
    9i             -       fx   S SK r S SKJr  S SKJr  S SKJr  S SKJrJ	r	J
r
Jr  S SKJr  S SKrS SKJr  S SKJrJrJr  S SKJrJrJrJr  S S	KJr  S S
KJrJr  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K0J1r1J2r2  S SK3J4r5  S SK6J7r8  \
" S5      r9\" S5      r:\Rv                  Rx                  r<\Rz                  R}                  SSS5      r?\@" S5      u  rArBrCS\\\:\94   /\\:\94   4   4S jrDS\#4S jrES rFS rG\D" \<R                  \<R                  /5      \/" 5       SSS\R                  SS4S j5       5       rK\D" \<R                  R                  \<R                  R                  /5      \/" 5       S 5       5       rO\D" \<R                  R                  \<R                  R                  /5      \/" 5       SS .S! j5       5       rP\D" \<R                  5      \/" 5       S" 5       5       rQ\D" \<R                  R                  \<R                  R                  \<R                  R                  \<R                  R                  /5      \/" S#S$5      S% 5       5       rT\D" \<R                  R                  \<R                  R                  /5      \/" 5       S& 5       5       rUS' rVGS$S(\S)\W\X   S*\Y4S+ jjrZ\D" \<R                  R                  \<R                  R                  /5      \/" 5       S, 5       5       r\Sr]S)\W\X   4S- jr^\D" \<R                  R                  \<R                  R                  /5      \/" 5       S. 5       5       r`\D" \<R                  R                  5      SS/.S0 j5       rc\D" \<R                  R                  5      \R                  SSSS1.S2 j5       re\D" \<R                  R                  \<R                  R                  /5      \/" 5       \R                  SSSS1.S3 j5       5       rg\D" \<R                  R                  \<R                  R                  /5      \/" 5       \R                  SSSS1.S4 j5       5       rj\D" \<R                  R                  \<R                  R                  /5      \/" 5       SSSSS1.S5 j5       5       rl\D" \<R                  R                  \<R                  R                  /5      \/" 5       S(\S)\W\X   S6\XS7\X4S8 j5       5       rn\D" \<R                  R                  5      GS$S9 j5       rpS: rq\D" \<R                  R                  5      S; 5       rs\D" \<R                  5         GS%S<\S=\S>\S?\	\   S@\	\u   SA\	\R                     4SB jj5       rw\D" \<R                  5       GS&SC\SD\SE\SA\	\R                     4SF jj5       ry\D" \<R                  5      SGSGSSH.S<\SC\SD\SE\SA\	\R                     4
SI jj5       r{\D" \<R                  5             GS'SJ\R(                  SK\R(                  S?\	\   SL\	\   SA\	\R                     SM\YSN\XSO\XSP\X4SQ jj5       r}\D" \<R                  R                  5      SRSS.S(\S)\XST\SU\R(                  SV\uSW\YS\4SX jj5       r\D" \<GR                   R                  5      SRSS.S(\S)\XST\SU\R(                  SV\uSW\YS\4SY jj5       r\/" 5       \D" \<GR                  R                  5      SZ 5       5       r\D" \<GR                  R                  5      SSSS SSS[.S\\SV\uS]\	\   S$\	\   S^\	\   S_\XS`\YS\4Sa jj5       r\D" \<GR                  R                  \<GR                  GR                  /5      \/" 5       Sb 5       5       r\D" \<GR                  GR                  5      GS$Sc j5       r\D" \<GR                  R                  \<GR                  GR                  /5      \/" 5       Sd 5       5       r\D" \<GR                  GR                  5      GS$Se j5       r\D" \<GR                  R                  5      Sf 5       r\D" \<GR                  R                  5      Sg 5       r\D" \<GR"                  R                  5      Sh 5       r\D" \<GR"                  GR&                  5      Si 5       r\D" \<GR*                  R                  5      Sj 5       r\D" \<GR.                  R                  5      SSSSSSk.Sl j5       r\D" \<GR2                  R                  5      GS(Sm j5       r\D" \<GR4                  R                  5      GS%Sn j5       r\D" \<GR8                  R                  5      GS(So j5       r\D" \<GR:                  R                  5      Sp 5       r\D" \<GR>                  GR&                  5      Sq 5       rS(\Sr\u4Ss jrS(\St\Su\u4Sv jr GS)Sw\Sr\uSx\Y4Sy jjrGS*St\Sr\uSz\u4S{ jjrSt\S|\S}\YSr\u4S~ jr GS+S\uS\S<\S\u4S jjrS\u4S jr\D" \<GRP                  R                  \<GRP                  GRR                  /5      \/" SS5      GS,St\S\uS\Y4S jj5       5       r\D" \<GRV                  R                  \<GRX                  R                  /5      \/" 5       S<\S\4S j5       5       r\D" \<GR\                  /5      \/" SS5      S<\4S j5       5       rS\S\4S jr\D" \<GRb                  5      \/" 5       S(\St\S\YS\4S j5       5       r\D" \<GRd                  5      \/" 5       GS$S(\St\S\YS\4S jj5       5       r\D" \<GRf                  5      \/" 5       GS$S(\S\YS\4S jj5       5       r\D" \<GRh                  5      \/" 5       GS$S(\S\YS\4S jj5       5       r\D" \<GRj                  R                  5      GS-St\S\YS\Y4S jj5       r\D" \<GRl                  R                  \<GRl                  R                  /5      \/" 5       S<\S\S\4S j5       5       r\D" \<GRn                  R                  5      GS$St\S\Y4S jj5       r\D" \<GRr                  R                  \<GRr                  R                  /5      \/" SSS5      SSS.S(\S\YS\YS\\\\4   4S jj5       5       r\D" \<GRx                  R                  \<GRx                  R                  /5      \/" 5       SS.S\S\S|\S\YS\4
S jj5       5       r\D" \<GR|                  R                  \<GR|                  R                  /5      \/" SSS5      SRS.St\S\YS\\\\4   4S jj5       5       r\D" \<GR                  R                  \<GR                  R                  /5      \/" SSS5      SRSS.St\S\YS\YS\\\\4   4S jj5       5       r\D" \<GR                  R                  \<GR                  R                  /5      \/" 5       SRSS.S\S\S|\S}\YS\YS\4S jj5       5       r\D" \<GR                  5      \/" SSS5        GS.S\S\S\YS\YS\\\\4   4
S jj5       5       rS\uS\\Y\Y4   4S jr\D" \<GR                  R                  \<GR                  R                  /5      \/" SS5      GS/St\S\uS\\\4   4S jj5       5       r\D" \<GR                  R                  \<GR                  GR                  /5      \/" SSSS5      St\S\\\\\4   4S j5       5       r\D" \<GR                  R                  5         GS0St\S\YS\YS\	\u   4S jj5       rS\S\S\\W\X   \W\X   4   4S jrS\S\Su\	\u   S\\\4   4S jrS<\S\S\Y4S jr\D" \<GR                  5      SRSSSSSS.St\S|\S}\YS\YS\	\   S\	\   S\	\   S\	\   S\\\\\4   4S jj5       r\D" \<GR                  R                  \<GR                  R                  /5      SRSSS.St\S|\S\YS}\YS\YS\	\   S\4S jj5       r\D" \<GR                  5      \/" SSSRS9   GS1S(\St\S\YS\YS\YS\\\4   4S jj5       5       r\D" \<GR                  R                  5      S 5       r\D" \<GR                  5      \/" 5         GS2S<\S\S\S}\YS\YS\4S jj5       5       rS rS r\D" \<GR                  5      \/" 5       S 5       5       r\D" \<GR                  5      \/" 5       S 5       5       rS r\D" \<GR                  5      \/" S5      S 5       5       r\D" \<GR                  5      \/" S5      S 5       5       rS r\D" \<GR                  5      \/" 5       S 5       5       r\D" \<GR                  5      \/" 5       S 5       5       r\D" \<GR                  R                  \<GR                  GR                  \<GR                  R                  \<GR                  GR                  /5      \/" S5      S 5       5       rS r\D" \<GR                  5      \/" 5       S 5       5       r\D" \<GR                  5      \/" 5       S 5       5       r\D" \<GR                  R                  \<GR                  GR                  \<GR                  R                  \<GR                  GR                  /5      \/" S5      S 5       5       r\D" \<GR                  5      \/" 5       GS3S(\S\S\4S jj5       5       r\D" \<GR                  5      \/" 5       S\S(\S\S\S\4
S j5       5       r\D" \<GR                  R                  \<GR                  R                  /5      \/" SRS9SGSGS.S j5       5       r\D" \<GR                  R                  \<GR                  R                  /5      \/" 5       SS/.S j5       5       r\D" \<GR                  GR                  5      GS4S j5       r\D" \<GR                  GR                  5      GS4S j5       Gr \D" \<GR                  R                  \<GR                  R                  /5      \/" 5       GS&S j5       5       Gr\D" \<GR                  R                  5        GS-S j5       Gr\D" \<GR
                  5      \/" SRS9S 5       5       GrS GrGS5S jGr GS&S\R(                  S=\R(                  S\\W\X   \X4   S\\W\X   \X4   S\\W\X   \X4   S\YS\XS\	\\W\X   \X4      4S jjGr	S Gr
\D" \<GR                  R                  5      S\R(                  S=\R(                  S?\	\R(                     S\	\R(                     S\	\R(                     S\YS\S\4S j5       Gr\D" \<GR                  R                  5      S\R(                  S=\R(                  S?\R(                  S\W\X   S\W\X   S\W\X   S\YS\W\X   S\X4S j5       Gr\GR                  GR                   (       Ga  \Rz                  R}                  SSS5      Gr\D" \Rv                  GR$                  GR&                  R                  5      S 5       Gr\D" \Rv                  GR$                  GR*                  R                  5      S 5       Gr\GR                  GR.                  (       aN  \Rz                  R}                  SSS5      Gr\D" \Rv                  GR2                  GR4                  5      GS  5       Gr\Rz                  R}                  GSSS5      Gr\D" \Rv                  GR:                  GR<                  R                  5      \D" \Rv                  GR:                  GR>                  R                  5      GS 5       5       Gr \D" \Rv                  GR:                  GR<                  GRB                  5      GS 5       Gr"\D" \Rv                  GR:                  GRF                  R                  5      \D" \Rv                  GR:                  GRF                  GRH                  5      GS 5       5       Gr%\D" \Rv                  GR:                  GRF                  GRB                  5      \D" \Rv                  GR:                  GRF                  GRL                  5      GS 5       5       Gr'\D" \Rv                  GR:                  GRP                  R                  5      \D" \Rv                  GR:                  GRR                  R                  5      GS 5       5       Gr*\Rz                  R}                  GSSS5      Gr+\D" \Rv                  GRX                  GRZ                  5          GS6GS
 j5       Gr.\D" \Rv                  GRX                  GR^                  5      GS 5       Gr0GS Gr1\D" \<GRd                  R                  5           GS7GS j5       Gr3GS Gr4\D" \<GRj                  R                  5      GS 5       Gr6\D" \<GRn                  5      \/" 5            GS7GS j5       5       Gr8\D" \<GRr                  5      \/" S5      GS 5       5       Gr:\D" \<GRv                  R                  5      GS 5       Gr<\D" \<GRz                  R                  5      GS 5       Gr>\D" \<GR~                  R                  5      GS 5       Gr@\D" \<GR                  5      \/" S5      GS 5       5       GrBGS\Sz\u4GS jGrC\D" \<GR                  5      \/" SS$5      GS 5       5       GrE\D" \<GR                  5      \/" S5      GS 5       5       GrG\D" \<GR                  5      \/" SS$5      GS 5       5       GrI\D" \<GR                  5      \/" S5      GS 5       5       GrK\D" \<GR                  R(                  5      GS&GS j5       GrM\D" \<GR                  R                  \<GR                  R                  /5      \/" 5       GS 5       5       GrO\D" \<GR                  R                  \<GR                  R                  /5      \/" 5       SGS.GS\X4GS  jj5       5       GrP\D" \Rv                  Rx                  GR                  R                  \Rv                  Rx                  GR                  R                  /5      \/" 5       GS! 5       5       GrQ\D" \<GR                  R(                  \<GR                  R(                  /5      GS" 5       GrT\D" \<GR                  R                  /5      GS# 5       GrV\D" \<GR                  R                  \<GR                  R                  /5      \/" SRS9SGSGS.GS$ j5       5       GrX\D" \<GR                  R(                  /5      GS% 5       GrZ\D" \<GR                  R                  \<GR                  R                  /5      SSGS&.GS' j5       Gr]\D" \<GR                  R                  /5      SSGS&.GS( j5       Gr_\D" \<GR                  /5      \/" 5       GS) 5       5       Gra\D" \<GR                  /5      GS* 5       Grc\D" \<GR                  /5      GS+ 5       Gre\D" \<GR                  /5      GS, 5       Grg\D" \<GR                  /5      GS- 5       Gri\D" \<GR                  /5      GS. 5       GrjGS/\XGS0\XS\X4GS1 jGrkGS2 Grl\D" \<GR                  /5      S?\	\   4GS3 j5       Grn\D" \<GR                  /5      GS4 5       Grp\D" \<GR                  /5      GS5 5       Grr\D" \<GR                  R                  5      GS6 5       Grt\D" \<GR                  5      \/" 5       GS7 5       5       Grv\D" \<GR                  R                  5            GS8GS8 j5       Grx\D" \<GR                  R                  5      GS9 5       GrzGS)GS: jGr{\D" \<GR                  R                  \<GR                  R                  /5      \/" 5       GS9SGS;.GS< jj5       5       Gr}\D" \<GR                  R                  \<GR                  R                  /5      GS= 5       Gr\D" \<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$5      GS:GS> j5       5       Gr\D" \<GR
                  R                  5      GS? 5       Gr\D" \<GR                  R                  5      GS@ 5       Gr\D" \<GR                  R                  5      GSA 5       Gr\D" \<GR                  GR                  \<GR                  GR                  \<GR                  R(                  \<GR                  R(                  \<GR                  R                  \<GR                  R                  \<GR                   R                  /5      GSB 5       Gr\D" \<GR$                  GR                  \<GR&                  GR                  \<GR$                  R(                  \<GR&                  R(                  /5      GS	GSC j5       Gr\D" \<GR*                  GR                  \<GR,                  GR                  /5      GS	GSD j5       Gr\D" \<GR0                  R                  \<GR0                  GR2                  /5      GSE 5       GrGSF Gr\D" \<GR8                  R(                  \<GR8                  GR                  /5      GSG 5       Gr\D" \<GR<                  R(                  \<GR<                  GR                  /5      GSH 5       Gr\D" \<GR@                  R                  5      GSI 5       Gr\D" \<GRD                  R(                  \<GRD                  GR                  /5      GSJ 5       Gr\D" \<GRH                  R(                  \<GRH                  GR                  /5      GSK 5       Gr\D" \<GRL                  R                  5      GSL 5       Gr\D" \<GRP                  R(                  5      \/" 5       GS	S\4GSM jj5       5       Gr\D" \<GRT                  /5      \/" 5        GS;GSN j5       5       Gr\D" \<GRX                  /5       GS;GSO j5       Gr\D" \<GR\                  /5       GS;GSP j5       Gr\D" \<GR`                  R                  \<GRb                  R                  /5      GS$GSQ j5       Gr\D" \<GRf                  GR                  5      GSR 5       Gr\D" \<GRj                  R                  5      GSS 5       Gr\D" \<GRn                  5      GST 5       Gr\D" \<GRr                  5      \/" 5       GSU 5       5       Gr\D" \<GRv                  5      GSV 5       Gr\D" \<GRz                  R                  5      GS$GSW j5       GrGS(GSX jGr\D" \<GR                  R                  5      GSY 5       Gr\D" \<GR                  R                  5      GSZ 5       GrGS[ GrGS\ GrGS] GrGS^ Gr GS$S<\GS_\XGS`\XGSa\XGSb\XGSc\XGSd\XGSe\XGSf\XGSg\XGSh\XGSi\XGSj\XGSk\XGSl\XGSm\XGSn\XGSo\XGSp\XGSq\XS\uGSr\Y4,GSs jjGrGSt GrS<\GS\GS_\XGS`\XGSa\XGSb\XGSc\XGSd\XGSe\XGSf\XGSg\XGSh\XGSl\XGSm\XGSn\XGSo\XGSp\XGSq\XS\u4&GSu jGrGSv Gr\D" \<GR                  R                  5      GSw 5       Gr\D" \<GR                  R                  5          GS6GSx j5       Gr\D" \<GR                  R                  5      GSy 5       Gr\D" \<GR                  5      \/" SS$5          GS6GSz j5       5       Gr\D" \<GR                  5      \/" S5      GS{ 5       5       GrS<\GS|\4GS} jGr " GS~ GS\5      GrS<\GS|\GS\X4GS jGr\D" \<GR                  R                  5      GS 5       Gr\D" \<GR                  5      \/" 5       GS 5       5       Gr\D" \<GR                  5      \/" SGS5      GS 5       5       Gr\D" \<GR                  R                  /5      GS 5       Gr\D" \<GR                  R                  5           GS<GS j5       Gr\D" \<GR                  R                  \<GR                  R                  /5      \/" 5       SSSSSGS.GS j5       5       Gr\D" \<GR                  R                  \<GR                  R                  /5      \/" 5       SSSSSGS.GS j5       5       Gr\D" \<GR                  R                  5      GS 5       Gr\D" \<GR                  R                  5      GS=GS j5       GrGS)S)\XGS\XGS\Y4GS jjGrGS GrGS Gr\D" \<GR                  R                  5      GS$GS j5       GrGS$GS jGrGS&GS jGrGS GrGS&GS jGrGS>GS jGr\D" \<GR                  R                  5      GS 5       Gr\D" \<GR                  5      GS 5       Gr\D" \<GR                  GR                  \<GR                  GR                  \<GR                  GR                  \<GR                  GR                  /5      \/" 5       GS&GS j5       5       Gr\D" \<GR                  GR                  \<GR                  GR                  \<GR                  GR                  \<GR                  GR                  /5      GS&GS j5       Gr\D" \<GR                  /5          GS?GS\GS\GS\GS\GS\YGS\YGS\	\   4GS jj5       GrGS\GS\\XGS4   4GS jGr\D" \<GR                  /5          GS?GS\GS\GS\GS\	\   GS\YGS\GS\YGS\YGS\	\   4GS jj5       Gr \D" \<GR                  /5           GS@GS\GS\GS\GS\	\   GS\GS\YGS\YGS\	\   4GS jj5       Gr\D" \<GR                  /5       GS&GS\GS\GS\GS\S\GS\GS\GS\GS\XGS\XGS\GS\YGS\GS\GS\	\   4GS jj5       Gr\D" \<GR
                  /5          GSAGS\GS\GS\GS\GS\YGS\	\   GS\	\   4GS jj5       Gr\D" \<GR                  /5        GS(GS\GS\GS\GS\S\GS\GS\GS\YGS\	\   GS\	\   4GS jj5       Gr\D" \<GR                  /5           GSBGS\GS\GS\GS\	\   GS\GS\YGS\	\   GS\	\   S\\\4   4GS jj5       Gr
\D" \<GR                  /5         GSCGS\GS\GS\GS\	\   GS\YGS\YGS\	\   4GS jj5       Gr\D" \<GR                  /5        GSDGS\GS\GS\GS\GS\	\   S\GS\GS\GS\GS\GS\W\Y   GS\YGS\	\   4GS jj5       Gr\D" \<GR                  /5       GS&GS\GS\GS\GS\S\GS\GS\GS\GS\GS\GS\GS\XGS\XGS\GS\YGS\	\   4 GS jj5       Gr\D" \<GR"                  /5           GS<GS\GS\GS\GS\	\   GS\	\   GS\XGS\XGS\GS\YGS\YGS\	\   GS\	\X   GS\	\X   GS\	\   GS\	\   4GS jj5       Gr\D" \<GR&                  /5         GS%GS\GS\GS\GS\S\GS\GS\GS\GS\XGS\XGS\GS\YGS\GS\GS\	\   GS\	\X   GS\	\X   4"GS jj5       Gr\D" \<GR*                  /5           GSEGS\GS\GS\S?\	\   GS\	\   GS\	\   GS\	\X   GS\	\X   GS\GS\XGS\YGS\	\   GS\	\   GS\	\   GS\	\X   4GS jj5       Gr\D" \<GR.                  /5         GS>GS\GS\GS\GS\S?\	\   GS\	\   GS\	\   GS\GR0                  GS\GR0                  GS\GS\GS\GS\GS\XGS\YGS\	\   GS\	\X   GS\Y4$GS jj5       Gr\D" \<GR4                  R                  /5          GSFS(\R(                  SE\R(                  GS\R(                  GS\R(                  S?\	\R(                     GS\	\R(                     SA\	\R                     GS\Y4GS jj5       Gr\D" \<GR8                  GR:                  \<GR8                  GR<                  /5      \/" 5       GS)GS j5       5       Gr\D" \<GR@                  GR:                  5      GS)GS j5       Gr!\D" \<GRD                  R                  \<GRD                  R                  /5      \/" 5       GS$SS/.GS jj5       5       Gr#GS Gr$GS Gr%\D" \<GRL                  R                  \<GRN                  R                  /5      GS&GS j5       Gr&\D" \<GRP                  R                  \<GRR                  R                  /5      GS(GS j5       Gr(\D" \<GRT                  R                  \<GRV                  R                  /5        GS(GS\GS\\\X\GR0                  4      GS\\\X\GR0                  4      GS\	\   GS\	\   4
GS jj5       Gr*\D" \<GRX                  R                  \<GRZ                  R                  /5      GS%GS j5       Gr,\D" \<GR\                  R                  \<GR\                  GR^                  \<GR\                  GR                  \<GR\                  GR`                  /5      GSGGS j5       Gr1GS Gr2\D" \<GRf                  R                  5        GS(GS j5       Gr4\D" \<GRj                  R                  5      GS 5       Gr5\D" \<GRl                  R                  5      GS 5       Gr6GS Gr7GS Gr8\D" \<GRr                  R                  \<GRt                  R                  /5      GS9GS j5       Gr;\D" \<GRx                  R                  5      GSHGS j5       Gr<\D" \<GRz                  R                  5      GSIGS j5       Gr>\D" \<GR~                  5      \/" 5        GSJGS j5       5       Gr@\D" \<GR                  R                  \<GR                  GR                  /5      \/" S#S$5      GS:GS j5       5       GrB\GR                  GrDGS GrE\D" \<GR                  R                  5      GS 5       GrF\D" \<GR                  R                  5      GS 5       GrG\D" \<GR                  R                  5      GS 5       GrI\D" \<GR                  R                  5      GS 5       GrJ\D" \<GR                  R(                  \<GR                  GR                  /5      \/" 5       SSGS.GS j5       5       GrM\D" \<GR                  /5      \/" 5       GSKGS j5       5       GrO\D" \<GR                  R                  \<GR                  R                  /5        GS(GS j5       GrR\D" \<GR                  R                  /5        GS(GS j5       GrT\D" \<GR                  R                  5      GS 5       GrU\D" \<GR                  R                  \<GR                  R                  /5      \/" 5       GS%GS j5       5       GrV\D" \Rv                  Rx                  GR                  5      GS 5       GrW\D" \Rv                  Rx                  GR                  5      GS 5       GrX\D" \<GR                  5      \/" 5       SSSSGS.GS j5       5       GrZGS Gr[\D" \<GR                  5      GS 5       Gr]\D" \<GR                  5       GSLGS  j5       Gr_\D" \<GR                  5       GSLGS j5       Gra\D" \<GR                  5       GSLGS j5       Grc\D" \<GR                  5      \/" 5       SSGS.GS j5       5       Gre\D" \<GR                  5      \/" 5       GS\XS(\S\4GS j5       5       Grg\D" \<GR                  5      S(\4GS j5       Gri\D" \<GR                  5      \/" SRS9S(\S\4GS j5       5       Grj\D" \<GR                  5      \/" 5       S(\S\4GS	 j5       5       GrkGS
 Grl     GSMGS\GS\GS\	\R(                     GS\	\R(                     GS\	\   S?\	\   GS\	\R(                     SA\	\R                     GS\Y4GS jjGrm\D" \<GR                  5      \/" 5          GS%GS\GS\GS\	\   S?\	\   SA\	\R                     S\4GS jj5       5       Gro\D" \<GR                  /5           GSMGS\R(                  GS\R(                  GS\R(                  GS\R(                  GS\	\R(                     S?\	\R(                     GS\	\R(                     SA\	\R                     GS\Y4GS jj5       Grq\D" \<GR                  5      \/" 5       GS\S)\XGS\YS\4GS j5       5       Grs\D" \<GR                  5      \/" 5       GSGS j5       5       Gru\D" \<GR                  5      \/" 5          GSNS=\S$\GS\XGS\YGS\YS\4GS jj5       5       Grv\D" \<GR                  R                  5       GSOS#\S^\W\   GS\W\X   GS\4GS jj5       GrxGS GryGS GrzG\y" \<GR                  5        G\y" \<GR                  5        G\y" \<GR                  5        G\y" \<GR                  5        G\y" \<GR                  5        G\y" \<GR                   5        G\y" \<GR                  5        G\y" \<GR                  5        G\y" \<GR                  5        G\z" \<GR                  5        G\z" \<GR
                  5        G\z" \<GR                  5        G\z" \<GR                  5        G\z" \<GR                  5        G\z" \<GR                  5        G\z" \<GR                  5        G\z" \<GR                  5        G\z" \<GR                  5        G\z" \<GR                  5        G\z" \<GR                  5        G\z" \<GR                  5        GS Gr\D" \<GR"                  5      \/" 5       GS 5       5       Gr\D" \<GR$                  5      \/" 5       SGGS .GS! j5       5       Gr\D" \<GR&                  5      \/" 5       SGGS .GS" j5       5       GrG\" \<GR"                  5      GrG\" \<GR$                  5      GrG\" \<GR&                  5      GrS SK0rS SGKrS SGKrGS# GrG\" 5         g(P      N)Sequence)Enum)wraps)CallableOptionalTypeVarUnion)	ParamSpec)SymBoolSymFloatTensor)_add_op_to_registry_convert_out_paramsglobal_decomposition_table
meta_table)
OpOverload)_prim_elementwise_meta$ELEMENTWISE_PRIM_TYPE_PROMOTION_KIND)BoolLikecorresponding_complex_dtypecorresponding_real_dtypeelementwise_dtypesELEMENTWISE_TYPE_PROMOTION_KIND	FloatLikeIntLikemake_contiguous_strides_forNumbersuggest_memory_format
TensorLike)_maybe_convert_to_dtype_maybe_resize_out_resize_output_check_safe_copy_outout_wrapper)_broadcast_shapes_maybe_broadcast)_config)_pytree_T_PatenIMPLMeta   returnc                    ^  U 4S jnU$ )Nc                 Z   >^  [        T 5      m U 4S jn[        R                  " UT5        T $ )Nc                 (   > [        [        U T5        g N)r   r   )opfns    Y/var/www/html/land-doc-ocr/venv/lib/python3.13/site-packages/torch/_meta_registrations.pyregister0register_meta.<locals>.wrapper.<locals>.register:   s    
B3    )r   pytree	tree_map_)r5   r7   r4   s   ` r6   wrapperregister_meta.<locals>.wrapper7   s)     $	4 	2&	r9    )r4   r<   s   ` r6   register_metar?   6   s     Nr9   type_promotionc                     [         R                  " USU 06u  p#U Vs/ s H  n[        XC5      PM     nn[        U6 n[	        US[
        R                  06$ s  snf )Ntype_promotion_kindr@   )utilsr   r    r&   r   r   DEFAULT)r@   args_result_dtypexs        r6   elementwise_metarI   C   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      $ r3   )torch	complex32halfcfloatfloatcdoubledoubleget)dtypefrom_complexs     r6   toRealValueTyperU   W   sC    ekku||L
 E))r9   c                 p   ^ ^ [        [        T /UQ76 5      m[        R                  " TT :H  UU 4S j5        g )Nc                     > ST ST  3$ )Nzoutput with shape z# doesn't match the broadcast shape r>   )broadcasted_shape
self_shapes   r6   <lambda>)check_inplace_broadcast.<locals>.<lambda>d   s    $ZL0STeSfgr9   )tupler%   rK   _check)rY   
args_shaperX   s   ` @r6   check_inplace_broadcastr_   `   s0    /
HZHI	LLZ'gr9   Fc	           	        ^ ^^^^	 [        T [        R                  5      (       a)  [        R                  " T R	                  5       S:H  S 5        [        T[        R                  5      (       a)  [        R                  " TR	                  5       S:H  S 5        [        S T TT4 5       5      (       a`  [        R                  " [        R                  " 5       5      m	Tc  T	mOO[        R                  " [        R                  " T5      U	U4S j5        OT=(       d    [        R                  " 5       m[        T[        R                  5      (       d   e[        R                  " [        T[        5      UU U4S j5        [        T[        5      (       d   e[        R                  " TS:  S 5        [        R                  " T4TUSUUS	9$ )
Nr   c                      gNz:linspace only supports 0-dimensional start and end tensorsr>   r>   r9   r6   rZ   (meta_linspace_logspace.<locals>.<lambda>x       Pr9   c                      grb   r>   r>   r9   r6   rZ   rc   }   rd   r9   c              3   B   #    U  H  n[        U[        5      v   M     g 7fr3   )
isinstancecomplex).0args     r6   	<genexpr>)meta_linspace_logspace.<locals>.<genexpr>   s     
C/B:c7##/Bs   c                     > ST  ST 3$ )Nzlinspace(): inferred dtype z& can't be safely cast to passed dtype r>   )default_complex_dtyperS   s   r6   rZ   rc      s    56K5LLrsxryzr9   c                     > S[        T5      R                   S[        T 5      R                   S[        T5      R                   S3$ )Nz4received an invalid combination of arguments - got (, ))type__name__)endstartstepss   r6   rZ   rc      sB     u+r$s),,-RU0D0D/EQHr9   c                      g)Nz$number of steps must be non-negativer>   r>   r9   r6   rZ   rc      s    %Kr9   metarS   layoutdevice
pin_memoryrequires_grad)rg   rK   r   r]   dimanyrC   r   get_default_dtypeis_complex_dtyperS   _check_typer   empty)
ru   rt   rv   baserS   r{   rz   r|   r}   rn   s
   ``` `    @r6   meta_linspace_logspacer   h   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;;	# r9   c                 6  ^ [         R                  " TR                  [         R                  :H  U4S j5        [         R                  " U R                  5       S:H  =(       a    TR                  5       S:g  (       + S 5        U R                  TR                  5      $ )Nc                  "   > ST R                    3$ )Nz2take(): Expected a long tensor for index, but got rS   indexs   r6   rZ   meta_take.<locals>.<lambda>   s    DU[[MRr9   r   c                      g)Nz*take(): tried to take from an empty tensorr>   r>   r9   r6   rZ   r      s    <r9   )rK   r]   rS   long_check_indexnumel	new_emptyshape)selfr   s    `r6   	meta_taker      sm     
LLuzz!R
 
ZZ\Q55;;=A#56< >>%++&&r9   r~   c                b  ^ ^^ T R                   nTR                   n[        R                  " X4:H  S 5        [        R                  " T R                  T5      S:H  =(       a    TR                  T5      S:H  UUU 4S j5        [	        T R
                  TR
                  5      nT R                  U5      $ )Nc                      g)Nz=linalg.cross: inputs must have the same number of dimensions.r>   r>   r9   r6   rZ   linalg_cross.<locals>.<lambda>       Or9   r.   c                  V   > ST  STR                  T 5       STR                  T 5       3$ )Nzlinalg.cross: inputs dimension z must have length 3. Got  and size)r~   otherr   s   r6   rZ   r      s1    -cU 399S>"%

3'8:r9   )ndimrK   r]   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>>)$$r9   c                 x    [        U S5        [        U S5        [        R                  " U [        R                  S9$ )Nzlinalg.matrix_expmemory_format)squareCheckInputscheckFloatingOrComplexrK   
empty_likecontiguous_formatr   s    r6   linalg_matrix_expr      s3     d/04!45D0G0GHHr9   valuesindicesc                 R   [         R                  " U R                  U R                  U R                  S9n[         R                  " U R                  U R                  [         R
                  S9nU R                  5       S:w  a%  U R                  S:w  a  [        XR                  5        X#4$ )Nr{   rS   r   )	rK   r   r   r{   rS   int64r   r   maybe_wrap_dim)r   r~   r   r   s       r6   	cummaxminr      sl    
 [[DKKtzzJFkk$**T[[LGzz|qTYY!^sII&?r9   c                 r    [        XR                  5        [        R                  " U [        R                  S9$ Nr   )r   r   rK   r   r   )r   r~   s     r6   logcumsumexpr      s)     3		"D0G0GHHr9   c                V  ^ UR                   n[        U5      nXV-
  n[        [        U5      5      n[        U5       V	s/ s H  n	SPM     n
n	U H  nSX'   M	     / / pU H0  nX   (       d  UR	                  U5        M  UR	                  U5        M2     X-   n[        U5      nUR                  5       mUS U nUR                  U4S jSS9  XUS  -   nUR                  U5      nS/[        UR                  US  5      -   nUR                  U5      nUR                  S5      nUUS'   [        U5      n[        [        U5      5       H  nX#U      UUS-   '   M     U R                  U[        R                  S9  [        U5       V	s/ s H  n	SPM     nn	SnUS-
  nUS:  a1  UU R                  S5      -  UUU   '   UX(U      -  nUS-  nUS:  a  M1  [        Xu5       H   nU R                  SUU-
  -   5      UUU   '   M"     U R                  UUU R                  5       5        U $ s  sn	f s  sn	f )	NFTc                    > TU    $ r3   r>   )rH   self_stridess    r6   rZ   _exec_fft.<locals>.<lambda>   s	    <?r9   keyreverser   r      r   )r   lenlistrangeappendstridesortpermuter   reshaper   resize_rK   r   as_strided_storage_offset)outr   	out_sizesr~   forwardr   signal_ndim
batch_dimsdim_permuterF   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    $ r3   r>   )r   r   s    r6   rZ   _sort_dims.<locals>.<lambda>"  s	    l1or9   )r   )r   r   r   intr   )r   r~   r   sorted_dimsr   s       @r6   
_sort_dimsr     sL    s)K;;=L6#k"S%667<<% =  r9   c                 
   [         R                  " U R                  R                  5        U(       d  U R	                  5       $ [        X5      nU R                  U R                  5       5      n[        XPU R                  5       XCS9$ )Nr   )	rK   r]   rS   
is_complexcloner   r   r   r   )r   r~   normalizationr   r   r   s         r6   meta_fft_c2cr   )  s\     
LL&&'zz|T'K
..
