ó ¡¼™\c@s¥dZddlmZmZddlmZddlmZddlm Z ddl m Z m Z ddl mZd„Zd efd „ƒYZd „Zd efd „ƒYZe dƒZd„Zdefd„ƒYZd„Zdefd„ƒYZd„Zdefd„ƒYZe dƒZd„Zdefd„ƒYZd„Zdefd„ƒYZd„Zd efd!„ƒYZ d"„Z!d#efd$„ƒYZ"d%S(&s# 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. iÿÿÿÿ(tArgumentIndexErrortFunction(tRational(tPow(tS(texptlog(tsqrtcCst|ƒtjS(N(RRtOne(tx((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyt_expm1stexpm1cBsYeZdZdZdd„Zd„Zd„ZeZed„ƒZ d„Z d„Z RS(s 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 icCs,|dkrt|jŒSt||ƒ‚dS(s@ Returns the first derivative of this function. iN(RtargsR(tselftargindex((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pytfdiff1s  cKs t|jŒS(N(R R (R thints((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyt_eval_expand_func:scKst|ƒtjS(N(RRR(R targtkwargs((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyt_eval_rewrite_as_exp=scCs*tj|ƒ}|dk r&|tjSdS(N(RtevaltNoneRR(tclsRtexp_arg((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyRBs cCs|jdjS(Ni(R tis_real(R ((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyt _eval_is_realHscCs|jdjS(Ni(R t is_finite(R ((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyt_eval_is_finiteKs( t__name__t __module__t__doc__tnargsRRRt_eval_rewrite_as_tractablet classmethodRRR(((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyR s   cCst|tjƒS(N(RRR(R ((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyt_log1pOstlog1pcBsteZdZdZdd„Zd„Zd„ZeZed„ƒZ d„Z d„Z d„Z d „Z d „ZRS( sS 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 icCs8|dkr%tj|jdtjSt||ƒ‚dS(s@ Returns the first derivative of this function. iiN(RRR R(R R((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyRqs cKs t|jŒS(N(R#R (R R((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyR{scKs t|ƒS(N(R#(R RR((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyt_eval_rewrite_as_log~scCs[|jrt|tjƒS|js7tj|tjƒS|jrWtt|ƒtjƒSdS(N(t is_RationalRRRtis_FloatRt is_numberR(RR((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyRƒs    cCs|jdtjjS(Ni(R RRtis_nonnegative(R ((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyRŒscCs)|jdtjjrtS|jdjS(Ni(R RRtis_zerotFalseR(R ((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyRscCs|jdjS(Ni(R t is_positive(R ((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyt_eval_is_positive”scCs|jdjS(Ni(R R*(R ((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyt _eval_is_zero—scCs|jdjS(Ni(R R)(R ((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyt_eval_is_nonnegativešs(RRRR RRR%R!R"RRRR-R.R/(((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyR$Ss      icCs tt|ƒS(N(Rt_Two(R ((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyt_exp2Ÿstexp2cBsGeZdZdZdd„Zd„ZeZd„Zed„ƒZ RS(s¦ 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 icCs-|dkr|ttƒSt||ƒ‚dS(s@ Returns the first derivative of this function. iN(RR0R(R R((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyR¼s cKs t|ƒS(N(R1(R RR((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyt_eval_rewrite_as_PowÅscKs t|jŒS(N(R1R (R R((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyRÊscCs|jrt|ƒSdS(N(R(R1(RR((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyRÍs ( RRRR RR3R!RR"R(((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyR2¢s  cCst|ƒttƒS(N(RR0(R ((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyt_log2Óstlog2cBsGeZdZdZdd„Zed„ƒZd„Zd„ZeZ RS(sµ 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 icCs;|dkr(tjttƒ|jdSt||ƒ‚dS(s@ Returns the first derivative of this function. iiN(RRRR0R R(R R((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyRñs cCsQ|jr.tj|dtƒ}|jrM|Sn|jrM|jtkrM|jSdS(Ntbase(R(RRR0tis_Atomtis_PowR6R(RRtresult((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyRûs   cKs t|jŒS(N(R4R (R R((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyRscKs t|ƒS(N(R4(R RR((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyR%s( RRRR RR"RRR%R!(((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyR5×s   cCs |||S(N((R tytz((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyt_fma stfmacBs2eZdZdZdd„Zd„Zd„ZRS(so 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 iicCsA|dkr|jd|S|dkr.tjSt||ƒ‚dS(s@ Returns the first derivative of this function. iiiN(ii(R RRR(R R((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyR$s   cKs t|jŒS(N(R<R (R R((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyR0scKs t|ƒS(N(R<(R RR((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyR!3s(RRRR RRR!(((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyR=s  i cCst|ƒttƒS(N(Rt_Ten(R ((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyt_log10:stlog10cBsGeZdZdZdd„Zed„ƒZd„Zd„ZeZ RS(s" 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 icCs;|dkr(tjttƒ|jdSt||ƒ‚dS(s@ Returns the first derivative of this function. iiN(RRRR>R R(R R((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyRSs cCsQ|jr.tj|dtƒ}|jrM|Sn|jrM|jtkrM|jSdS(NR6(R(RRR>R7R8R6R(RRR9((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyR]s   cKs t|jŒS(N(R?R (R R((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyRfscKs t|ƒS(N(R?(R RR((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyR%is( RRRR RR"RRR%R!(((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyR@>s   cCst|tjƒS(N(RRtHalf(R ((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyt_SqrtostSqrtcBs8eZdZdZdd„Zd„Zd„ZeZRS(sÍ 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 icCs;|dkr(t|jdtj ƒtSt||ƒ‚dS(s@ Returns the first derivative of this function. iiN(RR RRAR0R(R R((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyRŒs cKs t|jŒS(N(RBR (R R((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyR•scKs t|ƒS(N(RB(R RR((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyR3˜s(RRRR RRR3R!(((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyRCss   cCst|tddƒƒS(Nii(RR(R ((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyt_CbrtžstCbrtcBs8eZdZdZdd„Zd„Zd„ZeZRS(sÔ 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 icCsB|dkr/t|jdtt dƒƒdSt||ƒ‚dS(s@ Returns the first derivative of this function. iiiN(RR RR0R(R R((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyR»s #cKs t|jŒS(N(RDR (R R((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyRÅscKs t|ƒS(N(RD(R RR((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyR3Ès(RRRR RRR3R!(((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyRE¢s   cCs tt|dƒt|dƒƒS(Ni(RR(R R:((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyt_hypotÎsthypotcBs8eZdZdZdd„Zd„Zd„ZeZRS(sÑ 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) iicCsF|dkr3d|j|dt|j|jŒSt||ƒ‚dS(s@ Returns the first derivative of this function. iiN(ii(R R0tfuncR(R R((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyRés 'cKs t|jŒS(N(RFR (R R((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyRóscKs t|ƒS(N(RF(R RR((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyR3ös(RRRR RRR3R!(((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyRGÒs   N(#Rtsympy.core.functionRRtsympy.core.numbersRtsympy.core.powerRtsympy.core.singletonRt&sympy.functions.elementary.exponentialRRt(sympy.functions.elementary.miscellaneousRR R R#R$R0R1R2R4R5R<R=R>R?R@RBRCRDRERFRG(((s7lib/python2.7/site-packages/sympy/codegen/cfunctions.pyts4 9 J  1 6 &  1 + ,