
    i$                    b
   d dl mZ 	 d dlZd dlZd dlZd dlZd dlZd dlZd dlZd dl	Z	d dlm
Z
mZ d dlmZmZmZ d dlZd dlmc mZ d dlmZmZmZmZmZmZmZmZ d dlmZ erd dlmZ  ej@                  e!      Z"ej$                  jG                  e!d      Z$g d	Z%d d
l&m'Z( d Z) G d d      Z* G d d      Z+ G d de+e,      Z-i dej\                  dej^                  dej`                  dejb                  dejb                  dejd                  dejf                  dejh                  dejj                  dejl                  dejn                  dejp                  dd d ejr                  d!ejt                  d"ejv                  d#ejx                  i d$ejz                  d%ej|                  d&ej~                  d'ej                  d(ej                  d)ej                  d*ej                  d+ej                  d,ej                  d-ej                  d.ej                  d/ed0ed1ed2ed3ed4ej                  d5ej                  iZGh d6ZHd7 ZId8ZJeJD ]J  ZKd9eK ZLd:eL ZM eNe*eL eIeK              eOeeM      eGeL<   eHja                  eL       e%j                  eL       L dhZQeHeQz  ZRh d;ZSh d<ZTdhZUeSeUz  ZVh d=ZWdd'hZXdd'd>d?ZYh d@ZZeJD ]  ZKd9eK ZLeZja                  eL        h dAZ[h dBZ\dC Z]dD Z^dE Z_dF Z`dG ZadH ZbdI ZcdJ ZddK ZedL ZfdM Zg	 dudNZhdO ZidP ZjdQ Zki dej`                  d.ej                  d$ejz                  d#e`d+ead*ebdecdeid'edd(ejd)ekd4e]d5e^de_d!eed-efZldR ZmdS ZndT ZodU ZpdV ZqdW ZrdX ZsdY ZtdZ Zud[ Zvd\ Zwd] Zxd^ Zye	j                  e!   Z{d_ Z|eJD ]'  ZKd`eK Z} e|eK      Z~e}xe~_        e~_!         eNe{e}e~       ) [~[K[}da ZdvdbZdc Zdd Zi eli d3ej                  dej\                  deqd%erdesd"etd eudevdendeod/edepd&ej~                  d2ewd1exd0eydeeedeZeJD ]  ZKd9eK ZL eOe{d`eK       eeL<    [K[L[J[{df Zdg Zdh Zdi Zdj Zdk Zdl Zdm ZeeeeeednZdo Zdp Zdq Zdr Zds Zej)                         D ]  \  ZZ eee        ej)                         D ]  \  ZZ eee        dt ZeD ]F  ZeeSv r
 eee       eeWv r
 eee       eeUv seeTv r	 eee        eee       eeYvs> eee       H [[y)w    )annotationsN)	lru_cacheupdate_wrapper)OptionalTYPE_CHECKINGUnion)	sym_floatsym_itesym_maxsym_minsym_notSymBoolSymFloatSymInt)dtrace_structured)ShapeEnvsym_node)SymNodemethod_to_operatormagic_methods
DynamicInt)py_sym_typesc                Z    | t         u rt        S | t        u rt        S | t        u rt
        S | S N)boolr   intr   floatr   )ts    X/var/www/html/engine/venv/lib/python3.12/site-packages/torch/fx/experimental/sym_node.py_to_symtyper    :   s+    DyCxEzH    c                     e Zd ZU dZdZded<   	 	 	 d\	 d]dZd^dZd_dZd`d	Z	e
d
        Ze
d        Zd ZdadZd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd ZdbdZdcdZdcdZdadcdZ dcd Z!dcd!Z"dcd"Z#dcd#Z$dcd$Z%dcd%Z&dcd&Z'dcd'Z(dcd(Z)dcd)Z*dcd*Z+dcd+Z,dcd,Z-dcd-Z.dcd.Z/dcd/Z0dcd0Z1dcd1Z2dcd2Z3dcd3Z4dcd4Z5dcd5Z6dcd6Z7dcd7Z8dcd8Z9dcd9Z:dcd:Z;dcd;Z<dcd<Z=dcd=Z>dcd>Z?dcd?Z@dcd@ZAdcdAZBdcdBZCdcdCZDdD ZEdE ZFdF ZGdG ZHdH ZIdI ZJdcdJZKdK ZLdL ZMdM ZNdcdNZOdddOZPdP ZQdQ ZRdR ZSdS ZTdT ZUdU ZVdV ZWdW ZXdX ZYdY ZZdZ Z[d[ Z\y)er   z
    This is a type erased SymInt/SymFloat which we use to do actual operations.
    End users don't touch this.  Magic methods are NOT defined on this object.
    Fr   _optimized_summationNc                    | _         | _        | _        | _         fd}|t	        |      |u s,t	        |      t        |      u sJ d| dt	        |               j                  rC j                  j                  r- |       }	||	k(  s!J | d|	 d j                   d        |       }| _        | _	         j                  xr  j                  j                  }
|
xr | _
        y )Nc                     ddl m}   | j                        ry j                  j	                  j                  d      }|#t        |t              sj                  |      n|}|S )Nr   )has_free_unbacked_symbolsT)compute_hint)%torch.fx.experimental.symbolic_shapesr&   expr	shape_env_maybe_evaluate_static
isinstanceSymTypespytype)r&   hintselfs     r   r'   z&SymNode.__init__.<locals>.compute_hint   sZ    W )3>>88QU8VD0:40Jt{{4(PTKr!   zCannot create SymNode of type z  with incompatible hint of type z != z (for ))_exprr*   r.   r#   typer    _translation_validation_enabledr)   _hintconstantfx_node)r0   r)   r*   r.   r/   r6   r7   optimized_summationr'   computed_hinttx_validation_ens   `          r   __init__zSymNode.__init__V   s     
"$7!:	 :'4:V9L+L 0(:4:,HL ~~$.."P"P !-}, fDvdii[B,  >D
;C NNMt~~MM 	 (3Gr!   c                    t        | j                  || j                  | j                  | j                  | j
                        S r   )r   r2   r.   r5   r6   r7   )r0   r*   s     r   with_shape_envzSymNode.with_shape_env   s0    JJ	4;;

DMM4<<
 	
r!   c                   | j                   |j                   k(  xrj | j                  |j                  k(  xrO | j                  |j                  k(  xr4 | j                  |j                  k(  xr | j                  |j                  k(  S r   )r2   r.   r5   r6   r7   r0   others     r   	_value_eqzSymNode._value_eq   sq     JJ%++% .u||+.

