -  PM     nnU R                  U5      $ s  snf )Nc                      g)NzZNumber of dimensions of repeat dims can not be smaller than number of dimensions of tensorrB   rB   r=   r:   r^   meta_repeat.<locals>.<lambda>  s    lr=   r   c                     > ST ST  3$ )Nz"Repeats cannot be negative, found r/  rB   )r!  reps   r:   r^   rb    s    8ZsKr=   r^  )	rO   ra   r   r   r:  r`   r   r   r   )r   r  num_new_dimensionspadded_sizer!  target_sizerd  s       ` @r:   meta_repeatrh    s    	LLG
"l G$31HK	
 % W
2++eDJJ.??K8=c'l8KL8K1q>GJ.8KKL>>+&& Ms   6Cc                     U $ r7   rB   r   s    r:   
meta_zero_rj    r  r=   c                     [        U[        R                  5      (       a   [        U R                  UR                  5        U $ r7   )rk   rO   r   rc   r   r   r   s     r:   meta_binop_inplacerm    s,     %&&

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

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

EKK8Kr=   c                 2    [        U [        R                  S9$ NrD   rM   r   rH   )r   r^  s     r:   
meta_roundr    s    <DD r=   c                   ^ ^^ [         R                  " [        R                  " TR                  5      U U4S j5        [        T[         R                  5      (       a;  [         R                  " [        R                  " TR                  5      U U4S j5        g [         R                  " [        T[        5      U U4S j5        g )Nc                  &   > T  STR                    3$ )Nz7: Expected input tensor to have an integral dtype. Got r   )r   r   s   r:   r^   #shift_dtype_check.<locals>.<lambda>  s    7)RSWS]S]R^_r=   c                  &   > T  STR                    3$ )Nz6: Expected shift value to have an integral dtype. Got r   r   r  s   r:   r^   r    s    wiUVYV_V_U`ar=   c                     > T  ST 3$ )Nz): Expected shift value to be an int. Got rB   r  s   r:   r^   r    s    wiHNr=   )rO   ra   rG   r  rW   rk   r   r   )r   r   r  s   ```r:   shift_dtype_checkr    ss    	LLtzz*_ #u||$$""399-a	

 	sG$N	
r=   c                 J    [        SX5        [        X[        R                  S9$ )Nrshiftr}  r  rM   r   rH   rl  s     r:   meta_rshiftsr    %    h,$C$K$K r=   c                 J    [        SX5        [        X[        R                  S9$ )Nlshiftr}  r  rl  s     r:   meta_lshiftsr    r  r=   c                 8    U R                  U R                  5      $ r7   r2  r   s    r:   	meta_zeror    s    >>$**%%r=   c                     U $ r7   rB   r   r  s     r:   
meta_fill_r    r  r=   c                 .    [         R                  " U 5      $ r7   r  r  s     r:   	meta_fillr  !      D!!r=   c                     U $ r7   rB   r   s    r:   
meta_relu_r  &  r  r=   c                 2    [        X[        R                  S9$ r|  r~  )r   r   r  s      r:   meta__add_relur  +  s     $C$K$K r=   c                 .    [         R                  " U 5      $ r7   r  r   noiselowerr,  r  rI  s         r:   meta_rrelu_with_noiser  3  s    
 D!!r=   c                 Z    [         R                  " U 5      [         R                  " U5      4$ r7   r  r  s         r:    meta_rrelu_with_noise_functionalr  ;  s%     D!5#3#3E#:::r=   c                     U $ r7   rB   )r   r  r,  r  rI  s        r:   meta_rrelu_with_noise_r  B  s	     Kr=   c                 .    [         R                  " U 5      $ r7   r  r   r   r   
accumulates       r:   meta_index_putr  I  r  r=   c                 F    [        U R                  UR                  5        U $ r7   rc   r   )r   r  values      r:   meta_masked_fill_r  N  s    DJJ

3Kr=   c                     U R                  U R                  5       5      R                  [        R                  " U 5      S9nU$ r   )r   r   rl  rG   r"   )r   r  r  masked_scales       r:   meta__masked_scaler  T  s<    >>$))+.1111$7 2 L r=   c                    ^ ^ [         R                  " UR                  [         R                  [         R                  4;   S 5        [         R                  " T R                  TR                  :H  U U4S j5        T $ )Nc                      g)NzMask must be bool or uint8rB   rB   r=   r:   r^   &meta_masked_scatter_.<locals>.<lambda>_  s    9Ur=   c                  <   > ST R                    STR                    3$ )NzEmasked_scatter: expected self and source to have same dtypes but got r   r   )r   r  s   r:   r^   r  c  s      **U6<<.:r=   )rO   ra   rW   rF  r<  )r   r  r  s   ` `r:   meta_masked_scatter_r  \  sU    	LL

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

fll"	:
 Kr=   c                 z    [        X5      u  p[        R                  " U [        R                  S9n[	        X1U5      $ r   )r*   rO   r   r   r  )r   r  r  rC  s       r:   meta_masked_scatterr  i  s5     "$-JDd%2I2IJFf55r=   c                 $    U R                  U5      $ r7   r  )r   r  r  s      r:   meta_masked_scatter_backwardr  q  s    >>%  r=   c                     U $ r7   rB   r  s       r:   meta_index_put_r  v  r  r=   c                 8    U R                  U R                  5      $ r7   )viewr   r   s    r:   
meta_aliasr  {  s    99TZZ  r=   c                   ^^
^^^ [         R                  " U R                  5       S:H  S 5        [         R                  " UR                  5       S:H  S 5        U R                  5       nUR                  5       m
US   mUS   mUS   nT
S   nTXg4m[         R                  " T
S   T:H  =(       a    T
S   T:H  U
UU4S j5        U(       a  U R                  [         R
                  :H  =(       d    U R                  [         R                  :H  =(       a    U[         R                  :H  n[         R                  " X@R                  :H  =(       d    US 5        UR                  T5      R                  U5      n	OUR                  T5      n	U(       dY  TbV  [         R                  " TR                  5       S:H  S	 5        [         R                  " TR                  5       T:H  UU4S
 j5        U	$ )Nr2   c                      gr  rB   rB   r=   r:   r^   )common_meta_baddbmm_bmm.<locals>.<lambda>  r  r=   c                      gr  rB   rB   r=   r:   r^   r    r  r=   r   r3  r   c            	      .   > ST ST ST S    ST S    S3	$ r  rB   r  s   r:   r^   r    s3    RSURV
l<?*;2l1o=NbRr=   c                      g)Nzfout_dtype only supported for torch.float32 output with float16/bfloat16 inputs or same as input dtypesrB   rB   r=   r:   r^   r    s    |r=   c                      g)Nzself must be a 3D tensorrB   rB   r=   r:   r^   r    s    6Pr=   c                  0   > ST  STR                  5        3$ )Nz*Expected an input tensor shape with shape z but got shape: r   )r  self_baddbmms   r:   r^   r    s    @M]^j^o^o^q]rsr=   )
rO   ra   r   r   rW   r  r  r  r   rl  )r  r  is_bmmr  r  r  res_rowsres_colssupported_out_dtyperC  r  r  r  r  s      `      @@@@r:   common_meta_baddbmm_bmmr    s   	LL"$HI	LL"$HI;;=L;;=L	aB#AAHAHx*K	LLQ2E,q/5E"E	R
 LLEMM)KV\\U^^-K)5==( 	 	%<)<|	
 !!+.11)< !!+.l.\%%'1,.PQ;.s	

 Mr=   c                     [        XS5      $ )NTr  )r   r  s     r:   meta_bmmr    s    "4t44r=   c                     [        XSUS9$ )NT)r  r  )r   r  r  s      r:   meta_bmm_dtyper    s    "4tyIIr=   c                 h    X-  nX-  nUS:w  a#  [        US:  5      [        US:  5      :w  a  US-  nU$ r7  )rF  )rL   yqr  s       r:   div_rtnr    s>    	A	A 	Av4A;$q1u+-	QHr=   c                     [        U U-   U-   XQS-
  -  -
  S-
  U(       a  US-
  OS-   U5      S-   nU(       a  US-
  U-  X-   :  a  US-  nU$ r>  )r  )	inputSize
kernelSizer,  r-  r   r  rd  
outputSizes           r:   pooling_output_shape_pad_lrr    s     	 q.)* 	
 'vzA/ 	
 		  Nf$	(99!OJr=   c           	         ^^^ [         R                  " US:g  S 5        [         R                  " TS:  U4S j5        [         R                  " TTS-
  T-  S-   S-  :*  UUU4S j5        [        U TTTUTU5      $ )Nr   c                      g)Nzstride should not be zerorB   rB   r=   r:   r^   &pooling_output_shape.<locals>.<lambda>  s    &Ar=   c                     > ST  3$ )Nz'pad must be non-negative, but got pad: rB   pads   r:   r^   r    s    %LSE#Rr=   r   r3  c                     > ST ST ST  3$ )NzApad should be at most half of effective kernel size, but got pad=z, kernel_size=z and dilation=rB   )r  r  r  s   r:   r^   r    s"    OPSu U%,nXJ@r=   )rO   ra   r  )r  r  r  r   r  rd  s    `` ` r:   r  r    ss    	LL1AB	LLRS	LLa8+a/A55	
 ':sC9 r=   c           	        ^ ^^^^^	^
^^^^ T R                  5       nT	m[        R                  " TS:  =(       a    TS:  S 5        [        R                  " US:  =(       a    US:  S 5        [        R                  " US:  =(       a    US:  S 5        T R                  S5      S:g  =(       a    T R                  S5      S:g  nU[        R                  :X  a@  [        R                  " US:H  =(       a    U=(       a    T R                  S5      S:g  S	 5        Or[        R                  " US:H  =(       a    T R                  S5      S:g  =(       a    U=(       d)    US:H  =(       a    U=(       a    T R                  S5      S:g  U 4S
 j5        [        R                  " TS-  T:  =(       a    TS-  T:  UUUU4S j5        [        R                  " TS:  =(       a    TS:  U
UU	UUU4S j5        g )Nr   c                      g)NzCkernel size should be greater than zero, but got kH: {kH}, kW: {kW}rB   rB   r=   r:   r^   $pool2d_shape_check.<locals>.<lambda>  r  r=   c                      g)Nz>stride should be greater than zero, but got dH: {dH}, dW: {dW}rB   rB   r=   r:   r^   r    s    Pr=   c                      g)Nz\dilation should be greater than zero, but got dilationH: {dilationH}, dilationW: {dilationW}rB   rB   r=   r:   r^   r    s    nr=   r   r3  r]  r2   c                      g)NzExpected 4D (batch mode) tensor expected for input with channels_last layout with optional 0 dim batch size for input, but got: {input.size()}rB   rB   r=   r:   r^   r    s     Qr=   c                  *   > ST R                  5        3$ )NzYExpected 3D or 4D (batch mode) tensor with optional 0 dim batch size for input, but got: r   rC  s   r:   r^   r    s    opupzpzp|o}~r=   c                      > ST ST ST ST  3$ )NzKpad should be smaller than or equal to half of kernel size, but got padW = z	, padH = z, kW = z, kH = rB   )r  r  r  r  s   r:   r^   r    s$     ygbT>r=   c                  .   > ST ST  ST ST ST ST S3$ NzGiven input size: (rL   z). Calculated output size: (z). Output size is too smallrB   )r  r  re  r  rf  rg  s   r:   r^   r    s8    %k]!K=* N$$0><.+ O##r=   )r   rO   ra   r   r  )r  r  r  r  r  r  r  	dilationH	dilationWre  r  r  rf  rg  r   r   
valid_dimsr  s   ```  ``  `````   @r:   r  r    s   " 99;DL	LL
Q26U 
LL
Q26P 
LLA')a-n
 A!#:

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

 	U	

 (RriXL&z2RIVK



$ k11r=   c                 |  ^ ^^^^^ [        TX#XEU5      u  nmm[        R                  " TR                  T R                  :H  U U4S j5        UmTR                  mUUUU4S jn	U	" T 5        U	" U5        [
        R                  " T5      n
[        R                  " TR                  TR                  TR                  U
S9$ )Nc                  <   > STR                    ST R                    3$ )NzExpected dtype z  for `gradOutput` but got dtype r   r  s   r:   r^   7meta_max_pool2d_with_indices_backward.<locals>.<lambda>V  s    /$**-MkN_N_M`ar=   c                 l   > [        U TTS-
  T5        [        U TTS-
  T5        [        U TTS-
  T5        g )Nr2   r3  r   )rv  )r  r  r   rf  rg  s    r:   _check_dim_size>meta_max_pool2d_with_indices_backward.<locals>._check_dim_size\  s9    q$q,7q$q,7q$q+6r=   r  )
rb  rO   ra   rW   r   rG   r"   r   r   r   )rQ  r   r  r   r  r  rd  r   re  r  r   r  r   rf  rg  s   ``         @@@@r:   %meta_max_pool2d_with_indices_backwardr  A  s     	,k7i		
 
LL

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

jj{{#	 r=   c                    [        XX#XE5      u  nnnU R                  5       S:X  a  U R                  S5      OSn	[        R                  " U 5      n
U R                  5       S:X  a  XgU/nOXXx/n[
        R                  " UU R                  U R                  U
S9[
        R                  " U[
        R                  U R                  U
S94$ r`  )
rb  r   r   rG   r"   rO   r   rW   r   r   rc  s               r:   meta_max_pool2d_with_indicesr  m  s     	,FX		
  %yy{a/UZZ^QF//6Myy{a;7\?++<<'		
 	++<<'		
 r=   c           	        ^ ^^^
^^ [         R                  " T R                  S;   U 4S j5        T R                  n[        US-
  U5       HA  m
[         R                  " T R	                  T
5      S:  ST R	                  5        ST
 S35        MC     [         R                  " [        T5      S:H  S	 5        [         R                  " [        U5      S:H  S
 5        T R	                  S5      nT R	                  S5      mT R	                  S5      mUS:X  a  T R	                  S5      nOSn[         R                  " T R                  TR                  :H  S 5        [         R                  " TR                  S:H  U4S j5        TR	                  S5      nTR	                  S5      nTR	                  S5      m
[         R                  " Xv:  S5        [         R                  " X:H  S 5        [         R                  " T
S:H  U
4S j5        [         R                  " US   TS   -   S-
  T:*  UU4S j5        [         R                  " US   TS   -   S-
  T:*  UU4S j5        T R                  5       S:X  a  XeUS   US   /n	O
XRS   US   /n	[         R                  " U	T R                  T R                  S9[         R                  " U	[         R                  T R                  S94$ )Nr;  c                  "   > ST R                    3$ )Nz:fractional_max_pool2d: Expected 3D or 4D tensor, but got: rI  r   s   r:   r^   ,meta_fractional_max_pool2d.<locals>.<lambda>  s    LTYYKXr=   r2   r   z^fractional_max_pool2d: Expected input to have non-zero  size for non-batch dimenions, but got r  z emptyr3  c                      g)NzNfractional_max_pool2d: kernel_size musteither be a single int or tuple of IntsrB   rB   r=   r:   r^   r         2r=   c                      g)NzOfractional_max_pool2d: output_size must either be a single int or tuple of IntsrB   rB   r=   r:   r^   r    r  r=   r  r  r   r]  r   c                      g)Nz6Expect _random_samples to have the same dtype as inputrB   rB   r=   r:   r^   r    s    Hr=   c                  "   > ST R                    3$ )Nz1Expect _random samples to have 3 dimensions got, rI  )random_sampless   r:   r^   r    s    CNDWDWCXYr=   z=Expect _random_samples.size(0) no less then input batch size.c                      g)Nz<Expect _random_samples.size(1) equals to input channel size.rB   rB   r=   r:   r^   r        Nr=   c                     > ST  S3$ )Nz/Expect _random_samples.size(2) equals to 2 got .rB   )r  s   r:   r^   r    s    #RSTRUUV!Wr=   c                     > STS    ST  3$ )Nz%fractional_max_pool2d: kernel height r   z' is too large relative to input height rB   )input_heightr  s   r:   r^   r    s    7A7GGno{n|}r=   c                     > STS    ST  3$ )Nz$fractional_max_pool2d: kernel width r   z& is too large relative to input width rB   )input_widthr  s   r:   r^   r    s    6{1~6FFlmxlyzr=   r$  )rO   ra   r   r   r   r   rW   r   r   r   r   )r   r  r  r  r   input_channelsinput_batchrL  cr   r  r#  r%  s   `` `      @@@r:   meta_fractional_max_pool2dr)    s   	LL		VX 99D4!8T"IIaL166:iik]BRSTRUU[]	
 # 
LLKA	2
 
