U 9%eG-@sdZddlmZddlmZddlmZddlmZddl m Z m Z ddl m Z mZddlmZmZmZdd lmZmZdd lmZmZmZmZdd lmZdd lmZdd lm Z ddl!m"Z"m#Z#ddl$m%Z%m&Z&ddl'm(Z(ddl)m*Z*ddl+m,Z,GdddZ-Gddde-Z.ddZ/e.ddddZ0edddgdZ1edd dgdZ2ed!Z3ed"Z4ed#d$dgdZ5e.ee4e4ee4Z6e.ee5e4e4e5ee5e4Z7e6e7fZ8e.e3e e4e d%e3ee4d&dd'Z9e.e d%ee4e e4Z:e.d(dd)dZ;Gd*d+d+e.Zee?fZId6S)7a Classes and functions useful for rewriting expressions for optimized code generation. Some languages (or standards thereof), e.g. C99, offer specialized math functions for better performance and/or precision. Using the ``optimize`` function in this module, together with a collection of rules (represented as instances of ``Optimization``), one can rewrite the expressions for this purpose:: >>> from sympy import Symbol, exp, log >>> from sympy.codegen.rewriting import optimize, optims_c99 >>> x = Symbol('x') >>> optimize(3*exp(2*x) - 3, optims_c99) 3*expm1(2*x) >>> optimize(exp(2*x) - 1 - exp(-33), optims_c99) expm1(2*x) - exp(-33) >>> optimize(log(3*x + 3), optims_c99) log1p(x) + log(3) >>> optimize(log(2*x + 3), optims_c99) log(2*x + 3) The ``optims_c99`` imported above is tuple containing the following instances (which may be imported from ``sympy.codegen.rewriting``): - ``expm1_opt`` - ``log1p_opt`` - ``exp2_opt`` - ``log2_opt`` - ``log2const_opt`` ) expand_log)S)Wild)sign)explog)MaxMin)cossinsinc)Qask)log1plog2exp2expm1) MatrixSolve)UnevaluatedExpr)Pow) logaddexp logaddexp2)cosm1powm1)Mul) MatrixSymbol)siftc@s"eZdZdZdddZddZdS) Optimizationz Abstract base class for rewriting optimization. Subclasses should implement ``__call__`` taking an expression as argument. Parameters ========== cost_function : callable returning number priority : number NcCs||_||_dSN) cost_functionpriority)selfr r!r#V/var/www/html/Darija-Ai-API/env/lib/python3.8/site-packages/sympy/codegen/rewriting.py__init__@szOptimization.__init__cGst||jddS)N)keyr)sortedr )r"argsr#r#r$cheapestDszOptimization.cheapest)Nr)__name__ __module__ __qualname____doc__r%r)r#r#r#r$r4s rcs(eZdZdZfddZddZZS) ReplaceOptima Rewriting optimization calling replace on expressions. Explanation =========== The instance can be used as a function on expressions for which it will apply the ``replace`` method (see :meth:`sympy.core.basic.Basic.replace`). Parameters ========== query : First argument passed to replace. value : Second argument passed to replace. Examples ======== >>> from sympy import Symbol >>> from sympy.codegen.rewriting import ReplaceOptim >>> from sympy.codegen.cfunctions import exp2 >>> x = Symbol('x') >>> exp2_opt = ReplaceOptim(lambda p: p.is_Pow and p.base == 2, ... lambda p: exp2(p.exp)) >>> exp2_opt(2**x) exp2(x) c stjf|||_||_dSr)superr%queryvalue)r"r0r1kwargs __class__r#r$r%hszReplaceOptim.__init__cCs||j|jSr)replacer0r1)r"exprr#r#r$__call__mszReplaceOptim.