ekk). /. -	
r!   c                    t        | j                  | j                  | j                  | j                  | j
                  f      S r   )hashr2   r.   r5   r6   r7   r0   s    r   _value_hashzSymNode._value_hash   s,    TZZdjj$--VWWr!   c                L    | j                   j                  | j                        S r   )r*   replacer2   rD   s    r   r)   zSymNode.expr   s    ~~%%djj11r!   c                    | j                   S r   r5   rD   s    r   r/   zSymNode.hint   s    zzr!   c                    | j                   d uS r   rI   rD   s    r   has_hintzSymNode.has_hint   s    zz%%r!   c                r   ddl m} | j                  |n || j                        }| j                  j                  D ci c]"  }|||v rdn| j
                  j                  |   $ }}| j                  j                  |      S | j
                  j                  | j                        S | j                  S c c}w )Nr   free_unbacked_symbolsi   )	r(   rN   r5   r)   free_symbolsr*   
var_to_valxreplace	size_hint)r0   fallbackrN   unbacked_symbolssreplacementss         r   require_hintzSymNode.require_hint   s    O::# $9#C  "YY33  q$44t$..:S:STU:VV    yy)),77>>++DII66zz s   'B4c                Z    | j                   j                  rt        | j                         S y r   )r)   	is_numberr   rD   s    r   maybe_as_intzSymNode.maybe_as_int   s     99tyy>!r!   c                v    dd l }t        | j                  |j                        rt	        | j                        S y Nr   )sympyr,   r)   Floatr   r0   r]   s     r   maybe_as_floatzSymNode.maybe_as_float   s)    dii-##r!   c                p    dd l }| j                  |j                  u ry| j                  |j                  u ryy )Nr   TF)r]   r)   truefalser_   s     r   maybe_as_boolzSymNode.maybe_as_bool   s.    99

"YY%++%r!   c                &    | j                   t        u S r   )r.   r   rD   s    r   is_intzSymNode.is_int   s    {{c!!r!   c                &    | j                   t        u S r   )r.   r   rD   s    r   is_floatzSymNode.is_float   s    {{e##r!   c                &    | j                   t        u S r   )r.   r   rD   s    r   is_boolzSymNode.is_bool   s    {{d""r!   c                    | j                   d uxr@ t        | j                   t              xr$ | j                   j                  j	                         S r   )r5   r,   r   nodeis_nested_intrD   s    r   rm   zSymNode.is_nested_int   sA     JJd" 04::v.0

--/	
r!   c                    t        |      t        u sJ dd l}t        |j	                  |      | j
                  t        |||      S Nr   )r6   r7   )r3   r   r]   r   Integerr*   r0   numr]   s      r   wrap_intzSymNode.wrap_int  s?    CyCMM#S3PS
 	
r!   c                    t        |      t        u sJ dd l}t        |j	                  |      | j
                  t        |||      S ro   )r3   r   r]   r   r^   r*   rq   s      r   
wrap_floatzSymNode.wrap_float  s?    CyE!!!KKdnneS3PS
 	
r!   c                    t        |      t        u sJ dd l}t        |r|j                  n|j
                  | j                  t        |||      S ro   )r3   r   r]   r   rb   rc   r*   rq   s      r   	wrap_boolzSymNode.wrap_bool  sF    CyD   EJJ5;;NN
 	
r!   c                    | S r    rD   s    r   clonezSymNode.clone%  s    r!   c                    | j                    S r   )r)   rD   s    r   strzSymNode.str(  s    ))r!   c                "    | j                         S r   r|   rD   s    r   __str__zSymNode.__str__+  s    xxzr!   c                z   d| j                    d| j                   d| j                   g}| j                  |j	                  d| j                          | j
                  |j	                  d| j
                          | j                  |j	                  d| j                          dj                  |      dz   S )	NzSymNode(z, shape_env=z	, pytype=zhint=z	constant=zfx_node=z, r1   )r2   r*   r.   r5   appendr6   r7   join)r0   reps     r   __repr__zSymNode.__repr__.  s    tzzl,t~~.>i}U
 ::!JJtzzl+,==$JJ4==/23<<#JJ$,,01yy~##r!   c                "    | j                         S r   r~   rD   s    r   _graph_reprzSymNode._graph_repr:  s    xxzr!   c                "    | j                         S r   )_absrD   s    r   abszSymNode.abs@      yy{r!   c                "    | j                         S r   )_posrD   s    r   poszSymNode.posC  r   r!   c                $    | j                  |      S r   )_round)r0   ndigitss     r   roundzSymNode.roundF  s    {{7##r!   c                "    | j                         S r   )_truncrD   s    r   trunczSymNode.truncI      {{}r!   c                $    | j                  |      S r   )_addr?   s     r   addzSymNode.addL      yyr!   c                $    | j                  |      S r   )_subr?   s     r   subzSymNode.subO  r   r!   c                $    | j                  |      S r   )_mulr?   s     r   mulzSymNode.mulR  r   r!   c                $    | j                  |      S r   )_modr?   s     r   modzSymNode.modU  r   r!   c                $    | j                  |      S r   )
_float_powr?   s     r   	float_powzSymNode.float_powX  s    u%%r!   c                $    | j                  |      S r   )_pow_by_naturalr?   s     r   pow_by_naturalzSymNode.pow_by_natural[  s    ##E**r!   c                $    | j                  |      S r   )_and_r?   s     r   and_zSymNode.and_^  s    zz%  r!   c                $    | j                  |      S r   )_or_r?   s     r   or_zSymNode.or_a  r   r!   c                $    | j                  |      S r   )_float_truedivr?   s     r   float_truedivzSymNode.float_truedivd  s    ""5))r!   c                $    | j                  |      S r   )_int_truedivr?   s     r   int_truedivzSymNode.int_truedivg        ''r!   c                $    | j                  |      S r   )_int_floordivr?   s     r   int_floordivzSymNode.int_floordivj      !!%((r!   c                $    | j                  |      S r   )_lshiftr?   s     r   lshiftzSymNode.lshiftm      ||E""r!   c                $    | j                  |      S r   )_rshiftr?   s     r   rshiftzSymNode.rshiftp  r   r!   c                "    | j                         S r   )_sym_notrD   s    r   r   zSymNode.sym_nots      }}r!   c                $    | j                  |      S r   )_eqr?   s     r   eqz
SymNode.eqv      xxr!   c                $    | j                  |      S r   )_ner?   s     r   nez
SymNode.ney  r   r!   c                $    | j                  |      S r   )_gtr?   s     r   gtz
SymNode.gt|  r   r!   c                $    | j                  |      S r   )_ltr?   s     r   ltz
SymNode.lt  r   r!   c                $    | j                  |      S r   )_ler?   s     r   lez
SymNode.le  r   r!   c                $    | j                  |      S r   )_ger?   s     r   gez
SymNode.ge  r   r!   c                "    | j                         S r   )_floorrD   s    r   floorzSymNode.floor  r   r!   c                "    | j                         S r   )_is_integerrD   s    r   
is_integerzSymNode.is_integer  s    !!r!   c                "    | j                         S r   )
_sym_floatrD   s    r   r	   zSymNode.sym_float  s      r!   c                "    | j                         S r   )_sym_intrD   s    r   sym_intzSymNode.sym_int  r   r!   c                "    | j                         S r   )_ceilrD   s    r   ceilzSymNode.ceil  s    zz|r!   c                "    | j                         S r   )_negrD   s    r   negzSymNode.neg  r   r!   c                $    | j                  |      S r   )_sym_minr?   s     r   r   zSymNode.sym_min      }}U##r!   c                $    | j                  |      S r   )_sym_maxr?   s     r   r   zSymNode.sym_max  r   r!   c                &    | j                  ||      S r   )_sym_ite)r0   then_valelse_vals      r   r
   zSymNode.sym_ite  s    }}Xx00r!   c                &    | j                  ||      S r   )_is_contiguousr0   sizesstridess      r   is_contiguouszSymNode.is_contiguous  s    ""5'22r!   c                &    | j                  ||      S r   )_is_channels_last_contiguous_2dr   s      r   is_channels_last_contiguous_2dz&SymNode.is_channels_last_contiguous_2d      33E7CCr!   c                &    | j                  ||      S r   )_is_channels_last_contiguous_3dr   s      r   is_channels_last_contiguous_3dz&SymNode.is_channels_last_contiguous_3d  r   r!   c                &    | j                  ||      S r   )_is_channels_last_strides_2dr   s      r   is_channels_last_strides_2dz#SymNode.is_channels_last_strides_2d      00@@r!   c                &    | j                  ||      S r   )_is_channels_last_strides_3dr   s      r   is_channels_last_strides_3dz#SymNode.is_channels_last_strides_3d  r  r!   c                &    | j                  ||      S r   )'_is_non_overlapping_and_dense_indicatorr   s      r   &is_non_overlapping_and_dense_indicatorz.SymNode.is_non_overlapping_and_dense_indicator  s    ;;E7KKr!   c                $    | j                  |      S r   )r   r?   s     r   sym_orzSymNode.sym_or  r   r!   c                $    | j                  |      S r   )r   r?   s     r   sym_andzSymNode.sym_and  r   r!   c                $    | j                  |      S r   )_bitwise_andr?   s     r   bitwise_andzSymNode.bitwise_and  r   r!   c                $    | j                  |      S r   )_bitwise_orr?   s     r   
bitwise_orzSymNode.bitwise_or  s    &&r!   c                $    | j                  |      S r   )_bitwise_xorr?   s     r   bitwise_xorzSymNode.bitwise_xor  r   r!   c                $    | j                  |      S r   )r   r?   s     r   truedivzSymNode.truediv  r   r!   c                $    | j                  |      S r   )r   r?   s     r   floordivzSymNode.floordiv  r   r!   c                $    | j                  |      S r   )r   r?   s     r   powzSymNode.pow  s    ~~e$$r!   c                X    | j                  ||      j                  t        | d            S )N   )r  r   to_noder   s      r   is_non_overlapping_and_densez$SymNode.is_non_overlapping_and_dense  s,    ::5'JMMD!
 	
