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For each element x returns `True` if and only if x is not :math:`\pm\infty` or :math:`\mathit{NaN}`. ) is_finite_prrs rU is_finiter&s   !  rWc6t|S)z%Elementwise exponential: :math:`e^x`.)exp_prrs rUexpr .rrWc6t|S)z,Elementwise base-2 exponential: :math:`2^x`.)exp2_prrs rUexp2r2rrWc6t|S)zElementwise :math:`e^{x} - 1`.)expm1_prrs rUexpm1r6rrWc6t|S)z7Elementwise natural logarithm: :math:`\mathrm{log}(x)`.)log_prrs rUlogr:rrWc6t|S)z(Elementwise :math:`\mathrm{log}(1 + x)`.)log1p_prrs rUlog1pr>rrWc6t|S)z9Elementwise hyperbolic tangent: :math:`\mathrm{tanh}(x)`.)tanh_prrs rUtanhrBrrWc6t|S)zFElementwise logistic (sigmoid) function: :math:`\frac{1}{1 + e^{-x}}`.) logistic_prrs rUlogisticrFs   rWc6t|S)z*Elementwise sine: :math:`\mathrm{sin}(x)`.)sin_prrs rUsinr JrrWc6t|S)z,Elementwise cosine: :math:`\mathrm{cos}(x)`.)cos_prrs rUcosr#NrrWyc8t||S)zQElementwise arc tangent of two variables: :math:`\mathrm{atan}({x \over y})`.)atan2_prrr$s rUatan2r(Rs a  rWc6t|S)zgElementwise extract real part: :math:`\mathrm{Re}(x)`. 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Builds a complex number from real and imaginary parts. ) complex_prr's rUrres 1  rWcTt|t|S)z=Elementwise complex conjugate function: :math:`\overline{x}`.) input_dtype)conj_pr_dtypers rUconjr6ls  QF1II . ..rWc6t|S)z(Elementwise absolute value: :math:`|x|`.)abs_prrs rUabsr9qrrWc8t||S)zElementwise power: :math:`x^y`.)pow_prr's rUpowr<u Aq  rWc:t||S)zCElementwise power: :math:`x^y`, where :math:`y` is a fixed integer.r$) integer_pow_prr's rU integer_powrAys   A  # ##rWc6t|S)z*Elementwise square root: :math:`\sqrt{x}`.)sqrt_prrs rUsqrtrD}rrWc6t|S)z>Elementwise reciprocal square root: :math:`1 \over \sqrt{x}`.)rsqrt_prrs rUrsqrtrGrrWc6t|S)z+Elementwise cube root: :math:`\sqrt[3]{x}`.)cbrt_prrs rUcbrtrJrrWc6t|S)z Elementwise NOT: :math:`\neg x`.)not_prrs rU bitwise_notrMrrWc8t||S)z$Elementwise AND: :math:`x \wedge y`.)and_prr's rU bitwise_andrPr=rWc8t||S)z!Elementwise OR: :math:`x \vee y`.)or_prr's rU bitwise_orrS 1arWc8t||S)z-Elementwise exclusive OR: :math:`x \oplus y`.)xor_prr's rU bitwise_xorrWr=rWc6t|S)zCElementwise popcount, count the number of set bits in each element.)population_count_prrs rUpopulation_countrZs   # ##rWc6t|S)z Elementwise count-leading-zeros.)clz_prrs rUclzr]rrWc8t||S)z$Elementwise addition: :math:`x + y`.)add_prr's rUaddr`r=rWc8t||S)z'Elementwise subtraction: :math:`x - y`.)sub_prr's rUsubrcr=rWc8t||S)z/Elementwise multiplication: :math:`x \times y`.)mul_prr's rUmulrfr=rWc8t||S)zElementwise division: :math:`x \over y`. Integer division overflow (division by zero or signed division of INT_SMIN with -1) produces an implementation defined value. )div_prr's rUdivris Aq  rWc8t||S)a=Elementwise remainder: :math:`x \bmod y`. The sign of the result is taken from the dividend, and the absolute value of the result is always less than the divisor's absolute value. Integer division overflow (remainder by zero or remainder of INT_SMIN with -1) produces an implementation defined value. )rem_prr's rUremrls Aq  rWc8t||S)zElementwise maximum: :math:`\mathrm{max}(x, y)` For complex numbers, uses a lexicographic comparison on the `(real, imaginary)` pairs.)max_prr's rUrRrR Aq  rWc8t||S)zElementwise minimum: :math:`\mathrm{min}(x, y)` For complex numbers, uses a lexicographic comparison on the `(real, imaginary)` pairs.)min_prr's rUrPrProrWc8t||S)z(Elementwise left shift: :math:`x \ll y`.) shift_left_prr's rU shift_leftrts   1a  rWc8t||S)z4Elementwise arithmetic right shift: :math:`x \gg y`.)shift_right_arithmetic_prr's rUshift_right_arithmeticrws ! & &q! , ,,rWc8t||S)z1Elementwise logical right shift: :math:`x \gg y`.)shift_right_logical_prr's rUshift_right_logicalrzs  # #Aq ) ))rWc8t||S)z"Elementwise equals: :math:`x = y`.)eq_prr's rUeqr}rTrWc8t||S)z)Elementwise not-equals: :math:`x \neq y`.)ne_prr's rUnerrTrWc8t||S)z5Elementwise greater-than-or-equals: :math:`x \geq y`.)ge_prr's rUgerrTrWc8t||S)z(Elementwise greater-than: :math:`x > y`.)gt_prr's rUgtrrTrWc8t||S)z2Elementwise less-than-or-equals: :math:`x \leq y`.)le_prr's rUlerrTrWc8t||S)z%Elementwise less-than: :math:`x < y`.)lt_prr's rUltrrTrWoperand new_dtype DTypeLike | dtypes.ExtendedDTypec&t||dS)aElementwise cast. Wraps XLA's `ConvertElementType `_ operator, which performs an elementwise conversion from one type to another. Similar to a C++ `static_cast`. Args: operand: an array or scalar value to be cast. new_dtype: a NumPy dtype representing the target type. Returns: An array with the same shape as `operand`, cast elementwise to `new_dtype`. Fr)rrrs rUconvert_element_typers w U C C CCrWF'DTypeLike | dtypes.ExtendedDType | NonerrshardingSharding | Nonect|dr|}tj|tjs.tjt |ddtjr+t ||t||Sttdz|}tj |d}tj |}||}ntj |}tj |d}tj|tjr=tj|tjsd}tj|t"d t%|t&ur)tj||}d}||f||fkrtt-|t.r_t-|t0jr,t-t1j|t0js|t |d d|kr|St ||t||S) N __jax_array__rSrrrF canonicalizeTz:Casting complex values to real discards the imaginary part) stacklevelr)hasattrrr issubdtypeextendedgetattrconvert_element_type_prr type_castr?rSrrMcomplexfloatingwarningswarnrFrrJrastyperr;rrget_avalr$)rrrr old_dtype old_weak_typergs rUrrs(  Wo&&&##%%G  6?33 $77II ! & &9Y '   D()44)l7777)(11-II##Il94888)  2#566:  Ir'9 : :: FC M#*q9999 ']]cj!!((33GM- Y $:::%  ; gt{ + +; dmG,,d.@ A A;77J==II N ! & &9Y '  rWr?cbtj|}t||S)aElementwise bitcast. Wraps XLA's `BitcastConvertType `_ operator, which performs a bit cast from one type to another. The output shape depends on the size of the input and output dtypes with the following logic:: if new_dtype.itemsize == operand.dtype.itemsize: output_shape = operand.shape if new_dtype.itemsize < operand.dtype.itemsize: output_shape = (*operand.shape, operand.dtype.itemsize // new_dtype.itemsize) if new_dtype.itemsize > operand.dtype.itemsize: assert operand.shape[-1] * operand.dtype.itemsize == new_dtype.itemsize output_shape = operand.shape[:-1] Args: operand: an array or scalar value to be cast new_dtype: the new type. Should be a NumPy type. Returns: An array of shape `output_shape` (see above) and type `new_dtype`, constructed from the same bits as operand. r)rcanonicalize_dtypebitcast_convert_type_prrs rUbitcast_convert_typer:s-4' 22)  $ $W $ B BBrWrPrRc:t|||S)zElementwise clamp. Returns :math:`\mathrm{clamp}(x) = \begin{cases} \mathit{min} & \text{if } x < \mathit{min},\\ \mathit{max} & \text{if } x > \mathit{max},\\ x & \text{otherwise} \end{cases}`. )clamp_pr)rPrrRs rUclamprWs c1c " ""rWoperandsArray | Sequence[ArrayLike] dimensionct|dkrtdt|dkr|\}t|tr|St j|d|iS)aConcatenates a sequence of arrays along `dimension`. Wraps XLA's `Concatenate `_ operator. Args: operands: a sequence of arrays to concatenate. The arrays must have equal shapes, except in the `dimension` axis. dimension: the dimension along which to concatenate the arrays. Returns: An array containing the concatenation. rz4concatenate requires a non-empty sequences of arraysrpr)rsrrr; concatenate_pr)rrops rU concatenaterbsi ]]a K L LL]]a CB"e i  X ; ; ;;rWzdict[Any, Precision]_precision_stringscfeZdZUded<ded<ded<ddZedd Zedd Zd S) PrecisionzClassVar[Precision]DEFAULTHIGHHIGHESTrjPrecision | int | str | NonerIctrLNotImplementedErrorclsrjs rU__new__zPrecision.__new__s rWstrctrLrselfs rUnamezPrecision.name rWrJctrLrrs rUrjzPrecision.valuerrWN)rjrrIrrIr)rIrJ)rrr__annotations__rpropertyrrjr_rWrUrrs               X    X   rWrcFeZdZdZdZdZdZedd Zdd Z dd Z d S)raPrecision enum for lax matrix multiply related functions. The device-dependent `precision` argument to JAX functions generally controls the tradeoff between speed and accuracy for array computations on accelerator backends, (i.e. TPU and GPU). Has no impact on CPU backends. This only has an effect on float32 computations, and does not affect the input/output datatypes. Members are: DEFAULT: Fastest mode, but least accurate. On TPU: performs float32 computations in bfloat16. On GPU: uses tensorfloat32 if available (e.g. on A100 and H100 GPUs), otherwise standard float32 (e.g. on V100 GPUs). Aliases: ``'default'``, ``'fastest'``. HIGH: Slower but more accurate. On TPU: performs float32 computations in 3 bfloat16 passes. On GPU: uses tensorfloat32 where available, otherwise float32. Aliases: ``'high'``.. HIGHEST: Slowest but most accurate. On TPU: performs float32 computations in 6 bfloat16. Aliases: ``'highest'``. On GPU: uses float32. rrprrjobjectrIPrecision | Nonec6t|SrL)rgetrs rU _missing_zPrecision._missing_s  # #E * **rWrc.|jjd|jS)Nrc) __class__rrrs rU__repr__zPrecision.__repr__s' 5 5$) 5 55rWc|jSrLrrs rU__str__zPrecision.__str__s YrWN)rjrrIrr) rrr__doc__rrr classmethodrrrr_rWrUrrsu,G DG+++[+6666rWhighestfloat32high bfloat16_3x tensorfloat32defaultbfloat16fastestlhsrhs precision PrecisionLikepreferred_element_typeDTypeLike | NonecHd|jcxkrdkrdnnad|jcxkrdkrOnnLtj|jd|jdr!t |||jdz fdfdf||St d|j|j) aVector/vector, matrix/vector, and matrix/matrix multiplication. Wraps XLA's `Dot `_ operator. For more general contraction, see the `dot_general` operator. Args: lhs: an array of dimension 1 or 2. rhs: an array of dimension 1 or 2. precision: Optional. Either ``None``, which means the default precision for the backend, a :class:`~jax.lax.Precision` enum value (``Precision.DEFAULT``, ``Precision.HIGH`` or ``Precision.HIGHEST``) or a tuple of two :class:`~jax.lax.Precision` enums indicating precision of ``lhs``` and ``rhs``. preferred_element_type: Optional. Either ``None``, which means the default accumulation type for the input types, or a datatype, indicating to accumulate results to and return a result with that datatype. Returns: An array containing the product. rprrr)r_r_rrz+Incompatible shapes for dot: got {} and {}.)rrrr[ dot_generalreformat)rrrrs rUdotrs0#(aA....Q.....43HSUX[XabcXd3e3e. sCCHqL?D"98!D!*.D F F FF AHH 39  rWdimension_numbersDotDimensionNumbersch|\\}}\}}tj|tj|f} tj|tj|f} |dn%tjt j|}t ||| | ft||S)ayGeneral dot product/contraction operator. Wraps XLA's `DotGeneral `_ operator. The semantics of ``dot_general`` are complicated, but most users should not have to use it directly. Instead, you can use higher-level functions like :func:`jax.numpy.dot`, :func:`jax.numpy.matmul`, :func:`jax.numpy.tensordot`, :func:`jax.numpy.einsum`, and others which will construct appropriate calls to ``dot_general`` under the hood. If you really want to understand ``dot_general`` itself, we recommend reading XLA's `DotGeneral `_ operator documentation. Args: lhs: an array rhs: an array dimension_numbers: a tuple of tuples of sequences of ints of the form ``((lhs_contracting_dims, rhs_contracting_dims), (lhs_batch_dims, rhs_batch_dims))`` precision: Optional. Either ``None``, which means the default precision for the backend, a :class:`~jax.lax.Precision` enum value (``Precision.DEFAULT``, ``Precision.HIGH`` or ``Precision.HIGHEST``) or a tuple of two :class:`~jax.lax.Precision` enums indicating precision of ``lhs``` and ``rhs``. preferred_element_type: Optional. Either ``None``, which means the default accumulation type for the input types, or a datatype, indicating to accumulate results to and return a result with that datatype. Returns: An array whose first dimensions are the (shared) batch dimensions, followed by the ``lhs`` non-contracting/non-batch dimensions, and finally the ``rhs`` non-contracting/non-batch dimensions. Nrrr) r_ensure_index_tuplerrrMrS dot_general_prcanonicalize_precision) rrrrr lhs_contract rhs_contract lhs_batch rhs_batchcdimsbdimss rUrrsF:K6< 6I  ' 5 5  ' 5 5 7%  ' 2 2  ' 2 2 4%%,dd )? @ @AA   C/4en&.>!