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d dlZd dlmZ d dlmZmZ d dlmZmZmZmZmZmZmZ d dlmZ d dlmZ d dlZd dlZd dlZd dl Zd dl!m"c m#Z$ d dl%m&Z& d d	l'm(Z( d d
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                  d|        Zdtdd}Zdtdd~ZdddZ	ddZ
d Z eej                  j                  j                  d=      d        Z eej                  d=      d        Z eej                  d=      d        Z eej                   j"                  d=      d        Z eej&                        d        Z ej(                  d      d        Zd Z eej.                  j                        Z eej.                  j2                        Z eej6                  j                        Z eej6                  j2                        Z e
ej<                          eej.                        d        Z eej6                        d        Z eeKj>                  d=      d        Z  eeKjB                  d=      dd       Z" eeKjF                  d=      d        Z$ eeKjJ                  d=      d        Z& eeKjN                  d=      d ddd       Z( eeKj<                  d=      d d	 	 	 	 	 	 	 	 	 dd       Z)ddZ*ddZ+ eejX                  jZ                  d=      d6d6ddd	 	 	 	 	 	 	 	 	 	 	 	 	 dd       Z, eej\                  e3j^                  =      d6d6d	 	 	 	 	 	 	 dd       Z.d Z0d Z1d Z2d Z3d Z4d Z5d Z6d Z7 e
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                        d        Z eej                        d        Zd Z eej                  j                        	 dd       Z eej$                  j                  d6Ы      Z	 eej                  j                  d6Ы      Z eej$                  d=      	 	 	 	 	 dd       Z eej                  d=      	 	 	 	 	 dd       Z
d Z eej&                  j                  d6Ы      Z eej&                  d=      	 dtd	       Z eej                  j                  d6Ы      Z eej                  d=      	 dtd
       Zd Zd ZdtddZd Z eej(                        dddd       Zd Zd Zd Zd Z eej2                  ej2                  g      dtdd6dd       Z eej6                        dtdd6dd       Zd Zed        Z eej<                  j>                  d6Ы      Z  eej<                  jB                  d6Ы      Z" eej<                  jF                  d6Ы      Z$ eej<                  dF      d        ZdpdZ% eejL                        d        Z& eejN                  d=      dpd       Z'ed        Z(ed         Z) eejT                  dF      dtd!       Z+ eejX                  gdF      d"        Z,dd#Z- eejT                  gdF      d$        Z. eej^                  ejT                  jZ                  gdFe3j`                  J      d%        Z* eejb                  ejb                  gdF      d&        Z1 eejd                  ejd                  g      dddd'       Z3 eejh                  j                        Z5 eejl                  j                        Z7 eejp                  j                        Z9 eejt                  j                        Z; eejx                  j                        Z= eejh                        dnd(       Z4 eejl                        dnd)       Z6 eejp                        d*        Z8 eejt                  d=      dtd+       Z: eejx                  d=      dtd,       Z< eej|                        dddd-       Z> eej~                        dd.       Z@ eej                  d=      dd/       ZB eej                  d=      dd0       ZD  eej                         ed1               eej                         ed2            ZG  eej                         ed3            ZI  eej                         ed4ejD                  5            ZK  eej                         ed6ejD                  5            ZM eej                  dFd78      ZN eej                  j                  d6Ы      ZO eej                  j                  d=      ddyd6d9d:       ZP eej                  j                  d=      dd;       Zfdnd<ZQdd=ZR eQej                        ZS eRej                        ZT eQej                        ZU eQej                        ZV eej                        ZW eRej                        ZX eRej                        ZY eej                        ZZ eej                  dF>      Z[ eRej                          eRej                          eej                        Z^ eej                        Z_ eej                        Z` eej                  d?@      Za eej                        Zb eej                        Zc eej                        Zd eQej                          eQej                        Zf  eej                  e3j`                  =      ef        eQej                          eQej                          eQej                          eRej                          eej                  ddFejP                  A      Zk eej                  ddFejP                  A      Zl eej                  ddFejP                  A      Zm eej                  ddFejP                  A      Zn eej                        Zo eej                        Zp  eej                        eo         eej                        ep        eej                        Zs eej                        Z^ eQej                        Zt eej                          eej                  dB@      Zv eej                          eej                  ejP                  5         eej                        es        eej                  ejP                  5        eej                  ejP                  5        eej                  ejP                  5        eej                  ejP                  5      Z| eej                  ejP                  5        eej                  ejP                  5        eQej                          eQej                           eQej                          eQej                          eQej                          eQej                          eQej
                          eQej                          eQej                          eQej                          eQej                          eQej                          eQej                          eQej                          eQej                          eQej                         ddClmZmZ dD ZeD ]S  Z eee      D ]  \  ZZZ eŐeeeeE         eee      D ]  \  ZZZ eŐeeeeE        U  eej.                  j0                  eNdF>      Z eej.                  jB                  eNdF>      Z eej.                  jZ                  eNdF>        eej6                  j0                  e,      Z eej6                  jZ                  e,        eej6                  jB                  e,      Z eej<                  j0                  e[        eej<                  jB                  e[        eej>                  j                  es        eej@                  j                  e^        eejB                  jB                  e        eejB                  j0                  e        eejB                  jD                  e        eejF                  j0                  e*      Z eejF                  jZ                  e*        eejF                  jB                  e*      Z eejL                  eY        eejN                  eS        eejP                  j0                  eo        eejP                  jB                  eo        eejR                  j0                  ep        eejR                  jB                  ep        eejT                  j0                  eo        eejT                  jB                  eo        eejV                  j0                  ep        eejV                  jB                  ep        eejX                  et        eejZ                  ev        eej\                  e      ZdF Z eejb                  j0                  ej.                  j0                  e        eejb                  jB                  ej.                  jB                  e        eejd                  j0                  ej6                  j0                  e        eejd                  jB                  ej6                  jB                  e        eejf                  j0                  ejF                  j0                  e        eejf                  jB                  ejF                  jB                  e        eejh                  j                  ej\                  j                  e       dG Z eejl                  eN        eejn                  e_        eejp                  e`        eejr                  ea        eejt                  eb        eejv                  ec        eejx                  ed        eejz                  e,        eej|                  jZ                  e*        eej|                  j~                  e+        eej                  ek        eej                  el        eej                  em        eej                  en        eej                  e[        eej                  eW        eej                  eX         eej                        e_         eej                        e`         eej                        eb         eej                        ec         eej                        ed        eej                  ej                          eej                  ej                          eej                  ej                          eej                  ej                          eej                  ej                          eej                        dndH       Z eej                  j                        dI        Z eej                  j                        dJ        Z eej                        dK        Z e:j                         D ]  \  ZאZ  e e;e׫            eث         eej                        dL        Z eej&                        dM        Z eej                  j                  j                        dN        Z eej                  j                  j                        dO        Z eej                  j                  j                  j                        dP        Z eej                  j                  dQ      r; eej                  j                  jN                  j                        dR        Z eej                  j                  j                        dddS       Zd dTlmZ  e
e        ee*      dU        Z eej                  j                  j                  d=      dV        Z eej                  j                  j                  d=      dpdW       Z  eej                  j                  j                  d=       ej                  edFX              eej                  j                  j                  d=      ddY       Z eej                  j                  d=      ddZdd[       Z ee(d=      	 	 	 	 dd\       Z eej                  j                  j                  j                        d]        Z eej                  j                  j                  d=      d^        Zdd_lmZ  e         eeKj                  d=      d`        ZddalImZ  eHe       ddblImZ  ej                           ej                          ddclImZ  ej                          dddlImZ  ej                          ej                  dde       Z y(      )annotationsN)defaultdict)IterableSequence)AnyCallablecastOptionalTYPE_CHECKINGTypeVarUnion)	ParamSpec)patch)counters)associative_scan_op)triton_kernel_wrapper_mutation)get_layout_constraint_tag)canonicalize_dimcanonicalize_dimscheckdtype_to_typeelementwise_dtypesELEMENTWISE_TYPE_PROMOTION_KINDget_computation_dtypeis_boolean_dtypeis_float_dtypeis_integer_dtypeNumber)magic_methodsmethod_to_operator)free_unbacked_symbolshas_free_unbacked_symbolsresolve_unbacked_bindings)
OrderedSet)CeilDivFloorDivIdentityModularIndexing   )import_submodule   )configinductor_primsirtest_operators)decompositionsget_decompositions)BaseView	DtypeView
ExpandViewIndexingConstantIRNode	is_triton
MutableBoxOnlineSoftmaxReductionops_wrapperPermuteView	Pointwise	ReductionShapeAsConstantBufferSqueezeView	TensorBoxvalidate_irView)ceildivdecode_device
is_dynamicis_gpuis_pointwise_useis_view,needs_fallback_due_to_atomic_add_limitationspad_listlike#register_op_dtype_propagation_rules#register_op_requires_libdevice_fp64sympy_productuse_scatter_fallback)opsV)ReductionType_T_Pztorchvision::roi_alignzaten::index_addz8dict[Union[Callable[..., Any], str], Callable[..., Any]]	loweringsz9dict[torch._ops.OpOverload, Optional[Callable[..., Any]]]_maybe_layout_constraintsz2dict[torch._ops.OpOverload, torch._ops.OpOverload]inplaceable_foreach_opsc                     t         j                  j                  j                  D ]7  } | j                  D ]&  }|j                  dk(  r|j
                  t        v r%  y 9 y)Ncall_functionTF)rP   graphcurrent_nodeusersoptargetforeach_ops)nodeusers     R/var/www/html/engine/venv/lib/python3.12/site-packages/torch/_inductor/lowering.pycur_node_has_non_foreach_usersrb      sS    $$** JJ 	DGG.DKK;4N	
     c                f   t        t              }d}t        |       D ]  \  }}t        |t              sd}|f}t        |  xs t        j                  }d }|D ].  }t        |t              s|j                  j                         } n |J d       |r|\  }|||f   j                  ||f        |S )NFTz.foreach op should have at least one tensor arg)r   list	enumerate
isinstancer   rE   r,   #combo_kernel_foreach_dynamic_shapesr@   data
get_deviceappend)	arg_pairsoutunpack_argsiargsuse_foreachdevicets           ra   group_foreach_argsrt      s    
d
CKY' 54$)K7DD!!OV%O%O 	  	A!Y'**,	 !S#SS!GTV[!"))1d)45  Jrc   c                    t        | t        j                  j                        syt	        | d      x}rt        |      S | t        v r	t        |    S y)zHGet layout constraints. Returns None if there are no layout constraints.NF)with_default)rg   torch_ops
OpOverloadr   tag_to_layout_constraintrU   )fnmaybe_layout_tags     ra   maybe_layout_constraintsr}      sO    b%**//04ReLLL'(899	&&(,,rc   c                |   | t         j                  j                  j                  k(  rt        S | t         j                  j                  j
                  k(  rt        S | t         j                  j                  j                  k(  rt        S | t         j                  j                  j                  k(  ry t        d|        )NzUnknown layout constraint tag: )rw   _CTagneeds_exact_stridesconstrain_to_fake_tensorsneeds_contiguous_stridesrequire_contiguous_stridesneeds_fixed_stride_orderconstrain_to_fx_stridesflexible_layoutAssertionError)tags    ra   rz   rz      s    
ehhll...((
ehhll333))
ehhll333&&
ehhll***
:3%@
AArc   c                $    | st        d|       y )Nzinductor does not support NotImplementedErrorcondmsgs     ra   
assert_nyir      s    !$>se"DEE rc   c                N    t         t        t        t        t        f      r D cg c]  }t        |       c}S t        j                          t         t        j                  j                        r-t        j                   fd j                         D               y y c c}w )Nc              3  6   K   | ]  }t        |        y wN)getattr).0overloadr{   s     ra   	<genexpr>z,add_needs_realized_inputs.<locals>.<genexpr>   s      %
&.GB!%
   )rg   re   settupler$   add_needs_realized_inputsneeds_realized_inputsaddrw   rx   OpOverloadPacketupdate	overloads)r{   xs   ` ra   r   r      sz    "tS%45689)!,99b!"ejj112$$ %
24,,.%
 	
 3 :s   B"c                    t        | t        j                  j                        r)| j	                         D ]  }|t
        t        | |      <    y |t
        | <   y r   )rg   rw   rx   r   r   rU   r   )r{   
constraintr   s      ra   add_layout_constraintr      sL    "ejj112 	JH?I%gb(&;<	J )3!"%rc   )r   r+   r)                     	   
         c                b    t        | t              s| S | t        v sJ d|  d       t        |    } | S )Nzid z missing from DTYPE_ID_LOOKUP)rg   intDTYPE_ID_LOOKUPdtypes    ra   decode_dtyper      s=    eS!O#Os5'1N%OO#E"ELrc   c                    t        | t              r4t        | j                               xs t	        | j                               S t        | t
        j                        r| j                  du S t        | t              S )NT)	rg   r@   r   	get_dtyper   sympyExpr
is_integerr   r   s    ra   is_integer_typer     sX    !Y.Q2B1;;=2QQ	Auzz	"||t##!S!!rc   c                t    t        | t              rt        | j                               S t        | t              S r   )rg   r@   r   r   boolr   s    ra   is_boolean_typer     s*    !Y..!T""rc   c                \    d }|D cg c]
  } ||       }}t        |d| i\  }}|S c c}w )Nc                    t        | t        t        j                  f      r| S t	        | j                               }t        j                  dg|z  | j                               S )Nr+   r   )	rg   r   r   Basiclenget_sizerw   zerosr   )inpdims     ra   construct_inputz+get_promoted_dtype.<locals>.construct_input  sG    cFEKK01Jclln%C;;sSy@@rc   type_promotion_kind)r   )r   rp   r   arginps_r   s          ra   get_promoted_dtyper     s@    A -11SOC 1D1!4Q=PQHAuL 2s   )c                0   t        | t        t        f      s| g} nt        |       } t        |       D ]b  }t        |t        j                  j
                        s(|j                         D ](  }t        ||      }|t        vs| j                  |       * d | S r   )
rg   re   r   rw   rx   r   r   r   rT   rk   )aten_fnr{   r   other_fns       ra   get_overloadsr   %  s    ge}-)w-7m -b%**556LLN -"2x09,NN8,-- Nrc   c                    t        | t        j                  j                        r|| j                  v S t        | t        j                  j
                        r|| j                         v S yNF)rg   rw   rx   r   _qualified_op_namery   name)r\   	namespaces     ra   in_namespacer   5  sO    "ejj112B1111	B

--	.BGGI%%rc   c           	     $   t        | j                  t        j                        rt	        | j                               r| S | j                         D cg c]+  }t        j                  j                  j                  |      - }}| j                         }|u|j                  dk(  rf||k7  rat        |      dk(  st        |      dk(  rE|d   dk(  r=t        t        j                  t        j                  j!                  | |d                  S | S c c}w )zB
    Copy cpu scalar if doesn't not match with given `device`
    cpur   r+   F)rg   ri   r.   ReinterpretViewr"   r   rP   rY   sizevarssize_hint_or_throwrj   typer   r@   
StorageBox
DeviceCopycreate)r   rr   ssize
cur_devices        ra   maybe_copy_cpu_scalarr   =  s     affb0015N	

6 <=JJLIqAGG//2IDIJOOu$& Y!^D	Q47a<r}}';';Az5'QRSSH Js   0Dc           	         t               D cg c]  \  }}t        |t              s| }}}j                         D 	cg c]  \  }}	t        |	t              s| }
}}	|s|
s fS |s|r|rt        j
                  nl D cg c]0  }t        |t        t        j                  f      st        |d      r|2 }}|j                  d j                         D               t        |d|i|r |d      n|
d      j                         |D ]  }t         |          |<    |
D ]  }t        |         |<    fd} D cg c]
  } ||       c} j                         D 	ci c]  \  }}	| ||	       c}	}|r1t        t!        t#        j$                   fd|D        fd|
D                     }t!        |d   j'                               }t)        ||dt+        |             D ]
  \  }}| |<    t)        |
|t+        |      d       D ]
  \  }}||<    t-        t+                     D ]<  }t         |   t.        j0                        s!t3        j4                   |   |       |<   > D ]<  }t        |   t.        j0                        s!t3        j4                  |   |      |<   >  fS c c}}w c c}	}w c c}w c c}w c c}	}w )	zB
    Transforms arguments for broadcasting and type promotion
    r   c              3  :   K   | ]  }t        |d       s|  yw)r   N)hasattr)r   as     ra   r   z!transform_args.<locals>.<genexpr>m  s     !T7@S!!Ts   r   r   c                    t        | t              rt        |       S t        | t        j                        r"t        j                  | j
                        S | S )Nvaluer   rr   )rg   r@   to_dtyper.   Constantr   )r   rr   r   s    ra   promoteztransform_args.<locals>.promote~  sD    #y)U++C-{{%OO
rc   c              3  (   K   | ]	  }|     y wr    )r   ro   rp   s     ra   r   z!transform_args.<locals>.<genexpr>  s     3T!W3   c              3  (   K   | ]	  }|     y wr   r   )r   kkwargss     ra   r   z!transform_args.<locals>.<genexpr>  s     71VAY7r   N)rf   rg   r@   itemsrw   r   r   r   r   r   extendvaluesr   rj   r   broadcast_tensorsre   	itertoolschainr   zipr   ranger.   r   r4   r   )rp   r   	broadcastr   convert_input_to_boolro   r   args_indicesr   vkwargs_indicesr   promoting_argsr   broadcastedr   rr   r   s   ``              @@ra   transform_argsr  Q  s    #,D/N$!QZ95MANLN$*LLNODAqjI6NaONOV|3 JJE
 a&%++!6771g;N N  !!!TV]]_!TT&$7E &2Da!vnQ>O7P
*, 	  	=A+DGV<DG	=   	AA-fQi@F1I	A	 %))q
),2LLN;DAq!WQZ-;'3l377
 KN++-.k2EC4E&FG 	DAqDG	C4E4G(HI 	DAqF1I	 s4y! 	;A$q'2;;/$++DGT:Q	;  	?A&)R[[1&--fQi>q		? <I OO> *;s(   KKKK
5KK3Kc                    t        j                        fd       }t        |       }t        j	                  |       t
        j	                  t        j                  ||             |S )a  
    Add a foreach lowering to lowerings dict.

    Arguments:
        aten_fn: torch.ops.aten.* fn we are lowering
        decomp_fn: alternate implementation on our IR
        broadcast: True to apply broadcasting to tensor inputs
        type_promotion_kind: kind of type promotion applied to tensor inputs, `None` means no type promotion
        convert_input_to_bool: some logical ops require inputs are converted to bool
    c                 N    t        |       dk  sJ  | i |}t        |       |S )Nr)   )r   rA   )rp   r   rm   	decomp_fns      ra   wrappedz+_register_foreach_lowering.<locals>.wrapped  s/    4yA~~((C
rc   )	functoolswrapsr   r^   r   rT   dictfromkeys)r   r  r  aten_fnss    `  ra   _register_foreach_loweringr    sX     __Y   W%Hx T]]8W56Nrc   c                     t        j                         fd       }t                |j                  t        j                   |             |S )a  
    Add a lowering to lowerings dict

    Arguments:
        aten_fn: torch.ops.aten.* fn we are lowering
        decomp_fn: alternate implementation on our IR
        broadcast: True to apply broadcasting to tensor inputs
        type_promotion_kind: kind of type promotion applied to tensor inputs, `None` means no type promotion
        convert_input_to_bool: some logical ops require inputs are converted to bool
    c                 l   t        |       } t        |      }d}t        |       dk(  r)t        | d   t         t        f      rd}t        | d         } t        d D              s't        d |j                         D              rJ d       t        | |      \  } }|r| g}  | i |}t        |       |S )NFr+   r   Tc              3  H   K   | ]  }|t         v xs t        |d         yw)_c10d_functionalN)	fallbacksr   )r   r{   s     ra   r   z6_register_lowering.<locals>.wrapped.<locals>.<genexpr>  s)      
JLR9_DR1C DD
s    "c              3  &   K   | ]	  }|d k(    yw)rm   Nr   r   r   s     ra   r   z6_register_lowering.<locals>.wrapped.<locals>.<genexpr>  s     =!1:=   zout= ops aren't yet supported)
re   r
  r   rg   r   allanykeysr  rA   )	rp   r   unpackedrm   r   r   r   r  r   s	       ra   r  z#_register_lowering.<locals>.wrapped  s    t*!%ft9>ja4-@HQ=D 
PW
 
 =v{{}== /= &&)%8:O
f 6D((C
rc   )r  r	  r   r   r
  r  )r   r  r   r   r   lowering_dictr  s   `````  ra   _register_loweringr    sJ    & __Y  : G$Gw89Nrc   Fc                @    t        j                  t        | ||||      S )z+
    Shim to support decorator syntax.
    )r   r   r   r  )r  partialr  )r   r   r   r   r  s        ra   register_loweringr    s)     /3# rc   c                   g }t        j                  t        |       t        |      t        j                  j
                        D ]  \  }}t        j                  j                  j                  |      r|j                  |       Bt        j                  j                  j                  |      r|j                  |       }t        j                  j                  j                  ||       t        t        j                  |      j                        t        t        j                  |      j                        k  r|j                  |       |j                  |        t        t        |            S )z
    Broadcasting logic based on symbolic shapes.

    We give the shapes 0 and 1 concrete values, while all other shapes
    are symbolic sympy formulas.
    )	fillvalue)r   zip_longestreversedr   SOnerP   rY   r   is_size_one_or_falserk   check_equalsr   expandfree_symbolsr   )r   boutputr   ys        ra   broadcast_symbolic_shapesr,  	  s     F%%hqk8A;%''++V 
!177003MM!WW2215MM!GG))!Q/5<<?//03u||A7S7S3TTa a 
! &!""rc   c                V   |	|J d       ||t         j                  }t        d | D              s| S t        d | D              r*|xs t	        | d|ifd}| D cg c]
  } ||       c}S t        d | D              }g }| D ]  }t        |t        t        f      ro|j                  t        j                  t        j                  ||j                         |j                               t!        |j#                                            t        |t$        j&                        rf|j                  t        j                  t)        ||j                         |j                               t!        |j#                                            	|j                  |        |S c c}w )	NzEonly one of override_return_dtype or type_promotion_kind may be givenc              3  f   K   | ])  }t        |t        j                  t        t        f       + y wr   )rg   r   r   r   floatr  s     ra   r   z$promote_constants.<locals>.<genexpr>'  s"     HAz!ekk367H   /1c              3  f   K   | ])  }t        |t        t        t        j                  f       + y wr   )rg   r   r/  r   r   r  s     ra   r   z$promote_constants.<locals>.<genexpr>)  s"     
D:a#uekk23
Dr0  r   c                    t        | t        j                        r!t        j                  | t        d             S t        j                  | t        d             S )Nindexr   rr   r   )rg   r   r   r.   r5   rD   r   r   r   s    ra   
const_funcz%promote_constants.<locals>.const_func.  sJ    !U[[)**5t1D  {{%d@STTrc   c              3  l   K   | ],  }t        |t        t        t        j                  f      s)| . y wr   )rg   r@   r4   r.   r   r  s     ra   r   z$promote_constants.<locals>.<genexpr>7  s$     WA:a)Z1U#VaWs   *44r   r3  )r   DEFAULTr  r  r   nextrg   r   r/  rk   r4   r   r.   r   r   get_device_or_errorre   r   r   r   r5   )inputsoverride_return_dtyper   r6  r   exrm   r   s          @ra   promote_constantsr>    s    (,?,G OG $)<)D=EEHHH

DV
DD% 
);*
)<*
	U (..!
1..	WW	WB
C a#u&JJ!!KKr||~b>T>T>V '	 5;;'JJ!!$r||~b>T>T>V '	 JJqM), J3 /s   F&c                .     d dd fd}|S )Nalphac           	       	
 t        d D              r	rJ   S t              r%| '| dk7  r"t              t        d   |       d<   n| J D cg c]  }|j	                          c}	d   j                         xs d   j                         dd  D ]`  }t        |t        j                        rt              t        |j                               k(  rDJ d d d|j                                  t        j                  t        j                  f
t        j                  d uxr t!        t        j                  dd       d uxrb t        j                  j"                  j$                  d uxr: t        j                  j"                  j$                  j'                  dd	      xr 
v 	
fd
}sSd }D ]7  }t)        |j+                         j,                        s'|j+                         } n |sd   j+                         }xs }t/        j0                  ||      S c c}w )Nc              3  V   K   | ]!  }t        |t              xr t        |       # y wr   rg   r6   r7   )r   r   s     ra   r   z0make_pointwise.<locals>.inner.<locals>.<genexpr>[  s(      /
;>JsF#6	#6/
   ')r+   r   zndim mismatch  rZ   low_precision_pointwise_barrierFc                
   t        |       t              k(  sJ d|  d        t        j                  k(  r D cg c]
  } ||        c} S g }t              D ]e  \  }} ||       }
|   j	                         }r2|v r.t        j                  ||d      }t        j                  ||      }|j                  |       g  	| }r.t        j                  |d      }t        j                  |      S |S c c}w )Nzwrong ndim rG  F)use_compute_types)r   rw   r   rf   r   rO   r   rk   )r4  loadinputs_loaded	inp_indexrm   	inp_dtypedowncastr   emulate_precision_castsr{   r;  loaders	low_pr_fpoverride_fn_when_input_boolrangess          ra   inner_fnz/make_pointwise.<locals>.inner.<locals>.inner_fn}  s
   u:V,LE7!F8.LL,