%CS		[JJr9   c                 n    [        U 5      [        :  d!  [        U 5      S:  a  U S   S:X  a
  U S   S:X  a  gg)N   r   r   FT)r   cufft_max_ndimr   s    r6   use_optimized_cufft_pathr   8  s3    
3x. SX]s1v{s1vQR{r9   c                 |  ^ [         R                  " U R                  R                  5        [	        U R                  5       5      n[	        U5      nUS   nXF   S-  S-   n[	        U5      nXxU'   U(       a  XuU'   [        U 5      S:X  d  [        U 5      S:X  Gax  U R                  U[        R                  " U R                  5      S9n	U n
[        U 5      S:X  a  [        U5      (       a  [        XXQSS9  O[        U5      S:X  a  UOUn[        XX/SS9  [        U5      S:  a.  U R                  U[        R                  " U R                  5      S9n
US S nU(       au  XpU
R                  5       mUR                  U4S	 jSS
9  [        [         [        U5      5      nU[        U5      U-
  S  n[        XXSS9  US [        U5      U-
   nU(       a  Mu  U(       d7  U	R                  U5      XV   :w  a   U
R#                  U[         R$                  S9  U
n	U	$ U R                  U[        R                  " U R                  5      S9$ )Nr   r   r   cudaxpur   Tr   c                    > TU    $ r3   r>   )r   stridess    r6   rZ   meta_fft_r2c.<locals>.<lambda>f  s	    '!*r9   r   r   )rK   r]   rS   is_floating_pointr   r   device_hintr   rC   r   r   r   r   r   r   minr   r   r   )r   r~   r   onesidedinput_sizesr   last_dimlast_dim_halfsizeonesided_sizesoutputworking_tensortarget_sizesr   max_dims	last_dimsr   s                  @r6   meta_fft_r2cr  ?  s+    
LL--.tyy{#K[!I2wH#-2Q6+&N08/(4F"k$&75&@ U>>tzzJ   
 t&+CC+H+HfidK ),CA9>LflJPTU3x!|!%U%F%Ftzz%R "0 "
 cr(K)7(//1  ,d !  ~s;/?@'K(88(C(EF	Nt **GC,<x,GH + {{8$	(;;&&y@W@W&X' ~~U>>tzzJ  
 	
r9   )	generatorc                D    [        U[        R                  " U /5      5      $ r3   )r!   rK   Size)nr  r   s      r6   meta_randpermr  |  s    S%**aS/22r9   rS   rz   r{   r|   c                .    [         R                  " XX#US9$ Nr  rK   r   )r  rS   rz   r{   r|   s        r6   meta_randperm_defaultr    s     ;;	v r9   c                t   ^ ^ Sm[         R                  " T T:  U U4S j5        [         R                  " XX4US9$ )Nr   c                     > ST ST  3$ Nz:random_ expects 'from' to be less than 'to', but got from=z >= to=r>   highlows   r6   rZ   meta_randint.<locals>.<lambda>      LSEQXY]X^_r9   r  rK   r]   r   )r  r   rS   rz   r{   r|   r  s   `     @r6   meta_randintr    s:     C	LLs
_ ;;&J r9   c                p   ^ ^ [         R                  " TT :  UU 4S j5        [         R                  " X#XEUS9$ )Nc                     > ST ST  3$ r  r>   r  s   r6   rZ   "meta_randint_low.<locals>.<lambda>  r  r9   r  r  )r  r  r   rS   rz   r{   r|   s   ``     r6   meta_randint_lowr    s5     
LLs
_ ;;&J r9   c                .    [         R                  " XX#US9$ r
  r  )r   rS   rz   r{   r|   s        r6   meta_rand_defaultr    s     ;;&J r9   r   lastdimc                    [         R                  " U R                  R                  5        [	        U 5      S:X  a  [        U R                  5       5      nX4US   '   U R                  U[        U R                  5      S9n[        U5      (       a(  [        UU R                  [         R                  S9UUSS9$ [        U5      S:  a  [        XS S SU5      nOU R                  [         R                  S9n[        XVXAS   /SS9$ U n[        U5      S:  a  US S n[        XUSS9nUSS  n[        UR                  5       5      nX4US   '   U R                  U[        U R                  5      S9n	[        XXASS9$ )	Nr   r   r   r   Fr   r   r   )rK   r]   rS   r   r   r   r   r   rU   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&	$#b'nnYodjj.InJYUCCr9   c                 `   SSK Jn  U" U 5      (       d%  [        R                  " U 5      S:X  a  [	        S5      e[        U[        5      (       a`  UR                  X5      nU R                  5       UR                  5       :w  a-  [        R                  R                  X@R                  5       5        U $ )Nr   )free_unbacked_symbolsr   zQmore than one element of the written-to tensor refers to a single memory location)%torch.fx.experimental.symbolic_shapesr#  rK   _debug_has_internal_overlapRuntimeErrorrg   r   tor   r+   expand_copydefault)r   srcnon_blockingr#  intermediates        r6   
meta_copy_r-    s     L "$''E,M,Md,SWX,X_
 	
 #vvvd199;,++--$$\99;?Kr9   c                     [        U R                  5       5      n[        U R                  5       5      nXR                  5       :  a  SOX!   X1   -  nUR	                  US5        UR	                  X5        X#4$ Nr   )r   r   r   r~   insert)tensorr~   result_sizesresult_strides
new_strides        r6   inferUnsqueezeGeometryr5    sf    &L&--/*NZZ\)|/@>CV/VJQ#*''r9   c                 z    [        XR                  5       S-   5      n[        X5      u  p#U R                  X#5        U $ r/  )r   r~   r5  r   )r   r~   g_sizes	g_stridess       r6   meta_unsqueeze_r9    s6    
hhj1n
-C/:GW(Kr9   r   weight_metabias_activation_opt	out_dtypec                 @   [        U R                  5      nUb+  UR                  S5      UR                  S5      :X  d   S5       eUR                  S5      U R                  S5      S-  :X  d   eUR                  S5      US'   [        U R                  5      S:X  d   S5       eSU R                  S5      4nUb9  U R                  [
        R                  :X  a  U[
        R                  :X  d   S5       eU R                  UUc  U R                  OUS9R                  Xg5      nU$ )	Nr   zoutput size mismatchr   r   r   z*we can only handle the squashed input case9out_dtype is only supported for i8i8->i32 linear operatorr   )
r   r   r   r   rS   rK   int8int32r   
as_strided)	r   r:  r;  r<  r=  r>  output_sizestransposed_stridesr   s	            r6   meta_sparse_structured_linearrF    s    $L{{1~1-E/EE-;;q>UZZ^a////{{1~L u{{q N"NN UZZ]+{{ejj(Y%++-E 	
G	
E __&.ekkI   j2 
 Mr9   mat1	mat1_metamat2c                    [        U R                  5      S:X  d   e[        UR                  5      S:X  d   e[        UR                  5      S:X  d   eU R                  S5      UR                  S5      S-  :X  d   eU R                  S5      UR                  S5      /nUb9  UR                  [        R
                  :X  a  U[        R                  :X  d   S5       eUR                  UUc  UR                  OUS9nU$ )Nr   r   r   r@  r   r   r   r   rS   rK   rA  rB  r   )rG  rH  rI  r>  rD  r   s         r6   meta_sparse_structured_mmrL  6  s     tzz?ay1$$$tzz?a99Q<499Q<!++++IIaL$))A,/LzzUZZ'I,D 	
G	
D ^^%-djj9  F
 Mr9   r   )alphabetar>  c                   [        U R                  5      S:X  d   S5       e[        UR                  5      S:X  d   e[        UR                  5      S:X  d   e[        UR                  5      S:X  d   eU R                  S5      UR                  S5      :X  d   S5       eUR                  S5      UR                  S5      S-  :X  d   eUR                  S5      UR                  S5      /nUb9  UR                  [        R
                  :X  a  U[        R                  :X  d   S5       eUR                  UUc  UR                  OUS9nU$ )Nr   zEonly input broadcasted to columns of mat1 * mat2 product is supportedr   r   r@  r   rK  )	r   rG  rH  rI  rM  rN  r>  rD  r   s	            r6   meta_sparse_structured_addmmrP  O  s/    u{{q  O  tzz?ay1$$$tzz?a::a=DIIaL( O( 99Q<499Q<!++++IIaL$))A,/LzzUZZ'I,D 	
G	
D ^^%-djj9  F
 Mr9   compressed_Adense_BrM  transpose_resultalg_idsplit_ksplit_k_modec	                    UR                   [        R                  [        R                  [        R                  [        R
                  [        R                  1;   d   S5       eU R                   UR                   :X  d   S5       e[        UR                  5      S:X  d   S5       eU R                   [        R
                  [        R                  4;   n	U	(       a  SOSn
U	(       a  UR                  5       (       a   S5       eUR                  S5      nUR                  S	5      nU R                  5       S
-  X-  -  nUb  XR                  S5      :X  d   eUbP  U	(       aB  U[        R                  [        R                  [        R                  [        R                  1;   d   S5       eU(       a  X4OX4nUR                  XS9$ )Nz;_cslt_sparse_mm only supports fp16, bf16, int8, and fp8e4m3zinputs must have the same dtyper   z'_cslt_sparse_mm only supports 2d inputs
   	   z.dense input must be transposed for 8bit dtypesr   r      z\out_dtype is not supported for {compressed_A.dtype} x {dense_B.dtype} -> {out_dtype} matmul!r   )rS   rK   float32float16bfloat16rA  float8_e4m3fnr   r   is_contiguousr   r   rB  r   )rQ  rR  r<  rM  r>  rS  rT  rU  rV  is_8bit_input_typecompression_factorkr  moutput_shapes                  r6   meta__cslt_sparse_mmre  r  s    ==

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

E<O<O/PP1q((** 	
<	
* 	QAQA					"(:(>?AIIaL   !iMMNNKK	4
 '
 	
 k	
 
 .A6A6L\;;r9   T)include_selfr   sourcereducerf  c                H    [         R                  " U [         R                  S9$ r   rK   r   r   r   r~   r   rg  rh  rf  s         r6   meta_index_reducerl    s     D0G0GHHr9   c                    U $ r3   r>   rk  s         r6   meta_index_reduce_rn    s	     Kr9   c                     [        U R                  5       5      nU R                  5       S:  a  UR                  5       X1'   U R	                  U5      $ Nr   )r   r   r~   r   r   )r   r~   r   result_sizes       r6   meta_index_selectrr    s>     tyy{#KxxzA~ ;;=>>+&&r9   )lengthsr   offsetsaxisunsafeinitialdatars  rt  ru  rv  c                   ^ ^ Ub  [        S5      eUU 4S jnUb  U" UR                  5      $ Ub+  UR                  S S UR                  S   S-
  4-   n	U" U	5      $ [        S5      e)Nz?segment_reduce(): indices based reduction is not supported yet.c                    > [         R                  " U TR                  TS-   S  -   TR                  S[         R                  S9$ )Nr   rx   rS   r{   r   )rK   r   r   rS   r   )lengths_shaperu  rx  s    r6   segment_reduce_lengths_tensor:meta_segment_reduce.<locals>.segment_reduce_lengths_tensor  s>    {{DJJtaxz22**11	
 	
r9   r   r   z<segment_reduce(): Either lengths or offsets must be defined.)NotImplementedErrorr   r&  )
rx  rh  rs  r   rt  ru  rv  rw  r}  r|  s
   `    `    r6   meta_segment_reducer    s|     !M
 	

 ,W]];; cr*gmmB.?!.C-EE,];;
U
VVr9   c                 $    U R                  S5      $ Nr>   r   r   s    r6   meta_maxr         >>"r9   c                     [         R                  " U R                  U45      n[        XU5      nU R	                  U5      U R	                  U[
        R                  S94$ Nr   rC   reduction_dimsr   _compute_reduction_shaper   rK   r   r   r~   keepdimrd  s       r6   meta_max_dimr    P    


tzzC6
2C+Dw?L|$|5::6 r9   c                 $    U R                  S5      $ r  r  r   s    r6   meta_minr    r  r9   c                     [         R                  " U R                  U45      n[        XU5      nU R	                  U5      U R	                  U[
        R                  S94$ r  r  r  s       r6   meta_min_dimr    r  r9   c                     U R                  5       (       a  [        U R                  5      nO[        U [        R
                  S9u  p![        R                  " XS9$ NrB   r   )r   r   rS   r   r   INT_TO_FLOATrK   r   )r   rG   rF   s      r6   
meta_angler    sH    /

;, ? L L
 D55r9   c                     [         R                  " XR                  5       U R                  5        UR	                  [         R
                  " U 5      5      $ r3   )rK   _resize_output_r   r{   copy_angle)r   r   s     r6   meta_angle_outr    s4    	#yy{DKK899U[[&''r9   c                     g r3   r>   )vals    r6   assert_asyncr        
r9   c                     g r3   r>   )r  
assert_msgs     r6   assert_async_metar  "  r  r9   c                     g r3   r>   )ss    r6   
print_metar  '  r  r9   rS   rz   r{   r|   r   c                 ,    [         R                  " SSS9$ )Nr   rx   r{   r  r  s        r6   make_dep_tokenr  ,  s     ;;q((r9   c                 j    SSK Jn  [        U [        [        45      (       a  [        S5      eU" XUS9  g )Nr   )constrain_range'Constraining SymFloat or Symbool is nyir   max)r$  r  rg   r   r   
ValueError)r   r   r  r  s       r6   sym_constrain_ranger  8  s0     F$7+,,BCCDs+r9   c                 .    [         R                  XUS9  U$ Nr  )r+   r  r   r   r  	dep_tokens       r6   functional_sym_constrain_ranger  B  s    T4r9   c                 6   SSK Jn  Uc  Uc  [        R                  " U 5        g [	        U [
        [        45      (       a  [        S5      e[        U 5      [        L a7  Ub  [        R                  " X:  5        Ub  [        R                  " X:*  5        g U" XUS9  g )Nr   )_constrain_range_for_sizer  r  )r$  r  rK   _check_is_sizerg   r   r   r  rr   r   r]   )r   r   r  r  s       r6   sym_constrain_range_for_sizer  H  s     P
{s{T"$7+,,BCCDzS?LL%?LL%d5r9   c                 .    [         R                  XUS9  U$ r  )r+   r  r  s       r6   'functional_sym_constrain_range_for_sizer  \  s    %%d%=r9   c                     U$ r3   r>   )r  r  r  s      r6   functional_assert_async_metar  b  s    r9   f_namec                     U R                  5       S:  d
   U S35       eU R                  S5      U R                  S5      :X  d.   U SU R                  S5       SU R                  S5       S35       eg )Nr   z3: The input tensor must have at least 2 dimensions.r   z5: A must be batches of square matrices, but they are  by 	 matrices)r~   r   )r   r  s     r6   r   r   h  s}    88:? (EF? 99R=DIIbM) (G		RTVZ[_[d[deg[hZiirs)r9   Anamec                   ^ ^^ [         R                  " T R                  TR                  :H  UU 4S j5        [         R                  " T R                  TR                  :H  UU 4S j5        [         R                  " TR	                  S5      TR	                  S5      :H  U4S j5        [         R                  " TR	                  S5      T R	                  S5      :H  UUU 4S j5        g )Nc                  >   > STR                    ST R                    S3$ )Nz:Expected b and A to be on the same device, but found b on z
 and A on 	 instead.r  r  r   s   r6   rZ   (linearSolveCheckInputs.<locals>.<lambda>w  s     H{{m:ahhZy:r9   c                  >   > STR                    ST R                    S3$ )Nz=Expected b and A to have the same dtype, but found b of type z and A of type r  r   r  s   r6   rZ   r    s     Kzzl/!'')=r9   r   r  c                  R   > ST R                  S5       ST R                  S5       S3$ )Nz3A must be batches of square matrices, but they are r  r  r   r  r   r  s   r6   rZ   r    s+    FF2J<tAFF2J<yBr9   c                     > ST ST R                  S5       ST R                  S5       STR                  S5       STR                  S5       3
$ )NzIncompatible matrix sizes for z: each A matrix is r   r  z but each b matrix is r  r   )r  r  r   s   r6   rZ   r    sM    ,TF 3D$TYYr]O4		"Hr9   )rK   r]   r{   rS   r   )r   r  r  s   ```r6   linearSolveCheckInputsr  t  s    	LLqxx	
 
LL

agg	
 
LL	r
affRj 	
 
LL	r
diim#	
r9   tallow_low_precision_dtypesc                 h  ^^ U R                   m[        R                  " U R                  5       =(       d    U R	                  5       UU4S j5        U(       d\  [        R                  " T[        R
                  [        R                  [        R                  [        R                  4;   UU4S j5        g g )Nc                     > T ST  3$ )Nz<: Expected a floating point or complex tensor as input. Got r>   rS   r  s   r6   rZ   (checkFloatingOrComplex.<locals>.<lambda>  s    6(VW\V]^r9   c                     > T ST  3$ )Nz*: Low precision dtypes not supported. Got r>   r  s   r6   rZ   r    s    vhHPr9   )	rS   rK   r]   r   r   rO   rQ   rN   rP   )r  r  r  rS   s    ` @r6   r   r     sn    
 GGE	LL	/^ &ekk5<<u}}MMP	
 &r9   arg_namec                 b   ^^ [         R                  " U R                  5       S:  UU4S j5        g )Nr   c                     > T ST  S3$ )Nz: The input tensor z! must have at least 2 dimensions.r>   )r  r  s   r6   rZ   checkIsMatrix.<locals>.<lambda>  s    6(-hZ7XYr9   )rK   r]   r~   )r  r  r  s    ``r6   checkIsMatrixr    s    	LL	1Yr9   Br   c                   ^ ^^^ [        T T5        [        TT5        [        R                  " T(       a#  T R	                  S5      TR	                  S5      :H  O"T R	                  S5      TR	                  S5      :H  U UUU4S j5        g )Nr  r   c                     > T ST(       a  SOS ST R                  S5       ST R                  S5       STR                  S5       STR                  S5       S	3$ )
Nz2: Incompatible shapes of A and B for the equation zAX = BzXA = Bz (r  rH   r   r   rq   r   )r  r  r  r   s   r6   rZ   #checkInputsSolver.<locals>.<lambda>  sV    hHxX.AaffRj\qvvbzl!AFF2J<qJr9   )r   r  rK   r]   r   )r  r  r   r  s   ````r6   checkInputsSolverr    sY    a !V	LL$(r
affRj affRjAFF2J.F	
r9   resultfn_nameresult_namec                 v   ^ ^^^ [         R                  " TR                  TR                  :H  U UUU4S j5        g )Nc            	      L   > T  ST ST STR                    STR                    3	$ )Nz: Expected z5 and input tensors to be on the same device, but got z on z and input on r  )r  r   r  r  s   r6   rZ   !checkSameDevice.<locals>.<lambda>  s0    i{;-/dm4nU\\NLr9   )rK   r]   r{   )r  r  r   r  s   ````r6   checkSameDevicer    s&     
LL%	
r9   UPLOc                    ^  T R                  5       n[        R                  " [        T 5      S:H  =(       a    US:H  =(       d    US:H  U 4S j5        g )Nr   ULc                     > ST  3$ )Nz1Expected UPLO argument to be 'L' or 'U', but got r>   )r  s   r6   rZ   checkUplo.<locals>.<lambda>  s    CD6Jr9   )upperrK   r]   r   )r  UPLO_uppercases   ` r6   	checkUplor    s<    ZZ\N	LLD	QKNc1J^s5JJr9   eigenvalueseigenvectorsr  	compute_vc                 P   [        U S5        [        U5        [        U R                  5      nU(       a,  U R	                  U5      nUR                  U[        USS95        OU R	                  S/5      nUR                  5         U R	                  U[        U R                  5      S9nXT4$ )Nzlinalg.eighF	row_majorr   r   )
r   r  r   r   r   r   r   poprU   rS   )r  r  r  r   vecsvalss         r6   meta__linalg_eighr    s     a'dOME{{5! ;EU ST{{A3	IIK;;uOAGG$<;=D:r9   c                     [        U S5        [        R                  " U R                  5      (       a  U R                  O[        R                  " U R                  5      nU R                  U R                  S S US9$ )Nzlinalg.eigvalsr   r   r   rC   r   rS   r   r   r   )r   complex_dtypes     r6   meta__linalg_eigvalsr    sf     e-. !!%++.. 	..u{{; 
 ??5;;s+=?AAr9   c                 0   [        U S5        [        R                  " U R                  5      (       a  U R                  O[        R                  " U R                  5      nU R                  U R                  S S US9nU R                  U R                  US9nX#4$ )Nz
linalg.eigr   r   r  )r   r  r   vectorss       r6   meta_linalg_eigr    s     e\* !!%++.. 	..u{{; 
 __U[["-]_CFooekko?G?r9   r*  c                 p    U R                   R                  [        R                  S9R	                  SS5      $ )Nr   r  r   )mTr   rK   r   	transpose)r*  s    r6   cloneBatchedColumnMajorr    s*    66<<e&=&=<>HHRPPr9   r  c                     [        U 5      $ r3   )r  )r   r  r  s      r6   _cholesky_solve_helperr    s     #4((r9   c                    ^ ^ [         R                  " T R                  S:  U 4S j5        [         R                  " TR                  S:  U4S j5        [        T TS5      u  p4[	        X4U5      $ )Nr   c                  $   > ST R                    S3$ )Nz-b should have at least 2 dimensions, but has  dimensions insteadr   r   s   r6   rZ    cholesky_solve.<locals>.<lambda>  s    ?		{J]^r9   c                  $   > ST R                    S3$ )Nz-u should have at least 2 dimensions, but has r
  r  r  s   r6   rZ   r    s    ?xGZ[r9   cholesky_solve)rK   r]   r   !_linalg_broadcast_batch_dims_namer  )r   r  r  self_broadcastedA_broadcasteds   ``   r6   r  r    sd     
LL		Q^ 
LL	![ 'Ha!'# ""25IIr9   c                     U R                  5       S:X  a#  [        R                  " U [        R                  S9$ [	        U S5        [        U 5      $ )Nr   r   cholesky)r   rK   r   legacy_contiguous_formatr   r  r   r  s     r6   r  r    s@     zz|qE4R4RSSdJ'"4((r9   c                 0    [        U S5        [        U 5      $ )Ncholesky_inverse)r   r  r  s     r6   r  r  &  s     d./"4((r9   check_errorsc                 
   [        U S5        [        U S5        U R                  n[        U5      n[	        US5      nU R                  U5      nUR                  X55        U R                  USUS-
   [        R                  S9nXg4$ )Nzlinalg.choleskyFr   r   r   )	r   r   r   r   r   r   r   rK   rB  )r  r  r  A_shaper   	L_stridesr  infoss           r6   linalg_cholesky_exr  .  s|    a*+1/0ggGw<D ,GU;I	GAMM'% KKD1H-U[[KAE8Or9   tauc                 J  ^ ^^ [         R                  " T R                  S:  S 5        [         R                  " T R                  S5      T R                  S5      :  S 5        [         R                  " T R                  S5      TR                  S5      :  S 5        [         R                  " T R                  TR                  -
  S:H  U U4S j5        T R                  S:  a<  T R                  S S nTR                  S S m[         R                  " TU:H  U4S	 j5        [         R                  " TR
                  T R
                  :H  U U4S
 j5        [        STT S5        [         R                  " T R                  [        T R                  SS9T R
                  T R                  S9$ )Nr   c                      g)NzHtorch.linalg.householder_product: input must have at least 2 dimensions.r>   r>   r9   r6   rZ   ,linalg_householder_product.<locals>.<lambda>G      Zr9   r  r   c                      g)Nzbtorch.linalg.householder_product: input.shape[-2] must be greater than or equal to input.shape[-1]r>   r>   r9   r6   rZ   r!  K  s    tr9   c                      g)Nz`torch.linalg.householder_product: input.shape[-1] must be greater than or equal to tau.shape[-1]r>   r>   r9   r6   rZ   r!  O  s    rr9   r   c                  <   > STR                    ST R                    3$ )Nzptorch.linalg.householder_product: Expected tau to have one dimension less than input, but got tau.ndim equal to  and input.ndim is equal to r  r   r  s   r6   rZ   r!  T  "    )),
2Nuzzl\r9   c                     > ST  3$ )Nzltorch.linalg.householder_product: Expected batch dimensions of tau to be equal to input.shape[:-2], but got r>   actual_batch_tau_shapes   r6   rZ   r!  ^      66L5MOr9   c                  <   > STR                    ST R                    3$ )Nz,torch.linalg.householder_product: tau dtype z does not match input dtype r   r'  s   r6   rZ   r!  f  s    :399+*5;;-9r9   z torch.linalg.householder_productr  Fr  r   r   rS   r{   )
rK   r]   r   r   r   rS   r  empty_stridedr   r{   )r   r  expected_batch_tau_shaper+  s   `` @r6   linalg_householder_productr1  @  sK   
 
LL

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

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

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

SXX"	
 zzA~#(;;s#3 !$3B"&>>	
 
LL		U[[ 	
 6UEJ[[*5;;%Hkk||	 r9   c                    [        U S5        [        U SSS9  U R                  U R                  5      nUR	                  U R                  [        U R                  SS95        U R                  U R                  S S [        R                  S9nX#4$ )Nzlinalg.inv_exF)r  r  r  r   r   r   r   r   r   r   rK   rB  )r  r  r  r  s       r6   linalg_inv_ex_metar4  v  so    a)1o%P	AGGAMM!''6qww%PQKKEKKK8E8Or9   LDpivotsinfo)	hermitianr  r8  c                t   [        U S5        [        U S5        [        R                  " U R                  [        U R                  SS9U R                  U R                  S9nU R                  U R                  S S [        R                  S9nU R                  U R                  S S [        R                  S9nX4U4$ )Nztorch.linalg.ldl_factor_exFr  r.  r   r   r  )
r   r   rK   r/  r   r   rS   r{   r   r   )r   r8  r  r5  r6  r7  s         r6   linalg_ldl_factor_ex_metar:    s     d894!=>			ZZ*4::Gjj{{	
B ^^DJJsO599^=F>>$**Sb/>;Dtr9   )r8  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$ )NzMtorch.linalg.ldl_solve: Expected B to have at least 2 dimensions, but it has r
  r  )r  s   r6   rZ   'linalg_ldl_solve_meta.<locals>.<lambda>      &&!46r9   r   c                  $   > ST R                    S3$ )Nzjtorch.linalg.ldl_solve: Expected LD.shape[:-1] and pivots.shape to be the same, but got pivots with shape  insteadr   r6  s   r6   rZ   r=        ))/h@r9   c                  "   > ST R                    3$ )Nz<torch.linalg.ldl_solve: Expected pivots to be integers. Got r   rB  s   r6   rZ   r=    s    Nv||n]r9   c                  <   > STR                    ST R                    3$ )Nz!torch.linalg.ldl_solve: LD dtype z does not match b dtype r   )r  r5  s   r6   rZ   r=    s     3BHH:=UVWV]V]U^_r9   Fr  r.  )r   r   r  rK   r]   r   r   rC   is_integer_dtyperS   _linalg_broadcast_batch_dimsr/  r   r{   )r5  r6  r  r8  expected_pivots_shapeB_broadcast_sizerF   s   ```    r6   linalg_ldl_solve_metarJ    s     b232781b":;	LL	!	
 HHSbM	LL-	
 
LLv||,] 
LL
AGG_ 7q"=*+;uMggxx	 r9   Pr  )pivotrL  c                j  ^  [         R                  " T R                  S:  U 4S j5        [        T R                  5      nUS   nUS   n[        X45      nX2S'   U(       a  T R                  U5      nOT R                  S/5      nXRS'   T R                  U5      nXRS'   XBS'   T R                  U5      nXgU4$ )Nr   c                  $   > ST R                    S3$ )Nz@linalg.lu: Expected tensor with 2 or more dimensions. Got size: r@  rA  r  s   r6   rZ    linalg_lu_meta.<locals>.<lambda>  s    RSTSZSZR[[cdr9   r  r   r   )rK   r]   r   r   r   r   r   )	r  rL  sizesrc  r  rb  rK  r  r  s	   `        r6   linalg_lu_metarQ    s     
LL	!d
 MEb	Ab	AA	A"IKKKK"I	EA"I"I	EA7Nr9   LU)rL  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$ )NzFtorch.lu_factor: Expected tensor with 2 or more dimensions. Got size: r@  rA  r  s   r6   rZ   *linalg_lu_factor_ex_meta.<locals>.<lambda>  s    XYZY`Y`Xaaijr9   r  r   Fr  r.  r   )rK   r]   r   r   r   r/  r   rS   r{   r  r   r   r   )	r  rL  r  rP  rc  r  rR  r6  r7  s	   `        r6   linalg_lu_factor_ex_metarV    s     
LL	!j
 MEb	Ab	A			*5EBggxx	
B 
IIKA	E"I[[eii[0F 
IIK;;uEII;.Dtr9   )r   adjointrW  c                
  ^ ^^ [        T S5        [        R                  " T R                  TR                  :H  UU 4S j5        [        R                  " TR                  [        R                  :H  S 5        [        T S5        [        T TUS5        [        R                  " T R                  S5      TR                  S5      :H  S 5        [        R                  " T R                  S S TR                  :H  U4S j5        [        TT 5      u  pV[        R                  " U[        XS(       + S9TR                  TR                  S	9nUR                  5       S
:w  a,  U(       d%  UR                  5       (       a  UR                  5       nU$ )Nztorch.linalg.lu_solvec                  >   > STR                    ST R                    S3$ )NzPlinalg.lu_solve: Expected LU and B to have the same dtype, but found LU of type  and B of type r@  r   )r  rR  s   r6   rZ   &linalg_lu_solve_meta.<locals>.<lambda>  s#    $$&HH:_QWWIXOr9   c                      g)NzElinalg.lu_solve: pivots should be a Tensor of scalar type torch.int32r>   r>   r9   r6   rZ   r[    s    Wr9   zlinalg.lu_solver   c                      g)NzYlinalg.lu_solve: Number of pivots per batch should be same as the dimension of the matrixr>   r>   r9   r6   rZ   r[     s    kr9   c                  $   > ST R                    S3$ )Nzclinalg.lu_solve: Expected LU.shape[:-1] and pivots.shape to be the same, but got pivots with shape r@  rA  rB  s   r6   rZ   r[  &  rC  r9   r  r.  r   )r   rK   r]   rS   r   r   r  r   r   rG  r/  r   r{   r   r   conj)rR  r6  r  r   rW  rI  rF   r  s   ```     r6   linalg_lu_solve_metar`    s-    267	LL
AGG	
 
LL		!W b12b!T#45	LL
v{{2&k 
LL
"%	
 7q"=  *+;xPggxx	F ||~4[[]FMr9   unpack_dataunpack_pivotsc                 6  ^  [         R                  " T R                  S:  U 4S j5        U(       a3  [         R                  " UR                  [         R                  :H  S 5        [        T R                  5      nUS   nUS   n[        XV5      nXTS'   U(       a  T R                  U5      nOT R                  S/5      nU(       a/  XtS'   T R                  U5      n	XtS'   XdS'   T R                  U5      n
O$T R                  S/5      n	T R                  S/5      n
XU
4$ )Nr   c                  $   > ST R                    S3$ )NzFtorch.lu_unpack: Expected tensor with 2 or more dimensions. Got size: r@  rA  )rR  s   r6   rZ    lu_unpack_meta.<locals>.<lambda>F  s    XY[YaYaXbbjkr9   c                      g)Nztorch.lu_unpack: LU_pivots is expected to be a contiguous tensor of torch.int32 dtype.
