From 57eee7251bfb133ed405a65c3a538e22e74d5b23 Mon Sep 17 00:00:00 2001 From: "mark.dickinson" Date: Mon, 21 Dec 2009 15:22:00 +0000 Subject: [PATCH] Issue #7518: Move substitute definitions of C99 math functions from pymath.c to Modules/_math.c. git-svn-id: http://svn.python.org/projects/python/trunk@76978 6015fed2-1504-0410-9fe1-9d1591cc4771 --- Include/pymath.h | 22 +-- Modules/Setup.dist | 2 +- Python/pymath.c => Modules/_math.c | 280 ++++++++++++----------------- Modules/_math.h | 36 ++++ Modules/cmathmodule.c | 11 +- Modules/mathmodule.c | 8 +- Python/pymath.c | 357 ++++++++----------------------------- setup.py | 4 +- 8 files changed, 246 insertions(+), 474 deletions(-) copy Python/pymath.c => Modules/_math.c (52%) rewrite Python/pymath.c (76%) diff --git a/Include/pymath.h b/Include/pymath.h index dc2c427944..e3cf22b823 100644 --- a/Include/pymath.h +++ b/Include/pymath.h @@ -8,9 +8,9 @@ Symbols and macros to supply platform-independent interfaces to mathematical functions and constants **************************************************************************/ -/* Python provides implementations for copysign, acosh, asinh, atanh, - * log1p and hypot in Python/pymath.c just in case your math library doesn't - * provide the functions. +/* Python provides implementations for copysign, round and hypot in + * Python/pymath.c just in case your math library doesn't provide the + * functions. * *Note: PC/pyconfig.h defines copysign as _copysign */ @@ -22,22 +22,6 @@ extern double copysign(double, double); extern double round(double); #endif -#ifndef HAVE_ACOSH -extern double acosh(double); -#endif - -#ifndef HAVE_ASINH -extern double asinh(double); -#endif - -#ifndef HAVE_ATANH -extern double atanh(double); -#endif - -#ifndef HAVE_LOG1P -extern double log1p(double); -#endif - #ifndef HAVE_HYPOT extern double hypot(double, double); #endif diff --git a/Modules/Setup.dist b/Modules/Setup.dist index 3a6c973b2a..e76e0dfe8f 100644 --- a/Modules/Setup.dist +++ b/Modules/Setup.dist @@ -168,7 +168,7 @@ GLHACK=-Dclear=__GLclear # Modules that should always be present (non UNIX dependent): #array arraymodule.c # array objects -#cmath cmathmodule.c # -lm # complex math library functions +#cmath cmathmodule.c _math.c # -lm # complex math library functions #math mathmodule.c _math.c # -lm # math library functions, e.g. sin() #_struct _struct.c # binary structure packing/unpacking #time timemodule.c # -lm # time operations and variables diff --git a/Python/pymath.c b/Modules/_math.c similarity index 52% copy from Python/pymath.c copy to Modules/_math.c index db2920ce20..e27c10092b 100644 --- a/Python/pymath.c +++ b/Modules/_math.c @@ -1,126 +1,11 @@ -#include "Python.h" - -#ifdef X87_DOUBLE_ROUNDING -/* On x86 platforms using an x87 FPU, this function is called from the - Py_FORCE_DOUBLE macro (defined in pymath.h) to force a floating-point - number out of an 80-bit x87 FPU register and into a 64-bit memory location, - thus rounding from extended precision to double precision. */ -double _Py_force_double(double x) -{ - volatile double y; - y = x; - return y; -} -#endif - -#ifdef HAVE_GCC_ASM_FOR_X87 - -/* inline assembly for getting and setting the 387 FPU control word on - gcc/x86 */ - -unsigned short _Py_get_387controlword(void) { - unsigned short cw; - __asm__ __volatile__ ("fnstcw %0" : "=m" (cw)); - return cw; -} - -void _Py_set_387controlword(unsigned short cw) { - __asm__ __volatile__ ("fldcw %0" : : "m" (cw)); -} - -#endif - - -#ifndef HAVE_HYPOT -double hypot(double x, double y) -{ - double yx; +/* Definitions of some C99 math library functions, for those platforms + that don't implement these functions already. */ - x = fabs(x); - y = fabs(y); - if (x < y) { - double temp = x; - x = y; - y = temp; - } - if (x == 0.) - return 0.; - else { - yx = y/x; - return x*sqrt(1.+yx*yx); - } -} -#endif /* HAVE_HYPOT */ - -#ifndef HAVE_COPYSIGN -double -copysign(double x, double y) -{ - /* use atan2 to distinguish -0. from 0. */ - if (y > 0. || (y == 0. && atan2(y, -1.) > 0.)) { - return fabs(x); - } else { - return -fabs(x); - } -} -#endif /* HAVE_COPYSIGN */ - -#ifndef HAVE_ROUND -double -round(double x) -{ - double absx, y; - absx = fabs(x); - y = floor(absx); - if (absx - y >= 0.5) - y += 1.0; - return copysign(y, x); -} -#endif /* HAVE_ROUND */ - -#ifndef HAVE_LOG1P +#include "Python.h" #include -double -log1p(double x) -{ - /* For x small, we use the following approach. Let y be the nearest - float to 1+x, then - - 1+x = y * (1 - (y-1-x)/y) - - so log(1+x) = log(y) + log(1-(y-1-x)/y). Since (y-1-x)/y is tiny, - the second term is well approximated by (y-1-x)/y. If abs(x) >= - DBL_EPSILON/2 or the rounding-mode is some form of round-to-nearest - then y-1-x will be exactly representable, and is computed exactly - by (y-1)-x. - - If abs(x) < DBL_EPSILON/2 and the rounding mode is not known to be - round-to-nearest then this method is slightly dangerous: 1+x could - be rounded up to 1+DBL_EPSILON instead of down to 1, and in that - case y-1-x will not be exactly representable any more and the - result can be off by many ulps. But this is easily fixed: for a - floating-point number |x| < DBL_EPSILON/2., the closest - floating-point number to log(1+x) is exactly x. - */ - - double y; - if (fabs(x) < DBL_EPSILON/2.) { - return x; - } else if (-0.5 <= x && x <= 1.) { - /* WARNING: it's possible than an overeager compiler - will incorrectly optimize the following two lines - to the equivalent of "return log(1.+x)". If this - happens, then results from log1p will be inaccurate - for small x. */ - y = 1.+x; - return log(y)-((y-1.)-x)/y; - } else { - /* NaNs and infinities should end up here */ - return log(1.+x); - } -} -#endif /* HAVE_LOG1P */ +/* The following copyright notice applies to the original + implementations of acosh, asinh and atanh. */ /* * ==================================================== @@ -138,45 +23,6 @@ static const double two_pow_m28 = 3.7252902984619141E-09; /* 2**-28 */ static const double two_pow_p28 = 268435456.0; /* 2**28 */ static const double zero = 0.0; -/* asinh(x) - * Method : - * Based on - * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] - * we have - * asinh(x) := x if 1+x*x=1, - * := sign(x)*(log(x)+ln2)) for large |x|, else - * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else - * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) - */ - -#ifndef HAVE_ASINH -double -asinh(double x) -{ - double w; - double absx = fabs(x); - - if (Py_IS_NAN(x) || Py_IS_INFINITY(x)) { - return x+x; - } - if (absx < two_pow_m28) { /* |x| < 2**-28 */ - return x; /* return