"'B'N2W4UTT%[4UVV "'0'9 .OItu+C &y 1 ; ; =I.9	3I#&<<YRW#X!ll8Y?!((-. -(*  #||C%PH<<%88
# 5Vs   D rr   r   rU  rT  )r  r>  re   mulmake_loaderr   r   rg   r.   BaseConstantr   rw   bfloat16float16rP   rY   r   rZ   metagetrF   rj   r   r<   r   )rA  r;  r   otherrU  rr   ro   r   rP  rQ  rR  rT  allow_alphar{   override_devicerS  r<  triton_fallbacks    `     @@@@@ra   innerzmake_pointwise.<locals>.innerZ  sD   &3 /
BH/
 ,
 #"?"F++"6+@A UaZf U3r
= =,23q1==?3##%%>)<)<)>ABZ 	AEeR__5V I : At1VHAenn.>-?@A 	A ^^U]]3	GG4 #6dB#$$))5# $$))--.OQVW# " 	 	 	, F !,,.--.\\^F --/ *F	
 	
m 4s    I)r;  r@   r   )r{   r<  r`  rS  r_  ra  rb  s   `````` ra   make_pointwiserc  R  s     )- I
 I
V Lrc   c                     ddd fd}|S )Nr+   r@  c                   t        t        j                  j                  j                        dk(  xs6 t        j                  j                  j
                  t        v xs
 t               }d }|D ]  }t        |t        t        f      s|} n |J d       g }|D ]H  }t        |t        t        f      s|j                  |gt        |      z         8|j                  |       J t        t        |       }d gt        |      z  }|j                         D ]  \  \  }}	}
g }|
D ]~  \  }}r	 |d| i}n | }|||<   t        j                  j                  |t         j"                        sJ|	sM|sP|j%                          |j                  |j'                                 |st        j                  j)                  |        t+        d |D              sJ |S )Nr   z1at least one input must be a list to a foreach oprA  c              3  $   K   | ]  }|d u 
 y wr   r   r  s     ra   r   z8make_foreach_pointwise.<locals>.inner.<locals>.<genexpr>  s     2Q1D=2   )r   rP   rY   rZ   r[   r]   inplace_foreach_opsrb   rg   re   r   rk   rt   r   r   has_featureBackendFeatureFOREACHrealizeget_operation_nameregister_operation_listr  )rA  r;  realize_outputsa_list_inputinputbroadcast_inputsgroupsoutputsrr   rq   groupoperation_list
output_indrp   r*  r_  pw_fns                  ra   rb  z%make_foreach_pointwise.<locals>.inner  s   $$**+q0 0ww##**.AA0-/ 	  	E%$/$	 ' 	
?	
'
  	/EedE]3 ''#l2C(CD ''.		/ $C)9$:;&3|,,,2LLN 	@(!V[5(*N G "D66F"D\F&,
# GG''0F0FG#'NN$"))&*C*C*EF#G& //?-	@0 2'2222rc   )r;  zlist[list[TensorBox]]r   )rx  r_  rb  s   `` ra   make_foreach_pointwisery    s    45 4 4l Lrc   c                    | j                         k(  r|rt        |       S | S fd} t        |      |       S )Nc                4    t        j                  |       S )N)	src_dtype)rO   r   )r   r   r|  s    ra   	_to_dtypezto_dtype.<locals>._to_dtype  s    ||Au	::rc   r<  )r   clonerc  )r   r   copyr}  r|  s    `  @ra   r   r     sE     IEuQx&Q&; B>)5A!DDrc   r   c                   ddl m} |}| j                  } ||t        j                        }t        j
                  |      5   |j                  |  ddd       |j                  }|sJ t        |      }dgt        |      z  }	|j                         D ]  \  \  }
}}g }|D ]k  \  }}||	|<   t        j                  j                  |
t        j                        s:|s=|j                          |j                  |j!                                m |s~t        j                  j#                  |        t%        d |	D              sJ |	S # 1 sw Y   xY w)aI  
    This lowers an invocation of foreach_map
    The way this works is that an arbitrary N-arg func is provided by the user, looped over by the
    polyfill with the same semantics as a foreach op (a loop applying an n-ary function to n args)
    and then traced into a subgraph by dynamo.
    This code allows us to inline the subgraph into the main graph lowering using the PontwiseSubgraphLowering.
    The graph outputs represent the vertically fused sequence of ops, and then register_operation_list
    below registers the buffers as horizontally fuseable in the scheduler.
    r+   )PointwiseSubgraphLowering)root_graph_loweringNc              3  $   K   | ]  }|d u 
 y wr   r   r  s     ra   r   z_foreach_map.<locals>.<genexpr>  s     .q}.rg  )subgraph_loweringr  graph_modulerP   rY   set_graph_handlerrungraph_outputsrt   r   r   ri  rj  rk  rl  rk   rm  rn  r  )subgraphrp   r   r  r;  gmpw_subgraphsub_outputsrs  rt  rr   rq   ru  rv  rw  r*  s                   ra   _foreach_mapr    sA    =F			B+BAGGLK	
		[	) ! ! ++K;,Ffs;''G(. <$u$& 	C 
"(GJww""6>+A+AB{ %%f&?&?&AB	C GG++N;< .g....N3! !s   E		Ec                @   |j                   s| j                         j                   rk| j                         r/t        | |      }t        j
                  j                  ||        |S  t        t        j                  j                  d      | |      S t        | |d      S )Nr   Fadd_to_fallback_setTr  )
is_complexr   r   
empty_liker.   InplaceCopyFallbackr   fallback_handlerprimsconvert_element_typedefaultr   )r   r   dsts      ra   _convert_element_typer    s    1;;=33::< Qe,C""))#q1J#**22  Au4((rc   r  c                  | j                         }||k(  r|rt        |       S | S d } ||      } ||      }||k7  r* t        t        j                  j
                        | |      S t        t        j                  | |            S )Nc                    | j                   rt        j                  |       j                  S t        j                  |       j                  S r   )is_floating_pointrw   finfobitsiinfor   s    ra   _get_primitive_bitwidthz1to_dtype_bitcast.<locals>._get_primitive_bitwidth1  s5    "";;u%***;;u%***rc   )	r   r  r  atenviewr   r@   r3   r   )r   r   r  x_dtyper  src_bitsdst_bitss          ra   to_dtype_bitcastr  ,  s~    kkmG%uQx&Q&+ 'w/H&u-H80		0E::))!U344rc   c                &   |j                   s| j                         j                   r`t        j                  t        j
                  j                  t        j                  j                  j                  j                  | |            S t        | |      S r   )r  r   r@   r   r.   ComplexViewrw   rO   r  r  r   r  r5  s     ra   _view_dtyper  @  se    1;;=33NN!!%)).."5"5";";QF
 	
 Au%%rc   r  non_blockingc                   t        |      }| j                         |k(  r|rt        |       S | S t        j                  t
        j                  j	                  | ||            S r   )rD   rj   r  r@   r   r.   r   )r   rr   r  r  s       ra   	to_devicer  I  sO    6"F||~uQx&Q&BMM00FLIJJrc   c                     t        | |d|      S )NTr  )r  )r   rr   r  s      ra   _device_putr  P  s    QTEErc   Tc	                   |xs | j                   }t        |      }	t        |||       |t        |      }t        |	||||      }	 t	        | |||      |	      }	t        t        |      r" t	        t        t        |      d|      |	       |	S )z3A pointwise function that maps ops.{name} to inputsN)r<  rS  r_  ra  )r   r   r   )r   r   )__name__r:   rK   rc  r  r   r  r   )
r   r   r   r   r   r<  rS  r_  ra  r{   s
             ra   register_pointwiser  U  s     #7##D	T	B'!#8 #.&12M&N#	
3$?'
B
	/3	

 	

B ud	
E4  $"7	
 		
 Irc   c                 .   d} t        d      fd}fd}t        |      t        |t        j                        gfd} t	        t
        j                        |      }t        t        |       r! t	        t        t        |       d      |       |S )z2A pointwise function that maps ops.frexp to inputsfrexpc                      | i |d   S Nr   r   rp   r   r  s     ra   frexp0zregister_frexp.<locals>.frexp0      d%f%a((rc   c                      | i |d   S Nr+   r   r  s     ra   frexp1zregister_frexp.<locals>.frexp1  r  rc   r~  c                 0     d   | i | d   | i |fS Nr   r+   r   )rp   r   pw_fnss     ra   r{   zregister_frexp.<locals>.fn  s.    vay$)&)96!9d+Ef+EEErc   Nr  )
r:   rc  rw   int32r  r  r  r   r  r   )r   r  r  r{   r  r  s       @@ra   register_frexpr    s    D E)) 	vvU[[AF
F
	




B ud	
E4  $	
 	 Irc   c                8    t        ||      }t        | |      }|S )Nr_  )ry  r  )r   pointwise_lowering_fnr_  r{   s       ra   register_foreach_pointwiser    s"    
 
  5;	OB	#GR	0BIrc   )r   r   c           
        d }t        |t        t        f      r t        |      |      }t        |t        t        f      r t        |      |      }| ||g}t	        |d   |d   t
        j                        }t        |      D cg c]  \  }}t        |t              s| }}}t        |t        |D cg c]  }||   	 c}       D ]
  \  }}|||<    t        t        |            D ]Y  }t        ||   t        j                        s!t        j                   ||   t#        ||d      j%                                     ||<   [  t'        ||      |d   t)        |d   |      t)        |d   |            S c c}}w c c}w )Nc                 &    t        j                  |  S r   )rO   whererp   s    ra   r{   zwhere.<locals>.fn  s    yy$rc   r+   r)   r  r   r~  )rg   r/  r   constant_liker   r   r8  rf   r@   r   r   r   r   r.   r   r4   r   re   r   rc  r   )	r   r   r)  r{   rp   r   ro   r   indicess	            ra   r  r    so     !eS\"M!Q!eS\"M!Q!Q<DQa.M.U.UE 't_ITQ
1i0HqIGIG.'0JQa0JKL 1Q3t9 Td1gr{{+ ''Qd71:6F6O6O6Q1RSDGT ;>"E:Q$q'5)8DGU+C  J0Js   E9 E96E?c                    t        |       dk(  r$t        | d   t        t        f      rt	        | d    S t        j                  t        | D cg c]  }|j                          c}g       }g }| D ]b  }|j                         }t        |      t        |      k7  st        d t        ||      D              rt        ||      }|j                  |       d |S c c}w )Nr+   r   c              3     K   | ]Z  \  }}t         j                  j                  j                  |      t         j                  j                  j                  |      k7   \ y wr   )rP   rY   r   r%  r   r   r)  s      ra   r   z$broadcast_tensors.<locals>.<genexpr>  sP      ,
 1 GG11!4ww44Q78,
s   A A")r   rg   re   r   r   r  reducer,  r   r  r   r'  rk   )r;  r   r]   rt  sizess        ra   r   r     s    
6{aJvay4-@ &),,(//!&#AQAJJL#A2 F G 	

u:V$ ,
 E6*,
 )

 q&!Aq	 N $Bs   C
c                    | S r   r   r   s    ra   nopr    s    Hrc   
lift_freshc                   t        | t              sJ |(t        t        j                  | j                              S t        |t
        t        j                  f      r)t        j                  j                  j                  |      nt        d |D              }t        t        | j                               |      }t!        t        |t              s|fn|      }g }t#        | j                               D ]X  \  }}||v r>t        j                  j                  j%                  t        j&                  |d            rH|j)                  |       Z || j                         k7  rt+        | |      S | S )Nc              3  n   K   | ]-  }t         j                  j                  j                  |       / y wr   )rP   rY   r   	guard_intr   ds     ra   r   zsqueeze.<locals>.<genexpr>  s%     >Q177##--a0>s   35r+   )rg   r@   r?   r   ri   r   r   r   rP   rY   r   r  r   r   r   r   r$   rf   guard_or_falseEqrk   r  )r   r   dims	new_shaper  r   s         ra   squeezer    s   a###
{++AFF344 cC,- 	
""3'>#>> 
 C

-s
3CJsE$:sfDDI!**,'  1T	agg..==ehhq!nMQ 
 "+ajjl!:49AArc   c                ,    t        t        | |            S r   )r  r  )r   r   s     ra   squeeze_copyr    s    C!!rc   c                    t        | |      }t        | t              sJ t        |t              sJ |j                  | _        | S r   )r  rg   r@   ri   r   r   vals      ra   squeeze_r    s=    
!S/Ca###c9%%%XXAFHrc   c                    t        |       rt        | dt        j                        S t	        d      } t        |t        j                        |       S )NFr   isinfr~  r   	full_likerw   r   r:   rc  r   r{   s     ra   r  r  
  ?    qE44	W	B?>"EJJ?BBrc   c                    t        |       rt        | dt        j                        S t	        d      } t        |t        j                        |       S )NFr   isnanr~  r  r  s     ra   r  r    r  rc   c                f    t        |       rt        |       S t        d      } t        |      |       S )Nceilr   r  r:   rc  r  s     ra   r  r    s/    qQx	V	B>"a  rc   c                f    t        |       rt        |       S t        d      } t        |      |       S )Nfloorr  r  s     ra   r  r  "  /    qQx	W	B>"a  rc   c                f    t        |       rt        |       S t        d      } t        |      |       S )Nroundr  r  s     ra   r  r  *  s/    qQx!!~b!!$$rc   c                f    t        |       rt        |       S t        d      } t        |      |       S )Ntruncr  r  s     ra   r  r  3  r  rc   c                   t        | g      \  } t        | t        j                        rt	        j
                  | t        |            S t        | t              sJ t        |t        t        f      sJ t        | j                               t        |      k(  r| S t        | j                               st        j                  j                  j                  t        | j                                     }|dkD  rOt        |      sD| j!                  t        j                  j                  j                  t        |            |z         t        t	        j
                  | j"                  t        |                  S r  )r>  rg   r.   rY  r4   r   r   r@   re   r   r!   rP   rY   r   r   rM   
mark_reuseri   )r   r  x_size_products      ra   r'  r'  ;  s   aS!DQ!R__%  E%L11a###edE]+++QZZ\eEl* .))<<!**,'
 A&;E&BLL  33M%4HI!" Z&&qvvuU|<==rc   c                    t        |      }|D ]  }d||<   	 | }t        |      D ]  \  }}|dk7  st        ||      } t        ||      S NrF  )re   rf   	unsqueezer'  )r   shapebroadcast_dimensionsr   broadcast_dimensionr   idxr   s           ra   broadcast_in_dimr  V  sf    UA3 $!#
$ 	
AA, "Q7!S!A" !Urc   c                6    t        | |j                               S r   )r'  r   )r   r+  s     ra   	expand_asr  d  s    !QZZ\""rc   c                j   t        | j                               t              t              kD  rKt        j                  j
                  gt              t              z
  z  z   t        | t                    } t              t        | j                               k(  sJ t        | j                               }d}t        t                    D ]  }|   dk(  rd}||   |   z  ||<    |r*t        || j                         | j                               S t        d t              D              rt        t        | |            S fd}t              st        |      s{t         j"                  j$                  j'                  t)                    }|dkD  rD| j+                  t         j"                  j$                  j'                  t)        |            |z         | j-                         t/        j0                  | j                         | j                         |t        |            S )NFr   Tr   rr   c              3  :   K   | ]  \  }}|d k(  xs |d k(    ywr+   Nr   r  s      ra   r   zrepeat.<locals>.<genexpr>{  s$     
A$!QAFa1f
A   c                   t        |       t              k(  sJ t        |       } t        t                    D ]G  }|   dk7  s|   dk(  rt        j                  j
                  | |<   2t        | |   d|         | |<   I  |       S r  )r   re   r   r   r#  Zeror(   )r4  ro   old_sizerepeatsx_loaders     ra   rU  zrepeat.<locals>.inner_fn  s    5zS\)))Us7|$ 	IAqzQA;!#$ww||E!H.uQxHQKHE!H	I rc   rV  )re   r   r   r   r#  r$  r  r   emptyr   rj   r  r   r  r'  r!   rP   rY   r   r   rM   r  rX  r<   r   )	r   r  new_sizezero_tensorro   rU  old_size_productr  r  s	    `     @@ra   repeatr  i  s   AJJL!H
7|c(m#GGKK=CL3x=$@AHLDN#w<3qzz|,,,,AJJL!HK3w<  /1:?KqkGAJ./
 XQ[[]1<<>JJ

A#gx*@
AAVAx())	 !*3H3R77++>>}X?VWa LL  33M(4KL#$
 }}H||~kkmH~	 rc   c                T    t        t        j                  | j                  |            S r   )r@   rB   r   ri   )r   r  s     ra   r  r    s     T[[/00rc   c                    t        | t              sJ t        |t        t        f      sJ t        t	        j
                  | j                  t        |                  S r   )rg   r@   re   r   r;   r   ri   )r   r  s     ra   permuter    sF    a###dT5M***[''d<==rc   c           
         t        | t              sJ t        | |d      }t        t        j                  j                  | j                  |||||            S )Nr   clamp)rg   r@   _validate_dimr.   	SliceViewr   ri   )r   r   startendstepr  s         ra   slice_r     sK    a###
3
"CR\\((eS$e(TUUrc   c                   t        | t              r>t        | j                  t        j                        r| j                  j                         } | j                          t        j                  |       st        d|  d      t        j                  |       \  }}t        j                  |j                  |j                  |D cg c]  }t        j                  |       c}|D cg c]  }t        j                  |       c}t        j                  |xs d            }t        t        j                  ||            S c c}w c c}w )Nzunrealized as_strided(z, ...)r   ri   layout)rg   r@   ri   r.   r2   unwrap_viewrl  is_storage_and_layoutr   as_storage_and_layoutFixedLayoutrr   r   r   r'  r   )r   r   stridestorage_offsetstorage
old_layoutr   
new_layouts           ra   
as_stridedr-    s    !YJqvvr{{$CFF IIK##A&!$:1#V"DEE2215GZ"&'Qa'"()Qa)^(q)J R''WZHII	 	()s   E&Ec                d    t        | t              sJ t        | |||      j                  | _        | S r   )rg   r@   r-  ri   )r   r   r(  r)  s       ra   as_strided_r/    s/    a###48==AFHrc   c                4    t        | |||      }t        |      S r   )r-  r  )r   r   r(  r)  results        ra   as_strided_copyr2    s    48F=rc   c                    g d} D ]1  }j                  |||j                            z   f       d   d   }3  D cg c]  }|j                          c} fd}t         d   j                               }d   d   |<   t	        j
                   d   j                          d   j                         ||      S c c}w )Nr   rF  c           	       
 t        j                  |    t        j                        }g }g }t	        t                    D ]?  

dk(  r$t        j                  dt        j                        n)t        j                  
   d   t        j                        }t        j                  
   d   t        j                        }t        j                  ||      }t        j                  ||      }
dk(  r|}n*
t              dz
  k(  r|}nt        j                  ||      }|j                  |       t        |       t           
   d   z
        <   |j                  t        j                  |
fdd             B |d   }	t	        t              dz
  dd      D ]  
t        j                  |
   |
   |	      }	! |	S )Nr   r+   c                                S r   r   )ro   idx_loadinputs_loaderss   ra   <lambda>z1pointwise_cat.<locals>.inner_fn.<locals>.<lambda>  s    -N1-h7 rc           rF  r)   )rO   
index_exprrw   int64r   r   constantgeltand_rk   re   r'   maskedr  )r  idx_dimmasksmasked_loadsr  r  
start_condend_condmasknext_valro   r6  r   r;  r7  inputs_rangess             @@ra   rU  zpointwise_cat.<locals>.inner_fn  s   ..S5;;7s6{#  	A 6 Q,^^M!$4Q$7E 
 ..q!1!!4ekkBC/Jvvgs+HAvc&kAo%!xx
H5LLCyH %Xc]]15Ea5H%HIHSM

75 	D  #Fq("b1 	AyyaQH	 rc   rV  )rk   r   rX  re   r<   r   rj   r   )r;  r   prev_endr   rU  r  r7  rH  s   ``    @@ra   pointwise_catrJ    s    9;MH )h3<<>#3F(FGH $R() 4::Ccoo':N.` F1I&&()H!"%b)HSMay##%Qi!!#	 k ;s   Cc           	       	
 t        j                               dk(  sJ d       t        j                               dk(  sJ d       | j                         t        j                  k(  rt        | t        j                        } | j                         t        j                  k(  sJ d| j                                 t        | j                               k  s!J dt        | j                                       | j                         j                         	j                         
	
f	d}t        j                  | j                         || j                               S )Nr+   expect scales 1 dimexpect zero_points 1 dim<Expecting input to have dtype torch.float32, but got dtype: Expecting axis to be < c                b  	 | 
   f} |       } |      } |      }t        t        j                        \  }}j                  t        j                  k7  r$t	        j
                  |t        j                        }j                  t        j                  k7  r$t	        j
                  |t        j                        }t	        j                  |      }t	        j                  ||z        |z   }t	        j                  |t	        j                  ||            }	t	        j
                  |	      S Nr   )_create_constantsrw   float32r   rO   r   r  
reciprocalr  maximumminimum)r  channel_idxrq  scale
zero_pointqminqmax	inv_scaler  clampedaxisr   input_loader	quant_max	quant_minscalesscales_loaderzero_pointszero_points_loaders             ra   rU  z;quantized_decomposed_quantize_per_channel.<locals>.inner_fn2  s    4ylS!k*'4
&y)5==Q
d<<5==(LL6E+j%++>JNN5)	ii	)*Z7++dCKKc$:;||GU++rc   rV  )r   r   r   rw   rZ  r   rS  rX  r<   r   rj   )rq  rb  rd  r^  ra  r`  r   rU  r_  rc  re  s    `````` @@@ra   )quantized_decomposed_quantize_per_channelrf    s?    v !Q&=(==&{##%&!+G-GG+ENN*.??- 
FuGXFYZ- #enn&'' 
!#enn&6"7!89' $$&L&&(M$002, ," !~~	 rc   c           	     "     j                          t         t        j                          fd}t	        j
                   j                          j                         |t         j                                     }|j                          |S )Nc                    t         j                  j                         5  t        j                   j                         |             cd d d        S # 1 sw Y   y xY wr   )r.   ComputedBufferforce_realizerO   device_assert_asyncrX  )r4  r   r   s    ra   rU  z_assert_async.<locals>.inner_fnO  sO    ,,. 	K**+=4+;+;+=e+DcJ	K 	K 	Ks   *AArV  )
rl  r   rw   r   r<   r   rj   r   re   r   )r   r   rU  assertion_ops   ``  ra   _assert_asyncrm  K  sm    LLND%**%DK ## nnDMMO$	L rc   c                    t        | |      S r   rm  r   s     ra   lower_assert_asyncrp  ]      s##rc   c                    t        | |      S r   ro  r   s     ra   lower_assert_functional_asyncrs  b  rq  rc   )	out_dtypec               v  	
 t        j                               dk(  sJ d       t        j                               dk(  sJ d       | j                         |k(  sJ d| d| j                                 t        | j                               k  s!J dt        | j                                       t        j                  | j                         	j                         
j                         	
fd}t        j                  | j                         || j                               S )	Nr+   rL  rM  Expecting input to have dtype , but got dtype: rO  c                   |    f} |       } 
|      } |      }	j                   t        j                  k7  r$t        j                  |t        j                        }j                   t        j                  k7  r$t        j                  |t        j                        }t        j
                  t        j                  |t        j                        |      |z  }t        j                  |      }|S r   )r   rw   rS  rO   r   sub)r  rW  rq  rX  rY  r  r^  r_  rt  rb  rc  rd  re  s         ra   rU  z=quantized_decomposed_dequantize_per_channel.<locals>.inner_fn  s    4ylS!k*'4
<<5==(LL6E-j%--@Jggcll5%--8*EMll3	*
rc   rV  	r   r   r   rw   rS  rX  r<   r   rj   )rq  rb  rd  r^  ra  r`  r   rt  rU  r_  rc  re  s    ```   ` @@@ra   +quantized_decomposed_dequantize_per_channelr{  g  s-    v !Q&=(==&{##%&!+G-GG+??% 
(/@AR@ST% #enn&'' 
!#enn&6"7!89' MM	$$&L&&(M$002  !~~	 rc   c                   | j                         t        j                  k(  rt        | t        j                        } | j                         t        j                  k(  sJ d| j                                 | j                         fd}t        j                  | j                         t        j                  |t        |      t        |            | j                               S )NrN  c                L    
|       }t        d|z  |t        j                        \  }}t        j                  ||z        |z   }t        t        j                        \  }}t        j
                  t        j                  ||      |      }t        j                  |	      S )N      ?r   )rR  rw   rS  rO   r  rV  rU  r   )r  rX  rY  rq  r\  r  rZ  r[  r]  r   r_  r`  ra  s            ra   rU  zBquantized_decomposed_quantize_per_tensor_default.<locals>.inner_fn  s    S! 1%K5==!
	: ii	)*Z7&y)5==Q
d++ckk#t4d;||GU++rc   rX  rY  rV  )r   rw   rZ  r   rS  rX  r<   r   rj   r  r  r/  r   r   )rq  rX  rY  ra  r`  r   rU  r_  s      ``` @ra   0quantized_decomposed_quantize_per_tensor_defaultr    s     ENN*.??- 
FuGXFYZ- $$&L, !""E%LS_
 ~~ rc   c               l   | j                         |k(  sJ d| d| j                                 t        j                  | j                         fd}t	        j
                  | j                         t        j                  |t        |      t        |            | j                               S )Nrv  rw  c                     |       }t        ||t        j                        \  }}t        j                  t        j
                  |t        j                        |      |z  }t        j
                  |      }|S rQ  )rR  rw   rS  rO   ry  r   )r  rX  rY  rq  r  r_  rt  s        ra   rU  zDquantized_decomposed_dequantize_per_tensor_default.<locals>.inner_fn  s]    S!-eZu}}Uzggcll5%--8*EMll3	*
rc   r  rV  )r   rw   rS  rX  r<   r   rj   r  r  r/  r   r   )	rq  rX  rY  ra  r`  r   rt  rU  r_  s	         ` @ra   2quantized_decomposed_dequantize_per_tensor_defaultr    s     ??% 
(/@AR@ST% MM	$$&L !""E%LS_
 ~~ rc   c                0  	 | j                         t        j                  k(  rt        | t        j                        } | j                         t        j                  k(  sJ d| j                                 t        j                               dk(  s9t        j                               dk(  rj                         d   dk(  sJ d       t        j                               dk(  s9t        j                               dk(  rj                         d   dk(  sJ d       | j                         j                         j                         		fd}t        j                  | j                         || j                               S )NrN  r   r+   expect scale as scalar tensor"expect zero_point as scalar tensorc                    	|       } t        j                               dk(  rdnd      } t        j                               dk(  rdnd      }j                  t        j                  k7  r$t        j                  |t        j                        }j                  t        j                  k7  r$t        j                  |t        j                        }t        j                  |t        j                  |      z        |z   }t        
t        j                        \  }}t        j                  t        j                  ||      |      }t        j                  |      S )Nr+   r   r   r   )r   r   r   rw   rS  rO   r   r  rT  rR  rV  rU  )r  rq  _scale_zero_pointr  rZ  r[  r]  r   r_  r`  ra  rX  scale_loaderrY  zero_point_loaders           ra   rU  zAquantized_decomposed_quantize_per_tensor_tensor.<locals>.inner_fn  s    S!c%..*:&;q&@dbI'ENN4D0E0JPRS;;%--'\\&%--8Fu}},,,{EMMBKiiv 667+E&y)5==Q
d++ckk#t4d;||GU++rc   rV  )r   rw   rZ  r   rS  r   r   rX  r<   r   rj   )
rq  rX  rY  ra  r`  r   rU  r_  r  r  s
    ````` @@@ra   /quantized_decomposed_quantize_per_tensor_tensorr    sf    ENN*.??- 
FuGXFYZ- u~~ A%ENN"u~~'7':a'?'&'  z""$%*J!"a'J,?,?,A!,D,I,+,  $$&L$$&L"..0, , !~~	 rc   c                 	
 t        j                               dk(  s9t        j                               dk(  rj                         d   dk(  sJ d       t        j                               dk(  s9t        j                               dk(  rj                         d   dk(  sJ d       | j                         |k(  sJ d| d| j                                 t        j                  | j                         j                         	j                         
	
fd}t        j                  | j                         || j                               S )	Nr   r+   r  r  rv  rw  c                V    |       } t        j                               dk(  rdnd      } 
t        j                               dk(  rdnd      }j                  t        j                  k7  r$t        j                  |t        j                        }	j                  t        j                  k7  r$t        j                  |t        j                        }t        j                  t        j                  |t        j                        |      |z  }t        j                  |      }|S )Nr+   r  r   )r   r   r   rw   rS  rO   r   ry  )r  rq  r  r  r  r_  rt  rX  r  rY  r  s        ra   rU  zCquantized_decomposed_dequantize_per_tensor_tensor.<locals>.inner_fn8  s    S!c%..*:&;q&@dbI'ENN4D0E0JPRS;;%--'\\&%--8Fu}},,,{EMMBKggcll5%--8+FOll3	*
rc   rV  rz  )rq  rX  rY  ra  r`  r   rt  rU  r_  r  r  s    ``   ` @@@ra   1quantized_decomposed_dequantize_per_tensor_tensorr    sU    u~~ A%ENN"u~~'7':a'?'&'  z""$%*J!"a'J,?,?,A!,D,I,+,  ??% 
(/@AR@ST% MM	$$&L$$&L"..0
 