Note: this function is intended to be used with the output produced by torch.linalg.lu_factorr>   r>   r9   r6   rZ   re  K  s    pr9   r  r   r   )	rK   r]   r   rS   rB  r   r   r   r   )rR  r6  ra  rb  rP  rc  r  rb  rK  r  r  s   `          r6   lu_unpack_metarg  <  s     
LL
1k LLEKK'	
 NEb	Ab	AA	A"ILLLL!b	LLb	b	LLLL!LL!7Nr9   modec                    ^  T S:X  a  SnSnX4$ T S:X  a  SnSnX4$ T S:X  a  SnSnX4$ [         R                  " SU 4S j5        WW4$ )NreducedTcompleteFrc                     > ST  S3$ )Nzqr received unrecognized mode 'z=' but expected one of 'reduced' (default), 'r', or 'complete'r>   )rh  s   r6   rZ    _parse_qr_mode.<locals>.<lambda>s  s    1$ 8N Or9   rK   r]   )rh  	compute_qrj  s   `  r6   _parse_qr_moderq  f  s    y	  
		  
	  		
 gr9   QRc                    [        U S5        [        U S5        [        U5      u  p#U R                  S   nU R                  S   n[	        XE5      nU(       aO  [        U R                  5      nU(       a  UOUUS'   U R                  U5      nUR                  U[        USS95        OU R                  S/5      n[        U R                  5      n	U(       d  U(       d  UOUU	S'   U R                  U	5      n
U
R                  U	[        U	SS95        X4$ )Nz	linalg.qrr  r   Fr  r   )	r  r   rq  r   r   r   r   r   r   )r  rh  rp  reduced_moderc  r  rb  Q_shaperr  R_shapers  s              r6   linalg_qr_metarx  {  s     ![!1k*,T2I	A	AA	Aqww-'aQKK 	g:7eTUKK 177mG#9!!GBK	GAMM'6w%PQ4Kr9   sign	logabsdetc                 t   [        U S5        [        U SS5        U R                  nU R                  US S 5      nU R                  US S [	        U R
                  5      S9n[        R                  " U[        US5      U R
                  U R                  S9nU R                  US S [        R                  S9nX#XE4$ )Nzlinalg.slogdetFr  r   r.  r   )r   r   r   r   rU   rS   rK   r/  r   r{   rB  )r  r   ry  rz  rR  r6  s         r6   _linalg_slogdetr|    s     a)*1.6GGE;;uSbz"DE#2Joagg.FGI			*5%8ggxx	
B [[s5;;[7FB&&r9   full_matrices
compute_uvdriverc                 b   [        U S5        [        U S5        [        U R                  S S 5      nU R                  S   nU R                  S   n[	        XV5      nU(       a  XEU(       a  UOU/-   nU R                  U5      n	U	R                  U[        USS95        XA(       a  UOUU/-   n
U R                  U
5      n[        U 5      S:H  nUR                  U
[        XS95        O$U R                  S/5      n	U R                  S/5      nU R                  XG/-   [        U R                  5      S9nXU4$ )	Nz
linalg.svdr  r   Fr  r   r   r   )r  r   r   r   r   r   r   r   r   rU   rS   )r  r}  r~  r  r   rc  r  rb  U_shaper  V_shapeVis_cuda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$OAGG,DEA7Nr9   arg1arg2c                    U R                   S S nUR                   S S n[        X#5      n[        U5      nXPR                  S5      U R                  S5      /-  n[        U5      nXaR                  S5      UR                  S5      /-  nXV4$ )Nr  r   )r   r%   r   r   )r  r  arg1_batch_sizesarg2_batch_sizesexpand_batch_portionarg1_expand_sizearg2_expand_sizes          r6   rG  rG    s    
 zz#2zz#2,-=P012		"66012		"66--r9   c                     U(       a  [        XU5        [        X5      u  p4X0R                  :X  a  U OU R                  U5      nXAR                  :X  a  UOUR                  U5      nXV4$ r3   )r  rG  r   expand)r  r  r  r  r  arg1_broadcastedarg2_broadcasteds          r6   r  r    sh     t40)Ed)Q& !JJ.DKK@P4Q  !JJ.DKK@P4Q  --r9   r   c                     U R                   S S nUR                  S:H  =(       d2    U R                  S-
  UR                  :H  =(       a    UR                   U:H  nU$ )Nr   r   )r   r   )r   r   expected_batched_rhs_shapevector_cases       r6   linalg_solve_is_vector_rhsr    sS    !&Sb!1**/ 

Q%**$R8R)R  r9   )r   r  r  rR  r6  r7  c                  ^ ^ [        T S5        [        R                  " T R                  TR                  :H  U U4S j5        [	        T T5      nU(       a  TR                  S5      OTn	[        T XS5        [        U	T 5      u  p[        R                  " U=(       d    U(       + S 5        U(       a  U
S S OU
n[        R                  " U[        X(       + 5      TR                  TR                  S9nT R                  n[        R                  " U[        US5      T R                  T R                  S9nT R                  US S [        R                  S9nT R                  US S [        R                  S9nXEXg4nXUU4n[        S	 U 5       5      (       aa  [        UU5       HQ  u  nn[!        UUR                  5        UR#                  UR                  UR%                  5       5        ['        UUSS
9  MS     U$ )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 rZ  r@  r   )r  r  s   r6   rZ   "_linalg_solve_ex.<locals>.<lambda>  s     Ywwiqwwix9r9   r   c                      g)Nzlinalg.solve: Vector broadcasting of the left hand side is not supported for left=False. In this case linalg.solve is equivalent to B / A.squeeze(-1)r>   r>   r9   r6   rZ   r    s    Kr9   r.  Fr   r  c              3   (   #    U  H  oS Lv   M
     g 7fr3   r>   )ri   rH   s     r6   rk   #_linalg_solve_ex.<locals>.<genexpr>/  s     
&#QD=#s   )	copy_fromcopy_toexact_dtype)r   rK   r]   rS   r  	unsqueezer  rG  r/  r   r{   r   r   rB  allzipr!   r   r   r#   )r  r  r   r  r  rR  r6  r7  r  B_B_broad_shaperF   result_shaperesult_r   LU_pivots_info_r   resrl  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 " Jr9   )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   rg   r   r  r  r  r_  is_conjr!   r   r"   r   
transpose_)	r  r  r  r   r  r   r  A_avoid_copy_As	            r6   linalg_solve_triangular_metar  9  s     {kk1#c:&&&&aD";<.qT:FB<<B'557HBJJLLXX. J  XX..KKR,223NN2r"Jr9   XM)r  r  c                   ^ ^ [         R                  " T R                  S:  U 4S j5        [         R                  " TR                  S:  U4S j5        [        T TS5        TR                  [         R
                  :X  aw  [        T T5      u  pV[         R                  " U[        USS9T R                  T R                  S9n[         R                  " U[        USS9TR                  TR                  S9nXx4$ TR                  [         R                  :X  d  TR                  [         R                  :X  a+  [         R                  " T 5      nT R                  S/5      nXx4$ [         R                  " SS	 5        WW4$ )
Nr   c                  $   > ST R                    S3$ )NzMtorch.triangular_solve: Expected b to have at least 2 dimensions, but it has r
  r  r   s   r6   rZ   'triangular_solve_meta.<locals>.<lambda>^  s    ))$79r9   c                  $   > ST R                    S3$ )NzMtorch.triangular_solve: Expected A to have at least 2 dimensions, but it has r
  r  r  s   r6   rZ   r  e  r>  r9   triangular_solveFr  r.  r   c                      g)Nz+triangular_solve: Got an unexpected layout.r>   r>   r9   r6   rZ   r    s    $Qr9   )rK   r]   r   r  rz   stridedrG  r/  r   rS   r{   
sparse_csr
sparse_bsrr   r   )	r   r  r  r  r  self_broadcast_sizeA_broadcast_sizesolutioncloned_coefficients	   ``       r6   triangular_solve_metar  S  sC    
LL		Q	
 
LL	!	
 4$67xx5== 0LTST0U-&&$./BeT**;;	
 #00!./?5Q''88	
 '' 
U%%	%U5E5E)E##D)!^^QC0 '' 	UQR'''r9   c                 ^   [        U S5        [        U S5        U R                  U R                  S S 5      nU R                  U R                  5      nUR	                  U R                  [        U R                  SS95        U R                  U R                  S S [        R                  S9nXU4$ )Nz
linalg.detr  Fr  r   r   r3  )r  detrR  r6  s       r6   _linalg_det_metar    s    a&1l+
++aggcrl
#C	
QWW	BNN17775QR[["U[[[9FF?r9   c                 X  ^ ^^^^^ [         R                  " T R                  S:  S 5        [         R                  " TR                  S:  S 5        U(       a  SOSm[         R                  " TR                  T   TR                  S   :  U4S j5        [         R                  " TR                  T   T R                  S   :H  U4S j5        [         R                  " TR                  S   T R                  S   :*  S 5        [         R                  " T R                  TR                  -
  S	:H  U U4S
 j5        [         R                  " T R                  TR                  :H  U U4S j5        T R                  S:  ai  T R                  S S nTR                  S S m[         R                  " TU:H  U4S j5        TR                  S S m[         R                  " TU:H  U4S j5        [         R                  " TR                  T R                  :H  U U4S j5        [         R                  " TR                  T R                  :H  U U4S j5        [        STT S5        [        STT S5        [         R                  " TR                  [        TR                  SS9TR                  TR                  S9$ )Nr   c                      g)Nz3torch.ormqr: input must have at least 2 dimensions.r>   r>   r9   r6   rZ   ormqr.<locals>.<lambda>      !Vr9   c                      g)Nz3torch.ormqr: other must have at least 2 dimensions.r>   r>   r9   r6   rZ   r    r  r9   r  r   c                     > ST  S3$ )Ntorch.ormqr: other.shape[z0] must be greater than or equal to tau.shape[-1]r>   left_size_conditions   r6   rZ   r    s    +,?+@@pqr9   c                     > ST  S3$ )Nr  z"] must be equal to input.shape[-2]r>   r  s   r6   rZ   r    s    +,?+@@bcr9   c                      g)NzHtorch.ormqr: tau.shape[-1] must be less than or equal to input.shape[-1]r>   r>   r9   r6   rZ   r    r"  r9   r   c                  <   > STR                    ST R                    3$ )Nz[torch.ormqr: Expected tau to have one dimension less than input, but got tau.ndim equal to r&  r  r'  s   r6   rZ   r    r(  r9   c                  <   > STR                    ST R                    3$ )Nzhtorch.ormqr: Expected other to have the same number of dimensions as input, but got other.ndim equal to r&  r  r   r   s   r6   rZ   r    s&    ++0::,6RSXS]S]R^`r9   c                     > ST  3$ )NzWtorch.ormqr: Expected batch dimensions of tau to be equal to input.shape[:-2], but got r>   r*  s   r6   rZ   r    r,  r9   c                     > ST  3$ )NzYtorch.ormqr: Expected batch dimensions of other to be equal to input.shape[:-2], but got r>   )actual_batch_other_shapes   r6   rZ   r    s    66N5OQr9   c                  <   > ST R                    STR                    3$ )NzPtorch.ormqr: Expected input and tau to have the same dtype, but input has dtype z and tau has dtype r   r'  s   r6   rZ   r    s"    ##(;;-/B399+Or9   c                  <   > ST R                    STR                    3$ )NzRtorch.ormqr: Expected input and other to have the same dtype, but input has dtype z and other has dtype r   r  s   r6   rZ   r    s"    ##(;;-/DU[[MSr9   ztorch.ormqrr  r   Fr  r.  )	rK   r]   r   r   rS   r  r/  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 $(<<	
 
LL		U[[ 	
 
LLu{{"	
 M3u5M5%9[[*5;;%Hkk||	 r9   c                  ^ ^^ [         R                  " [        T5      ST-  :H  UU4S j5        T R                  nUTS-   :H  nUnU(       + nU(       a1  [	        SU5       H   nU=(       a    T R                  U5      S:g  nM"     O0[	        SU5       H   nU=(       a    T R                  U5      S:g  nM"     [         R                  " U=(       d    UUU 4S j5        g )Nr   c                  ,   > SST -   S[        T5       3$ )Nzpadding size is expected to be r   z, but got: r   )r~   paddings   r6   rZ   ,_padding_check_valid_input.<locals>.<lambda>  s    1!c'+c'l^Tr9   r   r   c                  :   > ST S-    ST S-    STR                    3$ )N	Expected r   zD or r   zcD (batch mode) tensor with possibly 0 batch size and other non-zero dimensions for input, but got: rA  )r~   r   s   r6   rZ   r    s-    aycAgY /AAFOr9   )rK   r]   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 % q)$A#7#NEJJqMQ<N  % 
LL00	
r9   c                  ^ ^^^^	^
 SnSmSnT R                   S:X  a  T R                  S5      nTS-  mUS-  n[        T USS9  Uu  m	m
T R                  U5      nT R                  T5      mTT	-   T
-   mU(       a-  [        R                  " T	T:  =(       a    T
T:  UU U	U
4S j5        [        R                  " TS:  UU4S j5        T R                   S:X  a  T R                  UT45      $ T R                  XET45      $ )Nr   r   r.   r   c                  4   > ST ST ST  STR                    3$ NzcArgument #4: Padding size should be less than the corresponding input dimension, but got: padding (rp   ) at dimension 
 of input rA  dim_wr   pad_lpad_rs   r6   rZ   _pad1d_common.<locals>.<lambda>"  -    %%*G2eWOE7*UZU`U`Tacr9   c                     > ST  ST 3$ )Nz
input (W: z%) is too small. Calculated output W: r>   )input_woutput_ws   r6   rZ   r  *  s    *WI%J8*Ur9   r   )r   r   r  rK   r]   r   )r   r  is_reflection	dim_planenbatchnplaner  r  r  r  r  s   `     @@@@@r6   _pad1d_commonr    s    IEFzzQA
Q	ug15LE5ZZ	"FjjG&HGO/	
 
LLAU
 zzQ1229::r9   c                     [        XSS9$ NTr  )r  r   r  s     r6   meta_reflection_pad1dr  3       t<<r9   c                    ^  [         R                  " T R                  [         R                  :g  U 4S j5        [	        T USS9$ )Nc                  @   > ST R                   R                  5        S3$ )Nz)"replication_pad1d" not implemented for ''rS   __str__r   s   r6   rZ   (meta_replication_pad1d.<locals>.<lambda>>      =ekk>Q>Q>S=TTUXr9   Fr  )rK   r]   rS   boolr  r  s   ` r6   meta_replication_pad1dr
  9  5     
LLuzz!X u==r9   c                  ^ ^^^^^ SmU(       d$  [         R                  " [        U5      S:H  S 5        TR                  S:X  a  TS-  mUu  mmTR	                  T5      nUT-   T-   mU(       a-  [         R                  " TU:  =(       a    TU:  UUUU4S j5        [         R                  " TT R	                  T5      :H  UU U4S j5        TR                  TR                  5      $ )Nr   r   c                      g)Nz padding size is expected to be 2r>   r>   r9   r6   rZ   (_pad1d_backward_common.<locals>.<lambda>F  s    0Rr9   r.   c                  4   > ST ST ST  STR                    3$ r  rA  r  s   r6   rZ   r  S  r  r9   c                  2   > ST STR                  T 5       3$ Nz(grad_output width unexpected. Expected: , Got: r   r  grad_outputr  s   r6   rZ   r  [       :8*GKL\L\]bLcKder9   rK   r]   r   r   r   r   r   )	r  r   r  r  r  r  r  r  r  s	   ``   @@@@r6   _pad1d_backward_commonr  C  s    ES\Q&(RSzzQ
LE5jjG&HGO/	
 
LLK$$U++e
 ??5;;''r9   
grad_inputc                     [        XUSS9$ r  r  r  r   r  s      r6   meta_reflection_pad1d_backwardr  a  s     "+gTRRr9   c                     [        XUSS9$ )NFr  r  r  s      r6   meta_replication_pad1d_backwardr  g  s     "+gUSSr9   c                  ^ ^^^	^
^^^^^^ SmSmSnSn[        T USS9  T R                  nUS:X  a   T R                  S5      nTS-  mTS-  mUS-  nUu  mmmmT R                  U5      nT R                  T5      m	T R                  T5      m
T	T-   T-   mT
T-   T-   mU(       aZ  [        R                  " TT
:  =(       a    TT
:  UU UU4S j5        [        R                  " TT	:  =(       a    TT	:  UU UU4S j5        [        R                  " TS:  =(       d    TS:  U	U
UU4S j5        T R                  S	:X  a  T R                  UTT45      $ T R                  XFTT45      $ )
Nr   r   r   r      c                  4   > ST ST ST  STR                    3$ r  rA  r  s   r6   rZ   _pad2d_common.<locals>.<lambda>  r  r9   c                  4   > ST ST ST  STR                    3$ NzcArgument #6: Padding size should be less than the corresponding input dimension, but got: padding (rp   r  r  rA  dim_hr   pad_bpad_ts   r6   rZ   r"    r  r9   c                      > ST  ST ST ST 3$ )Nz
input (H:  W: z%) is too small. Calculated output H: r>   )input_hr  output_hr  s   r6   rZ   r"    s%    	gY /$$,:T(=r9   r.   r  r   r   rK   r]   r   )r   r  r  
dim_slicesr  r   r  r&  r  r+  r  r,  r  r'  r  r  r(  s   `      @@@@@@@@@@r6   _pad2d_commonr/  m  sS   EEJFug15::DqyA

a
!(E5%ZZ
#FjjGjjG&H&HGO/	
 	GO/	
 
LLA&Q	
 zzQ(;<<(CDDr9   c                     [        XSS9$ r  )r/  r  s     r6   meta_reflection_pad2dr1    r   r9   c                    ^  [         R                  " T R                  [         R                  :g  U 4S j5        [	        T USS9$ )Nc                  @   > ST R                   R                  5        S3$ )Nz)"replication_pad2d" not implemented for 'r  r  r  s   r6   rZ   (meta_replication_pad2d.<locals>.<lambda>  r  r9   Fr  )rK   r]   rS   r	  r/  r  s   ` r6   meta_replication_pad2dr5    r  r9   c                   ^ ^^^^ SmSmSnUR                   nUR                  5       S:X  a  TS-  mTS-  mUS-  nUu  pVpxUT   n	UT   n
X-   U-   mX-   U-   m[        R                  " TT R	                  T5      :H  UU U4S j5        [        R                  " TT R	                  T5      :H  UU U4S j5        UR                  UR                   5      $ )Nr   r   r   r   c                  2   > ST STR                  T 5       3$ r  r   r  s   r6   rZ   %meta_pad2d_backward.<locals>.<lambda>  r  r9   c                  2   > ST STR                  T 5       3$ Nz)grad_output height unexpected. Expected: r  r   r&  r  r,  s   r6   rZ   r8         ;H:W[M]M]^cMdLefr9   )r   r~   rK   r]   r   r   )r  r   r  r  rY   r  r  r(  r'  r+  r  r&  r  r,  r  s   `          @@@@r6   meta_pad2d_backwardr=    s     EEIJxxzQ

Q	!(E%GG&H&H	LLK$$U++e 
LLK$$U++f >>$**%%r9   c          	      ~  ^ ^^^	^
^^^^^^^^^^^ Sm	SmSmSn[        T USS9  T R                  S:H  nU(       a%  T R                  S5      nT	S-  m	TS-  mTS-  mUS-  nUu  mmmmmmT R                  U5      nT R                  T5      m
T R                  T5      mT R                  T	5      mT
T-   T-   mTT-   T-   mTT-   T-   mU(       a  [        R                  " TT:  =(       a    TT:  U	U UU4S j5        [        R                  " TT:  =(       a    TT:  UU UU4S j5        [        R                  " TT
:  =(       a    TT
:  UU UU4S	 j5        [        R                  " TS:  =(       d    TS:  =(       d    TS:  U
UUUUU4S
 j5        U(       a  T R                  WUTTT45      $ T R                  UTTT45      $ )Nr.   r   r   r   r      c                  4   > ST ST ST  STR                    3$ r  rA  r  s   r6   rZ   _pad3d_common.<locals>.<lambda>  r  r9   c                  4   > ST ST ST  STR                    3$ r$  rA  r%  s   r6   rZ   rA    r  r9   c                  4   > ST ST ST  STR                    3$ )NzcArgument #8: Padding size should be less than the corresponding input dimension, but got: padding (rp   r  r  rA  )dim_dr   pad_bkpad_fs   r6   rZ   rA    s-    %%*G2fX_UG:V[VaVaUbdr9   c                  ,   > ST  ST ST ST ST ST 3$ )Nz
input (D:  H: r*  z%) is too small. Calculated output D: r>   )input_dr+  r  output_dr,  r  s   r6   rZ   rA    s2    	gYd7) <$$,:T(4zKr9   r-  )r   r  r  r  
batch_moder  r  rD  r&  r  rI  r+  r  rJ  r,  r  r'  rE  rF  r  r  r(  s   `      @@@@@@@@@@@@@@@r6   _pad3d_commonrL    s   EEEIug15qJA


Q	07-E5%vZZ	"FjjGjjGjjG'H&H&HGO/	
 	GO/	
 	GO0 0	
 
LLA7Q7(a-	
 	
 (HMNN(HEFFr9   c                     [        XSS9$ r  )rL  r  s     r6   meta_reflection_pad3drN    r   r9   c                    ^  [         R                  " T R                  [         R                  :g  U 4S j5        [	        T USS9$ )Nc                  @   > ST R                   R                  5        S3$ )Nz)"replication_pad3d" not implemented for 'r  r  r  s   r6   rZ   (meta_replication_pad3d.<locals>.<lambda>"  r  r9   Fr  )rK   r]   rS   r	  rL  r  s   ` r6   meta_replication_pad3drR    r  r9   c                   ^ ^^^^^^ [         R                  " [        U5      S:H  S 5        UR                  S:  d   eT R                  UR                  :X  d   eSmSmSmUR                  S:X  a  TS-  mTS-  mTS-  mUu  p4pVpxUR	                  T5      n	UR	                  T5      n
UR	                  T5      nX-   U-   mX-   U-   mX-   U-   m[         R                  " TT R	                  T5      :H  UU U4S j5        [         R                  " TT R	                  T5      :H  UU U4S j5        [         R                  " TT R	                  T5      :H  UU U4S	 j5        UR                  UR                  5      $ )
N   c                      g)Nz padding size is expected to be 6r>   r>   r9   r6   rZ   %meta_pad3d_backward.<locals>.<lambda>1  s    ,Nr9   r.   r   r   r?  c                  2   > ST STR                  T 5       3$ r  r   r  s   r6   rZ   rV  I  r  r9   c                  2   > ST STR                  T 5       3$ r:  r   r;  s   r6   rZ   rV  M  r<  r9   c                  2   > ST STR                  T 5       3$ )Nz(grad_output depth unexpected. Expected: r  r   )rD  r  rJ  s   r6   rZ   rV  Q  r  r9   r  )r  r   r  r  r  r(  r'  rF  rE  rI  r+  r  rD  r&  r  rJ  r,  r  s   `           @@@@@@r6   meta_pad3d_backwardrZ  '  sS    
LLW"$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;;''r9   pc                 @   [         R                  " U R                  5       S 5        U R                  S5      nUS::  a-  U R	                  S/5      R                  [         R                  S9$ U R	                  X"S-
  -  S-  45      R                  [         R                  S9$ )Nc                      g)Nz(_pdist_forward requires contiguous inputr>   r>   r9   r6   rZ   %meta__pdist_forward.<locals>.<lambda>[  s    &Pr9   r   r   r   r   )rK   r]   r_  r   r   r'  r  )r   r[  r  s      r6   meta__pdist_forwardr_  W  s     
LLP 			!AAv~~qc"%%E4R4R%SS~~qE{a/125588 6 
 	
r9   gradpdistc                     [         R                  " UR                  5       S 5        [         R                  " UR                  5       S 5        [         R                  " U[         R                  S9$ )Nc                      g)Nz._pdist_backward requires self to be contiguousr>   r>   r9   r6   rZ   &meta__pdist_backward.<locals>.<lambda>j  s    &Vr9   c                      g)Nz/_pdist_backward requires pdist to be contiguousr>   r>   r9   r6   rZ   rd  m  s    'Xr9   r   )rK   r]   r_  r   r  )r`  r   r[  ra  s       r6   meta__pdist_backwardrf  f  sW     
LLV 
LLX D0N0NOOr9   )rN  rM  c          
      b  ^ ^^^^^ SSK JnJn  TR                  S5      nTR                  S5      nTR                  S5      n	U" [        R
                  " U" T R                  XxU	45      5      5      (       a  T R                  XxU	45      m [        R                  " TR                  5       S:H  S 5        [        R                  " TR                  5       S:H  S 5        [        R                  (       dN  [        R                  " T R                  TR                  s=:H  =(       a    TR                  :H  Os  UUU 4S j5        TR                  n
TR                  mU
S   mU
S   m[        R                  " TS   T:H  =(       a    TS   T:H  UUU4S	 j5        T R                  T R                  5       5      $ )
Nr   )guard_or_truesym_eqr   r   r.   c                      gNzbatch1 must be a 3D tensorr>   r>   r9   r6   rZ   meta_baddbmm.<locals>.<lambda>|      ,Hr9   c                      gNzbatch2 must be a 3D tensorr>   r>   r9   r6   rZ   rl  }  rm  r9   c                  V   > STR                    ST R                    STR                    3$ )Nz+Input dtypes must be the same, got: input: z
, batch1: z
, batch2: r   )batch1batch2r   s   r6   rZ   rl    s.    A$**ZX^XdXdWeeopvp|p|o}~r9   c            	      .   > ST ST ST S    ST S    S3	$ Nz@Expected size for first two dimensions of batch2 tensor to be: [rp   z] but got: [r   r   ].r>   batch2_sizesbscontraction_sizes   r6   rZ   rl    s5    t2&'|LO3DB|TUFWWY[r9   )r$  rh  ri  r   rK   sym_notr   r  r]   r~   
exp_config&skip_dtype_check_in_meta_registrationsrS   r   )r   rq  rr  rN  rM  rh  ri  dim1dim2dim3batch1_sizesrw  rx  ry  s   ```        @@@r6   meta_baddbmmr  r  s9    L;;q>D;;q>D;;q>DU]]6$**t46H#IJKK{{D-.	LL"$HI	LL"$HI<<JJ&,,66&,,6~	
 <<L<<L	aB#A	LLQ2E,q/5E"E	
 >>$))+&&r9   c                H    [         R                  " U [         R                  S9$ r   rj  r   r  s     r6   meta_bernoullir    s     D0G0GHHr9   c                     U $ r3   r>   r   r[  r  s      r6   meta_bernoulli_r        Kr9   c                 H    [         R                  " U [         R                  S9$ r   rj  r  s      r6   meta_bernoulli_pr    s     D0G0GHHr9   c                 .    [         R                  " U 5      $ r3   rK   r   r  s     r6   meta_poissonr         D!!r9   c                     [         R                  " XR                  5       :  S 5        [         R                  " U [         R                  S9n[         R                  " U 5      U4$ )Nc                      g)NzJError in fused_moving_avg_obs_fake_quant_cpu: ch_axis must be < self.dim()r>   r>   r9   r6   rZ   6meta__fused_moving_avg_obs_fq_helper.<locals>.<lambda>      \r9   r   )rK   r]   r~   r   r	  )r   observer_onfake_quant_onrunning_minrunning_maxscale
zero_pointaveraging_const	quant_min	quant_maxch_axisper_row_fake_quantsymmetric_quantmasks                 r6   $meta__fused_moving_avg_obs_fq_helperr    sM      
LL((*\ D

3DT"D))r9   c                 P  ^^^^ [         R                  " U R                  5       S:H  S 5        [         R                  " UR                  5       S:H  S 5        U R                  u  mmUR                  u  mm[         R                  " TT:H  UUUU4S j5        U R	                  TT5      $ )Nr   c                      g)Nza must be 2Dr>   r>   r9   r6   rZ   meta_mm.<locals>.<lambda>      ~r9   c                      g)Nzb must be 2Dr>   r>   r9   r6   rZ   r    r  r9   c            	      "   > ST ST  ST ST S3	$ )Nz/a and b must have same reduction dim, but got [rp   z] X [ru  r>   )M1M2NrK  s   r6   rZ   r    s&    A!Brd%PRtSUVWUXXZ[r9   )rK   r]   r~   r   r   )abr  r  r  rK  s     @@@@r6   meta_mmr    sz     
LLA56	LLA56GGEArGGEB	LL
b[ ;;q!r9   c                    ^ ^ U(       a)  [        UU 4S j[        T R                  5       5       5      $ [        R                  " T R
                  T5      $ )Nc              3   P   >#    U  H  oT;  a  TR                   U   OS v   M     g7f)r   NrA  )ri   r   dimsr   s     r6   rk   +_compute_reduction_shape.<locals>.<genexpr>  s$     UDTqtmTZZ]:DTs   #&)r\   r   r   rC   compute_reduction_output_shaper   )r   r  r  s   `` r6   r  r    s7    UE$))DTUUU//

DAAr9   c                 :   [        U [        R                  R                  5      (       a  U R                  R
                  $ [        U S5      (       aK  [        U R                  S5      (       a0  U R                  R
                  S:w  a  U R                  R
                  $ g)Nr{   rr   rx   r   )rg   rK   _subclasses
FakeTensorfake_devicerr   hasattrr{   )r1  s    r6   r   r     sp    &%++6677!!&&&!!FMM6**MM&(}}!!!r9   input_tensorr   r  dilationis_transposedgroupsoutput_paddingc                 r  ^^ S[         S[         S[         S[         S[         S[         4S jnS[         S[         S[         S[         S[         S[         S[         4S	 jn	UR                  S
S  n
U R                  S
S  mU(       a  XaR                  S   -  nO=UR                  S   nUR                  S   U-  U R                  S   :w  a  [        S5      eU R                  S   U/m[        U[        5      (       a  U/[        T5      -  nO![        U5      S:X  a  US   /[        T5      -  n[        U[        5      (       a  U/[        T5      -  nO![        U5      S:X  a  US   /[        T5      -  n[        U[        5      (       a  U/[        T5      -  nO![        U5      S:X  a  US   /[        T5      -  nS nU(       aI  [        U[        5      (       a  U/[        T5      -  nO$[        U5      S:X  a  US   /[        T5      -  nOUn[        [        T5      5       H[  nU(       a+  TR                  U	" TU   X=   XM   X   X-   X   5      5        M5  TR                  U" TU   X=   XM   X   X-   5      5        M]     SSKJ	n  [        R                  " U" TS
S   Vs/ s H  oS:  PM	     sn6 UU4S j5        T$ s  snf )Nlnr[  r   rb  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   r   r>   )r  r[  r   rb  r  s        r6   _formula+calc_conv_nd_return_shape.<locals>._formula  s,     QU
Qa%[(1,2Q66r9   r4   c                 :    U S-
  U-  SU-  -
  X#S-
  -  -   U-   S-   $ )a  
Formula to apply to calculate the length of some dimension of the output
if transposed convolution is used.
See: https://pytorch.org/docs/stable/generated/torch.nn.ConvTranspose2d.html

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

Returns:
    The output length
r   r   r>   )r  r[  r   rb  r  r4   s         r6   _formula_transposed6calc_conv_nd_return_shape.<locals>._formula_transposed	  s0    " Q!|a!e#aq5k1B6::r9   r   r   r   zInvalid channel dimensions)sym_orc                  .   > S[        T 5       STSS   S3$ )NzGiven input size per channel: z&. Calculated output size per channel: r   z. Output size is too small)r   )r  	ret_shapes   r6   rZ   +calc_conv_nd_return_shape.<locals>.<lambda>L	  s(    0d =//8}o >#$r9   )r   r   r&  rg   r   r   r   r   r$  r  rK   r]   )r  r:  r   r  r  r  r  r  r  r  kernel_sizeout_channelsoutput_padding_listr   r  rH   r  r  s                   @@r6   calc_conv_nd_return_shaper    s   7S 7S 7S 7S 7S 7S 7"; ; ; ; ; ; ;QT ;& ,,qr"Kab!DQ/||A<<?V#|'9'9!'<<;<<##A&5I&'""CI%	V	)s4y('7##)c$i'	W	1:,T*(G$$:D	)	X!	QK=3t9,/3ng..#1"2SY"> A%#1!#4"5D	"A"03t9#GJKNI'*	 a'*hk;>69U " =	LL	!".1Q./	$  /s   J4c                 b    [         R                  R                  U 5      [         R                  :H  $ r3   rK   _prims_commonr   channels_lasttens    r6   is_channels_lastr  T	  s$    44S9U=P=PPPr9   running_meanrunning_vartrainingexponential_average_factorepsilonc                 z  ^  T R                   nUb  UR                   OUR                   n	Ub  UR                   OUR                   n
U 4S jnT R                  U5      R                  U" 5       S9nU(       a#  T R                  U	5      nT R                  U
5      nO"T R                  S5      nT R                  S5      nXU4$ )Nc                     > [        T 5      (       a  [        R                  $ T R                  [        R                  S9(       a  [        R                  $ [        R                  $ r   )r  rK   r  r_  r   )r  s   r6   pick_memory_format2meta_miopen_batch_norm.<locals>.pick_memory_formatk	  sI    L))&&&%%E4K4K%L***&&&r9   r   r   )r   r   r'  )r  r:  r<  r  r  r  r  r  r   save_mean_shapesave_var_shaper  r   	save_meansave_vars   `              r6   meta_miopen_batch_normr  X	  s     ""I -9,Dl((&,,O*5*A[&&v||N' 
 
 
+
.
.=O=Q
.
RC **?;	)).9 **40	))$/8##r9   c	           
         ^ ^ U U4S jn	[        T TUUUUUU(       a  UOS 5      n
SnSnT R                  U5      S:X  a  SX'   T R                  U
5      nUR                  U	" 5       S9nU$ )Nc                    > [        T 5      S:X  a1  [        T 5      (       d  [        T5      (       a  [        R                  $ O [        T 5      (       a  [        R                  $ T R	                  [        R
                  S9(       a  [        R
                  $ T R	                  [        R                  S9(       a  [        R                  $ g Nr   r   )r   r  rK   r  r_  r   preserve_format)r  r:  s   r6   r  %meta_conv.<locals>.pick_memory_format	  s    |$.--1A&1I1I*** 2J  --***%%E4K4K%L***''e6K6K'L((( Mr9   r   r   r   )r  r   r   r'  )r  r:  r<  r   r  r  r  r  r  r  	shape_outinput_channels_dimoutput_channels_dimr   s   ``            r6   	meta_convr  ~	  s    
) *'T	I +,1)*	&

 
 
+C
&&13&
4CJr9   mkldnnc
           
          [        XXCUSU/ 5      n
U R                  U
5      n[        R                  nU R	                  5       S:X  a  [        R
                  nUR                  US9nU$ )NFr?  r   )r  r   rK   r  r~   channels_last_3dr'  )r  r:  r<  r  r   r  r  attrscalars	algorithmr  r   out_memory_formats                r6   meta_mkldnn_convolution_defaultr  	  sl     .&8UFB
	 $$Y/!//" % 6 6ff#4f5
r9   c                 b    U R                  / U R                  S S QUR                  S   P75      $ Nr   r   r   r   )r  r:  r<  r  r  r  s         r6   meta_linear_pointwise_defaultr  	  s5     %%&Q(:(:3B(?&Qa&QRRr9   mklc                 b    U R                  / U R                  S S QUR                  S   P75      $ r  r  )r  packed_weightorig_weightr<  r   s        r6   meta_mkl_linearr  	  s:    ))@,$$Sb)@;+<+<Q+?@ r9   onednnc           
         [        U UUUU	SU
S 5      nUc  U R                  nU[        R                  [        R                  [        R
                  [        R                  [        R                  4;   d   eU R                  UUS9n[        U5      S;   d   S5       e[        R                  [        R                  [        R                  S.[        U5         nUR                  US9nU$ )NFr   )r.   r   r?  z-Expect output to be 3d/4d/5d for conv1d/2d/3dr   )r  rS   rK   r[  r]  uint8rA  r^  r   r   r   r  r  r'  )rH   x_scalex_zpww_scalew_zpr<  r   r  r  r  output_scaleoutput_zero_pointoutput_dtyper  r  r  r  r   formats                       r6   meta_qconv_pointwiser  	  s    * .	