__call__)r*r+r,r-r%r7 __classcell__r#r#r3r$r.Hs r.cCs@t|ddddD](}||}|jdkr.|}q|||}q|S)a Apply optimizations to an expression. Parameters ========== expr : expression optimizations : iterable of ``Optimization`` instances The optimizations will be sorted with respect to ``priority`` (highest first). Examples ======== >>> from sympy import log, Symbol >>> from sympy.codegen.rewriting import optims_c99, optimize >>> x = Symbol('x') >>> optimize(log(x+3)/log(2) + log(x**2 + 1), optims_c99) log1p(x**2) + log2(x + 3) cSs|jSr)r!)optr#r#r$zoptimize..T)r&reverseN)r'r r))r6Z optimizationsZoptimZnew_exprr#r#r$optimizeqs  r=cCs|jo|jdkS)N)is_Powbasepr#r#r$r:r;r:cCs t|jSr)rrrAr#r#r$r:r;dcCs|jSr)Zis_Dummyxr#r#r$r:r;) propertiesucCs|j o|j Sr) is_numberis_AddrDr#r#r$r:r;vwncCs|jSrrHrDr#r#r$r:r;r>cCs|ddS)NcSs*|jr|jjp(t|ttfo(|jdj S)Nr)r?rZ is_negative isinstancerrr(rHer#r#r$r:s..)countr6r#r#r$r:sr cCsDt|toB|jdjoBt|jdjdkoBtdd|jdjDS)Nrr>css|]}t|tVqdSr)rNr).0tr#r#r$ sz..)rNrr(rIlenalllr#r#r$r:s  cCs<tdd|jdjDtttdd|jdjDS)NcSsg|]}|jdqSrr(rUrPr#r#r$ sz..rcSsg|]}|jdqSr\r]r^r#r#r$r_s)rr(rrr rZr#r#r$r:s cs>eZdZdZd fdd ZddZddZfd d ZZS) FuncMinusOneOptimaSpecialization of ReplaceOptim for functions evaluating "f(x) - 1". Explanation =========== Numerical functions which go toward one as x go toward zero is often best implemented by a dedicated function in order to avoid catastrophic cancellation. One such example is ``expm1(x)`` in the C standard library which evaluates ``exp(x) - 1``. Such functions preserves many more significant digits when its argument is much smaller than one, compared to subtracting one afterwards. Parameters ========== func : The function which is subtracted by one. func_m_1 : The specialized function evaluating ``func(x) - 1``. opportunistic : bool When ``True``, apply the transformation as long as the magnitude of the remaining number terms decreases. When ``False``, only apply the transformation if it completely eliminates the number term. Examples ======== >>> from sympy import symbols, exp >>> from sympy.codegen.rewriting import FuncMinusOneOptim >>> from sympy.codegen.cfunctions import expm1 >>> x, y = symbols('x y') >>> expm1_opt = FuncMinusOneOptim(exp, expm1) >>> expm1_opt(exp(x) + 2*exp(5*y) - 3) expm1(x) + 2*expm1(5*y) Tcs<dtjdd|jfddd||_|_||_dS)N cSs|jSr)rIrOr#r#r$r:r;z,FuncMinusOneOptim.__init__..cs||Sr)Z count_opsrRrSfunc_m_1weightr#r$r:r;rT)r/r%replace_in_Addfuncrc opportunistic)r"rfrcrgr3rbr$r%s zFuncMinusOneOptim.