 !~~	 rc   c                   | d   j                         j                  dk(  }|rt        d | D              rp| D ]  }|j                           t        d | D              rt	        t
        j                  g|  \  } } t        t
        j                  j                        | |      S t        |       dk(  rt        | d         S t        | d   |d      }t        | dt        j                  i}| D cg c]  }t        ||       } }ddd fd	t!        fd
| D              }dfdt"        j$                  rt'        | |      S |r)t)        t*        j,                  j/                  | |            S fdd}dddt        |       |k  s1t        |       t"        j0                  k  rt        fd| D              rt        fdt2        j4                  j6                  D              }	t!        fd| D              xr |	}
t        fd| D              xr t!        fd| D               }|
s|r|st'        | |      S t)        t*        j,                  j/                  | |            S c c}w )Nr   r   c              3  |   K   | ]4  }|j                         t        j                  t        j                  fv  6 y wr   )r   rw   int8uint8r   rq  s     ra   r   zcat.<locals>.<genexpr>O  s.      ;@ejj%++66s   :<c              3  T   K   | ]   }t        |j                               d k(   " yw)r   N)r   r   r  s     ra   r   zcat.<locals>.<genexpr>V  s!     >es5>>#$)>s   &(r+   r   c                   t        | t              rJt        | j                  t        j                        r| j                  j                         S | j                  S t        | t        j                        r| j                  S | S r   )rg   r@   ri   r.   r2   r$  r   r   s    ra   unwrap_tensorzcat.<locals>.unwrap_tensorc  sV    a#!&&"++.vv))++vva'66Mrc   c                    t        | t        j                        xr$ t        | j                  t        j                        S r   )rg   r.   ri  ri   r=   )rs   s    ra   is_reductionzcat.<locals>.is_reductiono  s)    !R../TJqvvr||4TTrc   c                    t        | t        t        j                  f      r  |             S  |       xs> t        | t        j                        xr" t        fd| j                         D              S )Nc              3  h   K   | ])  } t         j                  j                  |             + y wr   )rP   rY   
get_buffer)r   readcan_fuse_reductions     ra   r   z2cat.<locals>.can_fuse_reduction.<locals>.<genexpr>x  s-       #177#5#5d#;<s   /2)rg   r@   r.   r   r<   r  get_read_names)rs   r  r  r  s    ra   r  zcat.<locals>.can_fuse_reductionr  sh    a)R]]34%mA&677O !R\\*  ,,. 	
rc   c              3  .   K   | ]  } |        y wr   r   r   rs   r  s     ra   r   zcat.<locals>.<genexpr>  s     Ba.q1B   c                6   t        j                  |       r:t        j                  | d      \  }}t         j                  j	                  |       S t        | t        t         j                  f      r  |             S t        | t         j                        ryy)NF)freezeT)	r.   r%  r&  ConcatKernelcan_realize_into_without_copyrg   r@   r   r<   )r   r*  r   should_lower_cat_inputr  s      ra   r  z#cat.<locals>.should_lower_cat_input  sx     ##A&11!EBJGQDDWMMMa)R]]34)-*:;;a&rc   c                H   t        | t        t        j                  f      r  |             S t        | t        j                        sy| j                         j                  }| j                         D ]*  }| t        j                  j                  |            z  }, |S r  )rg   r@   r.   r   r<   inner_fn_opcountnum_opsr  rP   rY   r  )r   countr  op_countr  s      ra   r  zcat.<locals>.op_count  s    a)R]]34M!,-- !R\\*""$,,$$& 	8DXagg00677E	8 rc   r   r)   c                n    | t         j                  j                  t         j                  j                  fv S r   )r  catr  constant_pad_ndr\   s    ra   additional_pointwise_opsz%cat.<locals>.additional_pointwise_ops  s(    dhh&&(<(<(D(DEEErc   c              3  4   K   | ]  } |      k    y wr   r   )r   rs   MAX_SIMPLE_OP_COUNTr  s     ra   r   zcat.<locals>.<genexpr>  s     Cq22Cs   c              3  6   K   | ]  }t        |        y wr   )rG   )r   user  s     ra   r   zcat.<locals>.<genexpr>  s!      
 S":;
r   c              3  .   K   | ]  } |        y wr   r   r   r   r  s     ra   r   zcat.<locals>.<genexpr>  s     >&s+>r  c              3  .   K   | ]  } |        y wr   r   r  s     ra   r   zcat.<locals>.<genexpr>  s      "
,/"3'"
r  c              3  .   K   | ]  } |        y wr   r   r  s     ra   r   zcat.<locals>.<genexpr>  s     <(+<r  )r   zUnion[TensorBox, ir.StorageBox]return	ir.IRNode)r  r   r\   torch._ops.OpOverload)rj   r   r  rl  require_channels_lastr  r  r  r  r   r  r  r   r   r8  r   r  r,   force_pointwise_catrJ  r@   r.   r  r   max_pointwise_cat_inputsrP   rZ   r[   )r;  r   
cpu_devicerq  r   r   r   fusable_reductionMAX_COMPLEX_POINTWISE_CATpointwise_usesfuse_pointwise_usehorizontal_fuse_catr  r  r  r  r  r  r  s               @@@@@@@ra   r  r  L  sI   %%',,5Jc DJ 
  	EMMO	>v>>-dhh@@IFA1 0 01&#>>
6{aVAY
q	3
*C	%D%L%LE /55shsE"5F5
U

 B6BB !!VS)) //<==$ !"F 6{//	V77	7CFCC 
~~++
 
 >v>>Q> 	 " "
39"
 
 =<V<<< 	 "5>O --R__++FC899K 6s   5I1c                  
 | j                         t              t              t              t        k7  fd       t        j
                  j                  j                  t        j                  |d            }|r\t        j
                  j                  j                  t        j
                  j                  j                     |z            d      }n[t        j
                  j                  j                  t        j
                  j                  j                        |z
        d      }d
|r| df
nd|f
t              D cg c]  \  }}|fvs| }}}|j                  |       
fd}	t        t        j                   j#                  | ||	            S c c}}w )N)r  rankc                     d  d S )Nz(diagonal dimensions cannot be identical z, r   )dim1dim2s   ra   r8  zdiagonal.<locals>.<lambda>  s     HbQUPVW rc   r   )r   r   c                    | d   }dgt        	      z  }d}t              D ]1  }|k(  r|d   z   ||<   |k(  r|d   z   ||<   %| |   ||<   |dz  }3 |t        	      dz
  k(  sJ |S )NrF  r   r+   r)   )r   r   )
r  diag_idxoriginal_idxcur_dimr  base_idxr  r  num_dimsoriginal_shapes
        ra   	reindexerzdiagonal.<locals>.reindexer  s    r7sS00x 	ADy"*Xa["8Qd"*Xa["8Q"%g,Q1	 #n-1111rc   )r   r   r   r   rP   rY   r   evaluate_exprr   Ltevaluate_maxevaluate_minrf   rk   r@   r.   GenericViewr   )rq  offsetr  r  offset_negative	diag_sizero   r   r  r  r  r  r  s     ``      @@@ra   diagonalr    s   ^^%N>"H84D84D	W gg&&44UXXfa5HIOGG$$11GG))t$v-~d/C 	
	 GG$$11GG))t$nT&:V&C 	
	 HGQ<v;$^4N41a$8MQNEN	LL   R^^**5%CDD' Os    F:/F:c                0    t        t        | |||            S r   )r  r  )rq  r  r  r  s       ra   diagonal_copyr     s    %t455rc   c                P    t        |       }t        ||||      }t        ||       |S r   )r  r  	mutate_to)rq  srcr  r  r  r*  r]   s          ra   diagonal_scatterr    s*    5\FffdD1FfcMrc   c                    t        j                  |      }t        j                  | j                         |         }d }t        j                  j
                  j                  t        j                  |d            r||z   }n?t        j                  j
                  j                  t        j                  |d            r|}|t        |      rW| j                         }| j                         }| j                         j                  ||   |z  z   }||= ||= t        | |||      S t        | |||dz         }t        ||      S t!        t        j                  j
                  j"                  t        j                  j$                  j&                  d         }	|	J t)        |	      dk(  sJ |	       t+        t-        |	j/                                     \  }
}| j                         }| j                         }|
}t1        j2                  |
|| j                         j                  ||   | j                         |         }t        j                  j5                  |      |_        t        j                  j9                  |       ||= ||= t        | |||      S )Nr   r+   unbacked_bindings)r   r'  r   rP   rY   r   r  r  Ger"   
get_stride
get_layoutr  r-  r   r  r#   	shape_envrZ   r\  r   r9  iterr   r.   DynamicSelectStorageOffsetregister_bufferr   register_operation)r   r   r  r   actual_indexr  
new_stridenew_storage_offsetslice_resultr  unbacked_offset_symr   buffers                ra   selectr    s)   
,,s
C<<

S)*DLww&&uxxQ'78Tz	
			(	(#q)9	:$S) zz|HJ!"!6!6C<9W!W3a:7IJJ!!S,q8HIL<-- 2	""AGG$8$8$=$=>Q$R ((( !Q&9(99&!$'8'>'>'@"ABzz|HJ,**	3	

SF ''))&1FKGGv&3a:/ABBrc   c           
     r   t        | |d      }|}t        |t        t        f      s`| j	                         |   }t
        j                  j                  j                  t        ||z   dz
  |            }|g|z  }||dz
  |z  z
  |d<   g }d}|D ](  }||z   }	|j                  t        | |||	d             |	}* |S )Nr   r+   rF  Fr  )r  rg   re   r   r   rP   rY   r   r  r&   rk   r   )
r   r  r   sizes_x_sizechunksr1  r  r   r  s
             ra   splitr  G  s    
3
"CF edE]+c"!!++HVe^a5G,OP6!vzU22r
 FE dl 	fQUCu=> Mrc   c                    t        | ||      S r   )r  )r   r  r   s      ra   split_with_sizesr  b  s    E3rc   c                    t        | |d      }t        j                  j                  j	                  | j                         |         }t        |      D cg c]  }t        | ||       }}|S c c}w r  )r  rP   rY   r   r  r   r   r  )r   r   r  ro   r1  s        ra   unbindr  g  s_    
3
"CWW''

S(9:F).v7AfQQ7F7M 8s   A-c                >   | j                         }t        |      }t        ||      |dk(  rt        t	        | d      |      S |   }t
        j                  j                  }|j                  ||       |j                  d       t        ||z
        dz   }|j                  |      dkD  r-| j                  |j                  t        ||z  |                   g |d  ||dz   d  |}	fd}
t        t        j                   j#                  | |	|
            S )Nr   )r  r+   c                D    | d   |    z  z   }g | d  || dz   d S )NrF  r+   r   )r  dim_idxr   r  s     ra   r  zunfold.<locals>.reindexer  s?    b'CHtO+8Tc8G8c#'B&788rc   )r   r   r   r   r  rP   rY   r   	check_leqcheck_ltr&   r   r  r%   r@   r.   r  r   )r   	dimensionr   r  r  ndimdim_sizer   new_dim_sizeout_sizer  r   s      `       @ra   unfoldr  o  s   JJLEu:D
4
+Cqyi1o400SzHwwHtX&aHtOT2Q6L""8,q0	''t0CX(NO	
 EtDlDU379-=DtDH9 R^^**1h	BCCrc   c                    t        | |d      }t        | j                               }|j                  |t        j
                  j                         t        | |      S r  )r  re   r   insertr   r#  r$  r  )r   r   r  s      ra   r  r    sE    
3
"CQZZ\"IS%''++&9rc   c                    t        | |      }t        | t              sJ t        |t              sJ |j                  | _        | S r   )r  rg   r@   ri   r  s      ra   
unsqueeze_r    s>    
As
Ca###c9%%%XXAFHrc   c                   t         j                  j                  j                  j	                  t        j                  |            }t        | j                               }|dk  r|||z   z  }d|cxk  r	||z   k  sJ  J |S r  )	rP   rY   r   r  r  r   sympifyr   r   )r   r   r  r  s       ra   r  r    sr    
''


$
$
2
25==3E
FCqzz|D
Qwtf}#dVm#####Jrc   rF  c                    t        | |d      }t        j                  j                  j	                  | j                         |         dz  }t        | |d|      }t        | |||dz        }t        |t        |            S )Nr   r)   )	r  rP   rY   r   r  r   r   rW  sigmoid)r   r   new_lenr   r)  s        ra   glur    so    
3
"Cgg((c):;q@Gq#q'"Aq#w!,Aq'!*rc   c                N     |rt         j                           fd}d|_        |S )Nc                 x    d }t        j                  |t        j                  j                  g| i |      S )Nc                d    t        | t        j                        rt        j                  |       S | S r   )rg   r.   r6   r@   r   r   s    ra   wrap_tensorsz7fallback_handler.<locals>.handler.<locals>.wrap_tensors  s%    *4Q		*B9##A&IIrc   )pytreetree_mapr.   FallbackKernelr   )rp   r   r  kernels      ra   handlerz!fallback_handler.<locals>.handler  s<    	J "++226KDKFK
 	
rc   T)r  r   _is_fallback_handler)r  r  r  s   `  ra   r  r    s&    f
 $(G Nrc   c                 .    t        j                  d       y )NzjTorchinductor does not support code generation for complex operators. Performance may be worse than eager.)warningswarnr   rc   ra   _warn_complex_not_supportedr     s    MMtrc   c                h   | j                         rt                y| j                  ry| j                  t        j
                  k(  r|syt        |j                  t        j                  j                        xrr |j                  t        j                  j                  t        j                  j                  t        j                  j                  t        j                  j                  fv xsE t        |j                  t        j                  j                        xr t!        |j                         S y)z0Do not support reading or writing to this tensorTF)r  r   is_metar   rw   float8_e8m0fnurg   r]   rx   ry   r  r  r  r  r  
_scaled_mmrH   )rs   r_   s     ra   unsupported_input_tensorr%    s    ||~#%yyww%&&&
 t{{EJJ$9$9: 		  

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

(=(=>W74;;CW

 
	
 rc   c                *   t         j                  j                  t        j                  j
                  j                  j                  f}||j                  |v r| j                         ryt        | |      ry| j                  xr t        j                  S )z2Do not support writing tensor but can read from itFT)r  r  r   rw   rO   r  r  r  r]   r  r%  is_cpur,   disable_cpp_codegen)rs   r_   supported_complex_viewss      ra   unsupported_output_tensorr*    so     					,,44 DKK+BBq||~4(882222rc   c                R     j                   t        j                  j                  u ry j                  dk(  ry j                   t        j
                  j                  u ry fd}t        j                   j                  i  j                  D ]  } ||d      s y  | d      S )NFplaceholderc                D   t        | t        j                  j                        syd| j                  vryt        j                  | j                  d         D ]F  }t        |t        j                  j                        s(|rt        |      s7 yt        |      sF y y)NFr  T)rg   rw   fxNoder\  r  tree_leaves_subclasses
FakeTensorr*  r%  )inp_out_node	is_outputr\  r_   s      ra   check_skip_conditionzCfallback_node_due_to_unsupported_type.<locals>.check_skip_condition  s    ,6)))&&|'8'8'?@ 		 DdE$5$5$@$@A,T48+D$7		  rc   )r4  T)
r]   r  view_as_complexr  r\   lift_fresh_copyr  arg_tree_leavesrp   r   )r_   allow_cpu_inputsr5  r   s   `   ra   %fallback_node_due_to_unsupported_typer:    s    {{d**222ww- {{d**222* %%tyy@DKK@ u5  55rc   c                *   | t         vs|s
J d|         |rt        t        j                  d            rt	        | g      rt
        j                  r&| t        j                  j                  j                  v si|sgt        j                  j
                  j                  r4dt        j                  j
                  _        t        j                  d       t        d|  d      fd}t!        | t        j"                  j$                        r*| j'                         D ]  }t)        | |      } ||        y t!        | t        j"                  j*                  t        j"                  j,                  f      r	 ||        y t/        d|  d	t1        |              )
Nz*both a fallback and a decomp for same op: CIFznA make_fallback error occurred in suppress_errors config, and suppress_errors is being disabled to surface it.zmake_fallback(a.  ): a decomposition exists, we should switch to it. To fix this error, either add a decomposition to core_aten_decompositions (preferred) or inductor_decompositions, and delete the corresponding `make_fallback` line. Get help from the inductor team if unsure, don't pick arbitrarily to unblock yourself.c                n    t        |        t        |         t        | d       t        |             S Nr  )r   r   r  r  )op_overloadlayout_constraints    ra   register_fallbackz(make_fallback.<locals>.register_fallback?  s;    !+.(!+/@AG $G[)
 	
rc   zUnsupported fallback z with type )r0   r   osgetenvr1   r,   fallback_randomrw   _decompdecompositions_for_rngextra_random_decomps_dynamosuppress_errorslogwarningr   rg   rx   r   r   r   ry   HigherOrderOperatorRuntimeErrorr   )r\   r@  r  override_decomprA  olr?  s    `     ra   make_fallbackrP    sQ   ^# 
4RD96 	4!t$ ""emm::OOO ==//38EMM  0KKH RD !f f
 	

 "ejj112,,. 	+B!"b/Kk*	+ 
B..

0N0NO	P"22$k$r(LMMrc   c                T    d}| D ]  }||z  }	 t        |t        j                        S )z
    TorchInductor offset calculation differs from PyTorch eager offset
    calculation for random ops (tl.rand vs torch.rand). In future, we should
    strive for same impl for tl.rand and torch.rand.
    r+   r   tensorrw   r;  )r  numelr   s      ra   philox_rand_offsetrU  Q  s2     E 	%u{{++rc   c                B  	
 t        j                  || t         j                  j                  |             j	                         
|j                         |j                         		
fd}t        j                  ||t        |             }t        |       }||fS )Nc                   t        j                   g       t        j                        }t        j                   g       t        j                        }t        j                  t        j
                   |       t        j                        |      }t        j                  ||      }t        j                  |      S r   )rO   r   rw   r  r   r:  rand)	r4  seed_index_exproffset_index_exprrand_index_exprr1  r   offset_loader
random_posseed_loaders	        ra   rU  zphilox_rand.<locals>.inner_fnj  s     ,,{2DLLr):EKKH''NN:e,ekk:<M
 
 ||FE**rc   rV  )
r.   r'  FlexibleLayoutcontiguous_stridesmake_indexerrX  r<   r   re   rU  )r   seedr  r(  rr   r   rU  random_values_nodeoffset_noder\  r]  r^  s        `   @@@ra   philox_randre  ]  s     
,,T2	
 ln  ""$K&&(M+ #))Dz	 %T*K{**rc   c           	         t         j                  r\t        j                  t        j
                  t        j                  j                  t        j                  j                  | ||            S t        d      )Nz&should be handled in replace_random.py)r,   rD  r  r  r@   r   r.   r  r  native_dropoutr  r   )r   ptrains      ra   rg  rg    sY    $$T%8%8%@%@!QN
 	

 EFFrc   c                x   t         j                  s-| j                         t        j                  d      k(  sJ d       | j                          t        |      dk(  st        |d   t              rt        j                  j                  nt        j                  j                  }t        j                  || g|  | S )Nr   Tthis should be handled in decomps unless config.fallback_random or the device is CPUr   )r,   rD  rj   rw   rr   rl  r   rg   r/  r  
bernoulli_Tensorr.   InplaceBernoulliFallback)r   rp   r?  s      ra   rl  rl    s    !!Q\\^u||E7J%J ^J IIK t9>ZQ7 	__## 
 Q66Hrc   c                    t         j                  s-| j                         t        j                  d      k(  sJ d       t        t        |       g| S )Nr   rk  )r,   rD  rj   rw   rr   rl  r  )r   rp   s     ra   bernoulli_prp    sG    !!Q\\^u||E7J%J ^J eAh&&&rc   c                    t         r   r   )r   s    ra   _foobarrs    s    
rc   c                .    t         j                  d       y )Nz1using triton random, expect difference from eager)rJ  info)salts    ra   _warn_triton_randomrw    s    HH@Arc   c                 J    t        t        j                  j                         y r   )rw  rP   rY   creation_timer   rc   ra   warn_triton_randomrz    s    --.rc   c                     |j                  dd       t        | i |S t        j                  r|j	                  dd        t        | i |S t        d      N	generatorz-should have been handled in replace_random.py)r]  fallback_rand_generatorr,   rD  popfallback_rand_defaultr   rp   r   s     ra   rX  rX    sV    zz+t$0&777			

;%$d5f55
H
IIrc   c                     |j                  dd       t        | i |S t        j                  r|j	                  dd        t        | i |S t        d      r|  )r]  fallback_randn_generatorr,   rD  r  fallback_randn_defaultr   r  s     ra   randnr    sV    zz+t$0'888			

;%%t6v66
H
IIrc   c                l    t        j                  |      }t         j                  j                  | |      S r   )r.   get_stride_orderExternKernelrequire_stride_order)input_tensorr(  stride_orders      ra   inductor_force_stride_orderr    s)    &&v.L??//lKKrc   c                    t        d      )Nz.should be handled in fuse_seed_creation_pass()rr  )rr   s    ra   inductor_seedr    s    
I
JJrc   c                z    t                t        j                  t        j                  | t        |                  S r   )rz  r@   r   r.   RandomSeedsrD   )r  rr   s     ra   inductor_seedsr    s)    BNN5-2GHIIrc   c                |      fd}t        j                   j                          j                         |g       S )Nc                L    t        j                  j                               S r   )rO   	load_seedget_name)r   r4  seedss    ra   rU  z&inductor_lookup_seed.<locals>.inner_fn  s    }}U^^-u55rc   rV  )r<   r   rj   r   )r  r4  rU  s   `` ra   inductor_lookup_seedr    s9    6 !oo	 rc   r  c                 	 t         j                  rJ dv sJ g | } t        j                  }|j	                         }t        j                  ||| t
        j                  j                  |       |      j                         |j                         		fd}t        j                  |||g |       }|j                          |S )N)rX  r  r  c                     t        t               g       t        j                   |       t        j                              S r   )r   rO   r:  rw   r  )r4  moder]  r^  s    ra   rU  z!inductor_random.<locals>.inner_fn  s7    !wsD!ONN:e,ekk:
 	
rc   rV  )r,   rD  rw   rS  r:  r.   r'  r_  r`  ra  rX  r<   r   rl  )
r   rb  r  r  r   rr   rU  r1  r]  r^  s
     `     @@ra   inductor_randomr    s    %%%%$$$$T7DMME%%'FtR..AA$GPVln  ""$K
 w	F NNMrc   c               f   	 t         j                  rJ g |}t        j                  }|j	                         }t        j                  |||t
        j                  j                  |      |      j                         |j                         	 	fd}t        j                  |||g |      S )Nr  c           	        t        j                   g       t        j                   |       t        j                        t        j                  t        j
                        t        j                  t        j
                              S r   )rO   	randint64r:  rw   r  r;  )r4  highlowr]  r^  s    ra   rU  z"inductor_randint.<locals>.inner_fn	  sV    }}ONN:e,ekk:NN3,NN4-	
 	
rc   rV  )r,   rD  rw   r;  r:  r.   r'  r_  r`  ra  rX  r<   r   )
r  r  r   rb  r  r   rr   rU  r]  r^  s
   ``      @@ra   inductor_randintr  	  s     %%%%T7DKKE%%'FtR..AA$GPVln  ""$K
 w	 rc   c                    | j                         | j                         d   | j                         d   | j                         d   z  | j                         d   fS NrF  r   )r  r   r  tbs    ra   _boundaries_helperr  (	  sO    

b
a2==?1--
	 rc   c                H    | j                         | j                         d   fS r  )r  r  r  s    ra   _sorter_helperr  1	  s    ;;="--/"---rc   	out_int32rightsidesorterc               J   
 d } |       r ||      r
9 |      s1 t        t        j                  j                  d       |||      S ||dk(  rd|rt        j
                  nt        j                  
|j                          j                          j                          t         j                               dk(  r

 fd}n	
 fd	}|j                         }t        j                  |
||j                  
      }	|	j                          |	S )Nc                ^    t         j                  j                  | t        j                        S r   )rP   rY   ri  rj  	BUCKETIZEr  s    ra   r8  zsearchsorted.<locals>.<lambda>?	  s     AGG$7$7
N$$% rc   Fr  r  r  Tr+   c           
          |       }t        j                  |t              dd n
t              d       S d      S )Nr   r  sorter_indicesrO   	bucketizer  r  )r  r  index_dtyper  sorted_sequencer  values_loaders     ra   rU  zsearchsorted.<locals>.inner_fnd	  sV    $C=="?3%~t>&3I'-~t  <= rc   c                             }d fd}t        j                  |t               |      d n
t              d       S  |            S )Nc                    | j                         }t        j                  t        j                  t
        j                  d t        |d d d d       D                    S )Nc              3  ,   K   | ]  \  }}||z    y wr   r   )r   r   ro   s      ra   r   zNsearchsorted.<locals>.inner_fn.<locals>.get_flattened_index.<locals>.<genexpr>{	  s     &UAq1u&U   rF  )r  rO   r:  r  r  operatorr   r   )r  stridesr  r  s     ra   get_flattened_indexz;searchsorted.<locals>.inner_fn.<locals>.get_flattened_indexw	  sU    --/~~$$ &UWSb\3sPR89T&U  	 rc   r  )r  r@   r  )r  r  r  r  r  r  r  r  s   `  ra   rU  zsearchsorted.<locals>.inner_fnr	  sh    $C =="?3#O4%~t>&3I'-~t  <Ov;V rc   rV  )r  r  searchsortedrm  rw   r  r;  rX  rl  r   r   rj   r<   r   r  )r  selfr  r  r  r  validate_bucketizerU  rr   r1  r  r  s   `  ` `    @@ra   r  r  5	  s    /!$''9&'AT 1 1 8 8eT
 	
 DGO!*%++K$$&M 
?##%&!+
	 
		 	0 __Fzz	F NNMrc   r  r  c                  t        j                               dk(  sJ t        j                  j	                  | t
        j                        r.t        j                  j	                  t
        j                        s/ t        t        j                  j                  d      | |      S j                          | j                         }| j                         |rt        j                  nt        j                   fd}t#        j$                  ||| j                               }|j                          |S )Nr+   Fr  r  c                \     |       }t        j                  |t              d      }|S r  )rO   r  r  )r4  r  r  
boundariesr  r_  r  s      ra   rU  zbucketize.<locals>.inner_fn	  s6    5!--z*
 rc   rV  )r   r   rP   rY   ri  rj  r  r  r  r  rm  rl  rj   rX  rw   r  r;  r<   r   )	rq  r  r  r  rr   rU  r1  r  r_  s	    ` `   @@ra   r  r  	  s     z""$%*** 	
E>#;#;<GG
N,D,DEQ 5 55Q:%
 	
 F$$&L!*%++K
 ~~	F NNMrc   c                    t        j                  t        j                  t        j                  j
                  ||f      \  }}||fS r   )r  tree_map_onlyr.   r6   r  require_stride1r   rp   r   s      ra   require_denser  	  s;    ''
		2??22T6NLD& <rc   c                    t        j                  t        j                  t        j                  j
                  ||f      \  }}||fS r   )r  r  r.   r6   r  require_contiguousr  s      ra   r  r  	  s;    ''
		2??55f~LD& <rc   c                    t        j                  t        j                  t        j                  j
                  ||f      \  }}||fS r   )r  r  r.   r6   r  r   r  s      ra   r   r   	  s=     ''
		2??==f~LD& <rc   c                    t        j                  t        j                  t        j                  j
                  ||f      \  }}||fS r   )r  r  r.   r6   r  r  r  s      ra   r  r  	  s;    ''
		2??884.LD& <rc   c           	        t        | t        j                        rm|j                         D cg c]4  }t        |t        j
                        r|j                  j                  n|6 }}t        j                  j                  | |      S t        | t              r/| j                         D ci c]  }|t        | |   ||          c}S t        | t        t        f      r" t        |       d t!        | |      D              S | S c c}w c c}w )Nc              3  :   K   | ]  \  }}t        ||        y wr   constrain_to_fake_tensor)r   r   f_as      ra   r   z+constrain_to_fake_tensor.<locals>.<genexpr>	  s!      
19!S$Q,
r
  )rg   r.   r6   r(  rw   SymIntr_   exprr  require_exact_stridesr
  r  r  r   re   r   r   )r   fake_argr   meta_stride_exprkeys        ra   r  r  	  s    #ryy!GOGX
BC:a6AFFKKA=
 