	 77LMMNNKKJJ 
 
 	
 
 kk)<k89~* 	
;	
* &&""%%
 i.	
 ff6f*
r9   c                     US:X  d   eU$ )Nsumr>   )rH   r  r   r  r  r  accumr<  r   r  r  r  r  r  r  accum_scaleaccum_zero_pointbinary_op_namerM  unary_op_nameunary_op_argsunary_op_algorithms                         r6   meta_qconv2d_pointwise_binaryr  
  s    2 &&&r9   c                    [        U R                  5      nUR                  S   US'   U	[        R                  [        R                  [        R
                  [        R                  [        R                  4;   d   eU R                  XS9nU$ )Nr   r   r   )	r   r   rK   r[  r]  rA  r  r^  r   )rH   r  r   r  r  r  r<  r  r  r  post_op_namepost_op_argspost_op_algorithmrd  r   s                  r6   meta_qlinear_pointwiser  ,
  sv    " AGG}771:RMMNNJJKK 
 
 	
 
 kk,k;
r9   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
  r   r   r   )	r   r   rK   r[  r]  r  rA  r^  r   )rH   r  r   r  r  r  x_2r<  r  r  r  x2_scalex2_zpr  rM  r  r  r  rd  r   s                       r6   meta_qlinear_pointwise_binaryr  J
  s    , U"JAGG}771:RMMNNKKJJ 
 
 	
 
 kk,lk;
r9   c                 v    [        U R                  5      nUR                  S   US'   U R                  U5      nU$ )Nr   r   )r   r   r   )rH   r  r<  rd  r   s        r6   meta_linear_dynamic_fp16r  o
  s6     AGG}771:Rkk,'
r9   	quantizedr  r   c                 "   [        XX#XE5      u  nnnU R                  5       S:X  a  U R                  S5      OSn	[        R                  n
U R                  5       S:X  a  XgU/nOXXx/n[        R
                  " UU R                  U R                  U
S9$ Nr   r   r.   r{  )#max_pool2d_checks_and_compute_shaper~   r   rK   r  r   rS   r{   r   r  r   r  r  	ceil_modenInputPlaneoutputHeightoutputWidthr  r   r   s               r6   meta_quantized_max_pool2dr*  
  s     0
		
 $)99;!#3B++99;!{;DCD{{++<<'	
 	
r9   c                    [         R                  " U R                  5       S:H  SU R                  5        S35        [         R                  " UR                  5       S:H  SUR                  5        S35        [         R                  " U R                  [         R                  [         R
                  [         R                  4;   SU R                   35        [         R                  " UR                  [         R                  :H  SUR                   35        [         R                  " UR                  [         R                  :H  SUR                   35        [         R                  " UR                  U R                  :H  SUR                   35        U R                  U R                  S	5      UR                  S	5      U R                  S
9$ )Nr   zx must be a 2D tensor, got Dzw must be a 2D tensor, got #expected x to be f32/f16/bf16, got expected w to be uint8, got z q_group_size must be int64, got z5q_scale_and_zeros must have the same dtype as x, got r   r   )rK   r]   r~   rS   r[  r\  r]  r  r   r   r   rH   r  q_group_sizeq_scale_and_zeross       r6   meta_int4mm_packed_weight_cpur2  
  s@   QUUW\%@	#KLQUUW\%@	#KLGGu}}ennEE1!'';	
 	QWW+/KAGG9-UV%++-.|/A/A.BC	
 	##qww.CDUD[D[C\]	
 {{166!9affQiqww{??r9   c                    ^ ^^^ [         R                  " T R                  5       T:H  =(       a    T R                  T   T:H  UUUU 4S j5        g )Nc                  j   > ST  ST ST S3STR                  5        ST STR                  T    3-   $ )NzExpected a tensor of dimension z and tensor.size[z] == rp   zbut got : dimension z] = r~   r   )r~   dim_sizer   r1  s   r6   rZ    check_dim_size.<locals>.<lambda>
  sN    1#6GzQVW[V\\^_ .?zfll[cNdMe
fgr9   )rK   r]   r~   r   )r1  r~   r6  r   s   ````r6   check_dim_sizer8  
  s6    	LL

>X 6$ >	gr9   c                   ^  S nU" SU5      u  p[         R                  " [        U5      S;   S 5        [         R                  " T R                  [         R                  [         R
                  [         R                  [         R                  4;  U 4S j5        [        U5      S:X  a  XpO$[        U5      S:X  a
  US   US   pOU" SU5      u  pU" S	U5      u  p[         R                  " US L =(       d    US:g  S
 5        T R                  5       S:X  a  T R                  S5      OSnT R                  S5      nT R                  S5      nT R                  S5      n[        UXU
SU5      n[        UXUSU5      n[        R                  " T 5      n[        T UU	U
UUUSSUUUUUU5        T R                  5       S:X  a  UUU/nOXUU/n[         R                  " UT R                  T R                  US9$ )Nc                    ^  [         R                  " [        U5      S;   U 4S j5        US   n[        U5      S:X  a  UOUS   nX#4$ )Nr   r   c                     > ST  S3$ )Nzavg_pool2d: 4 must either be a single int, or a tuple of two intsr>   r  s   r6   rZ   1meta_avg_pool2d.<locals>.unpack.<locals>.<lambda>
      l4&(\]r9   r   r   rK   r]   r   r  r  HWs   `   r6   unpackmeta_avg_pool2d.<locals>.unpack
  E    H]	
 FSQACFtr9   r  r   r   r   c                      gNzOavg_pool2d: stride must either be omitted, a single int, or a tuple of two intsr>   r>   r9   r6   rZ   !meta_avg_pool2d.<locals>.<lambda>
      ar9   c                  @   > ST R                   R                  5        S3$ )Nz""avg_pool2d" not implemented for 'r  r  r  s   r6   rZ   rK  
      6u{{7J7J7L6MQQr9   r   r   r   r  c                      gNzdivisor must be not zeror>   r>   r9   r6   rZ   rK  
      *r9   r   r#  r  r   r.   r{  )rK   r]   r   rS   r  uint16uint32uint64r~   r   pooling_output_shaperC   r   pool2d_shape_checkr   r{   )r   r  r   r  r&  count_include_paddivisor_overriderE  kHkWdHdWpadHpadWr  r'  inputHeight
inputWidthr(  r)  r   r   s   `                     r6   meta_avg_pool2drb  
  s    M;/FB	LLFy a 
LLEKKu||U\\RRQ 6{aB	V	F1IB&)	7+JD	LLD 9$4$9*
  %yy{a/UZZ^QF**R.K**R.KBJ'Rr1iPL&z2RINK//6M



		$ yy{a\;7\;?;;kk||#	 r9   c                     [        U UUUUUUSSU	U
UUUU5        U R                  5       nU	n[        XUS-
  U5        [        XUS-
  U5        [        XUS-
  U5        g )Nr   r.   r   )rW  r~   r8  )r   
gradOutputr  rZ  r[  r\  r]  r^  r_  r'  r`  ra  r(  r)  
mem_formatr   nOutputPlanes                    r6   avg_pool2d_backward_shape_checkrg    s{    " 



		$ 99;DL:TAX|<:TAX|<:TAX{;r9   c                    [         R                  " [        U5      S:H  =(       d    [        U5      S:H  S 5        US   n[        U5      S:X  a  UOUS   n	[         R                  " [        U5      S:H  =(       d#    [        U5      S:H  =(       d    [        U5      S:H  S 5        [        U5      S:X  a  UOUS   n
[        U5      S:X  a  U	O[        U5      S:X  a  U
OUS   n[         R                  " [        U5      S:H  =(       d    [        U5      S:H  S 5        US   n[        U5      S:X  a  UOUS   n[         R                  " US L =(       d    US:g  S 5        UR                  nUR	                  5       S:X  a  US	   OSnUS
   nUS   nUS   n[        UXU
SU5      n[        UXUSU5      n[        R                  " U5      n[        UU UUU	U
UUUUUUUUU5        [         R                  " UUR                  UR                  US9$ )Nr   r   c                      g)NzKavg_pool2d: kernel_size must either be a single int, or a tuple of two intsr>   r>   r9   r6   rZ   *meta_avg_pool2d_backward.<locals>.<lambda>F  s    ]r9   r   c                      grJ  r>   r>   r9   r6   rZ   rj  L  rL  r9   c                      g)NzGavg_pool2d: padding must either be a single int, or a tuple of two intsr>   r>   r9   r6   rZ   rj  R  s    Yr9   c                      grP  r>   r>   r9   r6   rZ   rj  Y  rQ  r9   r   r#  rR  r  r   r{  )rK   r]   r   r   r~   rV  rC   r   rg  r   rS   r{   )gradOutput_r   r  r   r  r&  rX  rY  rZ  r[  r\  r]  r^  r_  
input_sizer  r'  r`  ra  r(  r)  re  s                         r6   meta_avg_pool2d_backwardrp  8  s    
LLKA6[!1Q!6] 
QB;1$+a.B	LLFq@CK1,@Fq0@a 6{aVAYB6{a3v;!+;RB	LLG.S\Q.Y 1:Dw<1$4'!*D	LLD 9$4$9*
 J$yy{a/Z^QFR.KR.KBJ'Rr1iPL&z2RINK,,U3J#

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
$ ;;kk|| 	 r9   c                 n  ^  [         R                  " [        U5      S;   S 5        US   n[        U5      S:X  a  UOUS   n[        U5      S:X  a  UOUS   n	[         R                  " U(       + =(       d    [        U5      S;   S 5        [         R                  " T R                  [         R                  [         R
                  [         R                  [         R                  4;  U 4S j5        U(       d  UOUS   n
U(       d  UO[        U5      S:X  a  U
OUS   nU(       d  U	O[        U5      S:X  a  U
OUS   n[         R                  " [        U5      S;   S 5        US   n[        U5      S:X  a  UOUS   n[        U5      S:X  a  UOUS   n[         R                  " T R                  S	;   S
 5        [         R                  " U(       + =(       d    US:g  S 5        T R                  S5      nT R                  S5      nT R                  S5      nT R                  S5      nT R                  S5      n[        UX}U
SU5      n[        UXUSU5      n[        UXUSU5      n[        T UUUU	U
UUUUUSSSUUUUUUSSS9  T R                  S:X  a  T R                  UUUU45      $ T R                  UUUUU45      $ )Nr   r.   c                      gNzFavg_pool3d: kernel_size must be a single int, or a tuple of three intsr>   r>   r9   r6   rZ   !meta_avg_pool3d.<locals>.<lambda>      Xr9   r   r   r   c                      gNzJavg_pool3d: stride must be omitted, a single int, or a tuple of three intsr>   r>   r9   r6   rZ   ru    r  r9   c                  @   > ST R                   R                  5        S3$ )Nz""avg_pool3d" not implemented for 'r  r  r  s   r6   rZ   ru    rN  r9   c                      gNzBavg_pool3d: padding must be a single int, or a tuple of three intsr>   r>   r9   r6   rZ   ru        Tr9   r   r?  c                      gNz9non-empty 4D or 5D (batch mode) tensor expected for inputr>   r>   r9   r6   rZ   ru        Kr9   c                      grP  r>   r>   r9   r6   rZ   ru    rQ  r9   r#  rR  r  r   zavg_pool3d()T)check_input_sizer   )rK   r]   r   rS   r  rS  rT  rU  r   r   rV  pool3d_shape_checkr   )r   r  r   r  r&  rX  rY  kTrZ  r[  dTr\  r]  padTr^  r_  r  nslicesitimeiheightiwidthotimeoheightowidths   `                       r6   meta_avg_pool3dr    s    
LLKF"X 
QB;1$+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Ir9   c                 B   [         R                  " [        U5      S;   S 5        US   n[        U5      S:X  a  UOUS   n	[        U5      S:X  a  UOUS   n
[         R                  " U(       + =(       d    [        U5      S;   S 5        U(       d  UOUS   nU(       d  U	O[        U5      S:X  a  UOUS   nU(       d  U
O[        U5      S:X  a  UOUS   n[         R                  " [        U5      S;   S 5        US   n[        U5      S:X  a  UOUS   n[        U5      S:X  a  UOUS   n[         R                  " UR                  S;   S	 5        [         R                  " U(       + =(       d    US:g  S
 5        UR	                  S5      nUR	                  S5      nUR	                  S5      nUR	                  S5      n[        UXUSU5      n[        UXUSU5      n[        UU
UUSU5      n[        UU UUU	U
UUUUUUUUUUUUS5        UR                  UR                  5      $ )Nrr  c                      grt  r>   r>   r9   r6   rZ   *meta_avg_pool3d_backward.<locals>.<lambda>  rv  r9   r   r   r   c                      grx  r>   r>   r9   r6   rZ   r    r  r9   c                      gr{  r>   r>   r9   r6   rZ   r    r|  r9   r}  c                      gr  r>   r>   r9   r6   rZ   r    r  r9   c                      grP  r>   r>   r9   r6   rZ   r    rQ  r9   r#  rR  r  r   zavg_pool3d_backward())	rK   r]   r   r   r   rV  avg_pool3d_backward_shape_checkr   r   )r  r   r  r   r  r&  rX  rY  r  rZ  r[  r  r\  r]  r  r^  r_  r  r  r  r  otime_for_shape_checkoheight_for_shape_checkowidth_for_shape_checks                           r6   meta_avg_pool3d_backwardr    s    
LLKF"X 
QB;1$+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#

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', ??5;;''r9   c                 8  ^  [         R                  " T R                  S:H  =(       d    T R                  S:H  U 4S j5        T R                  S S [	        U5      -   n[
        R                  " T 5      n[         R                  " UT R                  T R                  US9$ )Nr.   r   c                  "   > ST R                    3$ )Nz"Expected 3D or 4D tensor, but got rA  r   s   r6   rZ   *meta_adaptive_avg_pool2d.<locals>.<lambda>/      4TZZLAr9   r  r{  )
rK   r]   r   r   r\   rC   r   r   rS   r{   )r   output_sizerd  r   s   `   r6   meta_adaptive_avg_pool2dr  +  s|    	LL		Q($))q.A ::cr?U;%77L//5M ;;jj{{#	 r9   c                    ^  [         R                  " T R                  S:H  =(       d    T R                  S:H  U 4S j5        T R                  T R                  S S [        U5      -   5      $ )Nr   r?  c                  "   > ST R                    3$ )Nz"Expected 4D or 5D tensor, but got rA  r   s   r6   rZ   *meta_adaptive_avg_pool3d.<locals>.<lambda>A  r  r9   rR  )rK   r]   r   r   r   r\   )r   r  s   ` r6   meta_adaptive_avg_pool3dr  =  sO    	LL		Q($))q.A >>$**Sb/E+,>>??r9   c                   ^ ^^ T R                   n[        SU5       H1  m[        R                  " T R	                  T5      S:  U U4S j5        M3     [        R                  " US:H  =(       d    US:H  U4S j5        [        R                  " TR
                  T R
                  :H  U U4S j5        [        R                  n[        T5      (       a  [        R                  nTR                  TR                  5      R                  US9$ )	Nr   r   c                  *   > ST R                    ST S3$ )Nz{adaptive_avg_pool2d_backward(): Expected grad_output to have non-zero                       size for non-batch dimensions,  with dimension  being emptyrA  )grad_outr   s   r6   rZ   4meta__adaptive_avg_pool2d_backward.<locals>.<lambda>L  s$     66>nn5EEUVWUXXdfr9   r.   r   c                  "   > ST R                    3$ )NzBadaptive_avg_pool2d_backward(): Expected 3D or 4D tensor, but got rA  r   s   r6   rZ   r  Q  s    TUYU_U_T`ar9   c                  <   > STR                    ST R                    3$ Nexpected dtype z! for `grad_output` but got dtype r   )r  r   s   r6   rZ   r  U  s    /$**-Nx~~N^_r9   r   )r   r   rK   r]   r   rS   r   r  r  r   r   r'  )r  r   r   r   r   s   ``  @r6   "meta__adaptive_avg_pool2d_backwardr  F  s    ==D1d^MM!q f	
  
LL	TQYa 
LL

hnn$_ ++M++>>$**%((}(EEr9   c                 `    [        U S5        [        R                  " U[        R                  S9$ )Nadaptive_avg_pool3d_backwardr   )!_adaptive_pool_empty_output_checkrK   r   r  r  r   s     r6   "meta__adaptive_avg_pool3d_backwardr  ]  s(     &k3QRD0N0NOOr9   r  c                    ^ ^^ T R                   n[        SU5       H2  m[        R                  " T R	                  T5      S:  UU U4S j5        M4     g )Nr   r   c                  .   > T  STR                    ST S3$ )Nzc(): Expected grad_output to have non-zero size for non-batch dimensions, but grad_output has sizes r  r  rA  )r  r  r   s   r6   rZ   3_adaptive_pool_empty_output_check.<locals>.<lambda>i  s*    * --8->->,??OPQsR^`r9   )r   r   rK   r]   r   )r  r  r   r   s   `` @r6   r  r  d  sB    D1d^Q!#	
 r9   c                   ^ ^ T R                   n[        R                  " US;   U 4S j5        [        SU5       H1  m[        R                  " T R	                  T5      S:  UU 4S j5        M3     [        R                  " [        U5      S:H  S 5        SnSnSnT R                   S:X  a  T R	                  S5      nUS-  nT R	                  US-
  5      nUu  pgT R                   S	:X  a6  XVU4nT R                  U5      n	T R                  U[        R                  S
9n
X4$ XEXg4n[        R                  " T 5      nT R                  U5      R                  US9n	T R                  U[        R                  S
9R                  US9n
X4$ )Nr.   r   c                  "   > ST R                    3$ )Nz:adaptive_max_pool2d(): Expected 3D or 4D tensor, but got: rA  r  s   r6   rZ   *meta_adaptive_max_pool2d.<locals>.<lambda>v      LU[[MZr9   r   r   c                  *   > STR                    ST  S3$ )Nzjadaptive_max_pool2d(): Expected input to have non-zero size for non-batch dimensions, but input has sizes r  r  rA  r   r   s   r6   rZ   r  {       '',{{m3CA3lTr9   r   c                      g)NzCadaptive_max_pool2d(): internal error: output_size.size() must be 2r>   r>   r9   r6   rZ   r        Ur9   r   r.   r   r   )r   rK   r]   r   r   r   r   r   rC   r   r'  )r   r  r   dimHsizeBsizeDosizeHosizeWr   r   r   r   r   s   `           @r6   meta_adaptive_max_pool2dr  p  sk    ::D	LLZ 1d^JJqMA	
  
LLKAU
 DEEzzQ

1	JJtax E NFzzQF+	ooi(//)5;;/?|62	33E:ooi(++-+H//)5;;/?BB' C 
 |r9   c                 T  ^ ^ T R                   n[        R                  " US;   U 4S j5        [        T S5        [        R                  " TR                  T R                  :H  U U4S j5        [
        R                  " T5      nTR                  TR                  5      R                  US9$ )Nr  c                  "   > ST R                    3$ )NzKadaptive_max_pooling2d_backward(): Expected 3D or 4D grad_output, but got: rA  r  s   r6   rZ   3meta_adaptive_max_pool2d_backward.<locals>.<lambda>  s    ]^i^o^o]pqr9   adaptive_max_pool2d_backwardc                  <   > STR                    ST R                    3$ r  r   )r  r   s   r6   rZ   r    s    /%++.OP[PaPaObcr9   r   )
r   rK   r]   r  rS   rC   r   r   r   r'  )r  r   r   r   r   s   ``   r6   !meta_adaptive_max_pool2d_backwardr    s     D	LLq
 &k3QR	LL{(((c
 //6M??5;;'***GGr9   c                   ^ ^ T R                   n[        R                  " US;   U 4S j5        [        SU5       H1  m[        R                  " T R	                  T5      S:  UU 4S j5        M3     [        R                  " [        U5      S:H  S 5        SnSnSnUS:X  a  T R	                  S5      nUS-  nT R	                  U5      nUu  pgnUS	:X  a  XVXx4n	OXEXgU4n	T R                  U	5      n
T R                  U	[        R                  S
9nX4$ )Nr}  c                  "   > ST R                    3$ )Nz:adaptive_max_pool3d(): Expected 4D or 5D tensor, but got: rA  r  s   r6   rZ   *meta_adaptive_max_pool3d.<locals>.<lambda>  r  r9   r   r   c                  *   > STR                    ST  S3$ )Nzjadaptive_max_pool3d(): Expected input to have non-zero size for non-batch dimensions, but input has sizes r  r  rA  r  s   r6   rZ   r    r  r9   r.   c                      g)NzCadaptive_max_pool3d(): internal error: output_size.size() must be 3r>   r>   r9   r6   rZ   r    r  r9   r?  r   r   )r   rK   r]   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:	
//)
$Cooiu{{o;G<r9   c                 P    [        U S5        UR                  UR                  5      $ )Nadaptive_max_pool3d_backward)r  r   r   )r  r   r   s      r6   !meta_adaptive_max_pool3d_backwardr    s"     &k3QR??5;;''r9   c                 @    Uc  [        S5      eU R                  U5      $ )Nz:cannot repeat_interleave a meta tensor without output_size)r&  r   )repeatsr  s     r6   meta_repeat_interleave_Tensorr    s%    WXX[))r9   c                 4   U R                   R                  (       d   eUR                   R                  (       d   e[        U R                  [	        U R                   5      5      UR                  [	        UR                   5      5      [
        R                  S9nU$ Nr@   )rS   r   rI   r'  r   r   rD   )realimagr  s      r6   meta_complexr    sp     ::''''::''''+DJJ78+DJJ786>>F
 Mr9   )
fill_valuer  c                \    U R                  XR                  5       4[        R                  S9$ r  )r   r~   rK   r   )r   r   r  s      r6   nonzero_staticr    s$     >>4,EJJ>??r9   c                    [         R                  " [        R                  S 5        [         R                  " U R                  5       U R                  5       4SU R                  5       4[         R                  U R                  S9$ )Nc                      g)NaY  The register_meta function for torch.nonzero() raises unimplemented by default, as a correct data-independent implementation does not exist. This implementation returns a fake value, assuming all elements of the tensor are non-zero. To enable this registration, please set 'torch.fx.experimental._config.meta_nonzero_assume_all_nonzero' to True.r>   r>   r9   r6   rZ   nonzero.<locals>.<lambda>  s     Sr9   r   rS   r{   )	rK   _check_not_implementedr{  meta_nonzero_assume_all_nonzeror/  r   r~   r   r{   r   s    r6   nonzeror    sf     
  22	S 	txxz"	
DJJLjj{{	 r9   c           
      j	  ^ ^^^^^^^^ [         R                  " [        T5      S 5        / n[        T5       GH  u  mmTGbr  [         R                  " TR                  [         R
                  [         R                  [         R                  [         R                  4;   S 5        TR                  [         R                  [         R                  4;   a  TR                  5       n[        U5      m[         R                  " TTR                  -   T R                  :*  U 4S j5        [        TR                  5       Hc  m[         R                  " TR                  T   T R                  TT-      :H  UUUUU 4S j5        UR                  UR                  ST5      5        Me     GMi  UR                  T5        GM}  UR                  T5        GM     Um[         R                  " [        T5      T R                  :*  UU 4S j5        SS KJn  [%        UR&                  " T6 5      m[        T5      T R                  :  a,  TR                  S 5        [        T5      T R                  :  a  M,  SnSnT H&  mUS:X  a	  Tb  SnM  M  US:X  a	  Tc  S	nM  M!  Tc  M&    O   S
nU(       d  / n/ n[        T5       H-  u  mmTc  M  UR                  T5        UR                  T5        M/     [        T5       H-  u  mmTb  M  UR                  T5        UR                  T5        M/     T R)                  U5      m Um/ m/ m/ m[        T5       He  u  n	mTcG  T(       a   TR                  T R                  U	   5        M0  TR                  T R                  U	   5        MP  [%        TR                  5      mMg     UUU4S jn
T R+                  TT-   T-   5      nSSKJn  U" T R1                  5       S:H  5      (       a  U$ U
" T 5      n[2        R4                  " U5      n[%        U5      [%        [        [        U5      5      5      :w  a  [2        R6                  " UR                  U5      n[2        R8                  " U5      n[2        R6                  " U[2        R:                  " U5      5      nUR=                  UR?                  5       U5      nU$ )Nc                      g)Nz#at least one index must be providedr>   r>   r9   r6   rZ   #meta_index_Tensor.<locals>.<lambda>  s    (Mr9   c                      g)Nz?tensors used as indices must be long, int, byte or bool tensorsr>   r>   r9   r6   rZ   r    s    Yr9   c                  "   > ST R                    3$ )N)too many indices for tensor of dimension r  r   s   r6   rZ   r  %  s    G		{Sr9   c            	      N   > STR                    ST  STR                    STT-    3$ )NzThe shape of the mask 
 at index z0 does not match the shape of the indexed tensor rA  )r   r   jrb  r   s   r6   rZ   r  *  s:    "8ZPQs SJJN**U_`ade`e_f!hr9   r   c                  <   > STR                    S[        T 5       S3$ )Nr  z (got rq   )r   r   )r   r   s   r6   rZ   r  5  s    ;DII;fSQX\NZ[\r9   r   Fr   Tc                    > TT-   T-   n[        U R                  5       5      nS/[        T5      -  U[        T5      [        U R                  5      [        T5      -
  & U R	                  X5      $ )z9
This follows restride_src in TensorAdvancedIndexing.cpp
r   )r   r   r   r   rC  )r   r   r   after_shapebefore_shapereplacement_shapes      r6   _restride_src(meta_index_Tensor.<locals>._restride_srcv  sm     00;>t{{}%KL#PSQ
 K
L!C

Oc+6F$FG u..r9   guard_or_false) rK   r]   r	  	enumeraterS   r   r   rA  r  r   r   r   r   r   r   selecttorch._refs_refsr   r&   r   r   r$  r  r   rC   3compute_elementwise_output_logical_to_physical_perm
apply_permr   invert_permrC  r   )r   r   r  r  refsstatehas_contiguous_subspacer  transposed_indicesr~   r  r   r  restrided_selfperm
perm_shaper4  r  r  r   r   r  rb  r  s   ``               @@@@@@@r6   meta_index_Tensorr    s   	LLg MN &(Fg&5LL

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

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

 #4(NDD^TD DzT%D	*++%%cii6
66zB
%%j%2C2CD2IJ
nnSXXZ4Jr9   c                     S nS nS nU
S   (       a  U R                  UR                  5       5      nU
S   (       a  U R                  UR                  5       5      nU
S   (       a  U R                  U5      nXU4$ )Nr   r   r   r   r   )grad_output_input_weight_bias_sizes_optr   r  r  
transposedr  r  output_maskbackend_grad_inputbackend_grad_weightbackend_grad_biass                 r6   meta_convolution_backwardr    sv      1~)33FKKMB1~*44W\\^D1~(22>B5FGGr9   c                  ^^ TR                  S5      nTR                  S5      nU R                  XV45      n [        R                  " TR	                  5       S:H  S 5        [        R                  " TR	                  5       S:H  S 5        [        R                  " TR                  S5      TR                  S5      :H  UU4S j5        [        R                  " TR                  S5      TR                  S5      :H  UU4S j5        [        R                  " U R                  S5      U:H  =(       a    U R                  S5      U:H  S	 5        U R                  U R                  5       5      $ )
Nr   r   r.   c                      grk  r>   r>   r9   r6   rZ   meta_addbmm.<locals>.<lambda>  rm  r9   c                      gro  r>   r>   r9   r6   rZ   r    rm  r9   r   c                  P   > ST R                  S5       STR                  S5       3$ )Nz8batch1 and batch2 must have same number of batches, got r   r   r   rq  rr  s   r6   rZ   r    s,    J6;;WX>JZZ_`f`k`klm`n_opr9   c            
         > ST R                  S5       ST R                  S5       STR                  S5       STR                  S5       S3	$ )Nz#Incompatible matrix sizes for bmm (r   rH   r   r   rq   r   r  s   r6   rZ   r    sL    1&++a.1A6;;q>BR S;;q>"!FKKN#316r9   c                      g)Nz.self tensor does not match matmul output shaper>   r>   r9   r6   rZ   r    s    @r9   )r   r  rK   r]   r~   r   )r   rq  rr  rN  rM  r}  r~  s    ``    r6   meta_addbmmr"    s     ;;q>D;;q>D;;|$D	LL"$HI	LL"$HI	LLA&++a.(p 
LLA&++a.(	
 
LL		!51!5@ >>$))+&&r9   c                 @    U R                  U R                  5       5      $ r3   r  )r   r  kwargss      r6   meta_randint_liker%    s    >>$))+&&r9   )
grad_scale	found_infc       	         p   ^ XX#XE4 H,  m[         R                  " [        T[        5      U4S j5        M.     g )Nc                      > S[        T 5       3$ Nz'exponent must be a tensor list but got rr   ls   r6   rZ   #meta__fused_adam_.<locals>.<lambda>      =d1gYGr9   rK   r]   rg   r   )r   gradsexp_avgsexp_avg_sqsmax_exp_avg_sqsstate_stepslrbeta1beta2weight_decayepsamsgradmaximizer&  r'  r-  s                  @r6   meta__fused_adam_r=    s0    & 8/Oq$G	
 Pr9   c       	            ^ XX#XE4 H,  m[         R                  " [        T[        5      U4S j5        M.     S nU" U 5      U" U5      U" U5      U" U5      U" U5      4$ )Nc                      > S[        T 5       3$ r*  r+  r,  s   r6   rZ   "meta__fused_adam.<locals>.<lambda>  r/  r9   c                 Z    U  Vs/ s H  n[         R                  " U5      PM     sn$ s  snf r3   r  )tensor_listr  s     r6   empty_like_list)meta__fused_adam.<locals>.empty_like_list  s%    -89[  #[999s    (r0  )r   r1  r2  r3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r&  r'  rC  r-  s                   @r6   meta__fused_adamrE    si    & 8/Oq$G	
 P: 	!$( r9   c                 t  ^ ^ [         R                  " T R                  5       S:H  S 5        [         R                  " TR                  5       S:H  S 5        [         R                  " T R                  [         R                  L U 4S j5        [         R                  " TR                  [         R                  L U4S j5        [         R                  " T R                  S5      TR                  S5      :H  U U4S j5        T R                  T R                  S5      TR                  S5      4[         R                  S	9$ )
Nr   c                      g)Nza must be a 2D tensorr>   r>   r9   r6   rZ   meta__int_mm.<locals>.<lambda>      '>r9   c                      g)Nzb must be a 2D tensorr>   r>   r9   r6   rZ   rH    rI  r9   c                  "   > ST R                    3$ )Nzexpected self to be int8, got r   )r  s   r6   rZ   rH        0	:r9   c                  "   > ST R                    3$ )Nzexpected mat2 to be int8, got r   )r  s   r6   rZ   rH    rL  r9   r   r   c            
         > ST R                  S5       ST R                  S5       STR                  S5       STR                  S5       S3	$ )Nz'Incompatible matrix sizes for _int_mm (r   rH   r   r   rq   r   r  r  s   r6   rZ   rH  "  sH    5affQi[!&&) M66!9+Qqvvayk,r9   r   )rK   r]   r~   rS   rA  r   r   rB  rO  s   ``r6   meta__int_mmrP    s     
LLA>?	LLA>?	LL	5::: 
LL	5::: 
LL	q	QVVAY	
 ;;q	166!9-U[[;AAr9   c                 d  ^  [         R                  " T R                  5       S:H  S 5        [         R                  " T R                  [         R                  L U 4S j5        T R                  S5      nT R                  S5      S-  nT R                  US-  X1S-  -  SUS-  4[         R                  S	9$ )
Nr   c                      gNzw must be a 2D tensorr>   r>   r9   r6   rZ   2meta__convert_weight_to_int4pack.<locals>.<lambda>,  rI  r9   c                  "   > ST R                    3$ Nr.  r   r  s   r6   rZ   rT  /      .qwwi8r9   r   r      rZ      r   )rK   r]   r~   rS   r  r   r   rB  r  inner_k_tilesr  rb  s   `   r6    meta__convert_weight_to_int4packr]  *  s    	LLA>?	LL	5;;8 	
q	A	q	AA;;F"$%Q		
 kk   r9   c                 H  ^  [         R                  " T R                  5       S:H  S 5        [         R                  " T R                  [         R                  L U 4S j5        T R                  S5      nT R                  S5      nT R                  X#S-  4[         R                  S9$ )Nr   c                      grS  r>   r>   r9   r6   rZ   :meta__convert_weight_to_int4pack_for_cpu.<locals>.<lambda>@  rI  r9   c                  "   > ST R                    3$ Nzexpected w to be int32, got r   rW  s   r6   rZ   r`  C  rX  r9   r   r   r   )rK   r]   r~   rS   rB  r   r   r  r[  s   `   r6   (meta__convert_weight_to_int4pack_for_cpurc  >  s}    	LLA>?	LL	5;;8 	
q	A	q	A;;	
Fkk   r9   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$ )
Nr   c                      gNzx must be a 2D tensorr>   r>   r9   r6   rZ   *meta__weight_int4pack_mm.<locals>.<lambda>O  rI  r9   r   c                      g)Nzw must be a 4D tensorr>   r>   r9   r6   rZ   rg  P  rI  r9   c                  "   > ST R                    3$ Nr-  r   rH   s   r6   rZ   rg  S      5aggY?r9   c                  "   > ST R                    3$ rb  r   rW  s   r6   rZ   rg  W  rX  r9   r   rY  r   
rK   r]   r~   rS   r[  r\  r]  rB  r   r   r/  s   ``  r6   meta__weight_int4pack_mmro  M  s    	LLA>?	LLA>?	LL	EMM5==%..AA? 
LL	5;;8 ;;qvvay!&&)a-qww;??r9   c                 0  ^ ^ [         R                  " T R                  5       S:H  S 5        [         R                  " TR                  5       S:H  S 5        [         R                  " T R                  [         R                  [         R
                  [         R                  4;   U 4S j5        [         R                  " TR                  [         R                  L U4S j5        T R                  T R                  S5      TR                  S5      T R                  S9$ )Nr   c                      grf  r>   r>   r9   r6   rZ   2meta__weight_int4pack_mm_for_cpu.<locals>.<lambda>^  rI  r9   c                      grS  r>   r>   r9   r6   rZ   rr  _  rI  r9   c                  "   > ST R                    3$ rj  r   rk  s   r6   rZ   rr  b  rl  r9   c                  "   > ST R                    3$ rV  r   rW  s   r6   rZ   rr  f  rX  r9   r   r   )
rK   r]   r~   rS   r[  r\  r]  r  r   r   r/  s   ``  r6    meta__weight_int4pack_mm_for_cpurv  \      	LLA>?	LLA>?	LL	EMM5==%..AA? 