LLKA	2 YYr]N99R=L))B-Kqyiil	LL

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

 	++;;	
 r=   c                    [         R                  " [        U5      S;   S 5        US   n[        U5      S:X  a  UOUS   n[        U5      S:X  a  UOUS   n[         R                  " U(       + =(       d    [        U5      S;   S 5        U(       d  UOUS   n	U(       d  UO[        U5      S:X  a  U	OUS   n
U(       d  UO[        U5      S:X  a  U	OUS   n[         R                  " [        U5      S;   S 5        US   n[        U5      S:X  a  UOUS   n[        U5      S:X  a  UOUS   n[         R                  " [        U5      S;   S 5        US   n[        U5      S:X  a  UOUS   n[        U5      S:X  a  UOUS   n[         R                  " U R                  S	;   S
 5        U R                  S:X  a  U R	                  S5      OSnU R	                  S5      nU R	                  S5      nU R	                  S5      nU R	                  S5      n[        UXlXU5      n[        UX}U
UU5      n[        UXUUU5      n[        U UUUUU	U
UUUUUUUUUUUUUS5        U R                  S:H  =(       a'    [        R                  " U 5      [         R                  :H  nU R                  S:X  aQ  U R                  S5      nUR                  5       (       + =(       a    UR                  [         R                  S9nUUUU4nOUUUUU4nU R                  U5      nU R                  U[         R                  S9nU(       a:  UR                  [         R                  S9nUR                  [         R                  S9nUU4$ )Nr  c                      gNzMmax_pool3d: kernel_size must either be a single int, or a tuple of three intsrB   rB   r=   r:   r^   .meta_max_pool3d_with_indices.<locals>.<lambda>      _r=   r   r   r3  c                      gNzQmax_pool3d: stride must either be omitted, a single int, or a tuple of three intsrB   rB   r=   r:   r^   r-        cr=   c                      gNzImax_pool3d: padding must either be a single int, or a tuple of three intsrB   rB   r=   r:   r^   r-        [r=   c                      gNzJmax_pool3d: dilation must be either a single int, or a tuple of three intsrB   rB   r=   r:   r^   r-    r  r=   r  c                      gr  rB   rB   r=   r:   r^   r-    r  r=   r|  ra  r  r  r   zmax_pool3d_with_indices()r]  r   r   )rO   ra   r   r   r   r  r  rG   r"   r*  r   r   r   r   rl  )r  r  r   r  r  rd  r  r  r  r  r  r  r  r  r  r  r  r  r5  r  r  r  r  r  r  r  r  input_channels_last_checkr   r  r   s                                  r:   meta_max_pool3d_with_indicesr:    sB    
LLKF"_ 
QB;1$+a.B;1$+a.B	LL
+c&kV+c vayBc&kQ&6F1IBc&kQ&6F1IB	LLG[ 
B7|q gajB7|q gajB	LLH\ I ]a/	Xa[I ]a/	Xa[I	LL

fK
  %zzQUZZ^AFjjnGJJrNEjjnGZZ^F yIE"7BB	9MG!&""iKF








#+2 	

aXE77>%BXBXX  zzQ$)OOA$6!)7799
'5500 6 
 	
 eWf5	WeWf=	
//)
$Cooiu{{o;Gff5#9#9f:**5+A+A*B<r=   c                 &   [         R                  " [        U5      S;   S 5        US   n[        U5      S:X  a  UOUS   n	[        U5      S:X  a  UOUS   n
[         R                  " U(       + =(       d    [        U5      S;   S 5        U(       d  UOUS   nU(       d  U	O[        U5      S:X  a  UOUS   nU(       d  U
O[        U5      S:X  a  UOUS   n[         R                  " [        U5      S;   S 5        US   n[        U5      S:X  a  UOUS   n[        U5      S:X  a  UOUS   n[         R                  " [        U5      S;   S 5        US   n[        U5      S:X  a  UOUS   n[        U5      S:X  a  UOUS   n[         R                  " UR                  S	;   S
 5        UR	                  S5      nUR	                  S5      nUR	                  S5      nUR	                  S5      nU R	                  S5      nU R	                  S5      nU R	                  S5      n[        UU UUUU	U
UUUUUUUUUUUUUUUS5        UR                  S:H  =(       a'    [        R                  " U5      [         R                  :H  nUR                  S:X  aJ  UR                  S5      nUR                  5       (       + =(       a    UR                  [         R                  S9nUR                  UR                  5      nU(       a  UR                  [         R                  S9nU$ )Nr  c                      gr,  rB   rB   r=   r:   r^   7meta_max_pool3d_with_indices_backward.<locals>.<lambda>`  r.  r=   r   r   r3  c                      gr0  rB   rB   r=   r:   r^   r=  h  r1  r=   c                      gr3  rB   rB   r=   r:   r^   r=  p  r4  r=   c                      gr6  rB   rB   r=   r:   r^   r=  x  r  r=   r  c                      gr  rB   rB   r=   r:   r^   r=    r  r=   ra  r  r  r   z"max_pool3d_with_indices_backward()r|  r]  r   )rO   ra   r   r   r   r  rG   r"   r*  r   r   r   r   rl  )rQ  r  r  r   r  r  rd  r   r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r9  rU  s                                 r:   %meta_max_pool3d_with_indices_backwardrB  R  s    
LLKF"_ 
QB;1$+a.B;1$+a.B	LL
+c&kV+c vayBc&kQ&6F1IBc&kQ&6F1IB	LLG[ 
B7|q gajB7|q gajB	LLH\ I ]a/	Xa[I ]a/	Xa[I	LL

fK
 jjnGJJrNEjjnGZZ^FR Er"Gb!F#








,/6 	

aXE77>%BXBXX  zzQ$)OOA$6!)7799
'5500 6 
 	 -J]]1G1G]H
r=   gridc                   ^ ^^ [         R                  " T R                  TR                  :H  UU 4S j5        [         R                  " T R                  [         R                  :H  =(       a    TR                  [         R                  :H  UU 4S j5        [         R                  " T R
                  S   TR
                  S   :H  UU 4S j5        [         R                  " TR
                  S   T R                  S-
  :H  UU 4S j5        [        ST R                  5       H/  m[         R                  " T R
                  T   S:  UU 4S j5        M1     g )	Nc                  <   > STR                    ST R                    3$ )NzNgrid_sampler(): expected input and grid to be on same device, but input is on z and grid is on r  rC  r  s   r:   r^   +check_grid_sampler_common.<locals>.<lambda>  s"    \\N"24;;-Ar=   c                  <   > STR                    ST R                    3$ )NzTgrid_sampler(): expected input and grid to have torch.strided layout, but input has z and grid has )r~   rF  s   r:   r^   rG    s!    nT[[MCr=   r   c                  <   > STR                    ST R                    3$ )NzZgrid_sampler(): expected grid and input to have same batch size, but got input with sizes  and grid with sizes r   rF  s   r:   r^   rG    s"      %},A$**Or=   r   r3  c                  B   > STR                   S-
   ST R                   3$ )Nz+grid_sampler(): expected grid to have size r3  z, in last dimension, but got grid with sizes )r   r   rF  s   r:   r^   rG    s'    9%**q.9I J226**?r=   c                  *   > STR                    ST  S3$ )NzYgrid_sampler(): expected input to have non-empty spatial dimensions, but input has sizes r  r  r   r  s   r:   r^   rG    r  r=   )rO   ra   r   r~   r  r   r   r   )r  rC  r!  s   ``@r:   check_grid_sampler_commonrM    s    	LL#	
 
LL%F$++*F	
 
LLA$**Q-'	
 
LL

2%**q.(	
 1ejj!KKNQ	
 "r=   c                        \ rS rSrSrSrSrSrg)GridSamplerInterpolationi  r   r   r3  rB   N)rw   
__module____qualname____firstlineno__BILINEARNEARESTBICUBIC__static_attributes__rB   r=   r:   rO  rO    s    HGGr=   rO  interpolation_modec                 6  ^ ^ [         R                  " T R                  S:H  =(       a    T R                  TR                  :H  UU 4S j5        [         R                  " T R                  S:H  =(       a    U[        R                  R
                  :H  (       + S 5        g )Nr|  c                  <   > STR                    ST R                    3$ )Nzdgrid_sampler(): expected 5D input and grid with same number of dimensions, but got input with sizes rJ  r   rF  s   r:   r^   'check_grid_sampler_3d.<locals>.<lambda>  s!    449KK=#DJJ<1r=   c                      g)Nz<grid_sampler(): bicubic interpolation only supports 4D inputrB   rB   r=   r:   r^   rZ    r  r=   )rO   ra   r   rO  rU  r  )r  rC  rW  s   `` r:   check_grid_sampler_3dr\    sp    	LL

a3EJJ$))3	
 
LLJJ!O M"&>&F&F&L&LL	
 	Or=   c                     US   nU(       a$  [         R                  " U[         R                  S9nOS n[         R                  " U[         R                  S9n	X4$ Nr   r   )rO   r#  r   r   
rQ  r  rC  rW  padding_modealign_cornersrO  input_requires_gradrU  	grad_grids
             r:   grid_sampler_2d_backward_metard    sO     &a.%%e5;R;RS

  U5L5LMI""r=   c                     [        X5        [        XU5        U R                  S   nU R                  S   nUR                  S   nUR                  S   nUR                  S   n	U R                  XVXxU	45      $ )Nr   r   r3  r2   )rM  r\  r   r   )
r  rC  rW  r`  ra  r  Cout_Dout_Hout_Ws
             r:   grid_sampler_3drj    sn     e*%'9:AAAAJJqMEJJqMEJJqME??A%677r=   rc  c                     [        X5        [        XU5        US   nU(       a$  [        R                  " U[        R                  S9nOS n[        R
                  " U[        R                  S9n	X4$ r^  )rM  r\  rO   r#  rR  r   r_  s
             r:   grid_sampler_3d_backwardrl    sg     e*%'9:%a.%%!?!?

 
  U5S5STI  r=   c                     UR                  SS 5      nU(       d  [        R                  " U5      nXCS'   [        R                  " U /UQ70 UD6$ )NrW   )rV   rG   	get_dtyperO   r   )r   r  rI   r^  rW   s        r:   fullro  7  sC    JJw%E
+7O;;t-d-f--r=   c           	      V   U[         R                  :X  a  [         R                  " US L S 5        [         R                  " SUc  U R                  OUUUc  U R
                  OUUS9nU R                  (       a>  UR                  U R                  5       U R                  5       U R                  5       5        O/UR                  U R                  5       U R                  5       S5        UR                  S5        U$ [        R                  R                  U UUUUUS9nUR!                  S5        U$ )Nc                      g)Nz9memory format option is only supported by strided tensorsrB   rB   r=   r:   r^   zeros_like.<locals>.<lambda>M  r
  r=   r   rN  Tr  )rO   
sparse_coora   r   rW   r   	is_sparsesparse_resize_and_clear_r   
sparse_dim	dense_dimr   _coalesced_r/   r   rn  fill_)r   rW   r~   r   r   r   r  s          r:   r#  r#  A  s     !!!T!O	

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

//
!
!# " C IIaLJr=   r}   c                    Uc  [         R                  " 5       nUc  [         R                  " 5       nUc  [         R                  n[         R                  " XX#US9$ rP  rO   r   get_default_devicer  r   r   rW   r~   r   r   r   s         r:   	meta_onesr~  n  P     }'')~))+~;;&J r=   c                    Uc  [         R                  " 5       nUc  [         R                  " 5       nUc  [         R                  n[         R                  " XX#US9$ rP  r{  r}  s         r:   
meta_zerosr    r  r=   c                   ^ ^^ SSK Jn  T R                  5       n[        R                  " US:g  S 5        TS:  a  TOTU-   mT R                  T5      n[        R                  " U" T* U:  5      =(       d    U" TU:  5      (       + UUU 4S j5        TS:  a  TOTU-   m[        T R                  5       5      n[        T R                  5       5      nT R                  5       TUT   -  -   nUT	 UT	 T R                  XgU5      $ )Nr   r8  c                      g)Nz-select() cannot be applied to a 0-dim tensor.rB   rB   r=   r:   r^   meta_select.<locals>.<lambda>  s    ?r=   c                  6   > ST STR                  5        ST  3$ )Nzselect(): index z! out of range for tensor of size z at dimension r   r   r   r   s   r:   r^   r    s#    "5')J99;-~cU,r=   )
r   r9  r   rO   r   r   r	  r   r  r   )	r   r   r   r9  r   r   new_sizer   new_storage_offsets	   ```      r:   meta_selectr    s    J88:D		?
 #sTzC99S>D	 %$/V3GQU3V	
	,	 aZEUT\EDIIK Hdkkm$J,,.C1HH3??81CDDr=   c                 .    [         R                  " U 5      $ r7   rG   clone_preserve_strides)r   ro  r   r   s       r:   meta_select_scatterr        ''--r=   c                 .    [         R                  " U 5      $ r7   r  )r   ro  r   ry   rx   steps         r:   meta_slice_scatterr    r  r=   dim_post_exprwrap_scalarc                     US::  a  U(       d   eSnU* nUS-
  nX:  d  X:  a   SU  SU SU S35       eU S:  a  X-  n U $ )Nr   r   zdim z out of bounds (rt   ru   rB   )r   r  r  r=  r   s        r:   r   r     sg    {.C
!
C	SYR4u4DSEC5PQ)RR'
QwJr=   c                 L    U R                  5       S:X  a  S$ U R                  U   $ r7  rs  )r  r   s     r:   ensure_nonempty_sizer    s!    11.!''#,.r=   c                 F  ^ ^^^ [        T R                  5       S5      n[        TR                  5       S5      n[        R                  " X4:H  S 5        [	        U5       H@  mTT:w  d  M  [        R                  " [        TT5      [        T T5      :*  UUUU 4S j5        MB     g )Nr   c                      g)NzDIndex tensor must have the same number of dimensions as input tensorrB   rB   r=   r:   r^   $gather_shape_check.<locals>.<lambda>  s    Vr=   c                  N   > ST STR                    3STR                    ST  3-   $ )Nz!Size does not match at dimension z expected index  to be no larger than self  apart from dimension r   )r   r!  r   r   s   r:   r^   r    s5    ;A3>Nu{{m\/

