Ed.dZddlmZmZddlmZddlmZddlm Z ddl m Z m Z ddl mZdZGd d eZd ZGd d eZe dZdZGddeZdZGddeZdZGddeZe dZdZGddeZdZGddeZdZGd d!eZ d"Z!Gd#d$eZ"d%S)&a# This module contains SymPy functions mathcin corresponding to special math functions in the C standard library (since C99, also available in C++11). The functions defined in this module allows the user to express functions such as ``expm1`` as a SymPy function for symbolic manipulation. )ArgumentIndexErrorFunction)Rational)Pow)S)explog)sqrtc:t|tjz SNrrOnexs 8lib/python3.11/site-packages/sympy/codegen/cfunctions.py_expm1rs q66AE>cPeZdZdZdZd dZdZdZeZe dZ dZ dZ d S) expm1a* Represents the exponential function minus one. Explanation =========== The benefit of using ``expm1(x)`` over ``exp(x) - 1`` is that the latter is prone to cancellation under finite precision arithmetic when x is close to zero. Examples ======== >>> from sympy.abc import x >>> from sympy.codegen.cfunctions import expm1 >>> '%.0e' % expm1(1e-99).evalf() '1e-99' >>> from math import exp >>> exp(1e-99) - 1 0.0 >>> expm1(x).diff(x) exp(x) See Also ======== log1p cJ|dkrt|jSt||@ Returns the first derivative of this function. r)rargsrselfargindexs rfdiffz expm1.fdiff4s, q= 5 ? "$T844 4rc t|jSr )rrrhintss r_eval_expand_funczexpm1._eval_expand_func=ty!!rc :t|tjz Sr r rargkwargss r_eval_rewrite_as_expzexpm1._eval_rewrite_as_exp@s3xx!%rcPtj|}||tjz SdSr )revalrr)clsr&exp_args rr*z expm1.evalEs-(3--  #QU? " # #rc&|jdjSNr)ris_realrs r _eval_is_realzexpm1._eval_is_realKy|##rc&|jdjSr.)r is_finiter0s r_eval_is_finitezexpm1._eval_is_finiteNsy|%%rNr) __name__ __module__ __qualname____doc__nargsrr"r(_eval_rewrite_as_tractable classmethodr*r1r5rrrrs8 E5555"""   "6##[# $$$&&&&&rrc:t|tjzSr )r rrrs r_log1pr@Rs q15y>>rcbeZdZdZdZd dZdZdZeZe dZ dZ dZ d Z d Zd Zd S)log1paf Represents the natural logarithm of a number plus one. Explanation =========== The benefit of using ``log1p(x)`` over ``log(x + 1)`` is that the latter is prone to cancellation under finite precision arithmetic when x is close to zero. Examples ======== >>> from sympy.abc import x >>> from sympy.codegen.cfunctions import log1p >>> from sympy import expand_log >>> '%.0e' % expand_log(log1p(1e-99)).evalf() '1e-99' >>> from math import log >>> log(1 + 1e-99) 0.0 >>> log1p(x).diff(x) 1/(x + 1) See Also ======== expm1 rc||dkr'tj|jdtjzz St||rrr)rrrrrs rrz log1p.fdiffws: q= 55$)A,./ /$T844 4rc t|jSr )r@rr s rr"zlog1p._eval_expand_funcr#rc t|Sr )r@r%s r_eval_rewrite_as_logzlog1p._eval_rewrite_as_logc{{rc|jrt|tjzS|js!tj|tjzS|jr)tt|tjzSdSr ) is_Rationalr rris_Floatr* is_numberrr+r&s rr*z log1p.evalso ? .sQU{## # .8C!