r!   c                &    | j                  dd      S N r   )	guard_intrD   s    r   int_zSymNode.int_  s    ~~b!$$r!   c           
        dd l }ddlm}m}  |       r3t	        |  |t
        j                  t        d |D              fi             S |D cg c]  }|j                   }} |j                  | }g }d }	|D ]+  }|j                   n(|j                  |j                         - t        |      }	| j                  j                  t
        j                  t        d |D              f      \  }
}t        || j                  t         |	|
      S c c}w )Nr   get_proxy_modehandle_sym_dispatchc              3  2   K   | ]  }t        |        y wr   )	wrap_node.0as     r   	<genexpr>z"SymNode.sym_sum.<locals>.<genexpr>  s     6A9Q<6s   c              3  4   K   | ]  }|j                     y wr   r7   r*  s     r   r-  z"SymNode.sym_sum.<locals>.<genexpr>  s     !:!))!:s   r/  )r]   "torch.fx.experimental.proxy_tensorr&  r'  r  torchsym_sumtupler)   Addr/   r   sumr*   _create_fx_call_functionr   r   )r0   argsr]   r&  r'  r,  exprsout
size_hintsout_hintr7   _s               r   r2  zSymNode.sym_sum  s    	

 #MM6668  "&&A&&eii
 	'Avv~aff%	'
 :H^^<<MME!:T!::<


 sDNNC7KK# 's   D
c                :    | j                   j                  | |      S r   )r*   evaluate_sym_node)r0   size_obliviouss     r   evaluatezSymNode.evaluate  s    ~~//nEEr!   c                    | j                         }	 t        |      S # t        $ r t        j	                  d|        w xY w)NzFailed to convert to int: %s)r@  r   	Exceptionlogwarningr0   fileliners       r   r"  zSymNode.guard_int  s>     MMO	q6M 	KK6:	   
 !>c                    | j                         }	 t        |      S # t        $ r t        j	                  d|        w xY w)NzFailed to convert to float: %s)r@  r   rB  rC  rD  rE  s       r   guard_floatzSymNode.guard_float  s>     MMO	8O 	KK8!<	rI  c                    | j                         }	 t        |      S # t        $ r t        j	                  d|        w xY w)NFailed to convert to bool: %sr@  r   rB  rC  rD  rE  s       r   
guard_boolzSymNode.guard_bool  s>     MMO	7N 	KK7;	rI  c                   ddl m} | j                         r: || j                        s(| j                  j
                  s| j                  ||      S | j                  j                  | j                  | d| | j                        S )Nr   rM   :r/  )	r(   rN   rK   r)   r*   +prefer_deferred_runtime_asserts_over_guardsrO  guard_or_defer_runtime_assertr7   )r0   rF  rG  rN   s       r   expect_truezSymNode.expect_true$  st    O MMO)$))4NNNN ??4..
 ~~;;II$q' < 
 	
r!   c                T    ddl m} | j                         sJ  |t        |             S )Nr   )statically_known_true)r(   rV  rj   r   )r0   rF  rG  rV  s       r   rV  zSymNode.statically_known_true6  s"    O||~~$WT]33r!   c                    | j                  d      }	 t        |      S # t        $ r t        j	                  d|        w xY w)aN  
        Like guard_bool, but if we encounter unbacked symbols, if those symbols
        are size-like, we will treat them as >= 2 for the purposes of the analysis.