x inexact except 0 */ - } - if (absx > two_pow_p28) { /* |x| > 2**28 */ - w = log(absx)+ln2; - } - else if (absx > 2.0) { /* 2 < |x| < 2**28 */ - w = log(2.0*absx + 1.0 / (sqrt(x*x + 1.0) + absx)); - } - else { /* 2**-28 <= |x| < 2= */ - double t = x*x; - w = log1p(absx + t / (1.0 + sqrt(1.0 + t))); - } - return copysign(w, x); - -} -#endif /* HAVE_ASINH */ - /* acosh(x) * Method : * Based on @@ -191,9 +37,8 @@ asinh(double x) * acosh(NaN) is NaN without signal. */ -#ifndef HAVE_ACOSH double -acosh(double x) +_Py_acosh(double x) { if (Py_IS_NAN(x)) { return x+x; @@ -225,7 +70,44 @@ acosh(double x) return log1p(t + sqrt(2.0*t + t*t)); } } -#endif /* HAVE_ACOSH */ + + +/* asinh(x) + * Method : + * Based on + * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] + * we have + * asinh(x) := x if 1+x*x=1, + * := sign(x)*(log(x)+ln2)) for large |x|, else + * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else + * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) + */ + +double +_Py_asinh(double x) +{ + double w; + double absx = fabs(x); + + if (Py_IS_NAN(x) || Py_IS_INFINITY(x)) { + return x+x; + } + if (absx < two_pow_m28) { /* |x| < 2**-28 */ + return x; /* return x inexact except 0 */ + } + if (absx > two_pow_p28) { /* |x| > 2**28 */ + w = log(absx)+ln2; + } + else if (absx > 2.0) { /* 2 < |x| < 2**28 */ + w = log(2.0*absx + 1.0 / (sqrt(x*x + 1.0) + absx)); + } + else { /* 2**-28 <= |x| < 2= */ + double t = x*x; + w = log1p(absx + t / (1.0 + sqrt(1.0 + t))); + } + return copysign(w, x); + +} /* atanh(x) * Method : @@ -244,9 +126,8 @@ acosh(double x) * */ -#ifndef HAVE_ATANH double -atanh(double x) +_Py_atanh(double x) { double absx; double t; @@ -275,4 +156,73 @@ atanh(double x) } return copysign(t, x); } -#endif /* HAVE_ATANH */ + +/* Mathematically, expm1(x) = exp(x) - 1. The expm1 function is designed + to avoid the significant loss of precision that arises from direct + evaluation of the expression exp(x) - 1, for x near 0. */ + +double +_Py_expm1(double x) +{ + /* For abs(x) >= log(2), it's safe to evaluate exp(x) - 1 directly; this + also works fine for infinities and nans. + + For smaller x, we can use a method due to Kahan that achieves close to + full accuracy. + */ + + if (fabs(x) < 0.7) { + double u; + u = exp(x); + if (u == 1.0) + return x; + else + return (u - 1.0) * x / log(u); + } + else + return exp(x) - 1.0; +} + +/* log1p(x) = log(1+x). The log1p function is designed to avoid the + significant loss of precision that arises from direct evaluation when x is + small. */ + +double +_Py_log1p(double x) +{ + /* For x small, we use the following approach. Let y be the nearest float + to 1+x, then + + 1+x = y * (1 - (y-1-x)/y) + + so log(1+x) = log(y) + log(1-(y-1-x)/y). Since (y-1-x)/y is tiny, the + second term is well approximated by (y-1-x)/y. If abs(x) >= + DBL_EPSILON/2 or the rounding-mode is some form of round-to-nearest + then y-1-x will be exactly representable, and is computed exactly by + (y-1)-x. + + If abs(x) < DBL_EPSILON/2 and the rounding mode is not known to be + round-to-nearest then this method is slightly dangerous: 1+x could be + rounded up to 1+DBL_EPSILON instead of down to 1, and in that case + y-1-x will not be exactly representable any more and the result can be + off by many ulps. But this is easily fixed: for a floating-point + number |x| < DBL_EPSILON/2., the closest floating-point number to + log(1+x) is exactly x. + */ + + double y; + if (fabs(x) < DBL_EPSILON/2.) { + return x; + } else if (-0.5 <= x && x <= 1.) { + /* WARNING: it's possible than an overeager compiler + will incorrectly optimize the following two lines + to the equivalent of "return log(1.