mirror of
https://sourceware.org/git/glibc.git
synced 2024-11-15 17:40:06 +00:00
ca2fcac629
The ldbl-128ibm implementation of tanhl is inaccurate for small arguments, because it returns x*(1+x) (maybe in an attempt to raise "inexact") when x itself would be the accurate return value but multiplying by 1+x introduces large errors. This patch fixes it to return x in that case (when the mathematical result is x plus a negligible remainder on the order of x^3) to avoid those errors. Tested for powerpc. [BZ #19349] * sysdeps/ieee754/ldbl-128ibm/s_tanhl.c (__tanhl): Return argument when small.
88 lines
2.3 KiB
C
88 lines
2.3 KiB
C
/* @(#)s_tanh.c 5.1 93/09/24 */
|
|
/*
|
|
* ====================================================
|
|
* 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(LIBM_SCCS) && !defined(lint)
|
|
static char rcsid[] = "$NetBSD: s_tanh.c,v 1.7 1995/05/10 20:48:22 jtc Exp $";
|
|
#endif
|
|
|
|
/* Tanh(x)
|
|
* Return the Hyperbolic Tangent of x
|
|
*
|
|
* Method :
|
|
* x -x
|
|
* e - e
|
|
* 0. tanh(x) is defined to be -----------
|
|
* x -x
|
|
* e + e
|
|
* 1. reduce x to non-negative by tanh(-x) = -tanh(x).
|
|
* 2. 0 <= x <= 2**-57 : tanh(x) := x*(one+x)
|
|
* -t
|
|
* 2**-57 < x <= 1 : tanh(x) := -----; t = expm1(-2x)
|
|
* t + 2
|
|
* 2
|
|
* 1 <= x <= 40.0 : tanh(x) := 1- ----- ; t=expm1(2x)
|
|
* t + 2
|
|
* 40.0 < x <= INF : tanh(x) := 1.
|
|
*
|
|
* Special cases:
|
|
* tanh(NaN) is NaN;
|
|
* only tanh(0)=0 is exact for finite argument.
|
|
*/
|
|
|
|
#include <float.h>
|
|
#include <math.h>
|
|
#include <math_private.h>
|
|
#include <math_ldbl_opt.h>
|
|
|
|
static const long double one=1.0L, two=2.0L, tiny = 1.0e-300L;
|
|
|
|
long double __tanhl(long double x)
|
|
{
|
|
long double t,z;
|
|
int64_t jx,ix;
|
|
double xhi;
|
|
|
|
/* High word of |x|. */
|
|
xhi = ldbl_high (x);
|
|
EXTRACT_WORDS64 (jx, xhi);
|
|
ix = jx&0x7fffffffffffffffLL;
|
|
|
|
/* x is INF or NaN */
|
|
if(ix>=0x7ff0000000000000LL) {
|
|
if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */
|
|
else return one/x-one; /* tanh(NaN) = NaN */
|
|
}
|
|
|
|
/* |x| < 40 */
|
|
if (ix < 0x4044000000000000LL) { /* |x|<40 */
|
|
if (ix == 0)
|
|
return x; /* x == +-0 */
|
|
if (ix<0x3c60000000000000LL) /* |x|<2**-57 */
|
|
{
|
|
math_check_force_underflow (x);
|
|
return x; /* tanh(small) = small */
|
|
}
|
|
if (ix>=0x3ff0000000000000LL) { /* |x|>=1 */
|
|
t = __expm1l(two*fabsl(x));
|
|
z = one - two/(t+two);
|
|
} else {
|
|
t = __expm1l(-two*fabsl(x));
|
|
z= -t/(t+two);
|
|
}
|
|
/* |x| > 40, return +-1 */
|
|
} else {
|
|
z = one - tiny; /* raised inexact flag */
|
|
}
|
|
return (jx>=0)? z: -z;
|
|
}
|
|
long_double_symbol (libm, __tanhl, tanhl);
|