LL	5;;8 ;;qvvay!&&)177;;;r9   c                 0  ^ ^ [         R                  " T R                  5       S:H  S 5        [         R                  " TR                  5       S:H  S 5        [         R                  " T R                  [         R                  [         R
                  [         R                  4;   U 4S j5        [         R                  " TR                  [         R                  L U4S j5        T R                  T R                  S5      TR                  S5      T R                  S9$ )Nr   c                      grf  r>   r>   r9   r6   rZ   ;_weight_int4pack_mm_with_scales_and_zeros.<locals>.<lambda>m  rI  r9   c                      grS  r>   r>   r9   r6   rZ   rz  n  rI  r9   c                  "   > ST R                    3$ rj  r   rk  s   r6   rZ   rz  q  rl  r9   c                  "   > ST R                    3$ rb  r   rW  s   r6   rZ   rz  u  rX  r9   r   r   rn  )rH   r  r0  qScaleqZeross   ``   r6   )_weight_int4pack_mm_with_scales_and_zerosr  k  rw  r9   r  r  c                     X-   S-
  U-  U-  $ r/  r>   rO  s     r6   kai_roundupr  z  s    UQY1!!r9   c                   ^	^
^^^^^^^^^ U S:X  a{  X2:X  a(  SnSnSnSmSmSmS mUUUU4S jmU4S jnU" XXEU5      $ US-  S	:X  aD  X#-  S	:X  a;  SnSnSnSmSmSmSm	U	UU4S
 jnU	U
UUUUU4S jmS m
U	4S jmU	4S jmU" XXEXc5      $ g g g )Nr   rY  rZ  r   c                 4    [        X-  S5      n[        X5      $ )Nr   r  )rb  krsrkr_sr_roundedup4s       r6   kai_k_roundedup3get_kai_packed_weight_size.<locals>.kai_k_roundedup  s     $/rw#: "177r9   c                 X   > T" XU5      nUS-  S:X  d   S5       eUUS-  T-   T-   T-   -  $ )Nr   r   zk_internal must be evenr>   )	rb  nrr  r  
k_internalr  kai_num_bytes_biaskai_num_bytes_multiplier_rhskai_num_bytes_sum_rhss	        r6   9kai_get_rhs_packed_stride_rhs_pack_nxk_qsi4cxp_qsu4cxs1s0]get_kai_packed_weight_size.<locals>.kai_get_rhs_packed_stride_rhs_pack_nxk_qsi4cxp_qsu4cxs1s0  sW     -QB7
"Q1,G.GG,1_23+, )) r9   c                 8   > [        X5      U-  nUT" XX45      -  $ r3   r  )r  rb  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r9   rZ  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      -  $ rp  r  )
r  rb  r  r  r  blr  kai_bl_multiple_of;kai_get_rhs_packed_stride_rhs_pack_nxk_qsi4c32p_qsu4c32s1s0kai_nr_multiple_ofs
          r6   9kai_get_rhs_packed_size_rhs_pack_nxk_qsi4c32p_qsu4c32s1s0]get_kai_packed_weight_size.<locals>.kai_get_rhs_packed_size_rhs_pack_nxk_qsi4c32p_qsu4c32s1s0  sh     A~%~//A555//A555&q-3 Qrrr9   c                    > XB-  S:X  d   eUT
-  S:X  d   eUT-  S:X  d   eT	" 5       nT" X5      nT" XE5      nUXv-  T-   T-   -  $ rp  r>   )rb  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"&='# (=+,() r9   c                      g)Nr   r>   r>   r9   r6   r  Gget_kai_packed_weight_size.<locals>.kai_get_bf16_datatype_size_in_bytes  s    r9   c                 6   > UT-  S:X  d   e[        X5      U-  $ rp  r  )rb  r  r  s     r6   r  :get_kai_packed_weight_size.<locals>.kai_num_blocks_per_row  s'    //A555"1)R//r9   c                 *   > U T-  S:X  d   eU S-  U-   $ )Nr   r   r>   )r  r  r  s     r6   r  ;get_kai_packed_weight_size.<locals>.kai_num_bytes_per_block  s'    //A555a#;;;r9   r>   )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 [ r9   c                 \  ^  [         R                  " T R                  [         R                  L U 4S j5        [         R                  R
                  R                  5       (       a  X4:X  a  UR                  [         R                  :X  d4  X4:  ac  US-  S:X  aZ  XC-  S:X  aR  UR                  [         R                  :X  a4  [        SXTU5      nT R                  [        U5      [         R                  S9$ T R                  5       UR                  5       -   nT R                  U[         R                  S9$ )Nc                  "   > ST R                    3$ rV  r   )weightss   r6   rZ   2meta__dyn_quant_pack_4bit_weight.<locals>.<lambda>  s    .w}}o>r9   rZ  r   r   r   )rK   r]   rS   r  backendskleidiaiis_availablerO   r]  r  r   r   r   )r  scales_zerosr<  
block_sizein_featuresout_featurespacked_weight_sizes   `      r6    meta__dyn_quant_pack_4bit_weightr    s     
LL$> ~~++--		"|'9'9U[['H$R1$(A-""enn4 8|*
   %7!8 LL <+=+=+??/u{{CCr9   c                   ^  [         R                  " T R                  5       S:H  S 5        [         R                  " T R                  [         R                  4;   U 4S j5        T R                  S5      nT R                  XTT R                  S9$ )Nr   c                      g)Nzinput must be a 2D tensorr>   r>   r9   r6   rZ   -meta__dyn_quant_matmul_4bit.<locals>.<lambda>  s    )Dr9   c                  "   > ST R                    3$ )Nzexpected input to be f32, got r   )inps   r6   rZ   r    s    0<r9   r   r   )rK   r]   r~   rS   r[  r   r   )r  packed_weightsr  r  r  r  s   `     r6   meta__dyn_quant_matmul_4bitr    se     
LLa!DE	LL		emm_$< 	A==		=::r9   c                 0  ^ ^ [         R                  " T R                  5       S:H  S 5        [         R                  " T R                  [         R                  [         R
                  [         R                  4;   U 4S j5        [         R                  " TR                  5       S:H  S 5        [         R                  " TR                  [         R                  L U4S j5        T R                  T R                  S5      TR                  S5      T R                  S9$ )Nr   c                      grf  r>   r>   r9   r6   rZ   *meta__weight_int8pack_mm.<locals>.<lambda>  rI  r9   c                  "   > ST R                    3$ rj  r   rk  s   r6   rZ   r    rl  r9   c                      grS  r>   r>   r9   r6   rZ   r    rI  r9   c                  "   > ST R                    3$ )Nzexpected w to be int8, got r   rW  s   r6   rZ   r    s    -aggY7r9   r   r   )
rK   r]   r~   rS   r[  r\  r]  rA  r   r   )rH   r  q_scaless   `` r6   meta__weight_int8pack_mmr    s    	LLA>?	LL	EMM5==%..AA? 
LLA>?	LL	5::7 ;;qvvay!&&)177;;;r9   c                   ^ ^^ [         R                  " T R                  5       S:  U 4S j5        [         R                  " TR                  5       S:  U4S j5        [         R                  " T R                  S5      TR                  S5      :H  U U4S j5        [         R                  " [        R
                  " T R                  5      S 5        [         R                  " [        R
                  " TR                  5      S 5        [         R                  " US:  S	 5        [         R                  " TS
;   U4S j5        T R                  S5      nTR                  S5      nT R                  S S nTR                  S S n[        [         R                  " Xg5      5      nUR                  XE/5        T R                  U5      $ )Nr   c                  ,   > ST R                  5        S3$ )Nz1cdist only supports at least 2D tensors, X1 got: r,  r   )x1s   r6   rZ   $meta_cdist_forward.<locals>.<lambda>(      CBFFH:QOr9   c                  ,   > ST R                  5        S3$ )Nz1cdist only supports at least 2D tensors, X2 got: r,  r   )x2s   r6   rZ   r  ,  r  r9   r   c                  P   > ST R                  S5       STR                  S5       3$ )Nz4X1 and X2 must have the same number of columns. X1: r   z X2: r   )r  r  s   r6   rZ   r  0  s*    Frwwr{mSXY[Y`Y`acYdXefr9   c                      g)Nz=cdist only supports floating-point dtypes, X1 got: {x1.dtype}r>   r>   r9   r6   rZ   r  4  r   r9   c                      g)Nz=cdist only supports floating-point dtypes, X2 got: {x2.dtype}r>   r>   r9   r6   rZ   r  8  r   r9   r   c                      g)Nz)cdist only supports non-negative p valuesr>   r>   r9   r6   rZ   r  :  s    !Lr9   Nr   r   c                     > ST  3$ )Nz%possible modes: None, 1, 2, but was: r>   )compute_modes   r6   rZ   r  =  s    7~Fr9   r  )rK   r]   r~   r   rC   is_float_dtyperS   r   r   broadcast_shapesextendr   )	r  r  r[  r  r1r2batch_tensor1batch_tensor2rd  s	   `` `     r6   meta_cdist_forwardr  $  sF   	LL
AO 
LL
AO 
LL
rwwr{"f 
LLRXX&O 
LLRXX&O 
LLaLM	LL$F 
B	BHHSbMMHHSbMM..}LML!<<%%r9   c                 <   UR                   S   nUR                   S   nUR                   S   nUR                   S S nUR                   S S n	[        [        R                  " X5      5      n
U
R	                  5       nUR                  Xe/5        [        R                  " U
5      nUS:X  d  US:X  d  US:X  d  US:X  a  [        R                  " U5      $ U[        UR                   5      :w  a  UR                  U5      n[        R                  " U[        R                  S9$ )Nr   r  r   r   )r   r   rK   r  copyr  mathprod
zeros_liker  r   r   )r`  r  r  r[  cdistc1r  r  r  r  r  tensor1_expand_sizebatch_products                r6   meta_cdist_backwardr  H  s     
"B	"B	"BHHSbMMHHSbMM 6 6} TU.335x(II23M	Qw"'R1W(:##d288n,YY*+Be.E.EFFr9   c	                 Z  ^ ^^^^^ [         R                  " TR                  [         R                  [         R                  4;   U4S j5        [         R                  " TR                  [         R                  [         R                  4;   U4S j5        [         R                  " [
        R                  " T R                  5      U 4S j5        TR                  S5      n	U(       a   [         R                  " U	S:  S 5        U	S-  n	T R                  U	T R                  S5      5      n
Tb  [         R                  " U[        :H  S 5        [         R                  " TR                  S:H  U4S j5        [         R                  " TR                  5       TR                  5       :H  UU4S	 j5        U4S
 jmS mUU4S jn[        T5      S:w  a}  TR                  TR                  S5      5      nTR                  TR                  5       5      nU[        :X  a"  TR                  U	T R                  S5      5      nOTR                  S5      nOU" T TX5      nU[        [        4;   d  U(       d!  TR                  TR                  S5      5      nOTR                  S5      nTR                  U	5      nTR                  S   nU[        :X  aG  U(       a   [         R                  " US:  S 5        US-  nTR                  UT R                  S   5      nOTR                  UR                  5       5      nXX4$ )Nc                  "   > ST R                    3$ )Nz(expected indices to be long or int, got r   )r   s   r6   rZ   $meta_embedding_bag.<locals>.<lambda>m      :7==/Jr9   c                  "   > ST R                    3$ )Nz(expected offsets to be long or int, got r   )rt  s   r6   rZ   r  q  r  r9   c                  "   > ST R                    3$ )Nz/expected weight to be floating point type, got r   )r:  s   r6   rZ   r  u  s    A&,,Pr9   r   r   c                      gNz1include_last_offset: numBags should be at least 1r>   r>   r9   r6   rZ   r  |  s    Gr9   c                      g)Nz@embedding_bag: per_sample_weights only supported with mode='sum'r>   r>   r9   r6   rZ   r    s    Vr9   c                  $   > ST R                    S3$ )Nz1expected per_sample_weights to be 1D tensor, got r,  r  )per_sample_weightss   r6   rZ   r    s    GHZH_H_G``abr9   c                  N   > STR                  5        ST R                  5        S3$ )Nz%expected per_sample_weights.numel() (z$ to be the same as indices.numel() (rq   r   )r   r  s   r6   rZ   r    s/    78J8P8P8R7S T66=mmo5FaIr9   c                 L   > T" XU5      =(       a    UR                  S5      S:H  $ Nr   r   r   )r*  r  r   padding_idxis_fast_path_index_selects       r6   is_fast_path_index_select_scale;meta_embedding_bag.<locals>.is_fast_path_index_select_scale  s&    %c;?XELLQROWXDX	
r9   c                    U R                   [        R                  :H  =(       d    U R                   [        R                  :H  =(       a;    U R	                  S5      S:H  =(       a     UR	                  S5      S:H  =(       a    US:  $ Nr   r   )rS   rK   rO   rM   r   )r*  r   r  s      r6   r   5meta_embedding_bag.<locals>.is_fast_path_index_select  sb    YY%++%@ejj)@  

1" a A%  a		
r9   c                 .   > Ub	  T" XX#5      $ T" XU5      $ r3   r>   )r*  r  r   r  r   r  s       r6   is_fast_path(meta_embedding_bag.<locals>.is_fast_path  s#    23vSS,S+FFr9   cpuc                      gr  r>   r>   r9   r6   rZ   r    s    Or9   )rK   r]   rS   r   r   rC   r  r   r   MODE_SUMr   r   r   MODE_MAX	MODE_MEANr   )r:  r   rt  scale_grad_by_freqrh  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4r9   c                     [        XU/UQ76 u  pEpg[        U5      S:X  a  UR                  UR                  5       5      nXEXg4$ )Nr	  )r  r   r   r   )r:  r   rt  rE   r   r  r  r  s           r6   meta_embedding_bag_forward_onlyr    sN    0B1#'1-F 7u$$$W\\^4x44r9   c                     U(       a  U$ U R                   R                  (       d  U R                   R                  (       a  U R                   $ U(       a  [        R                  $ U R                   $ r3   )rS   r   r   rK   r   )r   rS   promote_int_to_longs      r6   _get_reduction_dtyper    sD    {{$$(>(>{{	zz;;r9   r   c                    [        XSS9n[        R                  " U R                  U5      n[	        XU5      nU R                  XTS9$ )NT)r  r   )r  rC   r  r   r  r   )r   r  r  rS   r  rd  s         r6   meta_nansumr    sC     ($OLT2D+EAL??<?<<r9   c           	          [         R                  " U R                  [        [	        U R                  5       5      5      5      nU R                  U5      $ r3   )rC   r  r   r\   r   r~   r   )r   rd  s     r6   meta_medianr     s<    77U5-.L ??<((r9   c                    [        U 5      S:X  a  [        R                  " S5        [        R                  " U R                  U45      n[        XU5      nU R                  U5      U R                  U[        R                  S94$ )Nr   zmedian CUDA with indices outputr   )	r   rC   alert_not_deterministicr  r   r  r   rK   r   )r   r~   r  rd  s       r6   meta_median_mode_dimr#    sn     5V#%%&GH


u{{SF
3C+E@L%EJJ7 r9   c                     U $ r3   r>   r   s    r6   meta_logical_not_r%    r  r9   c                   ^^ [         R                  " [        U5      U R                  5       :  S 5        [	        U5       H%  u  mm[         R                  " TS:  UU4S j5        M'     [        U5      U R                  5       -
  nSU-  [        U R                  5      -   n[        [        U5      5       Vs/ s H  oCU   X   -  PM     nnU R                  U5      $ s  snf )Nc                      g)NzZNumber of dimensions of repeat dims can not be smaller than number of dimensions of tensorr>   r>   r9   r6   rZ   meta_repeat.<locals>.<lambda>
  s    lr9   r   c                     > ST ST  3$ )Nz"Repeats cannot be negative, found r  r>   )r   reps   r6   rZ   r(    s    8ZsKr9   r   )	rK   r]   r   r~   r  r\   r   r   r   )r   r  num_new_dimensionspadded_sizer   target_sizer*  s       ` @r6   meta_repeatr.    s    	LLG
"l G$31HK	
 % W
2++eDJJ.??K8=c'l8KL8K1q>GJ.8KKL>>+&& Ms   6Cc                     U $ r3   r>   r   s    r6   
meta_zero_r0    r  r9   c                     [        U[        R                  5      (       a   [        U R                  UR                  5        U $ r3   )rg   rK   r   r_   r   r   r   s     r6   meta_binop_inplacer3    s,     %&&

EKK8Kr9   c                 *   S nS nS nU" U 5      (       a  U" U5      (       a  [        S5      eU" U 5      (       a  U" U5      (       d  [        S5      e[        U[        R                  5      (       a   [	        U R
                  UR
                  5        U $ )a  
Some checks for inplace ops.
Checks for promotion rules for some dtypes.
int.add/sub_(float) and bool.add/sub_(others) are rejected.
Promoting in these in-place operations would require reallocating
and copying over elements, hence not allowed.
Checks for alpha param.
c                     [        U [        5      (       a   [        R                  " U R                  5      $ [        U [
        5      $ r3   )rg   r   rC   rF  rS   r   rj   s    r6   is_integeric.meta_binop_inplace_alpha.<locals>.is_integericB  s1    c:&&))#))44c7++r9   c                     [        U [        5      (       a   [        R                  " U R                  5      $ [        U [
        5      $ r3   )rg   r   rC   r  rS   r   r6  s    r6   
is_floatic,meta_binop_inplace_alpha.<locals>.is_floaticH  s1    c:&&''		22c9--r9   c                     [        U [        5      (       a   [        R                  " U R                  5      $ [        U [
        5      $ r3   )rg   r   rC   is_boolean_dtyperS   r   r6  s    r6   is_booleanic.meta_binop_inplace_alpha.<locals>.is_booleanicN  s1    c:&&))#))44c8,,r9   z]Promotion of int.add/sub_(float) in in-place ops are not possible due to element size change.z_Promotion of book.add/sub_(others) in in-place ops are not possible due to element size change.)r&  rg   rK   r   r_   r   )r   r   rM  r7  r:  r>  s         r6   meta_binop_inplace_alphar@  0  s    $,.- Dj//k
 	

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

EKK8Kr9   c                 2    [        X[        R                  S9$ r  rI   r   rD   r   r   rM  s      r6   meta_binop_alpharD  e  s     $C$K$K r9   c                 2    [        U [        R                  S9$ r  rB  )r   r$  s     r6   
meta_roundrF  q  s    <DD r9   c                   ^ ^^ [         R                  " [        R                  " TR                  5      U U4S j5        [        T[         R                  5      (       a;  [         R                  " [        R                  " TR                  5      U U4S j5        g [         R                  " [        T[        5      U U4S j5        g )Nc                  &   > T  STR                    3$ )Nz7: Expected input tensor to have an integral dtype. Got r   )r  r   s   r6   rZ   #shift_dtype_check.<locals>.<lambda>{  s    7)RSWS]S]R^_r9   c                  &   > T  STR                    3$ )Nz6: Expected shift value to have an integral dtype. Got r   r  r  s   r6   rZ   rI    s    wiUVYV_V_U`ar9   c                     > T  ST 3$ )Nz): Expected shift value to be an int. Got r>   rK  s   r6   rZ   rI    s    wiHNr9   )rK   r]   rC   rF  rS   rg   r   r   )r  r   r  s   ```r6   shift_dtype_checkrM  x  ss    	LLtzz*_ #u||$$""399-a	

 	sG$N	
r9   c                 J    [        SX5        [        X[        R                  S9$ )Nrshiftr  rM  rI   r   rD   r2  s     r6   meta_rshiftsrQ    %    h,$C$K$K r9   c                 J    [        SX5        [        X[        R                  S9$ )Nlshiftr  rP  r2  s     r6   meta_lshiftsrU    rR  r9   c                 8    U R                  U R                  5      $ r3   r  r   s    r6   	meta_zerorW    s    >>$**%%r9   c                     U $ r3   r>   r   r  s     r6   
meta_fill_rZ    r  r9   c                 .    [         R                  " U 5      $ r3   r  rY  s     r6   	meta_fillr\        D!!r9   c                     U $ r3   r>   r   s    r6   
meta_relu_r_    r  r9   c                 2    [        X[        R                  S9$ r  rB  rC  s      r6   meta__add_relura    s     $C$K$K r9   c                 .    [         R                  " U 5      $ r3   r  r   noiselowerr  r  r  s         r6   meta_rrelu_with_noiserf    s    
 D!!r9   c                 Z    [         R                  " U 5      [         R                  " U5      4$ r3   r  rc  s         r6    meta_rrelu_with_noise_functionalrh    s%     D!5#3#3E#:::r9   c                     U $ r3   r>   )r   re  r  r  r  s        r6   meta_rrelu_with_noise_rj    s	     Kr9   c                 .    [         R                  " U 5      $ r3   r  r   r   r   
accumulates       r6   meta_index_putrn    r]  r9   c                 F    [        U R                  UR                  5        U $ r3   r_   r   )r   r  values      r6   meta_masked_fill_rr    s    DJJ

3Kr9   c                     U R                  U R                  5       5      R                  [        R                  " U 5      S9nU$ r   )r   r   r'  rC   r   )r   r  r  masked_scales       r6   meta__masked_scaleru    s<    >>$))+.1111$7 2 L r9   c                    ^ ^ [         R                  " UR                  [         R                  [         R                  4;   S 5        [         R                  " T R                  TR                  :H  U U4S j5        T $ )Nc                      g)NzMask must be bool or uint8r>   r>   r9   r6   rZ   &meta_masked_scatter_.<locals>.<lambda>  s    9Ur9   c                  <   > ST R                    STR                    3$ )NzEmasked_scatter: expected self and source to have same dtypes but got r   r   )r   rg  s   r6   rZ   rx    s      **U6<<.:r9   )rK   r]   rS   r	  r  )r   r  rg  s   ` `r6   meta_masked_scatter_rz    sU    	LL

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

fll"	:
 Kr9   c                 z    [        X5      u  p[        R                  " U [        R                  S9n[	        X1U5      $ r   )r&   rK   r   r   rz  )r   r  rg  r   s       r6   meta_masked_scatterr|    s5     "$-JDd%2I2IJFf55r9   c                 $    U R                  U5      $ r3   r  )r   r  rP  s      r6   meta_masked_scatter_backwardr~    s    >>%  r9   c                     U $ r3   r>   rl  s       r6   meta_index_put_r    r  r9   c                   ^^
^^^ [         R                  " U R                  5       S:H  S 5        [         R                  " UR                  5       S:H  S 5        U R                  5       nUR                  5       m
US   mUS   mUS   nT
S   nTXg4m[         R                  " T
S   T:H  =(       a    T
S   T:H  U
UU4S j5        U(       a  U R                  [         R
                  :H  =(       d    U R                  [         R                  :H  =(       a    U[         R                  :H  n[         R                  " X@R                  :H  =(       d    US 5        UR                  T5      R                  U5      n	OUR                  T5      n	U(       dY  TbV  [         R                  " TR                  5       S:H  S	 5        [         R                  " TR                  5       T:H  UU4S
 j5        U	$ )Nr.   c                      grk  r>   r>   r9   r6   rZ   )common_meta_baddbmm_bmm.<locals>.<lambda>  rm  r9   c                      gro  r>   r>   r9   r6   rZ   r    rm  r9   r   r   r   c            	      .   > ST ST ST S    ST S    S3	$ rt  r>   rv  s   r6   rZ   r    s3    RSURV
l<?*;2l1o=NbRr9   c                      g)Nzfout_dtype only supported for torch.float32 output with float16/bfloat16 inputs or same as input dtypesr>   r>   r9   r6   rZ   r    s    |r9   c                      g)Nzself must be a 3D tensorr>   r>   r9   r6   rZ   r    s    6Pr9   c                  0   > ST  STR                  5        3$ )Nz*Expected an input tensor shape with shape z but got shape: r   )r  self_baddbmms   r6   rZ   r     s    @M]^j^o^o^q]rsr9   )
rK   r]   r~   r   rS   r\  r]  r[  r   r'  )rq  rr  is_bmmr  r>  r  res_rowsres_colssupported_out_dtyper   rw  rx  ry  r  s      `      @@@@r6   common_meta_baddbmm_bmmr    s   	LL"$HI	LL"$HI;;=L;;=L	aB#AAHAHx*K	LLQ2E,q/5E"E	R
 LLEMM)KV\\U^^-K)5==( 	 	%<)<|	
 !!+.11)< !!+.l.\%%'1,.PQ;.s	

 Mr9   c                     [        XS5      $ )NTr  )r   rI  s     r6   meta_bmmr  &  s    "4t44r9   c                     [        XSUS9$ )NT)r>  r  )r   rI  r>  s      r6   meta_bmm_dtyper  +  s    "4tyIIr9   c                 h    X-  nX-  nUS:w  a#  [        US:  5      [        US:  5      :w  a  US-  nU$ r  )r	  )rH   yqrl  s       r6   div_rtnr  0  s>    	A	A 	Av4A;$q1u+-	QHr9   c                     [        U U-   U-   XQS-
  -  -
  S-
  U(       a  US-
  OS-   U5      S-   nU(       a  US-
  U-  X-   :  a  US-  nU$ r  )r  )	inputSize
kernelSizer  r  r   r  r&  
outputSizes           r6   pooling_output_shape_pad_lrr  :  s     	 q.)* 	
 'vzA/ 	
 		  Nf$	(99!OJr9   c           	         ^^^ [         R                  " US:g  S 5        [         R                  " TS:  U4S j5        [         R                  " TTS-
  T-  S-   S-  :*  UUU4S j5        [        U TTTUTU5      $ )Nr   c                      g)Nzstride should not be zeror>   r>   r9   r6   rZ   &pooling_output_shape.<locals>.<lambda>V  s    &Ar9   c                     > ST  3$ )Nz'pad must be non-negative, but got pad: r>   pads   r6   rZ   r  W  s    %LSE#Rr9   r   r   c                     > ST ST ST  3$ )NzApad should be at most half of effective kernel size, but got pad=z, kernel_size=z and dilation=r>   )r  r  r  s   r6   rZ   r  Z  s"    OPSu U%,nXJ@r9   )rK   r]   r  )r  r  r  r   r  r&  s    `` ` r6   rV  rV  U  ss    	LL1AB	LLRS	LLa8+a/A55	
 ':sC9 r9   c           	        ^ ^^^^^	^
^^^^ T R                  5       nT	m[        R                  " TS:  =(       a    TS:  S 5        [        R                  " US:  =(       a    US:  S 5        [        R                  " US:  =(       a    US:  S 5        T R                  S5      S:g  =(       a    T R                  S5      S:g  nU[        R                  :X  a@  [        R                  " US:H  =(       a    U=(       a    T R                  S5      S:g  S	 5        Or[        R                  " US:H  =(       a    T R                  S5      S:g  =(       a    U=(       d)    US:H  =(       a    U=(       a    T R                  S5      S:g  U 4S
 j5        [        R                  " TS-  T:  =(       a    TS-  T:  UUUU4S j5        [        R                  " TS:  =(       a    TS:  U
UU	UUU4S j5        g )Nr   c                      g)NzCkernel size should be greater than zero, but got kH: {kH}, kW: {kW}r>   r>   r9   r6   rZ   $pool2d_shape_check.<locals>.<lambda>z  r  r9   c                      g)Nz>stride should be greater than zero, but got dH: {dH}, dW: {dW}r>   r>   r9   r6   rZ   r  ~  s    Pr9   c                      g)Nz\dilation should be greater than zero, but got dilationH: {dilationH}, dilationW: {dilationW}r>   r>   r9   r6   rZ   r    s    nr9   r   r   r   r.   c                      g)NzExpected 4D (batch mode) tensor expected for input with channels_last layout with optional 0 dim batch size for input, but got: {input.size()}r>   r>   r9   r6   rZ   r    s     Qr9   c                  *   > ST R                  5        3$ )NzYExpected 3D or 4D (batch mode) tensor with optional 0 dim batch size for input, but got: r   r  s   r6   rZ   r    s    opupzpzp|o}~r9   c                      > ST ST ST ST  3$ )NzKpad should be smaller than or equal to half of kernel size, but got padW = z	, padH = z, kW = z, kH = r>   )rZ  r[  r^  r_  s   r6   rZ   r    s$     ygbT>r9   c                  .   > ST ST  ST ST ST ST S3$ NzGiven input size: (rH   z). Calculated output size: (z). Output size is too smallr>   )r`  ra  r'  rf  r(  r)  s   r6   rZ   r    s8    %k]!K=* N$$0><.+ O##r9   )r~   rK   r]   r   r  )r   rZ  r[  r\  r]  r^  r_  	dilationH	dilationWr'  r`  ra  r(  r)  r   r   
valid_dimsrf  s   ```  ``  `````   @r6   rW  rW  d  s   " 99;DL	LL
Q26U 
LL
Q26P 
LLA')a-n
 A!#:

1(:J+++AI;*;A!);Q	
 	QY<5::a=A-<* A	?j?UZZ]a-?~	
 
LL
a4+B!GtO	> 
LLq.\Q.	# 	#r9   r  r  rZ  r[  r  r\  r]  pTpHpW	dilationTr  r  r  r  r  r  r  r  r  c           
        ^ ^^^^^^^^^	^
^^^^^^^^^^^ T R                   n[        R                  " TS:  =(       a    TS:  =(       a    TS:  UUU4S j5        [        R                  " TS:  =(       a    TS:  =(       a    TS:  UUU4S j5        [        R                  " TS:  =(       a    TS:  =(       a    TS:  UUU4S j5        [        R                  " US;   UU 4S j5        [        U5       H@  mUS:X  a  TS:X  a  M  [        R                  " T R	                  T5      S:  UUU 4S j5        MB     U(       a;  [        R                  " TT:  =(       a    TT:  =(       a    TT:  UUUUUU4S	 j5        [        R                  " TS
-  T:  =(       a    TS
-  T
:  =(       a    TS
-  T	:  UUUU	UU
4S j5        [        R                  " TS:  =(       a    TS:  =(       a    TS:  UUUUUUU4S j5        g )Nr   c                     > ST ST  ST 3$ )Nz5kernel size should be greater than zero, but got kT: z, kH: z, kW: r>   )rZ  r  r[  s   r6   rZ   $pool3d_shape_check.<locals>.<lambda>  s    $fRDrd,r9   c                     > ST ST  ST 3$ )Nz0stride should be greater than zero, but got dT: z, dH: z, dW: r>   )r\  r  r]  s   r6   rZ   r    s    >rd&FSURVWr9   c                     > ST ST  ST 3$ )Nz9dilation should be greater than zero, but got dilationT: z, dilationH: z, dilationW: r>   )r  r  r  s   r6   rZ   r    s    #M)M)Vr9   r}  c                  &   > T  STR                    3$ )Nz/: Expected 4D or 5D tensor for input, but got: rA  )r  r   s   r6   rZ   r    s    7)J5;;-Xr9   r?  c                  L   > T  STR                    STR                  T5       S3$ )NzZ: Expected input's non-batch dimensions to have positive length, but input has a shape of z and non-batch dimension z has length zero!)r   r   )r  r   r   s   r6   rZ   r    s.    ) --2[[M+EJJqM?:KMr9   c                  .   > ST ST  ST ST ST ST S3$ )Nzinput image (T: rH  r*  z ) smaller than kernel size (kT:  kH:  kW: rq   r>   )r  r  r  rZ  r  r[  s   r6   rZ   r    s4    "5'gYd6( C$$&4uRDbT<r9   r   c                  ,   > ST ST ST  ST ST ST 3$ )NzHpad should be smaller than or equal to half of kernel size, but got kT: r  r  z padT: z padW: z padH: r>   )rZ  r  r[  r  r  r  s   r6   rZ   r    s1    $eB4uRDt72$gbTKr9   r   c                  :   > ST ST ST  ST ST ST ST ST S3$ r  r>   )r  r  r  r  r  r  r  s   r6   rZ   r    sD    !'!E7!G9AfX F((/y%'!F8 L'(r9   )r   rK   r]   r   r   )r   r  r  rZ  r[  r  r\  r]  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!|	
 	
r9   c                 j   U R                   n[        U UUUUUUU	U
UUUUUUUUUUUU5        [        UUUS-
  U5        [        UUUS-
  U5        [        UUUS-
  U5        [        UUUS-
  U5        [        UUUS-
  U5        [        UUUS-
  U5        [        UUUS-
  U5        [        UUUS-
  U5        g )Nr   r.   r   r   r   r  r8  )r   r  r   r  r  rZ  r[  r  r\  r]  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3r9   c                     U R                   n[        U UUUUUUUU	U
USSSUUUUUUUS5        [        UUUS-
  U5        [        UUUS-
  U5        [        UUUS-
  U5        [        UUUS-
  U5        g )Nr   Tr   r.   r   r  )r   r  r  r  rZ  r[  r  r\  r]  r  r  r  r  r  r  r  r  r  r  r   s                       r6   r  r  <  s    * ::D








			-2 ;dQh8;dQh6;dQh8;dQh7r9   c                    S nU" SU5      u  px[         R                  " [        U5      S;   S 5        [        U5      S:X  a  XxpOU" SU5      u  pU" SU5      u  pU" SU5      u  pU R                  S	5      nU R                  S
5      nU R                  S5      n[        R
                  " U 5      nU[         R                  :X  a*  [         R                  " U R                  5       S:H  S 5        OVU[         R                  :X  a*  [         R                  " U R                  5       S;   S 5        O[         R                  " SS 5        [        UX{XU5      n[        UXXU5      n[        U UUU	U
UUUUUUUUUU5        UUU4$ )Nc                    ^  [         R                  " [        U5      S;   U 4S j5        US   n[        U5      S:X  a  UOUS   nX#4$ )Nr;  c                     > ST  S3$ )Nzmax_pool2d: r=  r>   r>  s   r6   rZ   Emax_pool2d_checks_and_compute_shape.<locals>.unpack.<locals>.<lambda>~  r@  r9   r   r   rA  rB  s   `   r6   rE  3max_pool2d_checks_and_compute_shape.<locals>.unpack{  rG  r9   r  rH  c                      g)NzOmax_pool2d: stride must either be omitted, a single int, or a tuple of two intsr>   r>   r9   r6   rZ   5max_pool2d_checks_and_compute_shape.<locals>.<lambda>  rL  r9   r   r   r  r  rR  r  r   r   c                      g)NzMnon-empty 4D (batch mode) tensor expected for input with channels_last layoutr>   r>   r9   r6   rZ   r    s    cr9   r  c                      g)Nz9non-empty 3D or 4D (batch mode) tensor expected for inputr>   r>   r9   r6   rZ   r        Or9   Fc                      g)NzAUnsupported memory format. Supports only ChannelsLast, Contiguousr>   r>   r9   r6   rZ   r    s    Wr9   )rK   r]   r   r   rC   r   r  r~   r   rV  rW  )r   r  r   r  r  r&  rE  rZ  r[  r\  r]  r^  r_  r  r  r'  r`  ra  r   r(  r)  s                        r6   r$  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



$ k11r9   c                 |  ^ ^^^^^ [        TX#XEU5      u  nmm[        R                  " TR                  T R                  :H  U U4S j5        UmTR                  mUUUU4S jn	U	" T 5        U	" U5        [
        R                  " T5      n
[        R                  " TR                  TR                  TR                  U
S9$ )Nc                  <   > STR                    ST R                    3$ )NzExpected dtype z  for `gradOutput` but got dtype r   r  s   r6   rZ   7meta_max_pool2d_with_indices_backward.<locals>.<lambda>  s    /$**-MkN_N_M`ar9   c                 l   > [        U TTS-
  T5        [        U TTS-
  T5        [        U TTS-
  T5        g )Nr.   r   r   )r8  )r  rf  r   r(  r)  s    r6   _check_dim_size>meta_max_pool2d_with_indices_backward.<locals>._check_dim_size  s9    q$q,7q$q,7q$q+6r9   r{  )
r$  rK   r]   rS   r   rC   r   r   r   r{   )r  r   r  r   r  r  r&  r   r'  r  r   rf  r   r(  r)  s   ``         @@@@r6   %meta_max_pool2d_with_indices_backwardr    s     	,k7i		
 
LL

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

jj{{#	 r9   c                    [        XX#XE5      u  nnnU R                  5       S:X  a  U R                  S5      OSn	[        R                  " U 5      n
U R                  5       S:X  a  XgU/nOXXx/n[