+x)". If this + happens, then results from log1p will be inaccurate + for small x. */ + y = 1.+x; + return log(y)-((y-1.)-x)/y; + } else { + /* NaNs and infinities should end up here */ + return log(1.+x); + } +} diff --git a/Modules/_math.h b/Modules/_math.h index 69c96b5ab7..c0ceece662 100644 --- a/Modules/_math.h +++ b/Modules/_math.h @@ -1,4 +1,32 @@ +double _Py_acosh(double x); +double _Py_asinh(double x); +double _Py_atanh(double x); double _Py_expm1(double x); +double _Py_log1p(double x); + +#ifdef HAVE_ACOSH +#define m_acosh acosh +#else +/* if the system doesn't have acosh, use the substitute + function defined in Modules/_math.c. */ +#define m_acosh _Py_acosh +#endif + +#ifdef HAVE_ASINH +#define m_asinh asinh +#else +/* if the system doesn't have asinh, use the substitute + function defined in Modules/_math.c. */ +#define m_asinh _Py_asinh +#endif + +#ifdef HAVE_ATANH +#define m_atanh atanh +#else +/* if the system doesn't have atanh, use the substitute + function defined in Modules/_math.c. */ +#define m_atanh _Py_atanh +#endif #ifdef HAVE_EXPM1 #define m_expm1 expm1 @@ -7,3 +35,11 @@ double _Py_expm1(double x); function defined in Modules/_math.c. */ #define m_expm1 _Py_expm1 #endif + +#ifdef HAVE_LOG1P +#define m_log1p log1p +#else +/* if the system doesn't have log1p, use the substitute + function defined in Modules/_math.c. */ +#define m_log1p _Py_log1p +#endif diff --git a/Modules/cmathmodule.c b/Modules/cmathmodule.c index 7b2e316d15..788a19dad5 100644 --- a/Modules/cmathmodule.c +++ b/Modules/cmathmodule.c @@ -3,6 +3,7 @@ /* much code borrowed from mathmodule.c */ #include "Python.h" +#include "_math.h" /* we need DBL_MAX, DBL_MIN, DBL_EPSILON, DBL_MANT_DIG and FLT_RADIX from float.h. We assume that FLT_RADIX is either 2 or 16. */ #include @@ -149,7 +150,7 @@ c_acos(Py_complex z) s2.imag = z.imag; s2 = c_sqrt(s2); r.real = 2.*atan2(s1.real, s2.real); - r.imag = asinh(s2.real*s1.imag - s2.imag*s1.real); + r.imag = m_asinh(s2.real*s1.imag - s2.imag*s1.real); } errno = 0; return r; @@ -181,7 +182,7 @@ c_acosh(Py_complex z) s2.real = z.real + 1.; s2.imag = z.imag; s2 = c_sqrt(s2); - r.real = asinh(s1.real*s2.real + s1.imag*s2.imag); + r.real = m_asinh(s1.real*s2.real + s1.imag*s2.imag); r.imag = 2.*atan2(s1.imag, s2.real); } errno = 0; @@ -238,7 +239,7 @@ c_asinh(Py_complex z) s2.real = 1.-z.imag; s2.imag = z.real; s2 = c_sqrt(s2); - r.real = asinh(s1.real*s2.imag-s2.real*s1.imag); + r.real = m_asinh(s1.real*s2.imag-s2.real*s1.imag); r.imag = atan2(z.imag, s1.real*s2.real-s1.imag*s2.imag); } errno = 0; @@ -342,7 +343,7 @@ c_atanh(Py_complex z) errno = 0; } } else { - r.real = log1p(4.*z.real/((1-z.real)*(1-z.real) + ay*ay))/4.; + r.real = m_log1p(4.*z.real/((1-z.real)*(1-z.real) + ay*ay))/4.; r.imag = -atan2(-2.