>?? @ @$ '5<<"(72C2C#CT J JJrWr@broadcast_dimensionscHtj|t|kr&t|st|tr|St jjrt|\}}ng|}}tj |g|Rt|t|dS)aWraps XLA's `BroadcastInDim `_ operator. Args: operand: an array shape: the shape of the target array broadcast_dimensions: to which dimension in the target shape each dimension of the operand shape corresponds to. That is, dimension i of the operand becomes dimension broadcast_dimensions[i] of the result. Returns: An array containing the result. See Also: jax.lax.broadcast : simpler interface to add new leading dimensions. r[r ) rMrrsrr;rrirjrbroadcast_in_dim_prr)rr[r rrs rUr r Ms&WWU##C0D,E,E#*U\^cJdJd# N  (9??I|| %|I    8 8 8!&|!4!4 !566 8 8 88rWrctj|}||krt|St|d||z zS)z=Adds leading dimensions of ``1`` to give ``x`` rank ``rank``.r~)rMrrr )rrrs rUbroadcast_to_rankrls= $ T\\ 1:: 1ddTk* + ++rW new_sizes dimensionsSequence[int] | Nonect|}t|}tjt j||}|d}d}nSt j|}t|ttt j |k}t j|r|r|rt|tr|St|\}}tj|g|Rt|||rdn|dS)adWraps XLA's `Reshape `_ operator. For inserting/removing dimensions of size 1, prefer using ``lax.squeeze`` / ``lax.expand_dims``. These preserve information about axis identity that may be useful for advanced transformation rules. Args: operand: array to be reshaped. new_sizes: sequence of integers specifying the resulting shape. The size of the final array must match the size of the input. dimensions: optional sequence of integers specifying the permutation order of the input shape. If specified, the length must match ``operand.shape``. Returns: out: reshaped array. Examples: Simple reshaping from one to two dimensions: >>> x = jnp.arange(6) >>> y = reshape(x, (2, 3)) >>> y Array([[0, 1, 2], [3, 4, 5]], dtype=int32) Reshaping back to one dimension: >>> reshape(y, (6,)) Array([0, 1, 2, 3, 4, 5], dtype=int32) Reshaping to one dimension with permutation of dimensions: >>> reshape(y, (6,), (1, 0)) Array([0, 3, 1, 4, 2, 5], dtype=int32) NTrr)r'rrrrMr[rrr rrr;r reshape_pr)rrr same_shape same_dimsr rstatic_new_sizess rUreshaperssN!++)I)*28G+<+:>)> 7E8R8R> N"  > > >%*+;%<%< > > >>rW padding_valuepadding_configSequence[tuple[int, int, int]]cVt||t|S)asApplies low, high, and/or interior padding to an array. Wraps XLA's `Pad `_ operator. Args: operand: an array to be padded. padding_value: the value to be inserted as padding. Must have the same dtype as ``operand``. padding_config: a sequence of ``(low, high, interior)`` tuples of integers, giving the amount of low, high, and interior (dilation) padding to insert in each dimension. Returns: The ``operand`` array with padding value ``padding_value`` inserted in each dimension according to the ``padding_config``. )r)pad_prr)rrrs rUpadr"s$( G]5;P;P Q QQrWcTt|t|S)zdWraps XLA's `Rev `_ operator. r)rev_prrrrs rUrevr's" Gj(9(9 : ::rWpredon_trueon_falsec:t|||S)aHSelects between two branches based on a boolean predicate. Wraps XLA's `Select `_ operator. In general :func:`~jax.lax.select` leads to evaluation of both branches, although the compiler may elide computations if possible. For a similar function that usually evaluates only a single branch, see :func:`~jax.lax.cond`. Args: pred: boolean array on_true: array containing entries to return where ``pred`` is True. Must have the same shape as ``pred``, and the same shape and dtype as ``on_false``. on_false: array containing entries to return where ``pred`` is False. Must have the same shape as ``pred``, and the same shape and dtype as ``on_true``. Returns: result: array with same shape and dtype as ``on_true`` and ``on_false``. ) select_n_pr)r(r)r*s rUselectr-s. x 1 11rWwhichcasescjt|dkrtdtj|g|RS)a{Selects array values from multiple cases. Generalizes XLA's `Select `_ operator. Unlike XLA's version, the operator is variadic and can select from many cases using an integer `pred`. Args: which: determines which case should be returned. Must be an array containing either a boolean or integer values. May either be a scalar or have shape matching ``cases``. For each array element, the value of ``which`` determines which of ``cases`` is taken. ``which`` must be in the range ``[0 .. len(cases))``; for values outside that range the behavior is implementation-defined. *cases: a non-empty list of array cases. All must have equal dtypes and equal shapes. Returns: An array with shape and dtype equal to the cases, whose values are chosen according to ``which``. rz&select_n() must have at least one case)rsrr,rr.r/s rUselect_nr2s:* ZZ1__ = > >>  ' ' ' ''rW permutationSequence[int] | np.ndarrayctd|D}|tttj|krt |t r|St ||S)zhWraps XLA's `Transpose `_ operator. c3>K|]}tj|VdSrL)operatorindexrs rUrbztranspose..s,==AhnQ''======rW)r3)rr rMrrr; transpose_pr)rr3s rU transposer:sr =======+E% 0 0112222z'57Q7Q2 N   G  = ==rWaxis index_dtypecbt||ftj|S)z9Computes the index of the minimum element along ``axis``.axesr<)argmin_prrrrr;r<s rUargminrB6 wdW#)#<[#I#I  K KKrWcbt||ftj|S)z9Computes the index of the maximum element along ``axis``.r>)argmax_prrrrAs rUargmaxrFrCrWr init_values computationCallable[[Any, Any], Any]ctj|\}}tj|\}}||krtd|d|t|t|kr/tdt|dt|t ||}|r5t j|o t j|} t|g||R| Stt|} t|t| |\} } tj g||R|| t|d} tj| | S)aWraps XLA's `Reduce `_ operator. ``init_values`` and ``computation`` together must form a `monoid `_ for correctness. That is ``init_values`` must be an identity of ``computation``, and ``computation`` must be associative. XLA may exploit both of these properties during code generation; if either is violated the result is undefined. z;Operands must have the same tree structure as init_values: z vs. z9Must have same total number of operands as init_values: r)rHjaxprr)r tree_flattenrrs_get_monoid_reducerrrrrC _abstractify_variadic_reduction_jaxprrreduce_prtree_unflatten)rrGrHr flat_operands operand_treeflat_init_valuesinit_value_treemonoid_reducerrflat_init_avals closed_jaxprout_treeouts rUreducer[s!* 6x @ @-&/&<[&I&I#O_$$ >%>>,;>> ? ??3/0000 J]++JJ256F2G2GJJ K KK&{4DEE. 3& 6d6;QSc;dI !K!K !K!K!K+4 6 6 66|-=>>O6U?++_>>L( - J J)9 J J{*uZ7H7H J J JC  #Hc 2 22rWctjfd}tj|||f\}}}\t d|Drt d|t |fS)Nc||}t|tjs6tj|s"t dt |d||fS)Nz-Invalid return type from reduction function: zE Reduction functions should only return an array. Full return value: )rrr valid_jaxtyperr)rr$resultrHs rUcompz_reduction_jaxpr..comp;sz [A  F vt{ + +*t/A&/I/I*  )$v,, ) ) & ) ) * ** 9rWc3JK|]}t|tjVdSrLrr`cs rUrbz#_reduction_jaxpr..E.44At{ # #444444rWgReduction computations can't close over Tracers. Please open an issue at https://github.com/google/jax.)lu wrap_initrtrace_to_jaxpr_dynamicanyrr)rHavalr`rK_constss` rU_reduction_jaxprrm9s<<24$FF%FB44V44444-  , - -- f rWctj||}tj||f\}}tj|}t j||\}}tj|t|\} } } \td| Drtdtj | | |fS)Nc3JK|]}t|tjVdSrLrrbs rUrbz,_variadic_reduction_jaxpr..RrdrWre)rrQrLrfrgrflatten_fun_nokwargsrrhrrirr ClosedJaxpr) rH flat_avals aval_treeavals flat_in_avalsin_treer` flat_comprYrKrkrls rUrOrOKs  "9j 9 9%$15%.AA- k " "$ 5dGDD)X29eM>R>RSS%FB44V44444-  , - --  % ( (((** 44rW monoid_oprxsSequence[Array]Callable | Nonect|dkrdS|\}tj|}t|}t |t ur|jdkr|tjkptj |tj }|tur#tj |jdrtndS|t ur#tj |jdrt"ndS|t$ur2|r0tj |jt'|rt(ndS|t*ur2|r0tj |jt-|rt.ndS|t0ur2|r0tj |jt'|rt2ndS|t4ur0tj |jt7|rt8ndS|t:ur0tj |jt=|rt>ndSdS)Nrpr_r) rsrrr5rr$r[rMbool_rrintegerr`equalrH _reduce_sumrf _reduce_prodrS_get_bitwise_or_identity _reduce_orrP_get_bitwise_and_identity _reduce_andrW _reduce_xorrR_get_max_identity _reduce_maxrP_get_min_identity _reduce_min)rxryrrjrS _is_intlikes rUrMrMXsWW\\ 4 "! q  $ ))% 4jjM!!tzR'7'728#Kv'8 'K'KKCHTXq11 ;[[t; c  Xdh22 <\\< j [ 8DH.Fu.M.MNN XZZTXX k ! !k !HTX/H/O/OPP Z[[VZZ k ! !k !HTX/G/N/NOO Y[[UYY c  HTX/@/G/GHH R[[dR c  HTX/@/G/GHH R[[dR rWrS np.ndarraycPtjd|SNr)rMrrrSs rUrrrs "  U # ##rWc,tjd|SNrrMrrs rUrru !U  rWc,tjd|Srrrs rU_get_sum_identityrxrrWc,tjd|SNrprrs rU_get_prod_identityr{rrWctj|tjrNtjtj|r tj ntj|j|Stj|tj r,tjtj |j|Stj|tj rtjdtj Std|)NrFzUnsupported dtype for max: ) rrrMinexactr supports_infinffinforPr~rNr}rrs rUrr~s ubj))< 8v2599VRVGGv|E?R?R?V ! ! !!  ++< 8FL''+U 3 33 ))< 8E28 $ $$ :5:: ; ;;rWctj|tjrMtjtj|r tjntj|j|Stj|tj r,tjtj |j|Stj|tj rtjdtj Std|)NrTzUnsupported dtype for min: ) rrrMrrrrrrRr~rNr}rrs rUrrs ubj))< 8f1%88UBFFfl5>Q>Q>U ! ! !!  ++< 8FL''+U 3 33 ))< 8D"( # ## :5:: ; ;;rWr?cTt|t|SNr?) reduce_sum_prrrr?s rUrr!   7t  5 55rWcTt|t|Sr) reduce_prod_prrrs rUrrs!   G%++  6 66rWcTt|t|Sr) reduce_max_prrrs rUrrrrWcTt|t|Sr) reduce_min_prrrs rUrrrrWcTt|t|Sr) reduce_or_prrrs rUrrs!   'd  4 44rWcTt|t|Sr) reduce_and_prrrs rUrrrrWcTt|t|Sr) reduce_xor_prrrs rUrrrrWrTrp is_stablenum_keyscdSrLr_rrrrs rUsortrs>AcrWtuple[Array, ...]cdSrLr_rs rUrrsJM#rWArray | Sequence[Array]Array | tuple[Array, ...]c :t|trt|dkrtdd|cxkrt|ks$nt d|dt|t |t|dj}ttj ||||dS|dkrt d|dt |t|j}t |||ddS)ayWraps XLA's `Sort `_ operator. For floating point inputs, -0.0 and 0.0 are treated as equivalent, and NaN values are sorted to the end of the array. For complex inputs, the sort order is lexicographic over the real and imaginary parts, with the real part primary. Args: operand : Array or sequence of arrays dimension : integer dimension along which to sort. Default: -1. is_stable : boolean specifying whether to use a stable sort. Default: True. num_keys : number of operands to treat as sort keys. Default: 1. For num_keys > 1, the sort order will be determined lexicographically using the first `num_keys` arrays, with the first key being primary. The remaining operands will be returned with the same permutation. Returns: operand : sorted version of the input or inputs. rz"Sort requires at least one operandrpz num_keys=z$ must be between 1 and len(operand)=rrrz# must equal 1 for a single operand.) rrrsrerrDr[rsort_prrs rUrrs-*"" Y 7||q : ; ;;  ) ) ) )S\\ ) ) ) ) K(KKCLLKK L LL!)S1A-B-BCCI g'0&.000 1 111}} H(HHH I II!)S-?-?@@I ;;w)yST; U UVW XXrWkeysvaluestuple[Array, Array]ct|t|j}t||||d\}}||fS)zRSorts ``keys`` along ``dimension`` and applies the same permutation to ``values``.rpr)rDrsr[rr)rrrrkvs rU sort_key_valrsD 3tz??;;) T6Y)VW X X$!Q A+rWrctj|rt|}|dkrtd|t||S)aReturns top ``k`` values and their indices along the last axis of ``operand``. Args: operand: N-dimensional array of non-complex type. k: integer specifying the number of top entries. Returns: A tuple ``(values, indices)`` where - ``values`` is an array containing the top k values along the last axis. - ``indices`` is an array containing the indices corresponding to values. See also: - :func:`jax.lax.approx_max_k` - :func:`jax.lax.approx_min_k` Examples: Find the largest three values, and their indices, within an array: >>> x = jnp.array([9., 3., 6., 4., 10.]) >>> values, indices = jax.lax.top_k(x, 3) >>> values Array([10., 9., 6.], dtype=float32) >>> indices Array([4, 0, 2], dtype=int32) r-k argument to top_k must be nonnegative, got r)ris_constant_dimrJrtop_k_pr)rrs rUtop_krsX6 ! AAUU HQHH I II g # ##rWc|S)z,Deprecated. Ignores ``x`` and returns ``y``.r_r's rUtie_inrs (rWr fill_valuect|}tj|r6d}t|tj|t j|t jr|j |||S|duot j |}t j |pt|}t|||}|mt|tsXt|t jr>||}t'||t!j||fdSt'||S)aReturns an array of `shape` filled with `fill_value`. Args: shape: sequence of integers, describing the shape of the output array. fill_value: the value to fill the new array with. dtype: the type of the output array, or `None`. If not `None`, `fill_value` will be cast to `dtype`. sharding: an optional sharding specification for the resulting array, note, sharding will currently be ignored in jitted mode, this might change in the future. zDfull must be called with scalar fill_value, got fill_value.shape {}.NcSrLr_)rkshards rUzfull..sUrW)r'rMr[rerrrr_rulesfullrrr5rrr:r ArrayImpl shard_shaper make_array_from_callback)r[rrSrrgrbroadcast_shapers @rUrrs= U # #%Xj6 PC CJJrx 3344 5 55 ufo..7 <  UJ 6 66tmB 6z B B)  #E$?VJ-?-? @ @%$Z BB* :h #E#EU_--**511O j/ 2 2E  )%???? K KK :u % %%rWrjr#ct|tsJtj|jtjr%|jj|j}nL|jtjkrtj d|j}ntd|j|j }t||jS)Nr_rr)rr#rrrSrrzerofloat0rMzerosrrr r[)rj scalar_zeros rUzeros_like_shaped_arrayr#s D+ & &&&& tz6?33G*#((44KK zV]""(2TZ000KK'4:t~FFK ; + ++rWstate.AbstractRefcore.MutableArrayc\tj|j}tj|SrL)rzeros_like_aval inner_avalr mutable_array)rjrHs rUzeros_like_abstract_refr/s%00# C  rWsizec&t||fdS)z^Wraps XLA's `Iota `_ operator. r)broadcasted_iota)rSrs rUiotar5s %$! , ,,rWctj|}t|}d|D}d|D}tjt |d}t j||t||dS)z$Convenience wrapper around ``iota``.cFg|]}t|tj|Sr_rrs rUrz$broadcasted_iota..