        R                  " UU R                  U R                  U
S9[
        R                  " U[
        R                  U R                  U
S94$ r"  )
r$  r~   r   rC   r   rK   r   rS   r{   r   r%  s               r6   meta_max_pool2d_with_indicesr    s     	,FX		
  %yy{a/UZZ^QF//6Myy{a;7\?++<<'		
 	++<<'		
 r9   c           	        ^ ^^^
^^ [         R                  " T R                  S;   U 4S j5        T R                  n[        US-
  U5       HA  m
[         R                  " T R	                  T
5      S:  ST R	                  5        ST
 S35        MC     [         R                  " [        T5      S:H  S	 5        [         R                  " [        U5      S:H  S
 5        T R	                  S5      nT R	                  S5      mT R	                  S5      mUS:X  a  T R	                  S5      nOSn[         R                  " T R                  TR                  :H  S 5        [         R                  " TR                  S:H  U4S j5        TR	                  S5      nTR	                  S5      nTR	                  S5      m
[         R                  " Xv:  S5        [         R                  " X:H  S 5        [         R                  " T
S:H  U
4S j5        [         R                  " US   TS   -   S-
  T:*  UU4S j5        [         R                  " US   TS   -   S-
  T:*  UU4S j5        T R                  5       S:X  a  XeUS   US   /n	O
XRS   US   /n	[         R                  " U	T R                  T R                  S9[         R                  " U	[         R                  T R                  S94$ )Nr  c                  "   > ST R                    3$ )Nz:fractional_max_pool2d: Expected 3D or 4D tensor, but got: r  r   s   r6   rZ   ,meta_fractional_max_pool2d.<locals>.<lambda>  s    LTYYKXr9   r.   r   z_fractional_max_pool2d: Expected input to have non-zero  size for non-batch dimensions, but got r  z emptyr   c                      g)NzNfractional_max_pool2d: kernel_size musteither be a single int or tuple of Intsr>   r>   r9   r6   rZ   r  #       2r9   c                      g)NzOfractional_max_pool2d: output_size must either be a single int or tuple of Intsr>   r>   r9   r6   rZ   r  (  r  r9   rR  r  r   r   r   c                      g)Nz6Expect _random_samples to have the same dtype as inputr>   r>   r9   r6   rZ   r  6  s    Hr9   c                  "   > ST R                    3$ )Nz1Expect _random samples to have 3 dimensions got, r  )random_sampless   r6   rZ   r  :  s    CNDWDWCXYr9   z=Expect _random_samples.size(0) no less then input batch size.c                      g)Nz<Expect _random_samples.size(1) equals to input channel size.r>   r>   r9   r6   rZ   r  F      Nr9   c                     > ST  S3$ )Nz/Expect _random_samples.size(2) equals to 2 got .r>   )r   s   r6   rZ   r  H  s    #RSTRUUV!Wr9   c                     > STS    ST  3$ )Nz%fractional_max_pool2d: kernel height r   z' is too large relative to input height r>   )input_heightr  s   r6   rZ   r  L  s    7A7GGno{n|}r9   c                     > STS    ST  3$ )Nz$fractional_max_pool2d: kernel width r   z& is too large relative to input width r>   )input_widthr  s   r6   rZ   r  P  s    6{1~6FFlmxlyzr9   r  )rK   r]   r   r   r   r   rS   r~   r   r{   r   )r   r  r  r  r   input_channelsinput_batchr  cr   r   r  r  s   `` `      @@@r6   meta_fractional_max_pool2dr    s   	LL		VX 99D4!8T"IIaL177;yy{mCSTUSVV\^	
 # 
LLKA	2
 
LLKA	2 YYr]N99R=L))B-Kqyiil	LL

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

 	++;;	
 r9   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$ )Nrr  c                      gNzMmax_pool3d: kernel_size must either be a single int, or a tuple of three intsr>   r>   r9   r6   rZ   .meta_max_pool3d_with_indices.<locals>.<lambda>r      _r9   r   r   r   c                      gNzQmax_pool3d: stride must either be omitted, a single int, or a tuple of three intsr>   r>   r9   r6   rZ   r  z      cr9   c                      gNzImax_pool3d: padding must either be a single int, or a tuple of three intsr>   r>   r9   r6   rZ   r        [r9   c                      gNzJmax_pool3d: dilation must be either a single int, or a tuple of three intsr>   r>   r9   r6   rZ   r    r  r9   r}  c                      gr  r>   r>   r9   r6   rZ   r    r  r9   r?  r#  rR  r  r   zmax_pool3d_with_indices()r   r   r   )rK   r]   r   r   r   rV  r  rC   r   r  r  r_  r   r   r'  )r   r  r   r  r  r&  r  rZ  r[  r  r\  r]  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  input_channels_last_checkr   r   r   s                                  r6   meta_max_pool3d_with_indicesr  f  sB    
LLKF"_ 
QB;1$+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<r9   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$ )Nrr  c                      gr  r>   r>   r9   r6   rZ   7meta_max_pool3d_with_indices_backward.<locals>.<lambda>  r  r9   r   r   r   c                      gr  r>   r>   r9   r6   rZ   r    r  r9   c                      gr  r>   r>   r9   r6   rZ   r    r  r9   c                      gr  r>   r>   r9   r6   rZ   r    r  r9   r}  c                      gr  r>   r>   r9   r6   rZ   r    r  r9   r#  rR  r  r   z"max_pool3d_with_indices_backward()r?  r   r   )rK   r]   r   r   r   r  rC   r   r  r  r_  r   r   r'  )r  r   r  r   r  r  r&  r   r  rZ  r[  r  r\  r]  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  s                                 r6   %meta_max_pool3d_with_indices_backwardr    s    
LLKF"_ 
QB;1$+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$6!)7799
'5500 6 
 	 -J]]1G1G]H
r9   gridc                   ^ ^^ [         R                  " T R                  TR                  :H  UU 4S j5        [         R                  " T R                  [         R                  :H  =(       a    TR                  [         R                  :H  UU 4S j5        [         R                  " T R
                  S   TR
                  S   :H  UU 4S j5        [         R                  " TR
                  S   T R                  S-
  :H  UU 4S j5        [        ST R                  5       H/  m[         R                  " T R
                  T   S:  UU 4S j5        M1     g )	Nc                  <   > STR                    ST R                    3$ )NzNgrid_sampler(): expected input and grid to be on same device, but input is on z and grid is on r  r  r   s   r6   rZ   +check_grid_sampler_common.<locals>.<lambda>9  s"    \\N"24;;-Ar9   c                  <   > STR                    ST R                    3$ )NzTgrid_sampler(): expected input and grid to have torch.strided layout, but input has z and grid has )rz   r
  s   r6   rZ   r  @  s!    nT[[MCr9   r   c                  <   > STR                    ST R                    3$ )NzZgrid_sampler(): expected grid and input to have same batch size, but got input with sizes  and grid with sizes rA  r
  s   r6   rZ   r  G  s"      %},A$**Or9   r   r   c                  B   > STR                   S-
   ST R                   3$ )Nz+grid_sampler(): expected grid to have size r   z, in last dimension, but got grid with sizes )r   r   r
  s   r6   rZ   r  N  s'    9%**q.9I J226**?r9   c                  *   > STR                    ST  S3$ )NzYgrid_sampler(): expected input to have non-empty spatial dimensions, but input has sizes r  r  rA  r  s   r6   rZ   r  W  r  r9   )rK   r]   r{   rz   r  r   r   r   )r   r  r   s   ``@r6   check_grid_sampler_commonr  6  s    	LL#	
 
LL%F$++*F	
 
LLA$**Q-'	
 
LL

2%**q.(	
 1ejj!KKNQ	
 "r9   c                        \ rS rSrSrSrSrSrg)GridSamplerInterpolationi^  r   r   r   r>   N)rs   
__module____qualname____firstlineno__BILINEARNEARESTBICUBIC__static_attributes__r>   r9   r6   r  r  ^  s    HGGr9   r  interpolation_modec                 6  ^ ^ [         R                  " T R                  S:H  =(       a    T R                  TR                  :H  UU 4S j5        [         R                  " T R                  S:H  =(       a    U[        R                  R
                  :H  (       + S 5        g )Nr?  c                  <   > STR                    ST R                    3$ )Nzdgrid_sampler(): expected 5D input and grid with same number of dimensions, but got input with sizes r  rA  r
  s   r6   rZ   'check_grid_sampler_3d.<locals>.<lambda>g  s!    449KK=#DJJ<1r9   c                      g)Nz<grid_sampler(): bicubic interpolation only supports 4D inputr>   r>   r9   r6   rZ   r  r  r  r9   )rK   r]   r   r  r  rq  )r   r  r  s   `` r6   check_grid_sampler_3dr   d  sp    	LL

a3EJJ$))3	
 
LLJJ!O M"&>&F&F&L&LL	
 	Or9   c                     US   nU(       a$  [         R                  " U[         R                  S9nOS n[         R                  " U[         R                  S9n	X4$ Nr   r   )rK   r  r   r   
r  r   r  r  padding_modealign_cornersr  input_requires_gradr  	grad_grids
             r6   grid_sampler_2d_backward_metar(  v  sO     &a.%%e5;R;RS

  U5L5LMI""r9   c                     [        X5        [        XU5        U R                  S   nU R                  S   nUR                  S   nUR                  S   nUR                  S   n	U R                  XVXxU	45      $ )Nr   r   r   r.   )r  r   r   r   )
r   r  r  r$  r%  r  Cout_Dout_Hout_Ws
             r6   grid_sampler_3dr.    sn     e*%'9:AAAAJJqMEJJqMEJJqME??A%677r9   r'  c                     [        X5        [        XU5        US   nU(       a$  [        R                  " U[        R                  S9nOS n[        R
                  " U[        R                  S9n	X4$ r"  )r  r   rK   r  r  r   r#  s
             r6   grid_sampler_3d_backwardr0    sg     e*%'9:%a.%%!?!?

 
  U5S5STI  r9   c                     UR                  SS 5      nU(       d  [        R                  " U5      nXCS'   [        R                  " U /UQ70 UD6$ )NrS   )rR   rC   	get_dtyperK   r   )r   r  rE   r$  rS   s        r6   fullr3    sC    JJw%E
+7O;;t-d-f--r9   c           	      V   U[         R                  :X  a  [         R                  " US L S 5        [         R                  " SUc  U R                  OUUUc  U R
                  OUUS9nU R                  (       a>  UR                  U R                  5       U R                  5       U R                  5       5        O/UR                  U R                  5       U R                  5       S5        UR                  S5        U$ [        R                  R                  U UUUUUS9nUR!                  S5        U$ )Nc                      g)Nz9memory format option is only supported by strided tensorsr>   r>   r9   r6   rZ   zeros_like.<locals>.<lambda>  r  r9   r   r  Tr  )rK   
sparse_coor]   r   rS   r{   	is_sparsesparse_resize_and_clear_r   
sparse_dim	dense_dimr~   _coalesced_r+   r   r)  fill_)r   rS   rz   r{   r|   r   r  s          r6   r  r    s     !!!T!O	

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

//
!
!# " C IIaLJr9   ry   c                    Uc  [         R                  " 5       nUc  [         R                  " 5       nUc  [         R                  n[         R                  " XX#US9$ r
  rK   r   get_default_devicer  r   r   rS   rz   r{   r|   r}   s         r6   	meta_onesrB    P     }'')~))+~;;&J r9   c                    Uc  [         R                  " 5       nUc  [         R                  " 5       nUc  [         R                  n[         R                  " XX#US9$ r
  r?  rA  s         r6   
meta_zerosrE    rC  r9   c                 .    [         R                  " U 5      $ r3   rC   clone_preserve_strides)r   r*  r~   r   s       r6   meta_select_scatterrI        ''--r9   c                 .    [         R                  " U 5      $ r3   rG  )r   r*  r~   ru   rt   steps         r6   meta_slice_scatterrM    rJ  r9   dim_post_exprwrap_scalarc                     US::  a  U(       d   eSnU* nUS-
  nX:  d  X:  a   SU  SU SU S35       eU S:  a  X-  n U $ )Nr   r   zdim z out of bounds (rp   rq   r>   )r~   rN  rO  r   r  s        r6   r   r   "  sg    {.C
!
C	SYR4u4DSEC5PQ)RR'
QwJr9   c                 L    U R                  5       S:X  a  S$ U R                  U   $ r  r5  )r  r~   s     r6   ensure_nonempty_sizerR  .  s!    11.!''#,.r9   c                 F  ^ ^^^ [        T R                  5       S5      n[        TR                  5       S5      n[        R                  " X4:H  S 5        [	        U5       H@  mTT:w  d  M  [        R                  " [        TT5      [        T T5      :*  UUUU 4S j5        MB     g )Nr   c                      g)NzDIndex tensor must have the same number of dimensions as input tensorr>   r>   r9   r6   rZ   $gather_shape_check.<locals>.<lambda>8  s    Vr9   c                  N   > ST STR                    3STR                    ST  3-   $ )Nz!Size does not match at dimension z expected index  to be no larger than self  apart from dimension rA  )r~   r   r   r   s   r6   rZ   rU  >  s5    ;A3>Nu{{m\/

|;QRUQVWXr9   )r  r~   rK   r]   r   rR  )r   r~   r   	self_dims
index_dimsr   s   ```  @r6   gather_shape_checkr[  3  s}    DHHJ"IUYY[!$J	LLV 98LL$UA.2FtQ2OOX r9   c                   ^ SSK Jn  [        XR                  5       5      nU" TR	                  5       S:H  5      nU(       df  [
        R                  " TR                  [
        R                  :H  =(       d    TR                  [
        R                  :H  U4S j5        [        XT5        U R                  TR                  5      $ )Nr   r  c                  "   > ST R                    3$ )Nz8gather(): Expected dtype int32/int64 for index, but got r   r   s   r6   rZ   meta_gather.<locals>.<lambda>L  s    Nu{{m\r9   )r$  r  r   r~   r   rK   r]   rS   r   r   r[  r   r   )r   r~   r   sparse_gradr  wrapped_dimis_index_emptys     `    r6   meta_gatherrb  C  s~    D hhj1K#EKKMQ$67NKK5::%A		)A\	
 	4e4>>%++&&r9   c                     U(       a<  U S:X  a  gU S:X  a  gU S:X  a  gU S:X  a  gU S	:X  a  g
[         R                  " SS 5        g U S:X  a  gU S:X  a  g[         R                  " SS 5        g )Nr
  
REDUCE_ADDr  REDUCE_MULTIPLYmeanREDUCE_MEANamaxREDUCE_MAXIMUMaminREDUCE_MINIMUMFc                      g)Nz=reduce argument must be either sum, prod, mean, amax or amin.r>   r>   r9   r6   rZ   #get_operator_enum.<locals>.<lambda>a  s    Sr9   addmultiplyc                      g)Nz/reduce argument must be either add or multiply.r>   r>   r9   r6   rZ   rm  i  s    $Ur9   ro  )reduce_use_new_optionss     r6   get_operator_enumrs  S  s{    e$ ##S	
 	e
"$UUVr9   c                 n  ^  SSK Jn  U" UR                  5       S:g  5      (       aZ  [        R                  " UR
                  [        R                  :H  =(       d    UR
                  [        R                  :H  U 4S j5        Ub3  [        R                  " UR
                  UR
                  :H  U 4S j5        g g )Nr   )rh  c                     > T  S3$ )Nz((): Expected dtype int32/int64 for indexr>   method_names   r6   rZ   ,scatter_gather_dtype_check.<locals>.<lambda>t  s    {m#KLr9   c                     > T  S3$ )Nz0(): Expected self.dtype to be equal to src.dtyper>   rv  s   r6   rZ   rx  z  s    {m#STr9   )r$  rh  r   rK   r]   rS   r   r   )rw  r   r   src_optrh  s   `    r6   scatter_gather_dtype_checkr{  n  sy    CU[[]a'((KK5::%A		)AL	

 JJ'--'T	
 r9   c                     [        U S5      $ r/  )r  r   s    r6   ensure_nonempty_dimr}  ~  s    sA;r9   c                 .  ^ ^^^ SSK Jn  U" TR                  5       S:H  5      (       a  g [        R                  " [        T R                  5       5      [        TR                  5       5      :H  S 5        Sn[        T R                  5       5      n[        U5       H+  n[        TU5      nUT:X  a  M  U[        T U5      :  d  M)  Sn  O   U(       d5  Tb2  [        U5       H#  n[        TU5      nU[        TU5      :  d  M!  Sn  O   Tbm  [        R                  " [        T R                  5       5      [        TR                  5       5      :H  S 5        [        R                  " U(       + UUU U4S j5        g [        R                  " U(       + UUU 4S j5        g )	Nr   r  c                      gNzCIndex tensor must have the same number of dimensions as self tensorr>   r>   r9   r6   rZ   %scatter_shape_check.<locals>.<lambda>  r  r9   FTc                      gr  r>   r>   r9   r6   rZ   r    s    Yr9   c                  b   > STR                    STR                    3ST  STR                    3-   $ )NExpected index rW  rX  z and to be no larger than src rA  )r~   r   r   rz  s   r6   rZ   r    s6    oekk]2Mdjj\Z&se+I'--YZr9   c                  H   > STR                    STR                    3ST  3-   $ )Nr  rW  rX  rA  )r~   r   r   s   r6   rZ   r    s*    oekk]2Mdjj\Z&se,-r9   )	r$  r  r   rK   r]   r}  r~   r   rR  )	r   r~   r   rz  r  is_wrong_shaperY  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	
 	-	
r9   c                     [        XR                  5       5      n[        SXU5        [        XX#5        Ub  [	        XE5        g g )Nscatter)r   r~   r{  r  rs  )r   r~   r   r*  rq  rr  r`  s          r6   scatter_meta_implr    s;     hhj1Ky$s;56'3 r9   c                 R    [        XX#S5        U R                  U R                  5      $ Nrn  r  r   r   r   r~   r   r*  s       r6   meta_scatter_addr    s!    dU3>>$**%%r9   c                      [        XX#S5        U $ r  r  r  s       r6   meta_scatter_add_r    s    dU3Kr9   c                     [        U[        R                  5      (       a  UOS n[        XX%U5        U R	                  U R
                  5      $ r3   )rg   rK   r   r  r   r   r   r~   r   src_or_valuerh  r*  s         r6   meta_scatterr    s:     %\5<<@@,dCdV4>>$**%%r9   c                 f    [        U[        R                  5      (       a  UOS n[        XX%U5        U $ r3   )rg   rK   r   r  r  s         r6   meta_scatter_r    s,     %\5<<@@,dCdV4Kr9   queryr   rq  	dropout_p	is_causalreturn_debug_maskr  c           	      \   U R                  S5      nU R                  S5      nU R                  S5      n	U R                  S5      n
UR                  S5      nU R                  SS5      n[        R                  " U5      R                  SS5      n[        R                  " XxU	4[        R
                  U R                  S9nU(       aa  U
S:  a  SOSn[        R                  " X-  5      nUS::  a  SnOUS::  a  Sn[        R                  " XxU	U4U R                  U R                  S9nO*[        R                  " SU R                  U R                  S9n[        R                  R                  (       al  [        R                  R                  5       (       aI  [        R                  " S	[        R                  S
S9n[        R                  " S	[        R                  S
S9nOH[        R                  " S[        R                  S
S9n[        R                  " S	[        R                  S
S9nUUS S U	UUUU4	$ )Nr   r   r   r.   r  @         r>   rx   )r   r  rK   r   r   rO   r{   r  ceilrS   versionhipr   r  r   rU  )r  r   rq  r  r  r  r  r   	num_headsmax_seqlen_batch_qhead_dimmax_seqlen_batch_kquery_t	attention	logsumexpblocksize_cmax_seqlen_k
debug_maskseedoffsets                       r6   (meta__scaled_dot_product_flash_attentionr    s    AJ

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

 [[%++ellK
 }}UZZ4466{{2UZZ?Ruzz&A{{Aell6BRu||FC 	
 
r9   	res_shape.c                   ^  [        T R                  5      U:X  a:  T R                  SS5      n[        R                  " U5      R                  SS5      nU$ [        / SQU 4S jSS9nU Vs/ s H  oQU   PM	     nn[        [        U5      5       Vs/ s H  otR                  U5      PM     nn[        R                  " UT R                  T R                  S9R                  U5      nU$ s  snf s  snf )Nr   r   )r   r   r   r.   c                 *   > TR                  5       U    $ r3   r  )idxr  s    r6   rZ   ,alloc_with_matching_layout.<locals>.<lambda>0  s    %,,.*=r9   Tr   r  )r\   r   r  rK   r   sortedr   r   r   r   rS   r{   r   )	r  r  r  r  	dim_orderr  permuted_shaper   final_permutes	   `        r6   alloc_with_matching_layoutr  '  s     U[[Y&//!Q'w'11!Q7 J =t
	 5>>ISC.I>5:3y>5JK5J+5JKkk%++ell

'-
  	 J ?Ks   *C'C,	attn_biascompute_log_sumexpc	           	         U R                  S5      n	U R                  S5      n
U R                  S5      nUR                  S5      nUR                  S5      nXX4n[        X5      n[        R                  " XU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   r   r   r   r  r>   rx   r   r  rK   r   rO   r{   r   )r  r   rq  r  r  r  r  r  r  r  rC  S_QS_KVD_Vr  r  
logsum_expr  r  s                      r6   (meta__scaled_dot_product_cudnn_attentionr  ;  s     	

1A

1A
**Q-C88A;D
**R.Cs I
$U
6C	
sAkk||J ;;rF;D[[5::f=F 	
 
r9   c           	         U R                  S5      nU R                  S5      n	U R                  S5      n
UR                  S5      nUR                  S5      nXX4n[        X5      n[        R                  " XU
4[        R                  U R
                  S9n[        R                  " S[        R                  SS9n[        R                  " S[        R                  SS9nUUS S U
UUUS 4	$ r  r  )r  r   rq  r  r  r  r  r  r  H_Qr  r  r  r  r  r  r  r  s                     r6   5meta__scaled_dot_product_fused_attention_overrideabler  g  s     	

1A
**Q-C
**Q-C88A;D
**R.C"I
$U
6C	
kk||J ;;rF;D[[5::f=F 	
 
r9   r  r  	cum_seq_q	cum_seq_kmax_qmax_kphilox_seedphilox_offsetc                 P   [         R                  " UR                  SS5      5      R                  SS5      n[         R                  " UR                  SS5      5      R                  SS5      n[         R                  " UR                  SS5      5      R                  SS5      nUUU4$ r  )rK   r   r  )r  r  r   rq  r   r  r  r  r  r  r  r  r  r  r  grad_qgrad_kgrad_vs                     r6   'meta__scaled_dot_product_flash_backwardr    s    , eooa34>>q!DFcmmAq12<<QBFeooa34>>q!DF66!!r9   	attn_maskc                    U R                  S5      nU R                  S5      nU R                  S5      n	[        R                  " U 5      n
[        R                  " UU	U4[        R                  U R
                  S9R                  SS5      nU
U4$ )Nr   r   r   r  )r   rK   r   r   rO   r{   r  )r  r   rq  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  	 r9   c
                 `   [         R                  " UR                  5       SUR                  UR                  S9n
[         R                  " UR                  5       SUR                  UR                  S9n[         R                  " UR                  5       SUR                  UR                  S9nXU4$ )Nr   r   r   r.   r  )rK   empty_permutedr   rS   r{   )r  r  r   rq  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!!r9   dropout_maskc                   ^ ^^^^^^^ S nU" T 5      u  mmU" U5      u  pU" U5      u  pTR                   u  mmmmU	R                   u  pmn
UUUUUU U4S jnUUUUU4S jnTS:  d  UT:  a  TS:  a  U" 5       $ U" 5       $ )Nc                 p   U R                  5       S:X  a  U R                  S5      S4$ U R                  5       S:  ax  Sn[        U R                  5       S-
  5       H  nXR                  U   -  nM     U R	                  XR                  S5      U R                  S5      U R                  S5      5      S4$ U S	4$ )
Nr.   r   Tr   r   rR  r  r   F)r~   r  r   r   viewr   )rH   r   r   s      r6   	ensure_4dBmeta__scaled_dot_product_attention_math_for_mps.<locals>.ensure_4d  s    557a<;;q>4''UUWq[J1557Q;'ggaj(
 (66*ffRj!&&*affRjI4OOe8Or9   c                  j  > TR                  TR                  5      n T	(       a  U R                  T5      n TR                  TTTT45      nT	(       aa  TR                  5       S:X  a  UR	                  S5      nX4$ [        TR                  S S 5      UR                  SS -   nUR                  U5      nX4$ )Nr.   r   rR  r   r   )r   r   view_asr~   squeezer   r  )
r   attnr   r   max_seq_lengthnum_headq_q_sizer  
unsqueezeds
      r6   sdpa_vector_fast_mpsMmeta__scaled_dot_product_attention_math_for_mps.<locals>.sdpa_vector_fast_mps  s    ll288$++e$C||Z6>JKyy{a||A y U[["-.Aa@yy'yr9   c                  p   > Sn TR                  TR                  5      nTR                  TTTU T45      nX4$ )NrZ  r  )blocksr   r,  r   	head_sizer  r  r  s      r6   sdpa_vector_2pass_mpsNmeta__scaled_dot_product_attention_math_for_mps.<locals>.sdpa_vector_2pass_mps$  s<    ll288$||Z669$UV  r9   i   i   rA  )r  r   rq  r  r  r  r  r  r  k_rF   v_k_sizer  r  r   r  r  r  r  r  r  s   `              @@@@@@@r6   /meta__scaled_dot_product_attention_math_for_mpsr    s    	 u%NB
cNEBeEB.0hh+J&)#%88 A~q ! ! 	$FVO$8N$&&#%%r9   c           	      R   U R                  SS5      n UR                  SS5      nUR                  SS5      nU R                  S5      nU R                  S5      n	U R                  S5      n
UR                  S5      n[        R                  " XXU R                  U R
                  S9n[        R                  R                  (       a0  [        R                  R                  5       (       a   U(       a  U	OSnO%U(       a  [        R                  " U	S-  5      S-  OSn[        R                  " XU4[        R                  U R
                  S9nUR                  SS5      n[        R                  " S[        R                  S	S9n[        R                  " S[        R                  S	S9nXUU4$ )
Nr   r   r   r  r   r  rZ  r>   rx   )r  r   rK   r   rS   r{   r  r  r   r  r  r  rO   r   )r  r   rq  r  r  r  r  r  r  r  r  Kvr  logsumexp_dimr  r  r  s                    r6   ,meta__scaled_dot_product_efficient_attentionr  0  s?    OOAq!E
--1
COOAq!E

1A

1A

2I	BB
++aIU\\
RC}}UZZ4466	 0Q2D		!b&)B.!	
}%kk||J --1
C ;;rF;D[[5::f=FD&((r9   grad_input_maskc                    UR                  S5      nUR                  S5      nUR                  S5      nUR                  S5      nUR                  S5      nUR                  S5      n[        R                  " XUU4SUR                  UR                  S9n[        R                  " XUU4SUR                  UR                  S9n[        R                  " XUU4SUR                  UR                  S9nS nUb  U
S   (       ax  UR                  S5      nUS-  S:X  a  UO
US-   US-  -
  n[        UR                  5       5      nUUS'   [        R                  " UUR                  UR                  S9nUS	S U24   nUUUU4$ )
Nr   r   r   r.   r  r  r   rZ  .)r   rK   r  rS   r{   r   r   )r  r  r   rq  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$57R<'TV,;V)*	&	"KKY__Y5E5E
	 c8G8m,	669,,r9   c                     [         R                  " U5      n[         R                  " U5      n[         R                  " U5      nUUU4$ r3   r  )r  r  r   rq  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$F66!!r9   window_size_leftwindow_size_right	seqused_kalibi_slopesc                    Uc  U R                  S5      OUR                  5       S-
  nUc  U R                  S5      OUnUc  UR                  S5      OUnU R                  S5      nU R                  S5      n[        R                  " U 5      nUc2  [        R                  " UUU4[        R
                  U R                  S9nOAU R                  S5      n[        R                  " UU4[        R
                  U R                  S9nU	(       ac  US:  a  SOSn[        R                  " UU-  5      nUS::  a  SnOUS::  a  Sn[        R                  " UUUU4U R                  U R                  S9nO*[        R                  " SU R                  U R                  S9nS	u  nn[        R                  R                  (       al  [        R                  R                  5       (       aI  [        R                  " S
[        R                  SS9n[        R                  " S
[        R                  SS9nOH[        R                  " S[        R                  SS9n[        R                  " S
[        R                  SS9nUUUUU4$ )Nr   r   r  r   r  r  r  r  NNr>   rx   r   )r   r   rK   r   r   rO   r{   r  r  rS   r  r  r   r  r   rU  )r  r   rq  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 r9   c                     [         R                  " U5      n[         R                  " U5      n[         R                  " U5      nUUU4$ r3   r  )r  r  r   rq  r   r  r  r  r  r  r  r  r  r  r  r  r  
grad_querygrad_key
grad_values                       r6   meta__flash_attention_backwardr    sA    0 !!%(J$H!!%(Jx++r9   cu_seqlens_qcu_seqlens_kmax_seqlen_qr  custom_mask_typecausal_diagonalseqlen_kwindow_sizec           	         U R                  S5      nU R                  S5      nUR                  S5      nU R                  S5      nUR                  S5      n[        R                  " UUUUU R                  U R                  S9nUb  UR                  S5      S-
  OUnUnUb  Uc   eUnUb  UOUnU
(       a  [
        R                  " US-  5      S-  OSn[        R                  " UUU4[        R                  U R                  S9n[        R                  " S[        R                  SS9n[        R                  " S[        R                  SS9nUUUUUU4$ )	Nr   r   r  r   r  rZ  r>   rx   )	r   rK   r   rS   r{   r  r  rO   r   )r  r   rq  r<  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  %  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Rr9   bias_requires_gradnum_splits_keyshared_storage_dqdkdvc                    U(       a  [         R                  " UR                  S   UR                  S   :H  S 5        [         R                  " UR                  S   UR                  S   :H  S 5        [         R                  " / UR                  SS QSPUR                  S   PUR                  S   P7UR                  UR
                  S9nUR                  S	S5      nUR                  S	S5      nUR                  S	S
5      nOB[         R                  " U5      n[         R                  " U5      n[         R                  " U5      nUby  UR                  S5      nUS-  S:X  a  UO
US-   US-  -
  n[        UR                  5       5      nUUS'   [         R                  " UUR                  UR
                  S9nUSS U24   nO[         R                  " SUR
                  S9nUUUU4$ )Nr   c                      g)Nz,seqlen must match for `shared_storage_dqdkdvr>   r>   r9   r6   rZ   4meta__efficient_attention_backward.<locals>.<lambda>u  s    Br9   r.   c                      g)Nz3embedding dim must match for `shared_storage_dqdkdvr>   r>   r9   r6   rZ   r!  y  s    Ir9   r   r  r   r  rR  r   rZ  .r>   r  )
rK   r]   r   r   rS   r{   r   r   r   r   )r  r  r   rq  r<  r  r  r  r  r  r  r  r  r  r  r  r  r  chunkr  r  r  r  r  r  r  s                             r6   "meta__efficient_attention_backwardr$  Y  s   2 KKNciil*B	
 	KKNciil*I	
 Eekk!BEEEKKOEU[[_E++<<

 \\"a(
<<A&\\"a(
%%e,
##C(%%e,
))B-$+bLA$57R<'TV,;V%	&	"KK	DKKP	c8G8m,	KK5<<8	xY66r9   scale_ascale_bscale_resultuse_fast_accumc                 
  ^ ^^^^^^^ S n[         R                  " T R                  5       S:H  =(       a    TR                  5       S:H  UU 4S j5        [         R                  " U" T R                  5      =(       a    U" TR                  5      UU 4S j5        [	        T 5      S:X  Gaw  S n	S n
S n[         R                  " U	" T R                  5       5      =(       d    U" T 5      U 4S	 j5        [         R                  " U
" TR                  5       5      =(       d    U" T5      U4S
 j5        [         R                  " T R                  S5      S-  S:H  U 4S j5        [         R                  " TR                  S5      S-  S:H  =(       a    TR                  S5      S-  S:H  U4S j5        T R                  u  mnTR                  S5      mTR                  [         R                  :H  =(       a    TR                  [         R                  :H  =(       dA    TR                  [         R                  :H  =(       a    TR                  [         R                  :H  nTR                  5       S:X  am  TR                  5       S:X  aY  [         R                  " TR                  [         R                  :H  =(       a    TR                  [         R                  :H  S 5        GOJU(       a  TR                  [         R                  :X  a  SnUS-  nOSnSnS nU" X5      nU" US5      S-  nUU" TU5      -  U-  mUU" TU5      -  U-  mTR                  5       T:X  ab  TR                  5       T:X  aN  [         R                  " TR                  5       S 5        [         R                  " TR                  5       S 5        GOn[         R                  " SUUUU4S j5        GON[         R                  " TR                  [         R                  :H  =(       a    TR                  [         R                  :H  S 5        [         R                  " TR                  5       S:H  =(       a    TR                  5       S:H  UU4S j5        TR                  S5      T:X  a}  TR                  S5      S:X  ah  TR                  S5      S:X  aS  TR                  S5      T:X  a>  [         R                  " TR                  5       =(       a    TR                  5       S 5        O[         R                  " SUUUU4S j5        Ub  UOT R                  n[         R                  " T R                  S5      TR                  S5      UT R                  S9$ )Nc                     U [         R                  [         R                  [         R                  [         R                  [         R
                  4;   $ r3   )rK   r^  float8_e5m2float8_e4m3fnuzfloat8_e5m2fnuzfloat4_e2m1fn_x2r   s    r6   is_fp8_or_fp4_type*meta_scaled_mm.<locals>.is_fp8_or_fp4_type  sA    !!!!""