*z.imag, (1-z.real)*(1+z.real) - ay*ay)/2.; errno = 0; } @@ -552,7 +553,7 @@ c_log(Py_complex z) if (0.71 <= h && h <= 1.73) { am = ax > ay ? ax : ay; /* max(ax, ay) */ an = ax > ay ? ay : ax; /* min(ax, ay) */ - r.real = log1p((am-1)*(am+1)+an*an)/2.; + r.real = m_log1p((am-1)*(am+1)+an*an)/2.; } else { r.real = log(h); } diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c index a7299a5ce8..6eb9e9175d 100644 --- a/Modules/mathmodule.c +++ b/Modules/mathmodule.c @@ -799,18 +799,18 @@ math_2(PyObject *args, double (*func) (double, double), char *funcname) FUNC1(acos, acos, 0, "acos(x)\n\nReturn the arc cosine (measured in radians) of x.") -FUNC1(acosh, acosh, 0, +FUNC1(acosh, m_acosh, 0, "acosh(x)\n\nReturn the hyperbolic arc cosine (measured in radians) of x.") FUNC1(asin, asin, 0, "asin(x)\n\nReturn the arc sine (measured in radians) of x.") -FUNC1(asinh, asinh, 0, +FUNC1(asinh, m_asinh, 0, "asinh(x)\n\nReturn the hyperbolic arc sine (measured in radians) of x.") FUNC1(atan, atan, 0, "atan(x)\n\nReturn the arc tangent (measured in radians) of x.") FUNC2(atan2, m_atan2, "atan2(y, x)\n\nReturn the arc tangent (measured in radians) of y/x.\n" "Unlike atan(y/x), the signs of both x and y are considered.") -FUNC1(atanh, atanh, 0, +FUNC1(atanh, m_atanh, 0, "atanh(x)\n\nReturn the hyperbolic arc tangent (measured in radians) of x.") FUNC1(ceil, ceil, 0, "ceil(x)\n\nReturn the ceiling of x as a float.\n" @@ -840,7 +840,7 @@ FUNC1A(gamma, m_tgamma, "gamma(x)\n\nGamma function at x.") FUNC1A(lgamma, m_lgamma, "lgamma(x)\n\nNatural logarithm of absolute value of Gamma function at x.") -FUNC1(log1p, log1p, 1, +FUNC1(log1p, m_log1p, 1, "log1p(x)\n\nReturn the natural logarithm of 1+x (base e).\n" "The result is computed in a way which is accurate for x near zero.") FUNC1(sin, sin, 0, diff --git a/Python/pymath.c b/Python/pymath.c dissimilarity index 76% index db2920ce20..83105f2668 100644 --- a/Python/pymath.c +++ b/Python/pymath.c @@ -1,278 +1,79 @@ -#include "Python.h" - -#ifdef X87_DOUBLE_ROUNDING -/* On x86 platforms using an x87 FPU, this function is called from the - Py_FORCE_DOUBLE macro (defined in pymath.h) to force a floating-point - number out of an 80-bit x87 FPU register and into a 64-bit memory location, - thus rounding from extended precision to double precision. */ -double _Py_force_double(double x) -{ - volatile double y; - y = x; - return y; -} -#endif - -#ifdef HAVE_GCC_ASM_FOR_X87 - -/* inline assembly for getting and setting the 387 FPU control word on - gcc/x86 */ - -unsigned short _Py_get_387controlword(void) { - unsigned short cw; - __asm__ __volatile__ ("fnstcw %0" : "=m" (cw)); - return cw; -} - -void _Py_set_387controlword(unsigned short cw) { - __asm__ __volatile__ ("fldcw %0" : : "m" (cw)); -} - -#endif - - -#ifndef HAVE_HYPOT -double hypot(double x, double y) -{ - double yx; - - x = fabs(x); - y = fabs(y); - if (x < y) { - double temp = x; - x = y; - y = temp; - } - if (x == 0.) - return 0.; - else { - yx = y/x; - return x*sqrt(1.