cpython.git - https://github.com/python/cpython.git

diff options

Diffstat (limited to 'Lib/idlelib/testcode.py')

0 files changed, 0 insertions, 0 deletions

#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 */


context:
space:
mode: