
    #Ki              -       P}   S SK r S SKJrJr  S SKJr  S SKJr  S SKJ	r	  S SK
Jr  S SKrS SKJr  S SKJrJrJr  S SKJrJrJrJr  S S	KJr  S S
KJrJr  S SKJrJrJrJ r J!r!J"r"J#r#J$r$J%r%J&r&J'r'  S SK(J)r)J*r*J+r+J,r,J-r-  S SK.J/r/J0r0  S SK1J2r3  S SK4J5r5J6r6  S SK7J8r9  \	" S5      r:\" S5      r;\Rx                  Rz                  r=\R|                  R                  SSS5      r@\A" S5      u  rBrCrDS rES rFS\\\;\:4   /\\;\:4   4   4S jrGS\!4S jrHS rIS rJ\G" \=R                  \=R                  /5      \-" 5       SSS\R                  SS4S  j5       5       rN\G" \=R                  R                  \=R                  R                  /5      \-" 5       S! 5       5       rR\G" \=R                  R                  \=R                  R                  /5      \-" 5       S"S#.S$ j5       5       rS\G" \=R                  5      \-" 5       S% 5       5       rT\G" \=R                  R                  \=R                  R                  \=R                  R                  \=R                  R                  /5      \-" S&S'5      S( 5       5       rW\G" \=R                  R                  \=R                  R                  /5      \-" 5       S) 5       5       rXS* rYGS2S+\S,\Z\[   S-\\4S. jjr]\G" \=R                  R                  \=R                  R                  /5      \-" 5       S/ 5       5       r_Sr`S,\Z\[   4S0 jra\G" \=R                  R                  \=R                  R                  /5      \-" 5       S1 5       5       rc\G" \=R                  R                  5      SS2.S3 j5       rf\G" \=R                  R                  5      \R                  SSSS4.S5 j5       rh\G" \=R                  R                  \=R                  R                  /5      \-" 5       \R                  SSSS4.S6 j5       5       rj\G" \=R                  R                  \=R                  R                  /5      \-" 5       \R                  SSSS4.S7 j5       5       rm\G" \=R                  R                  \=R                  R                  /5      \-" 5       SSSSS4.S8 j5       5       ro\G" \=R                  R                  \=R                  R                  /5      \-" 5       S+\S,\Z\[   S9\[S:\[4S; j5       5       rq\G" \=R                  R                  5      GS2S< j5       rsS= rt\G" \=R                  R                  5      S> 5       rv\G" \=R                  5         GS3S?\S@\SA\SB\S-  SC\xS-  SD\R                  S-  4SE jj5       rz\G" \=R                  5       GS4SF\SG\SH\SD\R                  S-  4SI jj5       r|\G" \=R                  5      SJSJSSK.S?\SF\SG\SH\SD\R                  S-  4
SL jj5       r~\G" \=R                  5             GS5SM\R$                  SN\R$                  SB\S-  SO\S-  SD\R                  S-  SP\\SQ\[SR\[SS\[4ST jj5       r\G" \=GR                  R                  5      SUSV.S+\S,\[SW\SX\R$                  SY\xSZ\\S\4S[ jj5       r\G" \=GR                  R                  5      SUSV.S+\S,\[SW\SX\R$                  SY\xSZ\\S\4S\ jj5       r\-" 5       \G" \=GR
                  R                  5      S] 5       5       r\G" \=GR                  R                  5      SSSS SSS^.S_\SY\xS`\S-  S'\S-  Sa\S-  Sb\[Sc\\S\4Sd jj5       r\G" \=GR                  R                  \=GR                  GR                  /5      \-" 5       Se 5       5       r\G" \=GR                  GR                  5      GS2Sf j5       r\G" \=GR                  R                  \=GR                  GR                  /5      \-" 5       Sg 5       5       r\G" \=GR                  GR                  5      GS2Sh j5       r\G" \=GR"                  R                  5      Si 5       r\G" \=GR"                  R                  5      Sj 5       r\G" \=GR(                  R                  5      Sk 5       r\G" \=GR(                  GR,                  5      Sl 5       r\G" \=GR0                  R                  5      Sm 5       r\G" \=GR4                  R                  5      SSSSSSn.So j5       r\G" \=GR8                  R                  5      GS6Sp j5       r\G" \=GR:                  R                  5      GS3Sq j5       r\G" \=GR>                  R                  5      GS6Sr j5       r\G" \=GR@                  R                  5      Ss 5       r\G" \=GRD                  GR,                  5      St 5       rS+\Su\x4Sv jrS+\Sw\Sx\x4Sy jr GS7Sz\Su\xS{\\4S| jjrGS8Sw\Su\xS}\x4S~ jjrSw\S\S\\Su\x4S jr GS9S\xS\S?\S\x4S jjrS\x4S jr\G" \=GRV                  R                  \=GRV                  GRX                  /5      \-" SS5      GS:Sw\S\xS\\4S jj5       5       r\G" \=GR\                  R                  \=GR^                  R                  /5      \-" 5       S?\S\4S j5       5       r\G" \=GRb                  /5      \-" SS5      S?\4S j5       5       rS\S\4S jr\G" \=GRh                  5      \-" 5       S+\Sw\S\\S\4S j5       5       r\G" \=GRj                  5      \-" 5       GS2S+\Sw\S\\S\4S jj5       5       r\G" \=GRl                  5      \-" 5       GS2S+\S\\S\4S jj5       5       r\G" \=GRn                  5      \-" 5       GS2S+\S\\S\4S jj5       5       r\G" \=GRp                  R                  5      GS;Sw\S\\S\\4S jj5       r\G" \=GRr                  R                  \=GRr                  R                  /5      \-" 5       S?\S\S\4S j5       5       r\G" \=GRt                  R                  5      GS2Sw\S\\4S jj5       r\G" \=GRx                  R                  \=GRx                  R                  /5      \-" SSS5      SSS.S+\S\\S\\S\\\\4   4S jj5       5       r\G" \=GR~                  R                  \=GR~                  R                  /5      \-" 5       SS.S\S\S\S\\S\4
S jj5       5       r\G" \=GR                  R                  \=GR                  R                  /5      \-" SSS5      SUS.Sw\S\\S\\\\4   4S jj5       5       r\G" \=GR                  R                  \=GR                  R                  /5      \-" SSS5      SUSS.Sw\S\\S\\S\\\\4   4S jj5       5       r\G" \=GR                  R                  \=GR                  R                  /5      \-" 5       SUSS.S\S\S\S\\S\\S\4S jj5       5       r\G" \=GR                  5      \-" SSS5        GS<S\S\S\\S\\S\\\\4   4
S jj5       5       rS\xS\\\\\4   4S jr\G" \=GR                  R                  \=GR                  R                  /5      \-" SS5      GS=Sw\S\xS\\\4   4S jj5       5       r\G" \=GR                  R                  \=GR                  GR                  /5      \-" SSSS5      Sw\S\\\\\4   4S j5       5       r\G" \=GR                  R                  5         GS>Sw\S\\S\\S\xS-  4S jj5       rS\S\S\\Z\[   \Z\[   4   4S jrS\S\Sx\xS-  S\\\4   4S jrS?\S\S\\4S jr\G" \=GR                  5      SUSSSSSS.Sw\S\S\\S\\S\S-  S\S-  S\S-  S\S-  S\\\\\4   4S jj5       r\G" \=GR                  R                  \=GR                  R                  /5      SUSSS.Sw\S\S\\S\\S\\S\S-  S\4S jj5       r\G" \=GR                  5      \-" SSSUS9   GS?S+\Sw\S\\S\\S\\S\\\4   4S jj5       5       r\G" \=GR                  R                  5      S 5       r\G" \=GR                  5      \-" 5         GS@S?\S\S\S\\S\\S\4S jj5       5       rS rS r\G" \=GR                  5      \-" 5       S 5       5       r\G" \=GR                  5      \-" 5       S 5       5       rS r\G" \=GR                  5      \-" S5      S 5       5       r\G" \=GR                  5      \-" S5      S 5       5       rS r\G" \=GR                  5      \-" 5       S 5       5       r\G" \=GR                  5      \-" 5       S 5       5       r\G" \=GR                  R                  5      S 5       r\G" \=GR                  R                  \=GR                  GR                  \=GR                  R                  \=GR                  GR                  /5      \-" S5      S 5       5       rS r\G" \=GR                  5      \-" 5       S 5       5       r\G" \=GR                  5      \-" 5       S 5       5       r\G" \=GR                  R                  \=GR                  GR                  \=GR                  R                  \=GR                  GR                  /5      \-" S5      S 5       5       r\G" \=GR                  5      \-" 5       GSAS+\S\S\4S jj5       5       r\G" \=GR                  5      \-" 5       S\S+\S\S\S\4
S j5       5       r\G" \=GR                  R                  \=GR                  R                  /5      \-" SUS9SJSJS.S j5       5       r\G" \=GR                   R                  \=GR                   R                  /5      \-" 5       SS2.S j5       5       Gr\G" \=GR                  GR                  5      GSBS j5       Gr\G" \=GR                   GR                  5      GSBS j5       Gr\G" \=GR                  R                  \=GR                  R                  /5      \-" 5       GS4S j5       5       Gr\G" \=GR                  R                  5        GS;S j5       Gr	\G" \=GR                  5      \-" SUS9GS4SD\R                  S-  4S jj5       5       GrS GrGSCS jGr GS4S\R$                  S@\R$                  S\Z\[   \[-  S\Z\[   \[-  S\Z\[   \[-  S\\S\[S\Z\[   \[-  S-  4S jjGrS Gr\G" \=GR                   R                  5      S\R$                  S@\R$                  SB\R$                  S-  S\R$                  S-  S\R$                  S-  S\\S\S\4S j5       Gr\G" \=GR$                  R                  5      S\R$                  S@\R$                  SB\R$                  S\Z\[   S\Z\[   S\Z\[   S\\S\Z\[   S\[4S j5       Gr\GR(                  GR*                  (       Ga
  \R|                  R                  GS SS5      Gr\G" \Rx                  GR.                  GR0                  R                  5      GS 5       Gr\G" \Rx                  GR.                  GR4                  R                  5      GS 5       Gr\GR(                  GR8                  (       aO  \R|                  R                  GSSS5      Gr\G" \Rx                  GR<                  GR>                  5      GS 5       Gr \R|                  R                  GSSS5      Gr!\G" \Rx                  GRD                  GRF                  R                  5      \G" \Rx                  GRD                  GRH                  R                  5      \G" \Rx                  GRD                  GRH                  GRJ                  5      GS 5       5       5       Gr&\G" \Rx                  GRD                  GRF                  GRN                  5      \G" \Rx                  GRD                  GRF                  GRP                  5      GS 5       5       Gr)\G" \Rx                  GRD                  GRT                  R                  5      \G" \Rx                  GRD                  GRT                  GRJ                  5      GS 5       5       Gr+\G" \Rx                  GRD                  GRT                  GRN                  5      \G" \Rx                  GRD                  GRT                  GRP                  5      GS	 5       5       Gr,\G" \Rx                  GRD                  GRZ                  R                  5      \G" \Rx                  GRD                  GR\                  R                  5      GS
 5       5       Gr/\R|                  R                  GSSS5      Gr0\G" \Rx                  GRb                  GRd                  5          GSDGS j5       Gr3\G" \Rx                  GRb                  GRh                  5      GS 5       Gr5GS Gr6\G" \=GRn                  R                  5           GSEGS j5       Gr8GS Gr9\G" \=GRt                  R                  5      GS 5       Gr;\G" \=GRx                  5      \-" 5            GSEGS j5       5       Gr=\G" \=GR|                  5      \-" S5      GS 5       5       Gr?\G" \=GR                  R                  5      GS 5       GrA\G" \=GR                  R                  5      GS 5       GrC\G" \=GR                  R                  5      GS 5       GrE\G" \=GR                  5      \-" S5      GS 5       5       GrGGS\S}\x4GS jGrH\G" \=GR                  5      \-" SS'5      GS 5       5       GrJ\G" \=GR                  5      \-" S5      GS 5       5       GrL\G" \=GR                  5      \-" SS'5      GS 5       5       GrN\G" \=GR                  5      \-" S5      GS 5       5       GrP\G" \=GR                  R$                  5      GS4GS  j5       GrR\G" \=GR                  R                  \=GR                  R                  /5      \-" 5       GS! 5       5       GrT\G" \=GR                  R                  \=GR                  R                  /5      \-" 5       S"GS".GS#\[4GS$ jj5       5       GrU\G" \Rx                  Rz                  GR                  R                  \Rx                  Rz                  GR                  R                  /5      \-" 5       GS% 5       5       GrV\G" \=GR                  R$                  \=GR                  R$                  /5      GS& 5       GrY\G" \=GR                  R                  /5      GS' 5       Gr[\G" \=GR                  R                  \=GR                  R                  /5      \-" SUS9SJSJS.GS( j5       5       Gr]\G" \=GR                  R$                  /5      GS) 5       Gr_\G" \=GR                  R                  \=GR                  R                  /5      SSGS*.GS+ j5       Grb\G" \=GR                  R                  /5      SSGS*.GS, j5       Grd\G" \=GR                  /5      \-" 5       GS- 5       5       Grf\G" \=GR                  /5      GS. 5       Grh\G" \=GR                  /5      GS/ 5       Grj\G" \=GR                  /5      GS0 5       Grl\G" \=GR                  /5      GS1 5       Grn\G" \=GR                  /5      GS2 5       GroGS3\[GS4\[S\[4GS5 jGrpGS6 Grq\G" \=GR                  /5      SB\S-  4GS7 j5       Grs\G" \=GR                  /5      GS8 5       Gru\G" \=GR                  /5      GS9 5       Grw\G" \=GR                  R                  5      GS: 5       Gry\G" \=GR                  5      \-" 5       GS; 5       5       Gr{\G" \=GR                  R                  5            GSFGS< j5       Gr}\G" \=GR                  R                  5      GS= 5       GrGS7GS> jGr\G" \=GR                  R                  \=GR                  R                  /5      \-" 5       GSGSGS?.GS@ jj5       5       Gr\G" \=GR                  R                  \=GR                  R                  /5      GSA 5       Gr\G" \=GR                  GR                  \=GR                  GR                  \=GR                  GR                  \=GR                  GR                  \=GR                  R                  \=GR                  GR                  /5      \-" S&S'5      GSHGSB j5       5       Gr\G" \=GR                  R                  5      GSC 5       Gr\G" \=GR                  R                  5      GSD 5       Gr\G" \=GR                  R                  5      GSE 5       Gr\G" \=GR                   GR"                  \=GR$                  GR"                  \=GR                   R$                  \=GR$                  R$                  \=GR&                  R                  \=GR(                  R                  \=GR*                  R                  /5      GSF 5       Gr\G" \=GR.                  GR"                  \=GR0                  GR"                  \=GR.                  R$                  \=GR0                  R$                  /5      GSGSG j5       Gr\G" \=GR4                  GR"                  \=GR6                  GR"                  /5      GSGSH j5       Gr\G" \=GR:                  R                  \=GR:                  GR<                  /5      GSI 5       GrGSJ Gr\G" \=GRB                  R$                  \=GRB                  GR"                  /5      GSK 5       Gr\G" \=GRF                  R$                  \=GRF                  GR"                  /5      GSL 5       Gr\G" \=GRJ                  R                  5      GSM 5       Gr\G" \=GRN                  R$                  \=GRN                  GR"                  /5      GSN 5       Gr\G" \=GRR                  R$                  \=GRR                  GR"                  /5      GSO 5       Gr\G" \=GRV                  R                  5      GSP 5       Gr\G" \=GRZ                  R$                  5      \-" 5       GSS\4GSQ jj5       5       Gr\G" \=GR^                  /5      \-" 5        GSIGSR j5       5       Gr\G" \=GRb                  /5       GSIGSS j5       Gr\G" \=GRf                  /5       GSIGST j5       Gr\G" \=GRj                  R                  \=GRl                  R                  /5      GS2GSU j5       Gr\G" \=GRp                  GR"                  5      GSV 5       Gr\G" \=GRt                  R                  5      GSW 5       Gr\G" \=GRx                  5      GSX 5       Gr\G" \=GR|                  5      \-" 5       GSY 5       5       Gr\G" \=GR                  5      GSZ 5       Gr\G" \=GR                  R                  5      GS2GS[ j5       GrGS6GS\ jGr\G" \=GR                  R                  5      GS] 5       Gr\G" \=GR                  R                  5      GS^ 5       GrGS_ GrGS` GrGSa GrGSb Gr GS2S?\GSc\[GSd\[GSe\[GSf\[GSg\[GSh\[GSi\[GSj\[GSk\[GSl\[GSm\[GSn\[GSo\[GSp\[GSq\[GSr\[GSs\[GSt\[GSu\[S\xGSv\\4,GSw jjGrGSx GrS?\GS\GSc\[GSd\[GSe\[GSf\[GSg\[GSh\[GSi\[GSj\[GSk\[GSl\[GSp\[GSq\[GSr\[GSs\[GSt\[GSu\[S\x4&GSy jGrGSz Gr\G" \=GR                  R                  5      GS{ 5       Gr\G" \=GR                  R                  5          GSDGS| j5       Gr\G" \=GR                  R                  5      GS} 5       Gr\G" \=GR                  5      \-" SS'5          GSDGS~ j5       5       Gr\G" \=GR                  5      \-" S5      GS 5       5       GrS?\GS\4GS jGr " GS GS\5      GrS?\GS\GS\[4GS jGr\G" \=GR                  R                  5      GS 5       Gr\G" \=GR                  5      \-" 5       GS 5       5       Gr\G" \=GR                  5      \-" SGS5      GS 5       5       Gr\G" \=GR                  R                  /5      GS 5       Gr\G" \=GR                  R                  5           GSJGS j5       Gr\G" \=GR                  R                  \=GR                  R                  /5      \-" 5       SSSSSGS.GS j5       5       Gr\G" \=GR                  R                  \=GR                  R                  /5      \-" 5       SSSSSGS.GS j5       5       Gr\G" \=GR                  R                  5      GS 5       Gr\G" \=GR                  R                  5      GSKGS j5       GrGS7S,\[GS\[GS\\4GS jjGrGS GrGS Gr\G" \=GR                  R                  5      GS2GS j5       GrGS2GS jGrGS4GS jGrGS GrGS4GS jGrGSLGS jGr\G" \=GR                  R                  5      GS 5       Gr\G" \=GR                  5      GS 5       Gr\G" \=GR                  GR                  \=GR                  GR                  \=GR                  GR                  \=GR                  GR                  /5      \-" 5       GS4GS j5       5       Gr\G" \=GR                  GR                  \=GR                  GR                  \=GR                  GR                  \=GR                  GR                  /5      GS4GS j5       Gr \G" \=GR                  /5          GSMGS\GS\GS\GS\GS\\GS\\GS\S-  4GS jj5       GrGS\GS\\[GS4   4GS jGr\G" \=GR                  /5          GSMGS\GS\GS\GS\S-  GS\\GS\GS\\GS\\GS\S-  4GS jj5       Gr\G" \=GR                  /5           GSNGS\GS\GS\GS\S-  GS\GS\\GS\\GS\S-  4GS jj5       Gr\G" \=GR                  /5       GS4GS\GS\GS\GS\S\GS\GS\GS\GS\[GS\[GS\GS\\GS\GS\GS\S-  4GS jj5       Gr	\G" \=GR                  /5          GSOGS\GS\GS\GS\GS\\GS\S-  GS\S-  4GS jj5       Gr\G" \=GR                  /5        GS6GS\GS\GS\GS\S\GS\GS\GS\\GS\S-  GS\S-  4GS jj5       Gr\G" \=GR                  /5           GSPGS\GS\GS\GS\S-  GS\GS\\GS\S-  GS\S-  S\\\4   4GS jj5       Gr\G" \=GR                   /5         GSQGS\GS\GS\GS\S-  GS\\GS\\GS\S-  4GS jj5       Gr\G" \=GR$                  /5        GSRGS\GS\GS\GS\GS\S-  S\GS\GS\GS\GS\GS\Z\\   GS\\GS\S-  4GS jj5       Gr\G" \=GR(                  /5       GS4GS\GS\GS\GS\S\GS\GS\GS\GS\GS\GS\GS\[GS\[GS\GS\\GS\S-  4 GS jj5       Gr\G" \=GR,                  /5           GSJGS\GS\GS\GS\S-  GS\S-  GS\[GS\[GS\GS\\GS\\GS\S-  GS\[S-  GS\[S-  GS\S-  GS\S-  4GS jj5       Gr\G" \=GR0                  /5         GS3GS\GS\GS\GS\S\GS\GS\GS\GS\[GS\[GS\GS\\GS\GS\GS\S-  GS\[S-  GS\[S-  4"GS jj5       Gr\G" \=GR4                  /5           GSSGS\GS\GS\SB\S-  GS\S-  GS\S-  GS\[S-  GS\[S-  GS\GS\[GS\\GS\S-  GS\S-  GS\S-  GS\[S-  4GS jj5       Gr\G" \=GR8                  /5         GSLGS\GS\GS\GS\SB\S-  GS\S-  GS\S-  GS\GR:                  GS\GR:                  GS\GS\GS\GS\GS\[GS\\GS\S-  GS\[S-  GS\\4$GS jj5       Gr    GSTS+\R$                  SH\R$                  GS\R$                  GS\R$                  SB\R$                  S-  GS\R$                  S-  SD\R                  S-  GS\\4GS jjGr\G" \=GR@                  R                  /5          GSTS+\R$                  SH\R$                  GS\R$                  GS\R$                  SB\R$                  S-  GS\R$                  S-  SD\R                  S-  GS\\4GS jj5       Gr!     GSUS+\R$                  SH\R$                  GS\Z\R$                     GS\Z\5   GS\Z\R$                     GS\Z\5   SB\R$                  S-  SD\R                  S-  GS\Z\6   S-  GS\Z\6   S-  GS\\4GS jjGr"\G" \=GRF                  R                  /5          GSTS+\R$                  SH\R$                  GS\Z\R$                     GS\Z\5   GS\Z\6   GS\Z\R$                     GS\Z\5   GS\Z\6   SB\R$                  S-  GS\R                  S-  GS\Z\[   S-  GS\\4GS jj5       Gr$\G" \=GRJ                  GRL                  \=GRJ                  GRN                  /5      \-" 5       GS7GS j5       5       Gr(\G" \=GRR                  GRL                  5      GS7GS j5       Gr*\G" \=GRV                  R                  \=GRV                  R                  /5      \-" 5       GS2SS2.GS jj5       5       Gr,GS Gr-GS Gr.\G" \=GR^                  R                  \=GR`                  R                  /5      GS4GS j5       Gr/\G" \=GRb                  R                  \=GRd                  R                  /5      GS6GS j5       Gr1\G" \=GRf                  R                  \=GRh                  R                  /5        GS6GS\GS\\[\GR:                  -     GS\\[\GR:                  -     GS\S-  GS\S-  4
GS jj5       Gr3\G" \=GRj                  R                  \=GRl                  R                  /5      GS3GS j5       Gr5\G" \=GRn                  R                  \=GRn                  GRp                  \=GRn                  GR                  \=GRn                  GRr                  /5      GSVGS j5       Gr:GS Gr;\G" \=GRx                  R                  5        GS6GS j5       Gr=\G" \=GR|                  R                  5      GS 5       Gr>\G" \=GR~                  R                  5      GS 5       Gr?GS Gr@GS GrA\G" \=GR                  R                  \=GR                  R                  /5      GSGGS j5       GrD\G" \=GR                  R                  5      GSWGS j5       GrE\G" \=GR                  R                  5      GSXGS j5       GrG\G" \=GR                  5      \-" 5        GSYGS j5       5       GrI\G" \=GR                  R                  \=GR                  GR                  /5      \-" S&S'5      GSHGS j5       5       GrK\GR                  GrMGS GrN\G" \=GR                  R                  5      GS 5       GrO\G" \=GR                  R                  5      GS 5       GrP\G" \=GR                  R                  5      GS 5       GrR\G" \=GR                  R                  5      GS 5       GrS\G" \=GR                  R$                  \=GR                  GR                  /5      \-" 5       SSGS .GS j5       5       GrV\G" \=GR                  /5      \-" 5       GSZGS j5       5       GrX\G" \=GR                  R                  \=GR                  R                  /5        GS6GS j5       Gr[\G" \=GR                  R                  /5        GS6GS j5       Gr]\G" \=GR                  R                  5      GS 5       Gr^\G" \=GR                  R                  \=GR                  R                  /5      \-" 5       GS3GS j5       5       Gr_\G" \Rx                  Rz                  GR                  5      GS 5       Gr`\G" \Rx                  Rz                  GR                  5      GS 5       Gra\G" \=GR                  5      \-" 5       SSSSGS	.GS
 j5       5       GrcGS Grd\G" \=GR                  5      GS 5       Grf\G" \=GR                  5       GS[GS j5       Grh\G" \=GR                  5       GS[GS j5       Grj\G" \=GR                  5       GS[GS j5       Grl\G" \=GR                  5      \-" 5       SSGS.GS j5       5       Grn\G" \=GR                  5      \-" 5       GS\[S+\S\4GS j5       5       Grp\G" \=GR                  5      S+\4GS j5       Grr\G" \=GR                  5      \-" SUS9S+\S\4GS j5       5       Grs\G" \=GR                  5      \-" 5       S+\S\4GS j5       5       GrtGS Gru     GSUGS\GS\GS\R$                  S-  GS\R$                  S-  GS\S-  SB\S-  GS\R$                  S-  SD\R                  S-  GS\\4GS jjGrv\G" \=GR                  5      \-" 5          GS3GS\GS\GS\S-  SB\S-  SD\R                  S-  S\4GS jj5       5       Grx\G" \=GR                  /5           GSUGS\R$                  GS\R$                  GS\R$                  GS\R$                  GS\R$                  S-  SB\R$                  S-  GS\R$                  S-  SD\R                  S-  GS\\4GS jj5       Grz\G" \=GR                  5      \-" 5       GS\S,\[GS\\S\4GS  j5       5       Gr|\G" \=GR                  5      \-" 5       GSGS! j5       5       Gr~\G" \=GR                  5      \-" 5          GS\S@\S'\GS"\[GS#\\GS$\\S\4GS% jj5       5       Gr\G" \=GR                   R                  5       GS]S&\Sa\Z\   GS&\Z\[   GS'\4GS( jj5       GrGS) Gr\G" \=GR                  R                  5          GS^GS* j5       GrGS+ GrG\" \=GR                  5        G\" \=GR                  5        G\" \=GR                  5        G\" \=GR                  5        G\" \=GR                  5        G\" \=GR                  5        G\" \=GR                  5        G\" \=GR                  5        G\" \=GR                  5        G\" \=GR                  5        G\" \=GR                   5        G\" \=GR"                  5        G\" \=GR$                  5        G\" \=GR&                  5        G\" \=GR(                  5        G\" \=GR*                  5        G\" \=GR,                  5        G\" \=GR.                  5        G\" \=GR0                  5        G\" \=GR2                  5        G\" \=GR4                  5        GS, Gr\G" \=GR8                  5      \-" 5       GS- 5       5       Gr\G" \=GR:                  5      \-" 5       SJGS..GS/ j5       5       Gr\G" \=GR<                  5      \-" 5       SJGS..GS0 j5       5       GrG\" \=GR8                  5      GrG\" \=GR:                  5      GrG\" \=GR<                  5      GrS SK.rS SGKrS SGKrGS1 GrG\" 5         g(_      N)CallableSequence)Enum)wraps)TypeVar)	ParamSpec)SymBoolSymFloatTensor)_add_op_to_registry_convert_out_paramsglobal_decomposition_table
meta_table)
OpOverload)_prim_elementwise_meta$ELEMENTWISE_PRIM_TYPE_PROMOTION_KIND)BoolLikecorresponding_complex_dtypecorresponding_real_dtypeelementwise_dtypesELEMENTWISE_TYPE_PROMOTION_KIND	FloatLikeIntLikemake_contiguous_strides_forNumbersuggest_memory_format
TensorLike)_maybe_convert_to_dtype_maybe_resize_out_resize_output_check_safe_copy_outout_wrapper)_broadcast_shapes_maybe_broadcast)_config)ScalingTypeSwizzleType)_pytree_T_PatenIMPLMeta   c                     X-   S-
  U-  $ N    abs     [/var/www/html/dynamic-report/venv/lib/python3.13/site-packages/torch/_meta_registrations.pyceil_divr7   7   s    EAI!    c                     X-   S-
  U-  U-  $ )z$Rounds up x to nearest multiple of yr1   r2   xys     r6   round_upr=   ;   s    UQY1!!r8   returnc                    ^  U 4S jnU$ )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    r6   register0register_meta.<locals>.wrapper.<locals>.registerD   s    
B3r8   )r   pytree	tree_map_)rD   rE   rC   s   ` r6   wrapperregister_meta.<locals>.wrapperA   s)     $	4 	2&	r8   r2   )rC   rI   s   ` r6   register_metarK   @   s     Nr8   type_promotionc                     [         R                  " USU 06u  p#U Vs/ s H  n[        XC5      PM     nn[        U6 n[	        US[
        R                  06$ s  snf )Ntype_promotion_kindrL   )utilsr   r   r$   r   r   DEFAULT)rL   args_result_dtyper;   s        r6   elementwise_metarT   M   sp    
 ..	*OA ?CCd#A4dDC T"D "	BJJ  Ds   Ac                     [         R                  [         R                  [         R                  [         R                  [         R
                  [         R                  0nUR                  X 5      $ rB   )torch	complex32halfcfloatfloatcdoubledoubleget)dtypefrom_complexs     r6   toRealValueTyper`   a   sC    ekku||L
 E))r8   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$ )Nzoutput with shape z# doesn't match the broadcast shape r2   )broadcasted_shape
self_shapes   r6   <lambda>)check_inplace_broadcast.<locals>.<lambda>n   s    $ZL0STeSfgr8   )tupler#   rV   _check)rd   
args_shaperc   s   ` @r6   check_inplace_broadcastrj   j   s0    /
HZHI	LLZ'gr8   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$ )
Nr   c                      gNz:linspace only supports 0-dimensional start and end tensorsr2   r2   r8   r6   re   (meta_linspace_logspace.<locals>.<lambda>       Pr8   c                      grm   r2   r2   r8   r6   re   rn      ro   r8   c              3   B   #    U  H  n[        U[        5      v   M     g 7frB   )
isinstancecomplex).0args     r6   	<genexpr>)meta_linspace_logspace.<locals>.<genexpr>   s     
C/B:c7##/Bs   c                     > ST  ST 3$ )Nzlinspace(): inferred dtype z& can't be safely cast to passed dtype r2   )default_complex_dtyper^   s   r6   re   rn      s    56K5LLrsxryzr8   c                     > S[        T5      R                   S[        T 5      R                   S[        T5      R                   S3$ )Nz4received an invalid combination of arguments - got (, ))type__name__)endstartstepss   r6   re   rn      sB     u+r$s),,-RU0D0D/EQHr8   c                      g)Nz$number of steps must be non-negativer2   r2   r8   r6   re   rn      s    %Kr8   metar^   layoutdevice
pin_memoryrequires_grad)rr   rV   r   rh   dimanyrO   r   get_default_dtypeis_complex_dtyper^   _check_typer   empty)
r   r   r   baser^   r   r   r   r   ry   s
   ``` `    @r6   meta_linspace_logspacer   r   s[    %&&IIK1P	
 #u||$$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;;	# r8   c                 6  ^ [         R                  " TR                  [         R                  :H  U4S j5        [         R                  " U R                  5       S:H  =(       a    TR                  5       S:g  (       + S 5        U R                  TR                  5      $ )Nc                  "   > ST R                    3$ )Nz2take(): Expected a long tensor for index, but got r^   indexs   r6   re   meta_take.<locals>.<lambda>   s    DU[[MRr8   r   c                      g)Nz*take(): tried to take from an empty tensorr2   r2   r8   r6   re   r      s    <r8   )rV   rh   r^   long_check_indexnumel	new_emptyshape)selfr   s    `r6   	meta_taker      sm     
LLuzz!R
 
ZZ\Q55;;=A#56< >>%++&&r8   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      $ )Nc                      g)Nz=linalg.cross: inputs must have the same number of dimensions.r2   r2   r8   r6   re   linalg_cross.<locals>.<lambda>       Or8   r.   c                  V   > ST  STR                  T 5       STR                  T 5       3$ )Nzlinalg.cross: inputs dimension z must have length 3. Got  and size)r   otherr   s   r6   re   r      s1    -cU 399S>"%

3'8:r8   )ndimrV   rh   r   r#   r   r   )r   r   r   x_dy_d	out_shapes   ```   r6   linalg_crossr      s     ))C
**C	LL
O 
LL		#!4

31 4	
 "$**ekk:I>>)$$r8   c                 x    [        U S5        [        U S5        [        R                  " U [        R                  S9$ )Nzlinalg.matrix_expmemory_format)squareCheckInputscheckFloatingOrComplexrV   
empty_likecontiguous_formatr   s    r6   linalg_matrix_expr      s3     d/04!45D0G0GHHr8   valuesindicesc                 R   [         R                  " U R                  U R                  U R                  S9n[         R                  " U R                  U R                  [         R
                  S9nU R                  5       S:w  a%  U R                  S:w  a  [        XR                  5        X#4$ )Nr   r^   r   )	rV   r   r   r   r^   int64r   r   maybe_wrap_dim)r   r   r   r   s       r6   	cummaxminr      sl    
 [[DKKtzzJFkk$**T[[LGzz|qTYY!^sII&?r8   c                 r    [        XR                  5        [        R                  " U [        R                  S9$ Nr   )r   r   rV   r   r   )r   r   s     r6   logcumsumexpr      s)     3		"D0G0GHHr8   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 $ s  sn	f s  sn	f )	NFTc                    > TU    $ rB   r2   )r;   self_stridess    r6   re   _exec_fft.<locals>.<lambda>
  s	    <?r8   keyreverser   r   r1   r   )r   lenlistrangeappendstridesortpermuter   reshaper   resize_rV   r   as_strided_storage_offset)outr   	out_sizesr   forwardr   signal_ndim
batch_dimsdim_permuterR   is_transformed_dimdleftright	batch_endtmpinputbatched_sizes
batch_sizebatched_out_sizesiout_stridesbatch_numelr   s                          @r6   	_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    $ rB   r2   )r   r   s    r6   re   _sort_dims.<locals>.<lambda>,  s	    l1or8   )r   )r   r   r   intr   )r   r   r   sorted_dimsr   s       @r6   
_sort_dimsr   (  sL    s)K;;=L6#k"S%667<<% =  r8   c                 
   [         R                  " U R                  R                  5        U(       d  U R	                  5       $ [        X5      nU R                  U R                  5       5      n[        XPU R                  5       XCS9$ )Nr   )	rV   rh   r^   
is_complexcloner   r   r   r   )r   r   normalizationr   r   r   s         r6   meta_fft_c2cr   3  s\     
LL&&'zz|T'K
..