+yx*yx); - } -} -#endif /* HAVE_HYPOT */ - -#ifndef HAVE_COPYSIGN -double -copysign(double x, double y) -{ - /* use atan2 to distinguish -0. from 0. */ - if (y > 0. || (y == 0. && atan2(y, -1.) > 0.)) { - return fabs(x); - } else { - return -fabs(x); - } -} -#endif /* HAVE_COPYSIGN */ - -#ifndef HAVE_ROUND -double -round(double x) -{ - double absx, y; - absx = fabs(x); - y = floor(absx); - if (absx - y >= 0.5) - y += 1.0; - return copysign(y, x); -} -#endif /* HAVE_ROUND */ - -#ifndef HAVE_LOG1P -#include - -double -log1p(double x) -{ - /* For x small, we use the following approach. Let y be the nearest - float to 1+x, then - - 1+x = y * (1 - (y-1-x)/y) - - so log(1+x) = log(y) + log(1-(y-1-x)/y). Since (y-1-x)/y is tiny, - the second term is well approximated by (y-1-x)/y. If abs(x) >= - DBL_EPSILON/2 or the rounding-mode is some form of round-to-nearest - then y-1-x will be exactly representable, and is computed exactly - by (y-1)-x. - - If abs(x) < DBL_EPSILON/2 and the rounding mode is not known to be - round-to-nearest then this method is slightly dangerous: 1+x could - be rounded up to 1+DBL_EPSILON instead of down to 1, and in that - case y-1-x will not be exactly representable any more and the - result can be off by many ulps. But this is easily fixed: for a - floating-point number |x| < DBL_EPSILON/2., the closest - floating-point number to log(1+x) is exactly x. - */ - - double y; - if (fabs(x) < DBL_EPSILON/2.) { - return x; - } else if (-0.5 <= x && x <= 1.) { - /* WARNING: it's possible than an overeager compiler - will incorrectly optimize the following two lines - to the equivalent of "return log(1.+x)". If this - happens, then results from log1p will be inaccurate - for small x. */ - y = 1.+x; - return log(y)-((y-1.)-x)/y; - } else { - /* NaNs and infinities should end up here */ - return log(1.+x); - } -} -#endif /* HAVE_LOG1P */ - -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -static const double ln2 = 6.93147180559945286227E-01; -static const double two_pow_m28 = 3.7252902984619141E-09; /* 2**-28 */ -static const double two_pow_p28 = 268435456.0; /* 2**28 */ -static const double zero = 0.0; - -/* asinh(x) - * Method : - * Based on - * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] - * we have - * asinh(x) := x if 1+x*x=1, - * := sign(x)*(log(x)+ln2)) for large |x|, else - * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else - * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) - */ - -#ifndef HAVE_ASINH -double -asinh(double x) -{ - double w; - double absx = fabs(x); - - if (Py_IS_NAN(x) || Py_IS_INFINITY(x)) { - return x+x; - } - if (absx < two_pow_m28) { /* |x| < 2**-28 */ - return x; /* return x inexact except 0 */ - } - if (absx > two_pow_p28) { /* |x| > 2**28 */ - w = log(absx)+ln2; - } - else if (absx > 2.0) { /* 2 < |x| < 2**28 */ - w = log(2.0*absx + 1.0 / (sqrt(x*x + 1.0) + absx)); - } - else { /* 2**-28 <= |x| < 2= */ - double t = x*x; - w = log1p(absx + t / (1.0 + sqrt(1.0 + t))); - } - return copysign(w, x); - -} -#endif /* HAVE_ASINH */ - -/* acosh(x) - * Method : - * Based on - * acosh(x) = log [ x + sqrt(x*x-1) ] - * we have - * acosh(x) := log(x)+ln2, if x is large; else - * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else - * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. - * - * Special cases: - * acosh(x) is NaN with signal if x<1. - * acosh(NaN) is NaN without signal. - */ - -#ifndef HAVE_ACOSH -double -acosh(double x) -{ - if (Py_IS_NAN(x)) { - return x+x; - } - if (x < 1.) { /* x < 1; return a signaling NaN */ - errno = EDOM; -#ifdef Py_NAN - return Py_NAN; -#else - return (x-x)/(x-x); -#endif - } - else if (x >= two_pow_p28) { /* x > 2**28 */ - if (Py_IS_INFINITY(x)) { - return x+x; - } else { - return