wgK.dZddlmZmZddlmZddlmZddlm Z ddl m Z m Z ddl mZdZGd d eZd ZGd d eZe dZdZGddeZdZGddeZdZGddeZe dZdZGddeZdZGddeZdZGd d!eZ d"Z!Gd#d$eZ"Gd%d&eZ#y')(a# This module contains SymPy functions mathcin corresponding to special math functions in the C standard library (since C99, also available in C++11). The functions defined in this module allows the user to express functions such as ``expm1`` as a SymPy function for symbolic manipulation. )ArgumentIndexErrorFunction)Rational)Pow)S)explog)sqrtc:t|tjz SNrrOnexs ]/home/mcse/projects/flask/flask-venv/lib/python3.12/site-packages/sympy/codegen/cfunctions.py_expm1rs q6AEE>cHeZdZdZdZd dZdZdZeZe dZ dZ dZ y ) expm1a* Represents the exponential function minus one. Explanation =========== The benefit of using ``expm1(x)`` over ``exp(x) - 1`` is that the latter is prone to cancellation under finite precision arithmetic when x is close to zero. Examples ======== >>> from sympy.abc import x >>> from sympy.codegen.cfunctions import expm1 >>> '%.0e' % expm1(1e-99).evalf() '1e-99' >>> from math import exp >>> exp(1e-99) - 1 0.0 >>> expm1(x).diff(x) exp(x) See Also ======== log1p cH|dk(rt|jSt||@ Returns the first derivative of this function. r)rargsrselfargindexs rfdiffz expm1.fdiff4s& q= ? "$T84 4rc &t|jSr )rrrhintss r_eval_expand_funczexpm1._eval_expand_func=tyy!!rc :t|tjz Sr r rargkwargss r_eval_rewrite_as_expzexpm1._eval_rewrite_as_exp@s3x!%%rcXtj|}||tjz Syr )revalrr)clsr&exp_args rr*z expm1.evalEs(((3-  QUU? " rc4|jdjSNr)ris_realrs r _eval_is_realzexpm1._eval_is_realKyy|###rc4|jdjSr.)r is_finiter0s r_eval_is_finitezexpm1._eval_is_finiteNsyy|%%%rNr) __name__ __module__ __qualname____doc__nargsrr"r(_eval_rewrite_as_tractable classmethodr*r1r5rrrrsA8 E5" "6## $&rrc:t|tjzSr )r rrrs r_log1pr@Rs q155y>rcZeZdZdZdZd dZdZdZeZe dZ dZ dZ d Z d Zd Zy )log1paf Represents the natural logarithm of a number plus one. Explanation =========== The benefit of using ``log1p(x)`` over ``log(x + 1)`` is that the latter is prone to cancellation under finite precision arithmetic when x is close to zero. Examples ======== >>> from sympy.abc import x >>> from sympy.codegen.cfunctions import log1p >>> from sympy import expand_log >>> '%.0e' % expand_log(log1p(1e-99)).evalf() '1e-99' >>> from math import log >>> log(1 + 1e-99) 0.0 >>> log1p(x).diff(x) 1/(x + 1) See Also ======== expm1 rc|dk(r1tj|jdtjzz St||rrr)rrrrrs rrz log1p.fdiffws8 q=55$))A,./ /$T84 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_log c{rc|jrt|tjzS|js&tj |tjzS|j r%tt|tjzSyr ) is_Rationalr rris_Floatr* is_numberrr+r&s rr*z log1p.evals^ ??sQUU{# #88C!%%K( ( ]]x}quu,- -rcV|jdtjzjSr.)rrris_nonnegativer0s rr1zlog1p._eval_is_reals ! quu$444rc|jdtjzjry|jdjS)NrF)rrris_zeror4r0s rr5zlog1p._eval_is_finites3 IIaL155 ) )yy|%%%rc4|jdjSr.)r is_positiver0s r_eval_is_positivezlog1p._eval_is_positivesyy|'''rc4|jdjSr.)rrQr0s r _eval_is_zerozlog1p._eval_is_zeror2rc4|jdjSr.)rrOr0s r_eval_is_nonnegativezlog1p._eval_is_nonnegativesyy|***rNr6)r7r8r9r:r;rr"rGr<r=r*r1r5rTrVrXr>rrrBrBVsP: E5""6..5& ($+rrBc"tt|Sr )r_Twors r_exp2r\s tQ<rc<eZdZdZdZddZdZeZdZe dZ y) 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 rcH|dk(r|ttzSt||r)r r[rrs rrz exp2.fdiffs& q=D > !