%CS		[JJr8   c                 n    [        U 5      [        :  d!  [        U 5      S:  a  U S   S:X  a
  U S   S:X  a  gg)N   r   r1   FT)r   cufft_max_ndimr   s    r6   use_optimized_cufft_pathr   B  s3    
3x. SX]s1v{s1vQR{r8   c                 |  ^ [         R                  " U R                  R                  5        [	        U R                  5       5      n[	        U5      nUS   nXF   S-  S-   n[	        U5      nXxU'   U(       a  XuU'   [        U 5      S:X  d  [        U 5      S:X  Gax  U R                  U[        R                  " U R                  5      S9n	U n
[        U 5      S:X  a  [        U5      (       a  [        XXQSS9  O[        U5      S:X  a  UOUn[        XX/SS9  [        U5      S:  a.  U R                  U[        R                  " U R                  5      S9n
US S nU(       au  XpU
R                  5       mUR                  U4S	 jSS
9  [        [         [        U5      5      nU[        U5      U-
  S  n[        XXSS9  US [        U5      U-
   nU(       a  Mu  U(       d7  U	R                  U5      XV   :w  a   U
R#                  U[         R$                  S9  U
n	U	$ U R                  U[        R                  " U R                  5      S9$ )Nr   r   r1   cudaxpur   Tr   c                    > TU    $ rB   r2   )r   stridess    r6   re   meta_fft_r2c.<locals>.<lambda>p  s	    '!*r8   r   r   )rV   rh   r^   is_floating_pointr   r   device_hintr   rO   r   r   r   r   r   r   minr   r   r   )r   r   r   onesidedinput_sizesr   last_dimlast_dim_halfsizeonesided_sizesoutputworking_tensortarget_sizesr   max_dims	last_dimsr   s                  @r6   meta_fft_r2cr  I  s+    
LL--.tyy{#K[!I2wH#-2Q6+&N08/(4F"k$&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  
 	
r8   )	generatorc                D    [        U[        R                  " U /5      5      $ rB   )r   rV   Size)nr  r   s      r6   meta_randpermr    s    S%**aS/22r8   r^   r   r   r   c                .    [         R                  " XX#US9$ Nr  rV   r   )r  r^   r   r   r   s        r6   meta_randperm_defaultr    s     ;;	v r8   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=r2   highlows   r6   re   meta_randint.<locals>.<lambda>      LSEQXY]X^_r8   r  rV   rh   r   )r  r   r^   r   r   r   r  s   `     @r6   meta_randintr     s:     C	LLs
_ ;;&J r8   c                p   ^ ^ [         R                  " TT :  UU 4S j5        [         R                  " X#XEUS9$ )Nc                     > ST ST  3$ r  r2   r  s   r6   re   "meta_randint_low.<locals>.<lambda>  r  r8   r  r  )r  r  r   r^   r   r   r   s   ``     r6   meta_randint_lowr$    s5     
LLs
_ ;;&J r8   c                .    [         R                  " XX#US9$ r  r  )r   r^   r   r   r   s        r6   meta_rand_defaultr&    s     ;;&J r8   r   lastdimc                    [         R                  " U R                  R                  5        [	        U 5      S:X  a  [        U R                  5       5      nX4US   '   U R                  U[        U R                  5      S9n[        U5      (       a(  [        UU R                  [         R                  S9UUSS9$ [        U5      S:  a  [        XS S SU5      nOU R                  [         R                  S9n[        XVXAS   /SS9$ U n[        U5      S:  a  US S n[        XUSS9nUSS  n[        UR                  5       5      nX4US   '   U R                  U[        U R                  5      S9n	[        XXASS9$ )	Nr   r   r   r   Fr   r1   r   )rV   rh   r^   r   r   r   r   r   r`   r   r   r   r   r   r   )
r   r   r   r'  r   r  tempr   c2c_dimsr   s
             r6   meta_fft_c2rr+    s^    
LL&&'4F"%	$#b'	1LM#C((

)@)@
A  3x!|#Dcr(Aw?zz0G0GzHV92wiOO s8a<3BxH NEbc(C&	$#b'nnYodjj.InJYUCCr8   c                 `   SSK Jn  U" U 5      (       d%  [        R                  " U 5      S:X  a  [	        S5      e[        U[        5      (       a`  UR                  X5      nU R                  5       UR                  5       :w  a-  [        R                  R                  X@R                  5       5        U $ )Nr   )free_unbacked_symbolsr1   zQmore than one element of the written-to tensor refers to a single memory location)%torch.fx.experimental.symbolic_shapesr-  rV   _debug_has_internal_overlapRuntimeErrorrr   r   tor   r+   expand_copydefault)r   srcnon_blockingr-  intermediates        r6   
meta_copy_r7    s     L "$''E,M,Md,SWX,X_
 	
 #vvvd199;,++--$$\99;?Kr8   c                     [        U R                  5       5      n[        U R                  5       5      nXR                  5       :  a  SOX!   X1   -  nUR	                  US5        UR	                  X5        X#4$ r0   )r   r   r   r   insert)tensorr   result_sizesresult_strides
new_strides        r6   inferUnsqueezeGeometryr>    sf    &L&--/*NZZ\)|/@>CV/VJQ#*''r8   c                 z    [        XR                  5       S-   5      n[        X5      u  p#U R                  X#5        U $ r0   )r   r   r>  r   )r   r   g_sizes	g_stridess       r6   meta_unsqueeze_rB    s6    
hhj1n
-C/:GW(Kr8   r   weight_metabias_activation_opt	out_dtypec                 @   [        U R                  5      nUb+  UR                  S5      UR                  S5      :X  d   S5       eUR                  S5      U R                  S5      S-  :X  d   eUR                  S5      US'   [        U R                  5      S:X  d   S5       eSU R                  S5      4nUb9  U R                  [
        R                  :X  a  U[
        R                  :X  d   S5       eU R                  UUc  U R                  OUS9R                  Xg5      nU$ )	Nr   zoutput size mismatchr1   r   r   z*we can only handle the squashed input case9out_dtype is only supported for i8i8->i32 linear operatorr   )
r   r   r   r   r^   rV   int8int32r   
as_strided)	r   rC  rD  rE  rF  rG  output_sizestransposed_stridesr  s	            r6   meta_sparse_structured_linearrO  !  s    $L{{1~1-E/EE-;;q>UZZ^a////{{1~L u{{q N"NN UZZ]+{{ejj(Y%++-E 	
G	
E __&.ekkI   j2 
 Mr8   mat1	mat1_metamat2c                    [        U R                  5      S:X  d   e[        UR                  5      S:X  d   e[        UR                  5      S:X  d   eU R                  S5      UR                  S5      S-  :X  d   eU R                  S5      UR                  S5      /nUb9  UR                  [        R
                  :X  a  U[        R                  :X  d   S5       eUR                  UUc  UR                  OUS9nU$ )Nr   r1   r   rI  r   r   r   r   r^   rV   rJ  rK  r   )rP  rQ  rR  rG  rM  r  s         r6   meta_sparse_structured_mmrU  C  s     tzz?ay1$$$tzz?a99Q<499Q<!++++IIaL$))A,/LzzUZZ'I,D 	
G	
D ^^%-djj9  F
 Mr8   r1   )alphabetarG  c                   [        U R                  5      S:X  d   S5       e[        UR                  5      S:X  d   e[        UR                  5      S:X  d   e[        UR                  5      S:X  d   eU R                  S5      UR                  S5      :X  d   S5       eUR                  S5      UR                  S5      S-  :X  d   eUR                  S5      UR                  S5      /nUb9  UR                  [        R
                  :X  a  U[        R                  :X  d   S5       eUR                  UUc  UR                  OUS9nU$ )Nr1   zEonly input broadcasted to columns of mat1 * mat2 product is supportedr   r   rI  r   rT  )	r   rP  rQ  rR  rV  rW  rG  rM  r  s	            r6   meta_sparse_structured_addmmrY  \  s/    u{{q  O  tzz?ay1$$$tzz?a::a=DIIaL( O( 99Q<499Q<!++++IIaL$))A,/LzzUZZ'I,D 	
G	
D ^^%-djj9  F
 Mr8   compressed_Adense_BrV  transpose_resultalg_idsplit_ksplit_k_modec	                 x   UR                   [        R                  [        R                  [        R                  [        R
                  [        R                  1;   d   S5       eU R                   UR                   :X  d   S5       e[        UR                  5      S:X  d   S5       eU R                   [        R
                  [        R                  4;   n	U	(       a  UR                  5       (       a   S5       eUR                  S5      n
U R                  S5      nUb  XR                  S5      :X  d   eUbn  U	(       aB  U[        R                  [        R                  [        R                  [        R                  1;   d%   SU R                    S	UR                    S
U S35       eU(       a  X4OX4nUR                  XS9$ )Nz;_cslt_sparse_mm only supports fp16, bf16, int8, and fp8e4m3zinputs must have the same dtyper   z'_cslt_sparse_mm only supports 2d inputsz.dense input must be transposed for 8bit dtypesr1   r   zout_dtype is not supported for z x z -> z matmul!r   )r^   rV   float32float16bfloat16rJ  float8_e4m3fnr   r   is_contiguousr   rK  r   )rZ  r[  rE  rV  rG  r\  r]  r^  r_  is_8bit_input_typer  moutput_shapes                r6   meta__cslt_sparse_mmri    s    ==

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

E<O<O/PP((** 	
<	
* 	QA!AIIaL   !iMMNNKK	4
 '
 	
 .l.@.@-AW]]OSWXaWbbjk	
 
 .A6A6L\;;r8   T)include_selfr   sourcereducerj  c                H    [         R                  " U [         R                  S9$ r   rV   r   r   r   r   r   rk  rl  rj  s         r6   meta_index_reducerp    s     D0G0GHHr8   c                    U $ rB   r2   ro  s         r6   meta_index_reduce_rr    s	     Kr8   c                     [        U R                  5       5      nU R                  5       S:  a  UR                  5       X1'   U R	                  U5      $ Nr   )r   r   r   r   r   )r   r   r   result_sizes       r6   meta_index_selectrv    s>     tyy{#KxxzA~ ;;=>>+&&r8   )lengthsr   offsetsaxisunsafeinitialdatarw  rx  ry  rz  c                   ^ ^ Ub  [        S5      eUU 4S jnUb  U" UR                  5      $ Ub+  UR                  S S UR                  S   S-
  4-   n	U" U	5      $ [        S5      e)Nz?segment_reduce(): indices based reduction is not supported yet.c                    > [         R                  " U TR                  TS-   S  -   TR                  S[         R                  S9$ )Nr1   r   r^   r   r   )rV   r   r   r^   r   )lengths_shapery  r|  s    r6   segment_reduce_lengths_tensor:meta_segment_reduce.<locals>.segment_reduce_lengths_tensor  s>    {{DJJtaxz22**11	
 	
r8   r   r1   z<segment_reduce(): Either lengths or offsets must be defined.)NotImplementedErrorr   r0  )
r|  rl  rw  r   rx  ry  rz  r{  r  r  s
   `    `    r6   meta_segment_reducer    s|     !M
 	

 ,W]];; cr*gmmB.?!.C-EE,];;
U
VVr8   c                 $    U R                  S5      $ Nr2   r   r   s    r6   meta_maxr         >>"r8   c                     [         R                  " U R                  U45      n[        XU5      nU R	                  U5      U R	                  U[
        R                  S94$ Nr   rO   reduction_dimsr   _compute_reduction_shaper   rV   r   r   r   keepdimrh  s       r6   meta_max_dimr    P    


tzzC6
2C+Dw?L|$|5::6 r8   c                 $    U R                  S5      $ r  r  r   s    r6   meta_minr    r  r8   c                     [         R                  " U R                  U45      n[        XU5      nU R	                  U5      U R	                  U[
        R                  S94$ r  r  r  s       r6   meta_min_dimr    r  r8   c                     U R                  5       (       a  [        U R                  5      nO[        U [        R
                  S9u  p![        R                  " XS9$ NrN   r   )r   r   r^   r   r   INT_TO_FLOATrV   r   )r   rS   rR   s      r6   
meta_angler    sH    /

;, ? L L
 D55r8   c                     [         R                  " XR                  5       U R                  5        UR	                  [         R
                  " U 5      5      $ rB   )rV   _resize_output_r   r   copy_angle)r   r   s     r6   meta_angle_outr  "  s4    	#yy{DKK899U[[&''r8   c                     g rB   r2   )vals    r6   assert_asyncr  (      
r8   c                     g rB   r2   )r  
assert_msgs     r6   assert_async_metar  -  r  r8   c                     g rB   r2   )ss    r6   
print_metar  2  r  r8   r^   r   r   r   r   c                 ,    [         R                  " SSS9$ )Nr   r   r   r  r  s        r6   make_dep_tokenr  7  s     ;;q((r8   c                 j    SSK Jn  [        U [        [        45      (       a  [        S5      eU" XUS9  g )Nr   )constrain_range'Constraining SymFloat or Symbool is nyir  max)r.  r  rr   r
   r	   
ValueError)r   r  r  r  s       r6   sym_constrain_ranger  C  s0     F$7+,,BCCDs+r8   c                 .    [         R                  XUS9  U$ Nr  )r+   r  r   r  r  	dep_tokens       r6   functional_sym_constrain_ranger  M  s    T4r8   c                 <   SSK Jn  Uc  Uc  [        R                  " U S:  5        g [	        U [
        [        45      (       a  [        S5      e[        U 5      [        L a7  Ub  [        R                  " X:  5        Ub  [        R                  " X:*  5        g U" XUS9  g )Nr   )_constrain_range_for_sizer  r  )
r.  r  rV   rh   rr   r
   r	   r  r}   r   )r   r  r  r  s       r6   sym_constrain_range_for_sizer  S  s     P
{s{TQY$7+,,BCCDzS?LL%?LL%d5r8   c                 .    [         R                  XUS9  U$ r  )r+   r  r  s       r6   'functional_sym_constrain_range_for_sizer  g  s    %%d%=r8   c                     U$ rB   r2   )r  r  r  s      r6   functional_assert_async_metar  m  s    r8   f_namec                     U R                  5       S:  d
   U S35       eU R                  S5      U R                  S5      :X  d.   U SU R                  S5       SU R                  S5       S35       eg )Nr   z3: The input tensor must have at least 2 dimensions.r   z5: A must be batches of square matrices, but they are  by 	 matrices)r   r   )r   r  s     r6   r   r   s  s}    88:? (EF? 99R=DIIbM) (G		RTVZ[_[d[deg[hZiirs)r8   Anamec                   ^ ^^ [         R                  " T R                  TR                  :H  UU 4S j5        [         R                  " T R                  TR                  :H  UU 4S j5        [         R                  " TR	                  S5      TR	                  S5      :H  U4S j5        [         R                  " TR	                  S5      T R	                  S5      :H  UUU 4S j5        g )Nc                  >   > STR                    ST R                    S3$ )Nz:Expected b and A to be on the same device, but found b on z
 and A on 	 instead.r  r  r   s   r6   re   (linearSolveCheckInputs.<locals>.<lambda>  s     H{{m:ahhZy:r8   c                  >   > STR                    ST R                    S3$ )Nz=Expected b and A to have the same dtype, but found b of type z and A of type r  r   r  s   r6   re   r    s     Kzzl/!'')=r8   r   r  c                  R   > ST R                  S5       ST R                  S5       S3$ )Nz3A must be batches of square matrices, but they are r  r  r   r  r   r  s   r6   re   r    s+    FF2J<tAFF2J<yBr8   c                     > ST ST R                  S5       ST R                  S5       STR                  S5       STR                  S5       3
$ )NzIncompatible matrix sizes for z: each A matrix is r   r  z but each b matrix is r  r   )r  r  r   s   r6   re   r    sM    ,TF 3D$TYYr]O4		"Hr8   )rV   rh   r   r^   r   )r   r  r  s   ```r6   linearSolveCheckInputsr    s    	LLqxx	
 
LL

agg	
 
LL	r
affRj 	
 
LL	r
diim#	
r8   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$ )Nz<: Expected a floating point or complex tensor as input. Got r2   r^   r  s   r6   re   (checkFloatingOrComplex.<locals>.<lambda>  s    6(VW\V]^r8   c                     > T ST  3$ )Nz*: Low precision dtypes not supported. Got r2   r  s   r6   re   r    s    vhHPr8   )	r^   rV   rh   r   r   rZ   r\   rY   r[   )r  r  r  r^   s    ` @r6   r   r     sn    
 GGE	LL	/^ &ekk5<<u}}MMP	
 &r8   arg_namec                 b   ^^ [         R                  " U R                  5       S:  UU4S j5        g )Nr   c                     > T ST  S3$ )Nz: The input tensor z! must have at least 2 dimensions.r2   )r  r  s   r6   re   checkIsMatrix.<locals>.<lambda>  s    6(-hZ7XYr8   )rV   rh   r   )r  r  r  s    ``r6   checkIsMatrixr    s    	LL	1Yr8   Br   c                   ^ ^^^ [        T T5        [        TT5        [        R                  " T(       a#  T R	                  S5      TR	                  S5      :H  O"T R	                  S5      TR	                  S5      :H  U UUU4S j5        g )Nr  r   c                     > T ST(       a  SOS ST R                  S5       ST R                  S5       STR                  S5       STR                  S5       S	3$ )
Nz2: Incompatible shapes of A and B for the equation zAX = BzXA = Bz (r  r;   r   r   r|   r   )r  r  r  r   s   r6   re   #checkInputsSolver.<locals>.<lambda>  sV    hHxX.AaffRj\qvvbzl!AFF2J<qJr8   )r   r  rV   rh   r   )r  r  r   r  s   ````r6   checkInputsSolverr    sY    a !V	LL$(r
affRj affRjAFF2J.F	
r8   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	$ )Nz: Expected z5 and input tensors to be on the same device, but got z on z and input on r  )r  r   r  r  s   r6   re   !checkSameDevice.<locals>.<lambda>  s0    i{;-/dm4nU\\NLr8   )rV   rh   r   )r  r  r   r  s   ````r6   checkSameDevicer    s&     
LL%	
r8   UPLOc                    ^  T R                  5       n[        R                  " [        T 5      S:H  =(       a    US:H  =(       d    US:H  U 4S j5        g )Nr1   ULc                     > ST  3$ )Nz1Expected UPLO argument to be 'L' or 'U', but got r2   )r  s   r6   re   checkUplo.<locals>.<lambda>  s    CD6Jr8   )upperrV   rh   r   )r  UPLO_uppercases   ` r6   	checkUplor    s<    ZZ\N	LLD	QKNc1J^s5JJr8   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$ )Nzlinalg.eighF	row_majorr   r   )
r   r  r   r   r   r   r   popr`   r^   )r  r  r  r   vecsvalss         r6   meta__linalg_eighr    s     a'dOME{{5! ;EU ST{{A3	IIK;;uOAGG$<;=D:r8   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$ )Nzlinalg.eigvalsr   r   )r   rO   r   r^   r   r   r   )r   complex_dtypes     r6   meta__linalg_eigvalsr     sf     e-. !!%++.. 	..u{{; 
 ??5;;s+=?AAr8   c                    [        U S5        [        R                  " U R                  5      (       a  U R                  O[        R                  " U R                  5      nU R                  U R                  S S US9nU R                  U R                  US9n[        U 5      S:H  nUR                  U R                  [        U R                  US95        X#4$ )Nz
linalg.eigr   r   r   r  )
r   rO   r   r^   r   r   r   r   r   r   )r   r  r   vectorsis_cudas        r6   meta_linalg_eigr    s     e\* !!%++.. 	..u{{; 
 __U[["-]_CFooekko?G% F*G0P ?r8   r4  c                 p    U R                   R                  [        R                  S9R	                  SS5      $ )Nr   r  r   )mTr   rV   r   	transpose)r4  s    r6   cloneBatchedColumnMajorr    s*    66<<e&=&=<>HHRPPr8   r  c                     [        U 5      $ rB   )r  )r   r  r  s      r6   _cholesky_solve_helperr
    s     #4((r8   c                    ^ ^ [         R                  " T R                  S:  U 4S j5        [         R                  " TR                  S:  U4S j5        [        T TS5      u  p4[	        X4U5      $ )Nr   c                  $   > ST R                    S3$ )Nz-b should have at least 2 dimensions, but has  dimensions insteadr   r   s   r6   re    cholesky_solve.<locals>.<lambda>   s    ?		{J]^r8   c                  $   > ST R                    S3$ )Nz-u should have at least 2 dimensions, but has r  r  r  s   r6   re   r  $  s    ?xGZ[r8   cholesky_solve)rV   rh   r   !_linalg_broadcast_batch_dims_namer
  )r   r  r  self_broadcastedA_broadcasteds   ``   r6   r  r    sd     
LL		Q^ 
LL	![ 'Ha!'# ""25IIr8   c                     U R                  5       S:X  a#  [        R                  " U [        R                  S9$ [	        U S5        [        U 5      $ )Nr   r   cholesky)r   rV   r   legacy_contiguous_formatr   r  r   r  s     r6   r  r  ,  s@     zz|qE4R4RSSdJ'"4((r8   c                 0    [        U S5        [        U 5      $ )Ncholesky_inverse)r   r  r  s     r6   r  r  5  s     d./"4((r8   check_errorsc                 
   [        U S5        [        U S5        U R                  n[        U5      n[	        US5      nU R                  U5      nUR                  X55        U R                  USUS-
   [        R                  S9nXg4$ )Nzlinalg.choleskyFr   r   r   )	r   r   r   r   r   r   r   rV   rK  )r  r  r  A_shaper   	L_stridesr  infoss           r6   linalg_cholesky_exr   =  s|    a*+1/0ggGw<D ,GU;I	GAMM'% KKD1H-U[[KAE8Or8   tauc                 J  ^ ^^ [         R                  " T R                  S:  S 5        [         R                  " T R                  S5      T R                  S5      :  S 5        [         R                  " T R                  S5      TR                  S5      :  S 5        [         R                  " T R                  TR                  -
  S:H  U U4S j5        T R                  S:  a<  T R                  S S nTR                  S S m[         R                  " TU:H  U4S	 j5        [         R                  " TR
                  T R
                  :H  U U4S
 j5        [        STT S5        [         R                  " T R                  [        T R                  SS9T R
                  T R                  S9$ )Nr   c                      g)NzHtorch.linalg.householder_product: input must have at least 2 dimensions.r2   r2   r8   r6   re   ,linalg_householder_product.<locals>.<lambda>V      Zr8   r  r   c                      g)Nzbtorch.linalg.householder_product: input.shape[-2] must be greater than or equal to input.shape[-1]r2   r2   r8   r6   re   r$  Z  s    tr8   c                      g)Nz`torch.linalg.householder_product: input.shape[-1] must be greater than or equal to tau.shape[-1]r2   r2   r8   r6   re   r$  ^  s    rr8   r1   c                  <   > STR                    ST R                    3$ )Nzptorch.linalg.householder_product: Expected tau to have one dimension less than input, but got tau.ndim equal to  and input.ndim is equal to r  r   r!  s   r6   re   r$  c  "    )),
2Nuzzl\r8   c                     > ST  3$ )Nzltorch.linalg.householder_product: Expected batch dimensions of tau to be equal to input.shape[:-2], but got r2   actual_batch_tau_shapes   r6   re   r$  m      66L5MOr8   c                  <   > STR                    ST R                    3$ )Nz,torch.linalg.householder_product: tau dtype z does not match input dtype r   r*  s   r6   re   r$  u  s    :399+*5;;-9r8   z torch.linalg.householder_productr!  Fr  r   r   r^   r   )
rV   rh   r   r   r   r^   r  empty_stridedr   r   )r   r!  expected_batch_tau_shaper.  s   `` @r6   linalg_householder_productr4  O  sK   
 
LL

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

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

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

SXX"	
 zzA~#(;;s#3 !$3B"&>>	
 
LL		U[[ 	
 6UEJ[[*5;;%Hkk||	 r8   c                    [        U S5        [        U SSS9  U R                  U R                  5      nUR	                  U R                  [        U R                  SS95        U R                  U R                  S S [        R                  S9nX#4$ )Nzlinalg.inv_exF)r  r  r  r   r   r   r   r   r   r   rV   rK  )r  r  r  r  s       r6   linalg_inv_ex_metar7    so    a)1o%P	AGGAMM!''6qww%PQKKEKKK8E8Or8   LDpivotsinfo)	hermitianr  r;  c                t   [        U S5        [        U S5        [        R                  " U R                  [        U R                  SS9U R                  U R                  S9nU R                  U R                  S S [        R                  S9nU R                  U R                  S S [        R                  S9nX4U4$ )Nztorch.linalg.ldl_factor_exFr  r1  r   r   r  )
r   r   rV   r2  r   r   r^   r   r   r   )r   r;  r  r8  r9  r:  s         r6   linalg_ldl_factor_ex_metar=    s     d894!=>			ZZ*4::Gjj{{	
B ^^DJJsO599^=F>>$**Sb/>;Dtr8   )r;  c                j  ^ ^^ [        T S5        [        T S5        [        TT S5        [        R                  " TR
                  S:  U4S j5        T R                  S S n[        R                  " UTR                  :H  U4S j5        [        R                  " [        R                  " TR                  5      U4S j5        [        R                  " T R                  TR                  :H  UU 4S j5        [        TT 5      u  pV[        R                  " U[        USS	9TR                  TR                  S
9$ )Nztorch.linalg.ldl_solver   c                  $   > ST R                    S3$ )NzMtorch.linalg.ldl_solve: Expected B to have at least 2 dimensions, but it has r  r  )r  s   r6   re   'linalg_ldl_solve_meta.<locals>.<lambda>      &&!46r8   r   c                  $   > ST R                    S3$ )Nzjtorch.linalg.ldl_solve: Expected LD.shape[:-1] and pivots.shape to be the same, but got pivots with shape  insteadr   r9  s   r6   re   r@        ))/h@r8   c                  "   > ST R                    3$ )Nz<torch.linalg.ldl_solve: Expected pivots to be integers. Got r   rE  s   r6   re   r@    s    Nv||n]r8   c                  <   > STR                    ST R                    3$ )Nz!torch.linalg.ldl_solve: LD dtype z does not match b dtype r   )r  r8  s   r6   re   r@    s     3BHH:=UVWV]V]U^_r8   Fr  r1  )r   r   r  rV   rh   r   r   rO   is_integer_dtyper^   _linalg_broadcast_batch_dimsr2  r   r   )r8  r9  r  r;  expected_pivots_shapeB_broadcast_sizerR   s   ```    r6   linalg_ldl_solve_metarM    s     b232781b":;	LL	!	
