Issue #7518: Move substitute definitions of C99 math functions from
pymath.c to Modules/_math.c.
This commit is contained in:
Mark Dickinson
parent
08dca0d6da
commit
12748b003c
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@ -8,9 +8,9 @@ Symbols and macros to supply platform-independent interfaces to mathematical
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functions and constants
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**************************************************************************/
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/* Python provides implementations for copysign, acosh, asinh, atanh,
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* log1p and hypot in Python/pymath.c just in case your math library doesn't
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* provide the functions.
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/* Python provides implementations for copysign, round and hypot in
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* Python/pymath.c just in case your math library doesn't provide the
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* functions.
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*
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*Note: PC/pyconfig.h defines copysign as _copysign
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*/
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@ -22,22 +22,6 @@ extern double copysign(double, double);
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extern double round(double);
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#endif
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#ifndef HAVE_ACOSH
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extern double acosh(double);
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#endif
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#ifndef HAVE_ASINH
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extern double asinh(double);
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#endif
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#ifndef HAVE_ATANH
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extern double atanh(double);
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#endif
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#ifndef HAVE_LOG1P
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extern double log1p(double);
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#endif
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#ifndef HAVE_HYPOT
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extern double hypot(double, double);
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#endif
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@ -168,7 +168,7 @@ GLHACK=-Dclear=__GLclear
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# Modules that should always be present (non UNIX dependent):
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#array arraymodule.c # array objects
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#cmath cmathmodule.c # -lm # complex math library functions
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#cmath cmathmodule.c _math.c # -lm # complex math library functions
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#math mathmodule.c _math.c # -lm # math library functions, e.g. sin()
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#_struct _struct.c # binary structure packing/unpacking
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#time timemodule.c # -lm # time operations and variables
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199
Modules/_math.c
199
Modules/_math.c
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@ -1,8 +1,161 @@
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/* Definitions of some C99 math library functions, for those platforms
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that don't implement these functions already. */
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#include "Python.h"
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#include <float.h>
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#include <math.h>
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/* The following copyright notice applies to the original
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implementations of acosh, asinh and atanh. */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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static const double ln2 = 6.93147180559945286227E-01;
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static const double two_pow_m28 = 3.7252902984619141E-09; /* 2**-28 */
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static const double two_pow_p28 = 268435456.0; /* 2**28 */
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static const double zero = 0.0;
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/* acosh(x)
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* Method :
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* Based on
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* acosh(x) = log [ x + sqrt(x*x-1) ]
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* we have
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* acosh(x) := log(x)+ln2, if x is large; else
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* acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
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* acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
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*
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* Special cases:
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* acosh(x) is NaN with signal if x<1.
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* acosh(NaN) is NaN without signal.
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*/
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double
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_Py_acosh(double x)
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{
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if (Py_IS_NAN(x)) {
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return x+x;
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}
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if (x < 1.) { /* x < 1; return a signaling NaN */
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errno = EDOM;
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#ifdef Py_NAN
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return Py_NAN;
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#else
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return (x-x)/(x-x);
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#endif
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}
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else if (x >= two_pow_p28) { /* x > 2**28 */
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if (Py_IS_INFINITY(x)) {
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return x+x;
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} else {
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return log(x)+ln2; /* acosh(huge)=log(2x) */
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}
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}
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else if (x == 1.) {
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return 0.0; /* acosh(1) = 0 */
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}
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else if (x > 2.) { /* 2 < x < 2**28 */
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double t = x*x;
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return log(2.0*x - 1.0 / (x + sqrt(t - 1.0)));
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}
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else { /* 1 < x <= 2 */
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double t = x - 1.0;
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return log1p(t + sqrt(2.0*t + t*t));
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}
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}
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/* asinh(x)
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* Method :
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* Based on
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* asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
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* we have
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* asinh(x) := x if 1+x*x=1,
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* := sign(x)*(log(x)+ln2)) for large |x|, else
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* := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
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* := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
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*/
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double
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_Py_asinh(double x)
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{
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double w;
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double absx = fabs(x);
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if (Py_IS_NAN(x) || Py_IS_INFINITY(x)) {
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return x+x;
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}
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if (absx < two_pow_m28) { /* |x| < 2**-28 */
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return x; /* return x inexact except 0 */
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}
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if (absx > two_pow_p28) { /* |x| > 2**28 */
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w = log(absx)+ln2;
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}
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else if (absx > 2.0) { /* 2 < |x| < 2**28 */
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w = log(2.0*absx + 1.0 / (sqrt(x*x + 1.0) + absx));
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}
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else { /* 2**-28 <= |x| < 2= */
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double t = x*x;
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w = log1p(absx + t / (1.0 + sqrt(1.0 + t)));
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}
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return copysign(w, x);
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}
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/* atanh(x)
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* Method :
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* 1.Reduced x to positive by atanh(-x) = -atanh(x)
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* 2.For x>=0.5
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* 1 2x x
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* atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
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* 2 1 - x 1 - x
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*
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* For x<0.5
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* atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
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*
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* Special cases:
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* atanh(x) is NaN if |x| >= 1 with signal;
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* atanh(NaN) is that NaN with no signal;
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*
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*/
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double
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_Py_atanh(double x)
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{
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double absx;
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double t;
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if (Py_IS_NAN(x)) {
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return x+x;
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}
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absx = fabs(x);
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if (absx >= 1.) { /* |x| >= 1 */
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errno = EDOM;
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#ifdef Py_NAN
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return Py_NAN;
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#else
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return x/zero;
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#endif
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}
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if (absx < two_pow_m28) { /* |x| < 2**-28 */
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return x;
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}
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if (absx < 0.5) { /* |x| < 0.5 */
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t = absx+absx;
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t = 0.5 * log1p(t + t*absx / (1.0 - absx));
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}
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else { /* 0.5 <= |x| <= 1.0 */
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t = 0.5 * log1p((absx + absx) / (1.0 - absx));
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}
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return copysign(t, x);
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}
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/* Mathematically, expm1(x) = exp(x) - 1. The expm1 function is designed
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to avoid the significant loss of precision that arises from direct
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@ -29,3 +182,47 @@ _Py_expm1(double x)
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else
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return exp(x) - 1.0;
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}
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/* log1p(x) = log(1+x). The log1p function is designed to avoid the
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significant loss of precision that arises from direct evaluation when x is
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small. */
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double
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_Py_log1p(double x)
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{
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/* For x small, we use the following approach. Let y be the nearest float
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to 1+x, then
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1+x = y * (1 - (y-1-x)/y)
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so log(1+x) = log(y) + log(1-(y-1-x)/y). Since (y-1-x)/y is tiny, the
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second term is well approximated by (y-1-x)/y. If abs(x) >=
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DBL_EPSILON/2 or the rounding-mode is some form of round-to-nearest
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then y-1-x will be exactly representable, and is computed exactly by
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(y-1)-x.
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If abs(x) < DBL_EPSILON/2 and the rounding mode is not known to be
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round-to-nearest then this method is slightly dangerous: 1+x could be
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rounded up to 1+DBL_EPSILON instead of down to 1, and in that case
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y-1-x will not be exactly representable any more and the result can be
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off by many ulps. But this is easily fixed: for a floating-point
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number |x| < DBL_EPSILON/2., the closest floating-point number to
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log(1+x) is exactly x.
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*/
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double y;
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if (fabs(x) < DBL_EPSILON/2.) {
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return x;
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} else if (-0.5 <= x && x <= 1.) {
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/* WARNING: it's possible than an overeager compiler
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will incorrectly optimize the following two lines
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to the equivalent of "return log(1.+x)". If this
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happens, then results from log1p will be inaccurate
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for small x. */
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y = 1.+x;
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return log(y)-((y-1.)-x)/y;
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} else {
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/* NaNs and infinities should end up here */
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return log(1.+x);
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}
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}
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@ -1,4 +1,32 @@
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double _Py_acosh(double x);
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double _Py_asinh(double x);
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double _Py_atanh(double x);
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double _Py_expm1(double x);
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double _Py_log1p(double x);
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#ifdef HAVE_ACOSH
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#define m_acosh acosh
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#else
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/* if the system doesn't have acosh, use the substitute
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function defined in Modules/_math.c. */
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#define m_acosh _Py_acosh
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#endif
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#ifdef HAVE_ASINH
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#define m_asinh asinh
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#else
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/* if the system doesn't have asinh, use the substitute
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function defined in Modules/_math.c. */
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#define m_asinh _Py_asinh
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#endif
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#ifdef HAVE_ATANH
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#define m_atanh atanh
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#else
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/* if the system doesn't have atanh, use the substitute
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function defined in Modules/_math.c. */
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#define m_atanh _Py_atanh
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#endif
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#ifdef HAVE_EXPM1
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#define m_expm1 expm1
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@ -7,3 +35,11 @@ double _Py_expm1(double x);
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function defined in Modules/_math.c. */
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#define m_expm1 _Py_expm1
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#endif
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#ifdef HAVE_LOG1P