        This CHANGES the runtime semantics, but all size-oblivious sites have been
        audited to ensure that the runtime semantics don't change in a material way.
        Acceptable runtime semantic changes are, e.g., squeeze() no longer dropping
        an unbacked one size, or a tensor reporting as non-contiguous even if it's
        contiguous if it would have been reported contiguous due to being empty.
        T)r?  rM  rN  rE  s       r   guard_size_obliviouszSymNode.guard_size_oblivious<  sC     MMM.	7N 	KK7;	s	   
 !A c                T    ddl m} | j                         sJ  |t        |             S )Nr   )guard_or_false)r(   rZ  rj   r   )r0   rF  rG  rZ  s       r   rZ  zSymNode.guard_or_falseP  s"    H||~~gdm,,r!   c                T    ddl m} | j                         sJ  |t        |             S )Nr   )guard_or_true)r(   r\  rj   r   )r0   rF  rG  r\  s       r   r\  zSymNode.guard_or_trueV  s"    G||~~WT]++r!   c                &    | j                  dd      S r   )rO  rD   s    r   bool_zSymNode.bool_\  s    r1%%r!   c                     y)NTry   rD   s    r   is_symboliczSymNode.is_symbolic_      r!   c                     y r   ry   rD   s    r   
nested_intzSymNode.nested_intb  ra  r!   c                     y)NFry   rD   s    r   is_constantzSymNode.is_constante  s    r!   )NNF)r/   z!Optional[Union[int, float, bool]])r*   r   returnr   )r@   r   rf  r   )rf  r   r   )rf  zbuiltins.str)rf  r   )F)]__name__
__module____qualname____doc__r#   __annotations__r;   r=   rA   rE   propertyr)   r/   rK   rW   rZ   r`   rd   rf   rh   rj   rm   rs   ru   rw   rz   r|   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r	   r   r   r   r   r   r
   r   r   r   r   r  r  r	  r  r  r  r  r  r  r  r  r#  r2  r@  r"  rK  rO  rT  rV  rX  rZ  r\  r^  r`  rc  re  ry   r!   r   r   r   G   s    "'$& !P4
 0P4d


X 2 2  &0"$#




$$    &+! *()##"!$$13DDAAL ('()(%

%#LJF
$4(-,&r!   r   c                       e Zd Z fdZ xZS )_DynamicScalarc                J    | t         u rt        d      t        |   | g| S )Nz9_DynamicScalar is an abstract base class, use DynamicInt.)rn  	TypeErrorsuper__new__)clsr7  	__class__s     r   rr  z_DynamicScalar.__new__j  s+    . WXXws*T**r!   )rg  rh  ri  rr  __classcell__rt  s   @r   rn  rn  i  s    + +r!   rn  c                  4     e Zd ZdZ fdZd Zd Zd Z xZS )r   a  
    User API for marking dynamic integers in `torch.compile`.
    Intended to be compatible with both compile and eager mode.

    Example usage::

