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Diffstat (limited to 'Python/pymath.c')
| -rw-r--r-- | Python/pymath.c | 232 |
1 files changed, 232 insertions, 0 deletions
diff --git a/Python/pymath.c b/Python/pymath.c new file mode 100644 index 0000000..7c00106 --- /dev/null +++ b/Python/pymath.c @@ -0,0 +1,232 @@ +#include "Python.h" + +#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 +static 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_LOG1P +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 */ |