%K(( ( ] .x}}qu,-- - . .rc@|jdtjzjSr.)rrris_nonnegativer0s rr1zlog1p._eval_is_reals ! qu$44rch|jdtjzjrdS|jdjS)NrF)rrris_zeror4r0s rr5zlog1p._eval_is_finites. IaL15 ) 5y|%%rc&|jdjSr.)r is_positiver0s r_eval_is_positivezlog1p._eval_is_positivesy|''rc&|jdjSr.)rrQr0s r _eval_is_zerozlog1p._eval_is_zeror2rc&|jdjSr.)rrOr0s r_eval_is_nonnegativezlog1p._eval_is_nonnegativesy|**rNr6)r7r8r9r:r;rr"rGr<r=r*r1r5rTrVrXr>rrrBrBVs: E5555""""6..[.555&&& ((($$$+++++rrBc,tt|Sr )r_Twors r_exp2r\s tQ<<rcDeZdZdZdZddZdZeZdZe dZ dS) exp2a Represents the exponential function with base two. Explanation =========== The benefit of using ``exp2(x)`` over ``2**x`` is that the latter is not as efficient under finite precision arithmetic. Examples ======== >>> from sympy.abc import x >>> from sympy.codegen.cfunctions import exp2 >>> exp2(2).evalf() == 4 True >>> exp2(x).diff(x) log(2)*exp2(x) See Also ======== log2 rc\|dkr|ttzSt||r)r r[rrs rrz exp2.fdiffs0 q= 5D > !$T844 4rc t|Sr )r\r%s r_eval_rewrite_as_Powzexp2._eval_rewrite_as_PowSzzrc t|jSr )r\rr s rr"zexp2._eval_expand_funcdi  rc2|jrt|SdSr )rLr\rMs rr*z exp2.evals" = ::   rNr6) r7r8r9r:r;rrar<r"r=r*r>rrr^r^sz2 E5555"6!!![rr^cJt|ttz Sr )r r[rs r_log2rg q66#d)) rcJeZdZdZdZd dZedZdZdZ dZ e Z dS) log2a Represents the logarithm function with base two. Explanation =========== The benefit of using ``log2(x)`` over ``log(x)/log(2)`` is that the latter is not as efficient under finite precision arithmetic. Examples ======== >>> from sympy.abc import x >>> from sympy.codegen.cfunctions import log2 >>> log2(4).evalf() == 2 True >>> log2(x).diff(x) 1/(x*log(2)) See Also ======== exp2 log10 rc|dkr/tjtt|jdzz St ||rD)rrr r[rrrs rrz log2.fdiff> q= 55#d))DIaL01 1$T844 4rc|jr&tj|t}|jr|SdS|jr|jtkr |jSdSdSN)base)rLr r*r[is_Atomis_Powrorr+r&results rr*z log2.evall = Xc---F~     Z CH, 7N    rcL|tj|i|Sr )rewriter evalf)rrr's r _eval_evalfzlog2._eval_evalfs&&t||C  &7777rc t|jSr )rgrr s rr"zlog2._eval_expand_funcrdrc t|Sr )rgr%s rrGzlog2._eval_rewrite_as_logrbrNr6) r7r8r9r:r;rr=r*rxr"rGr<r>rrrjrjs4 E5555[888!!!"6rrjc||z|zSr r>)ryzs r_fmar~s Q37Nrc,eZdZdZdZddZdZd dZdS) fmaa Represents "fused multiply add". Explanation =========== The benefit of using ``fma(x, y, z)`` over ``x*y + z`` is that, under finite precision arithmetic, the former is supported by special instructions on some CPUs. Examples ======== >>> from sympy.abc import x, y, z >>> from sympy.codegen.cfunctions import fma >>> fma(x, y, z).diff(x) y rcn|dvr|jd|z S|dkr tjSt||)rrrYrYr)rrrrrs rrz fma.fdiff6sE v  59Q\* * ] 55L$T844 4rc t|jSr )r~rr s rr"zfma._eval_expand_funcBsTYrNc t|Sr )r~)rr&limitvarr's rr<zfma._eval_rewrite_as_tractableEsCyyrr6r )r7r8r9r:r;rr"r<r>rrrr s\& E 5 5 5 5   rr cJt|ttz Sr )r _Tenrs r_log10rLrhrcDeZdZdZdZddZedZdZdZ e Z dS) log10a" Represents the logarithm function with base ten. Examples ======== >>> from sympy.abc import x >>> from sympy.codegen.cfunctions import log10 >>> log10(100).evalf() == 2 True >>> log10(x).diff(x) 1/(x*log(10)) See Also ======== log2 rc|dkr/tjtt|jdzz St ||rD)rrr rrrrs rrz log10.fdifferlrc|jr&tj|t}|jr|SdS|jr|jtkr |jSdSdSrn)rLr r*rrprqrorrrs rr*z log10.evalortrc t|jSr )rrr s rr"zlog10._eval_expand_funcxr#rc t|Sr )rr%s rrGzlog10._eval_rewrite_as_log{rHrNr6) r7r8r9r:r;rr=r*r"rGr<r>rrrrPsv$ E5555[""""6rrc6t|tjSr )rrHalfrs r_Sqrtrs q!