 44S:JKK#tNQhhj
GJC)#c(HSMBB
 	
 
C%	'tCy 
=@h=O
 
 	
 J


s   9D*Dc           
         t        d t        | |      D              } |j                         D ci c]  \  }}|t        |||          }}}| |fS c c}}w )Nc              3  :   K   | ]  \  }}t        ||        y wr   r  )r   r   r  s      ra   r   z,constrain_to_fake_tensors.<locals>.<genexpr>
  s#      C 	!h/r
  )r   r   r   r  )rp   r   	fake_argsfake_kwargsr   r   s         ra   r   r   
  sb      y1 D JPXAa)![^<<XFX< Ys   Ac           
         fdt        fdt        || j                        D              }|j                         D ci c]  \  }}| || j                  |          }}}||fS c c}}w )Nc           	        t        | t        j                        rst        j                  |j                  d   j                         t        j                  j                  j                        }t        j                  j                  | |      S t        | t              r,| j                         D ci c]  }| | |   ||          c}S | S c c}w )Nr  )rg   r.   r6   r  r\  r(  rP   rY   r   r  r  r  r
  r  )r   fx_argr  r  apply_constraints       ra   r  z1constrain_to_fx_strides.<locals>.apply_constraint
  s    c299%..E"))+QWW-=-=-G-GL ??77\JJc4 LOHHJWSC)#c(F3K@@WW
 Xs   1Cc              3  6   K   | ]  \  }} ||        y wr   r   )r   r   r  r  s      ra   r   z*constrain_to_fx_strides.<locals>.<genexpr>
  s"      *5#vf%r   )r   r   rp   r   r   fx_noderp   r   r   r   r  s        @ra   r   r   
  ss      9<T7<<9P D EKLLNSDAqa!!W^^A%677SFS< Ts   !A*c                      fdt        fdt        t        | j                              D              }|j	                         D ci c]  \  }}| d| j
                  |          }}}||fS c c}}w )Nc           
     `
   t        |t        j                        s|S |j                  d   }|j	                         D cg c]4  }t        |t
        j                        r|j                  j                  n|6 }}t        j                  |j	                               }|r<|d   dk7  r4t        t        t        t        |j                                                 }j                  t         j"                  j$                  k(  r| dv rt        |      dk(  sJ d}|j&                  s t        j(                  j+                  ||      S dj                  t
        j,                  j                   j.                  j$                  k(  xr | dk(  }t        |t0              sJ t        |j                               d	vr|S t        j2                  |      }|r3t        j4                  t        j(                  j7                  |      |      S t        |t              rE|j9                         5|r3t        j4                  t        j(                  j7                  |      |      S |rt        |j                               }	g }
|j9                         }t        t        |j                               d
z
        D ]q  }t:        j<                  j>                  jA                  ||   d      s1|3t:        j<                  j>                  jA                  ||   d      sa|
jC                  |       s dgt        |	      z  }d
|d<   d
}t        t        |	      dz
  dd      D ]  }||d
z      dk7  r||	|d
z      z  }||
v r9t:        j<                  j>                  jA                  ||d
z      z  d      rd||<   Vt:        j<                  j>                  jA                  |z  d      stE        |      z  }|||<    t        j(                  jG                  ||      S |r3t        j4                  t        j(                  j7                  |      |      S t        |t              rE|j9                         5|r3t        j4                  t        j(                  j7                  |      |      S fd}t        |jH                  t        jJ                        rQ ||      sI ||jM                               r3t        j4                  t        j(                  j7                  |      |      S t        j(                  j+                  ||      S c c}w )Nr  rF  r   )r   r   r   )r   r+   r)   r   r   r   r   r   r+   r)   c                    t         j                  j                  j                  | j	                         d         z  dk(  S r  )rP   rY   r   	size_hintr   )r   	ALIGNMENTs    ra   
is_alignedz=sdpa_constraint.<locals>.apply_constraint.<locals>.is_aligned
  s4    GG$$..qzz|B/?@9LQRRRrc   )'rg   r.   r6   r\  r(  rw   r  r_   r  r  re   r"  r   r   r   r]   r  0_scaled_dot_product_efficient_attention_backwardr  is_cudar  r  rO   '_scaled_dot_product_efficient_attentionr@   is_aligned_realized_tensor_hinttry_match_insignificant_stridesrealize_inputmaybe_get_striderP   rY   r   statically_known_equalsrk   rC   r  ri   r2   r$  )r  r   r  meta_valr   r  r  effn_attn_fwd_biasis_aligned_tensorr  expanded_dimsmaybe_stridero   out_stridesr(  r  r  r  s                   @ra   r  z)sdpa_constraint.<locals>.apply_constraint!
  sv   #ryy)J;;u%GOGX
BC:a6AFFKKA=
 
 **8??+<=L,1s3<<>/B)C DEL NNDDLLMv|$)))
 (L??77\JJ 	 NNyy~~EEMMN q 	 #y)))s||~f,J>>sIN55--c24D 
 sF#$$&2!55--c24D  CLLN+HM //1L3s||~.23 ,77##;;<LQ<OQRS ,((@@aRST!((+, $X.KKOF3x=1,b"5 (q1u%*#hq1uo5F %ww''??#AE*Y6 *+A ww''??@RTUV$VY7)CF!'A!($ ??88kJJ55--c24D 
 sF#$$&2!55--c24D 	S chh,c?coo/0==55c:<L  33CFFk
s    9T+c              3  >   K   | ]  \  }\  }} |||        y wr   r   )r   r  r   r  r  s       ra   r   z"sdpa_constraint.<locals>.<genexpr>
  s*      C#v 	c6*s   rF  )r   rf   r   rp   r   r   r  s   `    @ra   sdpa_constraintr  
  s}    zGx  "+Cgll,C"D D IOW1a!"a):;;WFW< Xs   "A5)r  )rN  c                   |}| j                         |j                         k7  rt        || j                               }| j                         |j                         k7  rt        || j                               }| j	                         |j	                         k7  r%t        || j	                               }t        |      S t        |      S r   )rj   r  r   r   r   r'  r  )r  r  r  r   rm   s        ra   r  r  z  s    ACNN,,a*+~~3==?*Q()}}#,,.(Q(Sz8Orc   )memory_formatc          	         t        j                  | j                         | j                         | j	                         t        | j                                     S NrV  )r<   r   rj   r   rX  re   r   )r   r  s     ra   r  r    s@     ||~kkmAJJL!	 rc   c                   g }t        | t              rt        | j                  t        j                        rw| j                  } t        | t        j                        rF|j                  | j                                | j                  } t        | t        j                        rFt        |       } t        |       } |r;| j                  } |d d d   D ]  }t        j                  | |      }  t        |       } | S )NrF  r"  )rg   r@   ri   r.   r   rk   r  r  )r   reinterpret_view_layoutsr#  s      ra   clone_preserve_reinterpret_viewr    s    !!YJqvvr7I7I$JFFB../$++ALLN;A B../ aLaAFF.tt4 	:F""&9A	:aLHrc   r7  c               \    fd}t        j                  t        |      || g      S )Nc                D    t        j                  | d   z  z         S )Nr   r   rO   r:  )r4  r   r  r  s    ra   r{   ziota.<locals>.fn  s!    ~~dU1Xo5UCCrc   rV  )r<   r   rD   )lengthr  r  r   rr   requires_gradr{   s    ```   ra   iotar
    s1    D V$x	 rc   c           	     
   | j                         |j                         k(  sJ | j                         t        | d      t        j                  j
                  j                  t        j                  d            r| j                            z   t        j                  j
                  j                  d       t        j                  j
                  j                  | j                                   t        t        |      | j                               }|j                         fd}t        j                  | j!                         | j                         |t#        | j                                     S )Nr   c           	         t        j                  t        j                  t        j                  |    t        j
                        t        j                  t        j
                               |        |             S r   )rO   r  eqr:  rw   r  )r  r   r4  
src_loaderr  s    ra   rU  z select_scatter.<locals>.inner_fn  sX    yyFFs3x5uekk2 sOSM
 	
rc   rV  )r   rX  r  rP   rY   r   r  r   r  r   r  r  r'  r  r<   r   rj   re   )r   r  r   r4  rU  r  r  s     `` @@ra   select_scatterr    s   ;;=CMMO+++}}H
3
"Cww%%ehhua&89

S))GGq%(GGeQZZ\#%67
3$ajjl
3C"J
 ||~kkmAJJL!	 rc   c           	     :   	
 t        | j                               } j                         
t         d       j	                            t
        j                  j                         \  t         j	                               }t        z
  dz
  z         |<   t        ||      }|j                         		 
fd}t        j                   j                          j                         |t         j	                                     S )Nr   r+   c                   	dk(  rk(  r
dk(  r |       S t        j                  |    t        j                        }t	        |       t        |    	z
  
      <   g }	dk7  rZ|j                  t        j                  |t        j                  t        j                  	      t        j                                     k7  rZ|j                  t        j                  |t        j                  t        j                        t        j                                     
dk7  rz|j                  t        j                  t        j                  t        |    	z
  d
      t        j                        t        j                  dt        j                                     |sJ t        j                  t         j                   |      }t        j"                  |fdt%              rdnd      }t        j&                  || |             S )Nr   r+   c                             S r   r   )src_idxr  s   ra   r8  z1slice_scatter.<locals>.inner_fn.<locals>.<lambda>  s    Jw' rc   r9  )rO   r:  rw   r;  re   r&   rk   r=  r   r'  r>  r  r(   r<  r  r  r?  r@  r   r  )r  rA  rF  src_valr  r   r  r  r  r  r  r   r  s       @ra   rU  zslice_scatter.<locals>.inner_fn  s   A:#/daic?"..S5;;7s)C5 0$7A:KKNN5<<#6D (?KKNN5<<#4ekkB 19KKNN'C5(8!TBEKK LLEKK0	 t$/**' #A

 yySM
 	
rc   rV  )r   r   rX  r  r   r.   r  normalize_start_endre   r&   r'  r<   r   rj   )r   r  r   r  r  r  src_sizerU  r  r  r  s   ` ````  @@@ra   slice_scatterr    s    
3
&C}}H
3
"Czz|C H11!S%EJE3AJJL!HS5[D1H5t<HSM
h
C"J,
 ,
\ ||~kkmAJJL!	 rc   c                j    t        | t        t        f      rt        |       dkD  rt	        | d         S | S r  )rg   re   r   r   _unwrapr   s    ra   r  r  "  s-    !dE]#A
qt}Hrc   r   rr   r#  
pin_memoryc                   t        |d t        j                  fv d|        t        | d       t        t	               t
              rxs t        j                  nxs t        j                         g }t         t        j                        r fd}nt         t        t
        f      r fd}nt               dk(  s't         d   t        t
        f      rBt               dk  r4|j                  t        j                  t                             fd}n5t        j                  j!                  t        j"                   |            S t%        j&                  t)        |      ||	      S )
Nlayout=r  c                0    t        j                        S r   r  r4  ri   r   s    ra   rU  ztensor.<locals>.inner_fn5  s    >>$..rc   c                0    t        j                        S r   rO   r<  r  s    ra   rU  ztensor.<locals>.inner_fn:  s    <<e,,rc   r   r   c                      fdt              dk(  rt        j                  d      S  dt                    S )Nc           	     j   | |k  sJ || z
  dk(  rt        j                  |          S || z
  dz  | z   }t        j                  t        j                  t        j                  d   t
        j                        t        j                  |t
        j                               | |       ||            S )Nr+   r)   r   )rO   r<  r  r>  r:  rw   r;  )r  r  midbinary_searchri   r   r4  s      ra   r%  z/tensor.<locals>.inner_fn.<locals>.binary_searchB  s    s{"{;!#<<UU;;U{q(50yyFFuQx=S%++6 "%-!#s+ rc   r   )r   rO   r<  )r4  r%  ri   r   s   `@ra   rU  ztensor.<locals>.inner_fnA  s7     4yA~||Au-- CI..rc   r  rV  )r   rw   stridedrg   r  r   r;  get_default_dtyper   r   r/  r   rk   IntegerrP   rY   add_tensor_constantrS  r<   r   rD   )ri   r   rr   r#  r  rT  rU  s   ``     ra   rS  rS  (  s   v$..'&0BC:~|,'$-%$2002!F$$	/ 
D5#,	'	- 
Ta:d1gs|<TaemmCI./	/( ww**LLU6:
 	
 V$	 rc   c                z    t        | t              r|t        | |      } |t        | |      } | S t	        | ||      S )Nr  )rg   r@   r   r  rS  )ri   r   rr   s      ra   	as_tensorr+  a  sD    $	"D%(DT6*D$eF33rc   c                8    t        | t        j                        S rQ  rR  )ri   s    ra   long_tensorr-  l  s    $ekk**rc   c                   t        t        j                  j                  j                  t        j                  j
                  j                  d         }|J t        |      dk(  sJ |       t        t        |j                                     \  }}t        j                  |||       }t        j                  j                  |      |_        t        j                  j                  |       t        j                  j
                  j                  d   }t!        |t"        j$                  t"        j&                  t"        j(                  f      r|j*                  j,                  S t/        j0                  |      S )Nr  r+   r  )r#   rP   rY   r   r  rZ   r\  r   r9  r  r   r.   DynamicScalarr  r   r  rg   rw   r  SymFloatSymBoolr_   r  r   r  )ri   r  binding_symkeypathr  r  s         ra   _local_scalar_denser4  q  s    2	""AGG$8$8$=$=>Q$R ((( !Q&9(99&   %6%<%<%> ?@Kk7D9F''))&1FKGGv& ''


#
#E
*C#ennemmDExx}}}}S!!rc   c                     y r   r   )ri   r   s     ra   _assert_scalarr6    s     rc   )rr   r#  c                    y r   r   )r   r   r(  r   rr   r#  s         ra   _assert_tensor_metadatar8    s     rc   c                   | t        | t        t        f      st        d      rj                  t        t        t        f      rfd}nTt        t
        j                        rfd}n3t        j                               dk(  sJ j                         fd}t        j                  ||t        |            S )Nr   c                0    t        j                        S r   r!  r4  r   r   s    ra   rU  z_full.<locals>.inner_fn  s    <<u--rc   c                0    t        j                        S r   r  r;  s    ra   rU  z_full.<locals>.inner_fn  s    >>%//rc   r   c                     g       S r   r   )r4  value_loaders    ra   rU  z_full.<locals>.inner_fn  s    ##rc   rV  )rg   r   r/  r   r   r   r   r   r   rX  r<   r   re   )
fill_valuerr   r   r   rU  r   r>  s     `  @@ra   _fullr@    s    Ej3,/GE74K%#u&	. 
E5;;	'	0 5>>#$)))((*	$ Dz	 rc   c                8     t        t        |            | fi |S r   create_tensor_liketensor_constructor)r   r?  r   s      ra   r  r    s     =0<=aJ6JJrc   c                "     d d d d dd d fd
}|S )NF)namesr   rr   r#  r  r  c                   t        | d u d       t        |d t        j                  fv d|        t        | d       t        |      }|xs t        j                         }t        |      dk(  r6t        |d   t        t        t        j                  f      rt        |d         }|D ]  }t        |t        j                        sJ  |D cg c]  }t        j                  |       }}t        |||      S c c}w )Nnamed tensorsr  r  r+   r   )r   rw   r&  rD   r'  r   rg   re   r   Sizer  r   r'  r@  )	rF  r   rr   r#  r  r  r   r   r?  s	           ra   rb  z!tensor_constructor.<locals>.inner  s     	5D=/26dEMM22gfX4FGz><0v&2002t9>ja4

2KLa>D  	3A!!U\\222	3)-.AQ..Z55 /s   C8r   )r?  rb  s   ` ra   rD  rD    s#     6. Lrc   )rF  r   r#  rr   r  r  c                    t        | d u d       t        |      }t        |      dk(  r6t        |d   t        t
        t        j                  f      rt        |d         }t        |d ||||      S )NrH  r+   r   r   r#  rr   r  )	r   rD   r   rg   re   r   rw   rI  empty_strided)rF  r   r#  rr   r  r  r   s          ra   r  r    sf     u}o.6"F
4yA~*T!WtUEJJ.GHT!W~d%v* rc   c                      dddddd fd
}|S )zZ
    Shim to convert X_like(...) into X(...).  For example zeros_like() into zeros().
    NF)r   rr   r#  r  r  c                  t        | d       t        |d t        j                  fv d|        || j                         }nt	        |      }|xs | j                         }t        | j                               } |||||      S )Nr  r  r  )r   rw   r&  r   r   rj   re   r   )r   r   rr   r#  r  r  r   creation_fns          ra   _constant_likez*create_tensor_like.<locals>._constant_like  s     	z><06dEMM22gfX4FG=KKME 'E)1<<>AJJL!fV

 	
rc   r   )rO  rP  s   ` ra   rC  rC     s     duTX
 rc   c                *    t        t        |             S r   rB  )r?  s    ra   r  r    s    0<==rc   c                     d d d d d fd
}|S )NrK  c               n   t        |t        t        f      sJ t        | d       t        |d t        j
                  fv d|        t        |      xs | j                         }|xs | j                         }|D cg c]  }t        j                  |       }}t        t        |      ||      S c c}w )Nr  r  )rg   re   r   r   rw   r&  r   r   rj   r   r(  r@  rD   )r   r   r   r#  rr   r  r   r?  s          ra   _new_constantz#new_constant.<locals>._new_constant!  s     $u...z><06dEMM22gfX4FGU#4q{{})1<<>*./Qa //Zv!6tDD 0s   =B2r   )r?  rT  s   ` ra   new_constantrU     s    tDT	E rc   rK  c          	     ~    || j                         }|| j                         }t        |d ||t        |      |      S NrK  r   rj   rL  rD   )r   r   r   r#  rr   r  s         ra   	new_emptyrY  /  sF    }~V$ rc   c                  t        | t        t        f      sJ t        |t        t        t        d       f      sJ t	        | d       t	        |d t
        j                  fv d|        t        |      xs t        j                         }|xs t        j                  d      j                  }t        |      }t        d|||       }|j                          |j                  j                  }t        j                   |j                  dgt#        |       z        |_        t        |t$        j&                        sJ | D cg c]  }t)        j*                  |       } }|r#|D cg c]  }t)        j*                  |       c}nt$        j,                  j/                  |       }t%        j0                  ||| |      |_        |S c c}w c c}w )Nr  r  r9  r   )r?  rr   r   r   )rT  )rr   r   r   r(  )rg   re   r   r   r   rw   r&  r   r'  rS  rr   rD   r@  rl  ri   dataclassesreplacer   r.   ri  r   r'  r_  r`  r'  r#  )	r   r(  r   r#  rr   r  	pointwiser  r   s	            ra   rL  rL  ?  s{    dT5M***ftUDJ7888:~|,v$..'&0BC<5#:#:#<E/u||C(//F6"F6TJI^^  F%%fkk1#D	/JFKfb//000%)*ELLO*D*  #))Qa)11$7 
 NN	FM  +)s    G$Gc          	     ~    || j                         }|| j                         }t        ||||t        |      |      S rW  rX  )r   r   r(  r   r#  rr   r  s          ra   new_empty_stridedr_  _  sH     }~V$ rc   c                
   |D cg c]+  }t         j                  j                  j                  |      - }}t	        t        t        |            |j                        }t        j                  j                  | |      S c c}w )N)r  )rP   rY   r   r   sortedr   r   __getitem__r.   r  r  )r   r(  r   r  s       ra   copy_stridedrc  q  sb    >DEagg11!4EFE%F,&2D2DEL??//<@@ Fs   0B c                V    |j                  d      J d        t        |      | fi |S )Nr   z(dtype should be handled by decomposition)r]  rD  )r   r?  r   s      ra   fullre  x  s5    ::g*V,VV*)j)$9&99rc   c                   t        | t              sJ |j                         dk(  rt        | |j	                               S | j	                         t              dk(  }t        | |      |rt        | dg      } dg| j                         |j                         fd}t        j                  | j                         | j                         ||j	                               S )Nr   r+   c                    t        |       } t        j                   |                }t        |       dk(  r|g} n|| <    |       S r  )re   rO   indirect_indexingr   )r  
gather_idxr   index_loaderr   r  s     ra   r{   zgather.<locals>.fn  sL    3i**<+<d3iH
s8q=,C!CH}rc   rV  )rg   r@   	get_numelrY  r   r   r  r'  rX  r<   r   rj   r   )	r   r   r4  sparse_gradr  r{   rj  r   r  s	    `    @@@ra   gatherrm  ~  s     a###AENN,--::<DY!^F
3
'C1qcNs}}H$$&L ||~kkm~~	 rc   c                0  	
 |r- t        t        j                  j                        | ||||      S |rJ t	        | t
              sJ t	        |t
              sJ dt        |j                               v sJ | j                         	|j                         t        |j                               | j                         
g |j                         
dd  	
fd}t        j                  | j                         | j                         |      S )Nr   r+   c                    t        |       t              k(  sJ |  d         | d        }t        j                  |d         gg | d  z   } |      S )Nz != r   )r   rO   rh  )r  	var_index
weight_idxindices_loaderindices_ndimr  weight_loaderweight_sizes      ra   r{   zembedding.<locals>.fn  s{    3x3x=(@SEhZ*@@("3}#56	++I{1~FG K
K
 

 Z((rc   rV  )r  r  	embeddingr  rg   r@   strr   rX  r   r   r<   r   rj   )weightr  padding_idxscale_grad_by_freqsparser{   rr  rs  r  rt  ru  s         @@@@@ra   rv  rv    s   7 6 67G[*<f
 	
 :fi(((gy)))C))+,,,,&&(M((*Nw'')*L//#K6!!#6k!"o6H) )   " 	 rc   c           
        t        d | D              s)J d| D cg c]  }||j                          c}        t        d | D              rt        d      t	        |       D cg c]  \  }}t        |t              s| }}}t        |      dkD  sJ d       d gt        |       z  }t        |t        |D cg c]  }| |   	 c}       D ](  \  }}|j                         |k7  rt        d      |||<   * ||fS c c}w c c}}w c c}w )Nc              3     K   | ]T  }|P|j                         t        j                  t        j                  t        j                  t        j
                  fv  V y wr   )r   rw   r;  r  r   r  r   ro   s     ra   r   z.check_and_broadcast_indices.<locals>.<genexpr>  sA      = 	
%++u{{EJJLLs   AAz)indices must be int64, byte or bool. Got c              3     K   | ]7  }||j                         t        j                  t        j                  fv  9 y wr   )r   rw   r   r  r~  s     ra   r   z.check_and_broadcast_indices.<locals>.<genexpr>  s1      78q}%**ekk22s   ?5?zFallback for bool indicesr   z"requires at least 1 non-None indexz.Fallback when indices is on a different device)r  r   r  r   rf   rg   r@   r   r   r   rj   )r  rr   ro   r   
valid_idxsnew_indicess         ra   check_and_broadcast_indicesr    s/      
 4G4eqWXWdQ[[]4e3fg   <C  ""=>> )' 2O1jI6N!OJOz?QD DD&3w<'KJ 1
3S1GAJ3S TU 1 <<>V#%&VWWA 
""# 5f P 4Ts   C=C='D D:Dc	           
     H   dt        dd        D ]  \  }	}
|
|	z
  dk7  sd t              D cg c]  \  }}|	| |    c}}g | t              t              z   d  d   }rz   nd | z   |d  z   f
d}|fS c c}}w )NFr+   Tr   c                  
 t        |       t              k(  sJ t              t        
      k(  sJ t              }g }d   }rdn|}d}t        d   dz         D ]}  }||k(  r||z  }|   *|t        |       k  sJ |j                  | |          |dz  }<|   }|J 
|   }|j                  t        j                   || |||z          |	              g || |d  }|S  |      S )Nr   rF  r+   r   wrap_neg)r   r   rk   rO   rh  )r  r  	new_indexfirst_tensor_indexstart_offsetnext_idxro   loaderr   r   indexed_sizer  indices_loadersnon_consecutive_tensorsoutput_sizetensor_indicestensor_sizer  r  s            ra   r{   z*index_output_size_and_inner_fn.<locals>.fn  sN   3x3{++++?#s<'8888;	+A.3q9K~b)A-. 	AL D qz!#c(***  X/A(+)))#A  ))s<,2EFG#!)		&

^
	 %,yE(92EErc   )r   rf   r   )r  r  r  r  r  r  r  r   r  previouscurrentro   r  r  r{   r  r  s    ````````      @@ra   index_output_size_and_inner_fnr    s    $ $ 1CD +'X"&*#+ ,5W+=MC6!9MKSKS&[)9C<O)O)Q"RSK'*!K/ ++,,-./ 	 F  FD ?_ Ns   
BBc                    t        | ||      \  }}}t        j                  | j                         | j	                         ||      S r  )index_impl_helperr<   r   rj   r   )r   r  r   r  rU  r   s         ra   
index_implr  (  sB    0GUCK1||~kkm	 rc   c                   t        |t        t        f      sJ | j                         t	        || j                               \  }}t        |      dkD  sJ d       |D cg c]  }||j                         nd  }}t        ||d      j                               }| j                         }t        t        |            D cg c]  }||   	||    }	}|rd|	v rd|vrt        d      t        t        |            D cg c]  }||   	 }	}t        ||||||	d ||	      \  }
fd}|
|fS c c}w c c}w c c}w )Nr   z Must have at least one valid idxz0index is out of bounds for dimension with size 0r  c                       |             S r   r   )r  index_inner_fnr  s    ra   rU  z#index_impl_helper.<locals>.inner_fnR  s    s+,,rc   )rg   re   r   rX  r  rj   r   r   r   
IndexErrorr  )r   r  r   r  r  ro   r  r  r  r  r  rU  r  r  s               @@ra   r  r  3  sS   ge}---}}H9'1<<>RG^~"F$FF"KRSa!-q}}TASOS w~a01::<=KZZ\F',S\':U!gaj>TF1IULUl"q';KLL',S\':;!F1I;L;"@
#K- .009 T V <s   !D2
D7D7D<c                    	 t        | |d      S # t        $ r? | j                           t        t        j
                  j                  d      | |      cY S w xY w)NTr   Fr  )r  r   rl  r  r  r4  rm  r   r  s     ra   r4  r4  X  sT    
!WD11 
			M

