diff options
Diffstat (limited to 'contrib/tools/python3/src/Modules/_math.c')
| -rw-r--r-- | contrib/tools/python3/src/Modules/_math.c | 530 |
1 files changed, 265 insertions, 265 deletions
diff --git a/contrib/tools/python3/src/Modules/_math.c b/contrib/tools/python3/src/Modules/_math.c index 68e3a234692..2ab022c0933 100644 --- a/contrib/tools/python3/src/Modules/_math.c +++ b/contrib/tools/python3/src/Modules/_math.c @@ -1,266 +1,266 @@ -/* Definitions of some C99 math library functions, for those platforms - that don't implement these functions already. */ - -#include "Python.h" -#include <float.h> -#include "_math.h" - -/* The following copyright notice applies to the original - implementations of acosh, asinh and atanh. */ - -/* - * ==================================================== - * 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. - * ==================================================== - */ - -#if !defined(HAVE_ACOSH) || !defined(HAVE_ASINH) -static const double ln2 = 6.93147180559945286227E-01; -static const double two_pow_p28 = 268435456.0; /* 2**28 */ -#endif -#if !defined(HAVE_ASINH) || !defined(HAVE_ATANH) -static const double two_pow_m28 = 3.7252902984619141E-09; /* 2**-28 */ -#endif -#if !defined(HAVE_ATANH) && !defined(Py_NAN) -static const double zero = 0.0; -#endif - - -#ifndef HAVE_ACOSH -/* 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. - */ - -double -_Py_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 m_log1p(t + sqrt(2.0 * t + t * t)); - } -} -#endif /* HAVE_ACOSH */ - - -#ifndef HAVE_ASINH -/* 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, +/* Definitions of some C99 math library functions, for those platforms + that don't implement these functions already. */ + +#include "Python.h" +#include <float.h> +#include "_math.h" + +/* The following copyright notice applies to the original + implementations of acosh, asinh and atanh. */ + +/* + * ==================================================== + * 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. + * ==================================================== + */ + +#if !defined(HAVE_ACOSH) || !defined(HAVE_ASINH) +static const double ln2 = 6.93147180559945286227E-01; +static const double two_pow_p28 = 268435456.0; /* 2**28 */ +#endif +#if !defined(HAVE_ASINH) || !defined(HAVE_ATANH) +static const double two_pow_m28 = 3.7252902984619141E-09; /* 2**-28 */ +#endif +#if !defined(HAVE_ATANH) && !defined(Py_NAN) +static const double zero = 0.0; +#endif + + +#ifndef HAVE_ACOSH +/* 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. + */ + +double +_Py_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 m_log1p(t + sqrt(2.0 * t + t * t)); + } +} +#endif /* HAVE_ACOSH */ + + +#ifndef HAVE_ASINH +/* 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 = m_log1p(absx + t / (1.0 + sqrt(1.0 + t))); - } - return copysign(w, x); - -} -#endif /* HAVE_ASINH */ - - -#ifndef HAVE_ATANH -/* 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; - * - */ - -double -_Py_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 * m_log1p(t + t*absx / (1.0 - absx)); - } - else { /* 0.5 <= |x| <= 1.0 */ - t = 0.5 * m_log1p((absx + absx) / (1.0 - absx)); - } - return copysign(t, x); -} -#endif /* HAVE_ATANH */ - - -#ifndef HAVE_EXPM1 -/* 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; -} -#endif /* HAVE_EXPM1 */ - - -/* 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) -{ -#ifdef HAVE_LOG1P - /* Some platforms supply a log1p function but don't respect the sign of - zero: log1p(-0.0) gives 0.0 instead of the correct result of -0.0. - - To save fiddling with configure tests and platform checks, we handle the - special case of zero input directly on all platforms. - */ - if (x == 0.0) { - return x; - } - else { - return log1p(x); - } -#else - /* 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 that 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 /* ifdef HAVE_LOG1P */ -} - + * := 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 = m_log1p(absx + t / (1.0 + sqrt(1.0 + t))); + } + return copysign(w, x); + +} +#endif /* HAVE_ASINH */ + + +#ifndef HAVE_ATANH +/* 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; + * + */ + +double +_Py_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 * m_log1p(t + t*absx / (1.0 - absx)); + } + else { /* 0.5 <= |x| <= 1.0 */ + t = 0.5 * m_log1p((absx + absx) / (1.0 - absx)); + } + return copysign(t, x); +} +#endif /* HAVE_ATANH */ + + +#ifndef HAVE_EXPM1 +/* 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; +} +#endif /* HAVE_EXPM1 */ + + +/* 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) +{ +#ifdef HAVE_LOG1P + /* Some platforms supply a log1p function but don't respect the sign of + zero: log1p(-0.0) gives 0.0 instead of the correct result of -0.0. + + To save fiddling with configure tests and platform checks, we handle the + special case of zero input directly on all platforms. + */ + if (x == 0.0) { + return x; + } + else { + return log1p(x); + } +#else + /* 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 that 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 /* ifdef HAVE_LOG1P */ +} + |