|;QRUQVWXr=   )r   r   rO   ra   r   r  )r   r   r   	self_dims
index_dimsr!  s   ```  @r:   gather_shape_checkr    s}    DHHJ"IUYY[!$J	LLV 98LL$UA.2FtQ2OOX r=   c                   ^ SSK Jn  [        XR                  5       5      nU" TR	                  5       S:H  5      nU(       df  [
        R                  " TR                  [
        R                  :H  =(       d    TR                  [
        R                  :H  U4S j5        [        XT5        U R                  TR                  5      $ )Nr   r8  c                  "   > ST R                    3$ )Nz8gather(): Expected dtype int32/int64 for index, but got r   r   s   r:   r^   meta_gather.<locals>.<lambda>  s    Nu{{m\r=   )r   r9  r   r   r   rO   ra   rW   r   r)  r  r   r   )r   r   r   sparse_gradr9  wrapped_dimis_index_emptys     `    r:   meta_gatherr    s~    J hhj1K)%++-1*<=NKK5::%A		)A\	
 	4e4>>%++&&r=   c                     U(       a<  U S:X  a  gU S:X  a  gU S:X  a  gU S:X  a  gU S	:X  a  g
[         R                  " SS 5        g U S:X  a  gU S:X  a  g[         R                  " SS 5        g )NrH  
REDUCE_ADDr"  REDUCE_MULTIPLYmeanREDUCE_MEANamaxREDUCE_MAXIMUMaminREDUCE_MINIMUMFc                      g)Nz=reduce argument must be either sum, prod, mean, amax or amin.rB   rB   r=   r:   r^   #get_operator_enum.<locals>.<lambda>  s    Sr=   addmultiplyc                      g)Nz/reduce argument must be either add or multiply.rB   rB   r=   r:   r^   r    s    $Ur=   r  )reduce_use_new_optionss     r:   get_operator_enumr    s{    e$ ##S	
 	e
"$UUVr=   c                 n  ^  SSK Jn  U" UR                  5       S:g  5      (       aZ  [        R                  " UR
                  [        R                  :H  =(       d    UR
                  [        R                  :H  U 4S j5        Ub3  [        R                  " UR
                  UR
                  :H  U 4S j5        g g )Nr   r8  c                     > T  S3$ )Nz((): Expected dtype int32/int64 for indexrB   method_names   r:   r^   ,scatter_gather_dtype_check.<locals>.<lambda>  s    {m#KLr=   c                     > T  S3$ )Nz0(): Expected self.dtype to be equal to src.dtyperB   r  s   r:   r^   r    s    {m#STr=   )r   r9  r   rO   ra   rW   r   r)  )r  r   r   src_optr9  s   `    r:   scatter_gather_dtype_checkr    sy    JEKKMQ.//KK5::%A		)AL	

 JJ'--'T	
 r=   c                     [        U S5      $ rt  )r   r   s    r:   ensure_nonempty_dimr  "  s    sA;r=   c                 .  ^ ^^^ SSK Jn  U" TR                  5       S:H  5      (       a  g [        R                  " [        T R                  5       5      [        TR                  5       5      :H  S 5        Sn[        T R                  5       5      n[        U5       H+  n[        TU5      nUT:X  a  M  U[        T U5      :  d  M)  Sn  O   U(       d5  Tb2  [        U5       H#  n[        TU5      nU[        TU5      :  d  M!  Sn  O   Tbm  [        R                  " [        T R                  5       5      [        TR                  5       5      :H  S 5        [        R                  " U(       + UUU U4S j5        g [        R                  " U(       + UUU 4S j5        g )	Nr   r8  c                      gNzCIndex tensor must have the same number of dimensions as self tensorrB   rB   r=   r:   r^   %scatter_shape_check.<locals>.<lambda>.  r  r=   FTc                      gr  rB   rB   r=   r:   r^   r  H  s    Yr=   c                  b   > STR                    STR                    3ST  STR                    3-   $ )NExpected index r  r  z and to be no larger than src r   )r   r   r   r  s   r:   r^   r  L  s6    oekk]2Mdjj\Z&se+I'--YZr=   c                  H   > STR                    STR                    3ST  3-   $ )Nr  r  r  r   r  s   r:   r^   r  R  s*    oekk]2Mdjj\Z&se,-r=   )	r   r9  r   rO   ra   r  r   r   r  )	r   r   r   r  r9  is_wrong_shaper  r  index_d_sizes	   ````     r:   scatter_shape_checkr  '  sI   JEKKMQ.//	LLDHHJ'+>uyy{+KKU
 N#DHHJ/I 9+E158.tQ77!N  g1y!A/q9L27A>>!%	 " 
+/B599;/OOY	
 	Z	
 	-	
r=   c                     [        XR                  5       5      n[        SXU5        [        XX#5        Ub  [	        XE5        g g )Nscatter)r   r   r  r  r  )r   r   r   ro  r  r  r  s          r:   scatter_meta_implr  X  s;     hhj1Ky$s;56'3 r=   c                 R    [        XX#S5        U R                  U R                  5      $ Nr  r  r   r   r   r   r   ro  s       r:   meta_scatter_addr  a  s!    dU3>>$**%%r=   c                      [        XX#S5        U $ r  r  r  s       r:   meta_scatter_add_r  g  s    dU3Kr=   c                     [        U[        R                  5      (       a  UOS n[        XX%U5        U R	                  U R
                  5      $ r7   )rk   rO   r   r  r   r   r   r   r   src_or_valuer   ro  s         r:   meta_scatterr  m  s:     %\5<<@@,dCdV4>>$**%%r=   c                 f    [        U[        R                  5      (       a  UOS n[        XX%U5        U $ r7   )rk   rO   r   r  r  s         r:   meta_scatter_r  |  s,     %\5<<@@,dCdV4Kr=   queryr  r  	dropout_p	is_causalreturn_debug_maskr  c           	      \   U R                  S5      nU R                  S5      nU R                  S5      n	U R                  S5      n
UR                  S5      nU R                  SS5      n[        R                  " U5      R                  SS5      n[        R                  " XxU	4[        R
                  U R                  S9nU(       aa  U
S:  a  SOSn[        R                  " X-  5      nUS::  a  SnOUS::  a  Sn[        R                  " XxU	U4U R                  U R                  S9nO*[        R                  " SU R                  U R                  S9n[        R                  R                  (       al  [        R                  R                  5       (       aI  [        R                  " S	[        R                  S
S9n[        R                  " S	[        R                  S
S9nOH[        R                  " S[        R                  S
S9n[        R                  " S	[        R                  S
S9nUUS S U	UUUU4	$ )Nr   r   r3  r2   r$  @         rB   r|   )r   rB  rO   r   r   rS   r   r!  ceilrW   versionhipr7  r  r   r  )r  r  r  r  r  r  r  r  	num_headsmax_seqlen_batch_qhead_dimmax_seqlen_batch_kquery_t	attention	logsumexpblocksize_cmax_seqlen_k
debug_maskseedoffsets                       r:   (meta__scaled_dot_product_flash_attentionr    s    AJ

1IAzz!}H!ooa#G  )33Aq9I	 23kk||I %]cyy!3!AB$L3&L[[$6E++<<

 [[%++ellK
 }}UZZ4466{{2UZZ?Ruzz&A{{Aell6BRu||FC 	
 
r=   	res_shape.c                   ^  [        T R                  5      U:X  a:  T R                  SS5      n[        R                  " U5      R                  SS5      nU$ [        / SQU 4S jSS9nU Vs/ s H  oQU   PM	     nn[        [        U5      5       Vs/ s H  otR                  U5      PM     nn[        R                  " UT R                  T R                  S9R                  U5      nU$ s  snf s  snf )Nr   r3  )r   r   r3  r2   c                 *   > TR                  5       U    $ r7   r8  )idxr  s    r:   r^   ,alloc_with_matching_layout.<locals>.<lambda>  s    %,,.*=r=   Tr  r$  )r`   r   rB  rO   r   sortedr   r   r   r   rW   r   r  )	r  r  r  r  	dim_orderr  permuted_shaper!  final_permutes	   `        r:   alloc_with_matching_layoutr    s     U[[Y&//!Q'w'11!Q7 J =t
	 5>>ISC.I>5:3y>5JK5J+5JKkk%++ell

'-
  	 J ?Ks   *C'C,	attn_biascompute_log_sumexpc	           	         U R                  S5      n	U R                  S5      n
U R                  S5      nUR                  S5      nUR                  S5      nXX4n[        X5      n[        R                  " XU4[        R                  U R
                  S9n[        R                  " S[        R                  SS9n[        R                  " S[        R                  SS9nUUS S UUUUS 4	$ Nr   r   r3  r   r$  rB   r|   r   r  rO   r   rS   r   r   )r  r  r  r   r  r  r  r  r  r  r  S_QS_KVD_Vr  r  
logsum_expr  r  s                      r:   (meta__scaled_dot_product_cudnn_attentionr	    s     	

1A

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

1A
**Q-C
**Q-C88A;D
**R.C"I
$U
6C	
kk||J ;;rF;D[[5::f=F 	
 
r=   r  r  	cum_seq_q	cum_seq_kmax_qmax_kphilox_seedphilox_offsetc                 P   [         R                  " UR                  SS5      5      R                  SS5      n[         R                  " UR                  SS5      5      R                  SS5      n[         R                  " UR                  SS5      5      R                  SS5      nUUU4$ r  )rO   r   rB  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  grad_qgrad_kgrad_vs                     r:   'meta__scaled_dot_product_flash_backwardr  6  s    , eooa34>>q!DFcmmAq12<<QBFeooa34>>q!DF66!!r=   	attn_maskc                    U R                  S5      nU R                  S5      nU R                  S5      n	[        R                  " U 5      n
[        R                  " UU	U4[        R                  U R
                  S9R                  SS5      nU
U4$ )Nr   r   r3  r$  )r   rO   r   r   rS   r   rB  )r  r  r  r  r  r  r  r  r  r  r  r  s               r:   0meta__scaled_dot_product_flash_attention_for_cpur  R  s     AJ

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

 kk|| i1o  	 r=   c
                    UR                  S5      n
UR                  S5      nUR                  S5      nUR                  S5      nUR                  S5      n[        R                  " XX4SUR                  UR                  S9n[        R                  " XX4SUR                  UR                  S9n[        R                  " XX4SUR                  UR                  S9nUUU4$ )Nr   r   r2   r3  r   r3  r   r2   r$  )r   rO   empty_permutedrW   r   )r  r  r  r  r  r  r  r  r  r  r  r  r  len_qlen_kr  r  r  s                     r:   9meta__scaled_dot_product_flash_attention_for_cpu_backwardr   t  s    & AJ

1Izz!}HJJqMEHHQKE!!	0kk||	F !!	0iizz	F !!	0kk||	F 66!!r=   c           	      R   U R                  SS5      n UR                  SS5      nUR                  SS5      nU R                  S5      nU R                  S5      n	U R                  S5      n
UR                  S5      n[        R                  " XXU R                  U R
                  S9n[        R                  R                  (       a0  [        R                  R                  5       (       a   U(       a  U	OSnO%U(       a  [        R                  " U	S-  5      S-  OSn[        R                  " XU4[        R                  U R
                  S9nUR                  SS5      n[        R                  " S[        R                  S	S9n[        R                  " S[        R                  S	S9nXUU4$ )
Nr   r3  r   r  r   r$  r  rB   r|   )rB  r   rO   r   rW   r   r  r  r7  r  r!  r  rS   r   )r  r  r  r   r  r  r  r  r  r  r  Kvr  logsumexp_dimr  r  r  s                    r:   ,meta__scaled_dot_product_efficient_attentionr$    s?    OOAq!E
--1
COOAq!E

1A

1A

2I	BB
++aIU\\
RC}}UZZ4466	 0Q2D		!b&)B.!	
}%kk||J --1
C ;;rF;D[[5::f=FD&((r=   grad_input_maskc                    UR                  S5      nUR                  S5      nUR                  S5      nUR                  S5      nUR                  S5      nUR                  S5      n[        R                  " XUU4SUR                  UR                  S9n[        R                  " XUU4SUR                  UR                  S9n[        R                  " XUU4SUR                  UR                  S9nS nUb  U
S   (       ax  UR                  S5      nUS-  S:X  a  UO
US-   US-  -
  n[        UR                  5       5      nUUS'   [        R                  " UUR                  UR                  S9nUS	S U24   nUUUU4$ )
Nr   r   r3  r2   r  r$  r   r  .)r   rO   r  rW   r   r	  r   )r  r  r  r  r   r  r  r  r  r  r%  r  r  r  r  r  r  
head_dim_vr  r  r  r  	grad_biaslastDimlastDimAligned	new_sizess                             r:   +meta__scaled_dot_product_efficient_backwardr,    su   ( AJ

1IJJqMEzz!}HAJHHQKE!!	x0kk||	F !!	x0iizz	F !!	z2kk||	F I!3..$$+bLA$57R<'TV,;V)*	&	"KKY__Y5E5E
	 c8G8m,	669,,r=   c                     [         R                  " U5      n[         R                  " U5      n[         R                  " U5      nUUU4$ r7   r  )r  r  r  r  r  r  r  r  r   r  r  r  r  r  r  r  r  r  r  s                      r:   'meta__scaled_dot_product_cudnn_backwardr.    sA    . e$Fc"Fe$F66!!r=   window_size_leftwindow_size_right	seqused_kalibi_slopesc                    Uc  U R                  S5      OUR                  5       S-
  nUc  U R                  S5      OUnUc  UR                  S5      OUnU R                  S5      nU R                  S5      n[        R                  " U 5      nUc2  [        R                  " UUU4[        R
                  U R                  S9nOAU R                  S5      n[        R                  " UU4[        R
                  U R                  S9nU	(       ac  US:  a  SOSn[        R                  " UU-  5      nUS::  a  SnOUS::  a  Sn[        R                  " UUUU4U R                  U R                  S9nO*[        R                  " SU R                  U R                  S9nS	u  nn[        R                  R                  (       al  [        R                  R                  5       (       aI  [        R                  " S
[        R                  SS9n[        R                  " S
[        R                  SS9nOH[        R                  " S[        R                  SS9n[        R                  " S
[        R                  SS9nUUUUU4$ )Nr   r   r  r   r$  r  r  r  NNrB   r|   r3  )r   r   rO   r   r   rS   r   r!  r  rW   r  r  r7  r  r   r  )r  r  r  r  r  r  r  r  r  r  r  r/  r0  r1  r2  r  r  r  r  r  r  r  total_qr  r  r  r  r  s                               r:   meta__flash_attention_forwardr6  )  s   4 #,"3A9JQ9NJ*3*;A(1(9!u

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

 [[%++ellK
 LD&}}UZZ4466{{2UZZ?Ruzz&A{{Aell6BRu||FC r=   c                     [         R                  " U5      n[         R                  " U5      n[         R                  " U5      nUUU4$ r7   r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r/  r0  
grad_querygrad_key
grad_values                       r:   meta__flash_attention_backwardr;  y  sA    0 !!%(J$H!!%(Jx++r=   cu_seqlens_qcu_seqlens_kmax_seqlen_qr  custom_mask_typecausal_diagonalseqlen_kwindow_sizec           	         U R                  S5      nU R                  S5      nUR                  S5      nU R                  S5      nUR                  S5      n[        R                  " UUUUU R                  U R                  S9nUb  UR                  S5      S-
  OUnUnUb  Uc   eUnUb  UOUnU
(       a  [
        R                  " US-  5      S-  OSn[        R                  " UUU4[        R                  U R                  S9n[        R                  " S[        R                  SS9n[        R                  " S[        R                  SS9nUUUUUU4$ )	Nr   r   r  r   r$  r  rB   r|   )	r   rO   r   rW   r   r!  r  rS   r   )r  r  r  r  r<  r=  r>  r  r  r?  r  r  r@  rA  rB  r  r  r  r  r"  r  logsumexp_batch_dimactual_max_seqlen_qactual_max_seqlen_kr#  r  r  r  s                               r:   !meta__efficient_attention_forwardrG    s9   , 	