__init__csDt|jdddd\}}t|}t|fdddd\}}|||fS)NcSs|jSrrMargr#r#r$r:r;z4FuncMinusOneOptim._group_Add_terms..Tbinarycs |jSr)hasrfrhr"r#r$r:r;)rr(sum)r"addnumbersZnon_numnumsumterms_with_funcotherr#rmr$_group_Add_termssz"FuncMinusOneOptim._group_Add_termsc s4|\}}}|dkr|Sgg}}|D]}|jrt|jfdddd\}} t|dkr|t| dkr||d| d}} qd} n|jjkr|tj}} nd} | dk r| jrt | t | krj rt | |t |k} n | |dk} | r|| 7}| | j |jq*| |q*|j|f|||S)z1 passed as second argument to Basic.replace(...) rcs |jjkSr)rfrhrmr#r$r:r;z2FuncMinusOneOptim.replace_in_Add..TrjrN)rtZis_Mulrr(rXrfrZOnerHrrgabsappendrc) r"rPrqrrZother_non_num_termsZ substitutedZ untouchedZ with_funcrfZcoeffZ do_substituter#rmr$res.  &  z FuncMinusOneOptim.replace_in_Addcs(t|}t|}|||Sr)r/r7factorr))r"r6Zalt1Zalt2r3r#r$r7 s zFuncMinusOneOptim.__call__)T) r*r+r,r-r%rtrer7r8r#r#r3r$r`s & r`cCs t|tSr)rNrrOr#r#r$r:r;cCs(t|tddttdttS)NcSs t|Sr)rrwrhr#r#r$r:r;rQr)rr5r_urrZr#r#r$r:s  cCs|jSr)Z is_symbol)br#r#r$r:r;)base_reqcstfddddS)a Creates an instance of :class:`ReplaceOptim` for expanding ``Pow``. Explanation =========== The requirements for expansions are that the base needs to be a symbol and the exponent needs to be an Integer (and be less than or equal to ``limit``). Parameters ========== limit : int The highest power which is expanded into multiplication. base_req : function returning bool Requirement on base for expansion to happen, default is to return the ``is_symbol`` attribute of the base. Examples ======== >>> from sympy import Symbol, sin >>> from sympy.codegen.rewriting import create_expand_pow_optimization >>> x = Symbol('x') >>> expand_opt = create_expand_pow_optimization(3) >>> expand_opt(x**5 + x**3) x**5 + x*x*x >>> expand_opt(x**5 + x**3 + sin(x)**3) x**5 + sin(x)**3 + x*x*x >>> opt2 = create_expand_pow_optimization(3, base_req=lambda b: not b.is_Function) >>> opt2((x+1)**2 + sin(x)**2) sin(x)**2 + (x + 1)*(x + 1) cs&|jo$|jo$|jjo$t|jkSr)r?r@rZ is_IntegerrurOrzlimitr#r$r:Br;z0create_expand_pow_optimization..cSsJ|jdkr(tt|jg|j ddiSdtt|jg|j ddiS)NrevaluateFr)rrrr@rAr#r#r$r:Cs()r.)r|rzr#r{r$create_expand_pow_optimizations# r~cCsZ|jrVt|jdkrV|j\}}|jrV|jddkrV|j}t|trVtt t |jSdS)Nr>rF) Z is_MatMulrXr(Z is_InverseshaperirNrboolrr Zfullrankr6leftrightZinv_argr#r#r$_matinv_predicateIs  rcCs|j\}}|j}t||Sr)r(rirrr#r#r$_matinv_transformTs rN)Jr-Zsympy.core.functionrZsympy.core.singletonrZsympy.core.symbolrZ$sympy.functions.elementary.complexesrZ&sympy.functions.elementary.exponentialrrZ(sympy.functions.elementary.miscellaneousrr Z(sympy.functions.elementary.trigonometricr r r Zsympy.assumptionsr rZsympy.codegen.cfunctionsrrrrZsympy.codegen.matrix_nodesrZsympy.core.exprrZsympy.core.powerrZsympy.codegen.numpy_nodesrrZsympy.codegen.scipy_nodesrrZsympy.core.mulrZ"sympy.matrices.expressions.matexprrZsympy.utilities.iterablesrrr.r=Zexp2_optZ_drx_v_wZ_nZ sinc_opt1Z sinc_opt2Z sinc_optsZlog2_optZ log2const_optZlogsumexp_2terms_optr`Z expm1_optZ cosm1_optZ powm1_optZ log1p_optr~rrZ matinv_optZ logaddexp_optZlogaddexp2_optZ optims_c99Z optims_numpyZ optims_scipyr#r#r#r$sz          ) * [   +   ,