&>>rc.eZdZdZdZddZdZdZeZdS)Sqrta Represents the square root function. Explanation =========== The reason why one would use ``Sqrt(x)`` over ``sqrt(x)`` is that the latter is internally represented as ``Pow(x, S.Half)`` which may not be what one wants when doing code-generation. Examples ======== >>> from sympy.abc import x >>> from sympy.codegen.cfunctions import Sqrt >>> Sqrt(x) Sqrt(x) >>> Sqrt(x).diff(x) 1/(2*sqrt(x)) See Also ======== Cbrt rc|dkr1t|jdtddtz St ||)rrrrYrrrr[rrs rrz Sqrt.fdiffsC q= 5ty|Xb!__55d: :$T844 4rc t|jSr )rrr s rr"zSqrt._eval_expand_funcrdrc t|Sr )rr%s rrazSqrt._eval_rewrite_as_PowrbrNr6 r7r8r9r:r;rr"rar<r>rrrrs[2 E5555!!!"6rrc>t|tddS)Nrr)rrrs r_Cbrtrs q(1a.. ! !!rc.eZdZdZdZddZdZdZeZdS)Cbrta Represents the cube root function. Explanation =========== The reason why one would use ``Cbrt(x)`` over ``cbrt(x)`` is that the latter is internally represented as ``Pow(x, Rational(1, 3))`` which may not be what one wants when doing code-generation. Examples ======== >>> from sympy.abc import x >>> from sympy.codegen.cfunctions import Cbrt >>> Cbrt(x) Cbrt(x) >>> Cbrt(x).diff(x) 1/(3*x**(2/3)) See Also ======== Sqrt rc|dkr4t|jdtt dz dz St ||)rrrrrrs rrz Cbrt.fdiffsI q= 5ty|XteAg%6%6779 9$T844 4rc t|jSr )rrr s rr"zCbrt._eval_expand_funcrdrc t|Sr )rr%s rrazCbrt._eval_rewrite_as_PowrbrNr6rr>rrrrs[2 E5555!!!"6rrc^tt|dt|dzS)NrY)r r)rr|s r_hypotrs% Aq C1II% & &&rc.eZdZdZdZddZdZdZeZdS) hypota Represents the hypotenuse function. Explanation =========== The hypotenuse function is provided by e.g. the math library in the C99 standard, hence one may want to represent the function symbolically when doing code-generation. Examples ======== >>> from sympy.abc import x, y >>> from sympy.codegen.cfunctions import hypot >>> hypot(3, 4).evalf() == 5 True >>> hypot(x, y) hypot(x, y) >>> hypot(x, y).diff(x) x/hypot(x, y) rYrc|dvr+d|j|dz zt|j|jzz St||)rrrYr)rr[funcrrs rrz hypot.fdiffsL v  5TYxz**DDI1F,FG G$T844 4rc t|jSr )rrr s rr"zhypot._eval_expand_funcr#rc t|Sr )rr%s rrazhypot._eval_rewrite_as_PowrHrNr6rr>rrrrs[. E5555""""6rrN)#r:sympy.core.functionrrsympy.core.numbersrsympy.core.powerrsympy.core.singletonr&sympy.functions.elementary.exponentialrr (sympy.functions.elementary.miscellaneousr rrr@rBr[r\r^rgrjr~rrrrrrrrrrr>rrrs=<<<<<<<'''''' """""";;;;;;;;999999:&:&:&:&:&H:&:&:&zK+K+K+K+K+HK+K+K+Z qtt111118111h96969696968969696x&&&&&(&&&R quu.6.6.6.6.6H.6.6.6b+6+6+6+6+68+6+6+6\""",6,6,6,6,68,6,6,6^'''*6*6*6*6*6H*6*6*6*6*6r