 HHSbM	LL-	
 
LLv||,] 
LL
AGG_ 7q"=*+;uMggxx	 r8   Pr  )pivotrO  c                j  ^  [         R                  " T R                  S:  U 4S j5        [        T R                  5      nUS   nUS   n[        X45      nX2S'   U(       a  T R                  U5      nOT R                  S/5      nXRS'   T R                  U5      nXRS'   XBS'   T R                  U5      nXgU4$ )Nr   c                  $   > ST R                    S3$ )Nz@linalg.lu: Expected tensor with 2 or more dimensions. Got size: rC  rD  r  s   r6   re    linalg_lu_meta.<locals>.<lambda>  s    RSTSZSZR[[cdr8   r  r   r   )rV   rh   r   r   r   r  r   )	r  rO  sizesrg  r  krN  r  r  s	   `        r6   linalg_lu_metarU    s     
LL	!d
 MEb	Ab	AA	A"IKKKK"I	EA"I"I	EA7Nr8   LU)rO  r  c                  ^  [         R                  " T R                  S:  U 4S j5        [        T R                  5      nUS   nUS   n[         R
                  " U[        USS9T R                  T R                  S9nUR                  5         [        XE5      US'   T R                  U[         R                  S9nUR                  5         T R                  U[         R                  S9nXgU4$ )	Nr   c                  $   > ST R                    S3$ )NzFtorch.lu_factor: Expected tensor with 2 or more dimensions. Got size: rC  rD  r  s   r6   re   *linalg_lu_factor_ex_meta.<locals>.<lambda>  s    XYZY`Y`Xaaijr8   r  r   Fr  r1  r   )rV   rh   r   r   r   r2  r   r^   r   r  r  r   r   )	r  rO  r  rS  rg  r  rV  r9  r:  s	   `        r6   linalg_lu_factor_ex_metarZ    s     
LL	!j
 MEb	Ab	A			*5EBggxx	
B 
IIKA	E"I[[eii[0F 
IIK;;uEII;.Dtr8   )r   adjointr[  c                
  ^ ^^ [        T S5        [        R                  " T R                  TR                  :H  UU 4S j5        [        R                  " TR                  [        R                  :H  S 5        [        T S5        [        T TUS5        [        R                  " T R                  S5      TR                  S5      :H  S 5        [        R                  " T R                  S S TR                  :H  U4S j5        [        TT 5      u  pV[        R                  " U[        XS(       + S9TR                  TR                  S	9nUR                  5       S
:w  a,  U(       d%  UR                  5       (       a  UR                  5       nU$ )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 rC  r   )r  rV  s   r6   re   &linalg_lu_solve_meta.<locals>.<lambda>   s#    $$&HH:_QWWIXOr8   c                      g)NzElinalg.lu_solve: pivots should be a Tensor of scalar type torch.int32r2   r2   r8   r6   re   r_  '  s    Wr8   zlinalg.lu_solver   c                      g)NzYlinalg.lu_solve: Number of pivots per batch should be same as the dimension of the matrixr2   r2   r8   r6   re   r_  /  s    kr8   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 rC  rD  rE  s   r6   re   r_  5  rF  r8   r  r1  r   )r   rV   rh   r^   r   r   r  r   r   rJ  r2  r   r   r   r   conj)rV  r9  r  r   r[  rL  rR   r  s   ```     r6   linalg_lu_solve_metard    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Mr8   unpack_dataunpack_pivotsc                 6  ^  [         R                  " T R                  S:  U 4S j5        U(       a3  [         R                  " UR                  [         R                  :H  S 5        [        T R                  5      nUS   nUS   n[        XV5      nXTS'   U(       a  T R                  U5      nOT R                  S/5      nU(       a/  XtS'   T R                  U5      n	XtS'   XdS'   T R                  U5      n
O$T R                  S/5      n	T R                  S/5      n
XU
4$ )Nr   c                  $   > ST R                    S3$ )NzFtorch.lu_unpack: Expected tensor with 2 or more dimensions. Got size: rC  rD  )rV  s   r6   re    lu_unpack_meta.<locals>.<lambda>U  s    XY[YaYaXbbjkr8   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_factorr2   r2   r8   r6   re   ri  Z  s    pr8   r  r   r   )	rV   rh   r   r^   rK  r   r   r  r   )rV  r9  re  rf  rS  rg  r  rT  rN  r  r  s   `          r6   lu_unpack_metark  K  s     
LL
1k LLEKK'	
 NEb	Ab	AA	A"ILLLL!b	LLb	b	LLLL!LL!7Nr8   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$ )Nzqr received unrecognized mode 'z=' but expected one of 'reduced' (default), 'r', or 'complete'r2   )rl  s   r6   re    _parse_qr_mode.<locals>.<lambda>  s    1$ 8N Or8   rV   rh   )rl  	compute_qrn  s   `  r6   _parse_qr_moderu  u  s    y	  
		  
	  		
 gr8   QRc                    [        U S5        [        U S5        [        U5      u  p#U R                  S   nU R                  S   n[	        XE5      nU(       aO  [        U R                  5      nU(       a  UOUUS'   U R                  U5      nUR                  U[        USS95        OU R                  S/5      n[        U R                  5      n	U(       d  U(       d  UOUU	S'   U R                  U	5      n
U
R                  U	[        U	SS95        X4$ )Nz	linalg.qrr  r   Fr  r   )	r  r   ru  r   r  r   r   r   r   )r  rl  rt  reduced_moderg  r  rT  Q_shaperv  R_shaperw  s              r6   linalg_qr_metar|    s     ![!1k*,T2I	A	AA	Aqww-'aQKK 	g:7eTUKK 177mG#9!!GBK	GAMM'6w%PQ4Kr8   sign	logabsdetc                 t   [        U S5        [        U SS5        U R                  nU R                  US S 5      nU R                  US S [	        U R
                  5      S9n[        R                  " U[        US5      U R
                  U R                  S9nU R                  US S [        R                  S9nX#XE4$ )Nzlinalg.slogdetFr  r   r1  r   )r   r   r   r   r`   r^   rV   r2  r   r   rK  )r  r   r}  r~  rV  r9  s         r6   _linalg_slogdetr    s     a)*1.6GGE;;uSbz"DE#2Joagg.FGI			*5%8ggxx	
B [[s5;;[7FB&&r8   full_matrices
compute_uvdriverc                 b   [        U S5        [        U S5        [        U R                  S S 5      nU R                  S   nU R                  S   n[	        XV5      nU(       a  XEU(       a  UOU/-   nU R                  U5      n	U	R                  U[        USS95        XA(       a  UOUU/-   n
U R                  U
5      n[        U 5      S:H  nUR                  U
[        XS95        O$U R                  S/5      n	U R                  S/5      nU R                  XG/-   [        U R                  5      S9nXU4$ )	Nz
linalg.svdr  r   Fr  r   r   r   )r  r   r   r   r  r   r   r   r   r`   r^   )r  r  r  r  r   rg  r  rT  U_shaper  V_shapeVr  Ss                 r6   _linalg_svd_metar    s    !\"1l+aggcrl#J	A	AA	A11==KK 	g:7eTU]1==KK 
 a.F*	g:7VW KKKK 	
J$OAGG,DEA7Nr8   arg1arg2c                    U R                   S S nUR                   S S n[        X#5      n[        U5      nXPR                  S5      U R                  S5      /-  n[        U5      nXaR                  S5      UR                  S5      /-  nXV4$ )Nr  r   )r   r#   r   r   )r  r  arg1_batch_sizesarg2_batch_sizesexpand_batch_portionarg1_expand_sizearg2_expand_sizes          r6   rJ  rJ    s    
 zz#2zz#2,-=P012		"66012		"66--r8   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$ rB   )r  rJ  r   expand)r  r  r  r  r  arg1_broadcastedarg2_broadcasteds          r6   r  r    sh     t40)Ed)Q& !JJ.DKK@P4Q  !JJ.DKK@P4Q  --r8   r   c                     U R                   S S nUR                  S:H  =(       d2    U R                  S-
  UR                  :H  =(       a    UR                   U:H  nU$ )Nr   r1   )r   r   )r   r   expected_batched_rhs_shapevector_cases       r6   linalg_solve_is_vector_rhsr    sS    !&Sb!1**/ 

Q%**$R8R)R  r8   )r   r  r  rV  r9  r:  c                  ^ ^ [        T S5        [        R                  " T R                  TR                  :H  U U4S j5        [	        T T5      nU(       a  TR                  S5      OTn	[        T XS5        [        U	T 5      u  p[        R                  " U=(       d    U(       + S 5        U(       a  U
S S OU
n[        R                  " U[        X(       + 5      TR                  TR                  S9nT R                  n[        R                  " U[        US5      T R                  T R                  S9nT R                  US S [        R                  S9nT R                  US S [        R                  S9nXEXg4nXUU4n[        S	 U 5       5      (       aa  [        UU5       HQ  u  nn[!        UUR                  5        UR#                  UR                  UR%                  5       5        ['        UUSS
9  MS     U$ )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^  rC  r   )r  r  s   r6   re   "_linalg_solve_ex.<locals>.<lambda>  s     Ywwiqwwix9r8   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)r2   r2   r8   r6   re   r  '  s    Kr8   r1  Fr   r  c              3   (   #    U  H  oS Lv   M
     g 7frB   r2   )rt   r;   s     r6   rv   #_linalg_solve_ex.<locals>.<genexpr>>  s     
&#QD=#s   )	copy_fromcopy_toexact_dtype)r   rV   rh   r^   r  	unsqueezer  rJ  r2  r   r   r   r   rK  allzipr   r   r   r!   )r  r  r   r  r  rV  r9  r:  r  B_B_broad_shaperR   result_shaperesult_r   LU_pivots_info_r   resrp  os   ``                    r6   _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 " Jr8   )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   rr   r   r  r  r  re  is_conjr   r   r    r   
transpose_)	r  r  r  r   r  r   r  A_avoid_copy_As	            r6   linalg_solve_triangular_metar  H  s     {kk1#c:&&&&aD";<.qT:FB<<B'557HBJJLLXX. J  XX..KKR,223NN2r"Jr8   XM)r  r  c                   ^ ^ [         R                  " T R                  S:  U 4S j5        [         R                  " TR                  S:  U4S j5        [        T TS5        TR                  [         R
                  :X  aw  [        T T5      u  pV[         R                  " U[        USS9T R                  T R                  S9n[         R                  " U[        USS9TR                  TR                  S9nXx4$ TR                  [         R                  :X  d  TR                  [         R                  :X  a+  [         R                  " T 5      nT R                  S/5      nXx4$ [         R                  " SS	 5        WW4$ )
Nr   c                  $   > ST R                    S3$ )NzMtorch.triangular_solve: Expected b to have at least 2 dimensions, but it has r  r  r   s   r6   re   'triangular_solve_meta.<locals>.<lambda>m  s    ))$79r8   c                  $   > ST R                    S3$ )NzMtorch.triangular_solve: Expected A to have at least 2 dimensions, but it has r  r  r  s   r6   re   r  t  rA  r8   triangular_solveFr  r1  r   c                      g)Nz+triangular_solve: Got an unexpected layout.r2   r2   r8   r6   re   r    s    $Qr8   )rV   rh   r   r  r   stridedrJ  r2  r   r^   r   
sparse_csr
sparse_bsrr   r   )	r   r  r  r  r  self_broadcast_sizeA_broadcast_sizesolutioncloned_coefficients	   ``       r6   triangular_solve_metar  b  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'''r8   c                 ^   [        U S5        [        U S5        U R                  U R                  S S 5      nU R                  U R                  5      nUR	                  U R                  [        U R                  SS95        U R                  U R                  S S [        R                  S9nXU4$ )Nz
linalg.detr  Fr  r   r   r6  )r  detrV  r9  s       r6   _linalg_det_metar    s    a&1l+
++aggcrl
#C	
QWW	BNN17775QR[["U[[[9FF?r8   c                 X  ^ ^^^^^ [         R                  " T R                  S:  S 5        [         R                  " TR                  S:  S 5        U(       a  SOSm[         R                  " TR                  T   TR                  S   :  U4S j5        [         R                  " TR                  T   T R                  S   :H  U4S j5        [         R                  " TR                  S   T R                  S   :*  S 5        [         R                  " T R                  TR                  -
  S	:H  U U4S
 j5        [         R                  " T R                  TR                  :H  U U4S j5        T R                  S:  ai  T R                  S S nTR                  S S m[         R                  " TU:H  U4S j5        TR                  S S m[         R                  " TU:H  U4S j5        [         R                  " TR                  T R                  :H  U U4S j5        [         R                  " TR                  T R                  :H  U U4S j5        [        STT S5        [        STT S5        [         R                  " TR                  [        TR                  SS9TR                  TR                  S9$ )Nr   c                      g)Nz3torch.ormqr: input must have at least 2 dimensions.r2   r2   r8   r6   re   ormqr.<locals>.<lambda>      !Vr8   c                      g)Nz3torch.ormqr: other must have at least 2 dimensions.r2   r2   r8   r6   re   r    r  r8   r  r   c                     > ST  S3$ )Ntorch.ormqr: other.shape[z0] must be greater than or equal to tau.shape[-1]r2   left_size_conditions   r6   re   r    s    +,?+@@pqr8   c                     > ST  S3$ )Nr  z"] must be equal to input.shape[-2]r2   r  s   r6   re   r    s    +,?+@@bcr8   c                      g)NzHtorch.ormqr: tau.shape[-1] must be less than or equal to input.shape[-1]r2   r2   r8   r6   re   r    r%  r8   r1   c                  <   > STR                    ST R                    3$ )Nz[torch.ormqr: Expected tau to have one dimension less than input, but got tau.ndim equal to r)  r  r*  s   r6   re   r    r+  r8   c                  <   > STR                    ST R                    3$ )Nzhtorch.ormqr: Expected other to have the same number of dimensions as input, but got other.ndim equal to r)  r  r   r   s   r6   re   r    s&    ++0::,6RSXS]S]R^`r8   c                     > ST  3$ )NzWtorch.ormqr: Expected batch dimensions of tau to be equal to input.shape[:-2], but got r2   r-  s   r6   re   r    r/  r8   c                     > ST  3$ )NzYtorch.ormqr: Expected batch dimensions of other to be equal to input.shape[:-2], but got r2   )actual_batch_other_shapes   r6   re   r    s    66N5OQr8   c                  <   > ST R                    STR                    3$ )NzPtorch.ormqr: Expected input and tau to have the same dtype, but input has dtype z and tau has dtype r   r*  s   r6   re   r    s"    ##(;;-/B399+Or8   c                  <   > ST R                    STR                    3$ )NzRtorch.ormqr: Expected input and other to have the same dtype, but input has dtype z and other has dtype r   r  s   r6   re   r    s"    ##(;;-/DU[[MSr8   ztorch.ormqrr!  r   Fr  r1  )	rV   rh   r   r   r^   r  r2  r   r   )	r   r!  r   r   r  expected_batch_shaper  r.  r  s	   ```   @@@r6   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 $(<<	
 
LL		U[[ 	
 
LLu{{"	
 M3u5M5%9[[*5;;%Hkk||	 r8   c                  ^ ^^ [         R                  " [        T5      ST-  :H  UU4S j5        T R                  nUTS-   :H  nUnU(       + nU(       a1  [	        SU5       H   nU=(       a    T R                  U5      S:g  nM"     O/[	        U5       H   nU=(       a    T R                  U5      S:g  nM"     [         R                  " U=(       d    UUU 4S j5        g )Nr   c                  ,   > SST -   S[        T5       3$ )Nzpadding size is expected to be r   z, but got: r   )r   paddings   r6   re   ,_padding_check_valid_input.<locals>.<lambda>   s    1!c'+c'l^Tr8   r1   r   c                  :   > ST S-    ST S-    STR                    3$ )N	Expected r1   zD or r   zcD (batch mode) tensor with possibly 0 batch size and other non-zero dimensions for input, but got: rD  )r   r   s   r6   re   r    s-    aycAgY /AAFOr8   )rV   rh   r   r   r   r   )r   r  r   	input_dimis_batch_modevalid_batch_modevalid_non_batch_moder   s   ```     r6   _padding_check_valid_inputr    s    	LLGCT
 

I#'*M$,,q)$A/FEJJqMQ4F % y!A#7#NEJJqMQ<N  " 
LL00	
r8   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   r1   r.   r   c                  4   > ST ST ST  STR                    3$ NzcArgument #4: Padding size should be less than the corresponding input dimension, but got: padding (r{   ) at dimension 
 of input rD  dim_wr   pad_lpad_rs   r6   re   _pad1d_common.<locals>.<lambda>1  -    %%*G2eWOE7*UZU`U`Tacr8   c                     > ST  ST 3$ )Nz
input (W: z%) is too small. Calculated output W: r2   )input_woutput_ws   r6   re   r  9  s    *WI%J8*Ur8   r   )r   r   r  rV   rh   r   )r   r  is_reflection	dim_planenbatchnplaner  r  r  r  r  s   `     @@@@@r6   _pad1d_commonr    s    IEFzzQA
Q	ug15LE5ZZ	"FjjG&HGO/	
 
LLAU
 zzQ1229::r8   c                     [        XSS9$ NTr  )r  r   r  s     r6   meta_reflection_pad1dr  B       t<<r8   c                    ^  [         R                  " T R                  [         R                  :g  U 4S j5        [	        T USS9$ )Nc                  @   > ST R                   R                  5        S3$ )Nz)"replication_pad1d" not implemented for ''r^   __str__r   s   r6   re   (meta_replication_pad1d.<locals>.<lambda>M      =ekk>Q>Q>S=TTUXr8   Fr   )rV   rh   r^   boolr  r  s   ` r6   meta_replication_pad1dr  H  5     
LLuzz!X u==r8   c                  ^ ^^^^^ SmU(       d$  [         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      $ )Nr1   r   c                      g)Nz padding size is expected to be 2r2   r2   r8   r6   re   (_pad1d_backward_common.<locals>.<lambda>U  s    0Rr8   r.   c                  4   > ST ST ST  STR                    3$ r  rD  r  s   r6   re   r  b  r  r8   c                  2   > ST STR                  T 5       3$ Nz(grad_output width unexpected. Expected: , Got: r   r  grad_outputr  s   r6   re   r  j       :8*GKL\L\]bLcKder8   rV   rh   r   r   r   r   r   )	r  r   r  r  r  r  r  r  r  s	   ``   @@@@r6   _pad1d_backward_commonr  R  s    ES\Q&(RSzzQ
LE5jjG&HGO/	
 
LLK$$U++e
 ??5;;''r8   
grad_inputc                     [        XUSS9$ r  r  r  r   r  s      r6   meta_reflection_pad1d_backwardr  p  s     "+gTRRr8   c                     [        XUSS9$ )NFr   r  r  s      r6   meta_replication_pad1d_backwardr!  v  s     "+gUSSr8   c                  ^ ^^^	^
^^^^^^ SmSmSnSn[        T USS9  T R                  nUS:X  a   T R                  S5      nTS-  mTS-  mUS-  nUu  mmmmT R                  U5      nT R                  T5      m	T R                  T5      m
T	T-   T-   mT
T-   T-   mU(       aZ  [        R                  " TT
:  =(       a    TT
:  UU UU4S j5        [        R                  " TT	:  =(       a    TT	:  UU UU4S j5        [        R                  " TS:  =(       d    TS:  U	U
UU4S j5        T R                  S	:X  a  T R                  UTT45      $ T R                  XFTT45      $ )
Nr   r1   r   r      c                  4   > ST ST ST  STR                    3$ r  rD  r  s   r6   re   _pad2d_common.<locals>.<lambda>  r  r8   c                  4   > ST ST ST  STR                    3$ NzcArgument #6: Padding size should be less than the corresponding input dimension, but got: padding (r{   r  r  rD  dim_hr   pad_bpad_ts   r6   re   r%    r  r8   c                      > ST  ST ST ST 3$ )Nz
input (H:  W: z%) is too small. Calculated output H: r2   )input_hr  output_hr  s   r6   re   r%    s%    	gY /$$,:T(=r8   r.   r  r   r   rV   rh   r   )r   r  r  
dim_slicesr  r   r  r)  r  r.  r  r/  r  r*  r  r  r+  s   `      @@@@@@@@@@r6   _pad2d_commonr2  |  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Dr8   c                     [        XSS9$ r  )r2  r  s     r6   meta_reflection_pad2dr4    r  r8   c                    ^  [         R                  " T R                  [         R                  :g  U 4S j5        [	        T USS9$ )Nc                  @   > ST R                   R                  5        S3$ )Nz)"replication_pad2d" not implemented for 'r  r  r	  s   r6   re   (meta_replication_pad2d.<locals>.<lambda>  r  r8   Fr   )rV   rh   r^   r  r2  r  s   ` r6   meta_replication_pad2dr8    r  r8   c                 `    [         R                  " U5      n[         R                  " U5      nXV4$ rB   rV   r   )grad_wsaved_vsaved_gsaved_normsr   grad_vgrad_gs          r6   meta_weight_norm_backwardrA    s,     g&Fg&F>r8   c                   ^ ^^^^ SmSmSnUR                   nUR                  5       S:X  a  TS-  mTS-  mUS-  nUu  pVpxUT   n	UT   n
X-   U-   mX-   U-   m[        R                  " TT R	                  T5      :H  UU U4S j5        [        R                  " TT R	                  T5      :H  UU U4S j5        UR                  UR                   5      $ )Nr   r1   r   r#  c                  2   > ST STR                  T 5       3$ r  r   r  s   r6   re   %meta_pad2d_backward.<locals>.<lambda>  r  r8   c                  2   > ST STR                  T 5       3$ Nz)grad_output height unexpected. Expected: r  r   r)  r  r/  s   r6   re   rD         ;H:W[M]M]^cMdLefr8   )r   r   rV   rh   r   r   )r  r   r  r  rd   r  r  r+  r*  r.  r  r)  r  r/  r  s   `          @@@@r6   meta_pad2d_backwardrI    s     EEIJxxzQ

Q	!(E%GG&H&H	LLK$$U++e 
LLK$$U++f >>$**%%r8   c          	      ~  ^ ^^^	^
^^^^^^^^^^^ Sm	SmSmSn[        T USS9  T R                  S:H  nU(       a%  T R                  S5      nT	S-  m	TS-  mTS-  mUS-  nUu  mmmmmmT R                  U5      nT R                  T5      m
T R                  T5      mT R                  T	5      mT
T-   T-   mTT-   T-   mTT-   T-   mU(       a  [        R                  " TT:  =(       a    TT:  U	U UU4S j5        [        R                  " TT:  =(       a    TT:  UU UU4S j5        [        R                  " TT
:  =(       a    TT
:  UU UU4S	 j5        [        R                  " TS:  =(       d    TS:  =(       d    TS:  U
UUUUU4S
 j5        U(       a  T R                  WUTTT45      $ T R                  UTTT45      $ )Nr.   r   r1   r   r      c                  4   > ST ST ST  STR                    3$ r  rD  r  s   r6   re   _pad3d_common.<locals>.<lambda>  r  r8   c                  4   > ST ST ST  STR                    3$ r'  rD  r(  s   r6   re   rM    r  r8   c                  4   > ST ST ST  STR                    3$ )NzcArgument #8: Padding size should be less than the corresponding input dimension, but got: padding (r{   r  r  rD  )dim_dr   pad_bkpad_fs   r6   re   rM    s-    %%*G2fX_UG:V[VaVaUbdr8   c                  ,   > ST  ST ST ST ST ST 3$ )Nz
input (D:  H: r-  z%) is too small. Calculated output D: r2   )input_dr.  r  output_dr/  r  s   r6   re   rM  #  s2    	gYd7) <$$,:T(4zKr8   r0  )r   r  r  r  
batch_moder  r  rP  r)  r  rU  r.  r  rV  r/  r  r*  rQ  rR  r  r  r+  s   `      @@@@@@@@@@@@@@@r6   _pad3d_commonrX    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Fr8   c                     [        XSS9$ r  )rX  r  s     r6   meta_reflection_pad3drZ  /  r  r8   c                    ^  [         R                  " T R                  [         R                  :g  U 4S j5        [	        T USS9$ )Nc                  @   > ST R                   R                  5        S3$ )Nz)"replication_pad3d" not implemented for 'r  r  r	  s   r6   re   (meta_replication_pad3d.<locals>.<lambda>:  r  r8   Fr   )rV   rh   r^   r  rX  r  s   ` r6   meta_replication_pad3dr^  5  r  r8   c                   ^ ^^^^^^ [         R                  " [        U5      S:H  S 5        UR                  S:  d   eT R                  UR                  :X  d   eSmSmSmUR                  S:X  a  TS-  mTS-  mTS-  mUu  p4pVpxUR	                  T5      n	UR	                  T5      n
UR	                  T5      nX-   U-   mX-   U-   mX-   U-   m[         R                  " TT R	                  T5      :H  UU U4S j5        [         R                  " TT R	                  T5      :H  UU U4S j5        [         R                  " TT R	                  T5      :H  UU U4S	 j5        UR                  UR                  5      $ )
N   c                      g)Nz padding size is expected to be 6r2   r2   r8   r6   re   %meta_pad3d_backward.<locals>.<lambda>I  s    ,Nr8   r.   r   r1   rK  c                  2   > ST STR                  T 5       3$ r  r   r  s   r6   re   rb  a  r  r8   c                  2   > ST STR                  T 5       3$ rF  r   rG  s   r6   re   rb  e  rH  r8   c                  2   > ST STR                  T 5       3$ )Nz(grad_output depth unexpected. Expected: r  r   )rP  r  rV  s   r6   re   rb  i  r  r8   r  )r  r   r  r  r  r+  r*  rR  rQ  rU  r.  r  rP  r)  r  rV  r/  r  s   `           @@@@@@r6   meta_pad3d_backwardrf  ?  sS    
LLW"$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;;''r8   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 inputr2   r2   r8   r6   re   %meta__pdist_forward.<locals>.<lambda>s  s    &Pr8   r   r1   r   r   )rV   rh   re  r   r   r1  r  )r   rg  r  s      r6   meta__pdist_forwardrk  o  s     
LLP 			!AAv~~qc"%%E4R4R%SS~~qE{a/125588 6 
 	
r8   gradpdistc                     [         R                  " UR                  5       S 5        [         R                  " UR                  5       S 5        [         R                  " U[         R                  S9$ )Nc                      g)Nz._pdist_backward requires self to be contiguousr2   r2   r8   r6   re   &meta__pdist_backward.<locals>.<lambda>  s    &Vr8   c                      g)Nz/_pdist_backward requires pdist to be contiguousr2   r2   r8   r6   re   rp    s    'Xr8   r   )rV   rh   re  r   r  )rl  r   rg  rm  s       r6   meta__pdist_backwardrr  ~  sW     
LLV 
LLX D0N0NOOr8   )rW  rV  c          
      b  ^ ^^^^^ SSK JnJn  TR                  S5      nTR                  S5      nTR                  S5      n	U" [        R
                  " U" T R                  XxU	45      5      5      (       a  T R                  XxU	45      m [        R                  " TR                  5       S:H  S 5        [        R                  " TR                  5       S:H  S 5        [        R                  (       dN  [        R                  " T R                  TR                  s=:H  =(       a    TR                  :H  Os  UUU 4S j5        TR                  n
TR                  mU
S   mU
S   m[        R                  " TS   T:H  =(       a    TS   T:H  UUU4S	 j5        T R                  T R                  5       5      $ )
Nr   )guard_or_truesym_eqr1   r   r.   c                      gNzbatch1 must be a 3D tensorr2   r2   r8   r6   re   meta_baddbmm.<locals>.<lambda>      ,Hr8   c                      gNzbatch2 must be a 3D tensorr2   r2   r8   r6   re   rx    ry  r8   c                  V   > STR                    ST R                    STR                    3$ )Nz+Input dtypes must be the same, got: input: z
, batch1: z
, batch2: r   )batch1batch2r   s   r6   re   rx    s.    A$**ZX^XdXdWeeopvp|p|o}~r8   c            	      .   > ST ST ST S    ST S    S3	$ Nz@Expected size for first two dimensions of batch2 tensor to be: [r{   z] but got: [r   r1   ].r2   batch2_sizesbscontraction_sizes   r6   re   rx    s5    t2&'|LO3DB|TUFWWY[r8   )r.  rt  ru  r   rV   sym_notr   r  rh   r   
exp_config&skip_dtype_check_in_meta_registrationsr^   r   )r   r}  r~  rW  rV  rt  ru  dim1dim2dim3batch1_sizesr  r  r  s   ```        @@@r6   meta_baddbmmr    s9    L;;q>D;;q>D;;q>DU]]6$**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	
 >>$))+&&r8   c                H    [         R                  " U [         R                  S9$ r   rn  r   r  s     r6   meta_bernoullir    s     D0G0GHHr8   c                     U $ rB   r2   r   rg  r  s      r6   meta_bernoulli_r        Kr8   c                 H    [         R                  " U [         R                  S9$ r   rn  r  s      r6   meta_bernoulli_pr    s     D0G0GHHr8   c                 .    [         R                  " U 5      $ rB   r:  r  s     r6   meta_poissonr         D!!r8   c                     [         R                  " XR                  5       :  S 5        [         R                  " U [         R                  S9n[         R                  " U 5      U4$ )Nc                      g)NzJError in fused_moving_avg_obs_fake_quant_cpu: ch_axis must be < self.dim()r2   r2   r8   r6   re   6meta__fused_moving_avg_obs_fq_helper.<locals>.<lambda>      \r8   r   )rV   rh   r   r   r  )r   observer_onfake_quant_onrunning_minrunning_maxscale
zero_pointaveraging_const	quant_min	quant_maxch_axisper_row_fake_quantsymmetric_quantmasks                 r6   $meta__fused_moving_avg_obs_fq_helperr    sM      
LL((*\ D

3DT"D))r8   c                 \  ^^^^ [         R                  " U R                  5       S:H  S 5        [         R                  " UR                  5       S:H  S 5        U R                  u  mmUR                  u  mm[         R                  " TT:H  UUUU4S j5        Ubr  [         R                  " X R                  :H  =(       dG    U[         R
                  :H  =(       a-    U R                  [         R                  [         R                  4;   S 5        Uc  U R                  OUnU R                  TT4US9$ )Nr   c                      g)Nza must be 2Dr2   r2   r8   r6   re   meta_mm.<locals>.<lambda>      ~r8   c                      g)Nzb must be 2Dr2   r2   r8   r6   re   r    r  r8   c            	      "   > ST ST  ST ST S3	$ )Nz/a and b must have same reduction dim, but got [r{   z] X [r  r2   )M1M2NrN  s   r6   re   r    s&    A!Brd%PRtSUVWUXXZ[r8   c                      g)NzFout_dtype must be the same as input dtype or fp32 for fp16/bf16 inputsr2   r2   r8   r6   re   r    s    \r8   r   )	rV   rh   r   r   r^   ra  rb  rc  r   )r4   r5   rG  rS   r  r  r  rN  s       @@@@r6   meta_mmr    s     
LLA56	LLA56GGEArGGEB	LL
b[   U]]* ?GGu~~>>\	
 (/177YL;;1v\;22r8   c                    ^ ^ U(       a)  [        UU 4S j[        T R                  5       5       5      $ [        R                  " T R
                  T5      $ )Nc              3   P   >#    U  H  oT;  a  TR                   U   OS v   M     g7f)r1   NrD  )rt   r   dimsr   s     r6   rv   +_compute_reduction_shape.<locals>.<genexpr>  s$     UDTqtmTZZ]:DTs   #&)rg   r   r   rO   compute_reduction_output_shaper   )r   r  r  s   `` r6   r  r    s7    UE$))DTUUU//

DAAr8   c                 :   [        U [        R                  R                  5      (       a  U R                  R
                  $ [        U S5      (       aK  [        U R                  S5      (       a0  U R                  R
                  S:w  a  U R                  R
                  $ g)Nr   r}   r   r   )rr   rV   _subclasses
FakeTensorfake_devicer}   hasattrr   )r:  s    r6   r   r     sp    &%++6677!!&&&!!FMM6**MM&(}}!!!r8   input_tensorr   r  dilationis_transposedgroupsoutput_paddingc                 r  ^^ S[         S[         S[         S[         S[         S[         4S jnS[         S[         S[         S[         S[         S[         S[         4S	 jn	UR                  S
S  n
U R                  S
S  mU(       a  XaR                  S   -  nO=UR                  S   nUR                  S   U-  U R                  S   :w  a  [        S5      eU R                  S   U/m[        U[        5      (       a  U/[        T5      -  nO![        U5      S:X  a  US   /[        T5      -  n[        U[        5      (       a  U/[        T5      -  nO![        U5      S:X  a  US   /[        T5      -  n[        U[        5      (       a  U/[        T5      -  nO![        U5      S:X  a  US   /[        T5      -  nS nU(       aI  [        U[        5      (       a  U/[        T5      -  nO$[        U5      S:X  a  US   /[        T5      -  nOUn[        [        T5      5       H[  nU(       a+  TR                  U	" TU   X=   XM   X   X-   X   5      5        M5  TR                  U" TU   X=   XM   X   X-   5      5        M]     SSKJ	n  [        R                  " U" TS
S   Vs/ s H  oS:  PM	     sn6 UU4S j5        T$ s  snf )Nlnrg  r   rT  r  r>   c                 4    U SU-  -   X#S-
  -  -
  S-
  U-  S-   $ )aE  
Formula to apply to calculate the length of some dimension of the output

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

Args:
    ln: length of the dimension
    p: padding in that dim
    d: dilation in that dim
    k: kernel size in that dim
    s: stride in that dim
Returns:
    The output length
r   r1   r2   )r  rg  r   rT  r  s        r6   _formula+calc_conv_nd_return_shape.<locals>._formula	  s,     QU
Qa%[(1,2Q66r8   rC   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
r1   r   r2   )r  rg  r   rT  r  rC   s         r6   _formula_transposed6calc_conv_nd_return_shape.<locals>._formula_transposed$	  s0    " Q!|a!e#aq5k1B6::r8   r   r1   r   zInvalid channel dimensions)sym_orc                  .   > S[        T 5       STSS   S3$ )NzGiven input size per channel: z&. Calculated output size per channel: r   z. Output size is too small)r   )r  	ret_shapes   r6   re   +calc_conv_nd_return_shape.<locals>.<lambda>v	  s(    0d =//8}o >#$r8   )r   r   r0  rr   r   r   r   r   r.  r  rV   rh   )r  rC  r   r  r  r  r  r  r  r  kernel_sizeout_channelsoutput_padding_listr   r  r;   r  r  s                   @@r6   calc_conv_nd_return_shaper  		  s   7S 7S 7S 7S 7S 7S 7"; ; ; ; ; ; ;QT ;& ,,qr"Kab!DQ/||A<<?V#|'9'9!'<<;<<##A&5I&'""CI%	V	)s4y('7##)c$i'	W	1:,T*(G$$:D	)	X!	QK=3t9,,0ng..#1"2SY"> A%#1!#4"5D	"A"03t9#GJKNI'*
 a'*hk;>69U# * =	LL	!".1Q./	$  /s   J4c                 b    [         R                  R                  U 5      [         R                  :H  $ rB   rV   _prims_commonr   channels_lasttens    r6   is_channels_lastr  ~	  s$    44S9U=P=PPPr8   running_meanrunning_vartrainingexponential_average_factorepsilonc                 z  ^  T R                   nUb  UR                   OUR                   n	Ub  UR                   OUR                   n
U 4S jnT R                  U5      R                  U" 5       S9nU(       a#  T R                  U	5      nT R                  U
5      nO"T R                  S5      nT R                  S5      nXU4$ )Nc                     > [        T 5      (       a  [        R                  $ T R                  [        R                  S9(       a  [        R                  $ [        R                  $ r   )r  rV   r  re  r   )r  s   r6   pick_memory_format2meta_miopen_batch_norm.<locals>.pick_memory_format	  sI    L))&&&%%E4K4K%L***&&&r8   r   r   )r   r   r1  )r  rC  rE  r  r  r  r  r  r   save_mean_shapesave_var_shaper  r   	save_meansave_vars   `              r6   meta_miopen_batch_normr  	  s     ""I -9,Dl((&,,O*5*A[&&v||N' 
 
 
+
.
.=O=Q
.
RC **?;	)).9 **40	))$/8##r8   c	           
          [        U UUUUUUU(       a  UOS 5      n	Sn
SnU R                  U
5      S:X  a  SX'   U R                  U	5      nU$ Nr1   r   )r  r   r   )r  rC  rE  r   r  r  r  r  r  	shape_outinput_channels_dimoutput_channels_dimr   s                r6   	meta_convr  	  si     *'T	I +,1)*	&

 
 
+CJr8   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$ )NFrK  r   )r  r   rV   r  r   channels_last_3dr1  )r  rC  rE  r  r   r  r  attrscalars	algorithmr  r   out_memory_formats                r6   meta_mkldnn_convolution_defaultr  	  sl     .&8UFB
	 $$Y/!//" % 6 6ff#4f5
r8   c                 b    U R                  / U R                  S S QUR                  S   P75      $ Nr   r   r   r   )r  rC  rE  r  r  r  s         r6   meta_linear_pointwise_defaultr  	  s5     %%&Q(:(:3B(?&Qa&QRRr8   mklc                 b    U R                  / U R                  S S QUR                  S   P75      $ r  r  )r  packed_weightorig_weightrE  r   s        r6   meta_mkl_linearr  	  s:    ))@,$$Sb)@;+<+<Q+?@ r8   onednnc           
         [        U UUUU	SU
S 5      nUc  U R                  nU[        R                  [        R                  [        R
                  [        R                  [        R                  4;   d   eU R                  UUS9n[        U5      S;   d   S5       e[        R                  [        R                  [        R                  S.[        U5         nUR                  US9nU$ )NFr   )r.   r#  rK  z-Expect output to be 3d/4d/5d for conv1d/2d/3dr   )r  r^   rV   ra  rc  uint8rJ  rd  r   r   r   r  r  r1  )r;   x_scalex_zpww_scalew_zprE  r   r  r  r  output_scaleoutput_zero_pointoutput_dtyper  r  r  r  r   formats                       r6   meta_qconv_pointwiser  	  s    , .	
	 77LMMNNKKJJ 
 
 	
 
 kk)<k89~* 	
;	
* &&""%%
 i.	
 ff6f*
r8   c                     US:X  d   eU$ )Nsumr2   )r;   r  r  r  r	  r
  accumrE  r   r  r  r  r  r  r  accum_scaleaccum_zero_pointbinary_op_namerV  unary_op_nameunary_op_argsunary_op_algorithms                         r6   meta_qconv2d_pointwise_binaryr  .
  s    4 &&&r8   c                    [        U R                  5      nUR                  S   US'   U	[        R                  [        R                  [        R
                  [        R                  [        R                  4;   d   eU R                  XS9nU$ )Nr1   r   r   )	r   r   rV   ra  rc  rJ  r  rd  r   )r;   r  r  r  r	  r
  rE  r  r  r  post_op_namepost_op_argspost_op_algorithmrh  r   s                  r6   meta_qlinear_pointwiser  K
  sv    " AGG}771:RMMNNJJKK 
 
 	
 
 kk,k;
r8   c                 *   US:X  a  U$ [        U R                  5      nUR                  S   US'   U
[        R                  [        R                  [        R
                  [        R                  [        R                  4;   d   eU R                  UU
S9nU$ )Nr  r1   r   r   )	r   r   rV   ra  rc  r  rJ  rd  r   )r;   r  r  r  r	  r
  x_2rE  r  r  r  x2_scalex2_zpr  rV  r  r  r  rh  r   s                       r6   meta_qlinear_pointwise_binaryr#  i
  s    , U"JAGG}771:RMMNNKKJJ 
 
 	
 
 kk,lk;
r8   c                 v    [        U R                  5      nUR                  S   US'   U R                  U5      nU$ )Nr1   r   )r   r   r   )r;   r  rE  rh  r   s        r6   meta_linear_dynamic_fp16r%  
  s6     AGG}771:Rkk,'
r8   	quantizedr  r1   c                 "   [        XX#XE5      u  nnnU R                  5       S:X  a  U R                  S5      OSn	[        R                  n
U R                  5       S:X  a  XgU/nOXXx/n[        R
                  " UU R                  U R                  U
S9$ Nr#  r1   r.   r  )#max_pool2d_checks_and_compute_shaper   r   rV   r  r   r^   r   r   r  r   r  r  	ceil_modenInputPlaneoutputHeightoutputWidthr  r   r   s               r6   meta_quantized_max_pool2dr1  
  s     0
		
 $)99;!#3B++99;!{;DCD{{++<<'	
 	
r8   c                   ^ ^^^ [         R                  " T R                  5       S:H  U 4S j5        [         R                  " TR                  5       S:H  U4S j5        [         R                  " T R                  [         R                  [         R
                  [         R                  4;   U 4S j5        [         R                  " TR                  [         R                  :H  U4S j5        [         R                  " TR                  [         R                  :H  U4S j5        [         R                  " TR                  T R                  :H  U4S j5        T R                  T R                  S5      TR                  S5      T R                  S	9$ )
Nr   c                  ,   > ST R                  5        S3$ )Nzx must be a 2D tensor, got Dr   r;   s   r6   re   /meta_int4mm_packed_weight_cpu.<locals>.<lambda>
      -H	QR+Sr8   c                  ,   > ST R                  5        S3$ )Nzw must be a 2D tensor, got r4  r   r  s   r6   re   r6  
  r7  r8   c                  "   > ST R                    3$ Nz#expected x to be f32/f16/bf16, got r   r5  s   r6   re   r6  
  s    9!''Cr8   c                  "   > ST R                    3$ Nzexpected w to be uint8, got r   r9  s   r6   re   r6  
  s    .J177),Tr8   c                  "   > ST R                    3$ )Nz q_group_size must be int64, got r   )q_group_sizes   r6   re   r6  
  s    6|7I7I6JKr8   c                  "   > ST R                    3$ )Nz5q_scale_and_zeros must have the same dtype as x, got r   )q_scale_and_zeross   r6   re   r6  
  s    KL]LcLcKder8   r   r   )rV   rh   r   r^   ra  rb  rc  r  r   r   r   r;   r  r?  rA  s   ````r6   meta_int4mm_packed_weight_cpurC  
  s    QUUW\#STQUUW\#STGGu}}ennEEC	
 	GGu{{"$T	
 	%++-K	
 	##qww.e	
 {{166!9affQiqww{??r8   c                    ^ ^^^ [         R                  " T R                  5       T:H  =(       a    T R                  T   T:H  UUUU 4S j5        g )Nc                  j   > ST  ST ST S3STR                  5        ST STR                  T    3-   $ )NzExpected a tensor of dimension z and tensor.size[z] == r{   zbut got : dimension z] = r   r   )r   dim_sizer   r:  s   r6   re    check_dim_size.<locals>.<lambda>
  sN    1#6GzQVW[V\\^_ .?zfll[cNdMe
fgr8   )rV   rh   r   r   )r:  r   rG  r   s   ````r6   check_dim_sizerI  
  s6    	LL

>X 6$ >	gr8   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$ )Nr1   r   c                     > ST  S3$ )Nzavg_pool2d: 4 must either be a single int, or a tuple of two intsr2   r  s   r6   re   1meta_avg_pool2d.<locals>.unpack.<locals>.<lambda>
      l4&(\]r8   r   r1   rV   rh   r   r  r  HWs   `   r6   unpackmeta_avg_pool2d.<locals>.unpack
  E    H]	
 FSQACFtr8   r  r   r1   r   c                      gNzOavg_pool2d: stride must either be omitted, a single int, or a tuple of two intsr2   r2   r8   r6   re   !meta_avg_pool2d.<locals>.<lambda>
      ar8   c                  @   > ST R                   R                  5        S3$ )Nz""avg_pool2d" not implemented for 'r  r  r	  s   r6   re   r\  
      6u{{7J7J7L6MQQr8   r   r1   r   r  c                      gNzdivisor must be not zeror2   r2   r8   r6   re   r\        *r8   r#  r*  r  r   r.   r  )rV   rh   r   r^   r  uint16uint32uint64r   r   pooling_output_shaperO   r   pool2d_shape_checkr   r   )r   r  r   r  r-  count_include_paddivisor_overriderV  kHkWdHdWpadHpadWr  r.  inputHeight
inputWidthr/  r0  r   r   s   `                     r6   meta_avg_pool2drs  
  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||#	 r8   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 )Nr1   r.   r   )rh  r   rI  )r   
gradOutputr  rk  rl  rm  rn  ro  rp  r.  rq  rr  r/  r0  
mem_formatr   nOutputPlanes                    r6   avg_pool2d_backward_shape_checkrx  -  s{    " 



		$ 99;DL:TAX|<:TAX|<:TAX{;r8   c                    [         R                  " [        U5      S:H  =(       d    [        U5      S:H  S 5        US   n[        U5      S:X  a  UOUS   n	[         R                  " [        U5      S:H  =(       d#    [        U5      S:H  =(       d    [        U5      S:H  S 5        [        U5      S:X  a  UOUS   n
[        U5      S:X  a  U	O[        U5      S:X  a  U
OUS   n[         R                  " [        U5      S:H  =(       d    [        U5      S:H  S 5        US   n[        U5      S:X  a  UOUS   n[         R                  " US L =(       d    US:g  S 5        UR                  nUR	                  5       S:X  a  US	   OSnUS
   nUS   nUS   n[        UXU
SU5      n[        UXUSU5      n[        R                  " U5      n[        UU UUU	U
UUUUUUUUU5        [         R                  " UUR                  UR                  US9$ )Nr1   r   c                      g)NzKavg_pool2d: kernel_size must either be a single int, or a tuple of two intsr2   r2   r8   r6   re   *meta_avg_pool2d_backward.<locals>.<lambda>g  s    ]r8   r   c                      gr[  r2   r2   r8   r6   re   r{  m  r]  r8   c                      g)NzGavg_pool2d: padding must either be a single int, or a tuple of two intsr2   r2   r8   r6   re   r{  s  s    Yr8   c                      gra  r2   r2   r8   r6   re   r{  z  rb  r8   r#  r*  rc  r  r   r  )rV   rh   r   r   r   rg  rO   r   rx  r   r^   r   )gradOutput_r   r  r   r  r-  ri  rj  rk  rl  rm  rn  ro  rp  
input_sizer  r.  rq  rr  r/  r0  rv  s                         r6   meta_avg_pool2d_backwardr  Y  s    
LLKA6[!1Q!6] 
QB;1$+a.B	LLFq@CK1,@Fq0@a 6{aVAYB6{a3v;!+;RB	LLG.S\Q.Y 1:Dw<1$4'!*D	LLD 9$4$9*
 J$yy{a/Z^QFR.KR.KBJ'Rr1iPL&z2RINK,,U3J#



$ ;;kk|| 	 r8   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r1   r.   c                      gNzFavg_pool3d: kernel_size must be a single int, or a tuple of three intsr2   r2   r8   r6   re   !meta_avg_pool3d.<locals>.<lambda>      Xr8   r   r1   r   c                      gNzJavg_pool3d: stride must be omitted, a single int, or a tuple of three intsr2   r2   r8   r6   re   r    r  r8   c                  @   > ST R                   R                  5        S3$ )Nz""avg_pool3d" not implemented for 'r  r  r	  s   r6   re   r    r_  r8   c                      gNzBavg_pool3d: padding must be a single int, or a tuple of three intsr2   r2   r8   r6   re   r        Tr8   r#  rK  c                      gNz9non-empty 4D or 5D (batch mode) tensor expected for inputr2   r2   r8   r6   re   r        Kr8   c                      gra  r2   r2   r8   r6   re   r    rb  r8   r*  rc  r  r   zavg_pool3d()T)check_input_sizer#  )rV   rh   r   r^   r  rd  re  rf  r   r   rg  pool3d_shape_checkr   )r   r  r   r  r-  ri  rj  kTrk  rl  dTrm  rn  padTro  rp  r  nslicesitimeiheightiwidthotimeoheightowidths   `                       r6   meta_avg_pool3dr    s    
LLKF"X 
QB;1$+a.B;1$+a.B	LL
+c&kV+\ 
LLEKKu||U\\RRQ vayBc&kQ&6F1IBc&kQ&6F1IB	LLGT 1:Dw<1$4'!*Dw<1$4'!*D	LL

fK
 
LL5 0A 5*
 ZZ]FjjnGJJrNEjjnGZZ^F "aCE"7Bb!YGG!&"B9EF





			-2 zzQ@AAHIIr8   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      $ )Nr  c                      gr  r2   r2   r8   r6   re   *meta_avg_pool3d_backward.<locals>.<lambda>
  r  r8   r   r1   r   c                      gr  r2   r2   r8   r6   re   r    r  r8   c                      gr  r2   r2   r8   r6   re   r    r  r8   r  c                      gr  r2   r2   r8   r6   re   r  "  r  r8   c                      gra  r2   r2   r8   r6   re   r  '  rb  r8   r*  rc  r  r   zavg_pool3d_backward())	rV   rh   r   r   r   rg  avg_pool3d_backward_shape_checkr   r   )r  r   r  r   r  r-  ri  rj  r  rk  rl  r  rm  rn  r  ro  rp  r  r  r  r  otime_for_shape_checkoheight_for_shape_checkowidth_for_shape_checks                           r6   meta_avg_pool3d_backwardr    s    
LLKF"X 
QB;1$+a.B;1$+a.B	LL
+c&kV+\ vayBc&kQ&6F1IBc&kQ&6F1IB	LLGT 1:Dw<1$4'!*Dw<1$4'!*D	LL

fK
 
LL5 0A 5*
 jjnGJJrNEjjnGZZ^F0"aS27Bb!YW1&"dB9U#





', ??5;;''r8   c                 8  ^  [         R                  " T R                  S:H  =(       d    T R                  S:H  U 4S j5        T R                  S S [	        U5      -   n[
        R                  " T 5      n[         R                  " UT R                  T R                  US9$ )Nr.   r#  c                  "   > ST R                    3$ )Nz"Expected 3D or 4D tensor, but got rD  r   s   r6   re   *meta_adaptive_avg_pool2d.<locals>.<lambda>P      4TZZLAr8   r  r  )
rV   rh   r   r   rg   rO   r   r   r^   r   )r   output_sizerh  r   s   `   r6   meta_adaptive_avg_pool2dr  L  s|    	LL		Q($))q.A ::cr?U;%77L//5M ;;jj{{#	 r8   c                    ^  [         R                  " T R                  S:H  =(       d    T R                  S:H  U 4S j5        T R                  T R                  S S [        U5      -   5      $ )Nr#  rK  c                  "   > ST R                    3$ )Nz"Expected 4D or 5D tensor, but got rD  r   s   r6   re   *meta_adaptive_avg_pool3d.<locals>.<lambda>b  r  r8   rc  )rV   rh   r   r   r   rg   )r   r  s   ` r6   meta_adaptive_avg_pool3dr  ^  sO    	LL		Q($))q.A >>$**Sb/E+,>>??r8   c                   ^ ^^ T R                   n[        SU5       H1  m[        R                  " T R	                  T5      S:  U U4S j5        M3     [        R                  " US:H  =(       d    US:H  U4S j5        [        R                  " TR
                  T R
                  :H  U U4S j5        [        R                  n[        T5      (       a  [        R                  nTR                  TR                  5      R                  US9$ )	Nr1   r   c                  *   > ST R                    ST S3$ )Nz{adaptive_avg_pool2d_backward(): Expected grad_output to have non-zero                       size for non-batch dimensions,  with dimension  being emptyrD  )grad_outr   s   r6   re   4meta__adaptive_avg_pool2d_backward.<locals>.<lambda>m  s$     66>nn5EEUVWUXXdfr8   r.   r#  c                  "   > ST R                    3$ )NzBadaptive_avg_pool2d_backward(): Expected 3D or 4D tensor, but got rD  r   s   r6   re   r  r  s    TUYU_U_T`ar8   c                  <   > STR                    ST R                    3$ Nexpected dtype z! for `grad_output` but got dtype r   )r  r   s   r6   re   r  v  s    /$**-Nx~~N^_r8   r   )r   r   rV   rh   r   r^   r   r  r  r   r   r1  )r  r   r   r   r   s   ``  @r6   "meta__adaptive_avg_pool2d_backwardr  g  s    ==D1d^MM!q f	
  
LL	TQYa 
LL

hnn$_ ++M++>>$**%((}(EEr8   c                 `    [        U S5        [        R                  " U[        R                  S9$ )Nadaptive_avg_pool3d_backwardr   )!_adaptive_pool_empty_output_checkrV   r   r  r  r   s     r6   "meta__adaptive_avg_pool3d_backwardr  ~  s(     &k3QRD0N0NOOr8   r  c                    ^ ^^ T R                   n[        SU5       H2  m[        R                  " T R	                  T5      S:  UU U4S j5        M4     g )Nr1   r   c                  .   > T  STR                    ST S3$ )Nzc(): Expected grad_output to have non-zero size for non-batch dimensions, but grad_output has sizes r  r  rD  )r  r  r   s   r6   re   3_adaptive_pool_empty_output_check.<locals>.<lambda>  s*    * --8->->,??OPQsR^`r8   )r   r   rV   rh   r   )r  r  r   r   s   `` @r6   r  r    sB    D1d^Q!#	
 r8   c                   ^ ^ T R                   n[        R                  " US;   U 4S j5        [        SU5       H1  m[        R                  " T R	                  T5      S:  UU 4S j5        M3     [        R                  " [        U5      S:H  S 5        SnSnSnT R                   S:X  a  T R	                  S5      nUS-  nT R	                  US-
  5      nUu  pgT R                   S	:X  a6  XVU4nT R                  U5      n	T R                  U[        R                  S
9n
X4$ XEXg4n[        R                  " T 5      nT R                  U5      R                  US9n	T R                  U[        R                  S
9R                  US9n
X4$ )Nr.   r#  c                  "   > ST R                    3$ )Nz:adaptive_max_pool2d(): Expected 3D or 4D tensor, but got: rD  r	  s   r6   re   *meta_adaptive_max_pool2d.<locals>.<lambda>      LU[[MZr8   r1   r   c                  *   > STR                    ST  S3$ )Nzjadaptive_max_pool2d(): Expected input to have non-zero size for non-batch dimensions, but input has sizes r  r  rD  r   r   s   r6   re   r         '',{{m3CA3lTr8   r   c                      g)NzCadaptive_max_pool2d(): internal error: output_size.size() must be 2r2   r2   r8   r6   re   r        Ur8   r#  r.   r   r   )r   rV   rh   r   r   r   r   r   rO   r   r1  )r   r  r   dimHsizeBsizeDosizeHosizeWr   r   r   r   r   s   `           @r6   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 
 |r8   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: rD  r  s   r6   re   3meta_adaptive_max_pool2d_backward.<locals>.<lambda>  s    ]^i^o^o]pqr8   adaptive_max_pool2d_backwardc                  <   > STR                    ST R                    3$ r  r   )r  r   s   r6   re   r    s    /%++.OP[PaPaObcr8   r   )
r   rV   rh   r  r^   rO   r   r   r   r1  )r  r   r   r   r   s   ``   r6   !meta_adaptive_max_pool2d_backwardr    s     D	LLq
 &k3QR	LL{(((c
 //6M??5;;'***GGr8   c                   ^ ^ T R                   n[        R                  " US;   U 4S j5        [        SU5       H1  m[        R                  " T R	                  T5      S:  UU 4S j5        M3     [        R                  " [        U5      S:H  S 5        SnSnSnUS:X  a  T R	                  S5      nUS-  nT R	                  U5      nUu  pgnUS	:X  a  XVXx4n	OXEXgU4n	T R                  U	5      n
T R                  U	[        R                  S
9nX4$ )Nr  c                  "   > ST R                    3$ )Nz:adaptive_max_pool3d(): Expected 4D or 5D tensor, but got: rD  r	  s   r6   re   *meta_adaptive_max_pool3d.<locals>.<lambda>  r  r8   r1   r   c                  *   > STR                    ST  S3$ )Nzjadaptive_max_pool3d(): Expected input to have non-zero size for non-batch dimensions, but input has sizes r  r  rD  r  s   r6   re   r    r  r8   r.   c                      g)NzCadaptive_max_pool3d(): internal error: output_size.size() must be 3r2   r2   r8   r6   re   r    r  r8   rK  r#  r   )r   rV   rh   r   r   r   r   r   )r   r  r   dimDr  r  osizeTr  r  r   r   r   r   s   `           @r6   meta_adaptive_max_pool3dr    s    ::D	LLZ 1d^JJqMA	
  
LLKAU
 DEEqy

1	JJtE(FFqyF3	66:	
//)
$Cooiu{{o;G<r8   c                 P    [        U S5        UR                  UR                  5      $ )Nadaptive_max_pool3d_backward)r  r   r   )r  r   r   s      r6   !meta_adaptive_max_pool3d_backwardr    s"     &k3QR??5;;''r8   c                 @    Uc  [        S5      eU R                  U5      $ )Nz:cannot repeat_interleave a meta tensor without output_size)r0  r   )repeatsr  s     r6   meta_repeat_interleave_Tensorr    s%    WXX[))r8   c                 4   U R                   R                  (       d   eUR                   R                  (       d   e[        U R                  [	        U R                   5      5      UR                  [	        UR                   5      5      [
        R                  S9nU$ NrL   )r^   r   rT   r1  r   r   rP   )realimagr  s      r6   meta_complexr    sp     ::''''::''''+DJJ78+DJJ786>>F
 Mr8   )
fill_valuer  c                \    U R                  XR                  5       4[        R                  S9$ r  )r   r   rV   r   )r   r   r  s      r6   nonzero_staticr    s$     >>4,EJJ>??r8   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.r2   r2   r8   r6   re   nonzero.<locals>.<lambda>'  s     Sr8   r1   r^   r   )	rV   _check_not_implementedr  meta_nonzero_assume_all_nonzeror2  r   r   r   r   r   s    r6   nonzeror  "  sf     
  22	S 	txxz"	
DJJLjj{{	 r8   c           
      n	  ^ ^^^^^^^^ [         R                  " [        T5      S 5        / n[        T5       GH  u  mmTGbr  [         R                  " TR                  [         R
                  [         R                  [         R                  [         R                  4;   S 5        TR                  [         R                  [         R                  4;   a  TR                  5       n[        U5      m[         R                  " TTR                  -   T R                  :*  U 4S j5        [        TR                  5       Hc  m[         R                  " TR                  T   T R                  TT-      :H  UUUUU 4S j5        UR                  UR                  ST5      5        Me     GMi  UR                  T5        GM}  UR                  T5        GM     Um[         R                  " [        T5      T R                  :*  UU 4S j5        SS KJn  [%        UR&                  " T6 5      m[        T5      T R                  :  a,  TR                  S 5        [        T5      T R                  :  a  M,  SnSnT H&  mUS:X  a	  Tb  SnM  M  US:X  a	  Tc  S	nM  M!  Tc  M&    O   S
nU(       d  / n/ n[        T5       H-  u  mmTc  M  UR                  T5        UR                  T5        M/     [        T5       H-  u  mmTb  M  UR                  T5        UR                  T5        M/     T R)                  U5      m Um/ m/ m/ m[        T5       He  u  n	mTcG  T(       a   TR                  T R                  U	   5        M0  TR                  T R                  U	   5        MP  [%        TR                  5      mMg     UUU4S jn
T R+                  TT-   T-   5      nSSKJn  U" T R1                  5       S:H  5      (       a  U$ U
" T 5      n[2        R4                  " U5      u  p[%        U5      [%        [        [        U5      5      5      :w  a  [2        R6                  " UR                  U5      n[2        R8                  " U5      n[2        R6                  " U[2        R:                  " U5      5      nUR=                  UR?                  5       U5      nU$ )Nc                      g)Nz#at least one index must be providedr2   r2   r8   r6   re   #meta_index_Tensor.<locals>.<lambda>7  s    (Mr8   c                      g)Nz?tensors used as indices must be long, int, byte or bool tensorsr2   r2   r8   r6   re   r   ?  s    Yr8   c                  "   > ST R                    3$ )N)too many indices for tensor of dimension r  r   s   r6   re   r   F  s    G		{Sr8   c            	      N   > STR                    ST  STR                    STT-    3$ )NzThe shape of the mask 
 at index z0 does not match the shape of the indexed tensor rD  )r   r   jrT  r   s   r6   re   r   K  s:    "8ZPQs SJJN**U_`ade`e_f!hr8   r1   c                  <   > STR                    S[        T 5       S3$ )Nr  z (got r|   )r   r   )r   r   s   r6   re   r   V  s    ;DII;fSQX\NZ[\r8   r   Fr   Tc                    > TT-   T-   n[        U R                  5       5      nS/[        T5      -  U[        T5      [        U R                  5      [        T5      -
  & U R	                  X5      $ )z9
This follows restride_src in TensorAdvancedIndexing.cpp
r   )r   r   r   r   rL  )r   r   r   after_shapebefore_shapereplacement_shapes      r6   _restride_src(meta_index_Tensor.<locals>._restride_src  sm     00;>t{{}%KL#PSQ
 K
L!C

Oc+6F$FG u..r8   guard_or_false) rV   rh   r  	enumerater^   r   r   rJ  r  r   r   r   r   r   r   selecttorch._refs_refsr   r$   r   r   r.  r  r   rO   3compute_elementwise_output_logical_to_physical_perm
apply_permr   invert_permrL  r   )r   r   r  r  refsstatehas_contiguous_subspacer  transposed_indicesr   r  r   r  restrided_selfpermrR   
perm_shaper=  r	  r
  r   r   r  rT  r  s   ``                @@@@@@@r6   meta_index_Tensorr  5  s   	LLg MN #%Fg&5LL

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

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

 #4(NGGWGD DzT%D	*++%%cii6
66zB
%%j%2C2CD2IJ
nnSXXZ4Jr8   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$ Nr   r1   r   r   r   )grad_output_input_weight_bias_sizes_optr   r  r  
transposedr  r  output_maskbackend_grad_inputbackend_grad_weightbackend_grad_biass                 r6   meta_convolution_backwardr+    sv      1~)33FKKMB1~*44W\\^D1~(22>B5FGGr8   c                  ^^ TR                  S5      nTR                  S5      nU R                  XV45      n [        R                  " TR	                  5       S:H  S 5        [        R                  " TR	                  5       S:H  S 5        [        R                  " TR                  S5      TR                  S5      :H  UU4S j5        [        R                  " TR                  S5      TR                  S5      :H  UU4S j5        [        R                  " U R                  S5      U:H  =(       a    U R                  S5      U:H  S	 5        U R                  U R                  5       5      $ )
Nr1   r   r.   c                      grw  r2   r2   r8   r6   re   meta_addbmm.<locals>.<lambda>  ry  r8   c                      gr{  r2   r2   r8   r6   re   r.    ry  r8   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   r6   re   r.    s,    J6;;WX>JZZ_`f`k`klm`n_opr8   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 (r1   r;   r   r   r|   r   r1  s   r6   re   r.    sL    1&++a.1A6;;q>BR S;;q>"!FKKN#316r8   c                      g)Nz.self tensor does not match matmul output shaper2   r2   r8   r6   re   r.    s    @r8   )r   r  rV   rh   r   r   )r   r}  r~  rW  rV  r  r  s    ``    r6   meta_addbmmr4    s     ;;q>D;;q>D;;|$D	LL"$HI	LL"$HI	LLA&++a.(p 
LLA&++a.(	
 
LL		!51!5@ >>$))+&&r8   c                 @    U R                  U R                  5       5      $ rB   r!  )r   r  kwargss      r6   meta_randint_liker7    s    >>$))+&&r8   )
grad_scale	found_infc       	         p   ^ XX#XE4 H,  m[         R                  " [        T[        5      U4S j5        M.     g )Nc                      > S[        T 5       3$ Nz'exponent must be a tensor list but got r}   ls   r6   re   #meta__fused_adam_.<locals>.<lambda>      =d1gYGr8   rV   rh   rr   r   )r   gradsexp_avgsexp_avg_sqsmax_exp_avg_sqsstate_stepslrbeta1beta2weight_decayepsamsgradmaximizer8  r9  r?  s                  @r6   meta__fused_adam_rO    s0    & 8/Oq$G	
 Pr8   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$ )Nc                      > S[        T 5       3$ r<  r=  r>  s   r6   re   "meta__fused_adam.<locals>.<lambda>&  rA  r8   c                 Z    U  Vs/ s H  n[         R                  " U5      PM     sn$ s  snf rB   r:  )tensor_listr  s     r6   empty_like_list)meta__fused_adam.<locals>.empty_like_list)  s%    -89[  #[999s    (rB  )r   rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  r8  r9  rU  r?  s                   @r6   meta__fused_adamrW    si    & 8/Oq$G	
 P: 	!$( r8   c                 t  ^ ^ [         R                  " T R                  5       S:H  S 5        [         R                  " TR                  5       S:H  S 5        [         R                  " T R                  [         R                  L U 4S j5        [         R                  " TR                  [         R                  L U4S j5        [         R                  " T R                  S5      TR                  S5      :H  U U4S j5        T R                  T R                  S5      TR                  S5      4[         R                  S	9$ )
Nr   c                      g)Nza must be a 2D tensorr2   r2   r8   r6   re   meta__int_mm.<locals>.<lambda>8      '>r8   c                      g)Nzb must be a 2D tensorr2   r2   r8   r6   re   rZ  9  r[  r8   c                  "   > ST R                    3$ )Nzexpected self to be int8, got r   )r4   s   r6   re   rZ  <      0	:r8   c                  "   > ST R                    3$ )Nzexpected mat2 to be int8, got r   )r5   s   r6   re   rZ  @  r^  r8   r1   r   c            
         > ST R                  S5       ST R                  S5       STR                  S5       STR                  S5       S3	$ )Nz'Incompatible matrix sizes for _int_mm (r   r;   r1   r   r|   r   r3   s   r6   re   rZ  D  sH    5affQi[!&&) M66!9+Qqvvayk,r8   r   )rV   rh   r   r^   rJ  r   r   rK  r3   s   ``r6   meta__int_mmra  5  s     
LLA>?	LLA>?	LL	5::: 
LL	5::: 
LL	q	QVVAY	
 ;;q	166!9-U[[;AAr8   c                 d  ^  [         R                  " T R                  5       S:H  S 5        [         R                  " T R                  [         R                  L U 4S j5        T R                  S5      nT R                  S5      S-  nT R                  US-  X1S-  -  SUS-  4[         R                  S	9$ )
Nr   c                      gNzw must be a 2D tensorr2   r2   r8   r6   re   2meta__convert_weight_to_int4pack.<locals>.<lambda>N  r[  r8   c                  "   > ST R                    3$ r=  r   r9  s   r6   re   re  Q      .qwwi8r8   r   r1             r   )rV   rh   r   r^   r  r   r   rK  r  inner_k_tilesr  rT  s   `   r6    meta__convert_weight_to_int4packrm  L  s    	LLA>?	LL	5;;8 	
q	A	q	AA;;F"$%Q		
 kk   r8   c                 H  ^  [         R                  " T R                  5       S:H  S 5        [         R                  " T R                  [         R                  L U 4S j5        T R                  S5      nT R                  S5      nT R                  X#S-  4[         R                  S9$ )Nr   c                      grd  r2   r2   r8   r6   re   :meta__convert_weight_to_int4pack_for_cpu.<locals>.<lambda>b  r[  r8   c                  "   > ST R                    3$ Nzexpected w to be int32, got r   r9  s   r6   re   rp  e  rg  r8   r   r1   r   )rV   rh   r   r^   rK  r   r   r  rk  s   `   r6   (meta__convert_weight_to_int4pack_for_cpurs  `  s}    	LLA>?	LL	5;;8 	
q	A	q	A;;	
Fkk   r8   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$ )
Nr   c                      gNzx must be a 2D tensorr2   r2   r8   r6   re   *meta__weight_int4pack_mm.<locals>.<lambda>q  r[  r8   r#  c                      g)Nzw must be a 4D tensorr2   r2   r8   r6   re   rw  r  r[  r8   c                  "   > ST R                    3$ r;  r   r5  s   r6   re   rw  u      5aggY?r8   c                  "   > ST R                    3$ rr  r   r9  s   r6   re   rw  y  rg  r8   r   rh  r   
rV   rh   r   r^   ra  rb  rc  rK  r   r   rB  s   ``  r6   meta__weight_int4pack_mmr}  o  s    	LLA>?	LLA>?	LL	EMM5==%..AA? 
LL	5;;8 ;;qvvay!&&)a-qww;??r8   c                 0  ^ ^ [         R                  " T R                  5       S:H  S 5        [         R                  " TR                  5       S:H  S 5        [         R                  " T R                  [         R                  [         R
                  [         R                  4;   U 4S j5        [         R                  " TR                  [         R                  L U4S j5        T R                  T R                  S5      TR                  S5      T R                  S9$ )Nr   c                      grv  r2   r2   r8   r6   re   2meta__weight_int4pack_mm_for_cpu.<locals>.<lambda>  r[  r8   c                      grd  r2   r2   r8   r6   re   r    r[  r8   c                  "   > ST R                    3$ r;  r   r5  s   r6   re   r    rz  r8   c                  "   > ST R                    3$ r=  r   r9  s   r6   re   r    rg  r8   r   r   )
rV   rh   r   r^   ra  rb  rc  r  r   r   rB  s   ``  r6    meta__weight_int4pack_mm_for_cpur  ~      	LLA>?	LLA>?	LL	EMM5==%..AA? 
LL	5;;8 ;;qvvay!&&)177;;;r8   c                 0  ^ ^ [         R                  " T R                  5       S:H  S 5        [         R                  " TR                  5       S:H  S 5        [         R                  " T R                  [         R                  [         R
                  [         R                  4;   U 4S j5        [         R                  " TR                  [         R                  L U4S j5        T R                  T R                  S5      TR                  S5      T R                  S9$ )Nr   c                      grv  r2   r2   r8   r6   re   ;_weight_int4pack_mm_with_scales_and_zeros.<locals>.<lambda>  r[  r8   c                      grd  r2   r2   r8   r6   re   r    r[  r8   c                  "   > ST R                    3$ r;  r   r5  s   r6   re   r    rz  r8   c                  "   > ST R                    3$ rr  r   r9  s   r6   re   r    rg  r8   r   r   r|  )r;   r  r?  qScaleqZeross   ``   r6   )_weight_int4pack_mm_with_scales_and_zerosr    r  r8   r4   r5   c                     X-   S-
  U-  U-  $ r0   r2   r3   s     r6   kai_roundupr    s    UQY1!!r8   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#  rh  ri  r   c                 4    [        X-  S5      n[        X5      $ )Nr#  r  )rT  krsrkr_sr_roundedup4s       r6   kai_k_roundedup3get_kai_packed_weight_size.<locals>.kai_k_roundedup  s     $/rw#: "177r8   c                 X   > T" XU5      nUS-  S:X  d   S5       eUUS-  T-   T-   T-   -  $ )Nr   r   zk_internal must be evenr2   )	rT  nrr  r  
k_internalr  kai_num_bytes_biaskai_num_bytes_multiplier_rhskai_num_bytes_sum_rhss	        r6   9kai_get_rhs_packed_stride_rhs_pack_nxk_qsi4cxp_qsu4cxs1s0]get_kai_packed_weight_size.<locals>.kai_get_rhs_packed_stride_rhs_pack_nxk_qsi4cxp_qsu4cxs1s0  sW     -QB7
"Q1,G.GG,1_23+, )) r8   c                 8   > [        X5      U-  nUT" XX45      -  $ rB   r  )r  rT  r  r  r  num_rowsr  s         r6   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r8   rj  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      -  $ rt  r  )
r  rT  r  r  r  blr  kai_bl_multiple_of;kai_get_rhs_packed_stride_rhs_pack_nxk_qsi4c32p_qsu4c32s1s0kai_nr_multiple_ofs
          r6   9kai_get_rhs_packed_size_rhs_pack_nxk_qsi4c32p_qsu4c32s1s0]get_kai_packed_weight_size.<locals>.kai_get_rhs_packed_size_rhs_pack_nxk_qsi4c32p_qsu4c32s1s0  sh     A~%~//A555//A555&q-3 Qrrr8   c                    > XB-  S:X  d   eUT
-  S:X  d   eUT-  S:X  d   eT	" 5       nT" X5      nT" XE5      nUXv-  T-   T-   -  $ rt  r2   )rT  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           r6   r  _get_kai_packed_weight_size.<locals>.kai_get_rhs_packed_stride_rhs_pack_nxk_qsi4c32p_qsu4c32s1s0  s     A~%~//A555//A555 ,O+P(%;A%B"&='# (=+,() r8   c                      g)Nr   r2   r2   r8   r6   r  Gget_kai_packed_weight_size.<locals>.kai_get_bf16_datatype_size_in_bytes  s    r8   c                 6   > UT-  S:X  d   e[        X5      U-  $ rt  r  )rT  r  r  s     r6   r  :get_kai_packed_weight_size.<locals>.kai_num_blocks_per_row  s'    //A555"1)R//r8   c                 *   > U T-  S:X  d   eU S-  U-   $ )Nr   r   r2   )r  r  r  s     r6   r  ;get_kai_packed_weight_size.<locals>.kai_num_bytes_per_block  s'    //A555a#;;;r8   r2   )n_bitsr  K	groupsizekai_nrkai_krkai_srr  r  r  r  r  r  r  r  r  r  r  r  r  s            @@@@@@@@@@@r6   get_kai_packed_weight_sizer    s    {>FFF$%!+,(!"8 
 Kff  ^q Q]a%7FFF$%!!"!"!#  ,0< Mff u &8 ] r8   c                   ^  [         R                  " T R                  [         R                  L U 4S j5        [         R                  R
                  R                  5       (       a  X4:X  a  UR                  [         R                  :X  d4  X4:  ac  US-  S:X  aZ  XC-  S:X  aR  UR                  [         R                  :X  a4  [        SXTU5      nT R                  [        U5      [         R                  S9$ T R                  5       UR                  5       -   nUb  XbR                  5       -  nT R                  U[         R                  S9$ )Nc                  "   > ST R                    3$ r=  r   )weightss   r6   re   2meta__dyn_quant_pack_4bit_weight.<locals>.<lambda>  s    .w}}o>r8   rj  r   r#  r   )rV   rh   r^   r  backendskleidiaiis_availablerZ   rc  r  r   r   r   )r  scales_zerosrE  
block_sizein_featuresout_featurespacked_weight_sizes   `      r6    meta__dyn_quant_pack_4bit_weightr    s    
LL$> ~~++--		"|'9'9U[['H$R1$(A-""enn4 8|*
   %7!8 LL <+=+=+??jjl*/u{{CCr8   c                   ^ ^^ [         R                  " T R                  5       S:H  S 5        [         R                  " T R                  [         R                  :H  =(       d)    T R                  [         R
                  :H  =(       a    TT:H  UUU 4S j5        T R                  S5      nT R                  XTT R                  S9$ )Nr   c                      g)Nzinput must be a 2D tensorr2   r2   r8   r6   re   -meta__dyn_quant_matmul_4bit.<locals>.<lambda>1  s    )Dr8   c                  .   > STR                    ST  ST 3$ )NzPexpected input to be f32 or bf16 (bf16 requires block_size == in_features), got z with block_size=z and in_features=r   )r  r  inps   r6   re   r  5  s%    99+.zl:KK=Zr8   r   r   )rV   rh   r   r^   ra  rc  r   r   )r  packed_weightsr  r  r  r  s   ` ``  r6   meta__dyn_quant_matmul_4bitr  )  s     
LLa!DE	LL	emm	# 	GII'EJ+,E	
 	A==		=::r8   c                 0  ^ ^ [         R                  " T R                  5       S:H  S 5        [         R                  " T R                  [         R                  [         R
                  [         R                  4;   U 4S j5        [         R                  " TR                  5       S:H  S 5        [         R                  " TR                  [         R                  L U4S j5        T R                  T R                  S5      TR                  S5      T R                  S9$ )Nr   c                      grv  r2   r2   r8   r6   re   *meta__weight_int8pack_mm.<locals>.<lambda>@  r[  r8   c                  "   > ST R                    3$ r;  r   r5  s   r6   re   r  C  rz  r8   c                      grd  r2   r2   r8   r6   re   r  E  r[  r8   c                  "   > ST R                    3$ )Nzexpected w to be int8, got r   r9  s   r6   re   r  H  s    -aggY7r8   r   r   )
rV   rh   r   r^   ra  rb  rc  rJ  r   r   )r;   r  q_scaless   `` r6   meta__weight_int8pack_mmr  >  s    	LLA>?	LL	EMM5==%..AA? 
