B ˜‘[[,ใ@sLdZddlZddlmZddlmZddlmZmZm Z ddl m Z ddl m Z ddlmZmZd d „ZGd d „d eƒZd d„ZGdd„deƒZedƒZdd„ZGdd„deƒZdd„ZGdd„deƒZdd„ZGdd„deƒZedƒZdd „ZGd!d"„d"eƒZd#d$„ZGd%d&„d&eƒZ d'd(„Z!Gd)d*„d*eƒZ"d+d,„Z#Gd-d.„d.eƒZ$dS)/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. ้N)ฺS)ฺRational)ฺArgumentIndexErrorฺFunctionฺLambda)ฺPow)ฺsqrt)ฺexpฺlogcCst|ƒtjS)N)r rฺOne)ฺxฉr ๚7lib/python3.7/site-packages/sympy/codegen/cfunctions.pyฺ_expm1src@sNeZdZdZdZddd„Zdd„Zdd„ZeZe d d „ƒZ d d „Z d d„Z dS)ฺexpm1a Represents the exponential function minus one. 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 ้cCs |dkrt|jŽSt||ƒ‚dS)z@ Returns the first derivative of this function. rN)r ฺargsr)ฺselfฺargindexr r rฺfdiff2s z expm1.fdiffcKs t|jŽS)N)rr)rฺhintsr r rฺ_eval_expand_func;szexpm1._eval_expand_funccCst|ƒtjS)N)r rr )rฺargr r rฺ_eval_rewrite_as_exp>szexpm1._eval_rewrite_as_expcCs t |ก}|dk r|tjSdS)N)r ฺevalrr )ฺclsrZexp_argr r rrCs z expm1.evalcCs |jdjS)Nr)rZis_real)rr r rฺ _eval_is_realIszexpm1._eval_is_realcCs |jdjS)Nr)rฺ is_finite)rr r rฺ_eval_is_finiteLszexpm1._eval_is_finiteN)r) ฺ__name__ฺ __module__ฺ __qualname__ฺ__doc__ฺnargsrrrฺ_eval_rewrite_as_tractableฺ classmethodrrrr r r rrs  rcCst|tjƒS)N)r rr )r r r rฺ_log1pPsr&c@sfeZdZdZdZddd„Zdd„Zdd„ZeZe d d „ƒZ d d „Z d d„Z dd„Z dd„Zdd„ZdS)ฺlog1paS Represents the natural logarithm of a number plus one. 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.core.function 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 rcCs,|dkrtj|jdtjSt||ƒ‚dS)z@ Returns the first derivative of this function. rrN)rr rr)rrr r rrrsz log1p.fdiffcKs t|jŽS)N)r&r)rrr r rr|szlog1p._eval_expand_funccCst|ƒS)N)r&)rrr r rฺ_eval_rewrite_as_logszlog1p._eval_rewrite_as_logcCsF|jrt|tjƒS|js*t |tjกS|jrBtt|ƒtjƒSdS)N)Z is_Rationalr rr Zis_Floatrฺ is_numberr)rrr r rr„s z log1p.evalcCs|jdtjjS)Nr)rrr ฺis_nonnegative)rr r rrszlog1p._eval_is_realcCs"|jdtjjrdS|jdjS)NrF)rrr ฺis_zeror)rr r rrszlog1p._eval_is_finitecCs |jdjS)Nr)rZ is_positive)rr r rฺ_eval_is_positive•szlog1p._eval_is_positivecCs |jdjS)Nr)rr+)rr r rฺ _eval_is_zero˜szlog1p._eval_is_zerocCs |jdjS)Nr)rr*)rr r rฺ_eval_is_nonnegative›szlog1p._eval_is_nonnegativeN)r)rr r!r"r#rrr(r$r%rrrr,r-r.r r r rr'Ts  r'้cCs tt|ƒS)N)rฺ_Two)r r r rฺ_exp2 sr1c@s>eZdZdZdZd dd„Zdd„ZeZdd„Ze d d „ƒZ d S) ฺexp2aฅ Represents the exponential function with base two. The benefit of using ``exp2(x)`` over ``2**x`` is that the latter is not as efficient under finite precision arithmetic. Examples ======== >>> from sympy.abc import x >>> from sympy.codegen.cfunctions import exp2 >>> exp2(2).evalf() == 4 True >>> exp2(x).diff(x) log(2)*exp2(x) See Also ======== log2 rcCs"|dkr|ttƒSt||ƒ‚dS)z@ Returns the first derivative of this function. rN)r r0r)rrr r rrผs z exp2.fdiffcCst|ƒS)N)r1)rrr r rฺ_eval_rewrite_as_Powลszexp2._eval_rewrite_as_PowcKs t|jŽS)N)r1r)rrr r rrสszexp2._eval_expand_funccCs|jrt|ƒSdS)N)r)r1)rrr r rrอsz exp2.evalN)r) rr r!r"r#rr3r$rr%rr r r rr2ฃs r2cCst|ƒttƒS)N)r r0)r r r rฺ_log2ำsr4c@s>eZdZdZdZd dd„Zedd„ƒZdd„Zd d „Z e Z d S) ฺlog2aด Represents the logarithm function with base two. 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 rcCs.