@s)BBBz!T['A'AB1BBBrWcJg|] }t|tjrdn|!SrLrrs rUrz$broadcasted_iota..As-KKK*Q 44;$$!KKKrWz*dimension argument of lax.broadcasted_iotarSr[r) rrr'rconcrete_or_errorrJiota_prr)rSr[r dynamic_shapers rUrr<s  #E * *% U # #%BBeBBB-KKUKKK,$ 9BDD) m5l8K8K( * * **rWoffsetc ^t|tj}tj|}t t ttj|dtj|ttj|d}t ||ddS)z:Like numpy.eye, create a 2D array with ones on a diagonal.rrpFNr) rVrMint32rrr}r`rrr)rSr[rbool_eyes rU_eyerGs #FBH 5 5&  #E * *% $RXua88"(6:J:JKK 5!4466(  $ $X%.2 % 4 44rWctt|}tj|}t t j||fdttD}dt|dd|ddD}t ttj||dd}t|||S)zAThis utility function exists for creating Kronecker delta arrays.cFg|]}ttj|Sr_)rrMuint32)r`i base_shapes rUrz_delta..Us7 , , , BIz1 5 5 , , ,rWc4g|]\}}t||Sr_)r})r`i1i2s rUrz_delta..Ws$ > > >R"R** > > >rWNrrpFr)rkrJrrrrMtaker rsziprrrr7and_r )rSr[r?iotaseyesr_rs @rU_deltarPs S$$  #E * *%RWUD))*** , , , ,#j//** , , ,% > >3uSbSz59#=#= > > >$ ! & & hmT""eu '  & &% . ..rWc t|tj}tj|}t t ttj|dttj | tjttj|d}t ||ddS)z=Like numpy.tri, create a 2D array with ones below a diagonal.rrpFNr)rVrMrrrrr`rrrdimension_as_valuerrr)rSr[rbool_tris rU_trir]s #FBH 5 5&  #E * *% $RXua88D3F;;<<CCBHMMOO 5!4466( $ $X%.2 % 4 44rWc(d}t||S)aStops gradient computation. Operationally ``stop_gradient`` is the identity function, that is, it returns argument `x` unchanged. However, ``stop_gradient`` prevents the flow of gradients during forward or reverse-mode automatic differentiation. If there are multiple nested gradient computations, ``stop_gradient`` stops gradients for all of them. For example: >>> jax.grad(lambda x: x**2)(3.) Array(6., dtype=float32, weak_type=True) >>> jax.grad(lambda x: jax.lax.stop_gradient(x)**2)(3.) Array(0., dtype=float32, weak_type=True) >>> jax.grad(jax.grad(lambda x: x**2))(3.) Array(2., dtype=float32, weak_type=True) >>> jax.grad(jax.grad(lambda x: jax.lax.stop_gradient(x)**2))(3.) Array(0., dtype=float32, weak_type=True) cdtjtj|jtjr|Stjt |tjs,tjt |tj rtj |S|SrL) rrrrrSrr5rMfloatingrrstop_gradient_prrs rUstopzstop_gradient..stop{s q))/AA h  F1IIr{ 3 3&))R%788  $ ) )! , ,, hrWr)rr s rU stop_gradientr gs#( $  rWfloat | ArrayLike exponent_bits mantissa_bitsctjtj|d}tjtj|d}t|||S)ztWraps XLA's `ReducePrecision `_ operator. z.exponent_bits argument of lax.reduce_precisionz.mantissa_bits argument of lax.reduce_precision)rr)rrr7r8reduce_precision_prrrrs rUreduce_precisionrs\( NM#SUU-( NM#SUU-   Ub c ccrWrctj|ttfd|D}|st |t r|St ||S)z6Squeeze any number of size 1 dimensions from an array.c38K|]}t|VdSrLrD)r`rrs rUrbzsqueeze..s.KK1-a66KKKKKKrWr$)rMrrsortedrr; squeeze_pr)rrrs @rUsqueezersn $VKKKK KKKKKLL*  5%00 L * 5 55rWcntt|t|krtd|tj|t|zfd|D}tt|t|krtd|t |t tj|}tD]}| |dfdtD}t|||S)z5Insert any number of size 1 dimensions into an array.z"repeated axis in lax.expand_dims: c0g|]}t|Sr_r)r`rndim_outs rUrzexpand_dims..s$ = = =Q Ax ( ( = = =rWrpcg|]}|v| Sr_r_)r`rdims_sets rUrzexpand_dims..s#DDD!!82C2CA2C2C2CrW) rssetrrMr frozensetrr[rinsertr r )rrr rrbroadcast_dimsrrs @@rU expand_dimsr#s ZS__,, F*FF G GG WU^^c*oo -( = = = =* = = =$T^^s4yy  @$@@ A AA t__(bhuoo&&, (  a1DDDDuXDDD. %~ > >>rWArrayLike | DuckTypedArray Shape | Nonec"|tj|nt|}|duotj|}|pt |}tj|tjr|j |||S|duoVt|tj  o;t|do+t|ddo| o|tj|k}|r|j}t|t!||||}|S)aCreate a full array like np.full based on the example array `x`. Args: x: example array-like, used for shape and dtype information. fill_value: a scalar value to fill the entries of the output array. dtype: optional, a dtype parameter for the output ndarray. shape: optional, a shape parameter for the output ndarray. sharding: an optional sharding specification for the resulting array. If not specified, the output will have the same sharding as the input, with a few exceptions/limitations in particular: 1. Sharding is not available during tracing, thus this will rely on jit. 2. If x is weakly typed or uncommitted, will use default sharding. 3. Shape is not None and is different from x.shape, default will be used. Returns: An ndarray with the same shape as `x` with its entries set equal to `fill_value`, similar to the output of np.full. Nr _committedTr)rMr[r'rrr5rrrrrrrrrrr) rrrSr[r fill_shaperuse_x_shardingrHs rU full_liker*s/*$mrx{{{1CE1J1J*tm9 6q 9 9)  6!99% ufo..< <  ZU ; ;; $$DK(( ( $ !Z $ !\4 ( ( $-$  #zH Z.z5)LL   # *rWstart_dimensionstop_dimension int | Nonec dt||t|j\}}}||krt d|jd|d|dt j|j||}|jd||fz|j|dz}t||S)aCollapses dimensions of an array into a single dimension. For example, if ``operand`` is an array with shape ``[2, 3, 4]``, ``collapse(operand, 0, 2).shape == [6, 4]``. The elements of the collapsed dimension are laid out major-to-minor, i.e., with the lowest-numbered dimension as the slowest varying dimension. Args: operand: an input array. start_dimension: the start of the dimensions to collapse (inclusive). stop_dimension: the end of the dimensions to collapse (exclusive). Pass None to collapse all the dimensions after start. Returns: An array where dimensions ``[start_dimension, stop_dimension)`` have been collapsed (raveled) into a single dimension. z,Invalid dimension range passed to collapse: [:]N)sliceindicesrsr[rmathprodr)rr+r,lohirkr new_shapes rUcollapser9s&O^44< >> 7=B' ( ($mCRC D7*W]233-??) ) $ $$rWct|j|jdkr-td|j|j|j|jkr-td|j|j|jdz f}|jdz f}t t |jdz }t ||||f||ff|S)zBatch matrix multiplication.rz9Arguments to batch_matmul must be at least 2D, got {}, {}z9Arguments to batch_matmul must have same ndim, got {}, {}rp)r)_minrrrrr r)rrrrrbatchs rU batch_matmulr=s #(CH!! PfSXsx00 2 22X PfSXsx00 2 22(Q,,(Q,, chl## $ $% S#| .f_wrappedsb 1IIE  ev66 !  q"* - -..777 1Q44KrW) functoolswraps)rFrGs` rU_upcast_fp16_for_computationrJs9 ?1 rWc6t|S)z-Elementwise tangent: :math:`\mathrm{tan}(x)`.)tan_prrs rUtanrMrrWc6t|S)z/Elementwise arc sine: :math:`\mathrm{asin}(x)`.)asin_prrs rUasinrP#rrWc6t|S)z1Elementwise arc cosine: :math:`\mathrm{acos}(x)`.)acos_prrs rUacosrS'rrWc6t|S)z2Elementwise arc tangent: :math:`\mathrm{atan}(x)`.)atan_prrs rUatanrV+rrWc6t|S)z6Elementwise hyperbolic sine: :math:`\mathrm{sinh}(x)`.)sinh_prrs rUsinhrY/rrWc6t|S)z8Elementwise hyperbolic cosine: :math:`\mathrm{cosh}(x)`.)cosh_prrs rUcoshr\3rrWc6t|S)z?Elementwise inverse hyperbolic sine: :math:`\mathrm{asinh}(x)`.)asinh_prrs rUasinhr_7rrWc6t|S)zAElementwise inverse hyperbolic cosine: :math:`\mathrm{acosh}(x)`.)acosh_prrs rUacoshrb;rrWc6t|S)zBElementwise inverse hyperbolic tangent: :math:`\mathrm{atanh}(x)`.)atanh_prrs rUatanhre?rrWcjdkrtdtjd}t djDrfdt |DSfdt |DS)Nrziteration over a 0-d arrayc3JK|]}t|tjVdSrLrrs rUrbz_iter..Os. < .PsI!!*61uEEE!!!!!!rWc3FK|]}tj|dVdSri)r/ index_in_dimrls rUrbz_iter..Ss5 P P!g"61u=== P P P P P PrW)rrerJr[rir )rmns` rU_iterrqJs [A 0 1 11 FLOA < ..js&*CE*J*JrWr_rs`rUrrjsJJJJrWcZtjtjd|jSNr_)rMr9rrSrs rUrrks"&"e)<)<"="="CrWcdSNFr_)rrks rUrrmserWc \jtjkrtd|dt fd|DsYd}t j}d|D}t|||d||jS)NCalled a with a float0 array. float0s do not support any operations by design, because they are not compatible with non-trivial vector spaces. 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Accepted dtypes are subtypes of {}.c3$K|] }|jV dSrLrr`rs rUrbz"unop_dtype_rule..}s$>>!*>>>>>>rW, )rSrrrerir1rjoin) result_dtypeaccepted_dtypesrrjryrgtypenameaccepted_typenamess ` rUunop_dtype_rulerps Z6=   @$ @ @ @ A AA G G G G G G G G GO LCtz**H>>o>>> CJJtXtyy9K/L/LMM N NN dj ! !!rWctt|||}ttd||}t j|t j||SNr[)rrr4 _attrgetterr) defvectorizedrdef_trivial_padding)rrr dtype_rulers rUunoprsU otLL* K00*d C C$  +rWcfdS)Nc$t|SrL)r)rryrs rUrz..swq$/?/?rWr_rs`rUrrs????rW) require_sameallow_extended_dtypec F ~t|t|ks J||ft|D]\} |r t jtjr'||}t fd|Ds jtjkrtd|d|dd} t j} d d|D} t| || ||| |r t|g|R||S)Nc3LK|]}tjj|VdSrLrrs rUrbz$naryop_dtype_rule..s2??Av Q//??????rWrz with a float0 at position ap. float0s do not support any operations by design, because they are not compatible with non-trivial vector spaces. No implicit dtype conversion is done. You can use np.zeros_like(arr, dtype=np.float) to cast a float0 array to a regular zeros array. 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Accepted dtypes at position {} are subtypes of {}.rc3$K|] }|jV dSrLrrs rUrbz$naryop_dtype_rule..s$88Qaj888888rW) rs enumeraterrSr ExtendedDTyperirrer1rrcheck_same_dtypes) rrrrrrtryrtypesrgr typenamesrjs @rUnaryop_dtype_rulersv Us?++ + + +e_-E + + +5!!EEga 4:v7K L L A E ??????? ? ?E v} $ $ Dd D Dq D D DEE ED"4:..II88%88888  41aCCDDDE 2$T2E2222 u rWc4d|D}|sdStd|Ddkr^d}t||dt t t t |g}t|D]tfdddDr| dAd Ds| detfd ddDr| dt|d dt t t t |d t |S) Nc*g|]}|j |jSr_r[r`rjs rUrz+broadcasting_shape_rule..s! 7 7 74DJ 7DJ 7 7 7rWr_c,h|]}t|Sr_rrrts rUruz*broadcasting_shape_rule..s ) ) )#e** ) ) )rWrpz7{}: arrays must have same number of dimensions, got {}.rc3NK|]}tj|dV dSr^rwrys rUrbz*broadcasting_shape_rule..r|rWrc<g|]}tj|d|Sr~rrs rUrz+broadcasting_shape_rule..rrWc3NK|]}tjd|V dSr^rrs rUrbz*broadcasting_shape_rule..rrWz+ got incompatible shapes for broadcasting: rc) rsrerrrkrrrrdr)rrtrXrgrr{rs @@rUbroadcasting_shape_rulers 7 75 7 7 7&  2 ) )& ) ) )**a// CC CJJtTYYs3E68J8J/K/K%L%LMM N NN, L G Gb 8 8 8 8ABB 8 8 888 G"Q%    BA2AAAf GA GGGGF122JGGG G GGF1I&&&&4FF99Sc%.@.@%A%ABBFFFGG G |  rWctt|||||}tt|}t|||}t j|t j||S)N)rr)rrrr4r)defbroadcastingrr)rrrrrequire_same_dtypesr shape_rulers rUnaryoprso(,,@$7999*.55* J D 9 9$ 4    +rWc ttjtfst dt j|}tjj|r|Sjr't|tjksJjs7t|ttt|Sdtt|jD}tjjrt#fd|DsJt%t||jS)Nz7transpose with implicit broadcasting of unshaped valuescHg|]\}\}}tj||| Sr_rr`rrubs rUrz _unbroadcast..s4 f f f)!Va$J_`acdJeJe fA f f frWc3:K|]}j|dkVdSrpNr)r`rrjs rUrbz_unbroadcast..s.-O-OQdjmq.@-O-O-O-O-O-OrW)rr DShapedArrayr#rerMr[rrsrrr rrr enable_checksrjrdr)rjrx_shaper s` rU _unbroadcastrs# D4,k: ; ;O M N NN HQKK'  W55 H Z:3w<<3tz??:::: 5 q$uS\\2233 4 44 f fyWdj)A)ABB f f fD !O#-O-O-O-O$-O-O-O*O*O#O#O#O ;q$'' 4 44rWc(tj|tj|r|Sst ||dSdt t |D}fd|D}t t||||S)Nr_cHg|]\}\}}tj||| Sr_rrs rUrz$_maybe_broadcast..sA , , ,)!Va$Q** ,A , , ,rWc g|] }| Sr_r_)r`rrs rUrz$_maybe_broadcast..s...AWQZ...rW)rMr[rrr rrr) target_shaperr  squeeze_shapers @rU_maybe_broadcastrs HQKK'  ,77K H K A|R 0 00 , ,yWl)C)CDD , , ,D.......M GA}55|T J JJrWaval_outcore.ShapedArrayrtSequence[core.ShapedArray]rSequence[ir.Value]c g}t||D]j\}}|j|jkr>t|jt|jks J||ftjt t t|jt|jz t|j}td|jDrAtj tj ||tj |j|}nAtj tj | |j||}||l|S)zLBroadcasts HLO values with broadcast-compatible shapes to the same shape. c3JK|]}t|tjVdSrL)rr7Valuers rUrbz broadcast_hlo..s. = =Z28 $ $ = = = = = =rWr)rr[rsr*dense_int_arrayrr rir9dynamic_broadcast_in_dimaval_to_ir_type shape_tensorr updater)rrtrrZrjargr s rU broadcast_hlorsU #ud##  idC zX^## __HN 3 3 3 3 3dH5E 3 3 3  ! uS((3tz??:C!B!B C CS JJsOOOO *rW) explicit_typerir.Valuec~|j|jc}\}tj||||j}|r|tj|g|RgS||gS)zLowers an elementwise operator to its MLIR equivalent. Args: explicit_type: does the MLIR op require its output type to be provided? )avals_in avals_outr*multi_broadcast_in_dimr[r)rctxrrrrrbroadcasted_argss rU_nary_lower_hlorsy , (KX0 48>++# Bt#H-- A0@ A A A BB B ! ""rWrc"t|gSrL)r)rrs rUrr"sQrWrc V|j\}tj|jtjrht jtj |tj |d|ddtj |d|tj |d|gSt j |gS)NrEQUNSIGNEDrp) rrrrSrMunsignedintegerr9r-r* compare_hlofull_like_avalr)rrx_avals rU_sign_lower_hlor(s L'& v|R%788. J D/Q??# % % CF++ CF++  - - .. (1++rWrrrrc|tjurtj|gS|tjusJtj|gSrL)rrr9round_nearest_afzrround_nearest_even)rrrs rU _round_lowerrBsL555  !! $ $ %% n< < < < <  "1 % % &&rWrr c"t||SrLrfgansrs rUrrOsC3KKrWrctttt|dt||S)Nr)rfr_constrs rUrrSs(SVAq\\):):C3KK%H%HrWc|j\}tjtjtjd|j}tj|||d}tj tj ||gS)Nrr_r ) rr* ir_constantrMrrrSr r9 exponentialmultiply)rrrlog2s rU _exp2_lowerrTsi L'& "(26!99fl;; < <$ sD&r J J J$ /#,tQ// 0 0 11rWrc"t||SrLrirrs rUrr\sc!QiirWrc Xt|t|t|SrL)rfr`_oners rUrr`s c!Sd3ii-@-@&A&ArWrc Xt|t|t|SrL)rir`rrs rUrresAs1d1gg 7 7rWrc tt|t||tt||SrL)rfr`rcrrs rUrris7SQAs )<)<),T!WWc):):&<&<rWrc tt|t|tt||SrL)rfrcrrs rUrrns*QCT#YY9L9L0M0M)N)NrWc t|d}t|t|tt |Sr)rrir`r r)rones rU logistic_implrrs5q! # S#c3s1vv;;'' ( ((rWmultiple_resultsc t|t|}}t|t|d}t |t |}}t |t | }}||z dz ||zdzdz } }|| z||z} } t|tt|d| t| | SNrr r+r/r}rr r#rr-r rrur a_is_zerosncse1me2msnhcshreims rU _sin_complexr ys a$q''Q!F1aLL!!) q663q66b" 1XXuaRyys#Ci1_sSy1}1s# 8R#Xb"  76!Q<<44gb"oo F FFrWctj|jdjtjr't jtd}|||Sttj ||SNrFr) rrrrSrMrr* lower_funr rr9sine)rrrs rU _sin_loweringrs[ s|A,b.