        fn = torch.compile(f)
        x = DynamicInt(4)
        fn(x)  # compiles x as a dynamic integer input; returns f(4)
    c                ^    t        |t              sJ t        |   | t        |            }|S r   )r,   r   rq  rr  )rs  valobjrt  s      r   rr  zDynamicInt.__new__|  s,    #s###goc3s8,
r!   c                "    d| j                    dS )NzDynamicInt(r1   )realrD   s    r   r   zDynamicInt.__repr__  s    TYYKq))r!   c                2    t        | j                  |z        S r   r   r|  r?   s     r   __floordiv__zDynamicInt.__floordiv__  s    $))u,--r!   c                2    t        || j                  z        S r   r~  r?   s     r   __rfloordiv__zDynamicInt.__rfloordiv__  s    %499,--r!   )	rg  rh  ri  rj  rr  r   r  r  ru  rv  s   @r   r   r   p  s    	
*..r!   r   r   r   r   andr  r   r   r   r   r   r   r   r   c                "    | j                         S r   )r   xs    r   <lambda>r    s    ALLN r!   r   r   r   r   r   r   r   orr  r  r   r   r   r   r   r	   r
   r   r   r   r   r   >	   r   r   r   r   r   r   r   r   r	   c                      fd}|S )Nc                ,     t        | d              S )N_sym_)getattr)r0   names    r   fnz_get_sym_node_fn.<locals>.fn  s    ,wtuTF^,..r!   ry   r  r  s   ` r   _get_sym_node_fnr    s    / Ir!   )sqrtcoscoshsinsinhtantanhasinacosatanlog2sym_r<  >   r  r  r
   r   >   r   r   r   >   r   r   sym_log2r   xor)r  r  r  >   r   r	   r   r   >   r   r   r   r   >   r   r   r   r   r   r   r  r  r   r   r  c                     ddl m}  || |      S )Nr   )FloatTrueDiv)torch.utils._sympy.functionsr  )r,  br  s      r   _sympy_float_truedivr        91r!   c                     ddl m}  || |      S )Nr   )
IntTrueDiv)r  r  )r,  r  r  s      r   _sympy_int_truedivr    s    7ar!   c                     ddl m}  || |      S )Nr   )FloorDiv)r  r  )r,  r  r  s      r   _sympy_floordivr        5Aq>r!   c                f    ddl m}m} | j                  r|j                  r	 || |      S  || |      S )Nr   Mod	PythonMod)r  r  r  is_nonnegative)r,  r  r  r  s       r   
_sympy_modr  !  s.    ;A,,1ayAr!   c                     ddl m}  || |      S )Nr   )PowByNatural)r  r  )r,  r  r  s      r   _sympy_pow_by_naturalr  *  r  r!   c                     ddl m}  || |      S )Nr   )FloatPow)r  r  )r,  r  r  s      r   _sympy_float_powr  0  r  r!   c                .    dd l }|j                  | |      S r\   )r]   Andr,  r  r]   s      r   
_sympy_andr  6  s    99Q?r!   c                .    dd l }|j                  | |      S r\   )r]   Orr  s      r   	_sympy_orr  <      88Aq>r!   c                     ddl m}  || |      S )Nr   )LShift)r  r  )r,  r  r  s      r   _sympy_lshiftr  B      3!Q<r!   c                     ddl m}  || |      S )Nr   )RShift)r  r  )r,  r  r  s      r   _sympy_rshiftr  H  r  r!   c                `   t        |       dk(  r|gS ddlm}m}  || d          ||      k  r| |gz   S  || d          ||      kD  r|g| z   S dt        |       dz
  }}||k  r9||z   dz  }|j	                  | |   |      }|dk(  ry|dk  r|dz   }n|dz
  }||k  r9| j                  ||       | S )zs
    If new_arg is found in ordered_args None is returned, else the new
    ordered_args with new_arg inserted
    r   )_args_sortkeyBasicr     N)lensympy.core.basicr  r  compareinsert)ordered_argsnew_argsort_keyr  lowhighmidcompare_results           r   _binary_search_insert_argr  N  s    
 <AyA R !HW$55wi'' Q 8G#44y<''3|$q(C
+Tza|C'8'BQa'C7D + W%r!   c                  
 ddl 
ddlm} 
fd}ddlm} | ||       z  }| ||      z  }|r|r || j
                  d          ||j
                  d         k  r || j
                  |j
                  z         S  || j
                  d          ||j
                  d         kD  r ||j
                  | j
                  z         S t        | j
                        dk  rXt        |j
                        dk  r@t        | j
                        }|j
                  D ]  }t        ||      }| n | ||      S |r5|j                  r)t        t        | j
                        |      }| ||      S |r5| j                  r)t        t        |j
                        |       }| ||      S 
j                  | |      }	 ||	      |	fS )a  
    Custom optimization for Add used to optimize incremental binary summations of certain properties. The idea
    is when we know the expression is a summation of unique symbols all we need to know is the correct order of symbols,
    and no other optimizations are needed. We pass evaluate=false, with the correct order of args and save the following.
    1. Avoid running other optimizations when the Add is constructed.
    2. Manually figure out the order of the args for the new expression in log(n) comparisons instead of nLog(n)
    (comparing terms is expensive and shows in the profiles).
    The function returns a tuple of (1) a boolean that indicates whether the output is a summation of unique symbols,
    (2) the result sympy expression.
    r   N)r  c                8    | J  j                   | ddi}d|fS )Nr@  FT)r4  )r  resultr]   s     r   make_optimizedz&_optimized_add.<locals>.make_optimized  s.    '''L959f~r!   )_is_symbols_binary_summationr  r  )r]   r  r  r  r  _argsr  listr  	is_symbolr4  )lhsrhslhs_is_optimized_summationrhs_is_optimized_summationsortkeyr  r  new_argsr,  r  r]   s             @r   _optimized_addr  p  s    9
 J">s"CC">s"CC!&@399R=!GCIIaL$99!#))cii"788399Q< 7399R=#99!#))cii"788 syy>Q3syy>Q#6CIIHYY 4XqA#
 #%h// "cmm,T#))_cB!(++ "cmm,T#))_cB!(++YYsC F(0&99r!   c                     ddl m}  || |      S )Nr   )BitwiseFn_bitwise_and)r  r  )r,  r  r  s      r   r  r        B A&&r!   c                     ddl m}  || |      S )Nr   )BitwiseFn_bitwise_or)r  r  )r,  r  r  s      r   r  r    s    A1%%r!   c                     ddl m}  || |      S )Nr   )BitwiseFn_bitwise_xor)r  r  )r,  r  r  s      r   r  r    r  r!   c                   dd l }t        | |j                        rf| j                  }t	        |      dk(  rLt        |d   |j
                        r3|d   j                  r$|j                  |d         }|d   |k(  r||d   z  S t        | |j
                        r| |j                  |       k(  st        | |j                        r|j                  |       S  ||       S )Nr   r  r  )r]   r,   Mulr7  r  r^   r   rp   )r,  r  r]   aacoefs        r   _floor_ceil_helperr    s    !UYYVVr7a<Jr!uekk:r!u?O?O==A'D!u}be|#1ekk"q!!a'}}Qa5Lr!   c                    ddl m}  ||       S )Nr   )
FloorToInt)r  r  )r,  r  s     r   _sympy_floorr        7a=r!   c                    ddl m}  ||       S )Nr   )
TruncToInt)r  r  )r,  r  s     r   _sympy_truncr    r  r!   c                    ddl m}  ||       S )Nr   )	CeilToInt)r  r  )r,  r  s     r   _sympy_ceilr    s    6Q<r!   c                .    dd l }|j                  | |      S r\   )r]   Eqr  s      r   	_sympy_eqr    r  r!   c                .    dd l }|j                  | |      S r\   )r]   Ner  s      r   	_sympy_ner    r  r!   c                .    dd l }|j                  | |      S r\   )r]   Gtr  s      r   	_sympy_gtr    r  r!   c                .    dd l }|j                  | |      S r\   )r]   Ltr  s      r   	_sympy_ltr    r  r!   c                .    dd l }|j                  | |      S r\   )r]   Ler  s      r   	_sympy_ler
    r  r!   c                .    dd l }|j                  | |      S r\   )r]   Ger  s      r   	_sympy_ger    r  r!   c                     ddl m}  || |      S )Nr   )Min)r  r  )r,  r  r  s      r   
_sympy_minr        0q!9r!   c                     ddl m}  || |      S )Nr   Max)r  r  )r,  r  r  s      r   
_sympy_maxr  %  r  r!   c                6    dd l }|j                  || f|df      S )Nr   T)r]   	Piecewise)r,  r   fr]   s       r   
_sympy_iter  +  s    ??Aq6At9--r!   c                      fd}|S )Nc                r    dd l } t        |j                  j                  j                  d       |       S )Nr   OpaqueUnaryFn_)r  r  utils_sympy	functions)r,  r1  r  s     r   r  z_get_sym_math_fn.<locals>.fn5  s1    +Mwu{{))33~dV5LMaPPr!   ry   r  s   ` r   _get_sym_math_fnr   4  s    Q
 Ir!   _sympy_c                ,    dd l }|j                  |       S r\   )r]   Abs)r,  r]   s     r   
_sympy_absr$  F  s    99Q<r!   c                8    ddl m}m} | ||       S  || |      S )Nr   )RoundDecimal
RoundToInt)r  r&  r'  )numberr   r&  r'  s       r   _sympy_roundr)  L  s"    E&!!FG,,r!   c                    ddl m}  ||       S Nr   )ToFloat)r  r,  )r,  r,  s     r   _sympy_sym_floatr-  U  s    4 1:r!   c                d    dd l }ddlm} |j                   ||j	                  |             |       S r+  )r]   r  r,  r  r   )r,  r]   r,  s      r   _sympy_is_integerr/  ]  s&    488GEKKN+Q//r!   )r   r   c                `    t        |       }t        | |t        t        |dz
  dd                  S )Nr  r  )r  sympy_is_contiguous_genericr  range)r   r   dims      r   sympy_is_contiguousr4    s,    
e*C&ugtE#'2r<R7STTr!   c                   dd l }t        |       }t        |      |k7  r|j                  S |j                  }|j                  j
                  }|D ]L  }||j                  | |   |j                  j
                        |j                  ||   |      z  z  }|| |   z  }N t        |      D ].  }||j                  | |   |j                  j                        z  }0 |S r\   )	r]   r  rc   rb   SOner  r2  Zero)r   r   	dim_orderr]   r3  r   zds           r   r1  r1    s    
e*C
9~{{JJMA %(EGGKK8588GAJPQ;RRR	U1X 3Z :%(EGGLL99:r!   c                     t        | |g d      S N)r     r  r   r1  r   r   s     r   $sympy_is_channels_last_contiguous_2drA    s    &ug|DDr!   c                     t        | |g d      S N)r     r>  r  r   r?  r@  s     r   $sympy_is_channels_last_contiguous_3drE    s    &ugGGr!   c                   dd l }ddlm} t        |       }|t        |      k7  r|j                  S |j
                  j                  }|j                  }||j                  |d   d      z  }|D ]R  }||j                  | |   d      ||   |k\  z  z  }|dk(  r||j                  ||d         z  }||    || |   d      z  }T |S )Nr   r  r  )	r]   r  r  r  rc   r6  r8  rb   r   )	r   r   r9  r]   r  r3  mrH  r;  s	            r   &sympy_is_channels_last_strides_genericrH    s    0
e*C
c)n{{A