$T84 4rc t|Sr )r\r%s r_eval_rewrite_as_Powzexp2._eval_rewrite_as_Pow Szrc &t|jSr )r\rr s rr"zexp2._eval_expand_funcdii  rc2|jr t|Syr )rLr\rMs rr*z exp2.evals ==:  rNr6) r7r8r9r:r;rrar<r"r=r*r>rrr^r^s92 E5"6!rr^c8t|ttz Sr )r r[rs r_log2rg q6#d) rcBeZdZdZdZd dZedZdZdZ dZ e Z y) log2a Represents the logarithm function with base two. Explanation =========== The benefit of using ``log2(x)`` over ``log(x)/log(2)`` is that the latter is not as efficient under finite precision arithmetic. Examples ======== >>> from sympy.abc import x >>> from sympy.codegen.cfunctions import log2 >>> log2(4).evalf() == 2.0 True >>> log2(x).diff(x) 1/(x*log(2)) See Also ======== exp2 log10 rc|dk(r0tjtt|jdzz St ||rD)rrr r[rrrs rrz log2.fdiff8 q=55#d)DIIaL01 1$T84 4rc|jr*tj|t}|jr|Sy|j r |j tk(r |jSyyN)base)rLr r*r[is_Atomis_Powrorr+r&results rr*z log2.evalL ==XXc-F~~  ZZCHH,77N-ZrcL|jtj|i|Sr )rewriter evalf)rrr's r _eval_evalfzlog2._eval_evalfs#&t||C &&777rc &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>rrrjrjs>4 E58!"6rrjc||z|zSr r>)ryzs r_fmar~s Q37Nrc*eZdZdZdZddZdZddZy) 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 cp|dvr|jd|z S|dk(rtjSt||)rrrYrYr)rrrrrs rrz fma.fdiff6s< v 99Q\* * ]55L$T84 4rc &t|jSr )r~rr s rr"zfma._eval_expand_funcBsTYYrNc t|Sr )r~)rr&limitvarr's rr<zfma._eval_rewrite_as_tractableEs Cyrr6r )r7r8r9r:r;rr"r<r>rrrr s& E 5 rr c8t|ttz Sr )r _Tenrs r_log10rLrhrc<eZdZdZdZddZedZdZdZ e Z y) log10a$ 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|dk(r0tjtt|jdzz St ||rD)rrr rrrrs rrz log10.fdifferlrc|jr*tj|t}|jr|Sy|j r |j tk(r |jSyyrn)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>rrrrPs9$ E5""6rrc6t|tjSr )rrHalfrs r_Sqrtrs q!&&>rc,eZdZdZdZddZdZdZeZy)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 rcx|dk(r*t|jdtddtz St ||)rrrrYrrrr[rrs rrz Sqrt.fdiffs8 q=tyy|Xb!_5d: :$T84 4rc &t|jSr )rrr s rr"zSqrt._eval_expand_funcrdrc t|Sr )rr%s rrazSqrt._eval_rewrite_as_PowrbrNr6 r7r8r9r:r;rr"rar<r>rrrrs%2 E5!"6rrc.t|tddS)Nrr)rrrs r_Cbrtrs q(1a. !!rc,eZdZdZdZddZdZdZeZy)Cbrta Represents the cube root function. Explanation =========== The reason why one would use ``Cbrt(x)`` over ``cbrt(x)`` is that the latter is internally represented as ``Pow(x, Rational(1, 3))`` which may not be what one wants when doing code-generation. Examples ======== >>> from sympy.abc import x >>> from sympy.codegen.cfunctions import Cbrt >>> Cbrt(x) Cbrt(x) >>> Cbrt(x).diff(x) 1/(3*x**(2/3)) See Also ======== Sqrt rc~|dk(r-t|jdtt dz dz St ||)rrrrrrs rrz Cbrt.fdiffs= q=tyy|XteAg%679 9$T84 4rc &t|jSr )rrr s rr"zCbrt._eval_expand_funcrdrc t|Sr )rr%s rrazCbrt._eval_rewrite_as_PowrbrNr6rr>rrrrs%2 E5!"6rrcFtt|dt|dzS)NrY)r r)rr|s r_hypotrs Aq C1I% &&rc,eZdZdZdZddZdZdZeZy)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) rYc|dvr6d|j|dz zt|j|jzz St||)rrrYr)rr[funcrrs rrz hypot.fdiffsJ v TYYxz**DDII1F,FG G$T84 4rc &t|jSr )rrr s rr"zhypot._eval_expand_funcr#rc t|Sr )rr%s rrazhypot._eval_rewrite_as_PowrHrNr6rr>rrrrs%. E5""6rrceZdZdZy)isnanrN)r7r8r9r;r>rrrrs ErrN)$r:sympy.core.functionrrsympy.core.numbersrsympy.core.powerrsympy.core.singletonr&sympy.functions.elementary.exponentialrr (sympy.functions.elementary.miscellaneousr rrr@rBr[r\r^rgrjr~rrrrrrrrrrrr>rrrs=' ";9:&H:&zK+HK+Z t181h96896x&(&R u.6H.6b+68+6\",68,6^'*6H*6ZHr