LLA>?	LL	5::7 ;;qvvay!&&)177;;;r8   c                   ^ ^^ [         R                  " T R                  5       S:  U 4S j5        [         R                  " TR                  5       S:  U4S j5        [         R                  " T R                  S5      TR                  S5      :H  U U4S j5        [         R                  " [        R
                  " T R                  5      U 4S j5        [         R                  " [        R
                  " TR                  5      U4S j5        [         R                  " US:  S	 5        [         R                  " TS
;   U4S j5        T R                  S5      nTR                  S5      nT R                  S S nTR                  S S n[        [         R                  " Xg5      5      nUR                  XE/5        T R                  U5      $ )Nr   c                  ,   > ST R                  5        S3$ )Nz1cdist only supports at least 2D tensors, X1 got: r4  r   x1s   r6   re   $meta_cdist_forward.<locals>.<lambda>Q      CBFFH:QOr8   c                  ,   > ST R                  5        S3$ )Nz1cdist only supports at least 2D tensors, X2 got: r4  r   x2s   r6   re   r  U  r  r8   r   c                  P   > ST R                  S5       STR                  S5       3$ )Nz4X1 and X2 must have the same number of columns. X1: r   z X2: r   )r  r  s   r6   re   r  Y  s*    Frwwr{mSXY[Y`Y`acYdXefr8   c                  "   > ST R                    3$ )Nz3cdist only supports floating-point dtypes, X1 got: r   r  s   r6   re   r  ]      EbhhZPr8   c                  "   > ST R                    3$ )Nz3cdist only supports floating-point dtypes, X2 got: r   r  s   r6   re   r  a  r  r8   r   c                      g)Nz)cdist only supports non-negative p valuesr2   r2   r8   r6   re   r  c  s    !Lr8   r   c                     > ST  3$ )Nz(possible modes: None, 0, 1, 2, but was: r2   )compute_modes   r6   re   r  f  s    :<.Ir8   r  )rV   rh   r   r   rO   is_float_dtyper^   r   r   broadcast_shapesextendr   )	r  r  rg  r  r1r2batch_tensor1batch_tensor2rh  s	   `` `     r6   meta_cdist_forwardr  M  sF   	LL
AO 
LL
AO 
LL
rwwr{"f 
LLRXX&P 
LLRXX&P 
LLaLM	LL'I 
B	BHHSbMMHHSbMM..}LML!<<%%r8   c                 <   UR                   S   nUR                   S   nUR                   S   nUR                   S S nUR                   S S n	[        [        R                  " X5      5      n
U
R	                  5       nUR                  Xe/5        [        R                  " U
5      nUS:X  d  US:X  d  US:X  d  US:X  a  [        R                  " U5      $ U[        UR                   5      :w  a  UR                  U5      n[        R                  " U[        R                  S9$ )Nr   r  r   r   )r   r   rV   r  copyr  mathprod
zeros_liker  r   r   )rl  r  r  rg  cdistc1r  r  r  r  r  tensor1_expand_sizebatch_products                r6   meta_cdist_backwardr  q  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Fr8   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$ )Nz(expected indices to be long or int, got r   )r   s   r6   re   $meta_embedding_bag.<locals>.<lambda>      :7==/Jr8   c                  "   > ST R                    3$ )Nz(expected offsets to be long or int, got r   )rx  s   r6   re   r    r  r8   c                  "   > ST R                    3$ )Nz/expected weight to be floating point type, got r   )rC  s   r6   re   r    s    A&,,Pr8   r   r1   c                      gNz1include_last_offset: numBags should be at least 1r2   r2   r8   r6   re   r    s    Gr8   c                      g)Nz@embedding_bag: per_sample_weights only supported with mode='sum'r2   r2   r8   r6   re   r    s    Vr8   c                  $   > ST R                    S3$ )Nz1expected per_sample_weights to be 1D tensor, got r4  r  )per_sample_weightss   r6   re   r    s    GHZH_H_G``abr8   c                  N   > STR                  5        ST R                  5        S3$ )Nz%expected per_sample_weights.numel() (z$ to be the same as indices.numel() (r|   r   )r   r	  s   r6   re   r    s/    78J8P8P8R7S T66=mmo5FaIr8   c                 L   > T" XU5      =(       a    UR                  S5      S:H  $ Nr   r1   r   )r4  r  r  padding_idxis_fast_path_index_selects       r6   is_fast_path_index_select_scale;meta_embedding_bag.<locals>.is_fast_path_index_select_scale  s&    %c;?XELLQROWXDX	
r8   c                    U R                   [        R                  :H  =(       d    U R                   [        R                  :H  =(       a;    U R	                  S5      S:H  =(       a     UR	                  S5      S:H  =(       a    US:  $ r  )r^   rV   rZ   rX   r   )r4  r  r  s      r6   r  5meta_embedding_bag.<locals>.is_fast_path_index_select  sb    YY%++%@ejj)@  

1" a A%  a		
r8   c                 .   > Ub	  T" XX#5      $ T" XU5      $ rB   r2   )r4  r  r  r  r  r  s       r6   is_fast_path(meta_embedding_bag.<locals>.is_fast_path  s#    23vSS,S+FFr8   cpuc                      gr  r2   r2   r8   r6   re   r    s    Or8   )rV   rh   r^   r   r   rO   r  r   r   MODE_SUMr   r   r   MODE_MAX	MODE_MEANr   )rC  r   rx  scale_grad_by_freqrl  sparser	  include_last_offsetr  num_bagsr  r  
offset2bagbag_sizemax_indicesfast_path_sumnumBagsr  r  s   ```   `          @@r6   meta_embedding_bagr&    sw    
LL%**eii00J 
LL%**eii00J 
LLV\\*P
 ||AHMG	
 	AhA7F%HV	
 	##q(b	
 	$$&'--/9	



G 7u$&&w||A7
$$W\\^48!++Hfkk!nEK!++A.K$V-?UIx(( **7<<?;J **1-J$$X.--"8"qLO 1!++GV\\!_EK!++HMMO<Kx44r8   c                     [        XU/UQ76 u  pEpg[        U5      S:X  a  UR                  UR                  5       5      nXEXg4$ )Nr  )r&  r   r   r   )rC  r   rx  rQ   r  r!  r"  r#  s           r6   meta_embedding_bag_forward_onlyr(    sN    0B1#'1-F 7u$$$W\\^4x44r8   c                     U(       a  U$ U R                   R                  (       d  U R                   R                  (       a  U R                   $ U(       a  [        R                  $ U R                   $ rB   )r^   r   r   rV   r   )r   r^   promote_int_to_longs      r6   _get_reduction_dtyper+    sD    {{$$(>(>{{	zz;;r8   r   c                    [        XSS9n[        R                  " U R                  U5      n[	        XU5      nU R                  XTS9$ )NT)r*  r   )r+  rO   r  r   r  r   )r   r  r  r^   r  rh  s         r6   meta_nansumr-    sC     ($OLT2D+EAL??<?<<r8   c           	          [         R                  " U R                  [        [	        U R                  5       5      5      5      nU R                  U5      $ rB   )rO   r  r   rg   r   r   r   )r   rh  s     r6   meta_medianr/    s<    77U5-.L ??<((r8   c                    [        U 5      S:X  a  [        R                  " S5        [        R                  " U R                  U45      n[        XU5      nU R                  U5      U R                  U[        R                  S94$ )Nr   zmedian CUDA with indices outputr   )	r   rO   alert_not_deterministicr  r   r  r   rV   r   )r   r   r  rh  s       r6   meta_median_mode_dimr2    sn     5V#%%&GH


u{{SF
3C+E@L%EJJ7 r8   c                     U $ rB   r2   r   s    r6   meta_logical_not_r4  *  r  r8   c                   ^^ [         R                  " [        U5      U R                  5       :  S 5        [	        U5       H%  u  mm[         R                  " TS:  UU4S j5        M'     [        U5      U R                  5       -
  nSU-  [        U R                  5      -   n[        [        U5      5       Vs/ s H  oCU   X   -  PM     nnU R                  U5      $ s  snf )Nc                      g)NzZNumber of dimensions of repeat dims can not be smaller than number of dimensions of tensorr2   r2   r8   r6   re   meta_repeat.<locals>.<lambda>3  s    lr8   r   c                     > ST ST  3$ )Nz"Repeats cannot be negative, found r  r2   )r   reps   r6   re   r7  8  s    8ZsKr8   r'  )	rV   rh   r   r   r  rg   r   r   r   )r   r  num_new_dimensionspadded_sizer   target_sizer9  s       ` @r6   meta_repeatr=  /  s    	LLG
"l G$31HK	
 % W
2++eDJJ.??K8=c'l8KL8K1q>GJ.8KKL>>+&& Ms   6Cc                     U $ rB   r2   r   s    r6   
meta_zero_r?  C  r  r8   c                     [        U[        R                  5      (       a   [        U R                  UR                  5        U $ rB   )rr   rV   r   rj   r   r   r   s     r6   meta_binop_inplacerB  H  s,     %&&

EKK8Kr8   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      $ rB   )rr   r   rO   rI  r^   r   ru   s    r6   is_integeric.meta_binop_inplace_alpha.<locals>.is_integerick  s1    c:&&))#))44c7++r8   c                     [        U [        5      (       a   [        R                  " U R                  5      $ [        U [
        5      $ rB   )rr   r   rO   r  r^   r   rE  s    r6   
is_floatic,meta_binop_inplace_alpha.<locals>.is_floaticq  s1    c:&&''		22c9--r8   c                     [        U [        5      (       a   [        R                  " U R                  5      $ [        U [
        5      $ rB   )rr   r   rO   is_boolean_dtyper^   r   rE  s    r6   is_booleanic.meta_binop_inplace_alpha.<locals>.is_booleanicw  s1    c:&&))#))44c8,,r8   z]Promotion of int.add/sub_(float) in in-place ops are not possible due to element size change.z_Promotion of book.add/sub_(others) in in-place ops are not possible due to element size change.)r0  rr   rV   r   rj   r   )r   r   rV  rF  rI  rM  s         r6   meta_binop_inplace_alpharO  Y  s    $,.- Dj//k
 	

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

EKK8Kr8   c                 2    [        X[        R                  S9$ r  rT   r   rP   r   r   rV  s      r6   meta_binop_alpharS    s     $C$K$K r8   c                 2    [        U [        R                  S9$ r  rQ  )r   r6  s     r6   
meta_roundrU    s    <DD r8   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$ )Nz7: Expected input tensor to have an integral dtype. Got r   )r  r   s   r6   re   #shift_dtype_check.<locals>.<lambda>  s    7)RSWS]S]R^_r8   c                  &   > T  STR                    3$ )Nz6: Expected shift value to have an integral dtype. Got r   r  r  s   r6   re   rX    s    wiUVYV_V_U`ar8   c                     > T  ST 3$ )Nz): Expected shift value to be an int. Got r2   rZ  s   r6   re   rX    s    wiHNr8   )rV   rh   rO   rI  r^   rr   r   r   )r  r   r  s   ```r6   shift_dtype_checkr\    ss    	LLtzz*_ #u||$$""399-a	

 	sG$N	
r8   c                 J    [        SX5        [        X[        R                  S9$ )Nrshiftr  r\  rT   r   rP   rA  s     r6   meta_rshiftsr`    %    h,$C$K$K r8   c                 J    [        SX5        [        X[        R                  S9$ )Nlshiftr  r_  rA  s     r6   meta_lshiftsrd    ra  r8   c                 8    U R                  U R                  5      $ rB   r  r   s    r6   	meta_zerorf    s    >>$**%%r8   c                     U $ rB   r2   r   r  s     r6   
meta_fill_ri    r  r8   c                 .    [         R                  " U 5      $ rB   r:  rh  s     r6   	meta_fillrk        D!!r8   c                     U $ rB   r2   r   s    r6   
meta_relu_rn    r  r8   c                 2    [        X[        R                  S9$ r  rQ  rR  s      r6   meta__add_relurp    s     $C$K$K r8   c                 .    [         R                  " U 5      $ rB   r:  r   noiselowerr  r  r  s         r6   meta_rrelu_with_noiseru    s    
 D!!r8   c                 Z    [         R                  " U 5      [         R                  " U5      4$ rB   r:  rr  s         r6    meta_rrelu_with_noise_functionalrw    s%     D!5#3#3E#:::r8   c                     U $ rB   r2   )r   rt  r  r  r  s        r6   meta_rrelu_with_noise_ry    s	     Kr8   c                 .    [         R                  " U 5      $ rB   r:  r   r   r   
accumulates       r6   meta_index_putr}    rl  r8   c                 F    [        U R                  UR                  5        U $ rB   rj   r   )r   r  values      r6   meta_masked_fill_r    s    DJJ

3Kr8   c                     U R                  U R                  5       5      R                  [        R                  " U 5      S9nU$ r   )r   r   r1  rO   r   )r   r  r  masked_scales       r6   meta__masked_scaler    s<    >>$))+.1111$7 2 L r8   c                    ^ ^ [         R                  " UR                  [         R                  [         R                  4;   S 5        [         R                  " T R                  TR                  :H  U U4S j5        T $ )Nc                      g)NzMask must be bool or uint8r2   r2   r8   r6   re   &meta_masked_scatter_.<locals>.<lambda>
  s    9Ur8   c                  <   > ST R                    STR                    3$ )NzEmasked_scatter: expected self and source to have same dtypes but got r   r   )r   rk  s   r6   re   r    s      **U6<<.:r8   )rV   rh   r^   r  r  )r   r  rk  s   ` `r6   meta_masked_scatter_r    sU    	LL

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

fll"	:
 Kr8   c                 z    [        X5      u  p[        R                  " U [        R                  S9n[	        X1U5      $ r   )r$   rV   r   r   r  )r   r  rk  r  s       r6   meta_masked_scatterr    s5     "$-JDd%2I2IJFf55r8   c                 $    U R                  U5      $ rB   r  )r   r  rS  s      r6   meta_masked_scatter_backwardr    s    >>%  r8   c                     U $ rB   r2   r{  s       r6   meta_index_put_r  !  r  r8   c           	        ^^^^^ SSK JnJn  [        R                  " U R                  5       S:H  S 5        [        R                  " UR                  5       S:H  S 5        U R                  5       nUR                  5       mUS   mUS   mUS   nTS   n	TX4m[        R                  " U" U" TS   T5      U" TS   T5      5      UUU4S j5        U(       a  U R                  [        R                  :H  =(       d    U R                  [        R                  :H  =(       a    U[        R                  :H  n
[        R                  " X@R                  :H  =(       d    U
S	 5        UR                  T5      R                  U5      nOUR                  T5      nU(       d]  TbZ  [        R                  " TR                  5       S:H  S
 5        [        R                  " U" TR                  5       T5      UU4S j5        U$ )Nr   )sym_andru  r.   c                      grw  r2   r2   r8   r6   re   )common_meta_baddbmm_bmm.<locals>.<lambda>)  ry  r8   c                      gr{  r2   r2   r8   r6   re   r  *  ry  r8   r   r1   c            	      .   > ST ST ST S    ST S    S3	$ r  r2   r  s   r6   re   r  7  s3    RSURV
l<?*;2l1o=NbRr8   c                      g)Nzfout_dtype only supported for torch.float32 output with float16/bfloat16 inputs or same as input dtypesr2   r2   r8   r6   re   r  @  s    |r8   c                      g)Nzself must be a 3D tensorr2   r2   r8   r6   re   r  H  s    6Pr8   c                  0   > ST  STR                  5        3$ )Nz*Expected an input tensor shape with shape z but got shape: r   )r  self_baddbmms   r6   re   r  K  s    @M]^j^o^o^q]rsr8   )r.  r  ru  rV   rh   r   r   r^   rb  rc  ra  r   r1  )r}  r~  is_bmmr  rG  r  ru  r  res_rowsres_colssupported_out_dtyper  r  r  r  r  s      `        @@@@r6   common_meta_baddbmm_bmmr  &  s   E	LL"$HI	LL"$HI;;=L;;=L	aB#AAHAHx*K	LL|A+VLOEU-VW	R
 LLEMM)KV\\U^^-K)5==( 	 	%<)<|	
 !!+.11)< !!+.l.\%%'1,.PQ<$$&4s	

 Mr8   c                     [        XS5      $ )NTr  )r   rR  s     r6   meta_bmmr  Q  s    "4t44r8   c                     [        XSUS9$ )NT)rG  r  )r   rR  rG  s      r6   meta_bmm_dtyper  V  s    "4tyIIr8   c                 h    X-  nX-  nUS:w  a#  [        US:  5      [        US:  5      :w  a  US-  nU$ r  )r  )r;   r<   qrp  s       r6   div_rtnr  [  s>    	A	A 	Av4A;$q1u+-	QHr8   c                     [        U U-   U-   XQS-
  -  -
  S-
  U(       a  US-
  OS-   U5      S-   nU(       a  US-
  U-  X-   :  a  US-  nU$ r  )r  )	inputSize
kernelSizer  r  r   r  r-  
outputSizes           r6   pooling_output_shape_pad_lrr  e  s     	 q.)* 	
 'vzA/ 	
 		  Nf$	(99!OJr8   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      $ )Nr   c                      g)Nzstride should not be zeror2   r2   r8   r6   re   &pooling_output_shape.<locals>.<lambda>  s    &Ar8   c                     > ST  3$ )Nz'pad must be non-negative, but got pad: r2   pads   r6   re   r    s    %LSE#Rr8   r1   r   c                     > ST ST ST  3$ )NzApad should be at most half of effective kernel size, but got pad=z, kernel_size=z and dilation=r2   )r  r  r  s   r6   re   r    s"    OPSu U%,nXJ@r8   )rV   rh   r  )r  r  r  r   r  r-  s    `` ` r6   rg  rg    ss    	LL1AB	LLRS	LLa8+a/A55	
 ':sC9 r8   c           	        ^ ^^^^^^^^^	^
^^^^ T R                  5       nT	m[        R                  " TS:  =(       a    TS:  UU4S j5        [        R                  " TS:  =(       a    TS:  UU4S j5        [        R                  " TS:  =(       a    TS:  UU4S j5        T R                  S5      S:g  =(       a    T R                  S5      S:g  nU[        R                  :X  aC  [        R                  " US:H  =(       a    U=(       a    T R                  S5      S:g  U 4S	 j5        Or[        R                  " US:H  =(       a    T R                  S5      S:g  =(       a    U=(       d)    US:H  =(       a    U=(       a    T R                  S5      S:g  U 4S
 j5        [        R                  " TS-  T:  =(       a    TS-  T:  UUUU4S j5        [        R                  " TS:  =(       a    TS:  U
UU	UUU4S j5        g )Nr   c                     > ST  ST 3$ )Nz5kernel size should be greater than zero, but got kH: , kW: r2   )rk  rl  s   r6   re   $pool2d_shape_check.<locals>.<lambda>  s    Gt6RTQUVr8   c                     > ST  ST 3$ )Nz0stride should be greater than zero, but got dH: , dW: r2   )rm  rn  s   r6   re   r    s    B2$fRDQr8   c                     > ST  ST 3$ )Nz9dilation should be greater than zero, but got dilationH: , dilationW: r2   )	dilationH	dilationWs   r6   re   r    s    KI;Vcdmcnor8   r1   r   r#  r.   c                  *   > ST R                  5        3$ )NzExpected 4D (batch mode) tensor expected for input with channels_last layout with optional 0 dim batch size for input, but got: r   r	  s   r6   re   r    s     CCH::<.Rr8   c                  *   > ST R                  5        3$ )NzYExpected 3D or 4D (batch mode) tensor with optional 0 dim batch size for input, but got: r   r	  s   r6   re   r    s    opupzpzp|o}~r8   c                      > ST ST ST ST  3$ )NzKpad should be smaller than or equal to half of kernel size, but got padW = z	, padH = z, kW = z, kH = r2   )rk  rl  ro  rp  s   r6   re   r    s$     ygbT>r8   c                  .   > ST ST  ST ST ST ST S3$ NzGiven input size: (r;   z). Calculated output size: (z). Output size is too smallr2   )rq  rr  r.  rw  r/  r0  s   r6   re   r    s8    %k]!K=* N$$0><.+ O##r8   )r   rV   rh   r   r  )r   rk  rl  rm  rn  ro  rp  r  r  r.  rq  rr  r/  r0  r   r   
valid_dimsrw  s   ``````````````   @r6   rh  rh    s   " 99;DL	LL
Q26V 
LL
Q26Q 
LLA')a-o
 A!#:

1(:J+++AI;*;A!);R	
 	QY<5::a=A-<* A	?j?UZZ]a-?~	
 
LL
a4+B!GtO	> 
LLq.\Q.	# 	#r8   r  r  rk  rl  r  rm  rn  pTpHpW	dilationTr  r  r  r  r  r  r  r  r  c           
        ^ ^^^^^^^^^	^
^^^^^^^^^^^ T R                   n[        R                  " TS:  =(       a    TS:  =(       a    TS:  UUU4S j5        [        R                  " TS:  =(       a    TS:  =(       a    TS:  UUU4S j5        [        R                  " TS:  =(       a    TS:  =(       a    TS:  UUU4S j5        [        R                  " US;   UU 4S j5        [        U5       H@  mUS:X  a  TS:X  a  M  [        R                  " T R	                  T5      S:  UUU 4S j5        MB     U(       a;  [        R                  " TT:  =(       a    TT:  =(       a    TT:  UUUUUU4S	 j5        [        R                  " TS
-  T:  =(       a    TS
-  T
:  =(       a    TS
-  T	:  UUUU	UU
4S j5        [        R                  " TS:  =(       a    TS:  =(       a    TS:  UUUUUUU4S j5        g )Nr   c                     > ST ST  ST 3$ )Nz5kernel size should be greater than zero, but got kT: z, kH: r  r2   )rk  r  rl  s   r6   re   $pool3d_shape_check.<locals>.<lambda>  s    $fRDrd,r8   c                     > ST ST  ST 3$ )Nz0stride should be greater than zero, but got dT: z, dH: r  r2   )rm  r  rn  s   r6   re   r    s    >rd&FSURVWr8   c                     > ST ST  ST 3$ )Nz9dilation should be greater than zero, but got dilationT: z, dilationH: r  r2   )r  r  r  s   r6   re   r    s    #M)M)Vr8   r  c                  &   > T  STR                    3$ )Nz/: Expected 4D or 5D tensor for input, but got: rD  )r  r   s   r6   re   r    s    7)J5;;-Xr8   rK  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   r6   re   r    s.    ) --2[[M+EJJqM?:KMr8   c                  .   > ST ST  ST ST ST ST S3$ )Nzinput image (T: rT  r-  z ) smaller than kernel size (kT:  kH:  kW: r|   r2   )r  r  r  rk  r  rl  s   r6   re   r    s4    "5'gYd6( C$$&4uRDbT<r8   r   c                  ,   > ST ST ST  ST ST ST 3$ )NzHpad should be smaller than or equal to half of kernel size, but got kT: r  r  z padT: z padW: z padH: r2   )rk  r  rl  r  r  r  s   r6   re   r    s1    $eB4uRDt72$gbTKr8   r1   c                  :   > ST ST ST  ST ST ST ST ST S3$ r  r2   )r  r  r  r  r  r  r  s   r6   re   r  !  sD    !'!E7!G9AfX F((/y%'!F8 L'(r8   )r   rV   rh   r   r   )r   r  r  rk  rl  r  rm  rn  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r   s   `````````````````````  @r6   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!|	
 	
r8   c                 j   U R                   n[        U UUUUUUU	U
UUUUUUUUUUUU5        [        UUUS-
  U5        [        UUUS-
  U5        [        UUUS-
  U5        [        UUUS-
  U5        [        UUUS-
  U5        [        UUUS-
  U5        [        UUUS-
  U5        [        UUUS-
  U5        g )Nr#  r.   r   r1   r   r  rI  )r   r  r   r  r  rk  rl  r  rm  rn  r  r  r  r  r  r  r  r  r  r  r  r  r  r   s                           r6   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3r8   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 )Nr1   Tr#  r.   r   r  )r   r  r  r  rk  rl  r  rm  rn  r  r  r  r  r  r  r  r  r  r  r   s                       r6   r  r  g  s    * ::D








			-2 ;dQh8;dQh6;dQh8;dQh7r8   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$ )Nc                    ^  [         R                  " [        U5      S;   U 4S j5        US   n[        U5      S:X  a  UOUS   nX#4$ )NrL  c                     > ST  S3$ )Nzmax_pool2d: rN  r2   rO  s   r6   re   Emax_pool2d_checks_and_compute_shape.<locals>.unpack.<locals>.<lambda>  rQ  r8   r   r1   rR  rS  s   `   r6   rV  3max_pool2d_checks_and_compute_shape.<locals>.unpack  rX  r8   r  rY  c                      g)NzOmax_pool2d: stride must either be omitted, a single int, or a tuple of two intsr2   r2   r8   r6   re   5max_pool2d_checks_and_compute_shape.<locals>.<lambda>  r]  r8   r   r   r  r  rc  r  r   r#  c                      g)NzMnon-empty 4D (batch mode) tensor expected for input with channels_last layoutr2   r2   r8   r6   re   r    s    cr8   r  c                      g)Nz9non-empty 3D or 4D (batch mode) tensor expected for inputr2   r2   r8   r6   re   r        Or8   Fc                      g)NzAUnsupported memory format. Supports only ChannelsLast, Contiguousr2   r2   r8   r6   re   r    s    Wr8   )rV   rh   r   r   rO   r   r  r   r   rg  rh  )r   r  r   r  r  r-  rV  rk  rl  rm  rn  ro  rp  r  r  r.  rq  rr  r   r/  r0  s                        r6   r+  r+    sy    M;/FB	LLFy a 6{aB&)	7+JD!*h7I**R.K**R.KBJ//6M+++IIK1c	
 
%11	1IIK6!O	

 	W	

 (RriXL&z2RIVK



$ k11r8   c                 |  ^ ^^^^^ [        TX#XEU5      u  nmm[        R                  " TR                  T R                  :H  U U4S j5        UmTR                  mUUUU4S jn	U	" T 5        U	" U5        [
        R                  " T5      n
[        R                  " TR                  TR                  TR                  U
S9$ )Nc                  <   > STR                    ST R                    3$ )NzExpected dtype z  for `gradOutput` but got dtype r   r  s   r6   re   7meta_max_pool2d_with_indices_backward.<locals>.<lambda>  s    /$**-MkN_N_M`ar8   c                 l   > [        U TTS-
  T5        [        U TTS-
  T5        [        U TTS-
  T5        g )Nr.   r   r1   )rI  )r  rw  r   r/  r0  s    r6   _check_dim_size>meta_max_pool2d_with_indices_backward.<locals>._check_dim_size  s9    q$q,7q$q,7q$q+6r8   r  )
r+  rV   rh   r^   r   rO   r   r   r   r   )r  r   r  r   r  r  r-  r   r.  r  r   rw  r   r/  r0  s   ``         @@@@r6   %meta_max_pool2d_with_indices_backwardr    s     	,k7i		
 
LL

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

jj{{#	 r8   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$ r)  )
r+  r   r   rO   r   rV   r   r^   r   r   r,  s               r6   meta_max_pool2d_with_indicesr    s     	,FX		
  %yy{a/UZZ^QF//6Myy{a;7\?++<<'		
 	++<<'		
 r8   c                   ^ ^^^
^^ [         R                  " T R                  S;   U 4S j5        T R                  n[        US-
  U5       H1  m
[         R                  " T R	                  T
5      S:  U
U 4S j5        M3     [         R                  " [        T5      S:H  S 5        [         R                  " [        U5      S:H  S 5        T R	                  S	5      nT R	                  S
5      mT R	                  S5      mUS:X  a  T R	                  S5      nOSn[         R                  " T R                  TR                  :H  S 5        [         R                  " TR                  S:H  U4S j5        TR	                  S5      nTR	                  S5      nTR	                  S5      m
[         R                  " Xv:  S 5        [         R                  " X:H  S 5        [         R                  " T
S:H  U
4S j5        [         R                  " US   TS   -   S-
  T:*  UU4S j5        [         R                  " US   TS   -   S-
  T:*  UU4S j5        T R                  5       S:X  a  XeUS   US   /n	O
XRS   US   /n	[         R                  " U	T R                  T R                  S9[         R                  " U	[         R                  T R                  S94$ )Nr  c                  "   > ST R                    3$ )Nz:fractional_max_pool2d: Expected 3D or 4D tensor, but got: r  r   s   r6   re   ,meta_fractional_max_pool2d.<locals>.<lambda>@  s    LTYYKXr8   r.   r   c                  2   > STR                  5        ST  S3$ )Nz_fractional_max_pool2d: Expected input to have non-zero  size for non-batch dimensions, but got r  z emptyr   )r   r   s   r6   re   r  G  s%     77;yy{mCSTUSVV\^r8   r   c                      g)NzNfractional_max_pool2d: kernel_size musteither be a single int or tuple of Intsr2   r2   r8   r6   re   r  N       2r8   c                      g)NzOfractional_max_pool2d: output_size must either be a single int or tuple of Intsr2   r2   r8   r6   re   r  S  r  r8   rc  r  r   r#  r1   c                      g)Nz6Expect _random_samples to have the same dtype as inputr2   r2   r8   r6   re   r  a  s    Hr8   c                  "   > ST R                    3$ )Nz1Expect _random samples to have 3 dimensions got, r  )random_sampless   r6   re   r  e  s    CNDWDWCXYr8   c                      g)Nz=Expect _random_samples.size(0) no less then input batch size.r2   r2   r8   r6   re   r  m  r   r8   c                      g)Nz<Expect _random_samples.size(1) equals to input channel size.r2   r2   r8   r6   re   r  q      Nr8   c                     > ST  S3$ )Nz/Expect _random_samples.size(2) equals to 2 got .r2   )r   s   r6   re   r  s  s    #RSTRUUV!Wr8   c                     > STS    ST  3$ )Nz%fractional_max_pool2d: kernel height r   z' is too large relative to input height r2   )input_heightr  s   r6   re   r  w  s    7A7GGno{n|}r8   c                     > STS    ST  3$ )Nz$fractional_max_pool2d: kernel width r1   z& is too large relative to input width r2   )input_widthr  s   r6   re   r  {  s    6{1~6FFlmxlyzr8   r  )rV   rh   r   r   r   r   r^   r   r   r   r   )r   r  r  r  r   input_channelsinput_batchr  cr   r   r  r  s   `` `      @@@r6   meta_fractional_max_pool2dr  <  sf   	LL		VX 99D4!8T"IIaL1^	
 # 
LLKA	2
 
LLKA	2 YYr]N99R=L))B-Kqyiil	LL

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

 	++;;	
 r8   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$ )Nr  c                      gNzMmax_pool3d: kernel_size must either be a single int, or a tuple of three intsr2   r2   r8   r6   re   .meta_max_pool3d_with_indices.<locals>.<lambda>      _r8   r   r1   r   c                      gNzQmax_pool3d: stride must either be omitted, a single int, or a tuple of three intsr2   r2   r8   r6   re   r        cr8   c                      gNzImax_pool3d: padding must either be a single int, or a tuple of three intsr2   r2   r8   r6   re   r        [r8   c                      gNzJmax_pool3d: dilation must be either a single int, or a tuple of three intsr2   r2   r8   r6   re   r    r  r8   r  c                      gr  r2   r2   r8   r6   re   r    r  r8   rK  r*  rc  r  r   zmax_pool3d_with_indices()r#  r   r   )rV   rh   r   r   r   rg  r  rO   r   r  r  re  r   r   r1  )r   r  r   r  r  r-  r  rk  rl  r  rm  rn  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  input_channels_last_checkr   r   r   s                                  r6   meta_max_pool3d_with_indicesr    sB    
LLKF"_ 
QB;1$+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<r8   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$ )Nr  c                      gr  r2   r2   r8   r6   re   7meta_max_pool3d_with_indices_backward.<locals>.<lambda>  r  r8   r   r1   r   c                      gr  r2   r2   r8   r6   re   r    r	  r8   c                      gr  r2   r2   r8   r6   re   r    r  r8   c                      gr  r2   r2   r8   r6   re   r     r  r8   r  c                      gr  r2   r2   r8   r6   re   r  (  r  r8   r*  rc  r  r   z"max_pool3d_with_indices_backward()rK  r#  r   )rV   rh   r   r   r   r  rO   r   r  r  re  r   r   r1  )r  r   r  r   r  r  r-  r   r  rk  rl  r  rm  rn  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  s                                 r6   %meta_max_pool3d_with_indices_backwardr    s    
LLKF"_ 
QB;1$+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$6!)7799
'5500 6 
 	 -J]]1G1G]H
r8   gridc                   ^ ^^ [         R                  " T R                  TR                  :H  UU 4S j5        [         R                  " T R                  [         R                  :H  =(       a    TR                  [         R                  :H  UU 4S j5        [         R                  " T R
                  S   TR
                  S   :H  UU 4S j5        [         R                  " TR
                  S   T R                  S-
  :H  UU 4S j5        [        ST R                  5       H/  m[         R                  " T R
                  T   S:  UU 4S j5        M1     g )	Nc                  <   > STR                    ST R                    3$ )NzNgrid_sampler(): expected input and grid to be on same device, but input is on z and grid is on r  r  r   s   r6   re   +check_grid_sampler_common.<locals>.<lambda>d  s"    \\N"24;;-Ar8   c                  <   > STR                    ST R                    3$ )NzTgrid_sampler(): expected input and grid to have torch.strided layout, but input has z and grid has )r   r  s   r6   re   r  k  s!    nT[[MCr8   r   c                  <   > STR                    ST R                    3$ )NzZgrid_sampler(): expected grid and input to have same batch size, but got input with sizes  and grid with sizes rD  r  s   r6   re   r  r  s"      %},A$**Or8   r   r   c                  B   > STR                   S-
   ST R                   3$ )Nz+grid_sampler(): expected grid to have size r   z, in last dimension, but got grid with sizes )r   r   r  s   r6   re   r  y  s'    9%**q.9I J226**?r8   c                  *   > STR                    ST  S3$ )NzYgrid_sampler(): expected input to have non-empty spatial dimensions, but input has sizes r  r  rD  r  s   r6   re   r    r  r8   )rV   rh   r   r   r  r   r   r   )r   r  r   s   ``@r6   check_grid_sampler_commonr%  a  s    	LL#	
 
LL%F$++*F	
 
LLA$**Q-'	
 
LL

2%**q.(	
 1ejj!KKNQ	
 "r8   c                        \ rS rSrSrSrSrSrg)GridSamplerInterpolationi  r   r1   r   r2   N)r~   
__module____qualname____firstlineno__BILINEARNEARESTBICUBIC__static_attributes__r2   r8   r6   r'  r'    s    HGGr8   r'  interpolation_modec                 6  ^ ^ [         R                  " T R                  S:H  =(       a    T R                  TR                  :H  UU 4S j5        [         R                  " T R                  S:H  =(       a    U[        R                  R
                  :H  (       + S 5        g )NrK  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 r"  rD  r  s   r6   re   'check_grid_sampler_3d.<locals>.<lambda>  s!    449KK=#DJJ<1r8   c                      g)Nz<grid_sampler(): bicubic interpolation only supports 4D inputr2   r2   r8   r6   re   r2    r  r8   )rV   rh   r   r'  r-  r  )r   r  r/  s   `` r6   check_grid_sampler_3dr4    sp    	LL

a3EJJ$))3	
 
LLJJ!O M"&>&F&F&L&LL	
 	Or8   c                     US   nU(       a$  [         R                  " U[         R                  S9nOS n[         R                  " U[         R                  S9n	X4$ Nr   r   )rV   r  r   r   
r  r   r  r/  padding_modealign_cornersr'  input_requires_gradr  	grad_grids
             r6   grid_sampler_2d_backward_metar<    sO     &a.%%e5;R;RS

  U5L5LMI""r8   c                     [        X5        [        XU5        U R                  S   nU R                  S   nUR                  S   nUR                  S   nUR                  S   n	U R                  XVXxU	45      $ )Nr   r1   r   r.   )r%  r4  r   r   )
r   r  r/  r8  r9  r  Cout_Dout_Hout_Ws
             r6   grid_sampler_3drB    sn     e*%'9:AAAAJJqMEJJqMEJJqME??A%677r8   r;  c                     [        X5        [        XU5        US   nU(       a$  [        R                  " U[        R                  S9nOS n[        R
                  " U[        R                  S9n	X4$ r6  )r%  r4  rV   r  r  r   r7  s
             r6   grid_sampler_3d_backwardrD    sg     e*%'9:%a.%%!?!?