1A

1AA

2I	BB
++aIrU\\
RC7C7O,++A.2VW'''**6*B,4F		%*+b0A  	i7kk||J ;;rF;D[[5::f=F
D&*=?RRRr=   bias_requires_gradnum_splits_keyshared_storage_dqdkdvc                    U(       a  [         R                  " UR                  S   UR                  S   :H  S 5        [         R                  " UR                  S   UR                  S   :H  S 5        [         R                  " / UR                  SS QSPUR                  S   PUR                  S   P7UR                  UR
                  S9nUR                  S	S5      nUR                  S	S5      nUR                  S	S
5      nOB[         R                  " U5      n[         R                  " U5      n[         R                  " U5      nUby  UR                  S5      nUS-  S:X  a  UO
US-   US-  -
  n[        UR                  5       5      nUUS'   [         R                  " UUR                  UR
                  S9nUSS U24   nO[         R                  " SUR
                  S9nUUUU4$ )Nr   c                      g)Nz,seqlen must match for `shared_storage_dqdkdvrB   rB   r=   r:   r^   4meta__efficient_attention_backward.<locals>.<lambda>  s    Br=   r2   c                      g)Nz3embedding dim must match for `shared_storage_dqdkdvrB   rB   r=   r:   r^   rM    s    Ir=   r   r  r   r$  r  r3  r  .rB   r  )
rO   ra   r   r   rW   r   r;  r   r   r	  )r  r  r  r  r  r<  r=  r>  r  r  r  r  r  r?  rH  r  rI  rJ  chunkr8  r9  r:  r)  r*  r+  r(  s                             r:   "meta__efficient_attention_backwardrP    s   2 KKNciil*B	
 	KKNciil*I	
 Eekk!BEEEKKOEU[[_E++<<

 \\"a(
<<A&\\"a(
%%e,
##C(%%e,
))B-$+bLA$57R<'TV,;V%	&	"KK	DKKP	c8G8m,	KK5<<8	xY66r=   scale_ascale_bscale_resultuse_fast_accumc                 
  ^ ^^^^^^^ S n[         R                  " T R                  5       S:H  =(       a    TR                  5       S:H  UU 4S j5        [         R                  " U" T R                  5      =(       a    U" TR                  5      UU 4S j5        [	        T 5      S:X  Gaw  S n	S n
S n[         R                  " U	" T R                  5       5      =(       d    U" T 5      U 4S	 j5        [         R                  " U
" TR                  5       5      =(       d    U" T5      U4S
 j5        [         R                  " T R                  S5      S-  S:H  U 4S j5        [         R                  " TR                  S5      S-  S:H  =(       a    TR                  S5      S-  S:H  U4S j5        T R                  u  mnTR                  S5      mTR                  [         R                  :H  =(       a    TR                  [         R                  :H  =(       dA    TR                  [         R                  :H  =(       a    TR                  [         R                  :H  nTR                  5       S:X  am  TR                  5       S:X  aY  [         R                  " TR                  [         R                  :H  =(       a    TR                  [         R                  :H  S 5        GOJU(       a  TR                  [         R                  :X  a  SnUS-  nOSnSnS nU" X5      nU" US5      S-  nUU" TU5      -  U-  mUU" TU5      -  U-  mTR                  5       T:X  ab  TR                  5       T:X  aN  [         R                  " TR                  5       S 5        [         R                  " TR                  5       S 5        GOn[         R                  " SUUUU4S j5        GON[         R                  " TR                  [         R                  :H  =(       a    TR                  [         R                  :H  S 5        [         R                  " TR                  5       S:H  =(       a    TR                  5       S:H  UU4S j5        TR                  S5      T:X  a}  TR                  S5      S:X  ah  TR                  S5      S:X  aS  TR                  S5      T:X  a>  [         R                  " TR                  5       =(       a    TR                  5       S 5        O[         R                  " SUUUU4S j5        Ub  UOT R                  n[         R                  " T R                  S5      TR                  S5      UT R                  S9$ )Nc                     U [         R                  [         R                  [         R                  [         R                  [         R
                  4;   $ r7   )rO   r  float8_e5m2float8_e4m3fnuzfloat8_e5m2fnuzfloat4_e2m1fn_x2r   s    r:   is_fp8_or_fp4_type*meta_scaled_mm.<locals>.is_fp8_or_fp4_type  sA    !!!!""
 
 	
r=   r3  c                  L   > STR                  5        ST R                  5        3$ )Nz%Inputs must be 2D but got self.dim()=z and mat2.dim()=r   r  r   s   r:   r^    meta_scaled_mm.<locals>.<lambda>  s%    7
|CSTXT\T\T^S_`r=   c                  <   > STR                    ST R                    3$ )Nz?Expected both inputs to be fp8 or fp4 types but got self.dtype=z and mat2.dtype=r   r^  s   r:   r^   r_  "  s$    QRVR\R\Q]]mnrnxnxmyzr=   r7  c                 6    U S   U S   :  =(       a    U S   S:H  $ r7  rB   r8  s    r:   is_row_major$meta_scaled_mm.<locals>.is_row_major'  s"    !9vay(;VAY!^;r=   c                 0    U S   S:H  =(       a    U S   S:  $ r7  rB   r8  s    r:   is_col_major$meta_scaled_mm.<locals>.is_col_major*  s    !9>3fQi!m3r=   c                 `    U R                  S5      S:H  =(       d    U R                  S5      S:H  $ r7  r   )	tensor_2ds    r:   has_zero_dim$meta_scaled_mm.<locals>.has_zero_dim-  s)    >>!$)CY^^A->!-CCr=   c                  *   > ST R                  5        3$ )Nz#self must be row_major, got stride r8  r   s   r:   r^   r_  2      9$++-Ir=   c                  *   > ST R                  5        3$ )Nz#mat2 must be col_major, got stride r8  r  s   r:   r^   r_  6  rl  r=   r   r  r   c                  ,   > ST R                  S5       3$ )NzBExpected self.size(1) to be divisible by 16, but got self.size(1)=r   r   r   s   r:   r^   r_  :  s    XY]YbYbcdYeXfgr=   c                  "   > ST R                    3$ )Nz>Expected both dimensions of mat2 to be divisble by 16 but got r   rn  s   r:   r^   r_  >  s    TUYU_U_T`ar=   c                      g)NzNFor tensorwise scaling, both scale_a and scale_b must be float (fp32) tensors.rB   rB   r=   r:   r^   r_  R  s    hr=   r  r  c                     X-   S-
  U-  $ rt  rB   r  s     r:   ceil_div meta_scaled_mm.<locals>.ceil_divb  s    	a''r=   r]  c                      g)Nzscale_a must be contiguousrB   rB   r=   r:   r^   r_  u      8r=   c                      g)Nzscale_b must be contiguousrB   rB   r=   r:   r^   r_  y  rv  r=   Fc            	      Z   > ST  STR                  5        ST STR                  5        S3	$ )NzTInvalid blockwise scaling configuration. For blockwise scaling, scale_a should have  elements, got z, scale_b should have r!  r5  )expected_a_sizeexpected_b_sizerQ  rR  s   r:   r^   r_  ~  sC    FFUEVVefmfsfsfuev w//>.?w}}N__`br=   c                      g)NzKFor rowwise scaling, both scale_a and scale_b must be float (fp32) tensors.rB   rB   r=   r:   r^   r_    s    er=   c                  P   > ST R                  5       < STR                  5       < 3$ )NzLFor non-tensorwise scaling, scale tensors must be 2D, but got scale_a.dim()=z and scale_b.dim()=r   )rQ  rR  s   r:   r^   r_    s*    gY`YdYdYfXhh|nunynyn{m}~r=   c                      g)Nz@Both scale_a and scale_b must be contiguous for rowwise scaling.rB   rB   r=   r:   r^   r_    s    ^r=   c                     > ST  ST STR                  S5       STR                  S5       STR                  S5       STR                  S5       S3$ )	Nz}Invalid scaling configuration. For tensorwise scaling, both scales should be scalar. For rowwise scaling, scale_a should be (z, 1), scale_b should be (1, z). Got scale_a.size()=(r   rt   r   z) and scale_b.size()=(ru   r   )r  rL  rQ  rR  s   r:   r^   r_    sf    CCD#Eabcad e//6||A.?r',,q/AR S//6||A.?r',,q/ARRS	Ur=   r$  )rO   ra   r   rW   r<  r   r   r   float8_e8m0fnur  r   r  r   r   r   )r   r  rQ  rR  r  rS  r  rT  r[  rb  re  ri  _kis_blockwise_scalingblock_size_kblock_size_mnrs  num_k_blockspadded_num_k_blocks
_out_dtyperz  r{  r  rL  s   ````                @@@@r:   meta_scaled_mmr    s   
 
LL
a+DHHJ!O` 
LL4::&I+=djj+Iz
 4F"	<	4	D 	'=<+=I	
 	'=<+=I	
 	IIaL2"g	
 	IIaL2"=tyy|b'8A'=a	
 

2IIaL MMU111 6!5!55 
 MMU000 5!4!44 	 ==?aGMMOq$8LL.Q7==EMM3Qh " }} 3 33  "!V!M( $B5L"*<";a"? M ::=PP  M ::=PP 
 ?2MMO6))+8 ))+8
  LL.Q7==EMM3Qe
 LL"9w{{}'9~ Q1$LLOq(LLOq(LLOq( ))+G0E0E0G^ 	 (3J;;tyy|TYYq\DKKXXr=   c           	      P    [        XX#USS9  U R                  U R                  5      $ NT)r  r  r   r   r   ro  r   r  s         r:   meta_scatter_reduce_twor    s%     dVTJ>>$**%%r=   c           	          [        XX#USS9  U $ r  r  r  s         r:   meta_scatter_reduce__twor    s    dVTJKr=   c                |  ^  [         R                  " ST R                  5       s=:  =(       a    S:*  Os  U 4S j5        T R                  5       S:X  a.  [         R                  " U[         R                  T R
                  S9$ [         R                  " T R                  S5      U[         R                  T R
                  S9$ )Nr   r3  c                  *   > ST R                  5        3$ )Nz@The probabilty distributions dimensions must be 1 or 2, but got r   rC  s   r:   r^   "meta_multinomial.<locals>.<lambda>  s    RSXS\S\S^R_`r=   r   r$  )rO   ra   r   r   r   r   r   )r  num_samplesreplacementrI  s   `   r:   meta_multinomialr    s     
LL	EIIK1` yy{a{{;ejjNN;;

1{%**U\\ r=   c                 $    SnU  H  nX-  nM	     U$ rt  rB   )vsr  vs      r:   multiply_integersr    s    	A	 Hr=   c                 ^  ^ ^^^ [         R                  " [        T5      T:H  UU4S j5        TS-   m[         R                  " [        T 5      T:H  UU 4S j5        [         R                  " [        S T SS   5       5      =(       a    [        S T 5       5      U U4S j5        T S S u  p4X4/TQ7$ )Nc                  &   > ST  S[        T5       3$ )Nz%It is expected output_size equals to , but got size r  )num_spatial_dimsr  s   r:   r^   'upsample_common_check.<locals>.<lambda>  s    78H7IY\]hYiXjkr=   r3  c                  &   > ST  S[        T5       3$ )Nz$It is expected input_size equals to r  r  )expected_input_dimsr  s   r:   r^   r    s    67J6K?[^_i[jZklr=   c              3   *   #    U  H	  oS :  v   M     g7fr  rB   rm   r   s     r:   ro   (upsample_common_check.<locals>.<genexpr>  s     *>aE>r  c              3   *   #    U  H	  oS :  v   M     g7fr  rB   r  s     r:   ro   r    s     2N+Qq5+r  c                     > ST  ST 3$ )NzDInput and output sizes should be greater than 0, but got input size z and output size rB   )r  r  s   r:   r^   r    s      \!2;-Ar=   )rO   ra   r   r  )r  r  r  r5  channelsr  s   ```  @r:   upsample_common_checkr    s    	LLK,,k +Q.	LLJ..l
 
LL*:ab>**Ns2N+2N/N	A ""1~F+{++r=   c                 8  ^  [         R                  " T R                  5       S:g  =(       d    [        T R	                  5       SS  5      U 4S j5        [        T R	                  5       USS9nT R                  U5      R                  [        R                  " T 5      S9$ )Nr   r   c                  *   > ST R                  5        3$ )Nz>Non-empty 3D data tensor expected but got a tensor with sizes r   rC  s   r:   r^   $upsample_nearest1d.<locals>.<lambda>      PQVQ[Q[Q]P^_r=   r  r   
rO   ra   r   r  r   r  r   rl  rG   r"   )r  r  scalesfull_output_sizes   `   r:   upsample_nearest1dr         
LLA/

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

kA ??+,//11%8 0  r=   c                   ^  [         R                  " T R                  5       S:g  =(       d    [        T R	                  5       SS  5      U 4S j5        [        T R	                  5       USS9nT R                  U5      n[        R                  " T 5      nT R                  u  px  nT R                  R                  S:X  a  US:  a  [         R                  nUR                  US9nU$ )	Nr   r   c                  *   > ST R                  5        3$ Nz>Non-empty 4D data tensor expected but got a tensor with sizes r   rC  s   r:   r^   $upsample_nearest2d.<locals>.<lambda>  r  r=   r3  r  r7  r]  r   )rO   ra   r   r  r   r  r   rG   r"   r   r   rv   r   
contiguous)	r  r  scales_hscales_wr  rC  r   rJ   
n_channelss	   `        r:   upsample_nearest2dr    s     
LLA/