A '!*a	  A *	UXXeAh"gajAo66 6!WQZ((A AJU1Xq))'** Hr!   c                     t        | |g d      S r=  rH  r@  s     r   !sympy_is_channels_last_strides_2drK    s    1%,OOr!   c                     t        | |g d      S rC  rJ  r@  s     r   !sympy_is_channels_last_strides_3drM    s    1%/RRr!   c                "    ddl m}  |g | | S )Nr   )!IsNonOverlappingAndDenseIndicator)r  rO  )r   r   rO  s      r   -_sympy_is_non_overlapping_and_dense_indicatorrP    s    N,>e>g>>r!   )r   r   r   r   r  r  c                   t        |t              r|j                  S t        |      t        u r| j                  |      S t        |      t        u r| j                  |      S t        |      t        u r| j                  |      S t        S r   )r,   r-   rl   r3   r   rw   r   rs   r   ru   NotImplemented)r0   rr   s     r   r  r    sn    #x xx	cd	~~c""	cc	}}S!!	ce	s## r!   c                   t        | t              r| j                  | j                  S | j                         rt	        |       S | j                         rt        |       S | j                         rt        |       S t        d|        )Nzunrecognized return type )
r,   r   r6   rf   r   rh   r   rj   r   AssertionErrorr  s    r   r)  r)    sk    !W!**"8zzxxzay	
{	
qz8<==r!   c                    t         |    S r   )METHOD_TO_OPERATOR)methods    r   r   r     s    f%%r!   c                l     t        d             t        v r  d}n }dd} fd}| fd       }| fd       } t        v rt        t        d| |       y  dk(  r fd}t        t        d| |       y  d	k(  rd fd
	}t        t        d| |       y t        t        d| |       y )N   r<  c                 L   dd l } | j                  j                  | j                  j                  | j                  j
                  j                  | g}dd l} |D ch c]  }t        j                  |       c}| j                  j                  j                         z  dhz  S c c}w )Nr   z<string>)r1  _dynamo
eval_framer  fxexperimentalr   torch._dynamo.guardsinspectgetfileguardsuninteresting_files)r1  modsrG  s      r   rc  z-_make_node_magic.<locals>.uninteresting_files  s     MM$$MMHH!!**	
 	$ *..AW__Q.mm""6689l	
.s   B!c                H     t        j                         d fd	       }|S )Nc                    |	 |       n	 | |      t         j                  j                  j                  r#|| |gn| gdfdt	        dfd       S )Nc                   dd l }| j                  y t        |       t              k(  ry t        | j                  |j
                  |j                  f      ry | j                  |j                  |j                  fv ry t        |       S r\   )	r]   r6   idr,   r)   rp   r^   rb   rc   )r   r]   r  s     r   get_idzM_make_node_magic.<locals>.capture_provenance.<locals>.wrapper.<locals>.get_id2  sl     ((4#HF3##HMMEMM5;;3OP#!5::u{{*CC#h<'r!   expression_createdc            
        t              t              D  cg c]  } t        |        c} D cg c]  } |       |       c}t        j                  d      t        j                  d      dS c c} w c c}w )Nr>  )rW  r  	result_id	argumentsargument_ids
user_stackstack)r|   rh  
structuredget_user_stackget_framework_stack)r,  irm  ri  rW  r  s     r   r  zO_make_node_magic.<locals>.capture_provenance.<locals>.wrapper.<locals>.<lambda>B  sv    "("%f+%'Z6?%@c!f%@/8)*+F1I<QF1I) '1&?&?&B!+!?!?!B
)  &A)s   A8
A=
A=)metadata_fn)rf  zOptional[int])r1  _logging	_internalGET_DTRACE_STRUCTUREDr   )r0   r@   rm  ri  r  r  rW  s     @@@r   wrapperz=_make_node_magic.<locals>.capture_provenance.<locals>.wrapper&  sc    }DD%~~''==$!%uI!%I( "(
! Mr!   r   )	functoolswraps)r  ry  rW  s   ` r   capture_provenancez,_make_node_magic.<locals>.capture_provenance%  s&    		(	 
(	T r!   c           
        ddl m}m} t              }d }| j                  )|j                   || j                  |j                        } |       r(t        |  ||t        |       t        |      fi             S t        |t              sJ d}	 dk(  rddl	m
}m} | j                  }	| j                  j                  s(|	j                  | j                        j                   dk\  r\|j                  j                  s(|	j                  |j                        j                   dk\  r || j                  |j                        }
nz || j                  |j                        }
n\dk(  r:t#        | j                  |j                  | j$                  |j$                        \  }}
n | j                  |j                        }
t,        j/                  d| j                  |j                  |
       t0        v rt2        }nFt4        v rt6        }n7| j8                  t2        u s|j8                  t2        u rt2        }n| j8                  }||t        |t:              s ||      }| j                  j=                  || j>                  |j>                  f      \  }}t        |
| j                  ||||	      }|S # t&        $ r. t(        j+                  d| j                  |j                          w xY w)
Nr   r%  Fr   r  r   failed to eval %s(%s, %s)z%s %s %s -> %s)r7   r8   ) r0  r&  r'  r   r/   r  r)  r,   r   r  r  r  r*   r)   r  bound_sympylowerr  r#   rB  rC  rD  sym_node_logdebugalways_float_magic_methodsr   always_bool_magic_methodsr   r.   r-   r6  r7   )r0   r@   r&  r'  opr;  r8   r  r  r*   r9  r.   r7   r<  r  funcrW  s                  r   binary_magic_implz+_make_node_magic.<locals>.binary_magic_implS  sw   	

  '99 UZZ%;$))UZZ0H)"y	%@P.QSUV  %)))#	G !NN	II,, ,,TYY7==BJJ-- ,,UZZ8>>!Cdii4C#DIIuzz:C5-;IIJJ--..	.*$c 499ejj1 	+VTYY