 
  U5S5STI  r8   c                     UR                  S5      nU(       d  [        R                  " U5      nXCS'   [        R                  " U /UQ70 UD6$ )Nr^   )r]   rO   	get_dtyperV   r   )r   r  rQ   r6  r^   s        r6   fullrG    sA    JJwE
+7O;;t-d-f--r8   c           	      V   U[         R                  :X  a  [         R                  " US L S 5        [         R                  " SUc  U R                  OUUUc  U R
                  OUUS9nU R                  (       a>  UR                  U R                  5       U R                  5       U R                  5       5        O/UR                  U R                  5       U R                  5       S5        UR                  S5        U$ [        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 tensorsr2   r2   r8   r6   re   zeros_like.<locals>.<lambda>  r  r8   r   r  Tr  )rV   
sparse_coorh   r   r^   r   	is_sparsesparse_resize_and_clear_r   
sparse_dim	dense_dimr   _coalesced_r+   r   r3  fill_)r   r^   r   r   r   r   r  s          r6   r  r    s     !!!T!O	

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

//
!
!# " C IIaLJr8   r   c                    Uc  [         R                  " 5       nUc  [         R                  " 5       nUc  [         R                  n[         R                  " XX#US9$ r  rV   r   get_default_devicer  r   r   r^   r   r   r   r   s         r6   	meta_onesrV    P     }'')~))+~;;&J r8   c                    Uc  [         R                  " 5       nUc  [         R                  " 5       nUc  [         R                  n[         R                  " XX#US9$ r  rS  rU  s         r6   
meta_zerosrY  -  rW  r8   c                 .    [         R                  " U 5      $ rB   rO   clone_preserve_strides)r   r4  r   r   s       r6   meta_select_scatterr]  C      ''--r8   c                 .    [         R                  " U 5      $ rB   r[  )r   r4  r   r   r   steps         r6   meta_slice_scatterra  H  r^  r8   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 $ )Nr   r1   zdim z out of bounds (r{   r|   r2   )r   rb  rc  r  r  s        r6   r   r   N  sg    {.C
!
C	SYR4u4DSEC5PQ)RR'
QwJr8   c                 L    U R                  5       S:X  a  S$ U R                  U   $ r  rF  )r  r   s     r6   ensure_nonempty_sizerf  Z  s!    11.!''#,.r8   c                 F  ^ ^^^ [        T R                  5       S5      n[        TR                  5       S5      n[        R                  " X4:H  S 5        [	        U5       H@  mTT:w  d  M  [        R                  " [        TT5      [        T T5      :*  UUUU 4S j5        MB     g )Nr1   c                      g)NzDIndex tensor must have the same number of dimensions as input tensorr2   r2   r8   r6   re   $gather_shape_check.<locals>.<lambda>d  s    Vr8   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 rD  )r   r   r   r   s   r6   re   ri  j  s5    ;A3>Nu{{m\/

|;QRUQVWXr8   )r  r   rV   rh   r   rf  )r   r   r   	self_dims
index_dimsr   s   ```  @r6   gather_shape_checkro  _  s}    DHHJ"IUYY[!$J	LLV 98LL$UA.2FtQ2OOX r8   c                   ^ SSK Jn  [        XR                  5       5      nU" TR	                  5       S:H  5      nU(       df  [
        R                  " TR                  [
        R                  :H  =(       d    TR                  [
        R                  :H  U4S j5        [        XT5        U R                  TR                  5      $ )Nr   r  c                  "   > ST R                    3$ )Nz8gather(): Expected dtype int32/int64 for index, but got r   r   s   r6   re   meta_gather.<locals>.<lambda>x  s    Nu{{m\r8   )r.  r  r   r   r   rV   rh   r^   r   r   ro  r   r   )r   r   r   sparse_gradr  wrapped_dimis_index_emptys     `    r6   meta_gatherrv  o  s~    D hhj1K#EKKMQ$67NKK5::%A		)A\	
 	4e4>>%++&&r8   c                     U(       a<  U S:X  a  gU S:X  a  gU S:X  a  gU S:X  a  gU S	:X  a  g
[         R                  " SS 5        g U S:X  a  gU S:X  a  g[         R                  " SS 5        g )Nr  
REDUCE_ADDr  REDUCE_MULTIPLYmeanREDUCE_MEANamaxREDUCE_MAXIMUMaminREDUCE_MINIMUMFc                      g)Nz=reduce argument must be either sum, prod, mean, amax or amin.r2   r2   r8   r6   re   #get_operator_enum.<locals>.<lambda>  s    Sr8   addmultiplyc                      g)Nz/reduce argument must be either add or multiply.r2   r2   r8   r6   re   r    s    $Ur8   rs  )reduce_use_new_optionss     r6   get_operator_enumr    s{    e$ ##S	
 	e
"$UUVr8   c                 n  ^  SSK Jn  U" UR                  5       S:g  5      (       aZ  [        R                  " UR
                  [        R                  :H  =(       d    UR
                  [        R                  :H  U 4S j5        Ub3  [        R                  " UR
                  UR
                  :H  U 4S j5        g g )Nr   )rt  c                     > T  S3$ )Nz((): Expected dtype int32/int64 for indexr2   method_names   r6   re   ,scatter_gather_dtype_check.<locals>.<lambda>  s    {m#KLr8   c                     > T  S3$ )Nz0(): Expected self.dtype to be equal to src.dtyper2   r  s   r6   re   r    s    {m#STr8   )r.  rt  r   rV   rh   r^   r   r   )r  r   r   src_optrt  s   `    r6   scatter_gather_dtype_checkr    sy    CU[[]a'((KK5::%A		)AL	

 JJ'--'T	
 r8   c                     [        U S5      $ r0   )r  r   s    r6   ensure_nonempty_dimr    s    sA;r8   c                 .  ^ ^^^ SSK Jn  U" TR                  5       S:H  5      (       a  g [        R                  " [        T R                  5       5      [        TR                  5       5      :H  S 5        Sn[        T R                  5       5      n[        U5       H+  n[        TU5      nUT:X  a  M  U[        T U5      :  d  M)  Sn  O   U(       d5  Tb2  [        U5       H#  n[        TU5      nU[        TU5      :  d  M!  Sn  O   Tbm  [        R                  " [        T R                  5       5      [        TR                  5       5      :H  S 5        [        R                  " U(       + UUU U4S j5        g [        R                  " U(       + UUU 4S j5        g )	Nr   r  c                      gNzCIndex tensor must have the same number of dimensions as self tensorr2   r2   r8   r6   re   %scatter_shape_check.<locals>.<lambda>  r  r8   FTc                      gr  r2   r2   r8   r6   re   r    s    Yr8   c                  b   > STR                    STR                    3ST  STR                    3-   $ )NExpected index rk  rl  z and to be no larger than src rD  )r   r   r   r  s   r6   re   r    s6    oekk]2Mdjj\Z&se+I'--YZr8   c                  H   > STR                    STR                    3ST  3-   $ )Nr  rk  rl  rD  )r   r   r   s   r6   re   r    s*    oekk]2Mdjj\Z&se,-r8   )	r.  r  r   rV   rh   r  r   r   rf  )	r   r   r   r  r  is_wrong_shaperm  r   index_d_sizes	   ````     r6   scatter_shape_checkr    sI   Dekkmq())	LLDHHJ'+>uyy{+KKU
 N#DHHJ/I 9+E158.tQ77!N  g1y!A/q9L27A>>!%	 " 
+/B599;/OOY	
 	Z	
 	-	
r8   c                     [        XR                  5       5      n[        SXU5        [        XX#5        Ub  [	        XE5        g g )Nscatter)r   r   r  r  r  )r   r   r   r4  r  r  rt  s          r6   scatter_meta_implr    s;     hhj1Ky$s;56'3 r8   c                 R    [        XX#S5        U R                  U R                  5      $ Nr  r  r   r   r   r   r   r4  s       r6   meta_scatter_addr    s!    dU3>>$**%%r8   c                      [        XX#S5        U $ r  r  r  s       r6   meta_scatter_add_r    s    dU3Kr8   c                     [        U[        R                  5      (       a  UOS n[        XX%U5        U R	                  U R
                  5      $ rB   )rr   rV   r   r  r   r   r   r   r   src_or_valuerl  r4  s         r6   meta_scatterr    s:     %\5<<@@,dCdV4>>$**%%r8   c                 f    [        U[        R                  5      (       a  UOS n[        XX%U5        U $ rB   )rr   rV   r   r  r  s         r6   meta_scatter_r    s,     %\5<<@@,dCdV4Kr8   queryr   r  	dropout_p	is_causalreturn_debug_maskr  c           	      4   U R                  S5      nU R                  S5      nU R                  S5      n	U R                  S5      n
UR                  S5      n[        R                  " U 5      n[        R                  " XxU	4[        R                  U R
                  S9nU(       a`  U
S:  a  SOSn[        R                  " X-  5      nUS::  a  SnOUS::  a  Sn[        R                  " XxX4U R                  U R
                  S9nO*[        R                  " SU R                  U R
                  S9n[        R                  R                  (       a#  [        R                  R                  5       (       d  [        U 5      S	:X  aI  [        R                  " S
[        R                  SS9n[        R                  " S
[        R                  SS9nOH[        R                  " S[        R                  SS9n[        R                  " S
[        R                  SS9nUUS S U	UUUU4	$ )Nr   r1   r   r.   r  @         r   r2   r   )r   rV   r   r   rZ   r   r  ceilr^   versionhipr   r  r   r   rf  )r  r   r  r  r  r  r  r   	num_headsmax_seqlen_batch_qhead_dimmax_seqlen_batch_k	attention	logsumexpblocksize_cmax_seqlen_k
debug_maskseedoffsets                      r6   (meta__scaled_dot_product_flash_attentionr    s    AJ

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

 [[%++ellK
 }}UZZ4466+e:LPU:U{{2UZZ?Ruzz&A{{Aell6BRu||FC 	
 
r8   	res_shape.c                   ^  [        T R                  5      U:X  a  [        R                  " T 5      nU$ [	        / SQU 4S jSS9nU Vs/ s H  oAU   PM	     nn[        [        U5      5       Vs/ s H  ocR                  U5      PM     nn[        R                  " UT R                  T R                  S9R                  U5      nU$ s  snf s  snf )N)r   r1   r   r.   c                 *   > TR                  5       U    $ rB   r  )idxr  s    r6   re   ,alloc_with_matching_layout.<locals>.<lambda>Z  s    %,,.*=r8   Tr   r  )rg   r   rV   r   sortedr   r   r   r   r^   r   r   )r  r  r  	dim_orderr  permuted_shaper   final_permutes   `       r6   alloc_with_matching_layoutr  R  s     U[[Y&u% J =t
	 5>>ISC.I>5:3y>5JK5J+5JKkk%++ell

'-
  	 J ?Ks   C.C
	attn_biascompute_log_sumexpc	           	         U R                  S5      n	U R                  S5      n
U R                  S5      nUR                  S5      nUR                  S5      nXX4n[        X5      n[        R                  " XUS4[        R                  U R
                  S9n[        R                  " S[        R                  SS9n[        R                  " S[        R                  SS9nUUS S UUUUS 4	$ Nr   r1   r   r   r  r2   r   r   r  rV   r   rZ   r   r   )r  r   r  r  r  r  r  r  r  r  rT  S_QS_KVD_Vr  r  
logsum_expr  r  s                      r6   (meta__scaled_dot_product_cudnn_attentionr  e  s     	

1A

1A
**Q-C88A;D
**R.Cs I
$U
6C	
sAkk||J ;;rF;D[[5::f=F 	
 
r8   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                     r6   5meta__scaled_dot_product_fused_attention_overrideabler    s     	

1A
**Q-C
**Q-C88A;D
**R.C"I
$U
6C	
kk||J ;;rF;D[[5::f=F 	
 
r8   r  r  	cum_seq_q	cum_seq_kmax_qmax_kphilox_seedphilox_offsetc                     [         R                  " U5      n[         R                  " U5      n[         R                  " U5      nUUU4$ rB   r:  )r  r  r   r  r   r  r  r  r  r  r  r  r  r  r  grad_qgrad_kr?  s                     r6   'meta__scaled_dot_product_flash_backwardr    sA    , e$Fc"Fe$F66!!r8   	attn_maskc                    U R                  S5      nU R                  S5      nU R                  S5      n	[        R                  " U 5      n
[        R                  " UU	U4[        R                  U R
                  S9R                  SS5      nU
U4$ )Nr   r1   r   r  )r   rV   r   r   rZ   r   r  )r  r   r  r  r  r  r  r   r  r  r  r  s               r6   0meta__scaled_dot_product_flash_attention_for_cpur    s     AJ

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

 kk|| i1o  	 r8   c
                 `   [         R                  " UR                  5       SUR                  UR                  S9n
[         R                  " UR                  5       SUR                  UR                  S9n[         R                  " UR                  5       SUR                  UR                  S9nXU4$ )Nr   r   r1   r.   r  )rV   empty_permutedr   r^   r   )r  r  r   r  r   r  r  r  r  r  r  r  r?  s                r6   9meta__scaled_dot_product_flash_attention_for_cpu_backwardr    s    & !!

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

kk||	F 6!!r8   dropout_maskc                   ^ ^^^^^^^ S nU" T 5      u  mmU" U5      u  pU" U5      u  pTR                   u  mmmmU	R                   u  pmn
UUUUUU U4S jnUUUUU4S jnTS:  d  UT:  a  TS:  a  U" 5       $ U" 5       $ )Nc                 p   U R                  5       S:X  a  U R                  S5      S4$ U R                  5       S:  ax  Sn[        U R                  5       S-
  5       H  nXR                  U   -  nM     U R	                  XR                  S5      U R                  S5      U R                  S5      5      S4$ U S	4$ )
Nr.   r   Tr#  r1   rc  r  r   F)r   r  r   r   viewr   )r;   r   r   s      r6   	ensure_4dBmeta__scaled_dot_product_attention_math_for_mps.<locals>.ensure_4d.  s    557a<;;q>4''UUWq[J1557Q;'ggaj(
 (66*ffRj!&&*affRjI4OOe8Or8   c                  j  > TR                  TR                  5      n T	(       a  U R                  T5      n TR                  TTTT45      nT	(       aa  TR                  5       S:X  a  UR	                  S5      nX4$ [        TR                  S S 5      UR                  SS -   nUR                  U5      nX4$ )Nr.   r   rc  r1   r#  )r   r   view_asr   squeezer   r  )
r   attnr   r   max_seq_lengthnum_headq_q_sizer  
unsqueezeds
      r6   sdpa_vector_fast_mpsMmeta__scaled_dot_product_attention_math_for_mps.<locals>.sdpa_vector_fast_mps@  s    ll288$++e$C||Z6>JKyy{a||A y U[["-.Aa@yy'yr8   c                  p   > Sn TR                  TR                  5      nTR                  TTTU T45      nX4$ )Nrj  r  )blocksr   r6  r   	head_sizer  r  r  s      r6   sdpa_vector_2pass_mpsNmeta__scaled_dot_product_attention_math_for_mps.<locals>.sdpa_vector_2pass_mpsN  s<    ll288$||Z669$UV  r8   i   i   rD  )r  r   r  r  r  r  r  r  r  k_rR   v_k_sizer  r  r   r   r  r  r  r  r  s   `              @@@@@@@r6   /meta__scaled_dot_product_attention_math_for_mpsr  #  s    	 u%NB
cNEBeEB.0hh+J&)#%88 A~q ! ! 	$FVO$8N$&&#%%r8   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$ )
Nr1   r   r   r  r   r  rj  r2   r   )r  r   rV   r   r^   r   r  r  r   r  r  r  rZ   r   )r  r   r  r  r  r  r  r  r  r  r  Kvr  logsumexp_dimr  r  r  s                    r6   ,meta__scaled_dot_product_efficient_attentionr
  Z  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&((r8   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   r1   r   r.   r  r  r   ri  .)r   rV   r  r^   r   r   r   )r  r  r   r  r  r   r  r  r  r  r  r  r  r   r  r  r  
head_dim_vr  r  r  r?  	grad_biaslastDimlastDimAligned	new_sizess                             r6   +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$57R<'TV,;V)*	&	"KKY__Y5E5E
	 c8G8m,	669,,r8   c                     [         R                  " U5      n[         R                  " U5      n[         R                  " U5      nUUU4$ rB   r:  )r  r  r   r  r   r  r  r  r  r  r  r  r  r  r  r  r  r  r?  s                      r6   'meta__scaled_dot_product_cudnn_backwardr    sA    . e$Fc"Fe$F66!!r8   window_size_leftwindow_size_right	seqused_kalibi_slopesc                    Uc  U R                  S5      OUR                  5       S-
  nUc  U R                  S5      OUnUc  UR                  S5      OUnU R                  S5      nU R                  S5      n[        R                  " U 5      nUc2  [        R                  " UUU4[        R
                  U R                  S9nOAU R                  S5      n[        R                  " UU4[        R
                  U R                  S9nU	(       ac  US:  a  SOSn[        R                  " UU-  5      nUS::  a  SnOUS::  a  Sn[        R                  " UUUU4U R                  U R                  S9nO*[        R                  " SU R                  U R                  S9nS	u  nn[        R                  R                  (       al  [        R                  R                  5       (       aI  [        R                  " S
[        R                  SS9n[        R                  " S
[        R                  SS9nOH[        R                  " S[        R                  SS9n[        R                  " S
[        R                  SS9nUUUUU4$ )Nr   r1   r  r   r  r  r  r  NNr2   r   r   )r   r   rV   r   r   rZ   r   r  r  r^   r  r  r   r  r   rf  )r  r   r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r  r  total_qr  r  r  r  r  s                               r6   meta__flash_attention_forwardr    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 r8   c                     [         R                  " U5      n[         R                  " U5      n[         R                  " U5      nUUU4$ rB   r:  )r  r  r   r  r   r  r  r  r  r  r  r  r  r  r  r  r  
grad_querygrad_key
grad_values                       r6   meta__flash_attention_backwardr!  0  sA    0 !!%(J$H!!%(Jx++r8   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$ )	Nr   r1   r  r   r  rj  r2   r   )	r   rV   r   r^   r   r  r  rZ   r   )r  r   r  rE  r"  r#  r$  r  r  r%  r  r  r&  r'  r(  r  r  r  r  r  r  logsumexp_batch_dimactual_max_seqlen_qactual_max_seqlen_kr	  r  r  r  s                               r6   !meta__efficient_attention_forwardr-  O  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Rr8   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$ )Nr1   c                      g)Nz,seqlen must match for `shared_storage_dqdkdvr2   r2   r8   r6   re   4meta__efficient_attention_backward.<locals>.<lambda>  s    Br8   r.   c                      g)Nz3embedding dim must match for `shared_storage_dqdkdvr2   r2   r8   r6   re   r3        Ir8   r   r  r   r  rc  r   ri  .r2   r  )
rV   rh   r   r   r^   r   r  r   r   r   )r  r  r   r  rE  r"  r#  r$  r  r  r  r  r  r%  r.  r  r/  r0  chunkr  r  r   r  r  r  r  s                             r6   "meta__efficient_attention_backwardr7    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6r8   scale_ascale_bscale_resultuse_fast_accumc                   ^ ^^^^^^^^ S n[         R                  " T R                  5       S:H  =(       a    TR                  5       S:H  UU 4S j5        [         R                  " U" T R                  5      =(       a    U" TR                  5      UU 4S j5        [	        T 5      S:X  d  [	        T 5      S:X  GaR  S n	S n
S	 n[         R                  " U	" T R                  5       5      =(       d    U" T 5      U 4S
 j5        [         R                  " U
" TR                  5       5      =(       d    U" T5      U4S j5        [         R                  " T R                  S5      S-  S:H  U 4S j5        [         R                  " TR                  S5      S-  S:H  =(       a    TR                  S5      S-  S:H  U4S j5        T R                  u  mmTR                  S5      mTR                  [         R                  :H  =(       a    TR                  [         R                  :H  =(       dA    TR                  [         R                  :H  =(       a    TR                  [         R                  :H  nTR                  5       S:X  am  TR                  5       S:X  aY  [         R                  " TR                  [         R                  :H  =(       a    TR                  [         R                  :H  S 5        GO%U(       a  TR                  [         R                  :X  a  SnTS-  mOSnSn[        TU5      n[        US5      S-  nU[        TU5      -  U-  mU[        TU5      -  U-  mTR                  5       T:X  ab  TR                  5       T:X  aN  [         R                  " TR                  5       S 5        [         R                  " TR                  5       S 5        GO?[         R                  " SUUUU4S j5        GO[         R                  " TR                  [         R                  :H  =(       a    TR                  [         R                  :H  S 5        [         R                  " TR                  5       S:H  =(       a    TR                  5       S:H  UU4S j5        TR                  S5      T:X  a}  TR                  S5      S:X  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        OTR                  S5      T:X  aX  TR                  S5      TR                  S5      s=:X  a  [        TS5      :X  a#  O  O TR                  S5      [        TS5      :X  a  OTR                  S5      T:X  aN  TR                  S5      TR                  S5      s=:X  a  [        TS5      :X  a  O  OTR                  S5      T:X  a  O[         R                  " SUUUUU4S j5        Ub  UOT R                  n[         R                  " T R                  S5      TR                  S5      UT R                  S9$ )Nc                     U [         R                  [         R                  [         R                  [         R                  [         R
                  4;   $ rB   rV   rd  float8_e5m2float8_e4m3fnuzfloat8_e5m2fnuzfloat4_e2m1fn_x2r   s    r6   is_fp8_or_fp4_type2_check_scaled_mm_sizes.<locals>.is_fp8_or_fp4_type  A    !!!!""
 
 	
r8   r   c                  L   > STR                  5        ST R                  5        3$ Nz%Inputs must be 2D but got self.dim()=z and mat2.dim()=r   rR  r   s   r6   re   (_check_scaled_mm_sizes.<locals>.<lambda>  %    7
|CSTXT\T\T^S_`r8   c                  <   > STR                    ST R                    3$ Nz?Expected both inputs to be fp8 or fp4 types but got self.dtype=z and mat2.dtype=r   rH  s   r6   re   rI    $    QRVR\R\Q]]mnrnxnxmyzr8   r   r   c                 6    U S   U S   :  =(       a    U S   S:H  $ r  r2   r  s    r6   is_row_major,_check_scaled_mm_sizes.<locals>.is_row_major  "    !9vay(;VAY!^;r8   c                 0    U S   S:H  =(       a    U S   S:  $ r  r2   r  s    r6   is_col_major,_check_scaled_mm_sizes.<locals>.is_col_major      !9>3fQi!m3r8   c                 `    U R                  S5      S:H  =(       d    U R                  S5      S:H  $ r  r   	tensor_2ds    r6   has_zero_dim,_check_scaled_mm_sizes.<locals>.has_zero_dim  )    >>!$)CY^^A->!-CCr8   c                  *   > ST R                  5        3$ Nz#self must be row_major, got stride r  r   s   r6   re   rI        9$++-Ir8   c                  *   > ST R                  5        3$ Nz#mat2 must be col_major, got stride r  rR  s   r6   re   rI    r^  r8   r1   ri  r   c                  ,   > ST R                  S5       3$ NzBExpected self.size(1) to be divisible by 16, but got self.size(1)=r1   r   r   s   r6   re   rI        XY]YbYbcdYeXfgr8   c                  "   > ST R                    3$ Nz?Expected both dimensions of mat2 to be divisible by 16 but got rD  ra  s   r6   re   rI        UVZV`V`Uabr8   c                      g)NzNFor tensorwise scaling, both scale_a and scale_b must be float (fp32) tensors.r2   r2   r8   r6   re   rI    s    hr8   rj  r  r#  c                      g)Nzscale_a must be contiguousr2   r2   r8   r6   re   rI  +      8r8   c                      g)Nzscale_b must be contiguousr2   r2   r8   r6   re   rI  /  rj  r8   Fc            	      Z   > ST  STR                  5        ST STR                  5        S3	$ )NzTInvalid blockwise scaling configuration. For blockwise scaling, scale_a should have  elements, got z, scale_b should have r  r  )expected_a_sizeexpected_b_sizer8  r9  s   r6   re   rI  4  sC    FFUEVVefmfsfsfuev w//>.?w}}N__`br8   c                      g)NzKFor rowwise scaling, both scale_a and scale_b must be float (fp32) tensors.r2   r2   r8   r6   re   rI  =  s    er8   c                  P   > ST R                  5       < STR                  5       < 3$ )NzLFor non-tensorwise scaling, scale tensors must be 2D, but got scale_a.dim()=z and scale_b.dim()=r   r8  r9  s   r6   re   rI  B  s*    gY`YdYdYfXhh|nunynyn{m}~r8   c                      g)Nz@Both scale_a and scale_b must be contiguous for rowwise scaling.r2   r2   r8   r6   re   rI  N  s    ^r8   c                  J  > ST ST ST S[        T S5       S3	S[        T S5       S[        TS5       ST S[        T S5       S3	-   S[        T S5       ST S	TR                  S
5       STR                  S5       STR                  S
5       STR                  S5       S3-   $ Nz}Invalid scaling configuration. For tensorwise scaling, both scales should be scalar. For rowwise scaling, scale_a should be (z, 1), scale_b should be (1, z>). For (BlockWise1x128, BlockWise128x128), scale_a should be (r{   r  z), zscale_b should be (z<). For (BlockWise1x128, BlockWise1x128), scale_a should be (z). Got scale_a.size()=(r   r1   z) and scale_b.size()=(r|   r7   r   )_krg  r  r8  r9  s   r6   re   rI  b  s    CCD#Eabcad eVVWUXXZ[cdfhk[lZmmpr 0S0A/B"XaQTEUDV WTTUSVVXYabdfiYjXkknp	p 0S0A/B"QC H//6||A.?r',,q/AR S//6||A.?r',,q/ARRSUUr8   r  )rV   rh   r   r^   r   r   r   r   float8_e8m0fnurd  r   ra  r7   re  r   r   )r   rR  r8  r9  rE  r:  rG  r;  rC  rO  rS  rY  is_blockwise_scalingblock_size_kblock_size_mnnum_k_blockspadded_num_k_blocks
_out_dtyperw  rn  ro  rg  r  s   ````              @@@@@r6   _check_scaled_mm_sizesr    s   
 
LL
a+DHHJ!O` 
LL4::&I+=djj+Iz
 4F"k$&75&@	<	4	D 	'=<+=I	
 	'=<+=I	
 	IIaL2"g	
 	IIaL2"=tyy|b'8A'=b	
 

2IIaL !5!55 :MMU%9%99
 !4!44 9MMU%8%88 	 ==?aGMMOq$8LL.Q7==EMM3Qh " }} 3 33  "!V!M#B5L"*<";a"? M ::=PP  M ::=PP 
 ?2MMO6))+8 ))+8
  LL.Q7==EMM3Qe
 LL"9w{{}'9~ Q1$LLOq(LLOq(LLOq( ))+G0E0E0G^
 Q1$LLOw||AK(2s:KKLLOx3'77 Q1$LLOw||AK(2s:KKLLOq(  
 
 (3J;;tyy|TYYq\DKKXXr8   c           
          [        XX#XEXg5      $ rB   )r  )r   rR  r8  r9  rE  r:  rG  r;  s           r6   meta_scaled_mmr  s  s     "Gd) r8   scale_recipe_ascale_recipe_b	swizzle_a	swizzle_bc           
        ^ ^^^^^	^^^^ ^!^"^#^$^% S nS n[         R                  " T R                  5       S:H  =(       a    TR                  5       S:H  UU 4S j5        [         R                  " U" T R                  5      =(       a    U" TR                  5      UU 4S j5        T R                  S   mT R                  S   mTR                  S   m U" T R                  5      (       a  U" TR                  5      (       a  SnTU-  mU Vs/ s H  n[        U5      PM     nnU Vs/ s H  n[        U5      PM     nnT(       a  T Vs/ s H  n[        U5      PM     snmO[        R                  /mT	(       a  T	 Vs/ s H  n[        U5      PM     snm	O[        R                  /m	[        T 5      S:X  d  [        T 5      S	:X  GaU  S
 nS nS n[         R                  " U" T R                  5       5      =(       d    U" T 5      U 4S j5        [         R                  " U" TR                  5       5      =(       d    U" T5      U4S j5        [         R                  " T R                  S5      S-  S:H  U 4S j5        [         R                  " TR                  S5      S-  S:H  =(       a    TR                  S5      S-  S:H  U4S j5        S[        [
           S[        [
           4S jnS[        [
           S[        [
           4S jnS[        [
           S[        [
           4S jnS[        [
           S[        [
           4S jnS[        [
           S[        [
           4S jnS[        [
           S[        [
           4S jnS[        [
           S[        [
           4S jnU" X55      (       a  [         R                  " TS   R                  5       S:H  =(       ad    TS   R                  5       S:H  =(       aG    TS   R                  [         R                  :H  =(       a     TS   R                  [         R                  :H  S 5        G	OU" X55      (       a  [         R                  " TS   R                  S   T:H  =(       a    TS   R                  5       T:H  =(       ad    TS   R                  [         R                  :H  =(       a=    TS   R                  5       T :H  =(       a     TS   R                  [         R                  :H  UUUU 4S j5        G	OU" X55      (       Ga  TS   R                  [         R                  :H  =(       a     TS   R                  [         R                  :H  nTS   m$T$R                  S   T:H  =(       a    T$R                  S   TS-  :H  =(       ac    T$R                  S5      S:H  =(       aH    T$R                  S5      T:H  =(       d-    T$R                  S   S:H  =(       a    T$R                  S5      S:H  nTS   m%T%R                  S   T :H  =(       a    T%R                  S   TS-  :H  =(       ac    T%R                  S5      S:H  =(       aH    T%R                  S5      T :H  =(       d-    T%R                  S   S:H  =(       a    T%R                  S5      S:H  n[         R                  " U=(       a    U=(       a    UUUU U$U%4S j5        GOIU" X55      (       Ga  TS   R                  [         R                  :H  =(       a     TS   R                  [         R                  :H  n[        TS-  S5      mTS   m$T$R                  S   T:H  =(       a    T$R                  S   TS-  :H  =(       ac    T$R                  S5      S:H  =(       aH    T$R                  S5      T:H  =(       d-    T$R                  S   S:H  =(       a    T$R                  S5      S:H  nTS   m%T%R                  S   T :H  =(       a    T%R                  S   TS-  :H  =(       ac    T%R                  S5      S:H  =(       aH    T%R                  S5      T :H  =(       d-    T%R                  S   S:H  =(       a    T%R                  S5      S:H  n[         R                  " U=(       a    U=(       a    UUUUU U$U%4S  j5        GOwU" X55      (       Ga  TS   R                  [         R                  :H  =(       a     TS   R                  [         R                  :H  n[        TS-  S5      mTS   m$T$R                  S   T:H  =(       a    T$R                  S   TS-  :H  =(       ac    T$R                  S5      S:H  =(       aH    T$R                  S5      T:H  =(       d-    T$R                  S   S:H  =(       a    T$R                  S5      S:H  nTS   m%T%R                  S   T:H  =(       a    T%R                  S   T S-  :H  =(       ac    T%R                  S5      S:H  =(       aH    T%R                  S5      T:H  =(       d-    T%R                  S   S:H  =(       a    T%R                  S5      S:H  n[         R                  " U=(       a    U=(       a    UUUUU U$U%4S! j5        GOU" X55      (       Ga  [         R                  R                   (       ac  [#        T R                  S   S"5      T R                  S   -  m![#        T R                  S   S"5      T R                  S   -  m"[        R                  m#O[        T R                  S   S5      [        [#        T R                  S   S"5      S5      -  m![        TR                  S   S5      [        [#        T R                  S   S"5      S5      -  m"[        R$                  m#[         R                  " TS   R                  5       T!:H  =(       a    TS   R                  [         R&                  :H  =(       a[    TS   R                  5       T":H  =(       a>    TS   R                  [         R&                  :H  =(       a    TS   T#:H  =(       a    T	S   T#:H  U!U"U#UUUU	4S# j5        GOU" X55      (       Ga  [        TS5      [        [#        TS5      S5      -  m![        T S5      [        [#        TS5      S5      -  m"[        R$                  m#[         R                  " TS   R                  5       T!:H  =(       Ga
    TS   R                  [         R(                  :H  =(       a    TS   R                  5       S:H  =(       a    TS   R                  [         R                  :H  =(       a    TS   R                  5       T":H  =(       a    TS   R                  [         R(                  :H  =(       a[    TS   R                  5       S:H  =(       a>    TS   R                  [         R                  :H  =(       a    TS   T#:H  =(       a    T	S   T#:H  U!U"U#UUUU	4S$ j5        O[         R                  " S%UUU UU4S& j5        Ub  UOT R                  n[         R*                  " TT UT R,                  S'9$ s  snf s  snf s  snf s  snf )(Nc                     U [         R                  [         R                  [         R                  [         R                  [         R
                  4;   $ rB   r>  r   s    r6   rC  5_check_scaled_mm_sizes_v2.<locals>.is_fp8_or_fp4_type  rE  r8   c                 *    U [         R                  4;   $ rB   )rV   rB  r   s    r6   is_fp4_type._check_scaled_mm_sizes_v2.<locals>.is_fp4_type  s    //111r8   r   c                  L   > STR                  5        ST R                  5        3$ rG  r   rH  s   r6   re   +_check_scaled_mm_sizes_v2.<locals>.<lambda>  rJ  r8   c                  <   > STR                    ST R                    3$ rL  r   rH  s   r6   re   r    rM  r8   r   r1   r   r   c                 6    U S   U S   :  =(       a    U S   S:H  $ r  r2   r  s    r6   rO  /_check_scaled_mm_sizes_v2.<locals>.is_row_major  rQ  r8   c                 0    U S   S:H  =(       a    U S   S:  $ r  r2   r  s    r6   rS  /_check_scaled_mm_sizes_v2.<locals>.is_col_major  rU  r8   c                 `    U R                  S5      S:H  =(       d    U R                  S5      S:H  $ r  r   rW  s    r6   rY  /_check_scaled_mm_sizes_v2.<locals>.has_zero_dim  r[  r8   c                  *   > ST R                  5        3$ r]  r  r   s   r6   re   r    r^  r8   c                  *   > ST R                  5        3$ r`  r  ra  s   r6   re   r    r^  r8   ri  c                  ,   > ST R                  S5       3$ rc  r   r   s   r6   re   r    rd  r8   c                  "   > ST R                    3$ rf  rD  ra  s   r6   re   r    rg  r8   recipe_arecipe_bc                     [        U 5      S:H  =(       aH    [        U5      S:H  =(       a3    U S   [        R                  :H  =(       a    US   [        R                  :H  $ r  )r   r&   
TensorWiser  r  s     r6   is_tensorwise0_check_scaled_mm_sizes_v2.<locals>.is_tensorwise  sT    H" :MQ&:QK;#9#99: QK;#9#99	r8   c                     [        U 5      S:H  =(       aH    [        U5      S:H  =(       a3    U S   [        R                  :H  =(       a    US   [        R                  :H  $ r  )r   r&   RowWiser  s     r6   
is_rowwise-_check_scaled_mm_sizes_v2.<locals>.is_rowwise  sT    H" 7MQ&7QK;#6#667 QK;#6#66	r8   c                     [        U 5      S:H  =(       aH    [        U5      S:H  =(       a3    U S   [        R                  :H  =(       a    US   [        R                  :H  $ r  )r   r&   BlockWise1x32r  s     r6   is_mx(_check_scaled_mm_sizes_v2.<locals>.is_mx  sT    H" =MQ&=QK;#<#<<= QK;#<#<<	r8   c                 0   [        U 5      S:H  =(       a    [        U5      S:H  =(       am    U S   [        R                  :H  =(       aP    U S   [        R                  :H  =(       a3    US   [        R                  :H  =(       a    US   [        R                  :H  $ )Nr   r   r1   )r   r&   BlockWise1x16r  r  s     r6   is_nv(_check_scaled_mm_sizes_v2.<locals>.is_nv  s    H" :MQ&:QK;#<#<<: QK;#9#99: QK;#<#<<	:
 QK;#9#99r8   c                     [        U 5      S:H  =(       aH    [        U5      S:H  =(       a3    U S   [        R                  :H  =(       a    US   [        R                  :H  $ r  )r   r&   BlockWise1x128r  s     r6   is_1x128_1x1281_check_scaled_mm_sizes_v2.<locals>.is_1x128_1x128  sT    H" >MQ&>QK;#=#==> QK;#=#==	r8   c                     [        U 5      S:H  =(       aH    [        U5      S:H  =(       a3    U S   [        R                  :H  =(       a    US   [        R                  :H  $ r  )r   r&   r  BlockWise128x128r  s     r6   is_1x128_128x1283_check_scaled_mm_sizes_v2.<locals>.is_1x128_128x128  sW    H" @MQ&@QK;#=#==@ QK;#?#??	r8   c                     [        U 5      S:H  =(       aH    [        U5      S:H  =(       a3    U S   [        R                  :H  =(       a    US   [        R                  :H  $ r  )r   r&   r  r  r  s     r6   is_128x128_1x1283_check_scaled_mm_sizes_v2.<locals>.is_128x128_1x128  sT    H" >MQ&>QK;#?#??> QK;#=#==	r8   c                      g)Nz\For Tensorwise scaling, both scale_a and scale_b must be single element float (fp32) tensorsr2   r2   r8   r6   re   r     s    vr8   c            	         > STR                   S    STS   R                  5        ST R                   S    STS   R                  5        S3	$ )Nz'For Rowwise scaling, scale_a must have r   z elements (got: z), and scale_b must have r1   r|   )r   r   )rR  r8  r9  r   s   r6   re   r  )  s\    =djjm_L\]def]g]m]m]o\p q//3zz!}o=MgVWjN^N^N`Maabdr8   r  c                     > ST ST S-   STR                    ST STR                   ST ST S-   STR                    ST STR                   S3$ )Nz>For 1x128 x 1x128 blockwise scaling, scale a must have shape [r{   r  ] (got: ) and stride [1, )scale b must have shape [r|   r   r   )r  r  r  sasbs   r6   re   r  F  sy    001s"Q#XJhrxxjPabcaddlmomvmvlw x001s"Q#XJhrxxjPabcaddlmomvmvlwwxzr8   r#  c                     > ST STS-   STR                    ST STR                   ST ST S-   STR                    ST STR                   S3$ )Nz]For 128x128 x 1x128 blockwise scaling, L4 = {round_up(K / 128, 4)}, scale a must have shape [r{   r  r  r  r  r|   r  r  L4r  r  r  r  s   r6   re   r  e  sy    002t2a3hZxzQbcebffnoqoxoxny z001s"Q#XJhrxxjPabcaddlmomvmvlwwxzr8   c                     > ST ST S-   STR                    ST STR                   ST STS-   STR                    ST STR                   S3$ )Nz]For 1x128 x 128x128 blockwise scaling, L4 = {round_up(K / 128, 4)}, scale a must have shape [r{   r  r  r  r  r|   r  r  s   r6   re   r    sy    001s"Q#XJhrxxjPabcaddlmomvmvlw x002t2a3hZxzQbcebffnoqoxoxnyyz|r8   rj  c                     > ST  STS   R                  5        ST STS   R                  5        S[        R                   STS   R                   STS   R                   ST S	TS    STS    S
3$ )Nz!for MX scaling scale_a must have  (got: r   ) and scale_b must have z). Scales must have types z (for self: 	, mat_b: z) Must have swizzle type  (got self: r|   )r   rV   rx  r^   expected_scale_a_elemsexpected_scale_b_elemsexpected_swizzler8  r9  r  r  s   r6   re   r    s    78N7OwW^_`WaWgWgWiVj k--C,DGGTUJL\L\L^K_ `""'"6"6!7|GAJDTDTCUU^_fgh_i_o_o^p q..>-?|IVWL>Ybclmncobppqsr8   c                     > ST  STS   R                  5        ST STS   R                  5        ST STS    STS    S3$ )	Nz!for NV scaling scale_a must have r  r   r  z). Must have swizzle type r  r  r|   r  r  s   r6   re   r    sq    78N7OwW^_`WaWgWgWiVj k--C,DGGTUJL\L\L^K_ `$$4#5\)A,yYbcdYeXffgir8   Fc                  b  > ST ST ST S[        T S5       S3	S[        T S5       S[        TS5       ST S[        T S5       S3	-   S[        T S5       ST S	TS
   R                  S
5       STS
   R                  S5       STS
   R                  S
5       STS
   R                  S5       S3-   $ ru  rv  )r  r  r  r8  r9  s   r6   re   r    s   ??@cA]^_]` aRRSQTTVW_`acfWgVhhkm ,HQ,<+=RC@P?Q RPPQsRTU]^_adUeTffik	k ,HQ,<+=Rs C++21:??1+=*>bQRAS@T U++21:??1+=*>bQRAS@TTUWWr8   r  )rV   rh   r   r^   r   r&   r'   
NO_SWIZZLEr   r   r   r   r   ra  r=   r  r  r7   SWIZZLE_32_4_4rx  rd  r   r   )&r   rR  r8  r  r9  r  rE  rG  r  r  r;  rC  r  K_packed_multipliersirO  rS  rY  r  r  r  r  r  r  r  types_ok
scale_a_ok
scale_b_okr~  r  r  r  r  r  r  r  r  r  s&   ``` `   ``                   @@@@@@@@@r6   _check_scaled_mm_sizes_v2r    s(   
2 
LL
a+DHHJ!O` 
LL4::&I+=djj+Iz 	

1A

1A

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

	D$5 	kAR 		k!2 	d;>O 		D- 	k9J 		D- 	k9J 		T+%6 	${BS 		tK'8 	DDU 		tK'8 	DDU 	 88LL
  "a' 6AJ$$&!+6AJ$$56 AJ$$5v 77LL
  #q( 6AJ$$&!+6AJ$$56 AJ$$&!+6 AJ$$5
 N;;
 
  EMM1Wgaj6F6F%--6W  Bq  THHQK18+TIIaLA%T YYq\Q&R288A;!+;+Q		!PQ@Q	  Bq  THHQK18+TIIaLA%T YYq\Q&R288A;!+;+Q		!PQ@Q	  LL6Z6J  n== 
  EMM1Wgaj6F6F%--6W  !c'1%BBr! UHHQK18+UIIaLA%U YYq\R'SBHHQK1,<,R1QRAR	  Bq  THHQK18+TIIaLA%T YYq\Q&R288A;!+;+Q		!PQ@Q	  LL6Z6J  n== 
  EMM1Wgaj6F6F%--6W  !c'1%BBq  THHQK18+TIIaLA%T YYq\Q&R288A;!+;+Q		!PQ@Q	  Br! UHHQK18+UIIaLA%U YYq\R'SBHHQK1,<,R1QRAR	  LL6Z6J  >22}}  )1$**Q-)DtzzRS})T&)1$**Q-)DtzzRS})T&#.#9#9 )1$**Q-)ETZZ]B/I *& *2$**Q-)ETZZ]B/I *& $/#=#= LL
  "&<< 5AJ$$(<(<<5AJ$$&*@@5 AJ$$(<(<<5 aL$44	5
 aL$44  >22%-a%5!RRS8T%T"%-a%5!RRS8T%T"*99LL
  "&<< 	5 	5AJ$$(;(;;	5AJ$$&!+	5 AJ$$5	5 AJ$$&*@@		5
 AJ$$(;(;;	5 AJ$$&!+	5 AJ$$5	5 aL$44	5 aL$44 $ LL
 
 (3J;;q!:dkkBBw @? : :s   y
#yy:yr  contraction_dimsc                 (    [        U UUUUUUU	UUUS9$ )N)rE  rG  r  r  r;  )r  )r   rR  r8  r  r  r9  r  r  rE  r  r  r;  s               r6   meta_scaled_mm_v2r    s2     %% r8   c           	      P    [        XX#USS9  U R                  U R                  5      $ NT)r  r  r   r   r   r4  rl  rj  s         r6   meta_scatter_reduce_twor    s%     dVTJ>>$**%%r8   c           	          [        XX#USS9  U $ r  r  r  s         r6   meta_scatter_reduce__twor    s    dVTJKr8   c                |  ^  [         R                  " ST R                  5       s=:  =(       a    S:*  Os  U 4S j5        T R                  5       S:X  a.  [         R                  " U[         R                  T R
                  S9$ [         R                  " T R                  S5      U[         R                  T R
                  S9$ )Nr   r   c                  *   > ST R                  5        3$ )NzAThe probability distributions dimensions must be 1 or 2, but got r   r	  s   r6   re   "meta_multinomial.<locals>.<lambda>  s    STYT]T]T_S`ar8   r1   r  )rV   rh   r   r   r   r   r   )r   num_samplesreplacementr  s   `   r6   meta_multinomialr    s     
LL	EIIK1a yy{a{{;ejjNN;;

1{%**U\\ r8   c                 $    SnU  H  nX-  nM	     U$ r0   r2   )vsrp  vs      r6   multiply_integersr    s    	A	 Hr8   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   r6   re   'upsample_common_check.<locals>.<lambda>  s    78H7IY\]hYiXjkr8   r   c                  &   > ST  S[        T5       3$ )Nz$It is expected input_size equals to r  r  )expected_input_dimsr  s   r6   re   r    s    67J6K?[^_i[jZklr8   c              3   *   #    U  H	  oS :  v   M     g7fr   Nr2   rt   r  s     r6   rv   (upsample_common_check.<locals>.<genexpr>  s     *>aE>   c              3   *   #    U  H	  oS :  v   M     g7fr  r2   r  s     r6   rv   r    s     2N+Qq5+r  c                     > ST  ST 3$ )NzDInput and output sizes should be greater than 0, but got input size z and output size r2   )r  r  s   r6   re   r    s      \!2;-Ar8   )rV   rh   r   r  )r  r  r  r  channelsr  s   ```  @r6   upsample_common_checkr    s    	LLK,,k +Q.	LLJ..l
 
LL*:ab>**Ns2N+2N/N	A ""1~F+{++r8   c                 8  ^  [         R                  " T R                  5       S:g  =(       d    [        T R	                  5       SS  5      U 4S j5        [        T R	                  5       USS9nT R                  U5      R                  [        R                  " T 5      S9$ )Nr   r1   c                  *   > ST R                  5        3$ )Nz>Non-empty 3D data tensor expected but got a tensor with sizes r   r	  s   r6   re   $upsample_nearest1d.<locals>.<lambda>*      PQVQ[Q[Q]P^_r8   r  r   
rV   rh   r   r  r   r  r   r1  rO   r   )r   r  scalesfull_output_sizes   `   r6   upsample_nearest1dr	  $       
LLA/

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

kA ??+,//11%8 0  r8   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$ )	Nr   r1   c                  *   > ST R                  5        3$ Nz>Non-empty 4D data tensor expected but got a tensor with sizes r   r	  s   r6   re   $upsample_nearest2d.<locals>.<lambda>:  r  r8   r   r  r   r#  r   )rV   rh   r   r  r   r  r   rO   r   r   r   r}   r   
contiguous)	r   r  scales_hscales_wr	  r  r   rR   
n_channelss	   `        r6   upsample_nearest2dr	  4  s     
LLA/

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

kA __-.F //6M  ++A1a||F"zA~//];FMr8   r  r  r		  r
	  c                 X  ^ ^^ [        X!SS9m[        R                  " T R                  S:H  U 4S j5        [	        S5       H5  m[        R                  " T R                  T5      TT   :H  UU U4S j5        M7     T R                  U5      R                  [        R                  " T 5      S9$ )Nr   r  r#  c                  "   > ST R                    3$ NzFExpected grad_output to be a tensor of dimension 4 but got: dimension r  r  s   r6   re   -upsample_nearest2d_backward.<locals>.<lambda>`      XYdYiYiXjkr8   c            
      D   > ST ST T    ST STR                  T5       3$ )NzCExpected grad_output to have the same shape as output; output.size() = z but got grad_output.size(r   r	  r  r   s   r6   re   r	  e  s9      !s$'7':&;,QCtK4D4DQ4G3HJr8   r   )
r  rV   rh   r   r   r   r   r1  rO   r   )r  r  r  r		  r
	  r	  r   s   `    @@r6   upsample_nearest2d_backwardr	  N  s     -! 
LLAk 1XQ#3A#66	
    ,//11+> 0  r8   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$ )Nr   r1   c                  *   > ST R                  5        3$ )Nz>Non-empty 5D data tensor expected but got a tensor with sizes r   r	  s   r6   re   $upsample_nearest3d.<locals>.<lambda>w  r  r8   r.   r  r   r  )r   r  scales_dr		  r
	  r	  s   `     r6   upsample_nearest3dr	  q  r	  r8   c                    [         R                  " U 5      [         R                  " U [         R                  S9pvUb  Ub  [        U[        5      (       d   e[        U[        5      (       d   eUR
                  nUR                  5       n	[        XH5      n[        XX5      nUR                  X5        UR                  X5        [        XdS9  [        XuS9  XE4$ Xg4$ )Nr   )r  r  )
rV   r   r   rr   r   r   r   r   r   r!   )
r   stabler   
descendingr   r   r  r   r   
out_strides
             r6   	meta_sortr	    s     D!5#3#3D#Lqg1&*----':.... GG	XXZ
"65#G791I2344Kr8   c           	      >  ^ ^^^^^^^ [         R                  " T R                  S:H  U 4S j5        [         R                  " T R                  TR                  :H  UU 4S j5        T R	                  S5      mTb  [         R                  " TR                  S:H  U4S j5        [         R                  " TR                  5       T:H  UU4S j5        [         R                  " TR                  TR                  :H  UU4S j5        [         R                  " TR                  S:H  U4S j5        T R	                  S	5      T-  T-  m[         R                  " TR                  5       T:H  UUUU U4S
 j5        [         R                  " [        U 4S jTTTT4 5       5      S 5        g )Nr   c                  "   > T R                    S3$ Nz != 2r  )input_gatess   r6   re   %rnn_cell_checkSizes.<locals>.<lambda>      ;3C3C2DE0Jr8   c                  :   > TR                    ST R                    3$ N != rD  )hidden_gatesr#	  s   r6   re   r$	    s    ;$$%T,*<*<)=>r8   r1   c                  "   > T R                    S3$ )Nz != 1r  )
input_biass   r6   re   r$	    s    joo5Fe3Lr8   c                  .   > TR                  5        ST  3$ r'	  r  )
gates_sizer+	  s   r6   re   r$	    s    z'')*$zl;r8   c                  :   > TR                    ST R                    3$ r'	  rD  )hidden_biasr+	  s   r6   re   r$	    s    z''([->->,?@r8   c                  "   > T R                    S3$ r"	  r  )prev_hiddens   r6   re   r$	    r%	  r8   r   c            
      `   > TR                  5        STR                  S5       ST ST ST  S3
$ )Nr(	  r   z * z // z (aka r|   )r   r   )expected_prev_hidden_numelfactorr-	  r#	  r1	  s   r6   re   r$	    s@    ;$$&'tK,<,<Q,?+@J<tTZS[[ab|a}}~r8   c              3   V   >#    U  H  nUR                   TR                   :H  v   M      g 7frB   r  )rt   r;   r#	  s     r6   rv   &rnn_cell_checkSizes.<locals>.<genexpr>  s*      
 J HH***Is   &)c                      g)Nz%expected all inputs to be same devicer2   r2   r8   r6   re   r$	    s    7r8   )rV   rh   r   r   r   r   r  )r#	  r)	  r+	  r/	  r4	  r1	  r3	  r-	  s   ``````@@r6   rnn_cell_checkSizesr8	    sE    
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r8   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$ )Nr#  r   )r8	  rV   r   r   )r#	  r)	  cxr+	  r/	  	workspacehycys           r6   _thnn_fused_lstm_cell_metar>	    se     :ArR  E<S<STI			"E,C,C	DB			"E,C,C	DBIr8   c                    [        U5      S:g  nU(       a   [        U5      nUS   nU R                  S   nOLU
(       a  U R                  S   OU R                  S   nU
(       a  U R                  S   OU R                  S   nSnU(       a  SOSnUS:w  a  UOUnU(       a  UUU-  /nOU
(       a  UUUU-  /OUUUU-  /nU R                  U5      nU	U-  UU/nUc   [        R                  " SU R
                  S9nOUR                  U5      nUR                  U	U-  UU/5      nU(       a  SOSnU R                  U[        R                  S9nUUUUU4$ )Nr   r1   r   r   r  r   )r   r   r   rV   r   r   r  )r   rC  weight_stride0
weight_bufhxr:	  rl  hidden_size	proj_size
num_layersbatch_firstdropouttrainbidirectionalbatch_sizesdropout_stateis_input_packed
seq_length
mini_batchbatch_sizes_sumnum_directionsout_sizer   r  
cell_shaper=	  r<	  reserve_shapereserves                                r6   
_cudnn_rnnrU	    sS   & +&!+O%
 ^
++a.'2U[[^A
'2U[[^A
'QQN%NyH$h&?@	  X%>?j(^*CD 	
 __Y'F~-z;GJ	z[[5<<0\\*%	zN2JI	JB AAMoom5;;o?G2r7J..r8   c                 >   U(       a  U R                   S   OU R                   S   nU(       a  U R                   S   OU R                   S   nU
nU(       a  UUU/OUUU/nU R                  U5      nUc   [        R                  " SU R                  S9nOUR                  UR                   5      nUc   [        R                  " SU R                  S9nOUR                  UR                   5      n[        R                  " SU R                  [        R
                  S9nUUUU4$ )Nr1   r   r  r   )r   r   rV   r   r   r  )r   w0w1w2w3hx_cx_r   rJ	  rl  rC	  rE	  
has_biasesrI	  rF	  rH	  rM	  rN	  output_chanelsr   r  r<	  r=	  r;	  s                           r6   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$$r8   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$ )Nz4: Expected reduction dim -1 or 0 for scalar but got r2   r   r  s   r6   re   'zero_numel_check_dims.<locals>.<lambda>7  s    wiSTWSXYr8   c                     > T ST  S3$ )Nz: Expected reduction dim z to have non-zero size.r2   rb	  s   r6   re   rc	  <  s    wi8=TUr8   )r   rV   r   r   )r   r   r  s    ``r6   zero_numel_check_dimsre	  3  sR    yyA~1H!r	Y	

 	IIcNaU	
r8   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$ )Nz@: Expected reduction dim to be specified for input.numel() == 0.r2   rO  s   r6   re   %check_argmax_argmin.<locals>.<lambda>H  s    tf\]r8   )r   r   re	  rV   rh   r   )r  r   r   s   `  r6   check_argmax_argminri	  A  s?    
S((*-d.JJLA]	
r8   c                     [        SX5        [        R                  " U R                  Ub  U4OS 5      n[	        XU5      nU R                  U[        R                  S9$ )Nargmaxr   )ri	  rO   r  r   r  r   rV   r   )r   r   r  r  r   s        r6   argmax_argmin_metarl	  L  sM    $,

coSF4PD$T9E>>%u{{>33r8   c                 v    U[         R                  :X  a  [         R                  n[         R                  " SXX4S9$ )Nr2   r  )rV   jaggedr  r   )r  r^   r   r   r   s        r6   scalar_tensorro	  T  s1    
 ;;
%v r8   c                    [        X R                  5       SS9nU R                  5       S:X  a  SOU R                  U5      n[        R                  " US:  5        [        R                  " X:*  S 5        [        U R                  5      n[        U5      S:  a  XU'   U R                  U5      U R                  U[        R                  S94$ )NTrc  r   r1   c                      g)Nzk not in range for dimensionr2   r2   r8   r6   re   topk_meta.<locals>.<lambda>f  s    )Gr8   r   )
r   r   r   rV   rh   r   r   r   r   r   )r   rT  r   largestr  	sliceSizetopKSizes          r6   	topk_metarw	  `  s     hhjd
;CXXZ1_$))C.I	LLa	LL!GHDJJH
8}q>>(#T^^HEKK^%PPPr8   c                     Uc
  Uc   S5       eUR                  5       nU R                  5       n	[        R                  " UU	R                  U	R                  U	R
                  S9$ )Nz;segment_reduce(): Either lengths or offsets must be defined)r^   r   r   )r	  rV   r   r^   r   r   )
rl  r  r|  rl  rw  rx  ry  r{  data_contiggrad_contigs
             r6   meta__segment_reduce_backwardr{	  n  sj    
 '"5 E5 //#K//#K!!!!	 r8   c                   ^ SSK Jn  [        TU R                  5       SS9mU R                  5       S:  a  U R	                  T5      OSn[
        R                  " U" US:  X:*  5      U4S j5        [        U R                  S T U R                  TS-   S  -   5      nU(       a&  U R                  5       S:  a  UR                  TS5        U R                  U5      U R                  U[
        R                  S94$ )Nr   )r  Trq	  r1   c                     > ST  3$ )Nz9kthvalue(): selected number k out of range for dimension r2   r   s   r6   re   kthvalue_meta.<locals>.<lambda>  s    KC5Qr8   r   )r.  r  r   r   r   rV   rh   r   r   r9  r   r   )r   rT  r   r  r  dimSizer   s     `    r6   kthvalue_metar	    s     >
dhhjd
;C $
QdiinAG	LLQ%Q
 DS!DJJsQwy$99:E488:>S!>>% $..ekk."JJJr8   c                    U b  U OUn[         R                  " UR                  5       S:H  S 5        UR                  5       nU b)  [         R                  " U R                  5       U:H  S 5        Ub)  [         R                  " UR                  5       U:H  S 5        [         R                  " UR                  5       U:H  S 5        [         R                  " UR                  5       U:H  S 5        [         R                  " UR                  5       S:H  S 5        [         R                  " UR	                  5       US   US	   -  S
-  :H  S 5        g )Nr   c                      gN r2   r2   r8   r6   re   (checkLSTMBackwardSizes.<locals>.<lambda>  s    "r8   c                      gr	  r2   r2   r8   r6   re   r	        r8   c                      gr	  r2   r2   r8   r6   re   r	    r	  r8   c                      gr	  r2   r2   r8   r6   re   r	        r8   c                      gr	  r2   r2   r8   r6   re   r	    r	  r8   c                      gr	  r2   r2   r8   r6   re   r	    s    rr8   r   r1   r#  c                      gr	  r2   r2   r8   r6   re   r	    s    Rr8   )rV   rh   r   r   r   )grad_hygrad_cyr:	  r=	  r;	  defined_gradexp_sizes          r6   checkLSTMBackwardSizesr	    s    %17wL	LL!!#q(*5  "HW\\^x/<W\\^x/<	LLh&
3	LLh&
3	LLA%z2	LL"hqkHQK&?!&CCZPr8   c                     U c  Uc  g[        XX#U5        [        R                  " U[        S9n[        R                  " U[        S9nU(       a  UR	                  SSS9OS nXgU4$ )NNNNr   r   F)r  )r	  rV   r   legacy_contiguous_memory_formatr  )	r	  r	  r:	  r=	  r;	  has_bias
grad_gatesgrad_cxr  s	            r6   #_thnn_fused_lstm_cell_backward_implr	    sf    7?7RY?!!!@J r1PQG4<
q%0$I	))r8   c                 2   S nS nS nUS   (       a  UR                  U R                  5       5      nUS   (       d
  US   (       aQ  UR                  UR                  S5      U R                  S5      45      nUR                  UR                  S5      5      nXEU4$ )Nr   r1   r   r   r!  )r#  r"  r$  r'  r  grad_weightr  s          r6   linear_backwardr	    s    JKI1~!++FKKM:
1~Q",,l.?.?.CV[[QS_-UV **<+<+<R+@A	Y//r8   c                   ^ ^ [        T R                  5      S:  a  T R                  S   X-  -  S:X  d   ST R                   SU 35       eS mUU 4S jnT R                  S   X-  -  nT R                  S   U-  nT R                  S	   U-  n/ T R                  S S QUPUPUP7nT R                  U5      nUR                  U" 5       S
9nU$ )Nr   rc  r   z'Invalid input shape for pixel_shuffle: z with upscale_factor = c                 b    [         R                  R                  U 5      [         R                  :H  $ rB   r  r  s    r6   r  ,meta_pixel_shuffle.<locals>.is_channels_last  s$    ""88=ATATTTr8   c                  F  > T " T5      (       a/  [        T5      S:X  a  [        R                  $ [        R                  $ TR	                  [        R                  S9(       a  [        R                  $ TR	                  [        R
                  S9(       a  [        R
                  $ g )Nr   r   )r   rV   r   r  re  preserve_format)r  r   s   r6   r  .meta_pixel_shuffle.<locals>.pick_memory_format  s    D!!4 F*...***e.E.EF***e.C.CD((( Er8   r  r   r   )r   r   r   r1  )	r   upscale_factorr  r>  HrWrr   r   r  s	   `       @r6   meta_pixel_shuffler	    s     	DJJ!

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

2>:;A	B.	(B	B.	(B-$**Sb/-1-b-"-I
..
#C
&&13&
4CJr8   c                 X   U R                  U R                  5      nUR                  UR                  5      nUR                  UR                  5      nUR                  UR                  5      nUR                  UR                  5      nUR                  UR                  5      nUUUUUUU4$ rB   r  )r   weight0weight1weight2weight3r[	  cx_tmpr  hy_cy_grad_output_r_optgrad_hy_r_optgrad_cy_r_optr   rl  rC	  rE	  r]	  rH	  rI	  rJ	  rF	  r;	  diff_xdiff_hxdiff_cxdiff_w1diff_w2diff_bs                                r6   mkldnn_rnn_layer_backwardr	    s    4 __U[[)FmmCII&Gv||,G.G.Gw}}-F7GVVWgEEr8   )	out_int32r   c                    [         R                  " U U(       a  [         R                  O[         R                  [         R                  S9$ )Nr^   r   )rV   r   rK  r   r   )r   
boundariesr	  r   s       r6   meta_bucketizer	    s2     &ekkEKK-- r8   c                   ^ ^^^^ Sm[        T 5      S:X  a)  [        R                  " T R                  5       U 4S j5        [        T 5      S:X  a+  T R                  5       (       a  [        R
                  " S5        [        R                  " [        T[        5      UU4S j5        [        R                  " TS:  UU4S j5        [        R                  " [        T[        5      UU4S	 j5        [        R                  " [        T[        5      UU4S
 j5        [        R                  " TT:  U4S j5        [        R                  " TT R                  T R                  S9$ )Nzhistc()r  c                  $   > ST R                    S3$ )Nz%"histogram_cpu" not implemented for 'r  r   r	  s   r6   re   meta_histc.<locals>.<lambda>  s    =ekk]!Lr8   r   z%_histc_cuda with floating point inputc                  $   > T S[        T 5       3$ )Nz#: argument 'bins' must be int, not r=  binsr  s   r6   re   r	    s    7)>tDzlKr8   r   c                     > T ST  3$ )Nz: bins must be > 0, but got r2   r	  s   r6   re   r	    s    gY.J4&#Qr8   c                  $   > T  S[        T5       3$ )Nz%: argument 'min' must be Number, not r=  )r  r  s   r6   re   r	        7)@cLr8   c                  $   > T  S[        T5       3$ )Nz%: argument 'max' must be Number, not r=  )r  r  s   r6   re   r	  #  r	  r8   c                     > T  S3$ )Nz: max must be larger than minr2   )r  s   r6   re   r	  %  s    y0M%Nr8   r   )r   rV   rh   r   rO   r1  rr   r   r   r   r   r^   )r   r	  r  r  r  s   ````@r6   
meta_histcr	    s     G5U"##%L	
 5V#(?(?(A(A%%&MN	LL4!K 
LLQR	LL3L 
LL3L 
LLNO;;tELLDDr8   c                 F  ^  [        T R                  5       USS9n[        R                  " T R	                  5       S:g  =(       d#    [        S T R                  5       SS   5       5      U 4S j5        T R                  U5      R                  [        R                  " T 5      S9$ )Nr   r  r   c              3   *   #    U  H	  oS :  v   M     g7fr  r2   )rt   r   s     r6   rv   ,meta_upsample_bimode2d_aa.<locals>.<genexpr>7  s     !H7Gt(7Gr  r1   c                  *   > ST R                  5        3$ r	  r   r	  s   r6   re   +meta_upsample_bimode2d_aa.<locals>.<lambda>8  r  r8   r   )
r  r   rV   rh   r   r  r   r1  rO   r   )r   r  r9  r		  r
	  r	  s   `     r6   meta_upsample_bimode2d_aar	  )  s     -

kA 
LLHc!Huzz|AB7G!HH_ ??+,//11%8 0  r8   c                 T  ^ ^^ [        X!SS9m[        R                  " T R                  S:H  U 4S j5        [	        S5       H3  m[        R                  " T R
                  T   TT   :H  UU U4S j5        M5     T R                  U5      R                  [        R                  " T 5      S9$ )Nr   r  r#  c                  "   > ST R                    3$ r	  r  r  s   r6   re   4meta_upsample_bimode2d_aa_backward.<locals>.<lambda>M  r	  r8   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   r6   re   r	  R  s>     DDE3dK[\]K^J_ `D!1!1!!4 59r8   r   )
r  rV   rh   r   r   r   r   r1  rO   r   )r  r  r  r9  r		  r
	  r	  r   s   `     @@r6   "meta_upsample_bimode2d_aa_backwardr	  ?  s     -! 
LLAk 1Xa $4Q$779	
    ,//11+> 0  r8   c                 X   [         R                  " UR                  5       S:H  S 5        [         R                  " UR                  5       S:H  S 5        [         R                  " UR                  R                  S 5        [         R                  " UR                  R                  S 5        g )Nr1   c                      g)Nz%found_inf must be a 1-element tensor.r2   r2   r8   r6   re   <_amp_foreach_non_finite_check_and_unscale_.<locals>.<lambda>_      (Or8   c                      g)Nz%inv_scale must be a 1-element tensor.r2   r2   r8   r6   re   r	  b  r	  r8   c                      g)Nz!found_inf must be a float tensor.r2   r2   r8   r6   re   r	  f      3r8   c                      g)Nz!inv_scale must be a float tensor.r2   r2   r8   r6   re   r	  j  r	  r8   )rV   rh   r   r^   r   )r   r9  	inv_scales      r6   *_amp_foreach_non_finite_check_and_unscale_r	  \  s|    	LLQ O 
LLQ O 
LL))3 
LL))3r8   c                 .    [         R                  " U 5      $ rB   r:  )r   nanposinfneginfs       r6   
nan_to_numr	  o  r  r8   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   rV   r  
sparse_cscr  
sparse_bscr   r   r   r   r   r   )r   dim0r  ndimsr   r   s         r6   r  r  u  s    ;;	   IU\]  IIE$&D$&D|		D$++- F!'v|FL&,!ZDJ
T"Kr8   c                 "   U R                   nU R                  (       a;  U R                  5       nU R                  5       nUS::  a  US:X  d   SU SU S35       eOU R	                  5       S::  d   SU S35       e[        U SUS:  a  S5      $ S5      $ )	Nr   r   zEt_ expects a tensor with <= 2 sparse and 0 dense dimensions, but got z sparse and z dense dimensionsz6t_ expects a tensor with <= 2 dimensions, but self is r4  r1   )r   rL  rN  rO  r   r  )r   r	  rN  rO  s       r6   t_r	    s    IIE~~__&
NN$	Q9> 	
!l,yk9JL	
1>
 xxzQ 	
DUG1M	
 dAEAIq55155r8   )r	  r   sidesorterc                  ^ ^^ [         R                  " [        T R                  5      S:*  =(       d    T R                  S S TR                  S S :H  UU 4S j5        [         R                  " TS L =(       d    T R                  TR                  :H  U U4S j5        [         R                  " US:g  =(       d    U(       + S 5        U(       a  [         R                  O[         R
                  n[        T[         R                  5      (       a$  [         R                  " TU[         R                  S9$ [         R                  " SUT R                  S	9$ )
Nr1   r   c                  `   > S[        TR                  5       S[        T R                  5       3$ )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   r6   re   #meta_searchsorted.<locals>.<lambda>  s3    3378M8M3N2O P""&tzz"2!35r8   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   r6   re   r	    sB    ##'(=(=#>"??V%+%7tFLL!@B=?@Br8   r   c                      g)Nzetorch.searchsorted(): side and right can't be set to opposites, got side of left while right was Truer2   r2   r8   r6   re   r	    s     $r8   r	  r2   r  )rV   rh   r   r   rK  r   rr   r   r   r   r   r   )r	  r   r	  r   r	  r	  r^   s   ``   ` r6   meta_searchsortedr	    s     
LLO!!"a' 	9  "%CR8	
	 
LL$?///6<<?	