 
 	
r9   r   c                  L   > STR                  5        ST R                  5        3$ )Nz%Inputs must be 2D but got self.dim()=z and mat2.dim()=r   rI  r   s   r6   rZ    meta_scaled_mm.<locals>.<lambda>  s%    7
|CSTXT\T\T^S_`r9   c                  <   > STR                    ST R                    3$ )Nz?Expected both inputs to be fp8 or fp4 types but got self.dtype=z and mat2.dtype=r   r2  s   r6   rZ   r3    s$    QRVR\R\Q]]mnrnxnxmyzr9   r   c                 6    U S   U S   :  =(       a    U S   S:H  $ r  r>   r  s    r6   is_row_major$meta_scaled_mm.<locals>.is_row_major  s"    !9vay(;VAY!^;r9   c                 0    U S   S:H  =(       a    U S   S:  $ r  r>   r  s    r6   is_col_major$meta_scaled_mm.<locals>.is_col_major  s    !9>3fQi!m3r9   c                 `    U R                  S5      S:H  =(       d    U R                  S5      S:H  $ r  r   )	tensor_2ds    r6   has_zero_dim$meta_scaled_mm.<locals>.has_zero_dim  s)    >>!$)CY^^A->!-CCr9   c                  *   > ST R                  5        3$ )Nz#self must be row_major, got stride r  r   s   r6   rZ   r3        9$++-Ir9   c                  *   > ST R                  5        3$ )Nz#mat2 must be col_major, got stride r  rI  s   r6   rZ   r3    r@  r9   r   rZ  r   c                  ,   > ST R                  S5       3$ )NzBExpected self.size(1) to be divisible by 16, but got self.size(1)=r   r   r   s   r6   rZ   r3    s    XY]YbYbcdYeXfgr9   c                  "   > ST R                    3$ )Nz?Expected both dimensions of mat2 to be divisible by 16 but got rA  rB  s   r6   rZ   r3    s    UVZV`V`Uabr9   c                      g)NzNFor tensorwise scaling, both scale_a and scale_b must be float (fp32) tensors.r>   r>   r9   r6   rZ   r3    s    hr9   rZ  r  c                     X-   S-
  U-  $ r/  r>   rO  s     r6   ceil_div meta_scaled_mm.<locals>.ceil_div  s    	a''r9   r   c                      g)Nzscale_a must be contiguousr>   r>   r9   r6   rZ   r3        8r9   c                      g)Nzscale_b must be contiguousr>   r>   r9   r6   rZ   r3    rJ  r9   Fc            	      Z   > ST  STR                  5        ST STR                  5        S3	$ )NzTInvalid blockwise scaling configuration. For blockwise scaling, scale_a should have  elements, got z, scale_b should have r  r  )expected_a_sizeexpected_b_sizer%  r&  s   r6   rZ   r3    sC    FFUEVVefmfsfsfuev w//>.?w}}N__`br9   c                      g)NzKFor rowwise scaling, both scale_a and scale_b must be float (fp32) tensors.r>   r>   r9   r6   rZ   r3    s    er9   c                  P   > ST R                  5       < STR                  5       < 3$ )NzLFor non-tensorwise scaling, scale tensors must be 2D, but got scale_a.dim()=z and scale_b.dim()=r   r%  r&  s   r6   rZ   r3    s*    gY`YdYdYfXhh|nunynyn{m}~r9   c                      g)Nz@Both scale_a and scale_b must be contiguous for rowwise scaling.r>   r>   r9   r6   rZ   r3  %  s    ^r9   c                     > ST  ST STR                  S5       STR                  S5       STR                  S5       STR                  S5       S3$ )	Nz}Invalid scaling configuration. For tensorwise scaling, both scales should be scalar. For rowwise scaling, scale_a should be (z, 1), scale_b should be (1, z). Got scale_a.size()=(r   rp   r   z) and scale_b.size()=(rq   r   )rc  r  r%  r&  s   r6   rZ   r3  +  sf    CCD#Eabcad e//6||A.?r',,q/AR S//6||A.?r',,q/ARRS	Ur9   r  )rK   r]   r~   rS   r   r   r   r   float8_e8m0fnur^  r   r[  r_  r   r{   )r   rI  r%  r&  r<  r'  r>  r(  r/  r6  r9  r=  _kis_blockwise_scalingblock_size_kblock_size_mnrG  num_k_blockspadded_num_k_blocks
_out_dtyperN  rO  rc  r  s   ````                @@@@r6   meta_scaled_mmr]    s   
 
LL
a+DHHJ!O` 
LL4::&I+=djj+Iz
 4F"	<	4	D 	'=<+=I	
 	'=<+=I	
 	IIaL2"g	
 	IIaL2"=tyy|b'8A'=b	
 

2IIaL MMU111 6!5!55 
 MMU000 5!4!44 	 ==?aGMMOq$8LL.Q7==EMM3Qh " }} 3 33  "!V!M( $B5L"*<";a"? M ::=PP  M ::=PP 
 ?2MMO6))+8 ))+8
  LL.Q7==EMM3Qe
 LL"9w{{}'9~ Q1$LLOq(LLOq(LLOq( ))+G0E0E0G^ 	 (3J;;tyy|TYYq\DKKXXr9   c           	      P    [        XX#USS9  U R                  U R                  5      $ NT)rr  r  r   r~   r   r*  rh  rf  s         r6   meta_scatter_reduce_twora  8  s%     dVTJ>>$**%%r9   c           	          [        XX#USS9  U $ r_  r  r`  s         r6   meta_scatter_reduce__tworc  ?  s    dVTJKr9   c                |  ^  [         R                  " ST R                  5       s=:  =(       a    S:*  Os  U 4S j5        T R                  5       S:X  a.  [         R                  " U[         R                  T R
                  S9$ [         R                  " T R                  S5      U[         R                  T R
                  S9$ )Nr   r   c                  *   > ST R                  5        3$ )NzAThe probability distributions dimensions must be 1 or 2, but got r   r  s   r6   rZ   "meta_multinomial.<locals>.<lambda>J  s    STYT]T]T_S`ar9   r   r  )rK   r]   r~   r   r   r{   r   )r   num_samplesreplacementr  s   `   r6   meta_multinomialri  E  s     
LL	EIIK1a yy{a{{;ejjNN;;

1{%**U\\ r9   c                 $    SnU  H  nX-  nM	     U$ r/  r>   )vsrl  vs      r6   multiply_integersrm  S  s    	A	 Hr9   c                 ^  ^ ^^^ [         R                  " [        T5      T:H  UU4S j5        TS-   m[         R                  " [        T 5      T:H  UU 4S j5        [         R                  " [        S T SS   5       5      =(       a    [        S T 5       5      U U4S j5        T S S u  p4X4/TQ7$ )Nc                  &   > ST  S[        T5       3$ )Nz%It is expected output_size equals to , but got size r  )num_spatial_dimsr  s   r6   rZ   'upsample_common_check.<locals>.<lambda>]  s    78H7IY\]hYiXjkr9   r   c                  &   > ST  S[        T5       3$ )Nz$It is expected input_size equals to rp  r  )expected_input_dimsro  s   r6   rZ   rr  b  s    67J6K?[^_i[jZklr9   c              3   *   #    U  H	  oS :  v   M     g7fr   Nr>   ri   r  s     r6   rk   (upsample_common_check.<locals>.<genexpr>f  s     *>aE>   c              3   *   #    U  H	  oS :  v   M     g7frv  r>   rw  s     r6   rk   rx  f  s     2N+Qq5+ry  c                     > ST  ST 3$ )NzDInput and output sizes should be greater than 0, but got input size z and output size r>   )ro  r  s   r6   rZ   rr  g  s      \!2;-Ar9   )rK   r]   r   r  )ro  r  rq  r  channelsrt  s   ```  @r6   upsample_common_checkr}  Z  s    	LLK,,k +Q.	LLJ..l
 
LL*:ab>**Ns2N+2N/N	A ""1~F+{++r9   c                 8  ^  [         R                  " T R                  5       S:g  =(       d    [        T R	                  5       SS  5      U 4S j5        [        T R	                  5       USS9nT R                  U5      R                  [        R                  " T 5      S9$ )Nr   r   c                  *   > ST R                  5        3$ )Nz>Non-empty 3D data tensor expected but got a tensor with sizes r   r  s   r6   rZ   $upsample_nearest1d.<locals>.<lambda>u      PQVQ[Q[Q]P^_r9   rq  r   
rK   r]   r   rm  r   r}  r   r'  rC   r   )r   r  scalesfull_output_sizes   `   r6   upsample_nearest1dr  o       
LLA/

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

kA ??+,//11%8 0  r9   c                   ^  [         R                  " T R                  5       S:g  =(       d    [        T R	                  5       SS  5      U 4S j5        [        T R	                  5       USS9nT R                  U5      n[        R                  " T 5      nT R                  u  px  nT R                  R                  S:X  a  US:  a  [         R                  nUR                  US9nU$ )	Nr   r   c                  *   > ST R                  5        3$ Nz>Non-empty 4D data tensor expected but got a tensor with sizes r   r  s   r6   rZ   $upsample_nearest2d.<locals>.<lambda>  r  r9   r   r  r   r   r   )rK   r]   r   rm  r   r}  r   rC   r   r   r{   rr   r   
contiguous)	r   r  scales_hscales_wr  r   r   rF   
n_channelss	   `        r6   upsample_nearest2dr    s     
LLA/

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

kA __-.F //6M  ++A1a||F"zA~//];FMr9   r  ro  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   rZ   -upsample_nearest2d_backward.<locals>.<lambda>      XYdYiYiXjkr9   c            
      D   > ST ST T    ST STR                  T5       3$ )NzCExpected grad_output to have the same shape as output; output.size() = z but got grad_output.size(r   r  r  r   s   r6   rZ   r    s9      !s$'7':&;,QCtK4D4DQ4G3HJr9   r   )
r}  rK   r]   r   r   r   r   r'  rC   r   )r  r  ro  r  r  r  r   s   `    @@r6   upsample_nearest2d_backwardr    s     -! 
LLAk 1XQ#3A#66	
    ,//11+> 0  r9   c                 8  ^  [         R                  " T R                  5       S:g  =(       d    [        T R	                  5       SS  5      U 4S j5        [        T R	                  5       USS9nT R                  U5      R                  [        R                  " T 5      S9$ )Nr   r   c                  *   > ST R                  5        3$ )Nz>Non-empty 5D data tensor expected but got a tensor with sizes r   r  s   r6   rZ   $upsample_nearest3d.<locals>.<lambda>  r  r9   r.   r  r   r  )r   r  scales_dr  r  r  s   `     r6   upsample_nearest3dr    r  r9   c                    [         R                  " U 5      [         R                  " U [         R                  S9pvUb  Ub  [        U[        5      (       d   e[        U[        5      (       d   eUR
                  nUR                  5       n	[        XH5      n[        XX5      nUR                  X5        UR                  X5        [        XdS9  [        XuS9  XE4$ Xg4$ )Nr   )r  r  )
rK   r   r   rg   r   r   r   r!   r   r#   )
r   stabler~   
descendingr   r   rl  r   r   
out_strides
             r6   	meta_sortr    s     D!5#3#3D#Lqg1&*----':.... GG	XXZ
"65#G791I2344Kr9   c           	      >  ^ ^^^^^^^ [         R                  " T R                  S:H  U 4S j5        [         R                  " T R                  TR                  :H  UU 4S j5        T R	                  S5      mTb  [         R                  " TR                  S:H  U4S j5        [         R                  " TR                  5       T:H  UU4S j5        [         R                  " TR                  TR                  :H  UU4S j5        [         R                  " TR                  S:H  U4S j5        T R	                  S	5      T-  T-  m[         R                  " TR                  5       T:H  UUUU U4S
 j5        [         R                  " [        U 4S jTTTT4 5       5      S 5        g )Nr   c                  "   > T R                    S3$ Nz != 2r  )input_gatess   r6   rZ   %rnn_cell_checkSizes.<locals>.<lambda>      ;3C3C2DE0Jr9   c                  :   > TR                    ST R                    3$ N != rA  )hidden_gatesr  s   r6   rZ   r    s    ;$$%T,*<*<)=>r9   r   c                  "   > T R                    S3$ )Nz != 1r  )
input_biass   r6   rZ   r    s    joo5Fe3Lr9   c                  .   > TR                  5        ST  3$ r  r  )
gates_sizer  s   r6   rZ   r    s    z'')*$zl;r9   c                  :   > TR                    ST R                    3$ r  rA  )hidden_biasr  s   r6   rZ   r    s    z''([->->,?@r9   c                  "   > T R                    S3$ r  r  )prev_hiddens   r6   rZ   r    r  r9   r   c            
      `   > TR                  5        STR                  S5       ST ST ST  S3
$ )Nr  r   z * z // z (aka rq   )r   r   )expected_prev_hidden_numelfactorr  r  r  s   r6   rZ   r    s@    ;$$&'tK,<,<Q,?+@J<tTZS[[ab|a}}~r9   c              3   V   >#    U  H  nUR                   TR                   :H  v   M      g 7fr3   r  )ri   rH   r  s     r6   rk   &rnn_cell_checkSizes.<locals>.<genexpr>  s'      
I HH***Is   &)c                      g)Nz%expected all inputs to be same devicer>   r>   r9   r6   rZ   r  
  s    7r9   )rK   r]   r   r   r   r   r  )r  r  r  r  r  r  r  r  s   ``````@@r6   rnn_cell_checkSizesr    sC    
LL!!Q&(JK	LL\///> !!!$JZ__)+LM*,;	
 	 1 11@	
 
LL!!Q&(JK!,!1!1!!4z!AV!K	LL99 
LL 
"J[I
 	
 	8r9   c                     [        XX4SU5        [        R                  " U [        R                  S9n[        R                  " U[        R                  S9n[        R                  " U[        R                  S9nXgU4$ )Nr   r   )r  rK   r   r   )r  r  cxr  r  	workspacehycys           r6   _thnn_fused_lstm_cell_metar    se     :ArR  E<S<STI			"E,C,C	DB			"E,C,C	DBIr9   c                    [        U5      S:g  nU(       a   [        U5      nUS   nU R                  S   nOLU
(       a  U R                  S   OU R                  S   nU
(       a  U R                  S   OU R                  S   nSnU(       a  SOSnUS:w  a  UOUnU(       a  UUU-  /nOU
(       a  UUUU-  /OUUUU-  /nU R                  U5      nU	U-  UU/nUc   [        R                  " SU R
                  S9nOUR                  U5      nUR                  U	U-  UU/5      nU(       a  SOSnU R                  U[        R                  S9nUUUUU4$ )Nr   r   r   r   r  r   )r   r   r   rK   r   r{   r  )r   r:  weight_stride0
weight_bufhxr  rh  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_rnnr    sS   & +&!+O%
 ^
++a.'2U[[^A
'2U[[^A
'QQN%NyH$h&?@	  X%>?j(^*CD 	
 __Y'F~-z;GJ	z[[5<<0\\*%	zN2JI	JB AAMoom5;;o?G2r7J..r9   c                 >   U(       a  U R                   S   OU R                   S   nU(       a  U R                   S   OU R                   S   nU
nU(       a  UUU/OUUU/nU R                  U5      nUc   [        R                  " SU R                  S9nOUR                  UR                   5      nUc   [        R                  " SU R                  S9nOUR                  UR                   5      n[        R                  " SU R                  [        R
                  S9nUUUU4$ )Nr   r   r  r   )r   r   rK   r   r{   r  )r   w0w1w2w3hx_cx_r   r  rh  r  r  
has_biasesr  r  r  r  r  output_chanelsr   r   r  r  r  s                           r6   mkldnn_rnn_layerr  U  s    & $/QEKKNJ#.QEKKNJ N  
Z0*n5 
 __Y'F
{[[5<<0]]399%
{[[5<<0]]399%Aell%++FI2r9$$r9   c                    ^^ U R                   S:X  a,  [        R                  " TS:H  =(       d    TS:H  UU4S j5        g [        R                  " U R                  T5      S:g  UU4S j5        g )Nr   r   c                     > T ST  3$ )Nz4: Expected reduction dim -1 or 0 for scalar but got r>   r~   r  s   r6   rZ   'zero_numel_check_dims.<locals>.<lambda>  s    wiSTWSXYr9   c                     > T ST  S3$ )Nz: Expected reduction dim z to have non-zero size.r>   r  s   r6   rZ   r    s    wi8=TUr9   )r   rK   r   r   )r   r~   r  s    ``r6   zero_numel_check_dimsr  }  sR    yyA~1H!r	Y	

 	IIcNaU	
r9   c                    ^  Ub&  [        X!R                  5       5      n[        XT 5        g [        R                  " UR                  5       S:g  U 4S j5        g )Nr   c                     > T  S3$ )Nz@: Expected reduction dim to be specified for input.numel() == 0.r>   r>  s   r6   rZ   %check_argmax_argmin.<locals>.<lambda>  s    tf\]r9   )r   r~   r  rK   r]   r   )r  r   r~   s   `  r6   check_argmax_argminr    s?    
S((*-d.JJLA]	
r9   c                     [        SX5        [        R                  " U R                  Ub  U4OS 5      n[	        XU5      nU R                  U[        R                  S9$ )Nargmaxr   )r  rC   r  r   r  r   rK   r   )r   r~   r  r  r   s        r6   argmax_argmin_metar    sM    $,

coSF4PD$T9E>>%u{{>33r9   c                 v    U[         R                  :X  a  [         R                  n[         R                  " SXX4S9$ )Nr>   r  )rK   jaggedr  r   )r  rS   rz   r{   r|   s        r6   scalar_tensorr    s1    
 ;;
%v r9   c                    [        X R                  5       SS9nU R                  5       S:X  a  SOU R                  U5      n[        R                  " U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$ )NTrO  r   r   c                      g)Nzk not in range for dimensionr>   r>   r9   r6   rZ   topk_meta.<locals>.<lambda>  s    )Gr9   r   )r   r~   r   rK   r  r]   r   r   r   r   r   )r   rb  r~   largestr  	sliceSizetopKSizes          r6   	topk_metar    s     hhjd
;CXXZ1_$))C.I		LL!GHDJJH
8}q>>(#T^^HEKK^%PPPr9   c                     Uc
  Uc   S5       eUR                  5       nU R                  5       n	[        R                  " UU	R                  U	R                  U	R
                  S9$ )Nz;segment_reduce(): Either lengths or offsets must be defined)rS   r{   rz   )r  rK   r   rS   r{   rz   )
r`  r   rx  rh  rs  rt  ru  rw  data_contiggrad_contigs
             r6   meta__segment_reduce_backwardr    sj    
 '"5 E5 //#K//#K!!!!	 r9   c                   ^ SSK Jn  [        TU R                  5       SS9mU R                  5       S:  a  U R	                  T5      OSn[
        R                  " U" US:  X:*  5      U4S j5        [        U R                  S T U R                  TS-   S  -   5      nU(       a&  U R                  5       S:  a  UR                  TS5        U R                  U5      U R                  U[
        R                  S94$ )Nr   )sym_andTr  r   c                     > ST  3$ )Nz9kthvalue(): selected number k out of range for dimension r>   r   s   r6   rZ   kthvalue_meta.<locals>.<lambda>  s    KC5Qr9   r   )r$  r	  r   r~   r   rK   r]   r   r   r0  r   r   )r   rb  r~   r  r	  dimSizer   s     `    r6   kthvalue_metar	    s     >
dhhjd
;C $
QdiinAG	LLQ%Q
 DS!DJJsQwy$99:E488:>S!>>% $..ekk."JJJr9   c                    U b  U OUn[         R                  " UR                  5       S:H  S 5        UR                  5       nU b)  [         R                  " U R                  5       U:H  S 5        Ub)  [         R                  " UR                  5       U:H  S 5        [         R                  " UR                  5       U:H  S 5        [         R                  " UR                  5       U:H  S 5        [         R                  " UR                  5       S:H  S 5        [         R                  " UR	                  5       US   US	   -  S
-  :H  S 5        g )Nr   c                      gN r>   r>   r9   r6   rZ   (checkLSTMBackwardSizes.<locals>.<lambda>  s    "r9   c                      gr	  r>   r>   r9   r6   rZ   r
	        r9   c                      gr	  r>   r>   r9   r6   rZ   r
	    r	  r9   c                      gr	  r>   r>   r9   r6   rZ   r
	        r9   c                      gr	  r>   r>   r9   r6   rZ   r
	    r	  r9   c                      gr	  r>   r>   r9   r6   rZ   r
	    s    rr9   r   r   r   c                      gr	  r>   r>   r9   r6   rZ   r
	    s    Rr9   )rK   r]   r~   r   r   )grad_hygrad_cyr  r  r  defined_gradexp_sizes          r6   checkLSTMBackwardSizesr	    s    %17wL	LL!!#q(*5  "HW\\^x/<W\\^x/<	LLh&
3	LLh&
3	LLA%z2	LL"hqkHQK&?!&CCZPr9   c                     U c  Uc  g[        XX#U5        [        R                  " U[        S9n[        R                  " U[        S9nU(       a  UR	                  SSS9OS nXgU4$ )NNNNr   r   F)r  )r	  rK   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$I	))r9   c                 2   S nS nS nUS   (       a  UR                  U R                  5       5      nUS   (       d
  US   (       aQ  UR                  UR                  S5      U R                  S5      45      nUR                  UR                  S5      5      nXEU4$ )Nr   r   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//r9   c                   ^ ^ [        T R                  5      S:  a  T R                  S   X-  -  S:X  d   ST R                   SU 35       eS mUU 4S jnT R                  S   X-  -  nT R                  S   U-  nT R                  S	   U-  n/ T R                  S S QUPUPUP7nT R                  U5      nUR                  U" 5       S
9nU$ )Nr   rR  r   z'Invalid input shape for pixel_shuffle: z with upscale_factor = c                 b    [         R                  R                  U 5      [         R                  :H  $ r3   r  r  s    r6   r  ,meta_pixel_shuffle.<locals>.is_channels_last  s$    ""88=ATATTTr9   c                  F  > T " T5      (       a/  [        T5      S:X  a  [        R                  $ [        R                  $ TR	                  [        R                  S9(       a  [        R                  $ TR	                  [        R
                  S9(       a  [        R
                  $ g r  )r   rK   r   r  r_  r  )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r9   r  r   r   )r   r   r   r'  )	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-$**Sb/-1-b-"-I
..
#C
&&13&
4CJr9   c                 X   U R                  U R                  5      nUR                  UR                  5      nUR                  UR                  5      nUR                  UR                  5      nUR                  UR                  5      nUR                  UR                  5      nUUUUUUU4$ r3   r  )r   weight0weight1weight2weight3r  cx_tmpr   hy_cy_grad_output_r_optgrad_hy_r_optgrad_cy_r_optr   rh  r  r  r  r  r  r  r  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Er9   )	out_int32r   c                    [         R                  " U U(       a  [         R                  O[         R                  [         R                  S9$ )NrS   r   )rK   r   rB  r   r   )r   
boundariesr=	  r   s       r6   meta_bucketizerA	  M  s2     &ekkEKK-- r9   c                   ^ ^^^^ Sm[        T 5      S:X  a)  [        R                  " T R                  5       U 4S j5        [        T 5      S:X  a+  T R                  5       (       a  [        R
                  " S5        [        R                  " [        T[        5      UU4S j5        [        R                  " TS:  UU4S j5        [        R                  " [        T[        5      UU4S	 j5        [        R                  " [        T[        5      UU4S
 j5        [        R                  " TT:  S 5        [        R                  " TT R                  T R                  S9$ )Nzhistc()r	  c                  $   > ST R                    S3$ )Nz%"histogram_cpu" not implemented for 'r  r   r  s   r6   rZ   meta_histc.<locals>.<lambda>^  s    =ekk]!Lr9   r   z%_histc_cuda with floating point inputc                  $   > T S[        T 5       3$ )Nz#: argument 'bins' must be int, not r+  binsr  s   r6   rZ   rD	  d  s    7)>tDzlKr9   r   c                     > T ST  3$ )Nz: bins must be > 0, but got r>   rF	  s   r6   rZ   rD	  f  s    gY.J4&#Qr9   c                  $   > T  S[        T5       3$ )Nz%: argument 'min' must be Number, not r+  )r  r   s   r6   rZ   rD	  i      7)@cLr9   c                  $   > T  S[        T5       3$ )Nz%: argument 'max' must be Number, not r+  )r  r  s   r6   rZ   rD	  m  rJ	  r9   c                      g)Nz&{fn_name}: max must be larger than minr>   r>   r9   r6   rZ   rD	  o  s    %Mr9   r   )r   rK   r]   r   rC   r"  rg   r   r   r   r{   rS   )r   rG	  r   r  r  s   ````@r6   
meta_histcrM	  W  s     G5U"##%L	
 5V#(?(?(A(A%%&MN	LL4!K 
LLQR	LL3L 
LL3L 
LLMN;;tELLDDr9   c                 F  ^  [        T R                  5       USS9n[        R                  " T R	                  5       S:g  =(       d#    [        S T R                  5       SS   5       5      U 4S j5        T R                  U5      R                  [        R                  " T 5      S9$ )Nr   r  r   c              3   *   #    U  H	  oS :  v   M     g7frv  r>   )ri   r   s     r6   rk   ,meta_upsample_bimode2d_aa.<locals>.<genexpr>  s     !H7Gt(7Gry  r   c                  *   > ST R                  5        3$ r  r   r  s   r6   rZ   +meta_upsample_bimode2d_aa.<locals>.<lambda>  r  r9   r   )
r}  r   rK   r]   r   r  r   r'  rC   r   )r   r  r%  r  r  r  s   `     r6   meta_upsample_bimode2d_aarS	  s  s     -

kA 
LLHc!Huzz|AB7G!HH_ ??+,//11%8 0  r9   c                 T  ^ ^^ [        X!SS9m[        R                  " T R                  S:H  U 4S j5        [	        S5       H3  m[        R                  " T R
                  T   TT   :H  UU U4S j5        M5     T R                  U5      R                  [        R                  " T 5      S9$ )Nr   r  r   c                  "   > ST R                    3$ r  r  r  s   r6   rZ   4meta_upsample_bimode2d_aa_backward.<locals>.<lambda>  r  r9   c            
      D   > ST ST T    ST STR                  T5       3$ )NzD
Expected grad_output to have the same shape as output; output.size(r  z
but got grad_output_size(r   r  s   r6   rZ   rV	    s>     DDE3dK[\]K^J_ `D!1!1!!4 59r9   r   )
r}  rK   r]   r   r   r   r   r'  rC   r   )r  r  ro  r%  r  r  r  r   s   `     @@r6   "meta_upsample_bimode2d_aa_backwardrX	    s     -! 
LLAk 1Xa $4Q$779	
    ,//11+> 0  r9   c                 X   [         R                  " UR                  5       S:H  S 5        [         R                  " UR                  5       S:H  S 5        [         R                  " UR                  R                  S 5        [         R                  " UR                  R                  S 5        g )Nr   c                      g)Nz%found_inf must be a 1-element tensor.r>   r>   r9   r6   rZ   <_amp_foreach_non_finite_check_and_unscale_.<locals>.<lambda>      (Or9   c                      g)Nz%inv_scale must be a 1-element tensor.r>   r>   r9   r6   rZ   r[	    r\	  r9   c                      g)Nz!found_inf must be a float tensor.r>   r>   r9   r6   rZ   r[	        3r9   c                      g)Nz!inv_scale must be a float tensor.r>   r>   r9   r6   rZ   r[	    r_	  r9   )rK   r]   r   rS   r   )r   r'  	inv_scales      r6   *_amp_foreach_non_finite_check_and_unscale_rb	    s|    	LLQ O 
LLQ O 
LL))3 
LL))3r9   c                 .    [         R                  " U 5      $ r3   r  )r   nanposinfneginfs       r6   
nan_to_numrg	    r  r9   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)rz   rK   r  
sparse_cscr  
sparse_bscr   r   r   r   r   r   )r   dim0r}  ndimsr   r   s         r6   r  r    s    ;;	   IU\]  IIE$&D$&D|		D$++- F!'v|FL&,!ZDJ
T"Kr9   c                 "   U R                   nU R                  (       a;  U R                  5       nU R                  5       nUS::  a  US:X  d   SU SU S35       eOU R	                  5       S::  d   SU S35       e[        U SUS:  a  S5      $ S5      $ )	Nr   r   zEt_ expects a tensor with <= 2 sparse and 0 dense dimensions, but got z sparse and z dense dimensionsz6t_ expects a tensor with <= 2 dimensions, but self is r,  r   )r   r8  r:  r;  r~   r  )r   rl	  r:  r;  s       r6   t_rn	    s    IIE~~__&
NN$	Q9> 	
!l,yk9JL	
1>
 xxzQ 	
DUG1M	
 dAEAIq55155r9   )r=	  r   sidesorterc                  ^ ^^ [         R                  " [        T R                  5      S:*  =(       d    T R                  S S TR                  S S :H  UU 4S j5        [         R                  " TS L =(       d    T R                  TR                  :H  U U4S j5        [         R                  " US:g  =(       d    U(       + S5        U(       a  [         R                  O[         R
                  n[        T[         R                  5      (       a$  [         R                  " TU[         R                  S9$ [         R                  " SUT R                  S	9$ )
Nr   r   c                  `   > S[        TR                  5       S[        T R                  5       3$ )Nztorch.searchsorted(): boundaries tensor should be 1 dimension or the first N-1 dimensions of boundaries tensor and input value tensor must match, but we got boundaries tensor z and input value tensor r   r   )r   sorted_sequences   r6   rZ   #meta_searchsorted.<locals>.<lambda>  s3    3378M8M3N2O P""&tzz"2!35r9   c                  n   > S[        T R                  5       STb  [        TR                  5       3$ /  3$ )Nz[torch.searchsorted(): boundary and sorter must have the same size, but got boundary tensor z and got sorter tensor rs	  )rt	  rp	  s   r6   rZ   ru	  
  sB    ##'(=(=#>"??V%+%7tFLL!@B=?@Br9   r   zetorch.searchsorted(): side and right can't be set to opposites, got side of left while right was Truer?	  r>   r  )rK   r]   r   r   rB  r   rg   r   r   r   r   r{   )rt	  r   r=	  r   ro	  rp	  rS   s   ``   ` r6   meta_searchsortedrw	    s     
LLO!!"a' 	9  "%CR8	
	 
LL$?///6<<?	
