Xh+0dZddlmZmZddlmZddlmZddlm Z ddl m Z m Z ddl mZddlmZmZmZd ZGd d eZd ZGd deZe dZdZGddeZdZGddeZdZGddeZe dZdZGddeZ dZ!GddeZ"d Z#Gd!d"eZ$d#Z%Gd$d%eZ&Gd&d'eZ'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)sqrt)BooleanFunctiontruefalsec:t|tjz SNrrOnexs j/var/www/tools.fuzzalab.pt/emblema-extractor/venv/lib/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== ? "$T844 4rc t|jSr)rrrhintss r_eval_expand_funczexpm1._eval_expand_func=ty!!rc :t|tjz Srrrargkwargss 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&|jdjSr1)r is_finiter3s r_eval_is_finitezexpm1._eval_is_finiteNsy|%%rNr) __name__ __module__ __qualname____doc__nargsr!r%r+_eval_rewrite_as_tractable classmethodr-r4r8rrrrs8 E5555"""   "6##[# $$$&&&&&rrc:t|tjzSr)r rrrs r_log1prCRs q15y>>rcbeZdZdZdZd dZdZdZeZe dZ dZ dZ d Z d Zd Zd S)log1paf Represents the natural logarithm of a number plus one. Explanation =========== The benefit of using ``log1p(x)`` over ``log(x + 1)`` is that the latter is prone to cancellation under finite precision arithmetic when x is close to zero. Examples ======== >>> from sympy.abc import x >>> from sympy.codegen.cfunctions import log1p >>> from sympy import expand_log >>> '%.0e' % expand_log(log1p(1e-99)).evalf() '1e-99' >>> from math import log >>> log(1 + 1e-99) 0.0 >>> log1p(x).diff(x) 1/(x + 1) See Also ======== expm1 rc||dkr'tj|jdtjzz St||rrr)rrrrrs rr!z log1p.fdiffws7 q==5$)A,./ /$T844 4rc t|jSr)rCrr#s rr%zlog1p._eval_expand_funcr&rc t|Sr)rCr(s r_eval_rewrite_as_logzlog1p._eval_rewrite_as_logc{{rc|jrt|tjzS|js!tj|tjzS|jr)tt|tjzSdSr) is_Rationalr rris_Floatr- is_numberrr.r)s rr-z log1p.evalso ? .sQU{## # .8C!%K(( ( ] .x}}qu,-- - . .rc@|jdtjzjSr1)rrris_nonnegativer3s rr4zlog1p._eval_is_reals ! qu$44rch|jdtjzjrdS|jdjS)NrF)rrris_zeror7r3s rr8zlog1p._eval_is_finites. IaL15 ) 5y|%%rc&|jdjSr1)r is_positiver3s r_eval_is_positivezlog1p._eval_is_positivesy|''rc&|jdjSr1)rrTr3s r _eval_is_zerozlog1p._eval_is_zeror5rc&|jdjSr1)rrRr3s r_eval_is_nonnegativezlog1p._eval_is_nonnegativesy|**rNr9)r:r;r<r=r>r!r%rJr?r@r-r4r8rWrYr[rArrrErEVs: E5555""""6..[.555&&& ((($$$+++++rrEc,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() == 4.0 True >>> exp2(x).diff(x) log(2)*exp2(x) See Also ======== log2 rc\|dkr|ttzSt||r)r r^rrs rr!z exp2.fdiffs- q==D > !$T844 4rc t|Sr)r_r(s r_eval_rewrite_as_Powzexp2._eval_rewrite_as_PowSzzrc t|jSr)r_rr#s rr%zexp2._eval_expand_funcdi  rc2|jrt|SdSr)rOr_rPs rr-z exp2.evals" = ::   rNr9) r:r;r<r=r>r!rdr?r%r@r-rArrrarasz2 E5555"6!!![rracJt|ttz Sr)r r^rs r_log2rj q66#d)) rcJeZdZdZdZd dZedZdZdZ dZ e Z dS) log2a Represents the logarithm function with base two. Explanation =========== The benefit of using ``log2(x)`` over ``log(x)/log(2)`` is that the latter is not as efficient under finite precision arithmetic. Examples ======== >>> from sympy.abc import x >>> from sympy.codegen.cfunctions import log2 >>> log2(4).evalf() == 