 
LL#e)	$ %EKK%++E$%%U-D-D
 	
 {{2U?3I3IJJr8   c                    ^  [         R                  " T [         R                  [         R                  [         R                  4;  U 4S j5        g )Nc                     > ST  3$ )Nz/Unsupported input type encountered for isin(): r2   r   s   r6   re   3_check_for_unsupported_isin_dtype.<locals>.<lambda>  s    A%Ir8   )rV   rh   r  
complex128	complex64r   s   `r6   !_check_for_unsupported_isin_dtyper	    s/    	LLejj%"2"2EOODDIr8   c                 H    U R                  X R                  S5      45      nU$ )Nr   r!  )r  r   num_weightsr  r  r	  s         r6   meta_embedding_dense_backwardr	    s(     ''6F6Fr6J(KLKr8   c                 t    U	(       a  [         R                  U UUUUUUUU
U5
      $ [        U UUUUUUUU
U5
      $ rB   )r+   _embedding_bag_sparse_backward!meta_embedding_bag_dense_backward)rl  r   rx  r!  r"  maximum_indicesr	  r  rl  r  r	  r  s               r6   meta_embedding_bag_backwardr
    se     22
 	
 1
 	
r8   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$Unsupported input type encountered: r   )rl  s   r6   re   3meta_embedding_bag_dense_backward.<locals>.<lambda>$  s    6tzzlCr8   r1   )
rV   rh   r^   rb  rc  ra  float64r  r   r   )rl  r   r!  r"  r
  r	  r  rl  r	  r  index_grad_weights   `          r6   r 
  r 
    sv     
LL

u}}ennemmU]]SSC x_D01TYYq\'BCr8   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	$ )Nr1   c                      g)NzHembedding_bag_backward: per_sample_weights only supported for mode='sum'r2   r2   r8   r6   re   @meta_embedding_bag_per_sample_weights_backward.<locals>.<lambda>9  r%  r8   r   r   )r   rV   rh   r  r   r   )
rl  rC  r   rx  r!  rl  r  embedding_featuresr  r  s
             r6   .meta_embedding_bag_per_sample_weights_backwardr
  ,  s     1	LLZ 
LLq!	LL!#$,,q/K	LL"#	LLQ#556^^[N+FMr8   )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$ )Nc                      g)Nz<At least one of elements and test_elements must be a Tensor.r2   r2   r8   r6   re   meta_isin.<locals>.<lambda>I  r  r8   r  r   )
rV   rh   rr   r   r:  r   r	  r^   r   r  )elementstest_elementsr
  r
  s       r6   	meta_isinr
  D  s     
LL8V$I
=&(IN h''<<1E1EFmV,,]??K%hnn5%m&9&9:HEJJ77r8   r  c                     [         R                  " U S:  S 5        [        U[        R                  S9u  p#[         R
                  " XS9$ )Nr   c                      g)Nz,polygamma(n, x) does not support negative n.r2   r2   r8   r6   re    meta_polygamma.<locals>.<lambda>Y  s    !Or8   r  r   )rV   rh   r   r   r  r   )r  r   rR   rS   s       r6   meta_polygammar
  V  sB     
LLaOP(;HHOA D55r8   c                     [        S5      e)Nz.Tensor.item() cannot be called on meta tensors)r0  r   s    r6   meta_local_scalar_denser
  a  s    
G
HHr8   c                 .    [         R                  " U 5      $ rB   r:  r   s    r6   silur
  f  r  r8   c                 ^    [        U [        R                  S9u  p[        R                  " XS9$ r  )r   r   r  rV   r   )r   rR   rS   s      r6   sigmoidr
  l  s/     );HHOA D55r8   c                 |   U R                  5       S:H  nUR                  5       S:H  nU(       a  U(       a4  UR                  S5      U R                  S5      UR                  S5      /nGO*[        R                  " UR                  S5      UR                  S5      :H  S 5        U R                  S5      UR                  S5      /nOU(       a\  [        R                  " UR                  S5      U R                  S5      :H  S 5        U R                  S5      UR                  S5      /nOk[        R                  " U R                  S5      UR                  S5      :H  S 5        U R                  S5      U R                  S5      UR                  S5      /nU=(       d    U R                  n[        R
                  R                  (       aV  SUR                  -  nUS   U-   S-
  U-  U-  nXE:X  a  US   U-  US/n	OUS/n	[        R                  " XiX0R                  S	9n
U
$ [        R                  " XcU R                  S	9n
U
$ )
Nr   r   r1   c                      gNz matrix batch sizes have to matchr2   r2   r8   r6   re   2_create_grouped_mm_output_tensor.<locals>.<lambda>      6Xr8   r   c                      gr!
  r2   r2   r8   r6   re   r"
    r#
  r8   c                      g)Nzbatched dimension has to matchr2   r2   r8   r6   re   r"
    s    6Vr8   ri  r  )r   r   rV   rh   r^   r  r   itemsizer2  r   r   )rP  rR  offsrG  
mat1_is_2d
mat2_is_2drQ	  	alignmentsize_paddedr	  r   s              r6    _create_grouped_mm_output_tensorr,
  v  s   qJqJ		!diilDIIaLAHLL		!		!,.X 		!diim4HLL		!		!,.X 		!diil3H LL		!		!,.V 		!diilDIIbMBH'TZZI}}),,,	|i/!3	AIM#"1+3[!DJ%q)J!!	++

 J kk(DKKHJr8   mat_amat_br'
  c	                   ^ ^^^^^ [         R                  " TS L TS L :H  S 5        TS L=(       a    TS Ln	U	(       a  [         R                  R                  (       a  [         R                  O[         R
                  n
[         R                  " T R                  U
:H  =(       a    TR                  U
:H  U U4S j5        O[[         R                  " T R                  [         R                  :H  =(       a    TR                  [         R                  :H  U U4S j5        [         R                  " T R                  5       S;   =(       a    TR                  5       S;   U U4S j5        T R                  5       S:H  nTR                  5       S:H  nU(       a  U(       d9  [         R                  " T R                  S5      TR                  S5      :H  S	 5        U	(       aH  S
 nS n[         R                  " U" T 5      U 4S j5        [         R                  " U" T5      U4S j5        S nU" ST 5        U" ST5        TGbD  TGb@  [         R                  " TR                  [         R                  :H  =(       a    TR                  [         R                  :H  =(       dA    TR                  [         R                  :H  =(       a    TR                  [         R                  :H  UU4S j5        TR                  [         R                  :H  =(       a    TR                  [         R                  :H  mSU4S jjnTb  U(       a  U(       a  TR                  S   OSnU" STT SU5        U" STTSU5        [         R                  " US L S 5        U(       d  U(       a  [         R                  " TS LU U4S j5        Tbb  [         R                  " TR                  5       S:H  U4S j5        [         R                  " TR                  [         R                  :H  U4S j5        O[         R                  " TS L S 5        [         R                  " US L S 5        [         R                  " US L =(       d    U[         R                  :H  S 5        [        T TTU5      $ )Nc                      g)Nz,Either both scale factors are given, or noner2   r2   r8   r6   re   )_meta_grouped_mm_common.<locals>.<lambda>  s    >r8   c                  >   > ST R                    STR                    S3$ )Nz5Expected inputs of E4M3 FP8 type but got mat_a.dtype= and mat_b.dtype=r  r   r-
  r.
  s   r6   re   r1
    s#    KEKK=Xijojujuivvwxr8   c                  >   > ST R                    STR                    S3$ )Nz1Expected inputs of BF16 type but got mat_a.dtype=r3
  r  r   r4
  s   r6   re   r1
    s#    G}Tefkfqfqerrstr8   )r   r.   c                  L   > ST R                  5        STR                  5        3$ )Nz3Multiplicands must be 2D or 3D but got mat_a.dim()=z and mat_b.dim()=r   r4
  s   r6   re   r1
    s%    Eeiik]Rcdidmdmdocpqr8   r   r   r  c                      g)Nz3contraction dimension of mat_a and mat_b must matchr2   r2   r8   r6   re   r1
    r5  r8   c                 P    U R                  5       nUS   S:  =(       a    US   S:H  $ Nr  r1   r   r  mat
mat_strides     r6   rO  -_meta_grouped_mm_common.<locals>.is_row_major  s*    Jb>A%=*R.A*==r8   c                 P    U R                  5       nUS   S:H  =(       a    US   S:  $ r9
  r  r:
  s     r6   rS  -_meta_grouped_mm_common.<locals>.is_col_major  s*    Jb>Q&=:b>A+==r8   c                  0   > ST R                  5       SS   3$ )NzNExpected mat_a tensor to be row major in the last two dimensions, got strides r  r  )r-
  s   r6   re   r1
    s!    dejeqeqestvtwexdyzr8   c                  0   > ST R                  5       SS   3$ )NzQExpected mat_b tensor to be column major in the last two dimensions, got strides r  r  )r.
  s   r6   re   r1
    s!    ghmhththvwywzh{g|}r8   c                   ^ ^^^ TR                  5       S-
  mSTR                  5       -  nTR                  5       mTTS-
     S:X  aJ  TT   [        STR                  TS-
     5      :  a'  [
        R                  " TT   U-  S:H  UU U4S j5        g TT   S:X  aM  TTS-
     [        STR                  T   5      :  a*  [
        R                  " TTS-
     U-  S:H  UU U4S j5        g [
        R                  " SUU4S j5        g )Nr1   ri  r   c                  "   > ST ST  STT     S3$ )Nr   stride along % dim to be multiple of 16 bytes, got r  r2   end_dimmat_namer<
  s   r6   re   F_meta_grouped_mm_common.<locals>.check_valid_strides.<locals>.<lambda>  s'    )H:^G9Dijtu|j}i~~  Ar8   c                  .   > ST ST S-
   STT S-
      S3$ )Nr  rD
  r1   rE
  r  r2   rF
  s   r6   re   rI
    sI    )H:^GaK=Hmnx  zA  DE  zE  oF  nG  GH  Ir8   Fc                  *   > ST ST R                    S3$ )NzInvalid strides/sizes, got z for strides and z for sizes.rD  r:
  s   r6   re   rI
    s    5j\ARSVS\S\R]]hir8   )r   element_sizer   r  r   rV   rh   )rH
  r;
  r*
  rG
  r<
  s   `` @@r6   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r8   r-
  r.
  c                  >   > ST R                    STR                    S3$ )NzhFor FP8 scales must both be float32, or for MXFP8 both scales must be float8_e8m0fnu. Got scale_a.dtype=z and scale_b.dtype=r  r   rr  s   r6   re   r1
    sR    ~  @G  @M  @M  N  Na  bi  bo  bo  ap  pq  rr8   r1   c                    >^ ^^^^^^	^
 TR                  5       S:X  a  [        R                  " TR                  5       U 4S j5        T(       a=  [        R                  " TR                  5       TR                  5       :H  UUU 4S j5        g [        R                  " TR                  5       S:H  UU 4S j5        [        R                  " TR                  S   TR                  T   T-  :H  UUUU U4S j5        g [        R                  " TR                  S5      S:H  U 4S	 j5        [        R                  " TR                  S   TR                  S   :H  UUU 4S
 j5        T(       a  [        R                  " TR                  TR                  S-
  :H  UUU 4S j5        TR                  u  mpVSn[        XW-  S5      m	[        US5      m
[        R                  " TR                  S   T:H  =(       a    TR                  S   T	T
-  :H  UU	U
UU4S j5        g [        R                  " TR                  5       S:H  UU 4S j5        [        R                  " TR                  S   TR                  ST-      :H  UUU U4S j5        g )Nr   c                     > ST  S3$ )Nr  z to be contiguous.r2   
scale_names   r6   re   >_meta_grouped_mm_common.<locals>.check_scale.<locals>.<lambda>  s    i
|3EFr8   c                  B   > ST ST R                    STR                    3$ )NzKFor MXFP8, scale must have same number of dimensions as target tensor, but  has mat.ndim= and scale.ndim=r  r;
  r  rS
  s   r6   re   rT
    sX    "mnxmy  zH  IL  IQ  IQ  HR  Rb  ch  cm  cm  bn  !or8   r1   c                  2   > ST ST R                  5        S3$ )Nr  z to be 1D tensor, but got 	D tensor.r   r  rS
  s   r6   re   rT
    !    )J<7QRWR[R[R]Q^^g hr8   r   c                  V   > ST ST R                   T   T-   STR                   S    S3$ )Nr  z	 to have rm  r   z
 elements.rD  )r;
  r  scale_multiplierrS
  
scaled_dims   r6   re   rT
  !  sU    )J<y:AVYiAi@jjyz  {F  {F  GH  {I  zJ  JT  !Ur8   r   c                     > ST  S3$ )Nr  z( to be contiguous in the last dimension.r2   rR
  s   r6   re   rT
  &  s    i
|3[\r8   c                  P   > ST ST R                   S    STR                   S    S3$ )Nr  z batch dimension to be r   , got r  rD  rX
  s   r6   re   rT
  *  s4    i
|3J399UV<.X^_d_j_jkl_m^nnopr8   c                  B   > ST ST R                    STR                    3$ )Nz0For MXFP8, 3d tensor should have 2d scales, but rV
  rW
  r  rX
  s   r6   re   rT
  1  sD    "RS]R^^lmpmumulv  wG  HM  HR  HR  GS  !Tr8   rj  r#  r  c                  N   > STR                    ST  STT-   STR                    3$ )NzFor MXFP8, expected mat.shape=z to have scale shape of (,z), but got rD  )G	blocked_K	blocked_Nr;
  r  s   r6   re   rT
  ;  sO    "@Kdefdgghiru~i~h  @K  LQ  LW  LW  KX  !Yr8   c                  2   > ST ST R                  5        S3$ )Nr  z to be 2D tensor, but got rZ
  r   r[
  s   r6   re   rT
  @  r\
  r8   c                  V   > ST ST R                   ST-       STR                   S    S3$ )Nr  z non-batch dimension to be r1   rb
  r  rD  )r;
  r  rS
  r_
  s   r6   re   rT
  D  sR    )J<7RSVS\S\]^ak]kSlRmmstytt  AB  uC  tD  DE  !Fr8   )r   rV   rh   re  r   r   r   r=   )rS
  r  r;
  r_
  r^
  r  r  r  rf
  rg
  rh
  is_mxfp8s   `````   @@@r6   check_scale,_meta_grouped_mm_common.<locals>.check_scale  s   wwyA~'')F LL		swwy0 o
 LL		q(h LLA#))J*?BR*RR U  U
 LL$)\ KKNciil2p LL

chhl2 T "iiGAq!#J ( ;I (C 0ILLA!+WA)iBW0W Y  Y
 LL		q(h LLA#))A
N*CC Fr8   r   r8  r9  c                      g)Nz:Scale result tensor provided, but it is not supported yet.r2   r2   r8   r6   re   r1
  O  ro   r8   c                  N   > ST R                  5        STR                  5        S3$ )Nz/Offsets tensor not provided, but is needed for zD/zD multiplicand layouts.r   r4
  s   r6   re   r1
  U  s(    Eeiik]RTUZU^U^U`Taaxyr8   c                  ,   > ST R                  5        S3$ )Nz.Offsets tensor must be 1D, but got offs.dim()=r  r   r'
  s   r6   re   r1
  Z  s    HTUVr8   c                  $   > ST R                    S3$ )Nz7Offsets tensor must be integer (int32) tensor, but got r  r   rq
  s   r6   re   r1
  ^  s    QRVR\R\Q]]^_r8   c                      g)NzJOffsets tensor provided, but is not needed for 3D/3D multiplicand layouts.r2   r2   r8   r6   re   r1
  c  s    `r8   c                      g)Nz2Bias tensor provided, but it is not supported yet.r2   r2   r8   r6   re   r1
  h  s    Dr8   c                      g)Nz4If output dtype provided, it must be torch.bfloat16.r2   r2   r8   r6   re   r1
  m  s    Fr8   r'  )rV   rh   r  r  r@  rd  r^   rc  r   r   ra  rx  r   rK  r,
  )r-
  r.
  r8  r9  r'
  rE  r:  rG  r;  scaled	fp8_dtypemat_a_is_2dmat_b_is_2drO  rS  rM
  rl
  r^
  rk
  s   `````             @r6   _meta_grouped_mm_commonrz
    s]    
LL	Dgo.> D 8WD%8F -2]]->->E))EDWDW	KK9$A	)Ax	

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

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

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

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

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

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

 
LLD
 
LLT8Y%..8F
 ,E5$	JJr8   c                 "    [        U US S UUS US9$ )N)r8  r9  r'
  rE  r:  rG  )rz
  )r-
  r.
  r'
  rE  rG  s        r6   meta_grouped_mmr|
  s  s)     #	 	r8   c	                 V    U=(       d    [         R                  n[        U UUUUUUUUS9	$ )N)r8  r9  r'
  rE  r:  rG  r;  )rV   rc  rz
  )	r-
  r.
  r8  r9  r'
  rE  r:  rG  r;  s	            r6   meta_scaled_grouped_mmr~
    s:     +U^^I"!%
 
r8   r;   half_to_floatc                 .   U(       a0  U R                   [        R                  [        R                  4;   d   e[        R
                  " U [        R                  R                  S9u  p4U(       d  UOUn[        R                  " X[        R                  S9nU$ )Nr  r	  )
r^   rV   rX   rc  rO   r   r   rP   r   r   )r;   r   r
  computation_dtyperS   r  s         r6   softmaxr
    st     ww5::u~~6666&+&>&>	uDDLL'# (5<:KL


1@W@W
XCJr8   c           	        ^^^^	^
^ [         R                  " [        T5      S-  S:H  U4S j5        U R                  m[        T5      m
[        T5      S-  nT
U-
  m	[         R                  " T
U:  U
U4S j5        [	        S T 5       5      (       a  U n[        T	T
5       Hx  mST
T-
  S-
  -  mTT   S:  a*  UR                  TTT   * UR                  T   TT   -   5      nTTS-      S:  d  MO  UR                  TSUR                  T   TTS-      -   5      nMz     UR                  5       $ [        TS T	 5      n[        U5       Ha  m[        T5      TS-   S-  -
  mTT	T-      TT   -   TTS-      -   n[         R                  " US:  UUU	UU4S j5        UR                  U5        Mc     [         R                  " UU R                  U R                  U R                  [        U 5      S9$ )	Nr   r   c                      > S[        T 5       3$ )Nz1Length of pad must be even but instead it equals r  r  s   r6   re   '_constant_pad_nd_meta.<locals>.<lambda>  s    CCH:Nr8   c                  (   > S[        T5       ST  S3$ )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   r6   re   r
    s      225c(;P'r8   c              3   n   #    U  H+  n[        U[        R                  5      =(       a    US :*  v   M-     g7fr  )rr   rO   IntWithoutSymInt)rt   rg  s     r6   rv   (_constant_pad_nd_meta.<locals>.<genexpr>  s)     
IS:a//0;Q!V;Ss   35r1   c            	      F   > STTT -       STT    STTS-       STT -    S3	$ )NzThe input size z, plus negative padding r   r1   zG resulted in a negative output size, which is invalid. Check dimension z of your input.r2   )r   r  l_diffr  pad_idxs   r6   re   r
    sE    ok&1*&=%>>V7|nE#gk"2!3 4117!OMr8   )r^   r   r   r   )rV   rh   r   r   r  r   narrowr   r   r   r   r^   r   r   r   )r   r  r  l_padc_input	new_shapenew_dimr   r  r
  r
  r
  s    `     @@@@@r6   _constant_pad_nd_metar
    s    
LLC1N
 ++KEHMEU]F	LL	 
IS
IIIvu%A519q=)G7|a!..G}gmmA&6W&E 7Q;!#!..Aw}}Q/?#gPQkBR/RS & }}[&)*I5\c(q1uk*fqj)CL83w{;KKqLM M	
 	!  ;;kk||))+E2 r8   r  r  r  c                    U R                  5       S:X  d   S5       eU R                  nUR                  nUR                  S:X  a  US   4nO%UR                  S:X  a  US   US   4nO
/ UQUS   P7nU R                  nU R	                  XxS9$ )Nr   z'weight' must be 2-Dr   r1   r   )r   r   r   r^   r   )	rC  r   r  r  r  weight_shapeindices_shaper   rG  s	            r6   	embeddingr
    s     ::<1444<<LMMM||q&21o%7			"1%|A7	5m5\!_5	II77r8   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      $ r  )r   r   r   )r   rx  r
  r
  r  r  rh  s          r6   $meta__jagged_to_padded_dense_forwardr
     st     w<1{q   
aAAA,6<<+,LL))r8   c                 B    [        U 5      [        5       S 5       5       nU$ )Nc                 2    [        U [        R                  S9$ r  rT   r   r  r5  s    r6   _f)_create_unary_float_meta_func.<locals>._f   s      =JJ
 	
r8   rK   r"   funcr
  s     r6   _create_unary_float_meta_funcr
     *    4]
  

 Ir8   c                 (   U R                   (       d"  UR                   (       d  UR                   (       a  [        S5      eU R                  5       S:X  a,  U R                  U R                  5      U R                  S5      4$ U R                  S5      nU R                  S5      nUR                  S5      nU R                  XU5      nU
(       a4  U(       a  U R                  XU5      nUU4$ U R                  XX5      n UU4$ U R                  S5      nUU4$ )NzP_native_multi_head_attention fake implementation does not support nested tensorsr   r1   )	is_nestedr  r   r   r   r   )r  r   r  	embed_dimr  
qkv_weightqkv_biasproj_weight	proj_biasr  need_weightsaverage_attn_weights	mask_typer  T
output_dimr  attn_weightss                     r6    native_multi_head_attention_faker
      s      #--5??!^
 	
 {{},eooa.@AA

1A

1A !!!$J__Q:.F !??13L L!!	 !??1=L L!! q)L!!r8   c                 B    [        U 5      [        5       S 5       5       nU$ )Nc                 2    [        X[        R                  S9$ r  r
  r:   s     r6   r
  *_create_binary_float_meta_func.<locals>._fR   s      !@!M!M
 	
r8   r
  r
  s     r6   _create_binary_float_meta_funcr
  Q   r
  r8   c                    ^  [        T 5      U 4S j5       nT R                   S3nX!l        [        [        [        U5      5      " U5      nU$ )Nc                 `   > T" U /UQ70 UD6n[        U R                  UR                  5        U $ rB   r  )r   rQ   r6  r   rD   s       r6   _fn#_register_inplace_meta.<locals>._fnv   s.    '''

CII6r8   rR   )r   r~   rK   getattrr+   )rD   r
  inplace_names   `  r6   _register_inplace_metar
  u   sK    
2Y 
 kk]!$LL
l3
4S
9CJr8   c                 z  ^ ^^ [         R                  " T R                  TR                  :H  UU 4S j5        T T/n[        T[        5      (       aT  TR
                  S:w  a3  [         R                  " T R                  TR                  :H  U U4S j5        UR                  T5        [        US[        R                  06$ )Nc                  <   > STR                    ST R                    3$ )Nr  z for `end`, but got dtype r   )r   r   s   r6   re   lerp.<locals>.<lambda>   s    /%++.HTr8   r   c                  <   > ST R                    STR                    3$ )Nr  z for `weight`, but got dtype r   )r   rC  s   r6   re   r
     s    /%++6STZT`T`Sabr8   rL   )
rV   rh   r^   rr   r   r   r   rT   r   rP   )r   r   rC  rQ   s   ``` r6   lerpr
     s     
LLsyy T 3<D&*%%;;!LLv||+b 	F	=EE r8   )r  c                4    [        XU[        R                  S9$ r  rQ  r   tensor1tensor2r  s       r6   addcmulr
     s     0O0W0W r8   c                    [         R                  " [        R                  " UR                  5      =(       a     [        R                  " UR                  5      (       + S 5        [        XU[        R                  S9$ )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.r2   r2   r8   r6   re   addcdiv.<locals>.<lambda>   s     	
r8   r  )rV   rh   rO   rI  r^   rT   r   rP   r
  s       r6   addcdivr
     s`     
LL""7==1 6&&w}}5	
		
  0O0W0W r8   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   itemsrr   rV   _opsHigherOrderOperatorr   py_impl_CDispatchKeyr-   %_dispatch_has_kernel_for_dispatch_keyr  r0  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_tabler}   registryopoop_overloadrD   s         r6   activate_metar
     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 $; ;  A    	 [--//BGGXK,,..?DD[U{//11BGGX+"2"2"44EJJ 8<<[Mm 7r8   )Fr	  rB   )NNNFr   r1   r   r  )Tr  )r  )r  T)FF)TT)rn  )FTN)TFF)TF)r   )g      ?N)r>   str)r2   r  r'  F)r2   r  FTN)Fr   FNFr   )NF)r   F)g      ?gUUUUUU?FN)NNNNN)r   NNr1   )NNF)        FFN)Nr
  FFN)r
  FNN)Nr
  FNN)r
  FN)FN)FNNNN)NNNF)NNNNF)Nr   FNN)NNNN)r   TT)NNr   N)d   r   r   )r   )r   FF)r
  )NTTN(  r  collections.abcr   r   enumr   	functoolsr   typingr   typing_extensionsr   rV   torch._prims_commonr  rO   r	   r
   r   torch._decompr   r   r   r   
torch._opsr   torch._primsr   r   r   r   r   r   r   r   r   r   r   r   r   torch._prims_common.wrappersr   r   r    r!   r"   r  r#   r$   torch.fx.experimentalr%   r  torch.nn.functionalr&   r'   torch.utilsr(   rG   r)   r*   opsr+   libraryLibraryr
  r   r  r  r  r7   r=   rK   rT   r`   rj   linspacelogspacer  r   taker3  r   r   r   r   cummaxcumminr   r   r   r   r   r  r   _fft_c2cr   r   r   _fft_r2cr  randpermgenerator_outr  r   r  randintr   r  low_outr$  randr&  _fft_c2rr+  r  r7  r>  
unsqueeze_rB  _sparse_semi_structured_linearr
  r^   rO  _sparse_semi_structured_mmrU  _sparse_semi_structured_addmmrY  _cslt_sparse_mmri  index_reducerp  index_reduce_rr  index_selectrv  segment_reducer  r  	unary_outr  r   r  r  r  r  r  r  r  _assert_asyncr  msgr  _printr  _make_dep_tokenr  r  _functional_sym_constrain_ranger  r  (_functional_sym_constrain_range_for_sizer  _functional_assert_asyncr  r   r  r   r  r  r  r  _linalg_eighr  r  _linalg_eigvalslinalg_eigvalsr   
linalg_eigr  r  r
  r  r  r  r   r4  linalg_inv_exr7  linalg_ldl_factor_exrg   r=  linalg_ldl_solverM  	linalg_lurU  linalg_lu_factor_exrZ  linalg_lu_solverd  	lu_unpackrk  ru  	linalg_qrr|  r  r}  _linalg_svdr  rJ  r  r  r  linalg_solve_triangularr  r  r  _linalg_detr  r  r  r  reflection_pad1dr  replication_pad1dr  r  reflection_pad1d_backwardr  replication_pad1d_backwardr!  r2  reflection_pad2dr4  replication_pad2dr8  _weight_norm_interface_backwardrA  reflection_pad2d_backwardr  replication_pad2d_backwardrI  rX  reflection_pad3drZ  replication_pad3dr^  reflection_pad3d_backwardreplication_pad3d_backwardrf  _pdist_forwardrZ   rk  _pdist_backwardrr  baddbmmr  	bernoullir  
bernoulli_r  rg  r  poissonr  _fused_moving_avg_obs_fq_helperr  mmr  r  r   r  r  miopen_batch_normr  convolutionr  r
  _has_mkldnnr
  r  _convolution_pointwiser  _linear_pointwiser  has_mklr
  r  _mkl_linearr  r
  r  qconv2d_pointwiseqconv_pointwiser:  r  binarybinary_tensorr  qlinear_pointwiser  r#  linear_dynamic_fp16linear_relu_dynamic_fp16r%  r
  r&  
max_pool2dr1  int4mm_packed_weight_cpurC  rI  
avg_pool2drs  rx  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  rs   r  r  r  r   _unsafe_indexr  convolution_backwardr+  addbmmr4  randint_liker7  _fused_adam__fused_adamw_rO  _fused_adamrW  _int_mmra  _convert_weight_to_int4packrm  #_convert_weight_to_int4pack_for_cpurs  _weight_int4pack_mmr}  _weight_int4pack_mm_for_cpur  r  r  r  _dyn_quant_pack_4bit_weightr  _dyn_quant_matmul_4bitr  _weight_int8pack_mmr  _cdist_forwardr  _cdist_backwardr  _embedding_bagr&  _embedding_bag_forward_onlyr(  r+  nansumr-  median	nanmedianr/  
dim_valuesrl  r   r2  logical_not_r4  repeatr=  zero_r?  mul_Scalardiv_logical_and_logical_or_logical_xor_rB  add_sub_rO  r  subrS  rounddecimalsrU  r\  
__rshift__r`  
__lshift__rd  zerorf  rQ  ri  fillrk  relu_rn  	_add_relurp  rrelu_with_noiseru  rrelu_with_noise_functionalrw  rrelu_with_noise_ry  	index_put_unsafe_index_putr}  masked_fill_r  _masked_scaler  masked_scatter_r  masked_scatterr  masked_scatter_backwardr  
index_put_r  r  bmmr  r  r  r  rg  rh  r  r  r  r+   max_pool2d_with_indices_backwardr  max_pool2d_with_indicesr  fractional_max_pool2dr  max_pool3d_with_indicesr   max_pool3d_with_indices_backwardr  r%  r'  r4  grid_sampler_2d_backwardr<  rB  rD  rG  r  onesrV  zerosrY  select_scatterr]  slice_scatterra  r   rf  ro  gatherrv  r  r  r  r  r  scatter_addr  scatter_add_r  r  r4  r  rl  value_reducer  scatter_r  #_scaled_dot_product_flash_attentionr  r  #_scaled_dot_product_cudnn_attentionr  0_scaled_dot_product_fused_attention_overrideabler  ,_scaled_dot_product_flash_attention_backwardr  +_scaled_dot_product_flash_attention_for_cpur  4_scaled_dot_product_flash_attention_for_cpu_backwardr  *_scaled_dot_product_attention_math_for_mpsr  '_scaled_dot_product_efficient_attentionr
  0_scaled_dot_product_efficient_attention_backwardr  ,_scaled_dot_product_cudnn_attention_backwardr  _flash_attention_forwardr  _flash_attention_backwardr!  _efficient_attention_forwardr-  _efficient_attention_backwardSymIntr7  r  
_scaled_mmr  r  _scaled_mm_v2r  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	  r8	  _thnn_fused_lstm_cellr>	  rU	  r_	  re	  ri	  rk	  argminrl	  ro	  topkrw	  _segment_reduce_backwardr{	  kthvaluer	  r   r	  r	  r	  r	  pixel_shuffler	  r	  	bucketize
Tensor_outr	  histcr	  _upsample_bilinear2d_aa_upsample_bicubic2d_aar	   _upsample_bilinear2d_aa_backwardr	  r	  r	  r  r	  searchsortedr	  r	  embedding_dense_backwardr	  _embedding_bag_backwardr
  _embedding_bag_dense_backwardr 
  *_embedding_bag_per_sample_weights_backwardr
  isinr
  	polygammar
  _local_scalar_denser
  r
  r
  r,
  rz
  _grouped_mmr|
  _scaled_grouped_mmr~
  _softmaxr
  constant_pad_ndr
  r
  _jagged_to_padded_dense_forwardr
  r
  _native_multi_head_attentionr
  r
  special_airy_aispecial_bessel_y0special_bessel_y1special_modified_bessel_i0special_modified_bessel_i1special_modified_bessel_k0special_modified_bessel_k1!special_scaled_modified_bessel_k0!special_scaled_modified_bessel_k1special_chebyshev_polynomial_tspecial_chebyshev_polynomial_uspecial_chebyshev_polynomial_vspecial_chebyshev_polynomial_w&special_shifted_chebyshev_polynomial_t&special_shifted_chebyshev_polynomial_u&special_shifted_chebyshev_polynomial_v&special_shifted_chebyshev_polynomial_wspecial_hermite_polynomial_hspecial_hermite_polynomial_hespecial_laguerre_polynomial_lspecial_legendre_polynomial_pr
  r
  r
  r
  lerp_addcmul_addcdiv_torch._refs.nn.functionaltorch._refs.specialr
  r2   r8   r6   <module>r     sfK    .    '  # + +  " U     < 7 8 ) 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%$ t%%&I  'I 	[[$++//4;;+>+>P Xy! " !!))4+<+<+@+@ABI  CI3lV $s) 4  %%t}}'8'89:K  ;K $s)  %%t}}'8'89:8
  ;8
v t}}**+"& 3 ,3 t}}$$% **
 &
 $$dll&6&678
 **  9&   $,,"6"678 **  9& 		!!499==12%)$tPT   3 %%t}}'8'89:$Dv $DDI $Dc $DC $D  ;$DN tzz!!" #0	( t&&' ( t223
 "&$(  4-	
 4Z {{T! 4B t../
 %)	
  {{T!	 00 t112 	
$(
  	 {{T! 3D t##$ $("+<,,+<\\+< 4-+< D=	+<
 {{T!+< +< +< +< +< %+<\ t  (() 	I
	I		I 	I LL		I
 	I 	I 	I *	I t!!))* 	
			 	 LL		
 	 	 	 +	 t  (()' * ' t""**+
 "!! W
 W W d]	 W
 d] W d] W  W  W  W , WF   $(("4"456  7 txx||    $(("4"456  7 txx||  tzz!!"6 #6 tzz~~( (
 t!!))* + t!!%%& ' t{{""# $ t##++, ) -) t''//0, 1, t33;;< =
 t008896 :6& t<<DDE F
 t,,001 2
F C    F  #  N (,


 !%
$V S C 
 
F 
$ 
 
"  	  	C  !!))4+<+<+H+HIJ]N+ s T  , K" $$,,d.A.A.E.EFGB B6 B  HB  !]N+6  , " Q QF Q t**+) )F )4 )F )  ,) t""#J JF J4 JF J  $J t}})6 )$ )6 )  ) t$$%)6 )$ )6 )  &) t&&../&  T  0" 	$$,,d.M.M.Q.QR .f .6 .f . .d t!!))*&   + ))1143L3L3P3PQRT8V$ 	
  	
 666!" % S& %%--t/D/D/H/HIJ ''' '
 ' '  K'T &&(:(:;<S#s/3 f  fff>T8U   =4 ((00$2J2J2N2NOPT8V$ 	  	
 666!" % QD $$,,d.B.B.F.FGH 444 4
 4 4 4  I4n t~~S#s 	$$$ $ 	$
 666!"$  $P tTz!2 * &&(:(:;<S#f C ffn8M   =4 $$,,d.B.B.G.GHIV[$1'v '%(F"G ' 2 J'$ t''(  	""" " $J	" )"J.
.
. 49d3i .".
.
. *. 66>	.(f V   t$$%
   777 	7
 7 TM7 	7 TM7 4-7 6666)*7 &7t ,,44d6R6R6V6VWX  	
   
$  Y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%%&>  '> ((00 &&..&&11''//''22	 \& &:<G~ t$$%=  &= t%%&>  '> &&..&&11''//''22	 \$( $(N t""#

f 

 

v 

  $

 t##$Pv PV P Pf PQW P  %P $$dll&6&678/0 '  9': &&(:(:;<&* I  =I
 t$$% & t~~ I !I
 $$dll&6&678"  9" t33;;< * =*. tww3U[[4/ 3  3,B
* .2r,,rLLr IOr #Y_	r
 3i#or r r IOd*rjQ t%%--."$,,"$LL"$ ,,
"$ ,,%	"$
 $"$ "$ !&"$ "$ /"$J t''(,,LL ,, I	
 #Y 3i  I  )> 	889>9N9N&&:6 599##::BBC D, 599##55==>S ?S
 xx:?--:O:O66;
7 
uyy}}00	1	 
2	
 :?9N9N&&:6 599##55==>599##33;;<599##33::;0 < = ?0d 599##55<<=599##55CCD E >6 599##55==>599##55<<= > ?8 599##55<<=599##55CCD! E >!F 599##77??@599##<<DDE	 F A	 =BMM<Q<QVV=9 599&&112 
 3
8 599&&??@@ A@, t&&' M (Mb(<X t''//0E 1EP t UJ   UJp t''(\K(  )K(\ t((001 2" t((001@ 2@ t1199:F ;F, t112\P  3P
	
6 	
S 	
 t''(UI+  )+\ t001\H  2H$ t''(UI'  )'T t001\(  2(
 t%%,,-* .* $$dll&6&678  9 ##++T-@-@-D-DEF46 @c @  G@ 		&&..		0F0F0J0JKL  M" 

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

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

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

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