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#define m_log1p log1p
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#else
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/* if the system doesn't have log1p, use the substitute
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function defined in Modules/_math.c. */
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#define m_log1p _Py_log1p
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#endif
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@ -3,6 +3,7 @@
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/* much code borrowed from mathmodule.c */
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#include "Python.h"
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#include "_math.h"
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/* we need DBL_MAX, DBL_MIN, DBL_EPSILON, DBL_MANT_DIG and FLT_RADIX from
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float.h. We assume that FLT_RADIX is either 2 or 16. */
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#include <float.h>
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@ -149,7 +150,7 @@ c_acos(Py_complex z)
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s2.imag = z.imag;
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s2 = c_sqrt(s2);
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r.real = 2.*atan2(s1.real, s2.real);
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r.imag = asinh(s2.real*s1.imag - s2.imag*s1.real);
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r.imag = m_asinh(s2.real*s1.imag - s2.imag*s1.real);
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}
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errno = 0;
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return r;
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@ -181,7 +182,7 @@ c_acosh(Py_complex z)
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s2.real = z.real + 1.;
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s2.imag = z.imag;
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s2 = c_sqrt(s2);
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r.real = asinh(s1.real*s2.real + s1.imag*s2.imag);
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r.real = m_asinh(s1.real*s2.real + s1.imag*s2.imag);
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r.imag = 2.*atan2(s1.imag, s2.real);
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}
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errno = 0;
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@ -238,7 +239,7 @@ c_asinh(Py_complex z)
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s2.real = 1.-z.imag;
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s2.imag = z.real;
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s2 = c_sqrt(s2);
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r.real = asinh(s1.real*s2.imag-s2.real*s1.imag);
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r.real = m_asinh(s1.real*s2.imag-s2.real*s1.imag);
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r.imag = atan2(z.imag, s1.real*s2.real-s1.imag*s2.imag);
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}
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errno = 0;
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@ -342,7 +343,7 @@ c_atanh(Py_complex z)
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errno = 0;
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}
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} else {
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r.real = log1p(4.*z.real/((1-z.real)*(1-z.real) + ay*ay))/4.;
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r.real = m_log1p(4.*z.real/((1-z.real)*(1-z.real) + ay*ay))/4.;
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r.imag = -atan2(-2.*z.imag, (1-z.real)*(1+z.real) - ay*ay)/2.;
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errno = 0;
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}
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@ -552,7 +553,7 @@ c_log(Py_complex z)
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if (0.71 <= h && h <= 1.73) {
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am = ax > ay ? ax : ay; /* max(ax, ay) */
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an = ax > ay ? ay : ax; /* min(ax, ay) */
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r.real = log1p((am-1)*(am+1)+an*an)/2.;
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r.real = m_log1p((am-1)*(am+1)+an*an)/2.;
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} else {
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r.real = log(h);
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}
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@ -799,18 +799,18 @@ math_2(PyObject *args, double (*func) (double, double), char *funcname)
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FUNC1(acos, acos, 0,
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"acos(x)\n\nReturn the arc cosine (measured in radians) of x.")
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FUNC1(acosh, acosh, 0,
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FUNC1(acosh, m_acosh, 0,
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"acosh(x)\n\nReturn the hyperbolic arc cosine (measured in radians) of x.")
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FUNC1(asin, asin, 0,
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"asin(x)\n\nReturn the arc sine (measured in radians) of x.")
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FUNC1(asinh, asinh, 0,
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FUNC1(asinh, m_asinh, 0,
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"asinh(x)\n\nReturn the hyperbolic arc sine (measured in radians) of x.")
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FUNC1(atan, atan, 0,
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"atan(x)\n\nReturn the arc tangent (measured in radians) of x.")
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FUNC2(atan2, m_atan2,
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"atan2(y, x)\n\nReturn the arc tangent (measured in radians) of y/x.\n"
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"Unlike atan(y/x), the signs of both x and y are considered.")
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FUNC1(atanh, atanh, 0,
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FUNC1(atanh, m_atanh, 0,
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"atanh(x)\n\nReturn the hyperbolic arc tangent (measured in radians) of x.")
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FUNC1(ceil, ceil, 0,
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"ceil(x)\n\nReturn the ceiling of x as a float.\n"
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@ -840,7 +840,7 @@ FUNC1A(gamma, m_tgamma,
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"gamma(x)\n\nGamma function at x.")
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FUNC1A(lgamma, m_lgamma,
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"lgamma(x)\n\nNatural logarithm of absolute value of Gamma function at x.")
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FUNC1(log1p, log1p, 1,
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FUNC1(log1p, m_log1p, 1,
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"log1p(x)\n\nReturn the natural logarithm of 1+x (base e).\n"
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"The result is computed in a way which is accurate for x near zero.")
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FUNC1(sin, sin, 0,
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199
Python/pymath.c
199
Python/pymath.c
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@ -77,202 +77,3 @@ round(double x)
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return copysign(y, x);
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}
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#endif /* HAVE_ROUND */
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#ifndef HAVE_LOG1P
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#include <float.h>
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double
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log1p(double x)
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{
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/* For x small, we use the following approach. Let y be the nearest
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float to 1+x, then
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1+x = y * (1 - (y-1-x)/y)
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|
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so log(1+x) = log(y) + log(1-(y-1-x)/y). Since (y-1-x)/y is tiny,
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the second term is well approximated by (y-1-x)/y. If abs(x) >=
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DBL_EPSILON/2 or the rounding-mode is some form of round-to-nearest
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then y-1-x will be exactly representable, and is computed exactly
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by (y-1)-x.
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If abs(x) < DBL_EPSILON/2 and the rounding mode is not known to be
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round-to-nearest then this method is slightly dangerous: 1+x could
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be rounded up to 1+DBL_EPSILON instead of down to 1, and in that
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case y-1-x will not be exactly representable any more and the
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result can be off by many ulps. But this is easily fixed: for a
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floating-point number |x| < DBL_EPSILON/2., the closest
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floating-point number to log(1+x) is exactly x.
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*/
|
||||
|
||||
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 */
|
||||
|
|
|
|||
4
setup.py
4
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'],
|
||||
|
|
|
|||
Loading…
Reference in New Issue