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

kA __-.F //6M  ++A1a||F"zA~//];FMr=   r  r  r  r  c                 X  ^ ^^ [        X!SS9m[        R                  " T R                  S:H  U 4S j5        [	        S5       H5  m[        R                  " T R                  T5      TT   :H  UU U4S j5        M7     T R                  U5      R                  [        R                  " T 5      S9$ )Nr3  r  r]  c                  "   > ST R                    3$ NzFExpected grad_output to be a tensor of dimension 4 but got: dimension rI  r  s   r:   r^   -upsample_nearest2d_backward.<locals>.<lambda>      XYdYiYiXjkr=   c            
      D   > ST ST T    ST STR                  T5       3$ )NzCExpected grad_output to have the same shape as output; output.size() = z but got grad_output.size(r   r  rQ  r!  s   r:   r^   r  #  s9      !s$'7':&;,QCtK4D4DQ4G3HJr=   r   )
r  rO   ra   r   r   r   r   rl  rG   r"   )rQ  r  r  r  r  r  r!  s   `    @@r:   upsample_nearest2d_backwardr    s     -! 
LLAk 1XQ#3A#66	
    ,//11+> 0  r=   c                 8  ^  [         R                  " T R                  5       S:g  =(       d    [        T R	                  5       SS  5      U 4S j5        [        T R	                  5       USS9nT R                  U5      R                  [        R                  " T 5      S9$ )Nr   r   c                  *   > ST R                  5        3$ )Nz>Non-empty 5D data tensor expected but got a tensor with sizes r   rC  s   r:   r^   $upsample_nearest3d.<locals>.<lambda>5  r  r=   r2   r  r   r  )r  r  scales_dr  r  r  s   `     r:   upsample_nearest3dr  /  r  r=   c                    [         R                  " U 5      [         R                  " U [         R                  S9pvUb  Ub  [        U[        5      (       d   e[        U[        5      (       d   eUR
                  nUR                  5       n	[        XH5      n[        XX5      nUR                  X5        UR                  X5        [        XdS9  [        XuS9  XE4$ Xg4$ )Nr   )r  r  )
rO   r   r   rk   r#   r   r   r%   r  r'   )
r   stabler   
descendingr   r   r  r!  r   
out_strides
             r:   	meta_sortr  ?  s     D!5#3#3D#Lqg1&*----':.... GG	XXZ
"65#G791I2344Kr=   c           	      >  ^ ^^^^^^^ [         R                  " T R                  S:H  U 4S j5        [         R                  " T R                  TR                  :H  UU 4S j5        T R	                  S5      mTb  [         R                  " TR                  S:H  U4S j5        [         R                  " TR                  5       T:H  UU4S j5        [         R                  " TR                  TR                  :H  UU4S j5        [         R                  " TR                  S:H  U4S j5        T R	                  S	5      T-  T-  m[         R                  " TR                  5       T:H  UUUU U4S
 j5        [         R                  " [        U 4S jTTTT4 5       5      S 5        g )Nr3  c                  "   > T R                    S3$ Nz != 2rI  )input_gatess   r:   r^   %rnn_cell_checkSizes.<locals>.<lambda>b      ;3C3C2DE0Jr=   c                  :   > TR                    ST R                    3$ N != r   )hidden_gatesr  s   r:   r^   r  e  s    ;$$%T,*<*<)=>r=   r   c                  "   > T R                    S3$ )Nz != 1rI  )
input_biass   r:   r^   r  i  s    joo5Fe3Lr=   c                  .   > TR                  5        ST  3$ r  r5  )
gates_sizer  s   r:   r^   r  l  s    z'')*$zl;r=   c                  :   > TR                    ST R                    3$ r  r   )hidden_biasr  s   r:   r^   r  p  s    z''([->->,?@r=   c                  "   > T R                    S3$ r  rI  )prev_hiddens   r:   r^   r  r  r  r=   r   c            
      `   > TR                  5        STR                  S5       ST ST ST  S3
$ )Nr  r   z * z // z (aka ru   )r   r   )expected_prev_hidden_numelfactorr  r  r  s   r:   r^   r  v  s@    ;$$&'tK,<,<Q,?+@J<tTZS[[ab|a}}~r=   c              3   V   >#    U  H  nUR                   TR                   :H  v   M      g 7fr7   r  )rm   rL   r  s     r:   ro   &rnn_cell_checkSizes.<locals>.<genexpr>y  s'      
I HH***Is   &)c                      g)Nz%expected all inputs to be same devicerB   rB   r=   r:   r^   r  }  s    7r=   )rO   ra   r   r   r   r   r  )r  r  r  r  r  r  r  r  s   ``````@@r:   rnn_cell_checkSizesr  Z  sC    
LL!!Q&(JK	LL\///> !!!$JZ__)+LM*,;	
 	 1 11@	
 
LL!!Q&(JK!,!1!1!!4z!AV!K	LL99 
LL 
"J[I
 	
 	8r=   c                     [        XX4SU5        [        R                  " U [        R                  S9n[        R                  " U[        R                  S9n[        R                  " U[        R                  S9nXgU4$ )Nr]  r   )r  rO   r   r   )r  r  cxr  r  	workspacehycys           r:   _thnn_fused_lstm_cell_metar    se     :ArR  E<S<STI			"E,C,C	DB			"E,C,C	DBIr=   c                    [        U5      S:g  nU(       a   [        U5      nUS   nU R                  S   nOLU
(       a  U R                  S   OU R                  S   nU
(       a  U R                  S   OU R                  S   nSnU(       a  SOSnUS:w  a  UOUnU(       a  UUU-  /nOU
(       a  UUUU-  /OUUUU-  /nU R                  U5      nU	U-  UU/nUc   [        R                  " SU R
                  S9nOUR                  U5      nUR                  U	U-  UU/5      nU(       a  SOSnU R                  U[        R                  S9nUUUUU4$ )Nr   r   r   r3  r  r   )r   r   r   rO   r   r   r<  )r  r~  weight_stride0
weight_bufhxr  r  hidden_size	proj_size
num_layersbatch_firstdropouttrainbidirectionalbatch_sizesdropout_stateis_input_packed
seq_length
mini_batchbatch_sizes_sumnum_directionsout_sizer   rC  
cell_shaper  r  reserve_shapereserves                                r:   
_cudnn_rnnr	    sS   & +&!+O%
 ^
++a.'2U[[^A
'2U[[^A
'QQN%NyH$h&?@	  X%>?j(^*CD 	
 __Y'F~-z;GJ	z[[5<<0\\*%	zN2JI	JB AAMoom5;;o?G2r7J..r=   c                 >   U(       a  U R                   S   OU R                   S   nU(       a  U R                   S   OU R                   S   nU
nU(       a  UUU/OUUU/nU R                  U5      nUc   [        R                  " SU R                  S9nOUR                  UR                   5      nUc   [        R                  " SU R                  S9nOUR                  UR                   5      n[        R                  " SU R                  [        R
                  S9nUUUU4$ )Nr   r   r  r   )r   r   rO   r   r   r<  )r  w0w1w2w3hx_cx_r  r  r  r  r  
has_biasesr  r  r  r  r  output_chanelsr   rC  r  r  r  s                           r:   mkldnn_rnn_layerr	    s    & $/QEKKNJ#.QEKKNJ N  
Z0*n5 
 __Y'F
{[[5<<0]]399%
{[[5<<0]]399%Aell%++FI2r9$$r=   c                    ^^ U R                   S:X  a,  [        R                  " TS:H  =(       d    TS:H  UU4S j5        g [        R                  " U R                  T5      S:g  UU4S j5        g )Nr   r   c                     > T ST  3$ )Nz4: Expected reduction dim -1 or 0 for scalar but got rB   r   r   s   r:   r^   'zero_numel_check_dims.<locals>.<lambda>  s    wiSTWSXYr=   c                     > T ST  S3$ )Nz: Expected reduction dim z to have non-zero size.rB   r	  s   r:   r^   r	    s    wi8=TUr=   )r   rO   r   r   )r   r   r   s    ``r:   zero_numel_check_dimsr	    sR    yyA~1H!r	Y	

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

coSF4PD$T9E>>%u{{>33r=   c                 v    U[         R                  :X  a  [         R                  n[         R                  " SXX4S9$ )NrB   rN  )rO   jaggedr  r   )r   rW   r~   r   r   s        r:   scalar_tensorr	    s1    
 ;;
%v r=   c                    [        X R                  5       SS9nU R                  5       S:X  a  SOU R                  U5      n[        R                  " U5        [        R
                  " X:*  S 5        [        U R                  5      n[        U5      S:  a  XU'   U R                  U5      U R                  U[        R                  S94$ )NTr  r   r   c                      g)Nzk not in range for dimensionrB   rB   r=   r:   r^   topk_meta.<locals>.<lambda>#  s    )Gr=   r   )r   r   r   rO   r  ra   r	  r   r   r   r   )r   r  r   largestr  	sliceSizetopKSizes          r:   	topk_metar$	    s     hhjd
;CXXZ1_$))C.I		LL!GHDJJH
8}q>>(#T^^HEKK^%PPPr=   c                     Uc
  Uc   S5       eUR                  5       nU R                  5       n	[        R                  " UU	R                  U	R                  U	R
                  S9$ )Nz;segment_reduce(): Either lengths or offsets must be defined)rW   r   r~   )r  rO   r   rW   r   r~   )
r  rC  r  r   r  r  r  r  data_contiggrad_contigs
             r:   meta__segment_reduce_backwardr(	  +  sj    
 '"5 E5 //#K//#K!!!!	 r=   c                   ^ SSK Jn  [        TU R                  5       SS9mU R                  5       S:  a  U R	                  T5      OSn[
        R                  " U" US:  X:*  5      U4S j5        [        U R                  S T U R                  TS-   S  -   5      nU(       a&  U R                  5       S:  a  UR                  TS5        U R                  U5      U R                  U[
        R                  S94$ )Nr   )sym_andTr	  r   c                     > ST  3$ )Nz9kthvalue(): selected number k out of range for dimension rB   r   s   r:   r^   kthvalue_meta.<locals>.<lambda>F  s    KC5Qr=   r   )r   r*	  r   r   r   rO   ra   r	  r   ru  r   r   )r   r  r   r  r*	  dimSizer   s     `    r:   kthvalue_metar.	  =  s     >
dhhjd
;C $
QdiinAG	LLQ%Q
 DS!DJJsQwy$99:E488:>S!>>% $..ekk."JJJr=   c                    U b  U OUn[         R                  " UR                  5       S:H  S 5        UR                  5       nU b)  [         R                  " U R                  5       U:H  S 5        Ub)  [         R                  " UR                  5       U:H  S 5        [         R                  " UR                  5       U:H  S 5        [         R                  " UR                  5       U:H  S 5        [         R                  " UR                  5       S:H  S 5        [         R                  " UR	                  5       US   US	   -  S
-  :H  S 5        g )Nr3  c                      gN rB   rB   r=   r:   r^   (checkLSTMBackwardSizes.<locals>.<lambda>U  s    "r=   c                      gr1	  rB   rB   r=   r:   r^   r3	  X      r=   c                      gr1	  rB   rB   r=   r:   r^   r3	  Z  r5	  r=   c                      gr1	  rB   rB   r=   r:   r^   r3	  [      r=   c                      gr1	  rB   rB   r=   r:   r^   r3	  \  r8	  r=   c                      gr1	  rB   rB   r=   r:   r^   r3	  ]  s    rr=   r   r   r]  c                      gr1	  rB   rB   r=   r:   r^   r3	  ^  s    Rr=   )rO   ra   r   r   r   )grad_hygrad_cyr  r  r  defined_gradexp_sizes          r:   checkLSTMBackwardSizesr@	  S  s    %17wL	LL!!#q(*5  "HW\\^x/<W\\^x/<	LLh&
3	LLh&
3	LLA%z2	LL"hqkHQK&?!&CCZPr=   c                     U c  Uc  g[        XX#U5        [        R                  " U[        S9n[        R                  " U[        S9nU(       a  UR	                  SSS9OS nXgU4$ )NNNNr   r   F)r  )r@	  rO   r   legacy_contiguous_memory_formatrH  )	r<	  r=	  r  r  r  has_bias
grad_gatesgrad_cxr(  s	            r:   #_thnn_fused_lstm_cell_backward_implrG	  b  sf    7?7RY?!!!@J r1PQG4<
q%0$I	))r=   c                 2   S nS nS nUS   (       a  UR                  U R                  5       5      nUS   (       d
  US   (       aQ  UR                  UR                  S5      U R                  S5      45      nUR                  UR                  S5      5      nXEU4$ )Nr   r   r3  r   rI  )rK  rJ  rL  rO  rU  grad_weightr(  s          r:   linear_backwardrJ	  p  s    JKI1~!++FKKM:
1~Q",,l.?.?.CV[[QS_-UV **<+<+<R+@A	Y//r=   c                   ^ ^ [        T R                  5      S:  a  T R                  S   X-  -  S:X  d   ST R                   SU 35       eS mUU 4S jnT R                  S   X-  -  nT R                  S   U-  nT R                  S	   U-  n/ T R                  S S QUPUPUP7nT R                  U5      nUR                  U" 5       S
9nU$ )Nr3  r  r   z'Invalid input shape for pixel_shuffle: z with upscale_factor = c                 b    [         R                  R                  U 5      [         R                  :H  $ r7   r
  r  s    r:   r  ,meta_pixel_shuffle.<locals>.is_channels_last  s$    ""88=ATATTTr=   c                  F  > T " T5      (       a/  [        T5      S:X  a  [        R                  $ [        R                  $ TR	                  [        R                  S9(       a  [        R                  $ TR	                  [        R
                  S9(       a  [        R
                  $ g r!  )r<  rO   r   r  r   r"  )r  r   s   r:   r  .meta_pixel_shuffle.<locals>.pick_memory_format  s    D!!4 F*...***e.E.EF***e.C.CD((( Er=   r  r   r   )r   r   r   rl  )	r   upscale_factorr  rf  HrWrr   r  r  s	   `       @r:   meta_pixel_shufflerS	  }  s     	DJJ!

2.2Q RVW W 2$**=TUcTdeW
U	) 	

2>:;A	B.	(B	B.	(B-$**Sb/-1-b-"-I
..
#C
&&13&
4CJr=   c                 X   U R                  U R                  5      nUR                  UR                  5      nUR                  UR                  5      nUR                  UR                  5      nUR                  UR                  5      nUR                  UR                  5      nUUUUUUU4$ r7   r2  )r  weight0weight1weight2weight3r	  cx_tmprC  hy_cy_grad_output_r_optgrad_hy_r_optgrad_cy_r_optr  r  r  r  r
	  r  r  r  r  r  diff_xdiff_hxdiff_cxdiff_w1diff_w2diff_bs                                r:   mkldnn_rnn_layer_backwardre	    s    4 __U[[)FmmCII&Gv||,G.G.Gw}}-F7GVVWgEEr=   )	out_int32r  c                    [         R                  " U U(       a  [         R                  O[         R                  [         R                  S9$ )NrW   r   )rO   r   r  r   r   )r   
boundariesrf	  r  s       r:   meta_bucketizerj	    s2     &ekkEKK-- r=   c                   ^ ^^^^ Sm[        T 5      S:X  a)  [        R                  " T R                  5       U 4S j5        [        T 5      S:X  a+  T R                  5       (       a  [        R
                  " S5        [        R                  " [        T[        5      UU4S j5        [        R                  " TS:  UU4S j5        [        R                  " [        T[        5      UU4S	 j5        [        R                  " [        T[        5      UU4S
 j5        [        R                  " TT:  S 5        [        R                  " TT R                  T R                  S9$ )Nzhistc()rC  c                  $   > ST R                    S3$ )Nz%"histogram_cpu" not implemented for 'r@  r   rC  s   r:   r^   meta_histc.<locals>.<lambda>  s    =ekk]!Lr=   r7  z%_histc_cuda with floating point inputc                  $   > T S[        T 5       3$ )Nz#: argument 'bins' must be int, not re  binsr   s   r:   r^   rm	    s    7)>tDzlKr=   r   c                     > T ST  3$ )Nz: bins must be > 0, but got rB   ro	  s   r:   r^   rm	    s    gY.J4&#Qr=   c                  $   > T  S[        T5       3$ )Nz%: argument 'min' must be Number, not re  )r   r=  s   r:   r^   rm	        7)@cLr=   c                  $   > T  S[        T5       3$ )Nz%: argument 'max' must be Number, not re  )r   r   s   r:   r^   rm	    rs	  r=   c                      g)Nz&{fn_name}: max must be larger than minrB   rB   r=   r:   r^   rm	    s    %Mr=   r   )r<  rO   ra   r;  rG   r\  rk   r   r!   r   r   rW   )r  rp	  r=  r   r   s   ````@r:   
meta_histcrv	    s     G5U"##%L	
 5V#(?(?(A(A%%&MN	LL4!K 
LLQR	LL3L 
LL3L 
LLMN;;tELLDDr=   c                 F  ^  [        T R                  5       USS9n[        R                  " T R	                  5       S:g  =(       d#    [        S T R                  5       SS   5       5      U 4S j5        T R                  U5      R                  [        R                  " T 5      S9$ )Nr3  r  r   c              3   *   #    U  H	  oS :  v   M     g7fr  rB   )rm   r   s     r:   ro   ,meta_upsample_bimode2d_aa.<locals>.<genexpr>  s     !H7Gt(7Gr  r   c                  *   > ST R                  5        3$ r  r   rC  s   r:   r^   +meta_upsample_bimode2d_aa.<locals>.<lambda>  r  r=   r   )
r  r   rO   ra   r   r  r   rl  rG   r"   )r  r  ra  r  r  r  s   `     r:   meta_upsample_bimode2d_aar|	    s     -