CP //F00F[[E!U\\U%:F[[F $x2h'H ^^<<u}}-

 NN 3
 U  	KK3VTYY

S	s   D-J- -7K$c           	        ddl m}m} t              } |       rt	        |  ||t        |       fi             S | j                  }dk(  sdk(  r| j                  j                  |      }	  
|      }t        j                  d
||       d }| j                   || j                        }t        v rt         }n*t"        v rt$        }nt&        v rt(        }n| j*                  }| j                  j-                  || j.                  f      \  }}	t1        || j                  |||      S # t        $ r t        j                  d|        w xY w)Nr   r%  r   ceilingzfailed to eval %s(%s)z%s %s -> %sr/  )r0  r&  r'  r   r  r)  r)   r*   _simplify_floor_divrB  rC  rD  r  r  r/   always_int_magic_methodsr   r  r   r  r   r.   r6  r7   r   )r0   r&  r'  r  r)   r9  r;  r.   r7   r<  r  rW  s             r   unary_magic_implz*_make_node_magic.<locals>.unary_magic_impl  s3   	

  '4!4R)D/9KR!PQQyyW) 3>>55d;D	t*C 	=$c:99 $))}H--F00F11F[[F^^<<R$,,Q
sDNNFHgNN%  	KK/>	s   ,D) )"Er
   c                   ddl m}m} | j                  r|j                  n|j                  } |       r6t	        |  |t
        t        |       t        |      t        |      fi             S 	  	| j                  |j                  |j                        }| j                  j                  t
        | j                  |j                  |j                  f      \  }}t        || j                  |j                  ||      S # t        $ r9 t        j                  d
| j                  |j                  |j                          w xY w)Nr   r%  zfailed to eval %s(%s, %s, %s)r/  )r0  r&  r'  r/   r  r
   r)  r)   rB  rC  rD  r*   r6  r7   r   r.   )	pred_node	then_node	else_noder&  r'  r;  r9  r7   r<  r  rW  s            r   sym_ite_implz&_make_node_magic.<locals>.sym_ite_impl  s   
 *3y~~Y^^H'%i0%i0%i0
  
9>>9>>9>>J #,,EE)++Y->->	@Q@QRJGQ Y(()*:*:Hg   3NNNNNN s   ,(C< <AD>r   c           	     (   ddl m}m} t        j                  } |       rt        |  ||t        |       |fi             S | j                  }	  ||      }|t        }n| j                  }d }| j                   || j                  |      }| j                  g}	||	j                  |       | j                   j#                  |t%        |	            \  }
}t'        || j                   |||
      S # t        $ r t        j                  d||        w xY w)Nr   r%  z!failed to eval %s(%s, ndigits=%s)r/  )r0  r&  r'  builtinsr   r  r)  r)   rB  rC  rD  r   r.   r/   r7   r   r*   r6  r3  r   )r0   r   r&  r'  r  r)   r9  r.   r;  r7  r7   r<  r  rW  s               r   
round_implz$_make_node_magic.<locals>.round_impl  s	   
 B-b9T?G2LbQ  99D4)
 Hyy$dii1 LL>D"G$@@U4[QJGQ3'RR1  ?wWs   	C. .#D)rf  zset[str]r   )r   2magic_methods_on_operator_with_trailing_underscoreunary_methodssetattrr   )	rW  r  method_attrrc  r|  r  r  r  r  s	   ``       r   _make_node_magicr    s    9S>$DCCl
",\ X Xt "O "OH 1[M*,<=	9	&	P 	1[M*L9	7	'	SR 	1[M*J71[M*,=>r!   c                      fd}t        t        d  |        fd}t        t        j                  t
                  s#t        t        j                  t
            |       y y )Nc                "   ddl m}m} t        t        j
                  t                 } |       rDt        |  |||D cg c]  }t        |       c}|D cg c]  }t        |       c}fi             S |D cg c]  }|j                   }}|D cg c]  }|j                   }}	  ||      }	g }
d }|D ]+  }|j                   nX|
j                  |j                         - g }|D ]+  }|j                   n&|j                  |j                         -  ||
|      }j                  d      rt         }nt"        }t%        |	| j&                  ||      S c c}w c c}w c c}w c c}w # t        $ r t        j                  d||        w xY w)Nr   r%  r~  
_indicator)r0  r&  r'  r  sysmodulesrg  r  r)  r)   rB  rC  rD  r/   r   endswithr   r   r   r*   )r0   r   r   r&  r'  r  rU   
size_exprsstride_exprsr9  r:  r;  stride_hintsr.   r  rW  s                 r   sizes_strides_implz4_make_node_sizes_strides.<locals>.sizes_strides_impl3  s   	

 S[[*F3#,12qil274SaYq\4ST  ',,aff,
,(/0100	z<0C 
 	8Avv~aff%	8
 L 866>##AFF+8
 j,7 ??<(FFsDNNFH==E 34S -0  	KK3VZV	s#   EE:E!E&)	E+ +#Fr<  c                "   dd l }ddlm} t        j                  | |      D ]~  }t        |t              st         t        |j                        | D cg c]  }t        |j                  |       c}|D cg c]  }t        |j                  |       c}            c S  dk(  r	 || |      S t         | D cg c]  }|j                  |       c}|D cg c]  }|j                  |       c}            S c c}w c c}w c c}w c c}w )Nr   )!eval_is_non_overlapping_and_denser  )r]   r(   r  	itertoolschainr,   r   r)  r  rl   r  r   sympify)r   r   r]   r  r,  r  r  rW  s         r   sizes_strides_userz4_make_node_sizes_strides.<locals>.sizes_strides_userh  s    	
 0 	A!V$ +GAFFF+5:;+;5<=+= 	 ==4UGDD /45!U]]1%5/67!U]]1%7  <= 67s   C=8D<DD)r  r   hasattrr  r  rg  )rW  r  r  r  s   ``  r   _make_node_sizes_stridesr  0  sS    .>` Gq\#56
6 3;;x(&1H%v/AB 2r!   c                   
  t         v rd  n dd
d  t        v rd nd  fd
 fd}
 fd}
 fd	}d
 } t        v r ||d  d|       y  t        v r!t	        |       } || t        ||             y  dk(  r
fd} ||d  d|       y  dk(  rd
 fd	} ||d  d|       y  }	 t        v r	t            }	 ||d|	 d|        t        v r ||d|	 d|       y y )Nr  c                   t        | t        t        t        f      r| S t        | t              r| j
                  j                  dd      S t        | t              r| j
                  j                  dd      S t        d      )Nr!  r   z*expect to be called with constant SymBools)
r,   r   r   r   r   rl   r"  r   rO  rT  r  s    r   get_constantz&_make_user_magic.<locals>.get_constant  sf    a#ud+,Ha 66##B**a!66$$R++IJJr!   c                    t        | t        t        t        f      ryt        | t        t
        t        f      r| j                  j                         S y)NTF)	r,   r   r   r   r   r   r   rl   re  r  s    r   re  z%_make_user_magic.<locals>.is_constant  s=    a#ud+,a&(G4566%%''r!   c                    t        | t              r-t        | j                  j	                  t        |                   S | S )z;Implements True+True=2, which works in python but not sympy)r,   r   r   rl   rs   r   r  s    r   promotez!_make_user_magic.<locals>.promote  s-    !W%affooc!f566Hr!   c                    | S r   ry   r  s    r   r  z!_make_user_magic.<locals>.promote  s    Hr!   c                    dvr| |fS t        | t        t        j                  f      }t        |t        t        j                  f      }|s|r.|st        j                  |       } |st        j                  |      }| |fS )N)r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   )r,   r   r1  r   r	   )r0   r@   f_selff_otherrW  s       r   promote2z"_make_user_magic.<locals>.promote2  sy      
 