@AA >, ? ? ?D 4Q<< 3 * **rWr c<t|t|SrL)rfr#rs rUrrsc!SVVnnrWc t|t|}}t|t|d}t |t |}}t |t | }}||z dz ||zdzdz } }|| z| |z} } t|t| t|dt| | Srrrs rU _cos_complexrs a$q''Q!F1aLL!!) q663q66b" 1XXuaRyys#Ci1_sSy1}1s# 8bS3Yb"  72va||44gb"oo F FFrWctj|jdjtjr't jtd}|||Sttj ||Sr) rrrrSrMrr*rrrr9cosine)rrrs rU _cos_loweringrs[ s|A,b.@AA ^L5 A A AF 6#q>> S! , ,,rWr#cVtt|t|SrL)rrfr rs rUrrsc#aQ..11rWcVtt|t|SrL)rir r#rs rU _tan_implrs SVVSVV  rWrMc^t|t|dt|zSr)rfrr@rs rUrrs#C6!Q<<&+++E$F$FrWctjt|tjrGt t |dtt t |d|St t |dt|tt |dttt |dt|S)Ny?rrp) rrr5rMrrfrr_r(r`rDrcr@rs rU asin_implrs vayy""455P va~~uS2%:%:;; < << va||QF1aLL$s6!Q<</K/K*L*LMMNN P PPrWrPc xt|tt|dt|z SrrfrGrr@rs rUrrs+s1eF1aLL6!99,D&E&EFFrWctjt|tjrtt t |dt|}t|}tt|t |d|t|Stt|t |dt t |dtttt |dt!|t#t |d|t%|tjS)Nrrgrrp)rrr5rMrrfrrbr+r-rrrr(rDrcr@r`r*pi)rr_rparts rU acos_implr$s  vayy""455 2a ) )F LLE ua  !!  &kk    1fQoo F1aLL $s6!Q<<3344c&A,,6J6J K K M M!RU   rWrSc zt|tt|dt|z  Srr rs rUrrs.s1uVAq\\F1II-E'F'F&FGGrWc>t|t|dSr)r(rrs rU atan_implr's q&A,,  rWrVc^t|t|dt|zSr)rirr@rs rUrrs#s1fQllVAYY&>??rWr(cL||t|t|zz zSrLr@rrr$s rUrrs!!qF1IIq $9:;rWcN|| zt|t|zz SrLr*r+s rUrrs"!qb&F1IIq $9:rWrYc<t|t|SrL)rfr\rs rUrrs1d1ggrWr\c<t|t|SrL)rfrYrs rUrrr.rWr_c vt|tt|t|zSrL)rfrGr@rrs rUrrs)AuVAYYa-@'A'A B BrWrbc t|t|t|z |t|zzSrL)rfrGrrs rUrrs1s1eQa[Qa[$ABBCCrWrec ttt||zt|t||z SrL)rfrBrrirs rUrrs6s:d1ggk22CDGGaK4I4IJJrWr+c dt|tjdt|gSr{)rrMrr5rrks rUrrs%GArxF1II/F/F$G$G#HrWr/c~ttjdt|t |gSr{)rrMrr5rr4s rUrrs+GBHR,C,CSVV$L$L#MrWc tj|stj|sJtj|rtj|rt|tjur2tj|jtj|jgSt |jt|t |jtt|gStj|rZt|tjurtj|jdgSt |jt|dgSt|tjurdtj|jgSdt |jtt|gSrL) r(is_undefined_primalrrZerorjrr+r/r)rrr$s rU_complex_transpose_ruler9s`  " "?b& >@@AA B BB "Qa//1c!ff - --rWcBt|rt|n|SrL)rCr6rs rUrr6:a==7QarWcBt|rt|n|SrL)rCr+rs rUrr7rJrWrDc Zt|tt|d|S)Ng?)rfrirrs rUrr:s"SCq#,D,D%E%ErWrGc vt|tt|dt||S)Ng)rfrrirs rUrr?s. q#fQoos3{{33 4 4rWrJc vt|tt|dt|dS)NgUUUUUU?)rfrrArs rUrrEs,SCq# C8L8L$M$MNNrWctj|jtjr+tj|jtjr|jS|j|jkr|jSt d|jd|jd)Nzthe first argument to pow must have an inexact dtype (float or complex), and the second argument must have an inexact or integer dtype, and two inexact dtypes must match, but got  and z respectively.)rrrSrMrr~rer's rU_pow_dtype_rulerRHs ,, ,, 7NW 7N;W;;$%7;;; < <.>'?'?@@ B BCC aQAuQxx(()) * *C QrWc tj|}tj|tjsJt t |t tt|||SrL) rrSrrMrrrfrrF)rrrr$rYs rU _pow_jvp_rhsr]cs^ LOO'  7BJ / //// c!S]1-=-=)>)>%D%DEEw O OOrWc|j\}}|j\}tjt t |jd}||j}||j}|||g|g|\} |||g|g|\} |||g} ttj | | | S)NrFrrr)r) rrr*rrrrSrreplacerr9power) rrr$ry_avalrconvertx_aval_y_aval_x_y_ctx_s rU _pow_lowerriis<.&&m)( N "hn===u F F' MMM / /' MMM / /' vh7)DDa H H$2 vh7)DDa H H$2 w0 1 1$ D"b 1 11rWcttttztzd|}|dkr5t j|tjrtd|d|d|S)NrArz>Integers cannot be raised to negative powers, got integer_pow(r)) rr_int_float_complexrrrMr~re)rr$rSs rU_integer_pow_dtype_rulerovsu )TF]X%=}a P P%UUv  33U -#$--()--- . .. ,rWc |dkrt|nYsA   $ $ $3>rWc|dkrtj||fS|dkr)tjtj|||fStjtd}tj|}||||S)NrFrr?)r9rr*rrvcache_lowering)rrr$lowerings rU_integer_pow_loweringr{s!VV LA    Avv La++Q / / 11~lUCCCH "8,,H 8Ca  rWc vtt|t|dt||Sr)r-r}rrXrs rUrrs*&Ava||!4!4eAhhBBrWnotandorxorrZr]c|\}}|\}}t||}t|t|cxurtjur$nn!|tj|fSt|tjur|t |j|fSt|tjur|t |j|fS|t||fSrL)r`rrr8 from_valuerr[primalstangentsrr$xdotydot primal_outs rU_add_jvprs $!Q*$1ayy* $ZZ4::--------- w|..z:: :: $ZZ7< ' (8$?? ?? DzzW\!! ' (8$?? ?? s4 &&rWcptj|r|jnt|}tj|r|jnt|}t |t jur(t j|t j|gSt||t||gSrL)r(r7rjrNrrr8rrrr$rrbs rU_add_transposers +A.. C166LOO&+A.. C166LOO& !WW  L ',v"6"6 77  # #\&!%<%< ==rWc||z }||z }||fSrLr_rrr$xryrs rU _add_inverser1u"1u" R-rWr`r!r_c|\}}|\}}t||}t|t|cxurtjur$nn!|tj|fSt|tjur$|t |jt|fSt|tjur|t |j|fS|t||fSrL)rcrrr8rrr[rrs rU_sub_jvprs $!Q*$1ayy* $ZZ4::--------- w|..z:: :: $ZZ7< ' (8#d))DD DD DzzW\!! ' (8$?? ?? s4 &&rWctj|r|jnt|}tj|r|jnt|}t |t jur(t j|t j|gSt||t|t|gSrL) r(r7rjrNrrr8rrrs rU_sub_transposers+A.. C166LOO&+A.. C166LOO& !WW  L ',v"6"6 77  # #\&#a&&%A%A BBrWrcctj|tj|z sJtj|r[t|tjurtj|jdgSt |jt||dgSt|tjurdtj|jgSdt |jt||gSrL)r(r7rrr8rjrrf)ctrr$s rU_mul_transposer s  " "R%;A%>%> >>>>A 6 Bxx7<l16""D ))163r1::.. 55 Bxx7<GL(( ))LQ44 55rWc||z }||z }||fSrLr_rs rU _mul_inverser rrWrfc"t||SrLr)rrr$s rUrr sSq\\rWc"t||SrLr)rrr$s rUrr sSD\\rWc tj|rtj|rJt|tjurtj|jdgSt |jt||dgSrL)r(r7rrr8rjrri) cotangentrr$s rU_div_transpose_ruler st  " "D2+A!+D+DDDD )__ $$ L $ '' Y!2!2 3 3T ::rWric"t||SrLrr+s rUrr% s#a))rWctttt||t|dS)NrO)rfrrAr+s rUrr& s(#c#a&&!nnk!R.@.@AArWrlctttj|tj||SrL)rrrMr[r+s rUrr- s-$%5bhqkk28A;;%O%OQRSSrWctt|ttt||t t t||SrL)rfrrrirr9r+s rUrr. sDCADQOOU3s1ayy>>5J5J K KLLrWc ttj|tj|}t||}t||}t |}t |}t t |||t|t||||}t |||SrL)rrMr[rr+r-r}r/)rr$lax_cmp_pick_xrrxrypick_xs rU_minmax_complex_loweringr1 s!"(1++rx{{;;,|Q''!|Q''! Aww" Aww" "R**nnT!WWd1gg>> .R(( * *& 1  rWzcore.Primitivernc@t|t|||SrLrf _balanced_eqrrrr$s rUrr= A|AsA'>'> ? ?rWc@t|t|||SrLrrs rUrr> rrWrqc@t|t|||SrLrrs rUrrC rrWc@t|t|||SrLrrs rUrrD rrWrtrwrzc |\}} tj|} tj| } tj| j|j} t t |j| j} tj |tt|d||| | g| g\}tj |tt||| || g|gS)NFr_r) r physical_avalr#r[rSrr rr*delegate_loweringr_compare_lower_hlo_unary_reduce_lower) direction reduction_opidentityrrrrr$aval_xaval_y base_aval_x base_aval_y base_aval_out reduce_axesress rU_opaque_comparison_hlorU s.&&"6**+"6**+";#4hnEE-eHM=+=>>??+  7%y% 8 8k;/M? L L L$#   7& h# % % % ]Oz ; ; ;;rWrNErrctfd|D}|dkrt||||S|dkrt||||Std|d|dj)Nc3VK|]#}tjj|jV$dSrL)rr#r[rS)r`rjrs rUrbz,_compare_lower_hlo_opaque..j sMII7;dx~tz22IIIIIIrWrrzHLO comparison z for extended dtype r)r_opaque_eq_hlo_opaque_ne_hlorrS)rrrrrr$broadcast_avals_ins ` rU_compare_lower_hlo_opaqueri sIIII?GIIIII$ #18Q B BBD #18Q B BB L)LL!9JLL N NNrW total_orderc|j|jc}\}|dj}tj|||f||j\}}t j|t jr|rJt||||||St j|tj r|rdnd}n$t j|tj rd}nd}tj ||||gS)Nr TOTALORDERFLOATSIGNEDr)rrrSr*rr[rrrrrMr signedintegerr) rrrrr$rrx_dtype compare_types rUrru s, (KX QK ' $S1a&(HN K K$!Q w00O $YXxA N NN w ++#.;<(>??L < ++&-5+QQ R RR ! & &w)1:X ' O OOrWc|\}|j\}t|tjhtjvr)t |jtj r tj |st j |j dtj stj5tjdt"jtj||j d}dddn #1swxYwY|jjs|gdfS|}tj|j|jjur|gdfSdg|fS)Nrignore)outvarsrrMrrpython_scalar_dtypesrrjrr"r[rrrrcatch_warnings simplefilterrrFrrritemrrS)rlrrcorZs rU_convert_elt_type_folding_ruler sq"! {"! 1gg"*;v:;;;+,,<57Xa[[<  CJ{3V_ E E<  " "88Hd&>??? HQKK  sz+6 7 7c888888888888888 6 UD[ ((**C }S16<//UD[ s(ADD  D c:|j\}tj|jdtjsdtj|jjtjs;|jj|jdkr |jj|jdkr|gdfSdg|fS)Nrr)invarsrrrrrjrSr)rrs rU_convert_elt_type_fwd_ruler s z"!  CJ{3V_ E E  AFL&/ : :flcj---f#*[111 39 63;rWct|j}|d|d=tj||||S)Nrr)dictrr_pp_eqnr`)rcontextsettingsrs rU_convert_elt_type_pp_ruler sH   & Jz ckkk00'8 D DDrWrctjt||||}| tj||}|S)Nr)rr!rrrTlaxwith_sharding_constraintrs rU_convert_element_type_bindr sO N   6*3y)1  3 3'g..wAAG .rWc4tj|jSrL)rMrrSrs rU _real_dtyper srx44rWcT|j\}|j\}tj|jt jr[tj|t js>G  3( ; ; <4F I I J JJ =" rWctj|j}tj|}tj|tjs]tj|tjs>tj|tjstj|tjr||krtd|d|d|S)Nzlax.bitcast_convert_type does not support bool or complex values unless the operand and destination types match. Got operand dtype=z , new_dtype=z/. Consider using the arr.view() method instead.)rrrSrrMr}rre)rrrs rU _bitcast_convert_type_dtype_ruler4 s' 66)' 22)  28,,G  2#566G  28,,G  2#566GI F+4FF8AFFF G GG rWr)weak_type_rulecd|j\}tjtj||gSrL)rr9bitcast_convertr*r)rrrrs rU_bitcast_convert_type_lowerrH s,m)( d28<.W sg P P<=  [! , , 8  3Q 7 728 P P P P P PrWzInput type is incompatible with `preferred_element_type`. The compatible combinations of (input_type, preferred_element_type) are (integral, integral), (integral, floating), (floating, floating), (complex, complex.zL`preferred_element_type` must have the same signedness as the original type.zE`preferred_element_type` must not be narrower than the original type.) rrrMr~r rrirerrSr )r3r allowed_typesinput_bitwidthpreferred_bitwidths`` rU _validate_preferred_element_typerO sH  RZ00/ . <</ Zb.@AM  P P P P PAN P P PPPB A B BB +r'788/  4b6F G G/ . / //8K((1.x 677@.(( % & &&)(rWcT|\\}}\}}tfd||fDsd|d|dj} t| tfd||fDsd|d|dj} t| t|t|kr%d } t| ||t |t |} } t |t |} } t| t|krd |d } t| t| t|krd |d } t| t| t|krd |d } t| t| t|krd|d } t| | | zr%d} t| ||| | zr%d} t| ||t fd|D}t fd|D}tj||s%d} t| ||t fd|D}t fd|D}tj||s%d} t| ||tj j |S)Nc3K|]W}tjtj|do+tjtj|jVXdSr^rMrd greater_equallessr)r`rzrs rUrbz*_dot_general_shape_rule..l k 4 4VB$Q** + + Lrwq#(7K7K0L0L 4 4 4 4 4 4rWzdot_general requires lhs dimension numbers to be nonnegative and less than the number of axes of the lhs value, got lhs_batch of z and lhs_contracting of z for lhs of rank c3K|]W}tjtj|do+tjtj|jVXdSr^r)r`rzrs rUrbz*_dot_general_shape_rule..s r rWzdot_general requires rhs dimension numbers to be nonnegative and less than the number of axes of the rhs value, got rhs_batch of z and rhs_contracting of z for rhs of rank zldot_general requires equal numbers of lhs_batch and rhs_batch dimensions, got lhs_batch {} and rhs_batch {}.zHdot_general requires lhs batch dimensions to be distinct, got lhs_batch rczHdot_general requires rhs batch dimensions to be distinct, got rhs_batch zTdot_general requires lhs contracting dimensions to be distinct, got lhs_contracting zTdot_general requires rhs contracting dimensions to be distinct, got rhs_contracting z~dot_general requires lhs batch dimensions to be disjoint from contracting dimensions, got lhs_batch {} and lhs_contracting {}.z~dot_general requires rhs batch dimensions to be disjoint from contracting dimensions, got rhs_batch {} and rhs_contracting {}.c32K|]}j|VdSrLrr`rrs rUrbz*_dot_general_shape_rule.. )::1#)A,::::::rWc32K|]}j|VdSrLrr`rrs rUrbz*_dot_general_shape_rule.. r$rWzidot_general requires lhs batch dimensions and rhs batch dimensions to have the same shape, got {} and {}.c32K|]}j|VdSrLrr#s rUrbz*_dot_general_shape_rule.. )FF ! FFFFFFrWc32K|]}j|VdSrLrr&s rUrbz*_dot_general_shape_rule.. r(rWzRdot_general requires contracting dimensions to have the same shape, got {} and {}.) rdrrersrrrrr_dot_general_shape_computationr[)rrrrrlhs_contractingrhs_contractingrrrglhs_contracting_set lhs_batch_setrhs_contracting_set rhs_batch_setlhs_batch_shaperhs_batch_shapelhs_contracting_shaperhs_contracting_shapes`` rU_dot_general_shape_ruler5i s?P<$?O&M ) )"h ) )C C..  4 4 4 4& 2 4 4 4 4 4 )$ ) )>M ) )"h ) )C C..^^s9~~%% >)) %! % % %C C..3y>>)) %! % % %C C.. _!5!555 5"1 5 5 5C C.. _!5!555 5"1 5 5 5C C..=(< NC CJJy/:: ; ;;=(< NC CJJy/:: ; ;;:::: :::::/:::: :::::/ $_o F FB 4C CJJ@@ A AAFFFFoFFFFFFFFFoFFFFF $%:O P PPrWc|\\}}\}}tfd|D}ttt|t|z}t|} ttt|t|z} t|| } || z| zS)Nc3(K|] }|V dSrLr_)r`r lhs_shapes rUrbz1_dot_general_shape_computation.. s'66qil666666rW)rr tuple_delete) r8 rhs_shaperr+r,rr batch_shapelhs_contract_or_batchlhs_tensored_shaperhs_contract_or_batchrhs_tensored_shapes ` rUr*r* s?P<$?O& >>rWct|tfdttDS)Nc30K|]}|v|VdSrLr_)r`ridx_tups rUrbztuple_delete.. s+@@!!4--s1v----@@rW)rrr rs)rCrarBs` @rUr9r9 sA S$ @@@@@uSXX@@@ @ @@rWc d}||j||j}}||kr|j}nD||kr|j}n6|j|jkrtd|jd|j|j}t||S)Nctj|tjrt |n|}tj|tjtj|tjrtj|jndtj|tjrtj|jndt|tj|tj  fSr) rrrMrrr rmaxexpnmant _bit_widthr)dtrcs rUtype_propertiesz0_dot_general_dtype_rule..type_properties s!,R1CDDL B"A  b""4 5 5&,&72;&G&G OFLOO " "R&,&72;&G&G OFLOO ! !R qMM!!R%788 8  ::rWz%lax.dot_general argument type error: r)rSre _maybe_upcast) rrrrrrJlhs_proprhs_proprs rU_dot_general_dtype_rulerN s :::'sy11??393M3MH( 9LL(9LL yCI  J#) J Jsy J J L LL9L |%; < <>Iuaa%gvv>>Iq% &/Iw/ 0$ BJz4J4J K KLL ZW .1GG H H( K1di7MOOO(OO % %% [AFL  !%qv7G H HE ,rWc |\\}}\}} ||f| |ff} t|||| ||d} | j|jjkr%t| |jj|jj} | S)NT)rrrrR)rdrSrjrr) rrr$rrrrXrYrZr[swapped_dimension_numbersy_bars rU_dot_general_transpose_rhsrh s1B.:z.Wg *J7'79KL $q!8I1    % [AFL  !