kA 
LLHc!Huzz|AB7G!HH_ ??+,//11%8 0  r=   c                 T  ^ ^^ [        X!SS9m[        R                  " T R                  S:H  U 4S j5        [	        S5       H3  m[        R                  " T R
                  T   TT   :H  UU U4S j5        M5     T R                  U5      R                  [        R                  " T 5      S9$ )Nr3  r  r]  c                  "   > ST R                    3$ r  rI  r  s   r:   r^   4meta_upsample_bimode2d_aa_backward.<locals>.<lambda>
  r  r=   c            
      D   > ST ST T    ST STR                  T5       3$ )NzD
Expected grad_output to have the same shape as output; output.size(r  z
but got grad_output_size(r   r  s   r:   r^   r	    s>     DDE3dK[\]K^J_ `D!1!1!!4 59r=   r   )
r  rO   ra   r   r   r   r   rl  rG   r"   )rQ  r  r  ra  r  r  r  r!  s   `     @@r:   "meta_upsample_bimode2d_aa_backwardr	    s     -! 
LLAk 1Xa $4Q$779	
    ,//11+> 0  r=   c                 X   [         R                  " UR                  5       S:H  S 5        [         R                  " UR                  5       S:H  S 5        [         R                  " UR                  R                  S 5        [         R                  " UR                  R                  S 5        g )Nr   c                      g)Nz%found_inf must be a 1-element tensor.rB   rB   r=   r:   r^   <_amp_foreach_non_finite_check_and_unscale_.<locals>.<lambda>      (Or=   c                      g)Nz%inv_scale must be a 1-element tensor.rB   rB   r=   r:   r^   r	    r	  r=   c                      g)Nz!found_inf must be a float tensor.rB   rB   r=   r:   r^   r	  #      3r=   c                      g)Nz!inv_scale must be a float tensor.rB   rB   r=   r:   r^   r	  '  r	  r=   )rO   ra   r   rW   r;  )r   ra  	inv_scales      r:   *_amp_foreach_non_finite_check_and_unscale_r	    s|    	LLQ O 
LLQ O 
LL))3 
LL))3r=   c                 V    [        U R                  5       5      nU R                  U5      $ r7   )r	  r   r   )r   nanposinfneginfr  s        r:   
nan_to_numr	  ,  s#     tyy{#K>>+&&r=   c                    U R                   [        R                  [        R                  [        R                  [        R
                  1;  d   SU R                    S35       eU R                  n[        X5      n[        X#5      nX:X  a  U $ [        U R                  5       5      n[        U R                  5       5      nXR   XQ   sXQ'   XR'   XB   XA   sXA'   XB'   U R                  XE5        U $ )Nz>torch.transpose_: in-place transposition is not supported for z layout)r~   rO   r  
sparse_cscr  
sparse_bscr   r   r	  r   r   r  )r   dim0r  ndimsr   r   s         r:   r  r  3  s    ;;	   IU\]  IIE$&D$&D|		D$++- F!'v|FL&,!ZDJ
T"Kr=   c                 "   U R                   nU R                  (       a;  U R                  5       nU R                  5       nUS::  a  US:X  d   SU SU S35       eOU R	                  5       S::  d   SU S35       e[        U SUS:  a  S5      $ S5      $ )	Nr3  r   zEt_ expects a tensor with <= 2 sparse and 0 dense dimensions, but got z sparse and z dense dimensionsz6t_ expects a tensor with <= 2 dimensions, but self is rj  r   )r   rt  rv  rw  r   r  )r   r	  rv  rw  s       r:   t_r	  P  s    IIE~~__&
NN$	Q9> 	
!l,yk9JL	
1>
 xxzQ 	
DUG1M	
 dAEAIq55155r=   )rf	  r  sidesorterc                  ^ ^^ [         R                  " [        T R                  5      S:*  =(       d    T R                  S S TR                  S S :H  UU 4S j5        [         R                  " TS L =(       d    T R                  TR                  :H  U U4S j5        [         R                  " US:g  =(       d    U(       + S5        U(       a  [         R                  O[         R
                  n[        T[         R                  5      (       a$  [         R                  " TU[         R                  S9$ [         R                  " SUT R                  S	9$ )
Nr   r   c                  `   > S[        TR                  5       S[        T R                  5       3$ )Nztorch.searchsorted(): boundaries tensor should be 1 dimension or the first N-1 dimensions of boundaries tensor and input value tensor must match, but we got boundaries tensor z and input value tensor r	  r   )r   sorted_sequences   r:   r^   #meta_searchsorted.<locals>.<lambda>s  s3    3378M8M3N2O P""&tzz"2!35r=   c                  n   > S[        T R                  5       STb  [        TR                  5       3$ /  3$ )Nz[torch.searchsorted(): boundary and sorter must have the same size, but got boundary tensor z and got sorter tensor r	  )r	  r	  s   r:   r^   r	  ~  sB    ##'(=(=#>"??V%+%7tFLL!@B=?@Br=   r  zetorch.searchsorted(): side and right can't be set to opposites, got side of left while right was Truerh	  rB   r$  )rO   ra   r   r   r  r   rk   r   r   r   r   r   )r	  r   rf	  r  r	  r	  rW   s   ``   ` r:   meta_searchsortedr	  c  s     
LLO!!"a' 	9  "%CR8	
	 
LL$?///6<<?	
 
LL#e)	$ %EKK%++E$%%U-D-D
 	
 {{2U?3I3IJJr=   c                    ^  [         R                  " T [         R                  [         R                  [         R                  4;  U 4S j5        g )Nc                     > ST  3$ )Nz/Unsupported input type encountered for isin(): rB   r   s   r:   r^   3_check_for_unsupported_isin_dtype.<locals>.<lambda>  s    A%Ir=   )rO   ra   rF  
complex128	complex64r   s   `r:   !_check_for_unsupported_isin_dtyper	    s/    	LLejj%"2"2EOODDIr=   c                 H    U R                  X R                  S5      45      nU$ )Nr   rI  )rQ  r   num_weightsr9  rH  rI	  s         r:   meta_embedding_dense_backwardr	    s(     ''6F6Fr6J(KLKr=   c                 t    U	(       a  [         R                  U UUUUUUUU
U5
      $ [        U UUUUUUUU
U5
      $ r7   )r/   _embedding_bag_sparse_backward!meta_embedding_bag_dense_backward)r  r   r  rL  rM  maximum_indicesr	  rH  r  rI  r3  r9  s               r:   meta_embedding_bag_backwardr	    se     22
 	
 1
 	
r=   c
                 X  ^  [         R                  " T R                  [         R                  [         R                  [         R
                  [         R                  4;   U 4S j5        U[        :X  a  [         R                  " US L5        T R                  UT R                  S5      45      n
U
$ )Nc                  "   > ST R                    3$ )Nz$Unsupported input type encountered: r   )r  s   r:   r^   3meta_embedding_bag_dense_backward.<locals>.<lambda>  s    6tzzlCr=   r   )
rO   ra   rW   r  r  r  float64rF  r   r   )r  r   rL  rM  r	  r	  rH  r  r3  r9  index_grad_weights   `          r:   r	  r	    sv     
LL

u}}ennemmU]]SSC x_D01TYYq\'BCr=   c                    U R                  S5      n[        R                  " U[        :H  S5        [        R                  " U R	                  5       S:H  5        [        R                  " UR	                  5       S:H  5        UR                  S5      n[        R                  " UR	                  5       S:H  5        [        R                  " UR                  S5      U:H  5        U R                  U45      n	U	$ )Nr   zHembedding_bag_backward: per_sample_weights only supported for mode='sum'r3  r   )r   rO   ra   rE  r   r   )
r  r~  r   r  rL  r  r9  embedding_featuresr  rC  s
             r:   .meta_embedding_bag_per_sample_weights_backwardr	    s     1	LLR 
LLq!	LL!#$,,q/K	LL"#	LLQ#556^^[N+FMr=   )assume_uniqueinvertc                   [         R                  " [        U [        5      =(       d    [        U[        5      S 5        [        U [        5      (       d  [         R                  " XR
                  S9n [        U[        5      (       d  [         R                  " XR
                  S9n[        U R                  5        [        UR                  5        [         R                  " U [         R                  S9$ )Nc                      g)Nz<At least one of elements and test_elements must be a Tensor.rB   rB   r=   r:   r^   meta_isin.<locals>.<lambda>  r  r=   r  r   )
rO   ra   rk   r   rv  r   r	  rW   r   rF  )elementstest_elementsr	  r	  s       r:   	meta_isinr	    s     
LL8V$I
=&(IN h''<<1E1EFmV,,]??K%hnn5%m&9&9:HEJJ77r=   rL  c                     [         R                  " U S:  S 5        [        U[        R                  S9u  p#[         R
                  " XS9$ )Nr   c                      g)Nz,polygamma(n, x) does not support negative n.rB   rB   r=   r:   r^    meta_polygamma.<locals>.<lambda>  s    !Or=   r  r   )rO   ra   r   r   r  r   )rL  r   rJ   rK   s       r:   meta_polygammar	    sB     
LLaOP(;HHOA D55r=   c                     [        S5      e)Nz.Tensor.item() cannot be called on meta tensors)rk  r   s    r:   meta_local_scalar_denser	    s    
G
HHr=   c                 .    [         R                  " U 5      $ r7   r  r   s    r:   silur	  $  r  r=   c                 ^    [        U [        R                  S9u  p[        R                  " XS9$ r  )r   r   r  rO   r   )r   rJ   rK   s      r:   sigmoidr	  *  s/     );HHOA D55r=   c                    U R                  5       S:H  nUR                  5       S:H  nU(       a  U(       a4  UR                  S5      U R                  S5      UR                  S5      /nGO'[        R                  " UR                  S5      UR                  S5      :H  S5        U R                  S5      UR                  S5      /nOU(       a[  [        R                  " UR                  S5      U R                  S5      :H  S5        U R                  S5      UR                  S5      /nOj[        R                  " U R                  S5      UR                  S5      :H  S5        U R                  S5      U R                  S5      UR                  S5      /nU=(       d    U R                  nSUR
                  -  nUS   U-   S-
  U-  U-  nXE:X  a  US   U-  US/n	OUS/n	[        R                  " XiX0R                  S9n
U
$ )	Nr3  r   r   z matrix batch sizes have to matchr   zbatched dimension has to matchr  r$  )r   r   rO   ra   rW   itemsizerm  r   )r  r  offsr  
mat1_is_2d
mat2_is_2dr  	alignmentsize_paddedr  r  s              r:    _create_grouped_mm_output_tensorr	  4  s   qJqJ		!diilDIIaLAHLL		!		!,.P 		!diim4HLL		!		!,.P 		!diil3H LL1157WX		!diilDIIbMBH'TZZIi(((IB<)+a/I=	IKqkK/a@
!1%