 1 1uMw
 	

s    AAAc                    t        | |d      S )NFr  )r  r  s     ra   _unsafe_indexr  d  s    a..rc   c                6    t        t        |       |||dd      S )NTFr   may_realizeindex_put_impl_r  r   r  r   
accumulates       ra   	index_putr  q  s     a'6:Tu rc   c                6    t        t        |       |||dd      S )NFr  r  r  s       ra   _unsafe_index_putr  x  s     a'6:U rc   c                    |j                         | j                         k7  rt        || j                               }|rt        | |      }t        | t	        |d   ||             S r  )rj   r  r   r  r  )r  r  r   r  s       ra   index_put_as_masked_fillr    sV    T__..%!23D% T5UD9::rc   c                   t        t        j                  j                  j                  t
        j                  j                        sJ t        j                  t        j                  j                  j                  | |||       | S r   )
rg   rP   rY   rZ   r]   rw   rx   ry   r.   IndexPutFallbackr  r  r   r  s       ra   index_put_fallbackr    sW    agg**115::3H3HIII,,33T7FJWKrc   c                $    t        | |||dd      S )NTr  r  r  s       ra   
index_put_r    s    gvz4 rc   c                $    t        | |||dd      S )NFTr  r  r  s       ra   _unsafe_index_put_r    s    gvzD rc   c           
     n   |rBd }d  ||       |j                         v r$t        fd|D              s|j                          |j                         dk(  rt	        |      dk(  r|d   j                         t        j                  t        j                  fv r_|d   }t        t	        |j                               t	        | j                                     D ]  }t        |d      } t        | |g||      S t        j                         rt        | |||      S |D ]E  }	|	|	j                         t        j                  t        j                  fv s7t        | |||      c S  | j                         }
t	        |
      }|rLt        | j                               r3|dk(  rt!        | dg      } t        | |||      } |dk(  rt!        | g       } | S t#        || j                               }	 t%        || j'                               \  }}|D cg c]  }||j+                         nd  }}t-        | t.              sJ | j                          |dk(  rt!        | dg      } t1        ||d      j                               }t        t	        |            D cg c]  }|
|   	 }}t3        |
|||||d |      \  }}t5        ||      }| j'                         }|J t7        j8                  || j                         |j+                         |||rdnd 	      }t7        j:                  d t7        j<                  |       |
      }t>        j@                  jC                  |      |_"        t>        j@                  jG                  |       |dk(  rt!        | g       } | S # t(        $ r t        | |||      cY S w xY wc c}w c c}w )Nc                F   t        | t        j                        r| j                  } t        | t        j                        r| j                         } t        | t        j                        r| j                  } t        | t        j                        r| j                         S d S r   )	rg   r.   r@   ri   r2   r$  r   Bufferr  r   s    ra   try_get_namez%index_put_impl_.<locals>.try_get_name  sg    !R\\*FF!R[[)MMO!R]]+FF#-a#;1::<EErc   c                   t        | t              rt        | j                  t        j                        r| j                  j                         } t        | t        j                        xr t        | j                  t        j                        xrh t        | j                  dd       xrO | j                  j                  j                  t        j                  j                  j                  j                  k(  S y)Nr  F)rg   r@   ri   r.   r2   r$  r   r  r   r  r]   rw   rO   r  randpermr  )indices    ra   indice_slice_from_randpermz3index_put_impl_.<locals>.indice_slice_from_randperm  s     &),FKK1U002vr}}5 V"6;;@VY=V ++22eiinn6M6M6U6UU	 rc   c              3  .   K   | ]  } |        y wr   r   )r   r  r  s     ra   r   z"index_put_impl_.<locals>.<genexpr>  s      E
39&v.E
r  r+   r   rF  r  
atomic_addrr   r   rU  rT  output_indexerscatter_moder   r#  ri   )$r  r  rl  rk  r   r   rw   r   r  r   r   r  r  $are_deterministic_algorithms_enabledr  rI   r  r   r  rj   r   rX  rg   r@   re   r  r'  r.   Scatterri  MutationLayoutSHOULDREMOVErP   rY   r  r   r  )r  r  r   r  r   r  r  rF  r   r4  r  x_ndimr  ro   r  r  r  expected_vals_sizerU  rr   scatterr  r  s                         @ra   r  r    s   	F	 !6!6!88 E
=DE
 B
 NN 	aLAAJ  "uzz5;;&??qzs4==?+S-AB 	'AT2&D	''tffjII 113!$DD  I!2uzz5;;6O!O%dGVZHHI ]]_F[FB4>>CSTQ;qc?D!$DQ;b>Dfdnn./FE"=T__&#
 LSSa!-q}}TASOSdI&&&LLN {D1# w~a01::<=K',S\':;!F1I;L;#A	$  F./F __Fjjnn##%!%/\TG ,,T2F
 ''))&1FKGGv&{D"~Ke  E!$DDE T <s   )N 
N-N2N*)N*r  c                   	 t        | |dd      \  }}j                         | j                         		fd}t        j                  | j	                         | j                         ||      S )NFr  c                     j                   t        j                  k7  r+t        j                          t        j                        }n        }t        j
                  | fd      S )Nc                                     S r   r   )_unsafe_index_fnr  self_loaders   ra   r8  z8_unsafe_masked_index.<locals>.inner_fn.<locals>.<lambda>1  s    K8H8M,N rc   )r   rw   r   rO   r   r@  )r  mask_valr  fillrF  mask_loaderr  s   ` ra   rU  z&_unsafe_masked_index.<locals>.inner_fn,  sK    ::#||K$4ejjAH"3'Hzz($NPTUUrc   rV  )r  rX  r<   r   rj   r   )
r  rF  r  r  rT  r   rU  r  r  r  s
    ` `   @@@ra   _unsafe_masked_indexr  $  sw    "3gUU#FA ""$K""$KV V  nn	 rc   c           	         t        ||d      }| j                         }t        t        |            D cg c]#  }||   rt	        ||   ||    ||   dz
        nd % }}t        | ||d      S c c}w )Nr   r+   T)r  )r  r   r   r   r  r  )r   rF  r  r   masked_valuer  ro   clamped_indicess           ra   #_unsafe_masked_index_put_accumulater  ;  s    vq)LJJLE s7|$ 7>ajgaj58)U1X\2dJO  Q$OOs   (A-c                V    t        j                  |t        j                  ||             S r   )rO   rU  rV  r   minmaxs      ra   r  r  H  s    ;;sCKKQ/00rc   c                P    t        |       }t        ||||      }t        ||       |S r   )r  r-  copy_)r  r  r   r(  r)  r*  output_views          ra   as_strided_scatterr  M  s*    4[FVT6>BK	+sMrc   c                2    t        t        |       |||fi |S r   )scatter_r  )r   r   r4  r  r   s        ra   r  r  U  s    E!Hc5#888rc   r  include_selfc               :   t        |t              }t        | ||j                         t	        t
        j                  |r|j                         n
t        |            |r|j                         j                  nd|      rt        j                  | ||||||       |S y )Nznot implr  )rg   r@   rN   r   r	   rw   r   r   rj   r.   ScatterFallback)r?  r  r   r4  r  r  r  src_is_tensors           ra   scatter_fallbackr  Z  s     sI.MU[[]#--/S	J!.J 	%	
 rc   r  c                  |dv sJ |[t        t        j                  t        j                  j
                  j                  j                        }t        || ||||      }||S |dk(  rd}n|dk(  rd}t        | ||||      S )N)Nr   multiplyr  r   sumr  prod)
r   r  r  rP   rY   rZ   r]   _overloadnamer  scatter_reduce_)r  r   r4  r  r  r?  fallback_results          ra   r  r  {  s    ....~dmmQWW-A-A-H-H-V-VW*sE3v
 &""	:	4eS&99rc   c                0    t        t        |       |||      S r   )scatter_add_r  r   r   r4  r  s       ra   scatter_addr    s    a#uc22rc   c                     t        | |||d      S )Nr  )r  r  s       ra   r  r    s    1c5#u55rc   c                4    t        t        |       ||||fi |S r   )r  r  )r   r   r4  r  reduction_typer   s         ra   scatter_reducer    s    58S%nOOOrc   )r  c          
         |dv sJ t        t        j                  j                               dk(  r dt        j                  j                         v sJ d       t	        t
              rt               t        t        j                  j                   |||      }|r|S t	         t              sJ dt        |j                               v sJ t         j                               }|dk(  rt         dg       t	        t              r)t        j                               dk(  rt        dg      t	        |t              r)t        |j                               dk(  rt        |dg      }|j                         dk(  r S t                j!                          |j#                         t	        t              rj#                         nd  fd} fd	}	d
 }
 j%                         }|J |st'        j(                  | j                          fd|j                         |d       }t'        j*                  d t'        j,                         |      }t.        j0                  j3                  |      |_        t.        j0                  j7                  |       t'        j(                  | j                         |	|j                         | |
|            }t'        j*                  d t'        j,                         |      }t.        j0                  j3                  |      |_        t.        j0                  j7                  |       |dk(  rt         g         S )N)Nr  r  meanamaxaminr+   twozKaten.scatter_reduce_.two is not the unique overload of aten.scatter_reduce_r  r   r   c                    j                         }t        |      }t        |       }t        j                   |       |dk(  rdn|   d      |<   |S )Nr   r+   F)r  )r   r   re   rO   rh  )r  r  r  indirect_idxr   rj  r  s       ra   r  z'scatter_reduce_.<locals>.output_indexer  sU    5zCy11DAIq5:
S rc   c                `    r |       S t        j                  j                               S r   rO   r<  r   )r  r  r  r  s    ra   r{   zscatter_reduce_.<locals>.fn  s*    c?" <<T^^%566rc   c                    | dk(  ry| J y )Nr  r  r   r  s    ra   backend_reduce_strz+scatter_reduce_.<locals>.backend_reduce_str  s    U? >!>rc   c                L    t        j                  dj                               S r  r  )r4  r  s    ra   r8  z!scatter_reduce_.<locals>.<lambda>  s    3<<4>>3C#D rc   r  r  )r   r  r  r   rg   r   r  r  r  r@   rw  r   r   r  rk  r  rl  rX  rj   r.   r  ri  r  rP   rY   r  r   r  )r  r   r4  r  r  r  r  r  r  r{   r  rr   zero_outr  r  rj  r  s   `` `           @@ra   r  r    s   BBBBD  **,-2T))3355U UU	6 #vc"&  !O dI&&&C)****t}}DqyD1##y!c#,,.&9Q&>3n%#ENN,<(=(BUQC A
c
"CLLN$$&L&0i&@"dJ7 __F::.."D>>#)
 ""006

 gg--f5	""6*
 jjnn~~%'/G ,,T2F
 ''))&1FKGGv&qyD"~Krc   c                T   | j                          | j                         | j                          d  | j                         d   }D cg c]+  }t        j                  j
                  j                  |      - c}t        |      k(  sJ |}t        |      D cg c]
  \  }}||z   c}}t        |      D ]  \  }}	|		d|	z  |<    fdfd}
t        j                  | j                         | j                         |
g ||      S c c}w c c}}w )Nr~  c                   t        j                  | t        j                        } r8t        j                  | t        j
                  dt        j                              } t        j                  | t        j
                  |t        j                              } t        j                  | t        j                        } t        j                  | |d      S )N      ?Fr  )
rO   r:  rw   rS  r   r<  rW  r   r  rh  )r   rX  r   exacts      ra   scale_fnz$upsample_nearestnd.<locals>.scale_fn%  s     NN1emm,3<<U]];<AGGAs||E5==9:LLEKK($$QE::rc   c                    |  d  }| d   } 
g |t        |      D cg c]  \  }}} 	|||       c}}}      S c c}}}w r   )r   )r  r   r)  ro   r   r   i_sizes
inv_scalesnr  r  s         ra   r{   zupsample_nearestnd.<locals>.fn0  s`    H!HWaW#aW:UVVJAq$8Aq$'VW
 	
Vs   ArV  )realize_hintrX  r   rP   rY   r   r  r   r   rf   r<   r   rj   r   )r   r  scales_xr  r  batchro   o_sizesorX  r{   r
  r  r  r  s      ``      @@@@ra   upsample_nearestndr    s    NN}}HjjlA23GJJL1"E6=>qww))!,>Gx=AG$'$9:DAq!a%:Jh' (5%KJqM(	;
 
 ||~kkm!!!	 9 ?
 ;s   0D'D$c                "    t        | ||fd      S )Nr+   r  r  r   r  rb  s      ra   upsample_nearest1dr  ?  s    avi1==rc   c                $    t        | ||fdd      S )Nr+   Tr  r  r  r  s      ra   _upsample_nearest_exact1dr  D  s    avi1DIIrc   c                $    t        | |||fd      S )Nr)   r  r  r   r  scales_hscales_ws       ra   upsample_nearest2dr  I  s     ax.BaHHrc   c                &    t        | |||fdd      S )Nr)   Tr  r  r  s       ra   _upsample_nearest_exact2dr!  P  s     ax.BatTTrc   c                &    t        | ||||fd      S )Nr   r  r  r   r  scales_dr  r  s        ra   upsample_nearest3dr%  W  s     ax8.LPQRRrc   c                (    t        | ||||fdd      S )Nr   Tr  r  r#  s        ra   _upsample_nearest_exact3dr'  b  s#     	;8X6!4 rc   c                ,     t         fd|D              S )Nc              3  J   K   | ]  }t        j                  |        y wr   r!  )r   r   r   s     ra   r   z$_create_constants.<locals>.<genexpr>p  s     6Aa'6s    #)r   )r   rp   s   ` ra   rR  rR  o  s    6666rc   c                    | j                         | j                         fd}t        j                  | j	                         | j                         |      S )Nc                    t        |       } t        |       t              k(  sJ D ]  }|   dz
  | |   z
  | |<     |       S r  )re   r   )r  r   r  r  r  s     ra   r  zrev.<locals>.loadery  sW    3i3x3u:%%% 	3Cc
Q#c(2CH	3 }rc   rV  )rX  r   r<   r   rj   r   )r   r  r  r  r  s    ` @@ra   revr,  s  sM     }}HJJLE ||~kkm	 rc   c                   d } |       ryt        |      dk7  st        | j                               dk7  ry| j                          t        | t        j
                        rt        | j                  t        j                        rt        | j                  j                  t        j                        s>t        j                  rNt        | j                  j                  t        j                        r | j                  j                  j                  sy| j                          t	        j                  |       \  }}|j                  }|d   dk7  ry|d   dk7  s|d   dk7  s|d   dk7  ry|d   }|dk(  ry|d   }|j                   d   }	||	|z   k  ry| j                  j                  j                  }
|j                   d   |j                   d   |z   g}|t"        j$                  j&                  |
<   t)        | ||j                  |j*                        }t-        |d|	|	|z         }t/        ||       t0        d	   d
xx   dz  cc<   |S )z
    This optimization changes the semantics of padding from 'clone'
    style to 'view' style.

    Thanks to functionalization, this change can still maintain numerical
    correctness.
    c                    t         j                  j                  } | yt        | j                        }t        |      dk(  rD|d   j                  t        j                  j                  t        j                  j                  fv ryy)a  
        Conservatively check if padding can be fused with downstream op.
        1. if the downstream op is a sum, then there is little benefit to
           do inplace padding
        2. if the downstream op is a matmul, doing inplace padding can
           save membw.
        Tr+   r   F)rP   rY   rZ   r   r[   r   r]   r  mmr  addmm)rZ   r[   s     ra   _padding_can_be_fusedz6inplace_constant_pad_nd.<locals>._padding_can_be_fused  sk     ww++l(()u:?uQxGGOOJJ3
  
 rc   Nr   r)   r+   r   r   )r   r  r  inductorinplace_padding)r   r   rl  rg   r.   r@   ri   r   ri  r,   can_inplace_pad_graph_inputInputBufferr   freeze_layoutr&  r(  r   rP   rY   buffer_to_padded_sizer-  r  r   fill_r   )r   paddingr?  r1  r   r#  r  npadstride0rowsizebufnamepadded_size	resized_xsliced_xs                 ra   inplace_constant_pad_ndrA    s   (  7|qC

-2
 IIK
 q",,'!&&"--0qvv{{B$5$5622qvv{{BNN; vv{{OO((+IAvmmGqzQqzQ'!*/WQZ1_1:DqyajGkk!nG4ffkkG;;q>6;;q>D#89K-8AGG!!'*		I iQg7T>JH	(JZ*+q0+rc   c                   t        |      dz  dk(  sJ t        d |D              rt        |       S t        j                  rt        | |      }|r|S | j                         }t        t        t        t        |d d d   |dd d                           t        |      t              z
  g D ]?  \  }}j                  t        j                  j                  j                  |      |f       A t        |d        }g t        |d        D ]C  \  \  }}	}
j                  |
       |j                  t        j                   |
|z   |	z                E t        |      t        |      k(  sJ  t#        | j%                                     fdfd}| j'                         t)        j*                  | j-                         | j%                         ||      S )Nr)   r   c              3  &   K   | ]	  }|d k(    ywr   Nr   r   rh  s     ra   r   z"constant_pad_nd.<locals>.<genexpr>  s     
#a16
#r  r+   c                B    g }t         	d        D ]J  \  }\  }}}|dk7  r|j                  t        |d             |dk7  s0|j                  t        ||             L t	        j
                  t        j                  |      }t        j                  | 
fd      S )Nr   c                             S r   r   )r4  r  s   ra   r8  z/constant_pad_nd.<locals>.mask.<locals>.<lambda>  s     rc   )	r   rk   range_mask_lowrange_mask_highr  r  rO   r?  r@  )r4  rF  r  r  r  r  boundsr?  
mask_sizesr  r  s   `     ra   rF  zconstant_pad_nd.<locals>.mask  s    (+E!"Ivz(J 	:$C#tfaxN323qyOC89		:
 $/zz$ 7DDrc   c                    t        | d        }t        | d        D ]  \  }\  }}|j                  ||z
          t        |      t        |       k(  sJ  |      S r   )re   r   rk   r   )r4  r  r  r  _highbounds_precomprF  r  s        ra   	offset_fnz"constant_pad_nd.<locals>.offset_fn  si    rO	!$U12Y!? 	(C#uS3Y'	(9~U+++Irc   rV  )r   r  r  r,   r3  rA  r   re   r"  r   rk   rP   rY   r   lookup_precomputed_sizer   r'  r   r   rX  r<   r   rj   )r   r9  r?  rm   r  lhr  r  r  r   rO  rJ  rN  rF  rK  r  r  s     `         @@@@@@ra   r  r    s   L1"""

#7
##Qx%a*=J JJLE(4GCaCL'!$Q$- @ABCFE
S[ A 68N P1qww//GGJANOP uRay/KJ qr3 <dT$5<<s
T(9:;< {s5z)))-q{{}-j9JE E }}H||~kkm	 rc   c                    t        j                  t        j                  | t        j                        t        j                  t        j                  |      t        j                              S r   )rO   r=  r:  rw   r;  r   r(  )ro   r  s     ra   rH  rH     s@    66q%++&u}}S)5;;7 rc   c                    t        j                  t        j                  | t        j                        t        j                  |t        j                              S r   )rO   r>  r:  rw   r;  )ro   r  s     ra   rI  rI  '  s7    66q%++&tU[[) rc   c                V    t        j                  t        | |      t        | |            S r   )rO   r?  rH  rI  )ro   r  r  s      ra   
range_maskrV  .  s'    88q#4  rc   c                      j                          d   j                         xs dgz   fd}|S )Nr   c                N   | d   |  d  t        j                  t        j                  t	              D cg c]  }t        |   |   
|   z   
|          ! c}      }	rt        j                  |fd      S t        j                  |fd      S c c}w )Nc                 4     t               g       S )Nr   )constant_boundary_condition)r   ihpad_fill_valueprefixr   s   ra   r8  z;constant_boundary_condition.<locals>.load.<locals>.<lambda>G  s$    O3A~3O"fNrN rc   c                      g        S r   r   )r\  r^  r  s   ra   r8  z;constant_boundary_condition.<locals>.load.<locals>.<lambda>M  s    (>V>b>*B rc   )r  r  rO   r?  r   rV  r@  )r4  ro   rF  r\  r^  r   r?  rR  r]  r9  	padding_hr   r  s      @@ra   rK  z)constant_boundary_condition.<locals>.load<  s    uC45\HHLQRUJWqZ1qtil2Yq\MBW
  JJ 
	
 D"BJO
	
 Xs   $B"
)r   rX  )	r   r?  r9  r]  r   rK  rR  r`  r  s	   ````` @@@ra   r[  r[  5  sE     	


cTUA}}H$A39I
 
( Krc   dilationc                  |dgt        |      z  }t        | d||   z  z   ||   ||   dz
  z  z
  ||   dz
  z   ||         }|rt        | d||   z  z   ||   ||   dz
  z  z
  d||   dz
  z  z   ||         }t        j                  j                  j                  |dz
  ||   z  | z
  ||   z
        dk\  r>|dz  }t        j                  j                  j                  d|||   z  | z
  ||   z
         t        j                  j                  j                  ||z
        dk(  r0t        j                  j                  j                  ||       d}||fS |}||fS )Nr+   r)   r   F)r   r&   rP   rY   r   r  r  r&  )	r   ro   kernel_sizer(  r9  	ceil_moderb  x_outx_alts	            ra   pooling_sizerh  S  s   3W%	A
NXa[KNQ,>??6!9q=Qq	E
 '!*nqk[^a/01 6!9q=!" 1I
 77%%uqyF1I&=&AGAJ&NOSTTQJEGG&&q%&)*;a*?'!**LM77%%eem49GG))%7I ) E)rc   c               l    t        | |      } t        j                  t        j                  |       }|dkD  S )N   )rJ   r  r  r  rW  )rd  n_dimwindow_sizes      ra   %should_fallback_max_pool_with_indicesrm  q  s/    {E2K""8<<=Krc   assert_fallbackc                  |dk(  rdg|z  }|dk(  rdg|z  }|s|}t        ||      }t        ||      }t        ||      }t        ||      }t        | t              sJ t        |      |k(  sJ t        |      |k(  sJ t        |      |k(  sJ t        |      |k(  sJ t        | j	                               |dz   |dz   fv sJ t        ||      }|||k(  sJ |||||fS )Nr   r+   r)   rk  )rJ   rg   r@   r   r   rm  )r   rd  r(  r9  rb  rk  ro  use_fallbacks           ra   max_pool_checksrs  w  s    !|#+1}3;{E2K&%(F7E*GHe,Ha###{u$$$v;%w<5   x=E!!!qzz|EAI 66668ERL"...<??rc   c                  | j                          | j                  d   }| j                   d  }t        t              D 	cg c]  }	t	        ||	   |	||       c}	 \  }
}| j
                  }|t        j                  u rdn5|j                  rt        d      nt        j                  |      j                  }t        |      t        |
      z   }t              st        |      st        d D              rt        | |      n| j                         fd}t!        j"                  d| | j%                         |||||      }t!        j"                  d	| | j%                         t        j&                  ||||      }t)        |j*                  j*                  t               r|j-                          t)        |j*                  j*                  t               r|j-                          ||fS c c}	w )
Nra  F-infc              3  &   K   | ]	  }|d kD    ywr	  r   r  s     ra   r   z)_max_pool_with_offsets.<locals>.<genexpr>  s     ,EqQU,Er  rZ  c                    | d   }|  d  }t              D cg c]  }||   	|   z  ||   |   z  z   |   z
  ! }} 
g ||      S c c}w r   r   )r  reduction_idxr^  bhro   r\  rb  rk  r9  r(  r  s         ra   fn_innerz(_max_pool_with_offsets.<locals>.fn_inner  s    Wuf%\ 5\
 UVAY=#3hqk#ABWQZO
 
 &2''	
s   $Ar  r  
input_noderr   	dst_dtyper|  rU  rT  reduction_rangesargmax)r  r  r   r   rh  r   rw   r   r  r/  r  r  re   r  r[  rX  r=   r   rj   r;  rg   ri   rl  )r   rd  r(  r9  rb  re  rk  r  dhwr  dhw_outr   	min_valuer  r{  r1  offsetsr  s     ``` `          @ra   _max_pool_with_offsetsr    s    NNGGGeVE
''5&'
C
 5\	

  A;X

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

s   G8c           
        t        |      }t        | |||||d      \  }}}}}t        j                  d      5  t	        | ||||||      \  }}	|t        |	t        j                        fcd d d        S # 1 sw Y   y xY w)NFrn  rj  unroll_reductions_thresholdrq  )r   rs  r,   r   r  r   rw   r  )
r   rd  r(  r9  rb  re  rk  r   r1  r  s
             ra   !_low_memory_max_pool_with_offsetsr    s     E 1@	1-K(A 
"	5 
50
 x44
5 
5 
5s   1A55A>c                P   t              | j                         t        j                  t	        j
                  t        j                              fd}t        j                  | j                         t        j                  || j                               }|S )Nc                     	|       }t        j                  |
      }t        j                  |      } | |      }t        j                  t        j
                  | d        t        j                        S r   )rO   rh  r-   _flattened_index_to_ndr:  _flatten_indexrw   r;  )r  r  offset_sympyry  idhwincrements_to_index
input_sizerd  rk  offsets_loaderrl  s        ra   offsets_to_indicesz4_pool_offsets_to_indices.<locals>.offsets_to_indices  sm    $,,V[A&==lKX"36~~))$
E670CDekk
 	
rc   rV  )r   rX  r   r  r  r  r  rW  r<   r   rj   rw   r;  r   )	r  rd  r  r  r  r  rk  r  rl  s	    ```  @@@ra   _pool_offsets_to_indicesr    s     E((*N--	 0 0{ KLK
 
 !!#kk#!	G Nrc   c                L    t        |      fd}t        | |||      S )Nc                    |  d  }t              D cg c]  }||   |   z  ||   |   z  z   |   z
  ! c}S c c}w r   rx  )r  ry  rz  ro   rb  rk  r9  r(  s       ra   r  zD_low_memory_max_pool_offsets_to_indices.<locals>.increments_to_index*  s_    %\ 5\
 UVAY=#3hqk#ABWQZO
 	
 
s   $<)r   r  )r  rd  r  r(  r9  rb  r  rk  s      ``` @ra   '_low_memory_max_pool_offsets_to_indicesr  !  s-     E
 $j*= rc   c           	         t        | |||||      \  }}}}}t        | ||||||      \  }}	t        |	|| j                  | d  |||      }
||
fS )Nrq  )rs  r  r  r  )r   rd  r(  r9  rb  re  rk  r   rm   r  r  s              ra   _max_pool_with_indicesr  6  s}     1@	;1-K(A *	;9ELC 6	G <rc   c           	     &    t        | |||||d      S Nr)   rq  r  r   rd  r(  r9  rb  re  s         ra   max_pool2d_with_indicesr  T        "	;9A rc   c           	     &    t        | |||||d      S Nr   rq  r  r  s         ra   max_pool3d_with_indicesr  c  r  rc   c                   dk(  rddg|dk(  rddg}st        |t              sJ t              dk(  sJ t              dk(  sJ t              dk(  sJ t        |      dk(  sJ t        |j                               dv sJ | j	                          | j                         }t        |t              rt        |j                  j                  t              r|j                  j                  }	|	j                         }
|
J t        j                  d t        j                  |
|	j                         |	j                               |	      }|j                          |j                         }n|j                         }|d uxr |d   dk(  xs |d uxr |d   dk(  }t        d |D              rt!        | ||||      S |j                         ^ }}| j                         ^ }|j#                         | j#                         t%        |j                               }t'        fdt)        d   dz        D              t'        fd	t)        d   dz        D              z  }|d
kD  rt!        | ||||      S |j                         fd}t        j*                  | j                         | j                         ||      }|rt        j,                  j/                  |      S |S )Nr   r+   r)   r  )rr   r   r   r  c              3  &   K   | ]	  }|d k7    ywr	  r   r  s     ra   r   z3max_pool2d_with_indices_backward.<locals>.<genexpr>  s     
$a16
$r  c           
   3  t   K   | ]/  }t        |d    z  t        d |d    z
  d    z        z
  d       1 ywr   r+   Nr  r   rR  rd  r(  s     ra   r   z3max_pool2d_with_indices_backward.<locals>.<genexpr>  F       	ANSQQ%7F1I$EFFJ   58c           
   3  t   K   | ]/  }t        |d    z  t        d|d    z
  d    z        z
  d        1 ywr+   r   Nr  r   wrd  r(  s     ra   r   z3max_pool2d_with_indices_backward.<locals>.<genexpr>  r  r  rj  c                   | ^ }}}t        j                  |z  |z   t        j                        }|d   z   }|d   z   }t        j                  t	        |d   z
  d   z   d         t        j                        }t        j                  t	        |d   z
  d   z   d         t        j                        }t        j                  t	        |d         dz   t        j                        }t        j                  t	        |d         dz   t        j                        }t        j
                  |t        j                  dt        j                              }t        j
                  |t        j                  dt        j                              }t        j                  |t        j                  t        j                              }t        j                  |t        j                  t        j                              }d }	t              D ]3  }
t              D ]!  }t        j                  |t        j                  |
t        j                              }t        j                  |t        j                  |t        j                              }g |t        j                  t        j                  |t        j                  |t        j                  dt        j                                    d   d      t        j                  t        j                  |t        j                  |t        j                  dt        j                                    d   d      } |      } |      }t        j                  ||      }|	;t        j                  ||t        j                  dt        j                              }	t        j                  t        j                  t        j                   ||      t        j                   ||            |      }t        j                  |t        j                  |	|      |	      }	$ 6 |	J |	S )Nr   r+   Fr  rF  r9  )rO   r:  rw   r  r&   rU  r<  rV  r   r   rh  ry  r  r  rS  r?  r>  )r  r^  rR  r  
index_testphstartpwstartphendpwendgradientph_pw_phpw
grad_indexindex_actual	grad_partr   rF  grad_loaderh_window_sizerr  indices_sizerd  r9  pooled_heightpooled_widthr(  w_window_sizewidths                      ra   r{   z,max_pool2d_with_indices_backward.<locals>.fn  sA   A^^AIM5;;?