%qv7G H HE ,rWc|\}}|\}}|\\} } \} } t|tur|jn|} t|tur|jn|}tt j|t j|f| |f|\}}t|tur6t j|t|}t j ||j }nt j |}t|tur6t j|t|}t j ||j }nt j |}t|||||}t j |t|||}||fSrT)rr. stacked_axis_dot_general_batch_dim_numsrMrr)mask_ragged_axesr bdim_as_shaper[r shape_as_bdimr*) batched_args batch_dimsrrrrrlbdrbdrrrrleft_stack_dimright_stack_dimnew_dimension_numbersresult_stack_dimr8r: batched_outresult_batch_dims rU_dot_general_batch_rulery s(#s (#s9J6< 6I'+CyyJ'>'>3##C.(,S Z(?(?C$$S/,G ws||RWS\\"^_$E--)) #YY*  #C):C @ @C&sCI66II I #YY*  #C):C @ @C&sCI66II IC&;&/3IKKK++$Y ;PQQSS & &&rWc f |\}}|\}}||J|\\ \ d}t|t|cxur tur?nn<|f| |z |f||z| | ||d}nt|turv|t fdt|D} t tt t j| |z}| | | | nt|tury|wfdt|D} |t z tt t j| |z}||||nJ f ff} | |fS)Nc lttj|tj||SrL)rrMr`r)r rs rU bump_dimsz._dot_general_batch_dim_nums..bump_dims7 s) b.tQ7788 9 99rWrc$g|] }|v|v | Sr_r_)r`rzrrs rUrz/_dot_general_batch_dim_nums..E :CCCi''A\,A,A,A,A,ArWc$g|] }|v|v | Sr_r_)r`rzrrs rUrz/_dot_general_batch_dim_nums..M r~rW)rrJr rssumrMr)ndimsrprlhs_ndimrhs_ndimrqrrr|rx lhs_tensor rhs_tensorrurrrrs @@@@rUrkrk$ sL(H(#s COOO9J6< 6I::: #YY$s))""""s"""""9c222I9c222I9\3//L9\3//L S SS[CCCCCU8__CCCJ9~~C C0H0H,I,I(J(JJ )S))I9\3//LL S SS[CCCCCU8__CCCJ 3|#4#44C C 8 899::; )S))I9\3//LLL(,7)Y9OP  0 00rWc ~ |\ }|\\}}} fd|D}t|d|} t| |fd|i|gS)Ncg|];}tj|tj'|j|jf.^ sWGGGx~a0"2DEEG!X^A&*+GGGrWrr)_replace_masked_valuesr) in_avals out_avalsrrrrrkr padded_axeslhs_rs @rU_dot_general_padding_rulerZ s{+(A*<QGGGG\GGG+ Q 4 4$ dC O O3D O O O PPrWpp.DoccFd|jD}|jd\\}}\}}t|t|ft|t|ff|d<tj||||S)Nci|] \}}||| SrLr_)r`rrs rU z(_dot_general_pp_rule..f sIIITQ1=Aq===rWrr)ritemsrrrr`)rrrprinted_paramslhs_contrhs_contrrs rU_dot_general_pp_rulerc sJISZ%5%5%7%7III.14.| s/===sSVV$$===rW)rrrrr7 ArrayAttrr)rfull_precisions rUprecision_attrrt sh'):;NN i ' '+NNN   ==n=== ? ??rW)platformnp.dtype | Nonerc d}~|j\}} |j| j} } |j\} |\\} }\}}| | kr|dkrd}|| r || sqtj|||t j|j| j}tj||| t j| j| j}| jx} } n}|| | sqtj|||t j|j| j}tj||| t j| j| j}| jx} } tj t|t|t| t|}tj tj | |||t|gS)Ncntjtjtjtjf}||vo||vSrL)r float8_e4m3fn float8_e5m2float8_e5m2fnuzfloat8_e4m3fnuz) _lhs_dtypes _rhs_dtypes fp8_dtypess rU_is_fp8_mixed_precision_matmulz:_dot_general_lower.._is_fp8_mixed_precision_matmul s5&(:(&*@BJ * $ B )BBrWtpuc~tj|tjptj|tjSrL)rrrMr r~)rIs rUrz$_dot_general_lower.. s/F-b"+>>>"-b"*==rW)lhs_batching_dimensionsrhs_batching_dimensionslhs_contracting_dimensionsrhs_contracting_dimensions)precision_config)rrSrr*rrr#r[r9rrrrrr)rrrrrrrrrrhs_aval lhs_dtype rhs_dtyperr+r,rrhandled dot_dnumss rU_dot_general_lowerr sCCC|(H!Y)m)(?P<$?O&.ragged_to_dense s#A&K !'!*agaj 1EG,,Qv>>M 7 # #K$5ua @ @D ,,J M:a=/1B C C C ssO  L))*eTBBJ7++L%FFL D TJ%6 7D 9??4 2 22rWrrpr) rr(r7rTrVmatrix_transposerrr)rrrrrrr$rrgrad_xy_tgrad_yx_densect_densers rU_ragged_dot_transpose_ruler s(!Q C D DD333$A  FF ) $ $Q ' 'C    5 FA  FFoa$$Gr2&&H#sqcA3Z0 W 5 !F  rWrcB|td|jd|jd|jdf}t||ddg}t|j|d}t j|}tt|dd|ddgd} t||d}t| |d} t| |k||k} t| |t|}t||t||S) Nrrrprrrrr)rr[r rrSrTrrrr=rPr-rr) rrrrrrr[rrrrs rU_ragged_dot_implr; s$ C D DD 9Q<1sy| 4%eaV,,# ++UA 6 6$w~~k*** k2A2 3B30A, E488*!,t<<, \T)4*+< = =$tS&++&&#   93    rWc $tddtddtj}|tkr%d}t ||t|kr2d}t ||tt t tts&d}t ||tfdt|DsBd}t |td j Dttt ks-tttkr$d }t |S) Nr r[r z~broadcast_in_dim broadcast_dimensions must have length equal to operand ndim; got broadcast_dimensions {} for operand ndim {}.zbroadcast_in_dim target broadcast shape must have equal or higher rank to the operand shape; got operand ndim {} and target broadcast ndim {}.zubroadcast_in_dim broadcast_dimensions must be a subset of output dimensions, got {} for operand ndim {} and shape {}.c3tK|]2}tjj|d|gV3dSr)rdefinitely_equal_one_of_dimr[)r`rr rr[s rUrbz/_broadcast_in_dim_shape_rule..l sb + + -gmA.>/0%8LQ8O2P.QSS + + + + + +rWzbroadcast_in_dim operand dimension sizes must either be 1, or be equal to their corresponding dimensions in the target broadcast shape; got operand of shape {}, target broadcast shape {}, broadcast_dimensions {} c3>K|]}tj|VdSrL)r replace_tracer_for_error_messagers rUrbz/_broadcast_in_dim_shape_rule..u s- N N1d3A66 N N N N N NrWz^broadcast_in_dim broadcast_dimensions must be strictly increasing; got broadcast_dimensions {}) _check_shapelikerMrrsrerrissubsetr rdrr[r)rr[r  operand_ndimrgs``` rU_broadcast_in_dim_shape_ruler[ s %w666%'=')))!!,S-.... LC CJJ3\BB C CCZZ, UC CJJ|SZZ88 9 99 ! " " + +Cc%jj0A0A,B,B C CK BC CJJ3\5II J JJ  + + + + + +L)) + + + + + & # CJJ N N N N NNN #%% & && 3s+?'@'@#A#AAA !!U62F+G+G%H%HHH )C CJJ344 5 55 ,rWc|s*t|j||\}}|g|fSt||}d|D}t jt ||jj|jj}|gtj fS)NrcVg|]&}t|tjur|jn|'Sr_rrLiteralrHr`rs rUrz4_broadcast_in_dim_typecheck_rule.. 0LLLQ$q''T\11qLLLrW) r abstract_evalrjrrrrrSrr)rkrr[r rrr out_shapes rU _broadcast_in_dim_typecheck_ruler s  '*88 E8L9NNHg :w ! 22ILL)LLLI y!1!17<3E!(!799H :t &&rWc t|tjurtj|jgSdt |jjD}t tj||}t tjtt||}tt|||gdgt|zzS)NcBg|]\}}tj|d|Sr~r)r`rss rUrz4_broadcast_in_dim_transpose_rule.. s=///TQ'1--/q///rW) rrr8rjrr[rrMdeleter rsr#r)rrr[r r unit_dimsrr?s rU _broadcast_in_dim_transpose_ruler s "XX L & & ''//Yw|'9::///)  . :: ; ;% rys5zz**E22 3 3$ {2t,,i 8 8 9 &3y>> ! "#rWc||^}}|^}}d}|t|tr|j} n|} tj|| d} t|tr|j}n |j| }dttj d|z} n$|} ttj d|} g} g} t||D]\}}|t|tsJ|}nR|j j }| ||t|}nd}t||ks J|| ||ft!|| z}t#| || }dt%|D}tj|jdt|| }||fS)Nrrrpz3All segments lengths arrays must be the same lengthc"g|] \}}||dz Srr_)r`rars rUrz0_broadcast_in_dim_batch_rule.. s!GGGvsAQYSUYYYrW)rr.rjr)moveaxisrr[rrMr`rrJrSboundrrsrr rmake_batch_axisr)rorpr[r rr operand_bdimdyn_shape_bdims stacked_sizerj new_operandnew_broadcast_dimensions dyn_limitsout_ragged_sizesrbdimrrgr8r_out_ragged_axesout_bdims rU_broadcast_in_dim_batch_ruler  s%'I#- ,,, ++"!.ll!l#G\1==K, ++1!&ll]<0l#eBF16J,K,K&L&LLK$RVA/C%D%DEE *O44  keT | s # ####eekee$$$  5zz C5zz\)))3)))eo 0 C CC) K4L M M&GG5)9)9GGG/  % k1c/+;<<>>(  rWc|j^}}|s/tj|jd|jjr|gdfSdg|fSr)rrrrrjr[)rrdyns rU_broadcast_in_dim_fwd_ruler sL J'!c ,SZ-@!&,OO 39 63;rWct||}|s|t|f|Stjt |||j|j}t|t||g|Ri|SNr) rdefault_process_primitiverrrrrSrr)rrr[r r rrjs rU_broadcast_in_dim_staging_ruler s e2F G G G& M  * *+=tV L LL +E377!+ N N$ (:D! +c + + +#) + ++rWc~~|\}g}g}|jD]} t| tjur|| j8t| t ur|| dt| tj sJ|d|| tj |g|Rt||dgSr) r[rrrrrrJrrrrrr) rrrr[r rrr8 new_dyn_shaperzs rU_broadcast_in_dim_padding_ruler s )()- >a Aww"$$$qw aCq 4; ' ''''t1  !! Mm M M5;K;K7K M M M NNrWc|^}}|^}}tj|g|R||d}t|tjur tj|} ntj|g|R||d} || fSr)rrrrr8r) rrr[r rr operand_dotrkr$y_dots rU_broadcast_in_dim_jvp_ruler s'I/+gI II3GIII! +',&& L # #A & &EE  #K O) O O59M O O OE E/rWc  |s/|t|g|Rt||Std|DsJ||}t |j|}t | fd|D}tjt||j |j }tj |tj|d} tj|g|| gtt||tjt%j} | | _| S)Nrc3HK|]}|jVdSrL)pvalis_knownrs rUrbz1_broadcast_in_dim_partial_eval.. s. 2 21QV__   2 2 2 2 2 2rWc6g|]}|tn|SrLr)r`rzdyn_shape_tracers_s rUrz2_broadcast_in_dim_partial_eval.. s+ H H HQ D# $ $ $q H H HrW)rrrrdinstantiate_constrkrrrrrSrr JaxprTracer PartialValunknownnew_eqn_reciperrrrecipe) rrr[r roperand_tracerdyn_shape_tracersshape_rrrrs @rU_broadcast_in_dim_partial_evalr) sT F  * *W1y11 5/CDDD F FF 2 2 2 2 2 2 2222**733.%19==-.. H H H H% H H H&  uV}}gmW=N O O(~eR]%:%:8%D%DdKK* *)*ZL:L -ABBB o'/11 3 3#* rWc|j\}|r$|t||}tj||||gS)Nrr)rrrr*r )rrr[r rrs rU_broadcast_in_dim_lowerr+ sam)(I%5eY%G%GHHH  Q5I K K K LLrWci}|jdr|jd|d<|||jdd}tj|||S)Nr rp)rr)rreplpacerrr)rrrrnew_eqns rU_broadcast_in_dim_pp_ruler/ s`.Z&'P-0Z8N-ON)* LLsz"1"~L F F' gw 1 11rWc|sKtd|Ds2t|||}tj||j|jStjt|||j|jS)Nc3K|]P}t|tjo1ttj|jtjuVQdSrLrrDArrayrrrSbintrs rUrbz2_broadcast_in_dim_abstract_eval..# nHH<=DK((84=##)**di7HHHHHHrWr)rirrr#rSrrr)rr[r rs rU_broadcast_in_dim_abstract_evalr6! s 9 HHAFHHH H H9 ) -A C C CE  E17AK 8 88  +E9==qw T TTrWr c|jr0|j|jkr td|jd|jd|jr0|j|jkr td|jd|jd|jS)NzLclamp requires min.shape == operand.shape or min.shape == (), got min.shape=z, operand.shape=rczLclamp requires max.shape == operand.shape or max.shape == (), got max.shape=r)rPrrRs rU_clamp_shape_ruler8= sYI39 -- H),HH6=mHHH I IIYI39 -- H),HH6=mHHH I II rWrc |\}}}|\}}}tdt||D} ||cxkr|kr;nn7tj|tj|cxkrtj|kr!nnt||||fStj|tj|cxkrdkr!nnt||||fStj|tj|cxkrdkrOnnt||j|g}t||j|g}t||||fSnPtj|dkr8tj|dkr |t||||fStj|rtj ||| n|}tj|rtj ||| n|}tj|rtj ||| n|}tj|dkr-tj|dkrt||j}tj|dkr-tj|dkrt||j}dtj|cxkrtj|krNnnKtj|dksJtj|t||jdg}dtj|cxkrtj|krNnnKtj|dksJtj|t||jdg}tj|tj|krItj|dksJtj|t||j}t|||dfS)Nc3:K|]\}}||j|VdSrLrr`rrs rUrbz$_clamp_batch_rule..L 9  TQgaj  rWrrp) rrrMr[rrrr r) bdim_at_frontr ) rorprrPrrRmin_bdimx_bdimmax_bdimrs rU_clamp_batch_rulerAI s+#q#)(FH   Sz%B%B     $####8##### x}} 4444rx}}44444 \\#q# & & ..  * * * * * * * * * \\#q# & & ..  * * * * * * * * * S!'H: 6 6c S!'H: 6 6c \\#q# & & .. + ws||qRWS\\Q..63E <<Q $ $f ,,79x}}MsHd333##79x}}MsHd333##13!ChQ---!!WS\\Q271::>> C ! !CWS\\Q271::>> C ! !C"""" """"" 73<<1   bgcll    3! - -C"""" """"" 73<<1   bgcll    3! - -CWS\\BGAJJ 71::???BGAJJ???!SYA c1c " "A %%rWc ttt||t|||t |SrLr-rPrrr=rrPrrRs rUrrp s= RW--r#s||<<F7OO % %rWc ttt||t|||t |SrLrCrDs rUrrs s? R--r'3/?/?@@F7OO % %rWcZtt|||t|SrL)r-rr=rDs rUrrv s& C!!1fWoo 6 6rWc  |d|sd}t|td|DsJd}td|D}t|t |t d|DdkrAd}t|d d |Dd cxkr|d jksDnd }t|d d |Dfd|D}|dd|ddksWd}d|D}t|d tt|tfd|D}|d j }|d|fz|dzdzS)Nrz0concatenate expects at least one operand, got 0.c3@K|]}t|tVdSrLrr"r`rs rUrbz*_concatenate_shape_rule.. s, H HGZ / / H H H H H HrWz2All objects to concatenate must be arrays, got {}.c3DK|]}t|t|VdSrLrIr`rs rUrbz*_concatenate_shape_rule.. s1 I IR:b-+H+H Ib I I I I I IrWch|] }|j Sr_rrJs rUruz*_concatenate_shape_rule.. s / / /7', / / /rWrpzGCannot concatenate arrays with different numbers of dimensions: got {}.rc3>K|]}t|jVdSrLrr[r`rs rUrbz*_concatenate_shape_rule.. s*(H(H!QW(H(H(H(H(H(HrWrz@concatenate dimension out of bounds: dimension {} for shapes {}.c6g|]}t|jSr_rPrQs rUrz+_concatenate_shape_rule.. s 4T4T4TaS\\4T4T4TrWcTg|]$}|jd|jdzdz%Srr)r`rrs rUrz+_concatenate_shape_rule.. sH % % % M*9* % ikll(C C % % %rWrzCannot concatenate arrays with shapes that differ in dimensions other than the one being concatenated: concatenating along dimension {} for shapes {}.cg|] }|j Sr_rrJs rUrz+_concatenate_shape_rule.. s 4 4 4gm 4 4 4rWc32K|]}|jVdSrLr)r`rrs rUrbz*_concatenate_shape_rule.. s*991AGI&999999rW) rrerdrrrrsrrrkrrr[)rryrgrrX concat_sizeex_shapers @rU_concatenate_shape_rulerX| s2jj%%)  C I I8 I I I I IB CJJtBxx(( ) )) / /h / / /00A55 SC CJJtyy(H(Hx(H(H(HHHII J JJ i * * * *(1+* * * * * LC CJJy$))4T4T84T4T4T*U*UVV W WW % % % %# % % %& qrr " " )C5 48 4 4 4F CJJy$))CV4D4D*E*EFF G GG999999999+ a[ ( *9*  .)A+,,1G GGrWc6tdg|R|djS)Nrr)rrS)rrys rU_concatenate_dtype_rulerZ s%M-H---- ! rWcd|D}ttjur d|DStjfd|D}tjt|jft}tj j t|df}t|ddD]\}}|dd||<t|D]\}} ||| <fdt|||DS)Nc\g|])}tj|r |jjn|j*Sr_)r(r7rjr[rQs rUrz/_concatenate_transpose_rule.. sB'''%'$:1$=$=JAFLL17'''rWclg|]1}tj|rtj|jnd2SrLr(r7rr8rjrQs rUrz/_concatenate_transpose_rule.. sI   %'$:1$=$= GGL 4   rWc g|] }| Sr_r_)r`r[rs rUrz/_concatenate_transpose_rule.. s666ey 666rWrrprcpg|]2\}}}tj|rtj||nd3SrL)r(r7r/r2)r`rstartlimitrs rUrz/_concatenate_transpose_rule.. s[ L L L)!UE/1.DQ.G.G GM!UE * * * L L LrW)rrr8rMrtolistrrsrrJtiler[rr) rrroperand_shapes limit_pointsstartslimitsrrls `` rU_concatenate_transpose_rulerj s''%'''. !WW      96666~666888> Xs8}}af-S 9 9 9 @ @ B BF WQWs8}}a0 1 1 8 8 : :F&*%%**1!#2#&q)a ll&!!%%1!!_a ll L L L L-066-J-J L L LLrWctdt||Dfdt||D}t||dzdfS)Nc3:K|]\}}||j|VdSrLr)r`rrs rUrbz*_concatenate_batch_rule.. s=##T!htn!!!!##rWchg|].