 
LL#e)	$ %EKK%++E$%%U-D-D
 	
 {{2U?3I3IJJr9   c                    ^  [         R                  " T [         R                  [         R                  [         R                  4;  U 4S j5        g )Nc                     > ST  3$ )Nz/Unsupported input type encountered for isin(): r>   r   s   r6   rZ   3_check_for_unsupported_isin_dtype.<locals>.<lambda>$  s    A%Ir9   )rK   r]   r	  
complex128	complex64r   s   `r6   !_check_for_unsupported_isin_dtyper}	  !  s/    	LLejj%"2"2EOODDIr9   c                 H    U R                  X R                  S5      45      nU$ )Nr   r  )r  r   num_weightsr  r  r 	  s         r6   meta_embedding_dense_backwardr	  (  s(     ''6F6Fr6J(KLKr9   c                 t    U	(       a  [         R                  U UUUUUUUU
U5
      $ [        U UUUUUUUU
U5
      $ r3   )r+   _embedding_bag_sparse_backward!meta_embedding_bag_dense_backward)r`  r   rt  r  r  maximum_indicesr	  r  rh  r  r  r  s               r6   meta_embedding_bag_backwardr	  4  se     22
 	
 1
 	
r9   c
                 X  ^  [         R                  " T R                  [         R                  [         R                  [         R
                  [         R                  4;   U 4S j5        U[        :X  a  [         R                  " US L5        T R                  UT R                  S5      45      n
U
$ )Nc                  "   > ST R                    3$ )Nz$Unsupported input type encountered: r   )r`  s   r6   rZ   3meta_embedding_bag_dense_backward.<locals>.<lambda>n  s    6tzzlCr9   r   )
rK   r]   rS   r\  r]  r[  float64r  r   r   )r`  r   r  r  r	  r	  r  rh  r  r  index_grad_weights   `          r6   r	  r	  _  sv     
LL

u}}ennemmU]]SSC x_D01TYYq\'BCr9   c                    U R                  S5      n[        R                  " U[        :H  S5        [        R                  " U R	                  5       S:H  5        [        R                  " UR	                  5       S:H  5        UR                  S5      n[        R                  " UR	                  5       S:H  5        [        R                  " UR                  S5      U:H  5        U R                  U45      n	U	$ )Nr   zHembedding_bag_backward: per_sample_weights only supported for mode='sum'r   r   )r   rK   r]   r  r~   r   )
r`  r:  r   rt  r  rh  r  embedding_featuresrg  r   s
             r6   .meta_embedding_bag_per_sample_weights_backwardr	  v  s     1	LLR 
LLq!	LL!#$,,q/K	LL"#	LLQ#556^^[N+FMr9   )assume_uniqueinvertc                   [         R                  " [        U [        5      =(       d    [        U[        5      S 5        [        U [        5      (       d  [         R                  " XR
                  S9n [        U[        5      (       d  [         R                  " XR
                  S9n[        U R                  5        [        UR                  5        [         R                  " U [         R                  S9$ )Nc                      g)Nz<At least one of elements and test_elements must be a Tensor.r>   r>   r9   r6   rZ   meta_isin.<locals>.<lambda>  r  r9   r  r   )
rK   r]   rg   r   r1  r{   r}	  rS   r   r	  )elementstest_elementsr	  r	  s       r6   	meta_isinr	    s     
LL8V$I
=&(IN h''<<1E1EFmV,,]??K%hnn5%m&9&9:HEJJ77r9   r  c                     [         R                  " U S:  S 5        [        U[        R                  S9u  p#[         R
                  " XS9$ )Nr   c                      g)Nz,polygamma(n, x) does not support negative n.r>   r>   r9   r6   rZ    meta_polygamma.<locals>.<lambda>  s    !Or9   r  r   )rK   r]   r   r   r  r   )r  r   rF   rG   s       r6   meta_polygammar	    sB     
LLaOP(;HHOA D55r9   c                     [        S5      e)Nz.Tensor.item() cannot be called on meta tensors)r&  r   s    r6   meta_local_scalar_denser	    s    
G
HHr9   c                 .    [         R                  " U 5      $ r3   r  r   s    r6   silur	    r  r9   c                 ^    [        U [        R                  S9u  p[        R                  " XS9$ r  )r   r   r  rK   r   )r   rF   rG   s      r6   sigmoidr	    s/     );HHOA D55r9   c                 |   U R                  5       S:H  nUR                  5       S:H  nU(       a  U(       a4  UR                  S5      U R                  S5      UR                  S5      /nGO*[        R                  " UR                  S5      UR                  S5      :H  S 5        U R                  S5      UR                  S5      /nOU(       a\  [        R                  " UR                  S5      U R                  S5      :H  S 5        U R                  S5      UR                  S5      /nOk[        R                  " U R                  S5      UR                  S5      :H  S 5        U R                  S5      U R                  S5      UR                  S5      /nU=(       d    U R                  n[        R
                  R                  (       aV  SUR                  -  nUS   U-   S-
  U-  U-  nXE:X  a  US   U-  US/n	OUS/n	[        R                  " XiX0R                  S	9n
U
$ [        R                  " XcU R                  S	9n
U
$ )
Nr   r   r   c                      gNz matrix batch sizes have to matchr>   r>   r9   r6   rZ   2_create_grouped_mm_output_tensor.<locals>.<lambda>      6Xr9   r   c                      gr	  r>   r>   r9   r6   rZ   r	    r	  r9   c                      g)Nzbatched dimension has to matchr>   r>   r9   r6   rZ   r	    s    6Vr9   rZ  r  )r~   r   rK   r]   rS   r  r   itemsizer/  r{   r   )rG  rI  offsr>  
mat1_is_2d
mat2_is_2dr  	alignmentsize_paddedr  r   s              r6    _create_grouped_mm_output_tensorr	    s   qJqJ		!diilDIIaLAHLL		!		!,.X 		!diim4HLL		!		!,.X 		!diil3H LL		!		!,.V 		!diilDIIbMBH'TZZI}}),,,	|i/!3	AIM#"1+3[!DJ%q)J!!	++

 J kk(DKKHJr9   mat_amat_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(       d8  [         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bH  TGbD  [         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 mSU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 noner>   r>   r9   r6   rZ   )_meta_grouped_mm_common.<locals>.<lambda>  s    >r9   c                  >   > ST R                    STR                    S3$ )Nz5Expected inputs of E4M3 FP8 type but got mat_a.dtype= and mat_b.dtype=r  r   r	  r	  s   r6   rZ   r	    s#    KEKK=Xijojujuivvwxr9   c                  >   > ST R                    STR                    S3$ )Nz1Expected inputs of BF16 type but got mat_a.dtype=r	  r  r   r	  s   r6   rZ   r	    s#    G}Tefkfqfqerrstr9   )r   r.   c                  L   > ST R                  5        STR                  5        3$ )Nz3Multiplicands must be 2D or 3D but got mat_a.dim()=z and mat_b.dim()=r   r	  s   r6   rZ   r	    s%    Eeiik]Rcdidmdmdocpqr9   r   r   r  z3contraction dimension of mat_a and mat_b must matchc                 P    U R                  5       nUS   S:  =(       a    US   S:H  $ Nr  r   r   r  mat
mat_strides     r6   r6  -_meta_grouped_mm_common.<locals>.is_row_major  s*    Jb>A%=*R.A*==r9   c                 P    U R                  5       nUS   S:H  =(       a    US   S:  $ r	  r  r	  s     r6   r9  -_meta_grouped_mm_common.<locals>.is_col_major  s*    Jb>Q&=:b>A+==r9   c                  0   > ST R                  5       SS   3$ )NzNExpected mat_a tensor to be row major in the last two dimensions, got strides r  r  )r	  s   r6   rZ   r	  %  s!    dejeqeqestvtwexdyzr9   c                  0   > ST R                  5       SS   3$ )NzQExpected mat_b tensor to be column major in the last two dimensions, got strides r  r  )r	  s   r6   rZ   r	  )  s!    ghmhththvwywzh{g|}r9   c                   ^ ^^^ TR                  5       S-
  mSTR                  5       -  nTR                  5       mTTS-
     S:X  aJ  TT   [        STR                  TS-
     5      :  a'  [
        R                  " TT   U-  S:H  UU U4S j5        g TT   S:X  aM  TTS-
     [        STR                  T   5      :  a*  [
        R                  " TTS-
     U-  S:H  UU U4S j5        g [
        R                  " SUU4S j5        g )Nr   rZ  r   c                  "   > ST ST  STT     S3$ )Nr   stride along % dim to be multiple of 16 bytes, got r  r>   end_dimmat_namer	  s   r6   rZ   F_meta_grouped_mm_common.<locals>.check_valid_strides.<locals>.<lambda>5  s'    )H:^G9Dijtu|j}i~~  Ar9   c                  .   > ST ST S-
   STT S-
      S3$ )Nr  r	  r   r	  r  r>   r	  s   r6   rZ   r	  <  sI    )H:^GaK=Hmnx  zA  DE  zE  oF  nG  GH  Ir9   Fc                  *   > ST ST R                    S3$ )NzInvalid strides/sizes, got z for strides and z for sizes.rA  r	  s   r6   rZ   r	  A  s    5j\ARSVS\S\R]]hir9   )r~   element_sizer   r  r   rK   r]   )r	  r	  r	  r	  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r9   r	  r	  c                  >   > ST R                    STR                    S3$ )NzhFor FP8 scales must both be float32, or for MXFP8 both scales must be float8_e8m0fnu. Got scale_a.dtype=z and scale_b.dtype=r  r   rR  s   r6   rZ   r	  N  sR    ~  @G  @M  @M  N  Na  bi  bo  bo  ap  pq  rr9   c                     X-   S-
  U-  U-  $ )z$Rounds up x to nearest multiple of yr   r>   rH   r  s     r6   round_up)_meta_grouped_mm_common.<locals>.round_upU  s    UQY1$))r9   r   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                  :H  UUU 4S j5        TR                  u  mpVSnT" XW-  S5      m	T" US5      m
[        R                  " TR                  S   T	:H  =(       a    TR                  S   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$ )Nr  z to be contiguous.r>   
scale_names   r6   rZ   >_meta_grouped_mm_common.<locals>.check_scale.<locals>.<lambda>]  s    i
|3EFr9   c                  B   > ST ST R                    STR                    3$ )NzKFor MXFP8, scale must have same number of dimensions as target tensor, but  has mat.ndim= and scale.ndim=r  r	  r  r	  s   r6   rZ   r	  f  sX    "mnxmy  zH  IL  IQ  IQ  HR  Rb  ch  cm  cm  bn  !or9   r   c                  2   > ST ST R                  5        S3$ )Nr  z to be 1D tensor, but got 	D tensor.r   r  r	  s   r6   rZ   r	  k  !    )J<7QRWR[R[R]Q^^g hr9   r   c                  V   > ST ST R                   T   T-   STR                   S    S3$ )Nr  z	 to have rM  r   z
 elements.rA  )r	  r  scale_multiplierr	  
scaled_dims   r6   rZ   r	  o  sU    )J<y:AVYiAi@jjyz  {F  {F  GH  {I  zJ  JT  !Ur9   r   c                     > ST  S3$ )Nr  z( to be contiguous in the last dimension.r>   r	  s   r6   rZ   r	  t  s    i
|3[\r9   c                  P   > ST ST R                   S    STR                   S    S3$ )Nr  z batch dimension to be r   , got r  rA  r	  s   r6   rZ   r	  x  s4    i
|3J399UV<.X^_d_j_jkl_m^nnopr9   c                  B   > ST ST R                    STR                    3$ )NzMFor MXFP8, scale should have same number of dimensions as target tensor, but r	  r	  r  r	  s   r6   rZ   r	    sX    "opzo{  |J  KN  KS  KS  JT  Td  ej  eo  eo  dp  !qr9   rZ  r   r  r  c            
      N   > STR                    ST  ST ST STR                    3
$ )NzFor MXFP8, expected mat.shape=z to have scale shape of (,z), but got rA  )G	blocked_K	blocked_Nr	  r  s   r6   rZ   r	    sR    "@Kdefdgghirhsstu~t  @K  LQ  LW  LW  KX  !Yr9   c                  2   > ST ST R                  5        S3$ )Nr  z to be 2D tensor, but got r	  r   r	  s   r6   rZ   r	    r	  r9   c                  V   > ST ST R                   ST-       STR                   S    S3$ )Nr  z non-batch dimension to be r   r	  r  rA  )r	  r  r	  r	  s   r6   rZ   r	    sR    )J<7RSVS\S\]^ak]kSlRmmstytt  AB  uC  tD  DE  !Fr9   )r~   rK   r]   r_  r   r   r   )r	  r  r	  r	  r	  r  r  r  r	  r	  r	  is_mxfp8r	  s   `````   @@@r6   check_scale,_meta_grouped_mm_common.<locals>.check_scaleY  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EJJ. q $kkGAq!#J ( ;I (C 0ILL		"2Qsyy}	7Q Y  Y
 LL		q(h LLA#))A
N*CC Fr9   r   r%  r&  c                      g)Nz:Scale result tensor provided, but it is not supported yet.r>   r>   r9   r6   rZ   r	    rd   r9   c                  N   > ST R                  5        STR                  5        S3$ )Nz/Offsets tensor not provided, but is needed for zD/zD multiplicand layouts.r   r	  s   r6   rZ   r	    s(    Eeiik]RTUZU^U^U`Taaxyr9   c                  ,   > ST R                  5        S3$ )Nz.Offsets tensor must be 1D, but got offs.dim()=r  r   r	  s   r6   rZ   r	    s    HTUVr9   c                  $   > ST R                    S3$ )Nz7Offsets tensor must be integer (int32) tensor, but got r  r   r	  s   r6   rZ   r	    s    QRVR\R\Q]]^_r9   c                      g)NzJOffsets tensor provided, but is not needed for 3D/3D multiplicand layouts.r>   r>   r9   r6   rZ   r	    s    `r9   c                      g)Nz2Bias tensor provided, but it is not supported yet.r>   r>   r9   r6   rZ   r	    s    Dr9   c                      g)Nz4If output dtype provided, it must be torch.bfloat16.r>   r>   r9   r6   rZ   r	    s    Fr9   r   )rK   r]   r  r  r,  r^  rS   r]  r~   r   r[  rU  r   rB  r	  )r	  r	  r%  r&  r	  r<  r'  r>  r(  scaled	fp8_dtypemat_a_is_2dmat_b_is_2dr6  r9  r	  r	  r	  r	  r	  s   `````             @@r6   _meta_grouped_mm_commonr	    sg    
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,A	

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

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

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

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

 
LLD
 
LLT8Y%..8F
 ,E5$	JJr9   c                 "    [        U US S UUS US9$ )N)r%  r&  r	  r<  r'  r>  r	  )r	  r	  r	  r<  r>  s        r6   meta_grouped_mmr
    s)     #	 	r9   c	                 $    [        U UUUUUUUUS9	$ )N)r%  r&  r	  r<  r'  r>  r(  r 
  )	r	  r	  r%  r&  r	  r<  r'  r>  r(  s	            r6   meta_scaled_grouped_mmr
    s,     #!%
 
r9   rH   half_to_floatc                    U(       a   U R                   [        R                  :X  d   e[        R                  " U [        R
                  R                  S9u  p4U(       d  UOUn[        R                  " X[        R                  S9nU$ )Nr  r?	  )	rS   rK   rM   rC   r   r   rD   r   r   )rH   r~   r
  computation_dtyperG   r  s         r6   softmaxr
    sk     ww%**$$$&+&>&>	uDDLL'# (5<:KL


1@W@W
XCJr9   c           	        ^^^^	^
^ [         R                  " [        T5      S-  S:H  U4S j5        U R                  m[        T5      m
[        T5      S-  nT
U-
  m	[         R                  " T
U:  U
U4S j5        [	        S T 5       5      (       a  U n[        T	T
5       Hx  mST
T-
  S-
  -  mTT   S:  a*  UR                  TTT   * UR                  T   TT   -   5      nTTS-      S:  d  MO  UR                  TSUR                  T   TTS-      -   5      nMz     UR                  5       $ [        TS T	 5      n[        U5       Ha  m[        T5      TS-   S-  -
  mTT	T-      TT   -   TTS-      -   n[         R                  " US:  UUU	UU4S j5        UR                  U5        Mc     [         R                  " UU R                  U R                  U R                  [        U 5      S9$ )	Nr   r   c                      > S[        T 5       3$ )Nz1Length of pad must be even but instead it equals r  r  s   r6   rZ   '_constant_pad_nd_meta.<locals>.<lambda>  s    CCH:Nr9   c                  (   > S[        T5       ST  S3$ )Nz`Length of pad should be no more than twice the number of dimensions of the input. Pad length is z while the input has z dimensions.r  )l_inpr  s   r6   rZ   r

    s      225c(;P'r9   c              3   n   #    U  H+  n[        U[        R                  5      =(       a    US :*  v   M-     g7frv  )rg   rC   IntWithoutSymInt)ri   r[  s     r6   rk   (_constant_pad_nd_meta.<locals>.<genexpr>  s)     
IS:a//0;Q!V;Ss   35r   c            	      F   > STTT -       STT    STTS-       STT -    S3	$ )NzThe input size z, plus negative padding r   r   zG resulted in a negative output size, which is invalid. Check dimension z of your input.r>   )r   r   l_diffr  pad_idxs   r6   rZ   r

  &  sE    ok&1*&=%>>V7|nE#gk"2!3 4117!OMr9   )rS   r{   r}   r   )rK   r]   r   r   r  r   narrowr   r   r   r   rS   r{   r}   r   )r   r  rq  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 r9   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$ )Nr   z'weight' must be 2-Dr   r   r   )r~   r   r   rS   r   )	r:  r   r  r  r  weight_shapeindices_shaper   r>  s	            r6   	embeddingr
  5  s     ::<1444<<LMMM||q&21o%7			"1%|A7	5m5\!_5	II77r9   max_lengthspadding_valuec                     [        U5      S:X  d   e[        U5      S:X  d   eUS   R                  S   S-
  nUS   nXE/U R                  SS  Q7nU R                  U5      $ r  )r   r   r   )r   rt  r
  r
  r  r  rd  s          r6   $meta__jagged_to_padded_dense_forwardr 
  M  st     w<1{q   
aAAA,6<<+,LL))r9   c                 B    [        U 5      [        5       S 5       5       nU$ )Nc                 2    [        U [        R                  S9$ r  rI   r   r  rk  s    r6   _f)_create_unary_float_meta_func.<locals>._f_  s      =JJ
 	
r9   r?   r$   funcr$
  s     r6   _create_unary_float_meta_funcr)
  ^  *    4]
  

 Ir9   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>._fj  s      !@!M!M
 	
r9   r&
  r'
  s     r6   _create_binary_float_meta_funcr.
  i  r*
  r9   c                    ^  [        T 5      U 4S j5       nT R                   S3nX!l        [        [        [        U5      5      " U5      nU$ )Nc                 `   > T" U /UQ70 UD6n[        U R                  UR                  5        U $ r3   rp  )r   rE   r$  r   r5   s       r6   _fn#_register_inplace_meta.<locals>._fn  s.    '''

CII6r9   rF   )r   rs   r?   getattrr+   )r5   r1
  inplace_names   `  r6   _register_inplace_metar5
    sK    
2Y 
 kk]!$LL
l3
4S
9CJr9   c                 z  ^ ^^ [         R                  " T R                  TR                  :H  UU 4S j5        T T/n[        T[        5      (       aT  TR
                  S:w  a3  [         R                  " T R                  TR                  :H  U U4S j5        UR                  T5        [        US[        R                  06$ )Nc                  <   > STR                    ST R                    3$ )Nr  z for `end`, but got dtype r   )rt   ru   s   r6   rZ   lerp.<locals>.<lambda>  s    /%++.HTr9   r   c                  <   > ST R                    STR                    3$ )Nr  z for `weight`, but got dtype r   )ru   r:  s   r6   rZ   r8
    s    /%++6STZT`T`Sabr9   r@   )
rK   r]   rS   rg   r   r   r   rI   r   rD   )ru   rt   r:  rE   s   ``` r6   lerpr:
    s     
LLsyy T 3<D&*%%;;!LLv||+b 	F	=EE r9   )rq  c                4    [        XU[        R                  S9$ r  rB  r   tensor1tensor2rq  s       r6   addcmulr?
    s     0O0W0W r9   c                    [         R                  " [        R                  " UR                  5      =(       a     [        R                  " UR                  5      (       + S 5        [        XU[        R                  S9$ )Nc                      g)N)zFInteger division with addcdiv is no longer supported, and in a future zErelease addcdiv will perform a true division of tensor1 and tensor2. z4The historic addcdiv behavior can be implemented as zA(input + value * torch.trunc(tensor1 / tensor2)).to(input.dtype) zfor integer inputs and as z6(input + value * tensor1 / tensor2) for float inputs. z?The future addcdiv behavior is just the latter implementation: z4(input + value * tensor1 / tensor2), for all dtypes.r>   r>   r9   r6   rZ   addcdiv.<locals>.<lambda>  s     	
r9   r  )rK   r]   rC   rF  rS   rI   r   rD   r<
  s       r6   addcdivrC
    s`     
LL""7==1 6&&w}}5	
		
  0O0W0W r9   c                      0 n S H"  n[         U   nU H  nX0;  d  M
  X#   X'   M     M$     U R                  5        GH  u  pE[        U[        R                  R
                  5      (       a  M1  [        U[        5      (       d   eUR                  [        R                  R                  R                  5      " U5        [        R                  R                  UR                  5       S5      (       a  U[         S   ;   a  [        U S35      eM  UR                  (       a  M  UR                  5       S;   a  M  SUR                  5       ;   a  [        R!                  XE5        GM&  SUR                  5       ;   a  ["        R!                  XE5        GMR  SUR                  5       ;   a  [$        R!                  XE5        GM~  S	UR                  5       ;   a  [&        R!                  XE5        GM  [(        R!                  XE5        GM     g )
N)rx   post_autogradpre_autogradCompositeImplicitAutogradrx   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   itemsrg   rK   _opsHigherOrderOperatorr   py_impl_CDispatchKeyr-   %_dispatch_has_kernel_for_dispatch_keyr  r&  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_tablerr   registryopoop_overloadr5   s         r6   activate_metara
    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 $; ;  A    	 [--//BGGXK,,..?DD[U{//11BGGX+"2"2"44EJJ 8<<[Mm 7r9   )Fr	  r3   )NNNFr   r   r   r  )Tr  )r  )r  T)FF)TT)rj  )FTN)TFF)TF)r   )g      ?N)r/   str)r>   r  r   F)r>   r  FTN)Fr   FNFr   )NF)r   F)g      ?gUUUUUU?FN)NNNNN)r   NNr   )NNF)        FFN)Nrc
  FFN)rc
  FNN)Nrc
  FNN)rc
  FN)FN)FNNNN)NNNF)Nr   FNN)NNNN)r   TT)NNr   N)d   r   r   )r   )NNNNF)r   FF)rc
  (  r  collections.abcr   enumr   	functoolsr   typingr   r   r   r	   typing_extensionsr
   rK   torch._prims_commonr  rC   r   r   r   torch._decompr   r   r   r   
torch._opsr   torch._primsr   r   r   r   r   r   r   r   r   r   r   r   r   torch._prims_common.wrappersr    r!   r"   r#   r$   r  r%   r&   torch.fx.experimentalr'   r{  torch.utilsr(   r:   r)   r*   opsr+   libraryLibraryr\
  r   r  r  r  r?   rI   rU   r_   linspacelogspacer  r   taker)  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  r-  r5  
unsqueeze_r9  _sparse_semi_structured_linearrb
  rS   rF  _sparse_semi_structured_mmrL  _sparse_semi_structured_addmmrP  _cslt_sparse_mmre  index_reducerl  index_reduce_rn  index_selectrr  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  r1  linalg_inv_exr4  linalg_ldl_factor_exr\   r:  linalg_ldl_solverJ  	linalg_lurQ  linalg_lu_factor_exrV  linalg_lu_solver`  	lu_unpackrg  rq  	linalg_qrrx  r|  ry  _linalg_svdr  rG  r  r  r  linalg_solve_triangularr  r  r  _linalg_detr  r  r  r  reflection_pad1dr  replication_pad1dr
  r  reflection_pad1d_backwardr  replication_pad1d_backwardr  r/  reflection_pad2dr1  replication_pad2dr5  reflection_pad2d_backwardr  replication_pad2d_backwardr=  rL  reflection_pad3drN  replication_pad3drR  reflection_pad3d_backwardreplication_pad3d_backwardrZ  _pdist_forwardrO   r_  _pdist_backwardrf  baddbmmr  	bernoullir  
bernoulli_r  r[  r  poissonr  _fused_moving_avg_obs_fq_helperr  mmr  r  r   r  r  miopen_batch_normr  convolutionr  rS
  _has_mkldnnrW
  r  _convolution_pointwiser  _linear_pointwiser  has_mklrY
  r  _mkl_linearr  rZ
  r  qconv2d_pointwiseqconv_pointwiser  binaryr  qlinear_pointwiser1  r  binary_tensorr  linear_dynamic_fp16linear_relu_dynamic_fp16r  r[
  r  
max_pool2dr*  int4mm_packed_weight_cpur2  r8  
avg_pool2drb  rg  avg_pool2d_backwardrp  
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  rh   r  r  r  r   _unsafe_indexr  convolution_backwardr  addbmmr"  randint_liker%  _fused_adam__fused_adamw_r=  _fused_adamrE  _int_mmrP  _convert_weight_to_int4packr]  #_convert_weight_to_int4pack_for_cpurc  _weight_int4pack_mmro  _weight_int4pack_mm_for_cpurv  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_valuesrh  r   r#  logical_not_r%  repeatr.  zero_r0  mul_Scalardiv_logical_and_logical_or_logical_xor_r3  add_sub_r@  rn  subrD  rounddecimalsrF  rM  
__rshift__rQ  
__lshift__rU  zerorW  r=  rZ  fillr\  relu_r_  	_add_relura  rrelu_with_noiserf  rrelu_with_noise_functionalrh  rrelu_with_noise_rj  	index_put_unsafe_index_putrn  masked_fill_rr  _masked_scaleru  masked_scatter_rz  masked_scatterr|  masked_scatter_backwardr~  
index_put_r  r  bmmr  r  r  r  rV  rW  r  r  r  r$   max_pool2d_with_indices_backwardr  max_pool2d_with_indicesr  fractional_max_pool2dr  max_pool3d_with_indicesr   max_pool3d_with_indices_backwardr  r  r  r   grid_sampler_2d_backwardr(  r.  r0  r3  r  onesrB  zerosrE  select_scatterrI  slice_scatterrM  r   rR  r[  gatherrb  rs  r{  r}  r  r  scatter_addr  scatter_add_r  r  r*  rq  rh  value_reducer  scatter_r  #_scaled_dot_product_flash_attentionr  r  #_scaled_dot_product_cudnn_attentionr  0_scaled_dot_product_fused_attention_overrideabler  ,_scaled_dot_product_flash_attention_backwardr  +_scaled_dot_product_flash_attention_for_cpur  4_scaled_dot_product_flash_attention_for_cpu_backwardr  *_scaled_dot_product_attention_math_for_mpsr  '_scaled_dot_product_efficient_attentionr  0_scaled_dot_product_efficient_attention_backwardr   ,_scaled_dot_product_cudnn_attention_backwardr  _flash_attention_forwardr
  _flash_attention_backwardr  _efficient_attention_forwardr  _efficient_attention_backwardSymIntr$  
_scaled_mmr]  scatter_reducetwotwo_outra  scatter_reduce_rc  multinomialri  rm  r}  r  _upsample_nearest_exact1dr  _upsample_nearest_exact2dr  "_upsample_nearest_exact2d_backwardr  _upsample_nearest_exact3dr   r  values_stabler  r  _thnn_fused_lstm_cellr  r  r  r  r  r  argminr  r  topkr  _segment_reduce_backwardr  kthvaluer	  r   r	  r	  r	  r!	  pixel_shuffler*	  r<	  	bucketize
Tensor_outrA	  histcrM	  _upsample_bilinear2d_aa_upsample_bicubic2d_aarS	   _upsample_bilinear2d_aa_backwardrX	  rb	  rg	  r  rn	  searchsortedrw	  r}	  embedding_dense_backwardr	  _embedding_bag_backwardr	  _embedding_bag_dense_backwardr	  *_embedding_bag_per_sample_weights_backwardr	  isinr	  	polygammar	  _local_scalar_denser	  r	  r	  r	  r	  _grouped_mmr
  _scaled_grouped_mmr
  _softmaxr
  constant_pad_ndr
  r
  _jagged_to_padded_dense_forwardr 
  r)
  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_pr5
  r:
  r?
  rC
  lerp_addcmul_addcdiv_torch._refs.nn.functionaltorch._refs.specialra
  r>   r9   r6   <module>rc     sH    $   5 5 '  # + +  " U     < 7 ) T]t_yy~~*/--*?*?PV*W ' %a )X
8BF#3"4hr2v6F"FG 
3(* t}}-.
 

==5  /5p 		!!499==12'  3' !!))4+<+<+@+@AB%' %  C%$ t%%&I  'I 	[[$++//4;;+>+>P Xy! " !!))4+<+<+@+@ABI  CI3lV $s) 4  %%t}}'8'89:K  ;K $s)  %%t}}'8'89:8
  ;8
v t}}**+"& 3 ,3 t}}$$% **
 &
 $$dll&6&678
 **  9&   $,,"6"678 **  9& 		!!499==12%)$tPT   3 %%t}}'8'89:$Dv $DDI $Dc $DC $D  ;$DN tzz!!" #0( t&&' ( t223
 "%)'+  6
	
 c] $ 4B t../
 (,	
  $	 00 t112 	
'+
  	 $ 3D t##$ ""'+"-<,,-<\\-< 6
-< F	-<
 $-< -< -< -< -< %-<` t  (() 	I
	I		I 	I LL		I
 	I 	I 	I *	I t!!))* 	
			 	 LL		
 	 	 	 +	 t  (()' * ' t""**+
 !% $ $ W
 W W f	 W
 f W f W  W  W  W , WF   $(("4"456  7 txx||    $(("4"456  7 txx||  tzz!!"6 #6 tzz~~( (
 t!!))* + t!!%%& ' t{{""# $ t##++, ) -) t''//0, 1, t33;;< =
 t008896 :6& t<<DDE F
 t,,001 2
F C    F  #  N (,


 !%
$V S C 
 
F 
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 
"  	  	C  !!))4+<+<+H+HIJ]N+ s T  , K" $$,,d.A.A.E.EFGB B6 B  HB  !]N+	6 	 , "	Q QF Q t**+) )F )4 )F )  ,) t""#J JF J4 JF J  $J t}})6 )$ )6 )  ) t$$%)6 )$ )6 )  &) t&&../&  T  0" 	$$,,d.M.M.Q.QR .f .6 .f . .d t!!))*&   + ))1143L3L3P3PQRT8V$ 	
  	
 666!" % S& %%--t/D/D/H/HIJ ''' '
 ' '  K'T &&(:(:;<S#s/3 f  fff>T8U   =4 ((00$2J2J2N2NOPT8V$ 	  	
 666!" % QD $$,,d.B.B.F.FGH 444 4
 4 4 4  I4n t~~S#s 	$$$ $ 	$
 666!"$  $P tTz!2 * &&(:(:;<S#f C ffn8M   =4 $$,,d.B.B.G.GHIV[$1'v '%(F"G ' 2 J'$ t''(   	""" " SM	" )"J.
.
. 49d3i .".
.
. 3-. 66>	.(f V   t$$%
 ##!777 	7
 7 V7 	7 V7 6
7 6666)*7 &7t ,,44d6R6R6V6VWX   	
   
&	  Y2 t$$%S#4( +(
+(+( +( 	+(
 +( 66>+( ) &+(^ t''(
 )
 tzz
 WW	W W 	W
 W W  Wt>#;L t$$%=  &= t%%&>  '>(< t--.\S  /S t../\T  0T2Ej t$$%=  &= t%%&>  '> &&..&&11''//''22	 \& &:<G~ t$$%=  &= t%%&>  '> &&..&&11''//''22	 \$( $(N t""#

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  $

 t##$Pv PV P Pf PQW P  %P $$dll&6&678/0 '  9': &&(:(:;<&* I  =I
 t$$% & t~~ I !I
 $$dll&6&678"  9" t33;;< * =*. tww	  	B
* 7;j,,jLLj $s)S.!j 49c>"	j
 DIsN#j j j U49c>23jZQ t%%--."$,,"$LL"$ 5<<
 "$ 5<<(	"$
 %,,'"$ "$ !&"$ "$ /"$J t''(),,)LL) ,,) I	)
 #Y) 3i) ) I) ) ))X 	889>9N9N&&:6 599##::BBC D, 599##55==>S ?S
 xx:?--:O:O66;
7 
uyy}}00	1	 
2	
 :?9N9N&&:6 599##55==>599##33;;<0 = ?0d 599##55<<= >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 	
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 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#<#<=> ?D ))1123H 4H: ##T[[__56./q '  7'0 !!(()*' +' !!))4+=+=+E+EFG  !
 H
2   (()*  !! +!H ~B  B* 0012 3& 889: ; (()*@ +@ 0012< 3< >>?@< A<"3 "3 "3 "jZ 0012D!)&!1D 3D0 ++,-; .;  (()*< +< t""**+ & , &F t##$G  %G* t""**+
 	
`5 ,`5F t//7785 95
 ##T[[__56=$ =  7= ##T^^%;%;<=) >) !!					 Xy! "	 t  (() * t{{""#' $'& tzz!!" # 								!!  !!

 									**Z  

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

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

""DJJNN34   5( t""**+. ,. t!!))*. +.
	 	C 	d 	/
  t{{""#' $'6
 
-
b4 t''(& )&
 t  ! "
 !!	 & & ""	 889:
 #!==	= = 	=
 = = E?= ;=@S#X( 889: #!((	( ( 	(
 ( ( ( ( E?( ;(V EEFG
 #'#!''	' ' 	'
 ' ' ' E?' H'T 99( """" 
" 	"
 
" " " " " " " " " " E?"
". 88 "&!	  	
   E?
: AA #'!!"!"!" 
!" 	!"
 
!" !" !" !" !" E?!"
!"H ??@A
 #'%)!3&3&	3& 3& 	3&
 3& 3& 6"3& E?3& 66>3& B3&l <<=> !))))	)) )) 	))
 )) )) E?)) ?))X ==" !4-4-4- 
4- 	4-
 4- 
4- 4- 4- 4- 4- $Z4- 4- E?4-
4-n 99* "!""" 
" 	"
 
" " " " " " " " " " "  E?!"
"0 %%  "&*'+"&%)HH	H H 	H
 H H H H H H E?H smH  }H H 6"H
HV &&( "&*'+#,,, 
, 	,
 
, , , , , , , , , , E?,  sm!,"  }#,
,4 ))   %!(,!%!%,S,S	,S ,S 6
	,S
 6",S 6",S 3-,S 3-,S ,S ,S ,S E?,S f%,S v,S #,S
,S^ *** "$("'%474747 
47 	47
 6
47 6"47 6"47 ,,47 ,,47 47 47 47 47 47 47  E?!47" SM#47$  %47
47n ''() $(+/'+ _Y
,,_Y
,,_Y \\_Y \\	_Y
 5<<
 _Y 5<<(_Y $_Y _Y *_YD ##'')<)<)D)DEF&  G&
 t##''( )
   (($*:*:*>*>?@	 	  A	,* 	$$d&D&D&L&LM

 	$$d&D&D&L&LM. ((00//77 !% $%U\\ 123 sELL012 uo	
 uo: 	$$d&D&D&L&LM

 									&$N t))112
  3 t&&'4/ (4/n t$$,,-$% .$%N


 ##T[[%8%89:4 ;4 t!!))* + tyy  !
Q "
Q t,,-LP  .  %%t}}';';<=Xy!K " >K  #("9"9 Q t77??@	* A	* t##++,	0 -	0 t!!))* +> t--556F 7FD %%t~~'@'@AB27u   C 

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 
	-K  "-K` t,,- . t++, '
 -'
T t112  3, t>>?  @. tyy8=e 8  8  t~~6c 6 6F 6  6 t''(I& I )I tyy"v "& "  " t||6& 6V 6  6'^ "!+/'+ TKTKTK ell#TK ell#	TK
 6
TK 6
TK 5<<(TK $TK TKn t  "!'+ 6
 6
	
 $   !& ''() $(#'+/'+ <<<< \\ \\	
 5<<
  5<<
  5<<( $  *0 t}}	v 	C 	 	 	  	 t##$3  %3l t~~ $888 8 	8
 8 8  8, t33;;<
 	**&\* c* 	* =*  d22 3 d44 5 d44 5 d== > d== > d== > d== > dDD E dDD E tBB C tBB C tBB C tBB C tJJ K tJJ K tJJ K tJJ K t@@ A tAA B tAA B tAA B tyy  $ t||./    t||./   , 	tyy)!$,,/!$,,/
    BNJ r9   