log(x)+ln2; /* acosh(huge)=log(2x) */ - } - } - else if (x == 1.) { - return 0.0; /* acosh(1) = 0 */ - } - else if (x > 2.) { /* 2 < x < 2**28 */ - double t = x*x; - return log(2.0*x - 1.0 / (x + sqrt(t - 1.0))); - } - else { /* 1 < x <= 2 */ - double t = x - 1.0; - return log1p(t + sqrt(2.0*t + t*t)); - } -} -#endif /* HAVE_ACOSH */ - -/* atanh(x) - * Method : - * 1.Reduced x to positive by atanh(-x) = -atanh(x) - * 2.For x>=0.5 - * 1 2x x - * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) - * 2 1 - x 1 - x - * - * For x<0.5 - * atanh(x) = 0.5*log1p(2x+2x*x/(1-x)) - * - * Special cases: - * atanh(x) is NaN if |x| >= 1 with signal; - * atanh(NaN) is that NaN with no signal; - * - */ - -#ifndef HAVE_ATANH -double -atanh(double x) -{ - double absx; - double t; - - if (Py_IS_NAN(x)) { - return x+x; - } - absx = fabs(x); - if (absx >= 1.) { /* |x| >= 1 */ - errno = EDOM; -#ifdef Py_NAN - return Py_NAN; -#else - return x/zero; -#endif - } - if (absx < two_pow_m28) { /* |x| < 2**-28 */ - return x; - } - if (absx < 0.5) { /* |x| < 0.5 */ - t = absx+absx; - t = 0.5 * log1p(t + t*absx / (1.0 - absx)); - } - else { /* 0.5 <= |x| <= 1.0 */ - t = 0.5 * log1p((absx + absx) / (1.0 - absx)); - } - return copysign(t, x); -} -#endif /* HAVE_ATANH */ +#include "Python.h" + +#ifdef X87_DOUBLE_ROUNDING +/* On x86 platforms using an x87 FPU, this function is called from the + Py_FORCE_DOUBLE macro (defined in pymath.h) to force a floating-point + number out of an 80-bit x87 FPU register and into a 64-bit memory location, + thus rounding from extended precision to double precision. */ +double _Py_force_double(double x) +{ + volatile double y; + y = x; + return y; +} +#endif + +#ifdef HAVE_GCC_ASM_FOR_X87 + +/* inline assembly for getting and setting the 387 FPU control word on + gcc/x86 */ + +unsigned short _Py_get_387controlword(void) { + unsigned short cw; + __asm__ __volatile__ ("fnstcw %0" : "=m" (cw)); + return cw; +} + +void _Py_set_387controlword(unsigned short cw) { + __asm__ __volatile__ ("fldcw %0" : : "m" (cw)); +} + +#endif + + +#ifndef HAVE_HYPOT +double hypot(double x, double y) +{ + double yx; + + x = fabs(x); + y = fabs(y); + if (x < y) { + double temp = x; + x = y; + y = temp; + } + if (x == 0.) + return 0.; + else { + yx = y/x; + return x*sqrt(1.+yx*yx); + } +} +#endif /* HAVE_HYPOT */ + +#ifndef HAVE_COPYSIGN +double +copysign(double x, double y) +{ + /* use atan2 to distinguish -0. from 0. */ + if (y > 0. || (y == 0. && atan2(y, -1.) > 0.)) { + return fabs(x); + } else { + return -fabs(x); + } +} +#endif /* HAVE_COPYSIGN */ + +#ifndef HAVE_ROUND +double +round(double x) +{ + double absx, y; + absx = fabs(x); + y = floor(absx); + if (absx - y >= 0.5) + y += 1.0; + return copysign(y, x); +} +#endif /* HAVE_ROUND */ diff --git a/setup.py b/setup.py index bad88f79fa..f25b8294ea 100644 --- a/setup.py +++ b/setup.py @@ -410,9 +410,9 @@ class PyBuildExt(build_ext): # array objects exts.append( Extension('array', ['arraymodule.c']) ) # complex math library functions - exts.append( Extension('cmath', ['cmathmodule.c'], + exts.append( Extension('cmath', ['cmathmodule.c', '_math.c'], + depends=['_math.h'], libraries=math_libs) ) - # math library functions, e.g. sin() exts.append( Extension('math', ['mathmodule.c', '_math.c'], depends=['_math.h'], -- 2.11.4.GIT