\}}|tj||dnt|f/Sr)r)rr )r`rrrs rUrz+_concatenate_batch_rule.. sS==="d150@hD!,,,R$))===rWrpr)rrr)rorprrrs @rU_concatenate_batch_rulern s ##Sz-J-J### # #$====!, ;;===( Xy1} - -q 00rWcjtfd|Drt|gSt)Nc3pK|]0}t|jttjfV1dSrL)rr[rJrMr~)r`rurs rUrbz(_concatenate_pad_rule.. sO    AGI&bj(9 : :      rW)rdrr)rrrrs ` rU_concatenate_pad_rulerq sT        ) , , -- rWrcRtj|tj|gSrL)r9rr*i64_attr)rrrys rU_concatenate_lowerrt s! /"dmI66 7 7 88rWc|j|jkr/d}t||j|jt||S)Nz@pad operand and padding_value must be same dtype: got {} and {}.)rSrerr0)rrrrgs rU_pad_dtype_rulerv sH ]m))) LC CJJw}m.ABB C CC g} - --rWc~tj|}t|tj|kst d|d|t d|Dst d|t dt||D}t d|Dsd|d|d |}t ||S) NzVlength of padding_config must equal the number of axes of operand, got padding_config  for operand shape c3*K|]\}}}|dkVdSr^r_)r`rkrs rUrbz"_pad_shape_rule.. s, 2 21aQ!V 2 2 2 2 2 2rWzKinterior padding in padding_config must be nonnegative, got padding_config c3`K|])\\}}}}||ztj||dzzV*dSr)r dilate_dim)r`rihrrzs rUrbz"_pad_shape_rule.. saDD!YaAQAE222DDDDDDrWc3"K|] }|dkV dSr^r_rs rUrbz"_pad_shape_rule.. s& $ $Q!V $ $ $ $ $ $rWzADimension size after padding is not at least 0, got result shape z, for padding_config z and operand shape )rMr[rsrrrdrr)rrrop_shaper_rgs rU_pad_shape_ruler sC Xg  ( ^   0 0 0 0 57E55*255 6 66 2 2> 2 2 2 2 2= <+9<< = == DD%(%B%BDDD D D& $ $V $ $ $ $ $ ,% , ,. s!k!T%--%8%899rWc fttjtjtj}t tjdj|}tj|tj|j tj dS)Ngrp) rBrMnegativerr"rrSr/r2r[r`) unpad_configunpaddedr7interiorr6rs rUt_opz_pad_transpose..t_op sbk"oor{2 mH5577lQQW--|<22BH 9 9 9 9E00000000099CtI020F}0U0U _Sq55++ , , ,[_F V rWc|\}}|\}}|d}t||j|f}t|}||d|t ||||fS|dks J|t |t ||}t t |dtjd|}t||j|f} t||| |fS)NrrrrTF) r r[rr!r"rGr*rMr}r r-) rorprrrrpadding_value_bdimrrbroadcasted_paddings rU_pad_batch_ruler s''=%/","L-"56H"I!KLLG''. i000 w ~ 6 6 DD q "4  '5>>>22! Ywbh / / G G$(*6:: a, - -| ;;rWr"c z|j\}tj|\}}}tj|||||||gSrL)rrrr*r")rrrrrlowrrs rU _pad_lowerrs@m)( N33#tX (3!]Cx H H IIrWc|jSrLrr&s rU_squeeze_dtype_ruler# rWcFttj||SrL)_compute_squeeze_shaperMr[r&s rU_squeeze_shape_ruler&s  1 1: > >>rWct|tt|krtd|tfdDstd|t fd|Drtdd|t fdt DS)Nzdimensions are not unique: c3RK|]!}d|cxkotkncV"dSr^rrr`rzr[s rUrbz)_compute_squeeze_shape..-sE 3 3QQ! c%jj 3 3 3 3 3 3rWz$dimensions outside range [0, ndim): c3PK|] }tj|d V!dSrrrs rUrbz)_compute_squeeze_shape../s7DDAT "58Q / / /DDDDDDrWzPcannot select an axis to squeeze out which has size not equal to one, got shape=z and dimensions=c3*K|] \}}|v |VdSrLr_)r`rrrs rUrbz)_compute_squeeze_shape..3s1CCTQ(1B1Bq1B1B1B1BCCrW)rrsrrdrirr)r[rrs` @rUrr)s __(]]c*oo%% ?:?? @ @@ 3 3 3 3( 3 3 3 3 3J HJHH I IIDDDDDDDDD0  / / /!+ / / 0 00 CCCCYu--CCC C CCrWcPtj|sJt||gSrL)r(r7r#)rrrs rU_squeeze_transpose_ruler5s,  ( (((( a $ $ %%rWc `|\}|\}tj||d\}}ttjd|}t |t r|jn|}tj|ttj ||j |}t|||fS)Nrrpr$) r)move_stacked_axisrrMr`rr.rjrnrrmr[r)rorprrr out_stack_dimbdim_outs rU_squeeze_batch_ruler9s (' %$,WdA>>-'4RVAz**++*'1$ 'C'CM$##-  #X3D'-HH*UUWW( Z 0 0 0( ::rWrcH~tj|||jdgSr)r*rr)rrrs rU_squeeze_lowerrJs# ,sGS]1%5 6 6 77rW core.Shapect|dkr-tdtjdtjSd|D}t |dS)z?Converts a shape that may contain Poly values into a JAX value.rrc g|]<}tttj|tjd=S)r)r#rrrrMint64rs rUrz"shape_as_value..UsQ    &t'>q'A'A28LL   rWr)rsrrMrrr)r[r s rUshape_as_valuerQsdZZ1__ bhq"(++ , ,,     $ TQ ' ' ''rWc td|Ds$d}t||tjt j|}tj|}tjj s6||ks0d|d|dt j|d|d }t||vt|ttt j |kr7d}t||t j|t|S)Nc3"K|] }|dkV dSr^r_rs rUrbz&_reshape_shape_rule..]s& ' 'Q!V ' ' ' ' ' 'rWz/reshape new_sizes must all be positive, got {}.z4reshape total size must be unchanged, got new_sizes z (of total size z ) for shape z).z_reshape dimensions must be a permutation of operand dimensions, got dimensions {} for shape {}.)rdrerr4r5rMr[rrirjrr rr)rrrrg operand_sizenew_sizes rU_reshape_shape_ruler\sD ' 'Y ' ' ' ' '+ ;C CJJy)) * **28G,,--, Yy ! !(   % ( " " .) . .% . .358G3D3D . .) . . .C C.. :#eBGG$4$4556666/c cjjRXg->->?? @ @@ y  rWc|s*t|j||\}}|g|fSt||}d|D}t jt ||jj|jj}|gtj fS)NrcVg|]&}t|tjur|jn|'Sr_rrs rUrz+_reshape_typecheck_rule..xrrW) rrrjrrrrrSrr)rkrrrrrrrs rU_reshape_typecheck_rulerps  '!// j0BBHg :w !I66ILL)LLLI y!1!17<3E!(!799H :t &&rWc|jSrLr)rrrs rU_reshape_dtype_ruler~rrWc tj|sJ|t||jjgSt t|t j|jj|t j|gSrL) r(r7rrjr[r:rMrrW)rrrrs rU_reshape_transpose_rulersx  ( (((( Aw|) * * ++ ga);Z!H!HIIj,, . . //rWc|\}|\}tj||d}|%dttjd|z}t ||jdd|z|dfS)Nrrrp)r)rrrMr`rr[)rorprrrrs rU_reshape_batch_rulerso (' %$  gtQ / /'bfQ 33444J '-+i7 D Da GGrWc|j\}|'tj|tj|}|r$|t ||}tj|||gS)Nr)rr9r:r*rrrr)rrrrrrs rU_reshape_lowerrskm)( a-j99::AM%5i%K%KLLH ,sAx ( ( ))rWct||}|s|t|f|Stjt |||j|j}t|t||g|Ri|S)Nr) rrrrrrrSrr)rrrrr ravs rU_reshape_staging_rulers~ ) ; ; ;& D  * *9qdF C CC ))S9917AKPP"  2q I3 I I I& I IIrWrc\tdd|tt|t|kr$d}t|||rBt ||jks*d}t|||j|jS)Nr'rz&rev dimensions must be unique, got {}.zYrev dimensions must all be less than operand ndim, got dimensions {} for operand ndim {}.)rrsrrerrrr[)rrrgs rU_rev_shape_rulers5, 333ZS__,, 2C CJJz** + ++:Z((7<77 %C CJJz7<88 9 99 rWcT|\}|\fd|D}t||fS)Nc*g|]}|kr|dzn|Sr~r_)r`rrs rUrz#_rev_batch_rule..s)BBB!Q$YYAEEABBBrWr')rorprrnew_dimensionsrs @rU_rev_batch_rulers? (' %$BBBBzBBB. Wn % %t ++rWr'c$t||gSrLr)rrkrs rUrrss1j/A/A.BrWcRtj|tj|gSrL)r9reverser*r)rrrs rU _rev_lowerrs" +a-j99 : : ;;rWct|tttjfs1d}t |t|tt|ttj kr*d}t ||j tfd|DS)Nz;transpose permutation must be a tuple/list/ndarray, got {}.zitranspose permutation isn't a permutation of operand dimensions, got permutation {} for operand shape {}.c32K|]}j|VdSrLr)r`old_idxrs rUrbz(_transpose_shape_rule..s*AA'w}W%AAAAAArW) rrrrMrrerrrr rr[)rr3rgs` rU_transpose_shape_rulers K%rz!: ; ;3 GC CJJtK0011 2 22 6+  5w|)<)<#=#=== 6C CJJ{GM:: ; ;; AAAA[AAA A AArWc2|\}|\}t|tr|jn|ftfd|Dz}t|tr)t j|d|}nd}t|||fS)Nc32K|]}|kr|n|dzVdSrr_)r`r stack_dims rUrbz(_transpose_batch_rule..s3OOa1y==aaacOOOOOOrWr)rr.rjrr)transpose_ragged_axesrr:)rorpr3rrpermres_bdimrs @rU_transpose_batch_rulers (' %$#-dJ#?#?IdT) OOOO;OOOOO O$j!!-d.D.DQ.G.GNNHHH 7D ! !8 ++rWc\|j\tjjtjrWjjjj}fdtt|D}g||}tj |tj |gS)Nc$g|] }j|z Sr_rN)r`rrs rUrz$_transpose_lower..s FFF1X]Q&FFFrW)rrrrSrrphysical_element_avalr[r rsr9r:r*r)rrr3 elt_shape trailing_dimsrs @rU_transpose_lowerrsm)( x~v771%;;FFFFc)nn0E0EFFFM0K0-0K -4/ << = = >>rWr:cHt|tj|gSrL)r:rMrW)rrkr3s rUrrs1bj6M6M)N)N(OrWctdkrtdtfdddDrAd}t|ddD|jrK|jdjkr5d}t||jdjdjS) Nrz"select must have at least one casec3DK|]}|jdjkVdSr^r)r`caser/s rUrbz%_select_shape_rule..s0<<$uQx~ %<<<<<.s )F)F)F1#ag,,)F)F)FrWzfselect `which` must be scalar or have the same shape as cases, got `which` shape {} but case shape {}.)rsrerirrr[)r.r/rgs ` rU_select_shape_rulersZZ1__ 8 9 99<<<<%)<<<<<J =C CJJtyy)F)F)F)F)FGGHH I II [=U[E!HN22 5C CJJu{E!HN;; < << qrWctdg|Rtj|jtjs 2 cases.r) rrrrSrMr}r~rersr1s rU_select_dtype_rulersH%u%%%%  EK 2 2'  EK 4 4' &{&&& ' '' u{BH--J#e**q.. H I II qrWc4td|DS)Nc3$K|] }|jV dSrLrrbs rUrbz)_select_weak_type_rule..s$ ( (QQ[ ( ( ( ( ( (rW)rdr1s rU_select_weak_type_rulers ( (% ( ( ( ( ((rWctjrJttjurdgd|DzSt dt jtjtj kr_tj|drtnd}tj|drtnd}d||fSdgfdt|DzS)Nclg|]1}tj|rtj|jnd2SrLr^rbs rUrz*_select_transpose_rule..sI%%%.0-CA-F-FPW\!&)))D%%%rWrrpc g|]H\}}tj|r-ttt |ndISrL)r(r7r-r}r)r`rrrr.rs rUrz*_select_transpose_rule..sb8?4R #D ) ) 4&E6%++,,a 7 7 7/3rW) r(r7rrr8r*rrSrMr}r-r)rr.r/ct0ct1rs`` @rU_select_transpose_rulers2  #E * **** !WW  6%%#%%% %% aOOE |Ebhrx0000')'=eAh'G'G QF5% # # #Tc')'=eAh'G'G QF5!U # # #TcC VCLUCSCSrWc  |^|^ tdt||Dt fdDrtjtjdkrt gR fStjdksJtdj gt gR fStjdkrtdDrtfdddDrt gRdfStfdDrJdfdtddddD}t dg|RfStjrtj  ntd Dsfd tDtfd ddDsJdtjcxkrtjdkr:nn7tjdksJtdjdgtjtjdkr.tjddksJfd Dt gRdfS) Nc3:K|]\}}||j|VdSrLrr;s rUrbz%_select_batch_rule..r<rWc3$K|] }|kV dSrLr_)r`r which_bdims rUrbz%_select_batch_rule..s(33t 333333rWrrpc3K|]}|duV dSrLr_)r`rs rUrbz%_select_batch_rule..%s'"K"K4t#3"K"K"K"K"K"KrWc30K|]}d|kVdSr^r_)r`r case_bdimss rUrbz%_select_batch_rule..&s, < .(s> > >1RXeAh  28A;; . > > > > > >rWcBg|]\}}tj||Sr_)r)r)r`rcc_bdimrs rUrz&_select_batch_rule..*sBFFF"F&q&$77FFFrWc3FK|]}dtj|kVdSr_Nrrbs rUrbz%_select_batch_rule..0s/ . .1R28A;;  . . . . . .rWcBg|]\}}tj||Sr_r)r=)r`rcrrs rUrz&_select_batch_rule..1s< 4 4 4D #AtT 2 2 4 4 4rWc3xK|]4}tjdtj|kV5dSr^rrs rUrbz%_select_batch_rule..3s> B B1RXeAh  28A;; . B B B B B BrWc:g|]}t|jSr_)r r[)r`rcr.s rUrz&_select_batch_rule..:s% 6 6 61Yq%+ & & 6 6 6rW) rrrdrMr[r2rr r)r=) rorp unused_kwargs other_casesrrr/rr.rs @@@@@@rU_select_batch_rulers-%%&*z   Sz%B%B     $ 3333 33333; x"(58,,,, e $e $ $ $j 00WU^^q ueAhnzlCCe e $e $ $ $j 00 wu~~s"K"K "K"K"KKK < < < > > > > > > > >; ]dFFFF&)%)Z^&D&DFFFk eU1X 4 4 4 4d ::>@huoo 8 !%T : : : . . . . . . .4 4 4 4 4z22 4 4 4E B B B Babb B B B B BBBB++++"'%(+++++++ 75>>Q     UE!HNQC 8 8EWU^^bgeAh'''' 758   ! ! ! ! 6 6 6 6 6 6 6E % % ! ##rWc6|^}}|dd}t|g|R}td|Dr tj|dj}nAt t d|Dfd|D}t|g|R}||fS)Nrpc3LK|]}t|tjuV dSrLrrr8rs rUrbz_select_jvp..As/88QaGL 888888rWrc3PK|]!}t|tju|V"dSrLrrs rUrbz_select_jvp..Ds4LL!Qw|0K0KA0K0K0K0KLLrWcNg|]!}t|tjurn|"Sr_r)r`rzs rUrz_select_jvp..Es/PPPQ$q''W\11QQqPPPrW)r2rdrr8rjr=r)rrr. case_primals case_tangentsrZout_dotrs @rU _select_jvpr =s %,122,-&&&&#88-88888.l=+011GGtLL}LLLLLMMAPPPP-PPPMu-}---G grWc  |j}|j\ t fd|ddDsJt}t j }|gt |dz z}|d}||j}|j d|j |j ksJtt|j } tj|||| } tj||| g|R|g||gddS)Nc3$K|] }|kV dSrLr_)r` aval_casers rUrbz._select_hlo_lowering_opaque..Ls( A AyY( " A A A A A ArWrprrrr_)rrrd_select_hlo_loweringrrrsrrSr[rrr r*r r) rr.r/r select_lowerphysical_aval_outphysical_avals_cases aval_whichaval_which_bcast bcast_dims which_bcastrs @rU_select_hlo_lowering_opaquerIsF \(m)( A A A AHQRRL A A A A AAAA%,(22+,H 0AB{*&--J4D-EE   0 0 1Z5E E E E EE*/**++*% 5"EEE+   < %', % % 8#78"# % % %&' ((rWc jdj\}tj|jtjrt g|RgSjtjtjkrMt|dksJt|dkr|Stj |d|dgStjjtj rdnddfdd|gS)Nrrrprrrc ^t|dksJt|dkr|dSt|dz}tjtj||z }t j|||d|||z||dS)Nrrpr)rsr*rrr9r-) rr/midr(_selectrrrr. which_avals rUrz%_select_hlo_lowering.._selectqs u::>>>> 5zzQ 1Xo e**/C  E /Vc\:NN  . .D :dGGFE$3$K88gfslE#$$K88 : ::rW) rrrrrSrrrMr}rsr9r-r)rr.r/rrrrrs`` @@@@rUrr_s$|A*m)( x~v77= 'U ;U ; ; ; <<"(++++ u::???? 5zzQu JueAha 1 1 22 z')9::LLL " : : : : : : : : : : '!U   rWr2ct|t|dzg\}}td|Drd|D}td|fd|DS)Nrc3,K|]}|jdkVdSrrr`rs rUrbz%_reduce_shape_rule..s(33Sb333333rWcg|] }|j Sr_rr`rus rUrz&_reduce_shape_rule..s7771qw777rWz'reduce found non-scalar initial value: c^g|])}ttj|j*Sr_rrMrr[)r`rrs rUrz&_reduce_shape_rule..s/ I I IR% "(J// 0 0 I I IrW)rErsrir)rHrKrrt operand_avalsinit_val_avalsinit_val_shapess ` rU_reduce_shape_ruler(s",USZZ1_4E"F"F-33N33333R77777O PPP Q QQ I I I I= I I IIrWct|t|dzg\}}d|D}d|D}||krtd|d||S)Nrc@g|]}tj|jSr_rrrSrLs rUrz&_reduce_dtype_rule..s%PPPBF-bh77PPPrWc@g|]}tj|jSr_r+)r`inits rUrz&_reduce_dtype_rule..s%VVVtV.tz::VVVrWzTreduce operand dtypes should match corresponding initial value dtypes, got operands=z and initial_values=)rErsre)rHrKrrtr%r&operand_dtypesinit_val_dtypess rU_reduce_dtype_ruler0s",USZZ1_4E"F"F-PP-PPP.VV~VVV/&&  L% L L;I L L M MM rWc~t|t|dzg\}}dt||DS)Nrc0g|]\}}|jo|jSr_r)r`rinit_vals rUrz*_reduce_weak_type_rule..s< G G Gb( , -8- G G GrW)rErsrB)rHrKrrtr%r&s rU_reduce_weak_type_ruler4sT",USZZ1_4E"F"F- G G&}nEE G G GGrWc t|dz}t||g\}}t||g\}} td| Drztdt ||D fdt ||D}d|D} dg|z} t j||z|t| |d| fSt)Nrc32K|]}|tjuVdSrL)r) not_mapped)r`init_value_bdims rUrbz%_reduce_batch_rule..s> 2 2  H/ / 2 2 2 2 2 2rWc3:K|]\}}||j|VdSrLr)r`raxs rUrbz%_reduce_batch_rule..s9##2> !>>>##rWcBg|]\}}tj||Sr_r)r`rrrs rUrz&_reduce_batch_rule..s<???C&sD$77???rWcg|]}|dzSr~r_rs rUrz&_reduce_batch_rule..s000a!e000rWr)rHrrK) rsrErdrrrPrrr) rorprHrKr num_operandsrrG operand_bdimsinit_value_bdimsrnew_operand_bdimsrs @rU_reduce_batch_rulerAs;\""a',$\L>BB(K$.zL>$J$J!-! 2 2 0 2 2 222  ##\:)F)F### # #D????!$X}!=!=???H00Z000Nl* =8k1%0$).$9$9$ & & &(9 99 rWc tj|djttjt |}tjtjt| |t z |ft z t fd|D}t fd|D}tt dzD]}tj dd fd }tj |||S)Nrrc3:K|]}t|VdSrLr)r`rr8r3s rUrbz_reduce_jvp..s/FF'!Y 44FFFFFFrWc3:K|]}t|VdSrLrD)r`rr8r3s rUrbz_reduce_jvp..s/HH!71i55HHHHHHrWrp)r;c|djdkr|dj}|dzdz|z }fd|D}fd|D}|kr?dgt|djzd<fdt|D} ||z}|djdk|djdkr fd DStfd |DS) z9Reduce by repeatedly splitting the array and multiplying.rrprc<g|]}tj|dSrr/ slice_in_dimr`rn1s rUrz5_reduce_jvp.._reduce_tree..s( 8 8 8W !!Q + + 8 8 8rWc<g|]}tj|dSrLrHrJs rUrz5_reduce_jvp.._reduce_tree..s( ; ; ;1W !!R . . ; ; ;rWr)rrprc8g|]\}}t||Sr_)r")r`rrpaddingss rUrz5_reduce_jvp.._reduce_tree..s)GGGAs2q(##GGGrWc<g|]}t|Sr_)r)r`r input_shapenon_axess rUrz5_reduce_jvp.._reduce_tree..s( B B Bd;x(!,, B B BrWc3:K|]}t|fVdSrL)r)r`rr;s rUrbz4_reduce_jvp.._reduce_tree..s/11TG$$111111rW)r[rsrr) r;ryrpn2xs1xs2rKrNrGrPrQreducers ` @@rU _reduce_treez!