h)KK
XCJr=   mat_amat_br	  c	                   ^ ^^ [         R                  " US L US L :H  S 5        US L=(       a    US Ln	U	(       a\  [         R                  " T R                  [         R                  :H  =(       a    TR                  [         R                  :H  U U4S j5        O[[         R                  " T R                  [         R                  :H  =(       a    TR                  [         R                  :H  U U4S j5        [         R                  " T R                  5       S;   =(       a    TR                  5       S;   U U4S j5        T R                  5       S:H  n
TR                  5       S:H  nU	(       aH  S nS n[         R                  " U" T 5      U 4S	 j5        [         R                  " U" T5      U4S
 j5        S nU" ST 5        U" ST5        Ub  Ub  [         R                  " UR                  [         R                  :H  =(       a    UR                  [         R                  :H  S 5        SS jnTb  U
(       a  U(       a  TR                  S   OSnU" SUT SU5        U" SUTSU5        [         R                  " US L S 5        U
(       d  U(       a  [         R                  " TS LU U4S j5        Tbb  [         R                  " TR                  5       S:H  U4S j5        [         R                  " TR                  [         R                  :H  U4S j5        O[         R                  " TS L S 5        [         R                  " US L S 5        [         R                  " US L =(       d    U[         R                  :H  S 5        [        T TTU5      $ )Nc                      g)Nz,Either both scale factors are given, or nonerB   rB   r=   r:   r^   )_meta_grouped_mm_common.<locals>.<lambda>d  s    >r=   c                  >   > ST R                    STR                    S3$ )Nz5Expected inputs of E4M3 FP8 type but got mat_a.dtype= and mat_b.dtype=r!  r   r	  r	  s   r:   r^   r	  o  s#    KEKK=Xijojujuivvwxr=   c                  >   > ST R                    STR                    S3$ )Nz1Expected inputs of BF16 type but got mat_a.dtype=r	  r!  r   r	  s   r:   r^   r	  t  s#    G}Tefkfqfqerrstr=   )r3  r2   c                  L   > ST R                  5        STR                  5        3$ )Nz3Multiplicands must be 2D or 3D but got mat_a.dim()=z and mat_b.dim()=r   r	  s   r:   r^   r	  y  s%    Eeiik]Rcdidmdmdocpqr=   r3  c                 P    U R                  5       nUS   S:  =(       a    US   S:H  $ Nr  r   r   r8  mat
mat_strides     r:   rb  -_meta_grouped_mm_common.<locals>.is_row_major  s*    Jb>A%=*R.A*==r=   c                 P    U R                  5       nUS   S:H  =(       a    US   S:  $ r	  r8  r	  s     r:   re  -_meta_grouped_mm_common.<locals>.is_col_major  s*    Jb>Q&=:b>A+==r=   c                  0   > ST R                  5       SS   3$ )NzNExpected mat_a tensor to be row major in the last two dimensions, got strides r  r8  )r	  s   r:   r^   r	    s!    dejeqeqestvtwexdyzr=   c                  0   > ST R                  5       SS   3$ )NzQExpected mat_b tensor to be column major in the last two dimensions, got strides r  r8  )r	  s   r:   r^   r	    s!    ghmhththvwywzh{g|}r=   c                   ^ ^^^ TR                  5       S-
  mSTR                  5       -  nTR                  5       mTTS-
     S:X  aJ  TT   [        STR                  TS-
     5      :  a'  [
        R                  " TT   U-  S:H  UU U4S j5        g TT   S:X  aM  TTS-
     [        STR                  T   5      :  a*  [
        R                  " TTS-
     U-  S:H  UU U4S j5        g [
        R                  " SUU4S j5        g )Nr   r  r   c                  "   > ST ST  STT     S3$ )Nr   stride along % dim to be multiple of 16 bytes, got r!  rB   end_dimmat_namer	  s   r:   r^   F_meta_grouped_mm_common.<locals>.check_valid_strides.<locals>.<lambda>  s'    )H:^G9Dijtu|j}i~~  Ar=   c                  .   > ST ST S-
   STT S-
      S3$ )Nr  r	  r   r	  r!  rB   r	  s   r:   r^   r	    sI    )H:^GaK=Hmnx  zA  DE  zE  oF  nG  GH  Ir=   Fc                  *   > ST ST R                    S3$ )NzInvalid strides/sizes, got z for strides and z for sizes.r   r	  s   r:   r^   r	    s    5j\ARSVS\S\R]]hir=   )r   element_sizer   r   r   rO   ra   )r	  r	  r	  r	  r	  s   `` @@r:   check_valid_strides4_meta_grouped_mm_common.<locals>.check_valid_strides  s    '')a-#**,,	ZZ\
gk"a'Jw,?3syy1%D
 -
 LL7#i/14 A  A%*Wq[*ASsyy!F
 +
 LL7Q;')3q8 I
 LLir=   r	  r	  c                      g)NzBoth scale_a and scale_b must be float (fp32) tensors, but got scale_a.dtype={scale_a.dtype} and scale_b.dtype={scale_b.dtype}.rB   rB   r=   r:   r^   r	    s      Vr=   r   c                   ^ ^^^^ TR                  5       S:X  a  [        R                  " TR                  5       S:H  UU 4S j5        [        R                  " TR                  5       U 4S j5        [        R                  " TR                  S   TR                  T   T-  :H  UUUU U4S j5        g [        R                  " TR                  5       S:H  UU 4S j5        [        R                  " TR                  S5      S:H  U 4S j5        [        R                  " TR                  S   TR                  S   :H  UUU 4S	 j5        [        R                  " TR                  S   TR                  ST-      :H  UUU U4S
 j5        g )Nr3  r   c                  2   > ST ST R                  5        S3$ )Nr  z to be 1D tensor, but got 	D tensor.r   r  
scale_names   r:   r^   >_meta_grouped_mm_common.<locals>.check_scale.<locals>.<lambda>      i
|3Meiik]Zcdr=   c                     > ST  S3$ )Nr  z to be contiguous.rB   r	  s   r:   r^   r	    s    i
|3EFr=   r   c                  V   > ST ST R                   T   T-   STR                   S    S3$ )Nr  z	 to have ry  r   z
 elements.r   )r	  r  scale_multiplierr	  
scaled_dims   r:   r^   r	    sU    i
|9SYYz=RUe=e<ffuv{  wB  wB  CD  wE  vF  FP  Qr=   c                  2   > ST ST R                  5        S3$ )Nr  z to be 2D tensor, but got r	  r   r	  s   r:   r^   r	    r	  r=   c                     > ST  S3$ )Nr  z( to be contiguous in the last dimension.rB   r	  s   r:   r^   r	    s    i
|3[\r=   c                  P   > ST ST R                   S    STR                   S    S3$ )Nr  z batch dimension to be r   , got r!  r   )r	  r  r	  s   r:   r^   r	    s4    i
|3J399UV<.X^_d_j_jkl_m^nnopr=   c                  V   > ST ST R                   ST-       STR                   S    S3$ )Nr  z non-batch dimension to be r   r
  r!  r   )r	  r  r	  r	  s   r:   r^   r	    sC    i
|3NsyyYZ]gYgOhNiiopup{p{|}p~o  @A  Br=   )r   rO   ra   r   r   r   )r	  r  r	  r	  r	  s   `````r:   check_scale,_meta_grouped_mm_common.<locals>.check_scale  s   wwyA~IIK1$d '')F KKNcii
&;>N&NN Q  Q
 IIK1$d LLOq(\ KKNciil2p KKNciiJ&?? Br=   r   rQ  rR  c                      g)Nz:Scale result tensor provided, but it is not supported yet.rB   rB   r=   r:   r^   r	    rh   r=   c                  N   > ST R                  5        STR                  5        S3$ )Nz/Offsets tensor not provided, but is needed for zD/zD multiplicand layouts.r   r	  s   r:   r^   r	    s(    Eeiik]RTUZU^U^U`Taaxyr=   c                  ,   > ST R                  5        S3$ )Nz.Offsets tensor must be 1D, but got offs.dim()=r!  r   r	  s   r:   r^   r	    s    HTUVr=   c                  $   > ST R                    S3$ )Nz7Offsets tensor must be integer (int32) tensor, but got r!  r   r	
  s   r:   r^   r	    s    QRVR\R\Q]]^_r=   c                      g)NzJOffsets tensor provided, but is not needed for 3D/3D multiplicand layouts.rB   rB   r=   r:   r^   r	    s    `r=   c                      g)Nz2Bias tensor provided, but it is not supported yet.rB   rB   r=   r:   r^   r	    s    Dr=   c                      g)Nz4If output dtype provided, it must be torch.bfloat16.rB   rB   r=   r:   r^   r	    s    Fr=   r^  )
rO   ra   rW   r  r  r   r  r   r  r	  )r	  r	  rQ  rR  r	  r  rS  r  rT  scaledmat_a_is_2dmat_b_is_2drb  re  r	  r
  r	  s   ``  `            r:   _meta_grouped_mm_commonr
  W  s    
LL	Dgo.> D 8WD%8F KK5...U5;;%BUBU3Ux	

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

 
LL		v7%))+"7q
 ))+"K))+"K	>	> 	z	
 	}	

0 ''w2MMU]]*Mw}}/M V	

	B "-++DJJqMST 	 	Iwq2BCIwq2BCD P	

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

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

 
LLD
 
LLT8Y%..8F
 ,E5$	JJr=   c                 "    [        U US S UUS US9$ )N)rQ  rR  r	  r  rS  r  r
  )r	  r	  r	  r  r  s        r:   
grouped_mmr
    s)     #	 	r=   c	                 $    [        U UUUUUUUUS9	$ )N)rQ  rR  r	  r  rS  r  rT  r
  )	r	  r	  rQ  rR  r	  r  rS  r  rT  s	            r:   meta_scaled_grouped_mmr
    s,     #!%
 
r=   rL   half_to_floatc                    U(       a   U R                   [        R                  :X  d   e[        R                  " U [        R
                  R                  S9u  p4U(       d  UOUn[        R                  " X[        R                  S9nU$ )Nr  rh	  )	rW   rO   rQ   rG   r   r   rH   r   r   )rL   r   r
  computation_dtyperK   r  s         r:   softmaxr
  -  sk     ww%**$$$&+&>&>	uDDLL'# (5<:KL


1@W@W
XCJr=   c           	      n  ^^^^^	^
 [         R                  " [        T5      S-  S:H  U4S j5        U R                  m[        T5      m	[        T5      S-  nT	U-
  m[         R                  " T	U:  U	U4S j5        [	        TS T 5      n[        U5       Ha  m[        T5      TS-   S-  -
  m
TTT-      TT
   -   TT
S-      -   n[         R                  " US:  UUUUU
4S j5        UR                  U5        Mc     [         R                  " UU R                  U R                  U R                  [        U 5      S9$ )Nr3  r   c                      > S[        T 5       3$ )Nz1Length of pad must be even but instead it equals r  r  s   r:   r^   '_constant_pad_nd_meta.<locals>.<lambda>A  s    CCH:Nr=   c                  (   > S[        T5       ST  S3$ )Nz`Length of pad should be no more than twice the number of dimensions of the input. Pad length is z while the input has z dimensions.r  )l_inpr  s   r:   r^   r
  K  s      225c(;P'r=   r   c            	      F   > STTT -       STT    STTS-       STT -    S3	$ )NzThe input size z, plus negative padding r   r   zG resulted in a negative output size, which is invalid. Check dimension z of your input.rB   )r!  r?  l_diffr  pad_idxs   r:   r^   r
  V  sE    ok&1*&=%>>V7|nE#gk"2!3 4117!OMr=   )rW   r   r   r   )rO   ra   r   r   r	  r   r
  r   rW   r   r   r"   )r  r  r  l_padr   new_dimr!  r?  r!
  r
  r"
  s    `    @@@@@r:   _constant_pad_nd_metar%
  ;  s'    
LLC1N
 ++KEHMEU]F	LL	 [&)*I5\c(q1uk*fqj)CL83w{;KKqLM M	
 	!  ;;kk||))+E2 r=   r9  rH  rI  c                    U R                  5       S:X  d   S5       eU R                  nUR                  nUR                  S:X  a  US   4nO%UR                  S:X  a  US   US   4nO
/ UQUS   P7nU R                  nU R	                  XxS9$ )Nr3  z'weight' must be 2-Dr   r   r   )r   r   r   rW   r   )	r~  r   r9  rH  rI  weight_shapeindices_shaper   r  s	            r:   	embeddingr)
  e  s     ::<1444<<LMMM||q&21o%7			"1%|A7	5m5\!_5	II77r=   max_lengthspadding_valuec                     [        U5      S:X  d   e[        U5      S:X  d   eUS   R                  S   S-
  nUS   nXE/U R                  SS  Q7nU R                  U5      $ r>  )r   r   r   )r   r  r*
  r+
  r  r  r  s          r:   $meta__jagged_to_padded_dense_forwardr-
  }  st     w<1{q   
aAAA,6<<+,LL))r=   c                 B    [        U 5      [        5       S 5       5       nU$ )Nc                 2    [        U [        R                  S9$ r|  rM   r   r  r  s    r:   _f)_create_unary_float_meta_func.<locals>._f  s      =JJ
 	
r=   rC   r(   funcr1
  s     r:   _create_unary_float_meta_funcr6
    *    4]
  

 Ir=   c                 B    [        U 5      [        5       S 5       5       nU$ )Nc                 2    [        X[        R                  S9$ r|  r0
  )rL   r  s     r:   r1
  *_create_binary_float_meta_func.<locals>._f  s      !@!M!M
 	
r=   r3
  r4
  s     r:   _create_binary_float_meta_funcr;
    r7
  r=   c                    ^  [        T 5      U 4S j5       nT R                   S3nX!l        [        [        [        U5      5      " U5      nU$ )Nc                 `   > T" U /UQ70 UD6n[        U R                  UR                  5        U $ r7   r  )r   rI   r^  r  r9   s       r:   _fn#_register_inplace_meta.<locals>._fn  s.    '''

CII6r=   rJ   )r   rw   rC   getattrr/   )r9   r>
  inplace_names   `  r:   _register_inplace_metarB
    sK    
2Y 
 kk]!$LL
l3
4S
9CJr=   c                 z  ^ ^^ [         R                  " T R                  TR                  :H  UU 4S j5        T T/n[        T[        5      (       aT  TR
                  S:w  a3  [         R                  " T R                  TR                  :H  U U4S j5        UR                  T5        [        US[        R                  06$ )Nc                  <   > STR                    ST R                    3$ )Nr  z for `end`, but got dtype r   )rx   ry   s   r:   r^   lerp.<locals>.<lambda>  s    /%++.HTr=   r   c                  <   > ST R                    STR                    3$ )Nr  z for `weight`, but got dtype r   )ry   r~  s   r:   r^   rE
    s    /%++6STZT`T`Sabr=   rD   )
rO   ra   rW   rk   r#   r   r
  rM   r   rH   )ry   rx   r~  rI   s   ``` r:   lerprG
    s     
LLsyy T 3<D&*%%;;!LLv||+b 	F	=EE r=   )r  c                4    [        XU[        R                  S9$ r|  r~  r  tensor1tensor2r  s       r:   addcmulrL
    s     0O0W0W r=   c                    [         R                  " [        R                  " UR                  5      =(       a     [        R                  " UR                  5      (       + S 5        [        XU[        R                  S9$ )Nc                      g)N)zFInteger division with addcdiv is no longer supported, and in a future zErelease addcdiv will perform a true division of tensor1 and tensor2. z4The historic addcdiv behavior can be implemented as zA(input + value * torch.trunc(tensor1 / tensor2)).to(input.dtype) zfor integer inputs and as z6(input + value * tensor1 / tensor2) for float inputs. z?The future addcdiv behavior is just the latter implementation: z4(input + value * tensor1 / tensor2), for all dtypes.rB   rB   r=   r:   r^   addcdiv.<locals>.<lambda>  s     	
r=   r}  )rO   ra   rG   r  rW   rM   r   rH   rI
  s       r:   addcdivrP
    s`     
LL""7==1 6&&w}}5	
		
  0O0W0W r=   c                      0 n S H"  n[         U   nU H  nX0;  d  M
  X#   X'   M     M$     U R                  5        GH  u  pE[        U[        R                  R
                  5      (       a  M1  [        U[        5      (       d   eUR                  [        R                  R                  R                  5      " U5        [        R                  R                  UR                  5       S5      (       a  U[         S   ;   a  [        U S35      eM  UR                  (       a  M  UR                  5       S;   a  M  SUR                  5       ;   a  [        R!                  XE5        GM&  SUR                  5       ;   a  ["        R!                  XE5        GMR  SUR                  5       ;   a  [$        R!                  XE5        GM~  S	UR                  5       ;   a  [&        R!                  XE5        GM  [(        R!                  XE5        GM     g )
N)r|   post_autogradpre_autogradCompositeImplicitAutogradr|   z is a CompositeImplicitAutograd op, we shouldn't register meta function for it. Instead, we should let the decomposition run and write meta kernels for the base operators.>   aten::cloneaten::copy_aten::rot90aten::_to_copyaten::empty_stridedaten::constant_pad_ndaten::as_strided_scatterzmkldnn::zmkl::zonednn::zquantized::)r   itemsrk   rO   _opsHigherOrderOperatorr   py_impl_CDispatchKeyr1   %_dispatch_has_kernel_for_dispatch_keyr  rk  is_view2_meta_lib_dont_use_me_use_register_meta_for_mkldnnimpl/_meta_lib_dont_use_me_use_register_meta_for_mkl2_meta_lib_dont_use_me_use_register_meta_for_onednn5_meta_lib_dont_use_me_use_register_meta_for_quantized'_meta_lib_dont_use_me_use_register_meta)activate_meta_tablerv   registryopoop_overloadr9   s         r:   activate_metarn
    s    :-d3C-+3=#(  : /446
 k5::#A#ABB+z2222EHH00556r:8899 ;
 