2.0 True >>> log2(x).diff(x) 1/(x*log(2)) See Also ======== exp2 log10 rc|dkr/tjtt|jdzz St ||rG)rrr r^rrrs rr!z log2.fdiff; q==5#d))DIaL01 1$T844 4rc|jr&tj|t}|jr|SdS|jr|jtkr |jSdSdSN)base)rOr r-r^is_Atomis_Powrrrr.r)results rr-z log2.evalf = Xc---F~     Z CH,,7N  ,,rcL|tj|i|Sr)rewriter evalf)rrr*s r _eval_evalfzlog2._eval_evalfs&&t||C  &7777rc t|jSr)rjrr#s rr%zlog2._eval_expand_funcrgrc t|Sr)rjr(s rrJzlog2._eval_rewrite_as_logrerNr9) r:r;r<r=r>r!r@r-r{r%rJr?rArrrmrms4 E5555[888!!!"6rrmc||z|zSrrA)ryzs r_fmars 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||)rrr\r\r)rrrrrs rr!z fma.fdiff6s@ v  9Q\* * ]]5L$T844 4rc t|jSr)rrr#s rr%zfma._eval_expand_funcBsTYrNc t|Sr)r)rr)limitvarr*s rr?zfma._eval_rewrite_as_tractableEsCyyrr9r)r:r;r<r=r>r!r%r?rArrrr s\& E 5 5 5 5   rr cJt|ttz Sr)r _Tenrs r_log10rLrkrcDeZdZdZdZddZedZdZdZ e Z dS) log10a$ Represents the logarithm function with base ten. Examples ======== >>> from sympy.abc import x >>> from sympy.codegen.cfunctions import log10 >>> log10(100).evalf() == 2.0 True >>> log10(x).diff(x) 1/(x*log(10)) See Also ======== log2 rc|dkr/tjtt|jdzz St ||rG)rrr rrrrs rr!z log10.fdifferorc|jr&tj|t}|jr|SdS|jr|jtkr |jSdSdSrq)rOr r-rrsrtrrrrus rr-z log10.evalorwrc t|jSr)rrr#s rr%zlog10._eval_expand_funcxr&rc t|Sr)rr(s rrJzlog10._eval_rewrite_as_log{rKrNr9) r:r;r<r=r>r!r@r-r%rJr?rArrrrPsv$ 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 ||)rrrr\rrrr^rrs rr!z Sqrt.fdiffs@ q==ty|Xb!__55d: :$T844 4rc t|jSr)rrr#s rr%zSqrt._eval_expand_funcrgrc t|Sr)rr(s rrdzSqrt._eval_rewrite_as_PowrerNr9 r:r;r<r=r>r!r%rdr?rArrrrs[2 E5555!!!"6rrc>t|tddS)Nrr)rrrs r_Cbrtrs q(1a.. ! !!rc.eZdZdZdZddZdZdZeZdS)Cbrta Represents the cube root function. Explanation =========== The reason why one would use ``Cbrt(x)`` over ``cbrt(x)`` is that the latter is internally represented as ``Pow(x, Rational(1, 3))`` which may not be what one wants when doing code-generation. Examples ======== >>> from sympy.abc import x >>> from sympy.codegen.cfunctions import Cbrt >>> Cbrt(x) Cbrt(x) >>> Cbrt(x).diff(x) 1/(3*x**(2/3)) See Also ======== Sqrt rc|dkr4t|jdtt dz dz St ||)rrrrrrs rr!z Cbrt.fdiffsF q==ty|XteAg%6%6779 9$T844 4rc t|jSr)rrr#s rr%zCbrt._eval_expand_funcrgrc t|Sr)rr(s rrdzCbrt._eval_rewrite_as_PowrerNr9rrArrrrs[2 E5555!!!"6rrc^tt|dt|dzS)Nr\)r r)rrs 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() == 5.0 True >>> hypot(x, y) hypot(x, y) >>> hypot(x, y).diff(x) x/hypot(x, y) r\rc|dvr+d|j|dz zt|j|jzz St||)rrr\r)rr^funcrrs rr!z hypot.fdiffsJ v  TYxz**DDI1F,FG G$T844 4rc t|jSr)rrr#s rr%zhypot._eval_expand_funcr&rc t|Sr)rr(s rrdzhypot._eval_rewrite_as_PowrKrNr9rrArrrrs[. E5555""""6rrc(eZdZdZedZdS)isnanrcL|tjurtS|jrtSdSr)rNaNr rOr rPs rr-z isnan.evals& !%<<K ] L4rNr:r;r<r>r@r-rArrrr2 E[rrc(eZdZdZedZdS)isinfrc>|jrtS|jrtSdSr) is_infiniter r7r rPs rr-z isinf.eval's% ? 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