N
N..QQ'&)3VAY?
 ..QQ'&)3VAY?
 x6!9595;;Gx6!9595;;G++gs||Au{{'CD++gs||Au{{'CDE3>>-#MNE3>>,#LM' #	WC]+ "WWWWcll3&DEWWWcll3&DE))Bs||Au{{7S(TU$R(# ))Bs||Au{{7S(TU$R(#
  .j9'
3	|Z8#"yyy#,,sEMM*J H 88FF2u-FF2u- D  #yyswwx/KXVHE"W#	WH ###rc   rV  )rg   r@   r   r   r  r  ri   r<   rj   r.   ri  r_  r   decide_layoutr  r  )fallback_max_pool2d_with_indices_backwardrX  re   r  r   r   r  r  )grad_outputr   rd  r(  r9  rb  re  r  	gO_strideri   rr   x_bufferx_strideis_channels_last_batch_heightr   r  rl  r{   rm   r  r  rr  r  r  r  r  r  s     ```                @@@@@@@@ra    max_pool2d_with_indices_backwardr  w  s    !|a&1}q6a###{q   v;!w<1x=Aqzz|&&& ,,.I!YJqvv{{I$Fvv{{"!!!$$$$nn&]]_
 
 	 &&(%%' ,A!1A 3)A,!"3  
$8
$$8K(Iw
 	
  jjlVWe&1&:&:&<#Q|((*N))+KAJJL!H {1~)* M  {1~)* M
  -/KR8K(Iw
 	
 ##%L9 9v 

%%'##%	C 44S99
rc   c                6    | j                         fd}|S )Nc           
        	
 |\  	|\  
|\  }}t        j                  t        j                  t        j                  z   t        j
                        t        j                  |t        j
                              t        j                  t        j                  
	z   t        j
                        t        j                  |t        j
                                    }t        j                  |	 
fd      S )Nc                 ,     g  z   z         S r   r   )h_start_indexr\  iwr^  w_start_indexr  s   ra   r8  z3pad_adaptive_loader.<locals>.load.<locals>.<lambda>  s&    HNvN}r'9N=2;MNO rc   )rO   r?  r>  r:  rw   r;  r@  )r^  
incrementsstart_indicesend_indicesh_end_indexw_end_indexrF  r  r\  r  r  pad_valr  s   `      @@@@ra   rK  z!pad_adaptive_loader.<locals>.load  s    B'4$}#. [xxFF}r15;;?{EKK8 FF}r15;;?{EKK8	
 zzOO
 	
rc   rX  )r   r  rK  r  s    ` @ra   pad_adaptive_loaderr  	  s    }}H
, Krc   c                    t        j                  | ||      }t        j                  |||      }t        j                  | ||      }t        j                  |||      }	||||	fS )N)out_diminp_dim)r  r  )
start_index	end_indexh_inw_inh_outw_outr  r  r  r  s
             ra    compute_indices_adaptive_poolingr  %  sa    %%k5$OM##IudKK%%k5$OM##IudKK+}kAArc   c                d    |\  }}|\  }}	t        | |||||	      \  fd}
|
S )Nc                   | ^ }}} |      } |      } |      } |      }d }	t        j                  t        d         t        d               D ]$  \  }
} |||
|g||g||g      }|	|}	 ||	      }	& |	S r  )r   productr   )r  r  r^  rz  bwr  r  r  r  r1  r\  r  r  h_end_index_fnh_start_index_fnkernel_maxes
pooling_fnw_end_index_fnw_start_index_fns                ra   r{   z _adaptive_pooling_fn.<locals>.fn>  s    R(,$R((,$R(''l1o(>lSTo@VW 
	1FBR.k*	C ~#C0
	1 rc   r  )r  r  r  in_sizes	out_sizesr  r  r  r  r  r{   r  r  r  r  s     `  `     @@@@ra   _adaptive_pooling_fnr  /  sP     JD$LE5 	)YdE5	
 . Irc   c                h   
 |\  }|\  }}t        | ||||      \  

fd}	|	S )Nc                   | ^ }}} |      } |      } |      } |      }d }	d }
t        j                  t        d         t        d               D ]  \  }} ||||g||g||g      }t        j                  ||z   z  |z   |z   t
        j                        }|
|}
n+t        j                  t        j                  ||	      ||
      }
|	|}	| ||	      }	 |
S r  )	r   r  r   rO   r:  rw   r;  r  gt)r  r  r^  rz  r  r  r  r  r  maxvalmaxindexr\  r  r  r4  r  r  r  r  r  r  r  s                  ra   r{   z)_adaptive_pooling_fn_with_idx.<locals>.fng  s   R(,$R((,$R(''l1o(>lSTo@VW 	1FBR.k*	C NN#t+m;b@%++E  99SVVC%8%J~#C0)	1, rc   r  )r  r  r  r  r  r  r  r  r  r{   r  r  r  r  r  s     `  `    @@@@@ra   _adaptive_pooling_fn_with_idxr  X  sQ     JD$LE5 	)YdE5	
! !F Irc   c                     j                         t        j                  k(  rt        d      t	         t
              sJ t        |      dk(  sJ  j                           j                         ^ }}}t        j                  j                  j                  |      }t        j                  j                  j                  |      }|\  }}||k(  r||k(  rt               S |dk(  s|dk(  r2g |||}t        | j                          j                               S ||z  dk(  r||z  dk(  r||z  ||z  g}t!         |      S t#        ||z   dz
  |      }	t#        ||z   dz
  |      }
t%        |      ||gz   } j                         }|	|
z  }|dkD  rt'         |      S d }d }t)        |||	|
g||g||gt*        j,                  	      t/        t1                      fd
}t3        j4                   j                         |||      }|S )Nz0'adaptive_avg_pool2d' not implemented for 'Long'r)   r   r  r+   rj  c                     t        | |z  |      S r   r&   r4  r  r  s      ra   r  z)_adaptive_avg_pool2d.<locals>.start_index      733rc   c                2    t        | dz   |z  |z   dz
  |      S r  r  r  s      ra   r  z'_adaptive_avg_pool2d.<locals>.end_index  "    g-7!;WEErc   r  r  r  r  r  r  c                ^    t        j                   | t                     |             S r   )rO   truedivr  )r  fn_sumones_loaderr   s    ra   r{   z _adaptive_avg_pool2d.<locals>.fn  s-    {{3+A./[1I
 	
rc   rV  )r   rw   r;  rM  rg   r@   r   r  r   rP   rY   r   r  r  r  rj   
avg_pool2drC   re   fallback_adaptive_avg_pool2dr  rO   r   r  	ones_liker<   r   )r   r  r  r  r  r  r  o_sizerd  h_kernel_maxw_kernel_maxr  r   rl  r  r  r{   rvr  r  s   `                 @@ra   _adaptive_avg_pool2dr    s   {{}#MNNa###{q   NNUD$77%%d+D77%%d+DLE5 u}QxzUaZ'5'%''V1;;=HHe|qTE\Q.u}dem4![))D5L1,u5LD5L1,u5LE{eU^+HKKME-KR+A{;;4F ""L1%.77F &il3K

 
		||~	
B Irc   c                     j                         t        j                  k(  rt        d      t	         t
              sJ t        |      dk(  sJ  j                           j                         ^ }}}t        j                  j                  j                  |      }t        j                  j                  j                  |      }|\  }}|dk(  s|dk(  r\g |||}t        | j                          j                               t        |t        j                   j                               fS ||z  dk(  r||z  dk(  rt        t!        ||z   dz
  |      }t!        ||z   dz
  |      }	t#        |      ||gz   }
 j                         }||	z  }|dkD  rt%         |      S d }d }t'        ||||	g||g||gt(        j*                  	      t-        ||||	g||g||gt(        j*                  	       fd
} fd}t/        j0                   j                         |||
      }t/        j0                   j                         t        j                  ||
      }||fS )Nz,adaptive_max_pool2d not implemented for Longr)   r   r  r+   rj  c                     t        | |z  |      S r   r  r  s      ra   r  z(adaptive_max_pool2d.<locals>.start_index  r  rc   c                2    t        | dz   |z  |z   dz
  |      S r  r  r  s      ra   r  z&adaptive_max_pool2d.<locals>.end_index  r  rc   r  c           	     <     | t        t        d                  S Nru  r  r/  )r  inner_func_max_valr   s    ra   inner_fn_max_valz-adaptive_max_pool2d.<locals>.inner_fn_max_val      !#':1eFm'LMMrc   c           	     <     | t        t        d                  S r  r  )r  inner_func_max_idxr   s    ra   inner_fn_max_idxz-adaptive_max_pool2d.<locals>.inner_fn_max_idx  r  rc   rV  )r   rw   r;  rM  rg   r@   r   r  r   rP   rY   r   r  r  rj   
ValueErrorrC   re   fallback_adaptive_max_pool2dr  rO   rU  r  r<   r   )r   r  r  r  r  r  r  r
  r  r  r  r   rl  r  r  r  r  r  rir  r  s   `                  @@ra   adaptive_max_pool2dr    sL   {{}#IJJa###{q   NNUD$77%%d+D77%%d+DLE5zUaZ'5'%''V1;;=H%%++allnK
 
 	
 e|qTE\Q.D5L1,u5LD5L1,u5LE{eU^+HKKME-KR+A{;;4F ."L1%.;; 7"L1%.;;NN 
		||~!	
B 
		||~kk!	
B r6Mrc   c                h               j                          fd}|S )Nc                `   j                         }t        |      dk(  r[t        |       dk(  r d| d   dz
  
z
  g      }nJt        |       dk\  r | d   | d   dz
  
z
  g      }n$ dddz
  
z
  g      }n g | dz
  
z
        }t        j                  |j	                               }t        j                  z
  t
        j                        }t        j                  dz
  t
        j                        }t        j                  t        j                  |t
        j                        t        j                  |t
        j                              }t        j                  t        j                  |d      d|      }t        j                  ||z   |z        t        j                  ||z        z
  }t        j                  |t
        j                        }t        j                  ||      }	t        j                  t        j                  |	||      t        j                               S )Nr   r+   r   r)   )r   r   rO   r:  r   rw   r;  r  r   float64r  r  r  r>  rh  r   r  )r^  ro   samples_shapesamplei_exprdiffout_sz_exprrA  seq_irF  r   in_sz	kernel_szndimsout_szsamplessamples_loaders             ra   rK  z)_fractional_pooling_offsets.<locals>.load5  s     ((*}"6{a (F1Iuqy3(GHV! (F1Iuqy3(OP (Auqy3(?@ $$>f$>eai#o$>?F7#4#4#67~~ei/=nnVaZ=LLu}}-s||K/W
 		#&&a0!U;		6F?e34syy%7PPUEKK0vvfk*$$SYYtUD%A5==QVCWXXrc   r  )r,  r(  r+  r)  r   r*  rK  r-  s   `````` @ra   _fractional_pooling_offsetsr.  /  s@    C[F#JE#I((*N!Y !YF Krc   c                "    t        | |||d      S r  _fractional_max_poolr   rd  r  random_sampless       ra   fractional_max_pool2dr4  [      ;^STUUrc   c                "    t        | |||d      S r  r0  r2  s       ra   fractional_max_pool3dr7  `  r5  rc   c                   | j                          | j                  d   | j                   d  }}t        j                  d      5  t	              D cg c]  }t        |||||       c}| j                         fd}fdt        |      t        |      z   }	| j                         }
t        j                  d| | j                         |
|
||	|      }t        j                  d| | j                         t        j                  |
||	|      }t        |t              sJ |       t        |j                   j                   t              r|j#                          t        |t              sJ |       t        |j                   j                   t              r|j#                          t%        ||| j                        }||fcd d d        S c c}w # 1 sw Y   y xY w)	Nrj  r  )r,  r(  r+  r)  r*  r   c                6    | d   } g | | |            S r   r   )r  ry  r^  r  rk  r  s      ra   r{  z&_fractional_max_pool.<locals>.fn_innerx  s.    5&\FOfO':3'NOPPrc   c                ~    | d   }|  d  }t              D cg c]  } |   |||         ||   z    c}S c c}w r   rx  )r  ry  r^  bdhwr  dhw_index_fnrk  s        ra   r  z1_fractional_max_pool.<locals>.increments_to_index|  s^    5&\Fvw<D u  QQ0=3CC  s   :r  r|  r  )r  r  r,   r   r   r.  rX  re   r   r=   r   rj   rw   r;  rg   r@   ri   rl  r  )r   rd  r  r3  rk  r  inp_dhwr  r{  r  r   r1  r  r  r<  r  r  s       `         @@@ra   r1  r1  e  s   NNWWWuf%qwwvw'77E	"	5 = 5\

  (&"%

 ==?	Q	 ;k!22!! <<>(	
 ""#<<>kk(	
 &),4f4,fkk&&	2NN'9-6w6-gll''3OO*[!''+>
 w{= =

= =s   GG1EGGG%c                b     j                           j                         ^ }}}t        j                  j                  j                  |      }t        j                  j                  j                  |      }|^ }}}	||z  dk(  r||	z  dk(  rt         ||z  ||	z  gd      S t        ||      }
t        ||	      }d fd}t        ||
|g||g||	gt        j                         fd}t        j                   j                          j                         |t        |            }|S )	Nr   r+   )divisor_overridec                F    t        | |z  t        j                  |            S r   )r%   r   r  r  s      ra   r  z0upsample_nearest2d_backward.<locals>.start_index  s    uwg(>??rc   c                     | dz   ||      S r  r   )r4  r  r  r  s      ra   r  z.upsample_nearest2d_backward.<locals>.end_index  s    EAI99rc   r  c                (     | t                    S r   )r  )r  r  r   s    ra   r{   z'upsample_nearest2d_backward.<locals>.fn  s    c.q122rc   rV  )r  r   rP   rY   r   r  r  rC   r  rO   r   r<   r   rj   r   re   )r   r  r  r  r  r  inp_hinp_wout_hout_wr  r  r  r{   r  r  r  s   `              @@ra   upsample_nearest2d_backwardrG    s"    NNJJLVUEGG&&u-EGG&&u-E&VUEu}eemq0!euneun=PQRR5%(L5%(L@: ""L1%.77F3 
		||~kkmJ	
B Irc   c           
     (    t        | ||||||d      S )Nr)   rZ  _avg_poolndr   rd  r(  r9  re  count_include_padr?  s          ra   r  r    )     		 	rc   c           
     (    t        | ||||||d      S )Nr   rZ  rI  rK  s          ra   
avg_pool3drO    rM  rc   c                v   ssdgz  t              t              t              t        | t              sJ t              k(  sJ t              k(  sJ t              k(  sJ t        | j	                               dz   dz   fv sJ | j                          | j	                         d   }| j	                          d  t        t              D 	cg c]  }	t        |	   |	|       c}	 \  }
}t              st        |      rt        | d      d}n| j                         d}t        |      t        |
      z   }| j                         t        j                  t         j"                        }|dkD  r4dk(  rt$        }nd	k(  rt&        }nt)        d
        || ||      S fd|r|r)|r|n|j*                  rdz  fd}nfd}nf	d}t-        j.                  | j1                         ||      }|S c c}	w )Nr   r+   r)   r9  rZ  TFrj  r   zUnknown dim: c           	     T   | d 	  }| 	 d  }d }t        j                  t        	      D cg c]  }t        
|          c} D ]V  }t        	      D cg c]  }||   |   z  ||   z   |   z
   }} |g ||      }||}At        j                  ||      }X |S c c}w c c}w r   )r   r  r   rO   r   )r  r  r^  r)  totalro   r\  r   r  r   rd  r9  r(  s            ra   r  z_avg_poolnd.<locals>.fn_sumL  s    UsdJ##U3Z%PeKN&;%PQ 	,BBG*MQ1Q4&)#be+gaj8MCM6C)C}U+	,  &QMs   B B%c                f    t        j                   |       t        j                              S r   )rO   rW  r<  )r  r   r  rX  r  s    ra   r{   z_avg_poolnd.<locals>.fn^  s&    wwvc84cll5%6PQQrc   c                f    t        j                   |       t        j                              S r   )rO   truncdivr<  )r  divisorr   r  r  s    ra   r{   z_avg_poolnd.<locals>.fnc  s'    ||F3$93<<QV;WXXrc   c                F  	 | 	 d  }g }t        	      D ]  }||   |   z  |   z
  }t        j                  ||   z   |   |   z         }s/t        j                  |d      }t        j                  ||         }t	        j
                  ||z
  t        j                        }|j                  |        t        j                  t        j                  |      }
j                  rt	        j                   |       |      S t	        j                   |       |      S r  )r   r   MinMaxrO   r:  rw   r  rk   r  r  rW  r  r  rU  )r  rz  divide_factorsro   hstarthendfactordivide_factorrL  r   r   r  rR  rd  r9  r(  r  s           ra   r{   z_avg_poolnd.<locals>.fni  s   cTUBN3Z .A*WQZ7yy+a.!8!A$:KL("YYvq1F 99T1Q40Dvu{{C%%f-. &,,SWWnEM&&{{6#x#8-HH<<sH 5}EErc   rV  )rJ   rg   r@   r   r   r  r   r   rh  r  r[  rX  re   r   r  r  r  rW  fallback_avg_pool2dfallback_avg_pool3dr  r  r<   r   rj   )r   rd  r(  r9  re  rL  r?  r   r  ro   r  
ceil_modeshad_paddingr  rl  fallbackr{   r  rV  r   r  rR  rX  r  s    ``` ` `          @@@@@@ra   rJ  rJ    sT    #){C0K&#&F7C(Ga###{s"""v;#w<3qzz|q#' 2222NNJJL3$E	

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

 1q+vw	J

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

s   -H6c                   dk7  sJ d       ssddgt        | t              sJ t        |t              sJ t              dk(  sJ t              dk(  sJ t              dk(  sJ t        |j                               dv sJ | j	                          |j                         ^ }t        d|      \  }	}
t        d|      \  }}| j                         d   xs d   xs |
xs || j                         ^ }t        |j                               }|j                         }t        fdt        d   dz        D              t        fdt        d   dz        D              z  }|dkD  rt        | ||      S fd	fd
}t        j                  | j                         |||      }|S )Nr   divisor must be not zeror)   r  r+   c           
   3  t   K   | ]/  }t        |d    z  t        d |d    z
  d    z        z
  d       1 ywr  r  r  s     ra   r   z&avg_pool2d_backward.<locals>.<genexpr>  r  r  c           
   3  t   K   | ]/  }t        |d    z  t        d|d    z
  d    z        z
  d        1 ywr  r  r  s     ra   r   z&avg_pool2d_backward.<locals>.<genexpr>  r  r  rj  c           	     @   t        j                  d   t        j                        }t        j                  d   t        j                        }t        j                  d   t        j                        }t        j                  d   t        j                        }t        j                  d   t        j                        }t        j                  d   t        j                        }t        j                  t        j
                  | |      |      }t        j                  t        j
                  ||      |      }	t        j                  t        j                  ||      t        j                  t        j                  t        j                        |            }
t        j                  t        j                  |	|      t        j                  t        j                  t        j                        |            }t        j                  |t        j                  dt        j                              }t        j                  |	t        j                  dt        j                              }	t        j                  |
t        j                  t        j                              }
t        j                  |t        j                  t        j                              }t        j
                  t        j                  |
|      t        j                  ||	            }|S )z{
        This computes the scaling factor that we will divide an element
        by when `count_include_pad=False`
        r   r+   )
rO   r<  rw   r  ry  rW  rV  r   r:  rU  )r  r  stride_hstride_wpad_hpad_wkernel_hkernel_wr[  wstartr\  wendr^  heightrd  r9  r(  r  s                ra   !compute_pool_size_without_paddingz>avg_pool2d_backward.<locals>.compute_pool_size_without_padding  s   
 <<q	5;;7<<q	5;;7WQZ5WQZ5<<A<<<A<X.6X.6{{GGFH%GGCNN65;;7?
 {{GGFH%GGCNN5%++6>
 VS\\!U[[%ABVS\\!U[[%AB{{4!DE{{4u{{!CDf 5swwtV7LMrc   c                8   | ^ }}}|d   z   }|d   z   }t        j                  t        |d   z
  d   z   d         t        j                        }t        j                  t        |d   z
  d   z   d         t        j                        }t        j                  t        |d         dz   t        j                        }t        j                  t        |d         dz   t        j                        }t        j
                  |t        j                  dt        j                              }t        j
                  |t        j                  dt        j                              }t        j                  |t        j                  t        j                              }t        j                  |t        j                  t        j                              }d }t              D ]+  }	t              D ]  }
t        j                  |t        j                  |	t        j                              }t        j                  |t        j                  |
t        j                              }}nssd   d   z  }n	 ||      }t        j                   g |t        j                  t        j                  |t        j                  |t        j                  dt        j                                    d      t        j                  t        j                  |t        j                  |t        j                  dt        j                                    d            |      }t        j                  t        j                  ||      t        j                  ||            }|;t        j                  ||t        j                  dt        j                               }t        j                  |t        j                  ||      |      } . |J |S )Nr   r+   Fr  r9  )rO   r:  r&   rw   r  rU  r<  rV  r   r   r  rh  ry  r?  r>  r  rS  )r  r^  rR  r  r  r  r  r  r  r  r  r  r  rX  partrF  rr  rL  r?  r  r  rb  rd  r9  r  r  r(  r  s                   ra   r{   zavg_pool2d_backward.<locals>.fn  s2   A
N
N..QQ'&)3VAY?
 ..QQ'&)3VAY?
 x6!9595;;Gx6!9595;;G++gs||Au{{'CD++gs||Au{{'CDE3>>-#MNE3>>,#LM' *	RC]+ )RWWWcll3&DEWWWcll3&DE#/,E&k'N[^;E=b"EE{{#11 #$&s||Au{{7S(T!" !.&+  11 #$&s||Au{{7S(T!" !-&+& ). xxFF2u%FF2u% #"yytS\\#u}}5UVH"yyswwx/FQHS)R*	RV ###rc   rV  )rg   r@   r   r   r  rh  rX  re   r   r  r   fallback_avg_pool2d_backwardr<   r   rj   )r  r   rd  r(  r9  re  rL  r?  r   _h_out
ceil_mode1_w_out
ceil_mode2r  r   rl  r{   r  rr  r  r  rb  rq  r  r  r  r  s     ``` ``          @@@@@@@@@ra   avg_pool2d_backwardrz    s    #'71'<X>XX<a&k9---a###{q   v;!w<1qzz|&&&

Q%;FJ &eQVWiXFJ))+K!*F
FjFJK&1&:&:&<#Q|AJJL!HKKME {1~)* M  {1~)* M
  -/KR+	
 		
 8? ?B 
		%%'	
B Irc   c                    dk7  sJ d       ssg dt        | t              sJ t        |t              sJ t              dk(  sJ t              dk(  sJ t              dk(  sJ t        |j                               dv sJ | j	                          |j                         ^ } t        d|      \  }	}
t        d|      \  }}t         d|      \  }}| j                         t              xs
 |
xs |xs || j                         ^ }t        |j                               }|j                         }fdt        d      D        \  z  z  }|d	kD  rt        | ||      S  fd
fd}t        j                  | j                         |||      }|S )Nr   re  )r   r   r   r   )r   r   r+   r)   c              3  j   K   | ])  t        fd t           dz        D               + yw)c           
   3  t   K   | ]/  }t        |   z  t        d |   z
     z        z
  d       1 ywr  r  )r   r  ro   rd  r(  s     ra   r   z0avg_pool3d_backward.<locals>.<genexpr>.<genexpr>c  sF      
 VAYQ[^);q	(I!JJAN
r  r)   N)r  r   )r   ro   rd  r(  s    @ra   r   z&avg_pool3d_backward.<locals>.<genexpr>b  s;      3
 	 	 
;q>A-.
 	
3s   /3}   c           	        d D        \  }}}d D        \  }}}d D        \  }	}
}d t        | ||g|||g|||g      D        \  }}}d t        |||g|	|
|gg|||g      D        \  }}}d |||fD        \  }}}d t        |||gg      D        \  }}}t        j                  t        j                  t        j                  ||      t        j                  ||            t        j                  ||            }|S )Nc              3  d   K   | ](  }t        j                  |t        j                         * y wr   rO   r<  rw   r  )r   r   s     ra   r   zQavg_pool3d_backward.<locals>.compute_pool_size_without_padding.<locals>.<genexpr>y  s     'UQ(D'U   .0c              3  d   K   | ](  }t        j                  |t        j                         * y wr   r  rE  s     ra   r   zQavg_pool3d_backward.<locals>.compute_pool_size_without_padding.<locals>.<genexpr>z  s     Ms||Au{{;Mr  c              3  d   K   | ](  }t        j                  |t        j                         * y wr   r  )r   r   s     ra   r   zQavg_pool3d_backward.<locals>.compute_pool_size_without_padding.<locals>.<genexpr>{  s$      (
-.CLLEKK((
r  c              3  x   K   | ]2  \  }}}t        j                  t        j                  ||      |       4 y wr   )rO   ry  rW  )r   rh  r   pads       ra   r   zQavg_pool3d_backward.<locals>.compute_pool_size_without_padding.<locals>.<genexpr>  s3      "
1c GGCGGAqM3'"
s   8:c           
   3     K   | ]i  \  }}}}t        j                  t        j                  ||      t        j                  t        j                  |t        j
                        |             k y wr   )rO   rV  r   r:  rw   r  )r   r  r   r   r  s        ra   r   zQavg_pool3d_backward.<locals>.compute_pool_size_without_padding.<locals>.<genexpr>  sU      

 #q#s KKq!3773>>#u{{+KS#Q

s   A/A1c              3     K   | ]<  }t        j                  |t        j                  d t        j                               > ywrD  rO   rU  r<  rw   r  )r   r  s     ra   r   zQavg_pool3d_backward.<locals>.compute_pool_size_without_padding.<locals>.<genexpr>  s2      "
 KKs||Au{{;<"
   AAc              3     K   | ]?  \  }}t        j                  |t        j                  |t        j                               A y wr   rO   rV  r:  rw   r  )r   r  r   s      ra   r   zQavg_pool3d_backward.<locals>.compute_pool_size_without_padding.<locals>.<genexpr>  s6      
S KKS^^C=>
   AA)r   rO   rW  ry  )pdr  r  stride_dri  rj  pad_drk  rl  kernel_drm  rn  dstartr[  ro  dendr\  rp  r^  depthrq  rd  r9  r(  r  s                      ra   rr  z>avg_pool3d_backward.<locals>.compute_pool_size_without_paddingx  sH   'Uf'U$(HMWMue(
2=(
$(H"
 Rx8<ueU>S"


 '*(8X.&u%	'	

dD"
 &&1"

tT 2UFE4JK
dD GGCGGD&)3774+@A3774QWCX
 rc   c                .   | ^ }}}}d t        |||g      D        \  }}}d t        |||g!      D        \  }}}d t        |||g!      D        \  }}	}
d |||fD        \  }}}d t        ||	|
g g      D        \  }}	}
d }t              D ]{  }t              D ]i  }t        "      D ]W  }d t        |||g|||g      D        \  }}}}n ssd   d   z  d	   z  }n
 |||      }t        j                   g |t        j                  t        j
                  |t        j                  |t        j                  dt        j                                    d
      t        j                  t        j
                  |t        j                  |	t        j                  dt        j                                    d
      t        j                  t        j
                  |t        j                  |
t        j                  dt        j                                     d
            |      }t        j                  t        j                  t        j                  ||      t        j                  ||	            t        j                  ||
            }|;t        j                  ||t        j                  dt        j                              }-t        j                  |t        j                  ||      |      }Z l ~ |J |S )Nc              3  ,   K   | ]  \  }}||z     y wr   r   )r   r   r  s      ra   r   z2avg_pool3d_backward.<locals>.fn.<locals>.<genexpr>  s     Avq#1s7Ar  c              3     K   | ]<  \  }}}t        j                  t        ||z
  |z   |      t        j                         > y wr   rO   r:  r&   rw   r  )r   r   r   r   s       ra   r   z2avg_pool3d_backward.<locals>.fn.<locals>.<genexpr>  s<      %
1a NN8AEAIq15;;?%
r  c              3     K   | ]8  \  }}t        j                  t        ||      d z   t        j                         : ywr	  r  )r   r   r   s      ra   r   z2avg_pool3d_backward.<locals>.fn.<locals>.<genexpr>  s6      
1 NN8Aq>A-u{{;
s   >A c              3     K   | ]<  }t        j                  |t        j                  d t        j                               > ywrD  r  )r   pstarts     ra   r   z2avg_pool3d_backward.<locals>.fn.<locals>.<genexpr>  s2      %
 KKQ <=%
r  c              3     K   | ]?  \  }}t        j                  |t        j                  |t        j                               A y wr   r  )r   pend
pooled_dims      ra   r   z2avg_pool3d_backward.<locals>.fn.<locals>.<genexpr>  s6      
 j KKcnnZEF
r  c              3     K   | ]?  \  }}t        j                  |t        j                  |t        j                               A y wr   )rO   r   r<  rw   r  )r   r  p_s      ra   r   z2avg_pool3d_backward.<locals>.fn.<locals>.<genexpr>  s6      "&FB R(EF"r  r   r+   r)   Fr  r9  )r   r   rO   r  rh  rV  ry  r<  rw   r  r?  r>  r  rS  r   )#r  r^  r  rR  r  pdstartr  r  pdendr  r  r  pd_r  r  r  r  r  rX  rt  rF  rr  rL  d_window_sizer?  r  r  rb  rd  r9  pooled_depthr  r  r(  r  s#                        ra   r{   zavg_pool3d_backward.<locals>.fn  s   AqAaAY)@A1a%
1ay+v>%
!'