$ ;D5%.."9:UUENN$;<Wt,.U{r!   c                     |       }  |       r t               |             S t         t        | j                                     S r   )r   r)  r  rl   )r0   r  re  rW  r  r  s    r   r  z*_make_user_magic.<locals>.unary_magic_impl  sH    t}t.&v.T0BCC8K8:;;r!   c           	        t        |t        t        t        t        t
        t        f      st        S t        j                  d| |        |       }  |      } 	| |      \  } } |       r t               |       |      S  |      r |      }t        | j                  |      }|t        u rt        S t         t        | j                        |            } |      r |      S |S )NzMAGIC %s %s %s)r,   r   r   r   r   r   r   rR  r  r  r   r  rl   r)  r  
r0   r@   
other_noderetr  re  rW  r  r  r  s
       r   r  z+_make_user_magic.<locals>.binary_magic_impl  s    %#udFHg!NO!!+VT5At}tU+et.&v.T0BEJJu 'ETYY.
'!!7		;7
CD$/$4|C =#=r!   c           	        t        |t        t        t        t        t
        t        f      st        S  |       }  |      } 	| |      \  } } |       r t              | |             S  |      r |      }t        | j                  |      }|t        u rt        S t         t        |      | j                              } |      r |      S |S r   )r,   r   r   r   r   r   r   rR  r   r  rl   r)  r  r  s
       r   rbinary_magic_implz,_make_user_magic.<locals>.rbinary_magic_impl  s    %#udFHg!NO!!t}tU+et.&v.|D7IJJu 'ETYY.
'!!8
K8CD$/$4|C =#=r!   c                ^    t        | |       fd}| t        u rt        t        |       yy)z
        Registers the SymNode magic method on SymInt/Float/Bool,
        and optionally registers a corresponding wrapped method on DynamicInt.
        c                     | D cg c]   }t        |t              r|j                  n|" } } t        t              |  }t        |t              rt        |t
              st        |      S |S c c}w r   )r,   r   r|  r  r   r   )r7  r  r9  attrs      r   dynamic_int_implz<_make_user_magic.<locals>.setattrs.<locals>.dynamic_int_impl(  sc    HLM1jJ7AFFQ>MDM$'#t$d+C#s#JsD,A!#&J	 Ns   %A-N)r  r   r   )	user_typer  symnode_implr  s    `  r   setattrsz"_make_user_magic.<locals>.setattrs  s2     		4.	 J&67 r!   __r
   c                   | j                   }t        ||      }t        ||      }|t        u s|t        u rt        S t        |t              r)t        |t              r|j
                  |j
                  k(  sJ t         t        | j                         ||            }|j                   j                         r |      S |S r   )	rl   r  rR  r,   r   r.   r)  r  re  )	predr   r   r  r  r  r  r  r  s	          r   sym_ite_magic_implz,_make_user_magic.<locals>.sym_ite_magic_impl9  s    		I	84I	84IN*i>.I%%9g.y'2$$	(8(889 ;GDII{;IyQRC(+(<(<(><$GCGr!   r   c                     |       rt        j                   |       |      S t         t        | j                        |            S r   )r  r   r)  r  rl   )r0   r   r  re  rW  s     r   round_magic_implz*_make_user_magic.<locals>.round_magic_implJ  s?    4 ~~l4&8'BB7WTYY7@AAr!   __r)r  z2Union[SymInt, int, SymFloat, float, SymBool, bool]r   )r  bool_becomes_int_magic_methodsunary_magic_methodsunary_nonmagic_methodsr  r   bitwise_opsreflectable_magic_methods)rW  r  r  r  r  r  origr  r  method_namer  re  r  r  r  s   `         @@@@@r   _make_user_magicr    sL    CCVHoKB //		!T< <> >"> > 8( $$bO-=>	)	)y&)FN3CT$JK	9		H 	bO-?@	7		B 	bO-=>[ %f-KbR02CD..Y#k]" 57IJ /r!   )FFr   )
__future__r   r  rz  r`  r  loggingmathoperatorr  r   r   typingr   r   r   r1  torch._logging.structuredrv  rq  r	   r
   r   r   r   r   r   r   torch._loggingr   r(   r   	getLoggerrg  rC  getArtifactLoggerr  __all__torch.typesr   r-   r    r   rn  r   r   r   r   r   r   r   r   r   r   r  r   r   r   r   r   r   r   r   r   r   r  r  r   r   r   r  rV  r  r  math_op_namesr  sym_namepriv_sym_namer  r  r   r  r  only_bool_magic_methodsr  also_bool_magic_methodsbool_magic_methodsonly_float_magic_methodsr  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r
  r  r  r  r  r  current_moduler   priv_sympy_namer  ri  r$  r)  r-  r/  invertr   r4  r1  rA  rE  rH  rK  rM  rP  sizes_strides_methodsr  r)  r   r  r  itemsrW  r  r  ry   r!   r   <module>r     sF   #        
 / 1 1  . .	 	 	 - >g!~~//*E K 1_ _D+ +. .8$	8<<$	8<<$ 
8<<$ 
8==	$
 8==$ DII$ 	(++$ TZZ$ TZZ$ H%%$ 	(++$ 	(++$ *$ 	(++$ hoo$  	(++!$" 
8<<#$$ 
8<<%$& 	(++'$( 
8<<)$* 	(,,+$, (,,-$. 8<</$0 1$2 hll3$4 X^^5$6 hoo7$8 
8<<9$: ;$< w=$> w?$@ wA$B wC$D X%%E$F 8##G$ L
   DdV}HzNMGX/56#*5-#@x H%NN8   $&<< > !6 & ,/FF  J  7<T] 2#4N X  -DdV}H""8,-
 H  "F LQ<:~'&'	8<<	8<< 
8<< 
:	
 + ! 
: < 	) + < ) % O m  m! ($. X&  1Dv&O	$	B$33BObkNOR0	1 o-0x 
8<< 	)	
 	) 	) 	) 	) 	) \ \ ! K 
8<< z  z!" z#$ 
:%& #)0  HDdV}H%nv6FGM(H 	(M>U
0EH%PPS? )&J&J#D#D.[	 >&a?H	TCn "'') #LFDVT"# *//1 +LFDVT*+IKX  +F(()))*((F6T,T)VV$[ *+ r!   