|dkr tjttƒ|jdSt||ƒ‚dS)z@ Returns the first derivative of this function. rrN)rr r r0rr)rrr r rr๐sz log2.fdiffcCs:|jr tj|td}|jr6|Sn|jr6|jtkr6|jSdS)N)ฺbase)r)r rr0ฺis_Atomฺis_Powr6r )rrฺresultr r rr๚s z log2.evalcKs t|jŽS)N)r4r)rrr r rrszlog2._eval_expand_funccCst|ƒS)N)r4)rrr r rr(szlog2._eval_rewrite_as_logN)r) rr r!r"r#rr%rrr(r$r r r rr5ืs r5cCs |||S)Nr )r ฺyฺzr r rฺ_fma sr<c@s.eZdZdZdZd dd„Zdd„Zdd „Zd S) ฺfmaan Represents "fused multiply add". The benefit of using ``fma(x, y, z)`` over ``x*y + z`` is that, under finite precision arithmetic, the former is supported by special instructions on some CPUs. Examples ======== >>> from sympy.abc import x, y, z >>> from sympy.codegen.cfunctions import fma >>> fma(x, y, z).diff(x) y ้rcCs2|dkr|jd|S|dkr$tjSt||ƒ‚dS)z@ Returns the first derivative of this function. )rr/r/r>N)rrr r)rrr r rr"s z fma.fdiffcKs t|jŽS)N)r<r)rrr r rr.szfma._eval_expand_funccCst|ƒS)N)r<)rrr r rr$1szfma._eval_rewrite_as_tractableN)r)rr r!r"r#rrr$r r r rr=s  r=้ cCst|ƒttƒS)N)r ฺ_Ten)r r r rฺ_log108srAc@s>eZdZdZdZd dd„Zedd„ƒZdd„Zd d „Z e Z d S) ฺ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 rcCs.|dkr tjttƒ|jdSt||ƒ‚dS)z@ Returns the first derivative of this function. rrN)rr r r@rr)rrr r rrPsz log10.fdiffcCs:|jr tj|td}|jr6|Sn|jr6|jtkr6|jSdS)N)r6)r)r rr@r7r8r6r )rrr9r r rrZs z log10.evalcKs t|jŽS)N)rAr)rrr r rrcszlog10._eval_expand_funccCst|ƒS)N)rA)rrr r rr(fszlog10._eval_rewrite_as_logN)r) rr r!r"r#rr%rrr(r$r r r rrB<s rBcCs t|tjƒS)N)rrฺHalf)r r r rฺ_SqrtlsrDc@s2eZdZdZdZd dd„Zdd„Zdd„ZeZd S) ฺSqrtaฬ Represents the square root function. The reason why one would use ``Sqrt(x)`` over ``sqrt(x)`` is that the latter is internally represented as ``Pow(x, S.Half)`` which may not be what one wants when doing code-generation. Examples ======== >>> from sympy.abc import x >>> from sympy.codegen.cfunctions import Sqrt >>> Sqrt(x) Sqrt(x) >>> Sqrt(x).diff(x) 1/(2*sqrt(x)) See Also ======== Cbrt rcCs.|dkr t|jdtj ƒtSt||ƒ‚dS)z@ Returns the first derivative of this function. rrN)rrrrCr0r)rrr r rrˆsz Sqrt.fdiffcKs t|jŽS)N)rDr)rrr r rr‘szSqrt._eval_expand_funccCst|ƒS)N)rD)rrr r rr3”szSqrt._eval_rewrite_as_PowN)r) rr r!r"r#rrr3r$r r r rrEps  rEcCst|tddƒƒS)Nrr>)rr)r r r rฺ_CbrtšsrFc@s2eZdZdZdZd dd„Zdd„Zdd„ZeZd S) ฺCbrtaิ Represents the cube root function. 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 rcCs4|dkr&t|jdtt dƒƒdSt||ƒ‚dS)z@ Returns the first derivative of this function. rrr>N)rrrr0r)rrr r rrทsz Cbrt.fdiffcKs t|jŽS)N)rFr)rrr r rrมszCbrt._eval_expand_funccCst|ƒS)N)rF)rrr r rr3ฤszCbrt._eval_rewrite_as_PowN)r) rr r!r"r#rrr3r$r r r rrGžs  rGcCstt|dƒt|dƒƒS)Nr/)rr)r r:r r rฺ_hypotสsrHc@s2eZdZdZdZd dd„Zdd„Zdd „ZeZd S) ฺhypotaั Represents the hypotenuse function. The hypotenuse function is provided by e.g. the math library in the C99 standard, hence one may want to represent the function symbolically when doing code-generation. Examples ======== >>> from sympy.abc import x, y >>> from sympy.codegen.cfunctions import hypot >>> hypot(3, 4).evalf() == 5 True >>> hypot(x, y) hypot(x, y) >>> hypot(x, y).diff(x) x/hypot(x, y) r/rcCs8|dkr*d|j|dt|j|jŽSt||ƒ‚dS)z@ Returns the first derivative of this function. )rr/r/rN)rr0ฺfuncr)rrr r rrๅs"z hypot.fdiffcKs t|jŽS)N)rHr)rrr r rr๏szhypot._eval_expand_funccCst|ƒS)N)rH)rrr r rr3๒szhypot._eval_rewrite_as_PowN)r) rr r!r"r#rrr3r$r r r rrIฮs  rI)%r"ZmathZsympy.core.singletonrZsympy.core.numbersrZsympy.core.functionrrrZsympy.core.powerrZ(sympy.functions.elementary.miscellaneousrZ&sympy.functions.elementary.exponentialr r rrr&r'r0r1r2r4r5r<r=r@rArBrDrErFrGrHrIr r r rฺs6    9J05%0*,