Q1Iv.
ue
%
"GW5%
!'
$'u%m\'R%
ue ' 8	VC]+ 7V / 6VC"*-$gw7#sC+"JBB (3 0*+ +AQ ?+a. P A"b" M;;#!' # 5 5$'KK(*CGGE3<<5;;;W,X%& %1*/!" !$ 5 5$'KK(*CGGE3<<5;;;W,X%& %2*/!"  !$ 5 5$'KK(*CGGE3<<5;;;W,X%& %1*/!"!4 7D< 88E!2CFF2u4EFr5)D  '#&99 $S%--(H$ $'99T3778T3JH#Um6V7V8	Vr ###rc   rV  )rg   r@   r   r   r  rh  rX  r  re   r   r   fallback_avg_pool3d_backwardr<   r   rj   )!r  r   rd  r(  r9  re  rL  r?  r  _d_outceil_mode_drv  ceil_mode_hrx  ceil_mode_wr   r  r   rl  r{   r  rr  r  r  r  r  rb  rq  r  r  r  r  r  s!     ``` ``             @@@@@@@@@@@@ra   avg_pool3d_backwardr  5  s    #'71'<X>XX<k9---a###{q   v;!w<1qzz|&&&$%JJL!VUFE&q+vw	FK ';FK 'q+vw	FK ))+Kg,K+KKK4?4H4H4J1Qm\AJJL!HKKME3
 q3/M=-  -/-?KS+	
 		
# #JU U Un 
		%%'	
B Irc   c                   | j                         }t        |t              r|g}n|st        t	        |            }t	        |      dk(  rt        |      dv s
J d|        g S t        |      }t        t	        |            D ]_  }||   dk  r#||xx   t	        |      rt	        |      ndz  cc<   d||   cxk  rt	        |      k  rFn t	        |      dk(  r	||   dk(  r_J  t	        t        |            t	        |      k(  sJ d       |S )Nr   )r   r  rF  zinvalid axis: r+   zreduction axis not unique)r   rg   r   r   r   r   re   r$   )r   r^  r   ro   s       ra   _validate_reduction_axisr    s    ::<D$vSY
4yA~T{//H>$1HH/	:D3t9 M7Q;GCIs4y14GDG'c$i'CINtAw!|LLM z$ CI-J/JJ-Krc   c               x  
 |t        | |      } | j                         t        t           t	        | |            }g }g g }g t        t                    D ]Q  }||v r&j                  |       |j                  |          -j                  |       |j                  |          S 
fd}r0t              }	D ]  }t        j                  j                  |	|<   ! n|}	| j                         
t        | j                         |xs | j                         | j                         ||	|      S )Nc                   t        |      t        	      k(  sJ r+t        |       t        
      k(  sJ D cg c]  }| |   	 } }t        |       t              k(  sJ d gt        |       t        |      z   z  }t        j                  t        |       t        	|            D ]
  \  }}|||<     |      S c c}w r   )r   r   r   r   )r4  reduction_indexro   r  r  varinner_loaderkeepdimskept_idxreduced_idxr   s         ra   r  z%_make_reduction_inner.<locals>.loader!  s    ?#s;'7777u:T***'/0!U1X0E05zS]***Fc%j3+??@	!% #k?"C
 	!HC !IcN	! I&& 1s   B;)rr   r~  r|  rU  rT  r  )r   r   r$   r   r  r   r   rk   re   r   r#  r$  rX  r
  rj   r   )r   r^  r  r   r<  
kept_sizesreduced_sizesro   r  r  r  r  r  r   s     `       @@@@ra   _make_reduction_innerr    s'   Q::<Dc?3At<=DJHMK3t9 '9q!  a)OOAd1g&'' ' : 	&A''++HQK	& ==?L||~'81;;=++-& rc   c                     dd d fd}|S )Nr   c                   t        | |||      }t        j                  d| d|}t        |j                  j                  t              r|j                          |S )Nr^  r  r   r<  )r  r}  r   )r  r=   r   rg   ri   rl  )r   r^  r  r   r   r1  r<  r  s         ra   rb  zmake_reduction.<locals>.innerA  sb    &"7
 !!XAXQWXKK
 NNrc   r   r   )r  r<  rb  s   `` ra   make_reductionr  @  s    T   Lrc   c                   |t        | |      } t        | |      }t        | j                         | j	                         f| j                         f| j                         |      S )N)rr   dtypes	inner_fnsr   r^  )r   r  r
  rj   r   rX  r   )r   r^  r   s      ra   _make_scan_innerr  T  sZ    QD!D||~==?$ZZ\ rc   r   c                   |t        | |      } | j                         t        | |      }| j                         }|t        j
                  t        j                  fv rt        | t        j                        } t        | ||      }t        fd|D              }t        j                  || j                         | j                               }t        j                  |t        |j                                     }t        t!        ||      |      S )Nc              3  (   K   | ]	  }|     y wr   r   r   ro   r   s     ra   r   zmean.<locals>.<genexpr>m       0a$q'0r   r3  )r   r   r  r   rw   r[  rZ  r/  sum_rM   r.   r5   rj   r4   r   re   div)r   r^  keepdimr   output_dtype
sum_resultdenomr   s          @ra   r  r  b  s    Q::<D#At,D;;=Lu~~66Q$aw'J0400Ee1;;=XEeT**=*=*?%@AEC
E*L99rc   c                2  
 |d}| j                         
t        | |      }t        | |d      }|r|j                          t	        t        | |            }t        |||      }t        
fd|D              }|rt        j                  ||z
  d      }t        j                  || j                         | j                               }t        j                  |t!        |j                                     }t#        ||      }	|s|	fS |r|nt%        ||      }|	|fS )Nr+   T)r  c              3  (   K   | ]	  }|     y wr   r   r  s     ra   r   z var_mean_sum_.<locals>.<genexpr>  r  r   r   r3  )r   r  r  rl  squarery  r  rM   r   rY  r.   r5   r   rj   r4   r   re   r  r  )r   r^  
correctionr  return_meanx_meandiffsr  r  x_varr   s             @ra   var_mean_sum_r  s  s    
::<D#At,D!T4(F3q&>"EeT7+J0400E		%*,a0e1;;=XEeT**=*=*?%@AE
E"ExVGFD$9F&=rc   c                    t        | |      }t        | ||d d       }|d   }t        |d         }t        |t        j
                        xr, t        |      t        j                  k  xr t        |      dk7  S )Nr  rT  r  r+   )	r  r  rM   rg   r   r(  r   r,   r  )r   r^  r  r   rT  reduction_numels         ra   use_two_step_variancer    s|    #At,D"	wd$F HF#F+=$>?O?EMM2 	' 6#E#EE	'&!Q&rc   c                  dt        | ||d d       }|j                  d      }|j                  d       |j                  d       t        j                  j                  d|fd| j                         d|\  }}}	|j                          | j                         | j                         t        | |      }t        fd|D              d	 fd
}
 t        |
      |      }|r|j                          ||fS |fS )Nr+   r  rU  r~  r|  welford_reduce)r  r  r   c              3  (   K   | ]	  }|     y wr   r   r  s     ra   r   z$var_mean_welford_.<locals>.<genexpr>  s     1q471r   c                    t        | t        j                        rD| j                  s8t	        j
                  t	        j                  | t        j                        |      S t	        j                  | |      S r   )
rg   r   r   	is_numberrO   r   r:  rw   r;  r<  r5  s     ra   get_constant_or_index_exprz5var_mean_welford_.<locals>.get_constant_or_index_expr  sG    a$Q[[<<q%++ >FF||Au%%rc   c                           }       }t        j                  d      }| t        j                  |||z
        z  S r  )rO   r<  rU  )ri   cNzeror  r   r  rnumels       ra   r  z#var_mean_welford_.<locals>.scale_fn  sE    &z59&vu5||Au%ckk$A...rc   r   )r  r  r.   WelfordReductionr   r   rl  r   r  rM   rc  )r   r^  r  r  r  r   r  r  m2r   r  r  r   r  r  r   s     `         @@@@ra   var_mean_welford_r    s    
"	wd$F ZZ
#F
JJ{
JJ{%%,, )'kkm 	KD"a JJLKKME::<D#At,D1D11F&
/ #.
"2
&CDy6Mrc   c                   | j                         t              }t        | |d      } t        | ||||      }t	        | ||      rt        di |n
t        di |}t        fd|D              }|s|d   S |S )NFr  )r   r^  r  r  r  )r^  r  c              3  :   K   | ]  }t        |d         yw)Fr  N)r   )r   r   rt  s     ra   r   z#var_mean_helper_.<locals>.<genexpr>  s     F!8Ayu55Fs   r   r   )r   r   r   r
  r  r  r  r   )	r   r^  r  r  r  compute_dtyper   r*  rt  s	           @ra   var_mean_helper_r    s    I))4MM.A
F !w? 	(( 
 FvFFF'6!93V3rc   )r  r  c               "    t        | |||d      S )NFr^  r  r  r  r  r   r^  r  r  s       ra   var_r    s    	W% rc   c               "    t        | |||d      S )NTr  r  r  s       ra   var_meanr    s    	W$ rc   c                   |dk  r!t        t        j                  |       | |      S |dk(  rt        j                  d|      S |dk(  r| S t        | |dz  |      }t        j                  ||      }|dz  dk(  rt        j                  ||       }|S )Nr   r+   r)   )pow_recursiverO   rT  r<  rW  )r   r+  r   r1  s       ra   r  r    s    1uS^^A.E::Av||Au%%Av1a1fe,FWWVV$F	A!|#Mrc   c                .    t        j                  | |      S r   )rO   powr   r)  s     ra   
pow_nativer    s    771a=rc   )r   c                v    t        t              r#t              k(  rt         t                    S t        t              rdk(  rt	               S t        t              rdk(  rt               S t        d  fD              }t        |      }t        t              xr dcxk  xr dk  nc xs	 |xr dk\  }|rZ j                          fd}t        j                   j                          j                         | j                               S t         t              r: dk(  rt        d      S  d	k(  r$t!        j                               rt#              S |rDt         t              rt%               S t        t              rt'               S t)               S t+               S )
Nr  r+   c              3  r   K   | ]/  }t        |t        j                        s|j                          1 y wr   )rg   r.   r@   r   r  s     ra   r   zpow.<locals>.<genexpr>  s#     N1*Q2MNs   77i    r   c                F    t         |       j                               S r   )r  r   )r  r   r)  r  s    ra   r{   zpow.<locals>.fn  s     a??rc   rV  r)   )rg   r/  r   r  sqrtr  r9  r   rX  r<   r   rj   r   r   r   r  r   exp2fallback_pow_scalarfallback_pow_tensor_scalarfallback_pow_tensor_tensorr  )r   r)  r   is_integer_powembed_exponentr{   r  s   ``    @ra   r  r    sx   !USV1c!f~	Au	!s(Aw	As	QQx NANNE%e,N  3' a"32AF  	@ <<>++-::<	
 	
 !V6Q?"6nQ[[]37Na &q!,,6"-a33-a33arc   c                   t        | t              r| j                  }n| }t        |t              r|j                  }t        |t        j                        st        j                  | j                         | j                         |j                         | j                               }t        |t        t        f      sJ |j                  }t        |t        j                        sJ t        |t        j                        rg|j                         sW|j                         sGt        |j                  t        j                        s#|j!                          |j                  |_        | S t        j"                  j%                  |||       | S )NrV  unsafe_alias)rg   r@   ri   r.   r   r<   r   rj   r   rX  r   r2   r8   is_input_bufferis_module_buffer	NopKernelrl  r  realize_into)changedr  r  changed_datar_   s        ra   r  r  7  s*   '9%||#y!hhc2==)%%'##%__&##%	
 $: 6777ii#r}}---,.$$&((*l''6 	HH!!..\ /  Nrc   c                .    t        | t        | |            S r   )r  r  )r   r?  s     ra   r8  r8  \  s    Q	!Z011rc   c                    | |u r| S t        || j                               }t        || j                               }t	        || j                               }t        | |      S r   r  rj   r   r   r'  r   r  )r  r  r  s      ra   r  r  a  sR    
cz

C)
*C
3
(C
clln
%CS#rc   c                .    t        j                  | |      S r   )rO   floordivr  s     ra   r  r  l      <<1rc   c                .    t        j                  | |      S r   )rO   rU  r  s     ra   rU  rU  q  r  rc   c                >   t        |       xr t        |      }t        |       xr t        |      }|dk(  r,|rJ d       |rt        | |      S t        t	        | |            S |dk(  r,|rJ d       |rt        | |      S t        t	        | |            S t	        | |      S )Nr  z5floordiv operands can not be boolean at the same timer  z5truncdiv operands can not be boolean at the same time)r   r   r  r  r  rU  r  )r   r)  rounding_modeboth_integerboth_booleans        ra   div_moder  v  s    "1%</!*<L"1%</!*<L X!XX!-x1~C5Q3CCX!XX!-x1~C5Q3CCq!9rc   c                    t        |       xr t        |      }|rt        | |      S t        t        j                  j
                        } t        |      | |      S r   )r   logical_andr:   r  rW  r  rc  )r   r)  	both_boolr{   s       ra   rW  rW    sN    "9q'9I1a  **+!~b!!Q''rc   c                f   t        | t        j                        rt        | j                        S t        | t        j
                        rt        | j                               S t        | t        j                        r| S t        | t        j                        syt        j                  j                  j                  | j                               }t        j                  |      5  t!        j"                  t        j$                  dd      5   | j&                  | j)                          }ddd       ddd       t        t        j                  j*                  j,                        sJ t        |j.                  t        j                        r|j.                  S y# 1 sw Y   rxY w# 1 sw Y   vxY w)z:Try convert an arbitrary IR node into an ir.Constant valueNallow_indexingT)rg   r.   r8   get_constant_valueri   r2   r$  r   Loopsrw   	_inductorops_handlerExtractConstantsHandlerrj   rP   set_ops_handlerr   objectr_  rU  inner_fn_argsvirtualizedOpsValuer   )r   r  rm   s      ra   r  r    s/   
 !R]]#!!&&))!R[[!!!--/22!R[[! a"oo))AA!,,.QG	'"-R&&(8$?- ajj!//+,	- - c5??66??@@@#))R[[)yy- - - -s$   &&F'F*F'F$	 F''F0c                l   t        d | |fD              }|rt        | |      S t        |      x}q| j                         j                  dk7  rT|j
                  dk(  r*t        j                  t        d      |j
                        }nd|j
                  z  }t        | |      S d } t        |      | |      S )Nc              3  L   K   | ]  }t        |      xs t        |        y wr   )r   r   r  s     ra   r   zdiv_prim.<locals>.<genexpr>  s"     O1oa(>OA,>>Os   "$r   r   infr~  c                 &    t        j                  |  S r   )rO   r  r  s    ra   r{   zdiv_prim.<locals>.fn  s    {{D!!rc   )r  rU  r  rj   r   r   mathcopysignr/  rW  rc  )r   r)  is_integralrV  rT  r{   s         ra   div_primr-    s    OAOOK1~ &a((5!,,.:M:MQV:V==AuU|W]]CJw}},J1j!!" >"a##rc   c                Z    t        | |ft        j                        \  } }t        | |      S r>  )r>  r   INT_TO_FLOATr-  r  s     ra   r  r    s0     	
A$C$P$PDAq Aq>rc   c                h    t        |       xs t        |       }|rd }nd } t        |      | |      S )Nc                .    t        j                  | |      S r   )rO   modr  s     ra   r{   zfmod.<locals>.fn  s    771a= rc   c                .    t        j                  | |      S r   )rO   fmodr  s     ra   r{   zfmod.<locals>.fn  s    88Aq>!rc   )r   r   rc  )r   r)  r,  r{   s       ra   r4  r4    s9    !!$:(:K	!
	" >"a##rc   c                   t        | j                               st        | j                               r|t        j                  }t        d|      } || |||      S )Nr  r~  r   r   r   r   rw   r;  r  r   r^  r  r   r{   s        ra   r  r    sK     	'+;AKKM+J
-	U	;Baxu--rc   c                   t        | j                               st        | j                               r|t        j                  }t        | j                               dk(  r(|dv sJ |xs | j                         }t        | |d      S d }t        | ||      }t        j                  j                  d	i |d|i\  }|t        | ||      S |S )
Nr   r   rF  Tr  c                @    | \  }|\  }t        j                  ||      fS r   )rO   r   a_tupleb_tupler   r)  s       ra   
combine_fnzcumsum.<locals>.combine_fn  #    1rc   r^  r   r>  r   r   r   )r   r   r   rw   r;  r   r   r   r  r.   Scanr   fallback_cumsumr   r^  r   r>  r   r1  s         ra   cumsumrE    s     	'+;AKKM+J
-
1::<Aw&5t,, 
 ad%8F??J?IV~qd%88Mrc   c                   t        | j                               st        | j                               r|t        j                  }t        | j                               dk(  r(|dv sJ |xs | j                         }t        | |d      S d }t        | ||      }t        j                  j                  d	i |d|i\  }|t        | ||      S |S )
Nr   r9  Tr  c                @    | \  }|\  }t        j                  ||      fS r   )rO   rW  r;  s       ra   r>  zcumprod.<locals>.combine_fn  r?  rc   r@  r>  rA  r   )r   r   r   rw   r;  r   r   r   r  r.   rB  r   fallback_cumprodrD  s         ra   cumprodrI    s     	'+;AKKM+J
-
1::<Aw&5t,, 
 ad%8F??J?IV~t599Mrc   c                
   d }| j                         }t        | j                               dk(  r|dv sJ t        |       S t	        | ||      }t        j                  j                  di |d|i\  }|t        | |      S |S )Nc           	     *   | \  }|\  }t        j                  ||      }t        j                  ||      }||k7  t        j                  |       z  }t        j                  |t        j
                  t        j                  ||z
              |z   |      fS r   )rO   rV  rU  r  r  log1pexp)r<  r=  r   r)  min_vmax_vrF  s          ra   log_add_exp_helperz(logcumsumexp.<locals>.log_add_exp_helper(  s{    Aq!Aq!CIIe$4#45		$		#''%%-*@ AE I1MOOrc   r   r9  r@  r>  rZ  r   )	r   r   r   r  r  r.   rB  r   fallback_logcumsumexp)r   r   rP  r   r   r1  s         ra   logcumsumexprR  &  s    P KKME
1::<Ag~~Qxac7FGG4FGIV~$QC00Mrc   c                   t        | j                               dk(  r,dv sJ t        |       t        | t        j
                        fS | j                         }t        j                  d|d      }t        | |      }|t        j
                  f|d<   | j                         fd	f|d
<   t        j                  j                  di |d|i\  }}|t        |       S ||fS )Nr   r9  r   r  Fr   arg_break_ties_leftr@  r  c                R    t        j                  |    t        j                        S r   rO   r:  rw   r;  r  r^  s    ra   r8  zcummax.<locals>.<lambda>K      CNN3t9ekk: rc   r  r>  rZ  r   )r   r   r  r  rw   r;  r   r.   get_reduction_combine_fnr  rX  rB  r   fallback_cummaxr   r^  r   r>  r   r   r  s    `     ra   cummaxr]  <      
1::<AwQxAU[[999KKME,,5J ad%8Fu{{+F8	:F; ggnnEvE*EOFG~qd++7?rc   c                   t        | j                               dk(  r,dv sJ t        |       t        | t        j
                        fS | j                         }t        j                  d|d      }t        | |      }|t        j
                  f|d<   | j                         fd	f|d
<   t        j                  j                  di |d|i\  }}|t        |       S ||fS )Nr   r9  r   argminFrT  r@  r  c                R    t        j                  |    t        j                        S r   rW  rX  s    ra   r8  zcummin.<locals>.<lambda>b  rY  rc   r  r>  rZ  r   )r   r   r  r  rw   r;  r   r.   rZ  r  rX  rB  r   fallback_cumminr\  s    `     ra   cumminrc  S  r^  rc   c                   t        | j                               st        | j                               r|t        j                  }t        d|      } || |||      S )Nr  r~  r   r6  r7  s        ra   r  r  j  sK     	'+;AKKM+J
-	e	<Baxu--rc   c                ^    t        | t        j                        }  t        d      | ||      S )Nr  r^  r  )r   rw   r   r  r   r   r  s      ra   
reduce_anyrh  u  s(    EJJA >% w??rc   c                Z    |t        | ||      t        | ||      fS t        | d |      S Nrf  )reduce_amaxreduce_argmaxrg  s      ra   
reduce_maxrm  {  :    
g6!#8
 	

 qtg66rc   c                Z    |t        | ||      t        | ||      fS t        | d |      S rj  )reduce_aminreduce_argminrg  s      ra   
reduce_minrr    rn  rc   xor_sumr  r  r  r~  r`  
logical_or)r_  rS  stabler   
descendingc          	        |d}| j                         }| j                         }t        t        |      |      }t        |      dk(  r't	        |       t        d|t        j                  |      fS t        |      r||   nd}t        j                  j                  j                  |t        j                  t        j                        j                        st        | |||      S t!        |ddt        j                  |d      }dgt        |      z  }t        |      r|||<   t#        ||      }t%        ||      }t&        j(                  j+                  || j,                  |j,                  f| j/                         |j/                         f||||      \  }	}|	t        | |||      S |J |	t1        |t        j                        fS )NFr   r+   ru  )r  r  r   rr   r	  )rr   r  r  r   r^  rv  rw  )r   rj   r   r   r  r@  rw   r;  rP   rY   r   statically_known_ltr  int16r  sort_fallbackr
  r  r'  r.   Sortr   r   rX  r   )
r   rv  r   rw  r  rr   r  r  
view_shaper   s
             ra   sort_stabler~    s   ~JJLE\\^F
3u:s
+C
5zQQxq&%++u=== ZuSzQH77//%++ekk:R:V:VWQv3:NNVSXG s5z!J
5z"
37J'GWe$Gggnn'==?G$7$7$9: % OFG ~Qv3:NN8GU[[111rc   c                     t        | d||      S )NFru  )r~  )r   r   rw  s      ra   sortr    s    qCJGGrc   c                <    t        | |t        j                  |      S )Nr   r   ra  )r  r   r/  )r\   r   ra  s      ra   register_pointwise_numericr    s!    
;HH'	 rc   c                b    t        | j                         t        | t        j                        S r>  )rL   r  r  r   r/  r  s    ra    register_pointwise_numeric_ldf64r    s'    '4
;HH rc   r  logical_not)rS  )r   r   r<  identity)rj  pointwise_overrides_datac              #  F  K   t         |   t        | j                  d       }|y fd}t        |t        j
                  j                        r9|j                         D ]%  }t        ||      }|j                   ||      f ' y |j                   ||      f y w)Nc                4    j                   t        |       S y r   )tritonr  )r\   ri   s    ra   make_triton_fallbackz6_get_pointwise_overrides.<locals>.make_triton_fallbackE  s    ;;#B'' rc   )	r  r   r   rg   rw   rx   r   r   r   )nsr   r\   r  olnamerO  ri   s         @ra   _get_pointwise_overridesr  ?  s     #D)D	TYY	%B	z( "ejj112lln 	IFV$Bd..0DR0HHH	I $**,@,DDDs   BB!r  c                d    | t         |<   t        j                  |        fd}t        | |       y )Nc                      | i |}g }t        | d   |      D ]"  \  }}|j                  t        ||d             $ |S )Nr   Tr  )r   rk   r  )rp   r   resultsmut_resultsr   r1  outplace_ops         ra   r{   z$register_foreach_inplace.<locals>.fn  sV    t.v.tAw0 	JKCyf4HI	J rc   )rV   rh  r   r  )aten_opoutplace_aten_opr  r{   s     ` ra   register_foreach_inplacer    s.    07,-G$ w+rc   c                2    t        | d       fd       }|S )Nr  c                 l     | i |}t        || d   j                               }t        | d   |      S r  )r   r   r  )rp   r   r1  r  s      ra   r{   zregister_inplace.<locals>.fn  s<    d-f-&$q'"3"3"56a&))rc   )r  )r  r  r{   s    ` ra   register_inplacer    s#    wD9* :*
 Irc   c                     y r   r   r  s      ra   sym_constrain_ranger        rc   c                    t         j                  j                  j                  d   }t	        |t
        j                        s
J d|        |j                  j                  S Nr  z*Expect val to be torch.SymInt but got val=	rP   rY   rZ   r\  rg   rw   r  r_   r  r   r   r  s      ra   sym_sizer    sS    
''


#
#E
*C c5<<( 
4SE:( 88==rc   c                    t         j                  j                  j                  d   }t	        |t
        j                        s
J d|        |j                  j                  S r  r  r  s      ra   
sym_strider    sQ    
''


#
#E
*Cc5<<( 
4SE:( 88==rc   c                "    | j                         S r   )rk  )r   s    ra   	sym_numelr    s    ;;=rc   c                &    t        j                  |  S r   )r   Addr  s    ra   sym_sumr    s    99drc   c                    t        d      )NzHelpful for debuggingr   )r  rp   r   s      ra   foobarr    s    
5
66rc   c                8    | j                          t        |       S r   )rl  r  r   s    ra   _realizer    s    IIK8Orc   c                R    | j                          t        j                  | |       | S r   )rl  r.   ResizeStorageBytes)variabler  s     ra   resize_storage_bytes_r    s#    (H-Orc   c                    | j                          |j                          t        j                  t        j                  | |            S r   )rl  r@   r   r.   SetSourceTensorKernel)r  source_tensors     ra   set__source_tensorr    s5    LLNB44T=IJJrc   r  c                    | |u r| S t        || j                               }t        || j                               }t	        || j                               }t        | |      S r   r  )r  r  s     ra   
fsdp_copy_r  (  sR    #:JS^^-.sCMMO,S#,,.)c""rc   c                 	
 t        | t              sJ t        |t        t        f      sJ |t        j
                  }|t        j                  k(  rt        d|       |t        j                  k(  rt        |      dk(  sJ |t        j                  k(  rt        |      dk(  sJ | j                         
| j                         }| j                         }t        | j                  t        j                         r| j                  j#                         | _        t	        j$                         rit        j&                  j(                  j*                  rEt-        |      rt/        d      n0t1        |      r t	        j2                  |      j4                  ndndt6        j8                  j:                  j=                  
d      rt?        |||      S tA        | 
gd	g      }|jC                         	t        jD                  jG                  ||      }t        jH                  ||||      jK                         	
fd
}tM        jN                  |||t        |            }|S )Nzunsupported memory format: r   r   nanTr9  r   r  r+   c                    |       t        j                  t        j                        }t        j                  t        j                        }t        j                  ||      }t        j
                  |fd      S )Nc                       g      S r   r   )
flat_indexflat_loaders   ra   r8  z*resize.<locals>.inner_fn.<locals>.<lambda>l  s    ZL(A rc   )rO   r:  rw   r;  r>  r@  )	r  flat_index_exprlimitrF  r  r  	old_numelout_indexeruninitialized_vals	       @ra   rU  zresize.<locals>.inner_fng  sZ     %
..U[[Ay%++6vvou-zz$ ACTUUrc   rV  )(rg   r@   re   r   rw   contiguous_formatpreserve_formatrM  channels_lastr   channels_last_3drk  r   r:  ri   r.   r2   r$  r  utilsdeterministicfill_uninitialized_memoryr   r/  r   r  r  rP   rY   r   r  re  r-  rX  r_   stride_ordered_for_memory_formatr'  ra  r<   r   )r   r   r  r   rr   x_flat
out_striderU  rm   r  r  r  r  s            @@@@ra   resizer  3  s   a###dT5M***//---8HII+++4yA~~...4yA~~IKKME""$F!&&"++&##% 	224KK%%??%  %ee$ %E 2 6 6 $  ww//	1=D+5HH		
 	