_reduce_jvp.._reduce_treesC Q%+d a   Q%+d a Ea.s/;;a $;;;;;;rWzeGradient of general lax.reduce with non-zero tangents for initial values to reduction not implemented)rErsrirr jaxpr_as_funr[) rrrHrKr primal_xsrG tangent_xs tangent_initrVs rU_reduce_jvp_rulerbs%gG 0A/BCC)['3x==A3E2FGG*l ;;l;;;;;5 4 5 55  e $ $' Wk9j* M MMrWr[c>td|jDsJ|jtj|t |dzg\}}|jt |dzd}t jd|jD||tj |}d|D} |j dj j | | z} tj| 5tj} |jrt%dtj|j|j| tj|jg| jRd|ji\} } t jtj| dddn #1swxYwY|jS)Nc3JK|]}t|tjVdSrLrrr#rs rUrbz _reduce_lower../ C CZ4+ , , C C C C C CrWrc6g|]}tj|Sr_r*rrs rUrz!_reduce_lower..#JJJDT)$//JJJrWc6g|]}tj|Sr_rhrs rUrz!_reduce_lower..s# F F FTd"4(( F F FrWrz Cannot lower effectful `reduce`.dim_var_values)rdrrrErsr9ReduceOprr*rregionsblocksrr7InsertionPointrnew_name_stackrr jaxpr_subcompmodule_contextrKTokenSetrl argumentsrkreturn_flatten_ir_valuesresults)rrHrKrrrrGinit_value_avalsrir_typesrV name_stack out_nodesrks rU _reduce_lowerr|s C Ccl C C C C CQQS\QQQ/&3v;;!3C2DEE(K\#f++"2"3"34 |JJCMJJJk4+? +K+KMM" F F5E F F F( 'BJqM '(X*= ?' !! 3 3!022J }D  B C CC%c&8%+&0$-//&+lI(/'8III695G IILIq K&y11222 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 s+BF  FFctj|jtjs5t d|t|jtj|jS)NzD{} does not accept dtype {}. Accepted dtypes are subtypes of number.) rrrSrMnumberrerr1r)rrrr>s rU_reduce_number_dtype_rulersb  7=") 4 4O !!'ogm.L.L!M!M O OO  "7= 1 11rWc$t||Sr)_reduce_op_shape_rulers rU_reduce_sum_shape_rulers wT 2 2 22rWc  tj|sJ|jj}t t jt jt||}t|||}|j|ksJ|gSrL) r(r7rjr[rrMrrXrsr )rrr?rPr r_s rU_reduce_sum_transpose_ruler s{  ( (((( "+ry3{3C3C)D)DdKKLL I{4H I I&  $ $ $ $ /rWc~|\}dt|jD}t|||j|}|||gS)NcZg|](\}}t|tj||jf)Sr_)rrrrH)r`rrzs rUrz$_reducer_padding..sC7771q""4557!QU777rW)rr[rrS) traceableidentrrrr?rjroperand_s rU_reducer_paddingrse %$77 $*(=(=777+ #GUU4:->-> L L( )Hd # # $$rWc|sStjtfd|D}tt t j|t|S)NcJg|]\}}tj||k Sr_)rr[)r`rrzrSrs rUrz*_replace_masked_values..s1 K K Ktq! E17A . . 2 K K KrW)r_scalar_type_to_dtyperJr-rr7rr*)rrHrmasksrSs` @rUrrsb Qh  &s + +% K K K K K{ K K K%  u--q)As2C2C D DDrW reduce_sum)rPc`~tttkrtdtfdDstdddt t fdt jDS)Nz(duplicate value in 'axes' of reduction: c3BK|]}d|cxko jkncVdSr^rN)r`rurs rUrbz(_reduce_op_shape_rule..-sA 1 1qQ! " " " "gl " " " " 1 1 1 1 1 1rWzreduction axes z$ contains out-of-bounds indices for rcc3*K|] \}}|v |VdSrLr_r`rrzr?s rUrbz(_reduce_op_shape_rule..0s+GGTQ$qGGrW)rsrrrdr rrr[)rr?rPs`` rUrr)sYY#c$ii..  FFF G GG 1 1 1 1D 1 1 1 1 1] [t[[QX[[[ \ \\ 4$ GGGGYw}55GGG G GGrWc~d}t|t|ddg|||\}}|d|dfS)Nc$t||gSrLrr's rUrz'_reduce_prod_jvp_rule..3s#a))rWrrp)r[r)rrr?rV primals_out tangents_outs rU_reduce_prod_jvp_ruler2sO $ $')'F71:q4I4I3J*18TCC+| Qa ((rW reduce_prodcPttj|j|SrLr$rs rU_reduce_chooser_shape_rulerAs ry-- . ..rWc fdt|jD}tt|t |||j}t |}tt t|||S)Nc&g|] \}}|vrdn|Sr~r_rs rUrz,_reduce_chooser_jvp_rule..Hs) F F FTQT 11q F F FrW) rr[r_eq_meetrrSrrirf)rrrr?r[location_indicatorscountss ` rU_reduce_chooser_jvp_rulerDs G F F FYw}-E-E F F F%,wU++,,ag77 *D 1 1& [Q 344d ; ;V D DDrW reduce_max reduce_minc$|\}d|cxkrt|jksntd|d|j|j|dkrtd|jd|tt j|j|S)Nrz Invalid axis rxrpzEargmin and argmax require non-empty reduced dimension. operand.shape=z axis=)rsr[rrrMr)rr?r<r;s rU_argminmax_shape_ruler_s %$ t ( ( ( (c'-(( ( ( ( ( MTMMgmMM N NN ]41 >&-m>>6:>> ? ?? ry-- . ..rWctj|tjs/t dt ||S)Nz/index_dtype must be an integer type, but got {})rrrMr~rerr1)rr?r<s rU_argminmax_dtype_rulerhsI  ; 3 3; EVOK8899 ; ;; rWc eZdZdZdZdZdS)_ArgMinMaxReducerc||_dSrL)_value_comparator)rvalue_comparators rU__init__z_ArgMinMaxReducer.__init__ps-DrWc"d|jjdS)Nz_ArgMinMaxReducer(rk)rrrs rUrz_ArgMinMaxReducer.__repr__ss C 6 ? B B BBrWc 2|\}}|\}}t|||t||}t|tt ||t ||}t |||t |||fSrL)rSrrrPr}rr-) r op_val_index acc_val_indexop_valop_indexacc_val acc_index pick_op_val pick_op_indexs rU__call__z_ArgMinMaxReducer.__call__ys#FH&GYT33FGDD//11K{*2fg+>+>+-h +B+B D DEEM ; 0 0 =(I 6 6 88rWN)rrrrrrr_rWrUrrnsD...CCC 8 8 8 8 8rWrc|\}t|tj||}t||g||jtjd|gt ||}|dSrq)rrMr[r[rSrr)r get_identityrr<r?r;r3rs rU_compute_argminmaxrsv %$ ["(7*;*;T B B'! W]++RXa-E-EF !122  # Q-rWrBrFc|jtjkr&B&BCCD(..00"$T%5b%%@%@AA+:a='..{KHH. ((66K.234555666666666666666 sC::C>C>ctj|}tj|}|dkrtd||dkrtd||jS)Nrpz6reduce_precision: exponent_bits must be positive; got rz:reduce_precision: mantissa_bits must be non-negative; got )r7r8rr[rs rU_reduce_precision_shape_rulersm.//-.//-Q ]m]] ^ ^^Q aR_aa b bb rWrrc (tj|fi|gSrL)rr)rrys rUrrs6H6Ma6Z6ZSY6Z6Z5[rWc|j\}tj|tj|tj|gSrL)rr9rr*i32_attr)rrrrrs rU_reduce_precision_lowerrs@m)( w m(D(D#}];; = = >>rW) @ctdDtfdddDr1ddD}td|S)Nc34K|]}t|VdSrL)r%r s rUrbz&_sort_abstract_eval..s*44s##444444rWc3DK|]}|jdjkVdSr^r)r`rrs rUrbz&_sort_abstract_eval..s088d1gm #888888rWrp c3>K|]}t|jVdSrLrPr"s rUrbz&_sort_abstract_eval..s*11qc!'ll111111rWz/Arguments to sort must have equal shapes, got: )rrirre)rryrXs` rU_sort_abstract_evalrs 44t444 4 4$8888tABBx88888P XX11D111 1 1F NfNN O OO +rWc<tt|t|t||}t jd5tt |t|tj |}dddn #1swxYwY|Sr}) r-r}rGr=rT debug_nans_isnanr*rMnan)rr_s rU_canonicalize_float_for_sortrs "Qa//6!99a 0 0& ~eBB F1IIy88& A AFBBBBBBBBBBBBBBB -s7BBB)rc Rt|d|i\}}d}t|ddd|dddD]r\}}|Ptt||t t |||nt||}s|SNrr)_operands_to_keysrrSlt_to_prrPeq_to_prrx_keysy_keysrxkyks rU_sort_lt_comparatorr$hBBB.&& !F44R4L&2,//$$fb"STS`GLLR((+gll2r6J6JA*N*N O O Oll2r""A (rWc Rt|d|i\}}d}t|ddd|dddD]r\}}|Ptt||t t |||nt||}s|Sr)rrrSrrrPrle_to_prs rU_sort_le_comparatorr(rrWc t|dkrt|dzdks J|t|dz|ks J||fgg}}t|dd|zd|dd|zdD]{\}}|j|jksJ|j|jftj|jt jr|tt|tt|g|tt|tt|gtj|jt j rF| t|| t|Q| || |}||fS)Nrrrp) rsrrSrrrMrextendrr+r/r r)rrrrrr$s rUrr0s X!  H  1Q 6 6 6 6 6 6 X! x ' ' '(H)= ' ' 'r&&(=AhJq=)8AajN+CDD  da 7ag   1    ""455 mm1$q''::.JsK**)^^gbkkq******rWc3bK|])}t|tjur|n|V*dSrLr)r`rras rUrbz_sort_jvp..Ls=RRADGGw|33qq3RRRRRRrWr)r[rrMrNrrRrrrrrrr rs) rrrrrr[dimrrSrrars ` ` @@rU _sort_jvprBs3 !* % %U##66ic4rx11555BHH28E LL!%445555 K'U9%5$77I"+h @ @ @' ******SZZ((*** * *#RRRRRRRRR, wss|  l **rWctdt||D\}}g}t||D]\}} | Vtjtj|j|} |t||j| ]|tj || ||||kz} |ft|z} tj || ||d| fS)Nc3(K|] \}}|||fVdSrLr_)r`rurs rUrbz#_sort_batch_rule..Ps7!G!Gq! QF !G!GrWr)rrrMrrXrrr r[r)rrsrr) rorprrr prototype_argnew_bdimnew_argsrrr  new_dimensionrs rU_sort_batch_rulerOs !G!G<44!G!G!GGG- (|Z00>>ic4 | Yry!344h ? ?doo&sM,?FFGGGGooh'T8<<====x945- +H %% +x=IX` a a a  rWrc td|jDsJ|jtjd|jDt j|t j|tj |}d|jD}tt j |}|j jjt!jt%||}tj|5t jt+t,d} |dt!jt%||t1jdt4jg} | | g|jRd |i} tjt j| dddn #1swxYwY|jS) Nc3JK|]}t|tjVdSrLrers rUrbz_sort_lower..hrfrWc6g|]}tj|Sr_rhrs rUrz_sort_lower..irirW)rrc:g|]}|dS)r_r)rrs rUrz_sort_lower..ms&AAAD$++B+''AAArWFrr_) primitiverrr)rdrr9SortOprr*rvrsr7BoolAttrrrCr comparatorrnrrflattenrrorrrr`rr#rMr}rtrurw) rrrrrr scalar_avals scalar_typesrlower_comparatorsub_ctxrZs rU _sort_lowerrgs C Ccl C C C C CQQS\QQQ JJCMJJJ*844"mI66 kooi88 : : :$BACLAAA,$. ==,,t%, |C l33446* $$--~g.A&B&B7<>>>kkD#'<L,0O0O#P#P%)%5b"(%C%C$DFFG  7 MZ%9 M M MH M MCK&s++,,,--------------- s B6G  GGcTtj|jtjrt d|dkrt d|t |jdkr'td |jt|j}|d|kr%d}t | ||||d<| ||j|j | |tjtj fS) Nz,top_k is not compatible with complex inputs.rrz.top_k operand must have >= 1 dimension, got {}rzDk argument to top_k must be no larger than minor dimension; {} vs {}r[rSr)r[rS)rrrSrMrrrsr[rerrrrr)rrr[rgs rU_top_k_abstract_evalrs w}b&899E C D DDUU HQHH I II1 DVGM** , ,, w}  % 2Y]] PC SZZ5)) * **%) ..uGM#*#4  6 6 ..uBHRX,>,>. ? ? AArWc 0|\}|\}t||}t|tjur'tj|d}n|\}}|j} t | } | dz} g} t| dz D]D} t|j | | }t|| | f}| |E| t|| t| | } d| z}tjdt!t| t!t| }tj|| ||}||tj|dffS)Nrr~rprr_) offset_dimscollapsed_slice_dimsstart_index_map)rrrr8rr[rsr rrSr rrrr/GatherDimensionNumbersrgather)rrrrrrrrkk_idxs idx_shapergather_index_shapegather_indicesr_iota slice_sizesdnumss rU _top_k_jvprs (' ('gq!!+ ']]gl"",))+a.99KKIAv I y>>D"T)N 46]]##6<1..eu&81$??eE""""'&*<==>>> 4@@@N+K  * t--E$KK(( * * *E..%MMK {GL$;$;KN$K$KL LLrWcP|\}|\}||jdz kr|tj|j}||||dz c||dz <||<tt |||\}}t ||t ||f||ffSt||||ffS)Nrpr)rrMrXrr:)rorprrrrtop_k_vtop_k_is rU_top_k_batch_rulers (' %$ W\!^ 9W\ " "D#Dz4Q<DaL$t*Yw55;;;GW gt $ $ gt $ $ &(,d| 44 A   t ,,rWrcNtj|r,tj|t j|jSt j||f\}|j\}}t j dt j |t j |g||gjS)Nzstablehlo.dynamic_top_k) result_typesr) rrr8TopKOpr*rsrweval_dynamic_shape_as_valsr custom_callr)rrrk_valueout_values_avalout_indices_avals rU _top_k_lowerr!s !: ;w a 0 0 1 1 99  ,S1$ 7 7(''*}$/# (99 ,--/!  # # #$+ +rWcf|\}t|tj|fSrL)r rr8r)rrrs rU_stop_gradient_jvp_ruler#s,"! q  7<22155 55rWc4|\}|\}t||fSrL)r )rorprrs rU_stop_gradient_batch_ruler%s#"! $# q  3 rWc4tS)zCreates an XLA token value with no preconditions for sequencing effects. Experimental. The argument is ignored. It exists for backward compatibility. )create_token_prrks rU create_tokenr)s     rWr)ctSrLr&r(s rUrrsNrWc<|j\}tjgSrL)rr9r)rrrs rU_create_token_loweringr.sm)(    rWctj|S)zVMerges one or more XLA token values. Experimental. Wraps the XLA AfterAll operator.) after_all_prrs rU after_allr2s  8 $$rWc`td|DrtdtS)Nc3(K|] }|tuVdSrLr+rs rUrbz+_after_all_abstract_eval..s'33Q. 333333rWz%Arguments to after_all must be tokens)rirer&r1s rU_after_all_abstract_evalr5s633(33333= ; < << rWr2c>|j\}tj|gSrL)rr9r2r-s rU_after_all_loweringr7sm)( - ! ! ""rWceZdZdS)InOutFeedEffectN)rrrr_rWrUr9r9s$rWr9ctj|\}}|D]9}t|ts"t d|:|/t |tkrtd||dz}t |t||}| |dd|dfS)zConsumes an infeed value of `shape` from the host. Experimental. `token` is used to sequence infeed and outfeed effects. `partitions` may be specified inside a `sharded_jit` function. zGshape argument to infeed must be a pytree of ShapedArray values, got {}Nz7'partitions' argument to infeed should be a tuple, got rL)rX partitionsr) rrLrr#rerrrrinfeed_pr unflatten)tokenr[r; flat_shapestreedef xs_and_tokens rUinfeedrBs #/66+wBBe e[ ) )B 3396%== B BBB J5  +(++ , ,,g%JuU;-?-?*466,   L"- . . R0@ AArWcZ|turtdg|tRthfS)Nz(First argument to infeed must be a token)r&re infeed_effect)r>rXr;s rU_infeed_abstract_evalrEs6 .  > ? ?? "6 "> " "]O 33rWrBc0ttj|jdd}tj|}t jd|D}tj |tj gz|t j d|}|'tj |tj||jd}|jdd}tj|||gzS)Nrc g|]O}tjdtt |jdz ddDPS)c6g|]}tj|Sr_)r*rs)r`rs rUrz/_infeed_lowering...0s2 8 8 8 =   8 8 8rWrpr)r7rrr rsr[rs rUrz$_infeed_lowering...sq  l 8 8#dj//A-r266 8 8 899rW) infeed_configlayout)rCr*rrflatten_ir_typesr7rrr9InfeedOp TokenType StringAttr set_shardingr-sharding_to_protorwunflatten_ir_values_like_types) rr>rXr; output_typesflat_output_typeslayoutsrBoutss rU_infeed_loweringrW*s$. crc0BCC,+L99 L     ' <3=,,..// M%%b))     & fc3J??@@@ . %  $ ,T< @ @ D rWc|*t|tkrtd|tj|\}}t j|g|Rd|iS)zOutfeeds value `xs` to the host. Experimental. `token` is used to sequence infeed and outfeed effects. `partitions` may be specified inside a `sharded_jit` or `pjit` function. Nz8'partitions' argument to outfeed should be a tuple, got r;)rrrrrL outfeed_pr)r>ryr;flat_xsrks rUoutfeedr[Dsu  J5  +(++ , ,,%b))*'1  ? ? ? ?J ? ??rWcP|turtdtthfS)Nz)First argument to outfeed must be a token)r&reoutfeed_effect)r>r;rys rU_outfeed_abstract_evalr^Rs* .  ? @ @@ .) ))rWr[ctjtj||tjd}|'tj|tj ||j S)NrI)outfeed_config) r9 OutfeedOpr*rvr7rOrrPr-rQrw)rr>r;ryr[s rU_outfeed_loweringrb]sj M R   ]&&r** , , ,'gs4Z@@AAA rWcVt||t|S)aStateful PRNG generator. Experimental and its use is discouraged. Returns uniformly distributed random numbers in the range [a, b). If b <= a, then the result is undefined, and different implementations may return different results. You should use jax.random for most purposes; this function exists only for niche use cases with special performance requirements. This API may be removed at any time. r) rng_uniform_prrrurr[s rU rng_uniformrfis%   Aqe  5 55rWcT|j|jkr-td|j|j|jdks |jdkr-td|j|j|||j|jo|jS)NzCArguments to rng_uniform must have identical dtypes, got {} and {}.r_z?Arguments to rng_uniform must be scalars; got shapes {} and {}.r)rSrrr[rrres rU_rng_uniform_abstract_evalrhwsW qw(( * **W]]agmm G vagqw ! !! QW[8Q[  ; ;;rWrfc|j\}tjtj|jtj}tj|||tj dgS)NUNIFORM) rr*rrMrr[rr9rngRngDistributionAttrr)rrurr[rs rU_rng_uniform_loweringrmsUm)(  28HNBH== > >% '!Qs6::9EE F F GGrWc2~~|jt|fSrL)r[rkeyr[rS algorithms rU_rng_bit_generator_shape_rulerrs Y )U5\\ ""rWc~~|j|fSrLrros rU_rng_bit_generator_dtype_rulerts Y )U rWc~~~|jdfSr}rros rU!