 8@@""m $; ;  A    	 [--//BGGXK,,..?DD[U{//11BGGX+"2"2"44EJJ 8<<[Mm 7r=   )F)TrB	  r7   )NNNFr   r   r   r4  r  )r  )r)  T)FF)TT)r  )FTN)TFF)TF)r3  )g      ?N)r3   str)rB   r  r^  F)rB   r  FTN)Fr   FNFr   )NF)r   F)g      ?gUUUUUU?FN)NNNNN)r   NNr   )NNF)        FFN)Nrp
  FFN)rp
  FNN)rp
  FN)FN)FNNNN)NNNF)Nr   FNN)NNNN)r   TT)NNr   N)d   r   r   )r   )NNNNF)r   FF)rp
  (  r!  r   collections.abcr   enumr   	functoolsr   r   typingr   r   r	   r
   typing_extensionsr   rO   torch._prims_commonr  rG   r   r   r   torch._decompr   r   r   r   
torch._opsr   torch._primsr   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   torch._prims_common.wrappersr$   r%   r&   r'   r(   r<  r)   r*   torch.fx.experimentalr+   r  torch.utilsr,   r>   r-   r.   opsr/   libraryLibraryri
  r   rE  rG  rF  rC   rM   rY   rc   linspacelogspacer  r   takern  r  r   r   r   r   r   r  r   r   cummaxcumminr   r  r$  r	  r)  rF  r+  _fft_c2cr1  r4  r5  _fft_r2crH  randpermgenerator_outrM  r   rR  randintr\  rX  low_outr`  randrb  _fft_c2rrg  r  rr  ry  
unsqueeze_r}  _sparse_semi_structured_linearro
  rW   r  _sparse_semi_structured_mmr  _sparse_semi_structured_addmmr  _cslt_sparse_mmr  index_reducer  index_reduce_r  index_selectr  segment_reducer  r   	unary_outr  r   r  r=  r  r  r  r  r  _assert_asyncr  r   r  _printr  _make_dep_tokenr  r  _functional_sym_constrain_ranger  r  (_functional_sym_constrain_range_for_sizer  _functional_assert_asyncr  r   r  r   r  r  r%  r.  _linalg_eighr/  r8  _linalg_eigvalslinalg_eigvalsr<  
linalg_eigr?  rC  rE  rL  rQ  rU  r[  ro  linalg_inv_exrr  linalg_ldl_factor_exr`   rx  linalg_ldl_solver  	linalg_lur  linalg_lu_factor_exr  linalg_lu_solver  	lu_unpackr  r  	linalg_qrr  r  r  _linalg_svdr  r  rM  r  r  linalg_solve_triangularr  r  r   _linalg_detr  r  r$  r7  reflection_pad1dr<  replication_pad1drG  rT  reflection_pad1d_backwardrY  replication_pad1d_backwardr[  rl  reflection_pad2drn  replication_pad2drr  reflection_pad2d_backwardrU  replication_pad2d_backwardrz  r  reflection_pad3dr  replication_pad3dr  reflection_pad3d_backwardreplication_pad3d_backwardr  _pdist_forwardrS   r  _pdist_backwardr  baddbmmr  	bernoullir  
bernoulli_r  r  r  poissonr  _fused_moving_avg_obs_fq_helperr  mmr  r  r<  r  r  miopen_batch_normr  convolutionr'  r`
  _has_mkldnnrd
  r(  _convolution_pointwiser/  _linear_pointwiser3  has_mklrf
  r4  _mkl_linearr8  rg
  r9  qconv2d_pointwiseqconv_pointwiserF  binaryrP  qlinear_pointwiserv  rU  binary_tensorrZ  linear_dynamic_fp16linear_relu_dynamic_fp16r\  rh
  r]  
max_pool2drh  int4mm_packed_weight_cpurp  rv  
avg_pool2dr  r  avg_pool2d_backwardr  
avg_pool3dr  avg_pool3d_backwardr  _adaptive_avg_pool2dr  _adaptive_avg_pool3dr  _adaptive_avg_pool2d_backwardr  _adaptive_avg_pool3d_backwardr  r  adaptive_max_pool2dr  r	  r  adaptive_max_pool3dr  r  r  repeat_interleaver  rl   r  r   r'  r   _unsafe_indexrG  convolution_backwardrS  addbmmr\  randint_liker_  _fused_adam__fused_adamw_rw  _fused_adamr  _int_mmr  _convert_weight_to_int4packr  #_convert_weight_to_int4pack_for_cpur  _weight_int4pack_mmr  _weight_int4pack_mm_for_cpur  r  r  r  _dyn_quant_pack_4bit_weightr  _dyn_quant_matmul_4bitr   _weight_int8pack_mmr  _cdist_forwardr  _cdist_backwardr(  _embedding_bagrQ  _embedding_bag_forward_onlyrS  rV  nansumrX  median	nanmedianrZ  
dim_valuesr  r   r]  logical_not_r_  repeatrh  zero_rj  mul_Scalardiv_logical_and_logical_or_logical_xor_rm  add_sub_rz  rounddecimalsr  r  
__rshift__r  
__lshift__r  zeror  ry  r  fillr  relu_r  	_add_relur  rrelu_with_noiser  rrelu_with_noise_functionalr  rrelu_with_noise_r  	index_put_unsafe_index_putr  masked_fill_r  _masked_scaler  masked_scatter_r  masked_scatterr  masked_scatter_backwardr  
index_put_r  aliasr  r  bmmr  r  r  r  r  r  r  r  r  rb   max_pool2d_with_indices_backwardr  max_pool2d_with_indicesr  fractional_max_pool2dr)  max_pool3d_with_indicesr:   max_pool3d_with_indices_backwardrB  rM  rO  r\  grid_sampler_2d_backwardrd  rj  rl  ro  r#  onesr~  zerosr  r;  r  select_scatterr  slice_scatterr  r   r  r  gatherr  r  r  r  r  r  scatter_addr  scatter_add_r  r  ro  r  value_reducer  scatter_r  #_scaled_dot_product_flash_attentionr  r  #_scaled_dot_product_cudnn_attentionr	  0_scaled_dot_product_fused_attention_overrideabler  ,_scaled_dot_product_flash_attention_backwardr  +_scaled_dot_product_flash_attention_for_cpur  4_scaled_dot_product_flash_attention_for_cpu_backwardr   '_scaled_dot_product_efficient_attentionr$  0_scaled_dot_product_efficient_attention_backwardr,  ,_scaled_dot_product_cudnn_attention_backwardr.  _flash_attention_forwardr6  _flash_attention_backwardr;  _efficient_attention_forwardrG  _efficient_attention_backwardSymIntrP  
_scaled_mmr  scatter_reducetwotwo_outr  scatter_reduce_r  multinomialr  r  r  r  _upsample_nearest_exact1dr  _upsample_nearest_exact2dr  "_upsample_nearest_exact2d_backwardr  _upsample_nearest_exact3dr  r  values_stabler  r  _thnn_fused_lstm_cellr  r	  r	  r	  r	  r	  argminr	  r	  topkr$	  _segment_reduce_backwardr(	  kthvaluer.	  r   rC	  r@	  rG	  rJ	  pixel_shufflerS	  re	  	bucketize
Tensor_outrj	  histcrv	  _upsample_bilinear2d_aa_upsample_bicubic2d_aar|	   _upsample_bilinear2d_aa_backwardr	  r	  r	  r  r	  searchsortedr	  r	  embedding_dense_backwardr	  _embedding_bag_backwardr	  _embedding_bag_dense_backwardr	  *_embedding_bag_per_sample_weights_backwardr	  isinr	  	polygammar	  _local_scalar_denser	  r	  r	  r	  r
  _grouped_mmr
  _scaled_grouped_mmr
  _softmaxr
  constant_pad_ndr%
  r)
  _jagged_to_padded_dense_forwardr-
  r6
  r;
  special_airy_aispecial_bessel_y0special_bessel_y1special_modified_bessel_i0special_modified_bessel_i1special_modified_bessel_k0special_modified_bessel_k1!special_scaled_modified_bessel_k0!special_scaled_modified_bessel_k1special_chebyshev_polynomial_tspecial_chebyshev_polynomial_uspecial_chebyshev_polynomial_vspecial_chebyshev_polynomial_w&special_shifted_chebyshev_polynomial_t&special_shifted_chebyshev_polynomial_u&special_shifted_chebyshev_polynomial_v&special_shifted_chebyshev_polynomial_wspecial_hermite_polynomial_hspecial_hermite_polynomial_hespecial_laguerre_polynomial_lspecial_legendre_polynomial_prB
  rG
  rL
  rP
  lerp_addcmul_addcdiv_torch._refs.nn.functionaltorch._refs.specialrn
  rB   r=   r:   <module>rn     sHH     $  # 5 5 '  # + +  " 
     < 7 ) T]t_yy~~*/--*?*?PV*W ' %a )X
8BF#3"4hr2v6F"FG 
3(* t}}-.
 

==5  /5p 		!!499==12'  3' !!))4+<+<+@+@AB%' %  C%&FRAH tyy  !M "M t%%&I  'I 	[[$++//4;;+>+>P Xy! " !!))4+<+<+@+@ABI  CI3lV $s) 4  %%t}}'8'89:K  ;K $s)  %%t}}'8'89:8
  ;8
v t}}**+"& 3 ,3 t}}$$% **
 &
 $$dll&6&678
 **  9&   $,,"6"678 **  9& 		!!499==12%)$tPT   3 %%t}}'8'89:$Dv $DDI $Dc $DC $D  ;$DN tzz!!" #0( t&&' ( t223
 "%)'+  6
	
 c] $ 4B t../
 (,	
  $	 00 t112 	
'+
  	 $ 3D t##$ ""'+"-<,,-<\\-< 6
-< F	-<
 $-< -< -< -< -< %-<` t  (() 	I
	I		I 	I LL		I
 	I 	I 	I *	I t!!))* 	
			 	 LL		
 	 	 	 +	 t  (()' * ' t""**+
 !% $ $ W
 W W f	 W
 f W f W  W  W  W , WF   $(("4"456  7 txx||    $(("4"456  7 txx||  tzz!!"6 #6 tzz~~( (
 t!!))* + t!!%%& ' t{{""# $ t##++, ) -) t''//0, 1, t33;;< =
 t008896 :6& t<<DDE F
 t,,001 2
F C    F  #  N (,


 !%
$V S C 
 
F 
$ 
 
"  	  	C  !!))4+<+<+H+HIJ]N+ s T  , K" $$,,d.A.A.E.EFGB B6 B  HB  !]N+	6 	 , "	Q QF Q t**+) )F )4 )F )  ,) t""#J JF J4 JF J  $J t}})6 )$ )6 )  ) t$$%)6 )$ )6 )  &) t&&../&  T  0" 	$$,,d.M.M.Q.QR .f .6 .f . .d t!!))*&   + ))1143L3L3P3PQRT8V$ 	
  	
 666!" % S& %%--t/D/D/H/HIJ ''' '
 ' '  K'T &&(:(:;<S#s/3 f  fff>T8U   =4 ((00$2J2J2N2NOPT8V$ 	  	
 666!" % QD $$,,d.B.B.F.FGH 444 4
 4 4 4  I4n t~~S#s 	$$$ $ 	$
 666!"$  $P tTz!2 * &&(:(:;<S#f C ffn8M   =4 $$,,d.B.B.G.GHIV[$1'v '%(F"G ' 2 J'$ t''(   	""" " SM	" )"J.
.
. 49d3i .".
.
. 3-. 66>	.(f V   t$$%
 ##!777 	7
 7 V7 	7 V7 6
7 6666)*7 &7t ,,44d6R6R6V6VWX   	
   
&	  Y2 t$$%S#4( +(
+(+( +( 	+(
 +( 66>+( ) &+(^ t''(
 )
 tzz
 WW	W W 	W
 W W  Wt>#;L t$$%=  &= t%%&>  '>(< t--.\S  /S t../\T  0T2Ej t$$%=  &= t%%&>  '> &&..&&11''//''22	 \& &:<G~ t$$%=  &= t%%&>  '> &&..&&11''//''22	 \$( $(N t""#

f 
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  $

 t##$Pv PV P Pf PQW P  %P $$dll&6&678/0 '  9': &&(:(:;<&* I  =I
 t$$% & t~~ I !I
 $$dll&6&678"  9" t33;;< * =*. tww	  	B
* 7;i,,iLLi $s)S.!i 49c>"	i
 DIsN#i i i U49c>23iXQ t%%--."$,,"$LL"$ 5<<
 "$ 5<<(	"$
 %,,'"$ "$ !&"$ "$ /"$J t''(),,)LL) ,,) I	)
 #Y) 3i) ) I) ) ))X 	889>9N9N&&:6 599##::BBC D, 599##55==>S ?S
 xx:?--:O:O66;
7 
uyy}}00	1	 
2	
 :?9N9N&&:6 599##55==>599##33;;<" = ?"H 599##55<<= >6 599##55==>599##55<<= > ?, 599##55<<=599##55CCD E >: 599##77??@599##<<DDE	 F A	 =BMM<Q<QVV=9 599&&112 
 3
8 599&&??@@ A@( t&&' M (Mb(<X t''//0E 1EP t UJ   UJp t''(\K(  )K(\ t((001 2" t((001@ 2@ t1199:F ;F, t112\P  3P
	
6 	
S 	
 t''(UI+  )+\ t001\H  2H$ t''(UI'  )'T t001\(  2(
 t%%,,-* .* $$dll&6&678T  9T ##++T-@-@-D-DEF46 @c @  G@ 		&&..		0F0F0J0JKL  M" 

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

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

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

""DJJNN34   5( t{{E  E@ t""**+. ,. t!!))*. +.
	 	C 	d 	/
  t{{""#' $'6
 
-
b4 t''(& )&
 t  ! "
 !!	 & & ""	 889:
 #!==	= = 	=
 = = E?= ;=@S#X( 889: #!((	( ( 	(
 ( ( ( ( E?( ;(V EEFG
 #'#!''	' ' 	'
 ' ' ' E?' H'T 99( """" 
" 	"
 
" " " " " " " " " " E?"
". 88 "&!	  	
   E?
: AA #'!'"'"'" 
'" 	'"
 
'" '" '" '" '" E?'"
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4- 	4-
 4- 
4- 4- 4- 4- 4- $Z4- 4- E?4-
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" 	"
 
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HV &&( "&*'+#,,, 
, 	,
 
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,4 ))   %!(,!%!%,S,S	,S ,S 6
	,S
 6",S 6",S 3-,S 3-,S ,S ,S ,S E?,S f%,S v,S #,S
,S^ *** "$("'%474747 
47 	47
 6
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47n ''() $(+/'+ _Y
,,_Y
,,_Y \\_Y \\	_Y
 5<<
 _Y 5<<(_Y $_Y _Y *_YD ##'')<)<)D)DEF&  G&
 t##''( )
   (($*:*:*>*>?@	 	  A	,* 	$$d&D&D&L&LM

 	$$d&D&D&L&LM. ((00//77 !% $%U\\ 123 sELL012 uo	
 uo: 	$$d&D&D&L&LM

 									&$N t))112
  3 t&&'4/ (4/n t$$,,-$% .$%N


 ##T[[%8%89:4 ;4 t!!))* + tyy  !
Q "
Q t,,-LP  .  %%t}}';';<=Xy!K " >K  #("9"9 Q t77??@	* A	* t##++,	0 -	0 t!!))* +> t--556F 7FD %%t~~'@'@AB27u   C 

|E  E4 	!!))4+F+F+N+NO & 55==>?  @8 t>>FFG H$ '')<)<=>'  ?'
 uyy~~(() *8 uyy~~  !6 "6$ t  !
 
	-K  "-K` t,,- . t++, '
 -'
T t112  3, t>>?  @. tyy8=e 8  8  t~~6c 6 6F 6  6 t''(I& I )I tyy"v "& "  " t||6& 6V 6  6 P "!+/'+ eKeKeK ell#eK ell#	eK
 6
eK 6
eK 5<<(eK $eK eKP t  "!'+ 6
 6
	
 $   !& ''//01 $(#'+/'+ <<<< \\ \\	
 5<<
  5<<
  5<<( $  20 t}}	v 	C 	 	 	  	 t##$%  %%P t~~ $888 8 	8
 8 8  8, t33;;<
 	**&\* c* 	* =*  d22 3 d44 5 d44 5 d== > d== > d== > d== > dDD E dDD E tBB C tBB C tBB C tBB C tJJ K tJJ K tJJ K tJJ K t@@ A tAA B tAA B tAA B tyy  $ t||./    t||./   , 	tyy)!$,,/!$,,/
    BNJ r=   