F $$&K""CCD-XJ..jANNPKV 

UXd4jC Jrc   )auto_functionalizedc                    ddl m} |j                  |      }t        j                  | ||i ||       |j                         D ci c]  \  }}t        |t              s|| c}}S c c}}w )Nr   )kernel_side_table)
kernel_idxgridtma_descriptor_metadatakernel_args)*torch._higher_order_ops.triton_kernel_wrapr  get_constant_argsr.   UserDefinedTritonKernelr   rg   r@   )	r  constant_args_idxr  r  r   r  constant_argsr  r  s	            ra   triton_kernel_wrap_r  z  sj     M%778IJM 7/v//	 &,\\^Rcz#y7QCHRRRs   A*!A*c                ^   t        d | g|D              rTd}t        j                  j                  j                  j                  dd       x}r| d| }|t        j                  _        t        j                  j                  | |||      }t        t        t        j                  |            S )Nc              3  V   K   | ]!  }t        |t              xr t        |       # y wr   rD  r  s     ra   r   zcond.<locals>.<genexpr>  s#     
Ma:a 1Yq\1
MrE  z"control flow operator: torch.cond.stack_trace Found from : 
 )r  rP   rY   rZ   r\  r]  disable_cudagraphs_reasonr.   Conditionalr   re   mapr@   )predtrue_fnfalse_fnoperandsr   r  r1  s          ra   r   r     s    

MD;L8;L
MM2''..3377tLL;LE*;-8C,/)^^""4(HEFI$$f-..rc   c                p   t        d ||z   D              rTd}t        j                  j                  j                  j                  dd       x}r| d| }|t        j                  _        dd}t        j                  j                  | ||||      }t        |t              sJ t        t        ||            S )Nc              3  V   K   | ]!  }t        |t              xr t        |       # y wr   rD  r  s     ra   r   zwhile_loop.<locals>.<genexpr>  s+       	1f.)A,.rE  z(control flow operator: torch.while_loop.r  r  c                    t        | t              r| S t        | t        j                        rt        |       S t        | t        j                        rt        j
                  |       S t        dt        |              )NzNYI unsupported output type: )rg   r@   r.   r   MultiOutputr   rM  r   )rm   s    ra   _map_outputzwhile_loop.<locals>._map_output  s_    c9%JR]]+S>!R^^,##C((!>tCykJKKrc   )rm   r   )r  rP   rY   rZ   r\  r]  r  r.   	WhileLoopr   rg   r   re   r  )	cond_fnbody_fncarried_inputsadditional_inputsstack_outputr   r  r  r1  s	            ra   
while_loopr    s    
 "33  9''..3377tLL;LE*;-8C,/)L \\  .*;\F fh'''K())rc   )r  c                    t        j                  j                  | g| }t        t	        t
        j                  |            S r   )r.   InvokeSubgraphr   re   r  r@   )subgraph_fn
identifierr  r1  s       ra   invoke_subgraphr    s5    %%k=H=FI$$f-..rc   )schemec                  d }t         j                  j                  j                  j	                  dd       }|J t        | j                  j                  j                        D ]  \  }}|j                  dk(  r!||   t         j                  j                  |<   7|j                  dk(  rt         j                  j                  |      \  }}t        j                  ||j                               D ]  }	|	j                          |j                  r7t         j                  j                   j#                  |	j%                                t         j                  j&                  j#                  |	j%                                 t(        j*                  j,                  j/                  t         j                  |||      }Xt         j                  j1                  |      t         j                  j                  |<    |S )Nquant_optionsr,  r*  )rP   rY   rZ   r\  r]  rf   r  nodesr\   envfetch_args_kwargs_from_envr   r   r   rl  codegen_low_precisionlow_precision_codegen_opsr   rm  invoke_quant_opsrw   r.  Interpreterr*  run_node)
r  r  r  r*  r  ro   r_   rp   r   r   s
             ra   invoke_quant_tracerr    sl   FGG((--11/4HM$$$[55;;AAB 7477m# (AGGKKWW 77==dCLD&__T6==?; E		 66GG5599!:N:N:PQ((,,Q-A-A-CDE XX))00$fMF ! 0 0 6AGGKK%7( Mrc   c                  
 ddl m}m} t        |      dkD  rt	        d      t        j                  ||      D cg c](  } ||j                         |j                               * }} || |      

fd}t        |d   dd       }t        d |D              |d	<   t        d
 |D              |d<   t        j                  j                  d|dd|}	|	d   t	        d      |	S c c}w )Nr+   )InputDescriptorlower_pointwise_subgraphr   zSUnable to generate code for associative_scan op, because there are lifted argumentsr  c                d     g t        j                  |       t        j                  |       S r   )r  r0  )lhsrhslowered_combine_fns     ra   wrapped_combine_fnz,associative_scan.<locals>.wrapped_combine_fn  s6    ! 
$
$
 	
rc   r@  c              3  <   K   | ]  }|j                           y wr   )r   r  s     ra   r   z#associative_scan.<locals>.<genexpr>  s     7qQ[[]7   r  c              3  <   K   | ]  }|j                           y wr   r  r  s     ra   r   z#associative_scan.<locals>.<genexpr>  s     <A<r  r  F)r>  can_fallback_to_atenz/Unable to generate code for associative_scan opr   )r  r  r  r   rM  r   r   r   rj   r  r   r.   rB  r   )r>  xsr  r  r  r   subgraph_inputsr
  r   r1  r	  s             @ra   associative_scanr    s     M
!a
 	
 R( 	akkmALLNCO  2*oN
 be!48F7B77F8<<<F;WW^^ %" F
 ayLMMM-s   -C'c                     y r   r   )tokenss    ra   _sink_tokensr    r  rc   c                N   t        j                  j                  |g|i |}ddlm}  ||||      }|J t
        j                  j                  |   }||fS t        j                  t         j                  t        j                  |      }t        |t              s||fS |g|S )Nr   )get_effect_key)r.   EffectfulKernelr   torch._higher_order_ops.effectsr  rP   rY   effectful_opsr  r  r  r@   rg   r   )tokenr\   rp   r   r1  r  effect_typeeffectful_kernels           ra   with_effectsr    s    &&r;D;F;F> T62K"""ww,,[9~ ""!!"..)2B2BFKF fe$ &)) *6**rc   )register_comm_loweringsc                x   t        | |ddd      }|d   }t        j                  j                  j	                  t        |            }t        j                  j                  di |d|d\  }}|dk(  rZt        j                  j                  j                  |      t        j                  k\  r t        j                  d| d|d	|\  }}||fS t        j                  t!        j"                  d
             t%        | |d      }	t'        t(        j*                     t-        | |	            }
t/        |
|d      }|	|fS )zn
    Lowering inductor_prims.prepare_softmax_online to compute max/sum in one pass if no split is needed.
    TNr  r  online_softmax_reduce)r  r  r+   r)   )r}  
num_outputreduction_hintz
            Online softmax is disabled on the fly since Inductor decides to
            split the reduction. Cut an issue to PyTorch if this is an
            important use case and you want to speed it up with online
            softmax.
            )r  r   )r  rP   rY   r   simplifyrM   r.   r=   
num_splitsr  r,   r  r9   r   r  r  textwrapdedentrk  rT   r  rM  ry  r  )r   r   r   r  r  hint	num_split
max_tensor
sum_tensorr  rM  xsums               ra   prepare_softmax_onliner,  $  s4   
 #	d$dF 01WW&&}5E'FGFll-- 
.OD) 	QGG&&v.&2T2TT!7!>!> "
Qt"
?E"

J :%% 	OO		
 1cD1!#a,/Ct,Tzrc   )r  )quantized_lowerings)mkldnn_lowerings)jagged_loweringsc              #  X  K   t        | t        j                  j                        sJ d       t        j                  |       }	  t        |       t        |              d |r
|t        | <   yt        j                  |        y# |r
|t        | <   w t        j                  |        w xY ww)z^
    A context manager to force fallback an op. Used in unit test
    for FallbackKernel.
    z+Only OpOverload to make the clean up easierN)	rg   rw   rx   ry   rT   r]  r  r  r  )r\   old_handlers     ra   force_fallbackr2  q  s      b%**//0 50 --#K".r23'IbMMM" 'IbMMM"s   AB*B ""B*#B''B*)rl   z%Iterable[Union[tuple[Any, Any], Any]])r{   zCallable[..., Any]r  zOptional[Callable[..., Any]])r   r   )r   r   )r   r@   rr   torch.devicer  r@   )rp   z	list[Any]r   zdict[str, Any]r   r   r   )Optional[ELEMENTWISE_TYPE_PROMOTION_KIND]r   r   r  z tuple[list[Any], dict[str, Any]])r   r4  )r   r4  r  z.Callable[[Callable[_P, _T]], Callable[_P, _T]])NN)NNNFN)F)r   'Union[TensorBox, ShapeAsConstantBuffer]r   torch.dtyper  r   )r   r@   r   r6  )r   r@   rr   r3  r   )r   r@   r  zSequence[sympy.Expr]r  r@   )r   r   l            r+   Tr  )rq  r@   rb  r@   rd  r@   r^  r   ra  r   r`  r   r   r6  r  r5  )rq  r@   rb  r@   rd  r@   r^  r   ra  r   r`  r   r   r6  rt  Optional[torch.dtype]r  r5  )rq  r@   rX  r/  rY  r   ra  r   r`  r   r   r6  r  r5  )rq  r@   rX  r/  rY  r   ra  r   r`  r   r   r6  rt  r7  r  r5  )rq  r@   rX  r@   rY  r@   ra  r   r`  r   r   r6  r  r5  )rq  r@   rX  r@   rY  r@   ra  r   r`  r   r   r6  rt  r7  r  r5  )r   r   r+   )r  r   r  r   r  r   r  )T)rs   ztorch.Tensor)r_   ztorch.fx.Node)NTF)rr   r3  )r   	list[int]rb  r@   r  rw  r  r   )
r  r   r  r   r   r8  rb  r@   r  r   )r  r@   r  z.tuple[str, sympy.Expr, sympy.Expr, sympy.Expr])r  r@   r  ztuple[str, sympy.Expr])r  r@   r  r@   r  r   r  r   r  Optional[str]r  Optional[TensorBox]r  r5  )rq  r@   r  r@   r  r   r  r   )r   r   r4  r   )r   NNr+   )NNN)rF  FF)r   r   )r?  r  r   r   r  r9  r  r   )r   r   r  r9  )r   r   r  r   )r)   F)r  ztuple[Optional[float], ...]r  r   r  r   )rb  Optional[float])r  r;  r  r;  )r$  r;  r  r;  r  r;  )r   r@   r9  zSequence[int]r?  r/  r  r:  )ro   
sympy.Exprr  zUnion[sympy.Expr, int])ro   r<  r  r<  )ro   r<  r  r<  r  r<  )Nr~  N)
r  r@   rd  "Sequence[Union[int, torch.SymInt]]r  r=  r  zxCallable[[Sequence[Union[int, torch.SymInt]], Sequence[Union[int, torch.SymInt]]], torch._inductor.virtualized.OpsValue]r  r5  )Nr   r+   F)r9  )NNNN)r   r   FTN)r  rQ   r   )r   r  r  zOptional[ir.Constant])rF  F)r\   ztorch._ops.OpOverloadPacket)r  ir.Subgraphr  rw  )r  r>  )r>  r>  r  ztuple[torch.Tensor]r  (  
__future__r   
contextlibr[  r  r   loggingr*  r  rB  r%  r  collectionsr   collections.abcr   r   typingr   r   r	   r
   r   r   r   typing_extensionsr   unittest.mockr   r   rw   $torch.ao.quantization.fx._decomposedtorch.fxtorch.utils._pytreer  _pytreer  torch._dynamo.utilsr   (torch._higher_order_ops.associative_scanr   r  r   torch._library.utilsr   torch._prims_commonr   r   r   r   r   r   r   r   r   r   r   torch.fx.experimental.sym_noder   r    %torch.fx.experimental.symbolic_shapesr!   r"   r#   torch.utils._ordered_setr$   torch.utils._sympy.functionsr%   r&   r'   r(   _dynamo.utilsr*    r,   r-   r.   r/   decompositionr0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   rF   rG   rH   rI   rJ   rK   rL   rM   rN   r$  rO   rP   r  rQ   rR   rS   FALLBACK_ALLOW_LIST	getLoggerr  rJ  rT   __annotations__rU   rx   ry   r  r  tr_c10dr  r   _higher_order_opsr  r^   rh  rV   quantized_decomposedrb   rt   r}   rz   r   r   r   r-  r2  r  rz  bmmconvolutionconvolution_backwardr  r  r  r/  r  r!  _int_mmr  r  rz  r  r;  r[  rS  r!  	complex32	complex64r   rZ  r   r   r   r   r   r   r   r   r  r  r  r8  r  r,  r>  rc  ry  r   r  r  r  r  r   r  r  
device_putr  r  r  r  r  r   aliasdetachdetach_liftview_ofr  r   r  r  r  r  r  r  r  r  r  r  r  r'  r  r  r  _unsafe_viewreshaper  slicer   r/  rJ  quantize_per_channelrf  rm  r   rp  _functional_assert_asyncrs  dequantize_per_channelr{  quantize_per_tensorr  dequantize_per_tensorr  rS  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  cacher   r%  r*  r:  rP  rU  rngprimsre  rg  rl  	bernoullirh  rp  rs  	lru_cacherw  rz  rX  r  r}  r~  r  r  r  randintforce_stride_orderr  rb  r  r  r  lookup_seedr  randomr  r  r  r  r  rm  r  	NO_OPMATHr  r  r   r  r  r   r   r  _adaptive_avg_pool3dadaptive_max_pool3d*_scaled_dot_product_attention_math_for_mpsuniformexponential_pdist_forwardsoft_margin_loss_backward_fused_rms_normxpuis_availableembedding_dense_backward_cdist_forward_cdist_backward
_trilinearsegment_reduce_segment_reduce_backwardhistc	histogrambin_ct_histogramdd_bin_edges_histogramdd_from_bin_ctsaddbmm_addmm_activation_grouped_mm
_cudnn_rnn_cudnn_rnn_backward_embedding_bag_embedding_bag_forward_only_embedding_bag_backward*_embedding_bag_per_sample_weights_backward_fused_moving_avg_obs_fq_helper*_fused_moving_avg_obs_fq_helper_functional max_pool3d_with_indices_backward_adaptive_avg_pool2d_backward_adaptive_avg_pool3d_backwardadaptive_max_pool2d_backwardadaptive_max_pool3d_backwardfractional_max_pool2d_backwardfractional_max_pool3d_backwardreplication_pad1d_backwardreplication_pad2d_backwardupsample_linear1d_backwardupsample_bicubic2d_backwardupsample_trilinear3d_backwardgrid_sampler_2d_backward_pdist_backwardr  rv  kthvaluetopkr  median	nanmedianr  resize_
resize_as__linalg_detlinalg_householder_productlinalg_inv_exlinalg_ldl_factor_exlinalg_ldl_solve	linalg_lulinalg_lu_factor_exlinalg_lu_solvelinalg_matrix_exp	linalg_qr_linalg_slogdet_linalg_solve_exlinalg_solve_triangular_linalg_svd	lu_unpackormqr_linalg_check_errorslinalg_pinvatol_rtol_tensor_linalg_eightriangular_solvelinalg_cholesky_excholesky_inversecholesky_solvegeqrf_fft_r2cnonzerogcd_thnn_fused_lstm_cell_prims	rng_primsrun_and_save_rng_staterun_with_rng_stategraphsafe_run_with_rng_statemasked_scattermasked_scatter_backwardr6  angle_efficientzerotensor(_sparse_coo_tensor_with_dims_and_tensors	to_sparse
_to_sparser   rF  r  r  #_scaled_dot_product_flash_attention,_scaled_dot_product_flash_attention_backward#_scaled_dot_product_cudnn_attention,_scaled_dot_product_cudnn_attention_backward+_scaled_dot_product_flash_attention_for_cpu4_scaled_dot_product_flash_attention_for_cpu_backward0_scaled_dot_product_fused_attention_overrideable9_scaled_dot_product_fused_attention_overrideable_backward_flash_attention_forward_flash_attention_backward_efficient_attention_forward_efficient_attention_backwardindex_reducerepeat_interleaver  r  r  r7  r
  r  r  r  scalar_tensorr+  
LongTensorr-  r4  r6  r8  r@  r  rD  r  rC  r  r  r	  
zeros_likerU  rY  rL  r_  rc  re  rm  rv  r  r  r  r  r4  r  r  r  r  r  r  r  r  r  fallback__unsafe_masked_indexr  ,fallback__unsafe_masked_index_put_accumulater  r  r  r  r  r  r  r  r  r  r  r  r%  r'  rR  r,  rA  r  rH  rI  rV  r[  rh  rm  rs  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r.  r4  r7  r1  rG  r_  rO  r`  rJ  ru  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  Tensor_Tensorr  Scalarr  Tensor_Scalarr  r  r8  r  r  rU  r  r  rW  r  r-  true_divider/  r4  r  r  rE  rC  rI  rH  rR  rQ  r]  r[  rc  rb  r  r  rh  r  rm  r  rr  rs  r  rk  r  rp  r  rl  r`  rq  r   r{  r~  r  r  rsqrtrM  r  expm1relur  r  r  ry  cossinabsbitwise_andbitwise_left_shiftbitwise_not
bitwise_orbitwise_right_shiftbitwise_xorlgammaerfspecial_erfrL  tantanhr  r  rt  logical_xorrU  rV  	clamp_min	clamp_maxnegrT  	remaindersignsignbit	_neg_viewler>  r=  r  r  necoshsinhacosacoshasinasinhatan2atanatanhr+  erfcerfinvhypotlog10log2	nextaftercodegen.commonrj  r  r  r   r\   r   ra  _foreach_addListforeach_add_listforeach_add_scalar_foreach_mulforeach_mul_listforeach_mul_scalar_foreach_sub_foreach_neg_foreach_abs_foreach_powScalarAndTensor_foreach_divforeach_div_listforeach_div_scalar_foreach_sqrt_foreach_rsqrt_foreach_maximum_foreach_minimum_foreach_clamp_min_foreach_clamp_max_foreach_reciprocal_foreach_sign_foreach_copyforeach_copyr  _foreach_add__foreach_mul__foreach_div__foreach_copy_r  add_bitwise_and_bitwise_left_shift_bitwise_not_bitwise_or_bitwise_right_shift_bitwise_xor_mul_div_Tensor_modelogical_and_logical_not_logical_or_logical_xor_sub_relu_sigmoid___and__
__lshift____or__
__rshift____xor____iand____ilshift____ior____irshift____ixor__r  r  r   r  r  r   methodfuncr  r  _inductor_testrl  r  r2  r  set_source_Tensorr  fsdpr  r  *torch._higher_order_ops.auto_functionalizer  r  higher_orderr   r  while_loop_stack_outputr  r  invoke_quantr  r  r  r  comm_loweringr  r,  r  r-  register_quantized_opsregister_woq_mm_opsr.  register_onednn_fusion_opsr/  register_jagged_opscontextmanagerr2  r   rc   ra   <module>r`	     s6   "        	   # . O O O '    +  $ $ ( H U :    M 
 0 U U , 8 8 =    &      * T]t_ !   g!FH	C H     .Juzz,,-/	yy~~
))

		9
5::#8#89; /j../
))*
 8j!6!679 NP K Pyy55 ,	BF

3   !!$$$$--&&, {{zz{{{{{{}}}}}}

."# (O
OO O C	O
  O &Od24 C	4r  	(// 4,#,0j  $Sl7v RW
E.
E7B
EJN
E 5**77TR) S)X 5--4H) I) @E 5( 499??=& >& ;@e K 5##>F ?F 
7?? $*Z>    4::DI J0 4))UPTU V( DJJT\\499emmTU V 4&doo&s+ 4<<T:B ;B, 4$$$?" @" DMM?# $ 4::C C 4::C C 499! ! 4::! ! 4::%%&% '% 4::! ! 4;;D9> :>4 5))tD
 E
 4>>t<# =# 4;;1  1h 4$$$?499$74<<T:1 ; 8 @1 4<<T:> ;> 4::48V 9V 4??=J >J$ 4##> ? 4''TB C
BJ '<<RVW/// / 	/
 / / / -/ X/d$ 4%%))*$ +$ 400445$ 6$ //T (,/// / 	/
 / / / %/ -//d ,,44$!!! ! 	!
 ! ! -!!H ..66D (,!!! ! 	!
 ! ! %! -!!H ,,33*** * 	*
 * * -**Z ..554 (,,,, , 	,
 , , %, -,,^ 488y: y:x 4==d;3E <3El 4%%4@6 A6 4((dC D 4;;D96C :6Cr 4::48 94 4((dC  D  4;;D9 : 4;;D9D :D8 4>>t< = 4??= > 488 $  >
3%6P/Nd	, 599%%11tL#+ M#+L 4&&DAG BG 4??= > 4>>##>' ?' 4<<  ! QB B/
 )):):; *499+>+>? )$***<*<= +DJJ,@,@A  dll  499J J 4::J J >44$OL PL
 >&&DAK BK >''TBJ CJ
 >--4H	 I	 >((dCRS  D6 >))tDLM	(09FI E8. 4$$++F
 "&^^
^ 	^
 ^ ^  ^ -^ G^B NN(G(Q(Q 777 	7
 77t"$DP d'' ( d&& ' d== > dll ' d&&U 3 d!! " d,,5 9 d"" /99%%E d!! " d"" # doo  d!!)) * d++33 4 djj  dnn## $ d))11 2 d,,44 5 dkk  d$$5 1 d . d'')@ A doo} - d&&(: ; d!!#5 6 d..0B C d** + d== > d== > d22 3 d== > d33 4 d00- @ d00 1 d// 0 d// 0 d11 2 d11 2 d-- . d-- . d-- . d..0B C d00 1 d++] ; d"" # dii  dii  dmm  dii  dii  dkk  dnn  dmm  dll  doo  d  d-- . d   ! d'' ( d## $ dnn  d&& ' d"" # d$$ % dnn  d"" # d## $ d** + d  dnn  djj  d'' ( d// 0 d   d## $ d%% & d## $ d!! " djj  dmm  dll"" # dhhU + d((- 8 ell$$;; < ell$$77 8 ell$$AA B
 d!! " d** + d""$6 7 djj  d'' ( d;; < dnn  doo  djj  0088	
 99AA	
 ,,44	
 55==	
 ,,44	
 55==	
 44<<	
 ==EE	
 99AA	
 BBJJ	
 d++33_ E d,,44o F d//77 I d0088/ J d   d$$++T B
 499$7
 8
 4::"  ( 4"#+d**+E2 5:: ( 4&&DA B: 4%%4@@ A@F ELL$"4"456tDU 5 75p 5??#4 $4 5##$+ %+ 4++,)" -)"X 4&&' ( 4//0%)59$ 1<K8 EKK,- 
 .$.> 0t/0B50IJ
1!45	 21 56
 4>>" $T$4  # 4%%&Td '> 4))*"4 +" 5%%--.A /A EJJ		*+: ,:
 4;;D9! :!H 4>>t< =B#F FR"1J 4::48
 9
 4%%4@/ A/ 4>>t< = 4))* +; 4??= > >44$O P}@ !1%%5!  0@,,44%0 ,
 4,,$G H, 4;;QUV	P W	P 1 1 4**E F 4<<T:9 ;9 !& 
  B 4==d;DH : <:" 4##>3 ?3 4$$$?6 @6 4&&DAP BP 4''TBPT p Cpn , *, 	,
 ,^ 4**223> 4> 41199:J ;J 4**223RVI-I@OI 4I 41199:RVU-U@OU ;U 4**223 !% $ $S S 	S
 S 4S 41199: !% $ $	 	 		
 	 ;	7 599$$% &*\\(\6;\\~ 4''TB4 C4n :>< MQ < JN@:HV 5::PTU 5 V5D3 3	 -> 	11t$< 4//TJ 
 K
 4//TJ 
 K
 -=))11- ) 488dSN TNb8B&R2j  0%%5  
 4,,-B .BJ  0$$%  
 4++,N -Nb)X 4--.V /V 4--.V /VAH 433;;<BF* =*Z 'OO  'OO 
 4??=  >* 4??=  >*wt  0$$%  
 4++F b GbJ  0$$%  
 4++F D GDN$.b ( 499:t : : 4 (V4( DHHeii()T5  * 4==!u  "   .HH  'txxER -HH 
 488t,, -,^"J 4::2 2 4::48 9     488t, - DHH:.( /(@ EII;$/$ 0$, 	txx'7DD

 DIIuzz*d;$ <$  DHHeii(). . *. #4;;#6#67#DLL$8$89 ():):)B)BC "4;;#6#67"4;;#6#67 4;;  . 4<<  !. 4$$% &* 4;;D9 :, 4;;D9 :, 499. . . 488@ @
 48867 77 48867 77 ! %--  	!: ;*		*>%+@A*		*>%+@A.!$++.85;;? /!$++.85;;? HH$L !!1!1uM 499##>!re $2 ?$2N 499$$$?H @H 	#4::.&txx0!$)),"4::.$))$
*4<<
8'		2	DKK	(t4   *   *" !1!12'(?(?@  -  0
()A)AB  !1!12 4;; ' * *I*V*V 4:: & 488 $ 499 %   * **	 !**	  OO**	
 !**	 T\\
*
T\\
* ! $.. !' * ! $.. !' *""'8
 4>> "$))L 499  4<<uzz B ! $.. !# & 477%** = 477%** = 477%** =uzzB 477%** = 477%** = 499 % 499 % 499 % 4:: & 499 % 4:: & 4:: & 499 % 4:: & 4== ) 499 % 4;; ' 4:: & 4:: & 499 % 4>> * D DE$ % 
D4Ld5 
0 	 3+		

 5Mt5 
0 	 3+		


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 C   ""K 0 ))+= > ""K 0 !!: . **,? @ ""K 0 C   !!3 ' && 1 ""K 0 ""K 0 !!: . ""K 0 C   T "  (   $,,  , " $// "#5 6  $++ z * " $// "#6 7  $,,  ,  - !!4?? 3 t{{ + !!4?? 3  - 4++, - 4==$$% &$ 4??&&' ( 4>>" # (M'') 8LFD1(01$78 5==! " 4<< 7 !7 599++334 5
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 599))99tT/ U/
 5**77TRDH  S8 &DA  4G  B F 599??//778 9 599))66DQ+ R+* 3 2   >88dS2 T2l     ! ! +  * * , '  ' ' )   ,  + + -   %  $ $ &  rc   