_rng_bit_generator_weak_type_rulervs UI - rWc|jSrLrrqs rUrrsINrWrqRandomAlgorithmc |tjkrtjdS|tjkrtjdS|tjkrtjdSJ)N THREE_FRYPHILOXr)ry RNG_THREE_FRYr9RngAlgorithmAttrr RNG_PHILOX RNG_DEFAULTrxs rU_rng_algorithmrsv////   # #K 0 00O...   # #H - --O///   # #I . ..LrWc tj|j}|j|j}}tjd}tjd} |dgkr||ks|dgkr|| ks J||ftj|}tj |} |tjdtjdtjdtjdfvr| } |} n|} tj } ||krgtj tjdg| tjtjddg||}t!|} |j\}}t%d |jDrtjtj||j}tjd |jtjt/j|| g||gt3|  j\}}nBtj|jtj|| | |j\}}||krgtjtjdg|tj tjddg||}| | krOtjtjtj|jj| |}||gS) Nrrruint8uint16ruint64c3JK|]}tj|j VdSrL)ris_constant_shaper[r"s rUrbz._rng_bit_generator_lowering..s2DDT #AG , , ,DDDDDDrWz#stablehlo.dynamic_rng_bit_generator) rng_algorithm)rrextra_attributes)r7RankedTensorTyperr[ element_type IntegerType get_unsignedrMrSr*dtype_to_ir_typerr9rrrrrrireval_dynamic_shaperrrr#rrwRngBitGeneratorOprc)rrpr[rSrqkey_type key_shape key_etypeu32_typeu64_typeetype rbg_etype rbg_dtypealgorithm_attrrk out_vals_aval output_shapeout_keyout_valss rU_rng_bit_generator_loweringrs$   * *(!)>Y)^ ( ( , ,( ^ ( ( , ,(    X 5 5    X 5 5 5)Y9O 5 5 5 (5//%   & &% rx  "(8"4"4bhx6H6Hx!!###IIII I(  X.. B'++QFH==sCC E EC"),,.]!]DDcmDDDDD %$ c=#67799L(-h*4+;E9+M+MNNP|$N;;; === >E GXX-  y11%GX(k X..    # #QFH 5 5w @ @AAG%{b1(-@@FNNH 8 rWrng_bit_generatorarrc6t|SrLcopy_pr)rs rU _array_copyrs S  rWrr:cd}t|jjD]/\}}t|tjtjfr|}n0|SrL)r sharding_specrrr, UnstackedChunked)r sharded_dimrs rU_which_dim_shardedrsY+011  da!dndl344 k e  rWc|SrLr_rs rU _identity_fnrsAXrWctjtddd||\}}}tjt||||ddd|| }t j|jg|jRd||j|j |j |j |j |jj |j|jd }t!j||S)Nr_) backend axis_name axis_sizeglobal_axis_sizedevicesin_axesout_axes_thunkrdonated_invarsis_explicit_global_axis_size)r_shared_code_pmapr _prepare_pmapr, xla_pmap_implflat_fun flat_argslocal_axis_sizerr in_axes_flatrrrrrrQrY)rrryrstatic_broadcasted_tuple donate_tuplerout_flats rU_copy_impl_pmap_shardingrs696K$B [7:7:3) %| K.FD$dF44! j;(, !A4Fi%AJ,?%#$#A (  !!**,, 9 99rWc|\}t|tjrUt|jtr;t |j}|t j|g|Ri|St|g|Ri|St j|g|Ri|SrL) rrTr;rr:rrapply_primitiver)rrryrurs rU _copy_implrs "!39B*QZ"F"FB$QZ00K  %d > ? ??rWc|stdd|tfdtDsXd}t}dtD}t ||d|d|cxkrt|ksntd|d ||s)td |Dst|Stj t||d S) Nrr[c3BK|]}tj|VdSrLr)r`rrSs rUrbz&_iota_abstract_eval..Ds0 7 7QV ua ( ( 7 7 7 7 7 7rWzBiota does not accept dtype {}. Accepted dtypes are subtypes of {}.c3$K|] }|jV dSrLrrs rUrbz&_iota_abstract_eval..Gs$33!*333333rWrrz?iota dimension must be between 0 and len(shape), got dimension=z for shape=c3K|]P}t|tjo1ttj|jtjuVQdSrLr2rs rUrbz&_iota_abstract_eval..Mr5rWF) rri_numr1rerrrsrr#rrr)rSr[rrrgrrs` rU_iota_abstract_evalr@sW -VWe,,, 7 7 7 7$ 7 7 7 7 7I NCu%%H33d333 CJJx3E)F)FGG H HH i $ $ $ $#e** $ $ $ $ 2!22).22 3 33 % HHAFHHH H H% ue $ $$ +E9==ue L LLrWrct|||}|s|td|Stjt |||d}t |t|g|Ri|S)Nrr_F)rrrrrrr)rrSr[rrrrjs rU_iota_staging_rulerWsw e5I > > >& ?  * *62v > >> +E9==ue L L$  Ky K K KF K KKrWc|s%t|||\}}|g|fSt||}d|D}tjt ||d}|gtjfS)NrcVg|]&}t|tjur|jn|'Sr_rrs rUrz(_iota_typecheck_rule..frrWF)rrrrrrr)rkrSr[rrrrrs rU_iota_typecheck_ruler_s ',,5I-77Hg :w   22ILL)LLLI y!1!15%@@H :t &&rWc~|j\}|r$|t||}tj|||gS)Nrr)rrrr*r)rrSr[rrrs rU _iota_lowerrksO m)(I%5eY%G%GHHH )CY 7 7 7 88rWc||c\}\}|dksJ|jj}dt|D\}t|ft ||fz}t |||dz} | t j||dz|fffS)Nrc3$K|] \}}||V dSrLr_)r`rrs rUrbz&_iota_batching_rule..ws&BB3ck!kkkkBBrWrp)rSrrrsrrr)r.) in_valsin_dimsrSr[rsegment_lengthsr:r ragged_axisrs rU_iota_batching_rulerss%w?er q   %%BB)E"2"2BBB,+    !$4UUH$E$E E% % ! 4 4$ x"2Q(H'JKK KKrWci}t|jddkr|jd|d<tj||||S)Nr[rprr)rsrrrr`)rrrrs rU _iota_pp_ruler}sT.G !!"%*["9N; ckkk88'8 L LLrWc|\}g}g}|jD]} t| tjur|| j8t| t ur|| dt| tj sJ|d|| tj |t|||dgS)N)r[rSr) r[rrrrrrJrrrrrr) rrrSr[rrrr8rrzs rU_iota_padding_rulers)()- >a Aww"$$$qw aCq 4; ' ''''t1 +}E),<,<!Y 8 8 8 99rWcLtjtj|ds$d}t||dt |t |z zt |z}t ttj ||S)zCUtility function for computing the shape resulting from a dilation.rz'All dilations must be positive, got {}.r~) rMrdgreaterrerrsrrkrr{)r[dilationrgs rU _dilate_shapers  8Q'' ( (* 3C CJJx(( ) )) SZZ#h--/ 05?? B( s4?E844 5 55rWcRtjtj|| SrL)rM floor_dividerrs rU _ceil_dividers /"+b//2 . . ..rWceZdZdZdZdZdS) PaddingTyperprrxN)rrrVALIDSAME SAME_LOWERr_rWrUrrs % $***rWrct|trwtjtjtjd} ||}n7#t$r*}d}t| ||d}~wwxYw|tjks|tjkrPt||}d|dz |z|z|z D}|tjkr d|DSd|DS|tjkrdgt|zSd }t| |) z6Convert padding string to list of pairs of pad values.)rrrz>Unrecognized padding type: expected 'VALID' or 'SAME', got {}.Nc3@K|]}tj|dVdSr^)rrOrs rUrbz"padtype_to_pads..sB33a##333333rWrpc(g|]}|dz||dzz fSrr_r`pad_sizes rUrz#padtype_to_pads..s78@8q=(X]2 3rWc(g|]}||dzz |dzfSrr_rs rUrz#padtype_to_pads..s78@8h!m #X] 3rW)rrzUnknown padding type: {}.) rrrrrrupperKeyError RuntimeErrorrrrsre) in_shape window_shapewindow_stridespaddingmappingerrrgr pad_sizess rUpadtype_to_padsr s 7" !,G 7 (gg 777 Lc G,, - -367    G{/E$E$EX~66I33$q=N:&')12333I+"""DMDM+### 8c(mm ## %C CJJw'' ( ((sA B  %BB fabsarccosarccosharcsinarcsinharctanarctan2arctanhrPrMrSrWdividerrrr less_equal logical_and logical_not logical_or logical_xormaximumminimumr not_equalr float_powerr-r left_shift right_shiftsubtractrcore.UnshapedArrayNonec td|DrdSt|dkrdStj|djtfd|ddDrad}|t vrt |}|d|d z }t ||d d |DdS) z;Check that dtypes agree, possibly ignoring float precision.c3^K|](}tj|jtjV)dSrL)rrrSrrs rUrbz$check_same_dtypes.. s3JJD 4:v 7 7JJJJJJrWNrrc3RK|]!}tj|jkV"dSrLr+)r`rjrSs rUrbz$check_same_dtypes..s5NND "4: . .% 7NNNNNNrWrpz:lax.{} requires arguments to have the same dtypes, got {}.z (Tip: jnp.zE is a similar function that does automatic type promotion on inputs).rc3>K|]}t|jVdSrL)rrSr"s rUrbz$check_same_dtypes..s*.K.Ks17||.K.K.K.K.K.KrW) rirsrrrS_JNP_FUNCTION_EQUIVALENTSrerr)rrtrgequivrSs @rUrrs JJEJJJJJ  FZZ!^^ F  #E!HN 3 3%NNNNE!""INNNNNN FC ((('-e g5 g g ggc CJJtTYY.K.KU.K.K.K%K%KLL M MM NNrWc ht|tttjfs3d}t |||t|t|sdStj j r7t|ttfrtd|DrdStj |}|jdkr)d}t ||j t|nY#t $rL}d}t |||tt!t||d}~wwxYw|rdnd\}t#fd |Ds'd }t |||||dS) zHCheck that `obj` is a shape-like value (e.g. tuple of nonnegative ints).z1{} {} must be of type tuple/list/ndarray, got {}.Nc3bK|]*}t|tjtjfV+dSrL)rrrr3rs rUrbz#_check_shapelike..#s5 A A*Qdk2 3 3 A A A A A ArWrpz${} {} must be 1-dimensional, got {}.z9{} {} must have every element be an integer type, got {}.)rpzstrictly positive)r nonnegativec3$K|] }|kV dSrLr_)r`rz lower_bounds rUrbz#_check_shapelike..0s( / /!Q+  / / / / / /rWz,{} {} must have every element be {}, got {}.)rrrrMrrerrrsrrirjrirrr'rkrd) fun_namearg_nameobjnon_zero_shapergobj_arrr bound_errorr& s @rUrrs C%rz2 3 3? =C CJJx499== > >> S  F ! judm&D&D  A AS A A AAA  F HSMM' \Q 0C CJJw|,, - --Tw TTT EC CJJx5T33H3HII J JPSST#1H6H+{ / / / /w / / / / /F 8C CJJx;DD E EEFFs>D E$AEE$ct|}tj|rGtj||}|t|kr|nt j||St j||SrL)r5ris_python_scalarscalar_type_ofrMr)examplerHrSs rUrr5ss //% W%%A (&  ( ( - -C6#;;&&33BHS%,@,@@ #u  rW)rr=r_)r[rrGrXr_twos_tworr5c"t||SrL)rrs rUrrFs Aq/rWcZtjt|tjSrL)rrr5rMrrs rUrCrCIs  6!99b&8 9 99rWc'jKd}|D]+}t|}t|||zV||z },dSr)rsr )ryrarx_lens rUrVrVMsT % a FFE uu} % %%%% UNEErWcVttj|fd|DS)Ncg|]}|v| Sr_r_)r`rremoveds rUrzremaining..Ws# 2 2 2'!1!1!!1!1!1rW)r itertoolschain)original removed_listsr9 s @rUrUrUUs1  / 0 0' 2 2 2 2X 2 2 22rW"tuple[Precision, Precision] | Nonec|tjjdS ttjjttjjfS#t$r8t dt tdtjjdwxYwt|tr'|tvrt|t|fSt|tr||fSt|t tfrSt|dkr@td|Dr'ttttf|St|t tfrt|dkrtd|Dr}|\}}ttttft|d}ttttft|d}||fSt dt td |d ) zTurns an API precision specification into a pair of enumeration values. The API can take the precision as a string, or int, and either as a single value to apply to both operands, or as a sequence of two values. NzDjax_default_matmul_precision flag must be set to None or a value in z , but got rc3@K|]}t|tVdSrL)rrrs rUrbz)canonicalize_precision..rs, 8 8Jq) $ $ 8 8 8 8 8 8rWc3@K|]}t|tVdSrL)rr)r`rs rUrbz)canonicalize_precision..us, 2 21Jq#   2 2 2 2 2 2rWrz-Precision argument must be None, a string in zO, a lax.Precision value or a tuple of two lax.Precision values or strings; got rc)rdefault_matmul_precisionrjrrerrrrrrrsrdrr)rrrp1p2s rUrrZsN  &,4 T  F39 : : F39 : :   Y $ % % Y Y171P1V Y Y   )S!!&i3E&E&E Y  9!5!5 55)Y''& i 9tUm,, &Y11D1D 8 8i 8 8 8882E U9i/0) < <<9tUm,, &Y11D1D 2 2 2 2 2222E FB 5I-.0Fr0J0J K KA NB 5I-.0Fr0J0J K KA NB 8O  %=O8P8P % %! % % % & &&s ;AABc ttt||t|t |tt||t |t|SrL)rir-rrXr=r1 )rrr$s rUrrsY VHQNNE!HHfQii 8 8 HQNNE!HHeAhh 7 7 9 99rWct|t|}}||kr.handlers-!#)SY77ch [s # ##rWr_) sticky_devicerjr` s ` rUresult_handlerzBIntRules.result_handlers#$$$$$ NrWctj}tjtj}t j|st|}||||fd}|S)Nc@tj|SrL)rr3)bufsrj phys_handlers rUr` z8BIntRules.global_sharded_result_handler..handlers [||D11 2 22rW)rrr,global_result_handlersr#ris_single_device_shardingr)rj out_sharding committedrQ phys_handler_maker phys_shardingr` rf s` @rUglobal_sharded_result_handlerz'BIntRules.global_sharded_result_handlersz"4((I4T5EF  -l ; ;# "m%%i JJL333333 NrWrcV|tjdtjdfvSNrrrMrS) bint_dtype other_dtypes rUrzBIntRules.convert_from& 28G,,bhw.?.?@ @@rWcV|tjdtjdfvSro rp )rr rq s rUrzBIntRules.convert_tors rWN)rIrrIr) rrr staticmethodrrb rm rrr_rWrUr[ r[ s333<3<   < AAA<AAAA<AAArWr[ )rHr=rIrJ)rXrY)rXrmrIrn)rr<rIr;)rXrrIr)rXrrIr)r[rrIr)rrrrrIr)rr<rr<rIr;)rr<rrrIr;)rr<r$r<rIr;)rr<r$rJrIr;)rr<rrrIr;)NFN)rr<rrrrrr)rr<rr?rIr;)rPr<rr<rRr<rIr;)rrrrJrIr;)NN) rr;rr;rrrrrIr;) rr<rr<rrrrrrrIr;)NNN)rr;rr;rr;rrrrrrrIr;)rr<rrrIr;)rr<r[r@r rrIr;)rr<rrJrIr;rL)rr<rr@rrrIr;)rr<rr<rrrIr;)rr<rrrIr;)r(r<r)r<r*r<rIr;)r.r<r/r<rIr;)rr<r3r4rIr;)rr<r;rJr<r?rIr;) rrrGrrHrIrrrIr)rxrryrzrIr{)rSr?rIr)rr<r?rrIr;)rTrp) rr;rrJrrrrJrIr;) rrzrrJrrrrJrIr) rrrrJrrrrJrIr)rT) rr;rr<rrJrrrIr)rr<rrJrIr)rrr$rGrIrG) r[r@rr<rSrrrrIr;)rjr#rIr;)rjrrIr)rSr?rrJrIr;)rSr?r[r@rrJrIr;)rSr?r[r@rr=rIr;)rSr?r[r@r?rrIr;)rrGrIrG)rr rrJrrJrIr;)rr<rrrIr;) rr$rr<rSrr[r%rrrIr;)rr;r+rJr,r-rIr;)rr;rr;rrrIr;)FF)rrrtrrrrIr)rrrrrIr)rr)rrrr)rr)rIr)rrrIr)rrrr)rr;rr;rr;rIr@) rr;rr;rr;rrrIr)rIr)r[r)rqry)rr<rIr;)rr:rIr-)rrrtr rIr )Fru )rrrIr> ( __future__rrcollections.abcrrenumrHrr: r4r7typingrrr r r rr r rrVrMrTr jax.shardingr jax.tree_utilrjax._srcrrrrrrrrrrrfrpprrrjax._src.abstract_arraysr jax._src.corer!r"r#r$r%r&r'jax._src.interpretersr(r)r*r+rr,r-jax._src.interpreters.batchingr. jax._src.laxr/jax._src.lax.utilsr0r1r2r3r4r5 jax._src.libr6jax._src.lib.mlirr7jax._src.lib.mlir.dialectsr8r9jax._src.sharding_implsr:jax._src.typingr;r<r=r>r?r@ jax._src.utilrArBrCrDrErFxbxcopsxops_xlaxerRrrPr;r[rrGrk unsafe_maprrrVrlrrrrrrrrrrrrrrrIntEnumrrrrr rrrrrrr r#r(r+r/rr6r9r<rArDrGrJrMrPrSrWrZr]r`rcrfrirlrtrwrzr}rrrrrrrrrrrrrEnumrrrrrrrrJrrrr r rrr"r'r-r2r:rBrFrmrOrMrrrrrrrrrrrrrrrrrrraval_zeros_likersr AbstractRefrrrrrr rrr#r*r9r=r@rBrJrMrPrSrVrYr\r_rbre aval_methodrqrv rrsrvr; rrrrraw_jaxval_adders _fixed_dtype_complex_basetype_strip_weak_typerr standard_unoprrrrstandard_naryoprrrrr rmrrnrfloat64_complex_elem_typesr~rlr}_boolr _signedintr_any _bool_or_int_orderedr deflinear2register_loweringnegater defjvp_zerorr next_afterrrrrrr defjvp2rr rrdefjvprexponential_minus_oner log_plus_onerrrrr rrrrr"rrLrrOr$rRr'rUr&rXr[r^rardr*r.r9_complex_dtyper1r4r?rA linear_jvpprimitive_jvpsprimitive_transposesr8rHrErDrCrFrIrRr;r[r]rirorrr@rrrvr{rFrLnot_rOrrRor_rVrrYpopcntr\count_leading_zerosrrrr_rrrbr rrrerrrhr rk remainderrrnmax_hlorqmin_hlorsrvryrAndOprOrOprrrr|rrrrrrrrrrrrrrrrrrdef_custom_binddef_implrdef_abstract_evalconst_fold_rulesforwarding_rules pp_eqn_rulesrr r rrrrr5r*r9rNrHrKrdrhryrkrrr defbilinearprimitive_batchers padding_rulesrrrrrrrrrrrrrr rrrrr)r+r/r6rcustom_partial_eval_rulescustom_staging_rulescustom_typechecksr8_clamp_dtype_rulerArrXrZrjrnrqrrtrvrrrr!rrrrrrrrrrrrrrrrrrrr%rrrrr9rrrrrr rrr,r(r0r4rAr[rbrPrr|rrrrrr defreducerrrrrrrrrrrrr@rEryrrrrrAddOpMulOpXorOprr deflinearrrSrrr _UINT_DTYPESint16rr _INT_DTYPESrrrrrrrrrrrrrr!r#r%r r)r'r.r2r5r0r7Effectr9rDr]rBrEr<def_effectful_abstract_evallowerable_effectsadd_typerWr[r^rYrbrfrhrdrmrrrtrvryrrrrrrrrrrrmemory_kind_propagate_rulerrrrrrrrrrr_ndimrrrr r rrrr=rGrXrr1 r2 r5rrCrVrUrrrrNrN rM rR rX r[ r4rr_rWrUr sO#""""""........  \\\\\\\\\\\\\\\\\\ !!!!!!""""""&&&&&&))))))%%%%%%000000PPPPPPPPPPPPPPPPPP$$$$$$******&&&&&&444444&&&&&&%%%%%%555555 ;;;;;;;;;;;;;; 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