20f421e1a1
2001-06-19 Andreas Jaeger <aj@suse.de> * sysdeps/ieee754/ldbl-128/s_tanhl.c: New file. * math/libm-test.inc (tanh_test): Test for 2^-56. * sysdeps/ieee754/ldbl-96/s_tanhl.c (__tanhl): Make sure result equals argument when x < 2^-55. Patches by Stephen L. Moshier <moshier@na-net.ornl.gov>.
96 lines
2.4 KiB
C
96 lines
2.4 KiB
C
/* s_tanhl.c -- long double version of s_tanh.c.
|
|
* Conversion to long double by Ulrich Drepper,
|
|
* Cygnus Support, drepper@cygnus.com.
|
|
*/
|
|
|
|
/*
|
|
* ====================================================
|
|
* 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: $";
|
|
#endif
|
|
|
|
/* tanhl(x)
|
|
* Return the Hyperbolic Tangent of x
|
|
*
|
|
* Method :
|
|
* x -x
|
|
* e - e
|
|
* 0. tanhl(x) is defined to be -----------
|
|
* x -x
|
|
* e + e
|
|
* 1. reduce x to non-negative by tanhl(-x) = -tanhl(x).
|
|
* 2. 0 <= x <= 2**-55 : tanhl(x) := x*(one+x)
|
|
* -t
|
|
* 2**-55 < x <= 1 : tanhl(x) := -----; t = expm1l(-2x)
|
|
* t + 2
|
|
* 2
|
|
* 1 <= x <= 23.0 : tanhl(x) := 1- ----- ; t=expm1l(2x)
|
|
* t + 2
|
|
* 23.0 < x <= INF : tanhl(x) := 1.
|
|
*
|
|
* Special cases:
|
|
* tanhl(NaN) is NaN;
|
|
* only tanhl(0)=0 is exact for finite argument.
|
|
*/
|
|
|
|
#include "math.h"
|
|
#include "math_private.h"
|
|
|
|
#ifdef __STDC__
|
|
static const long double one=1.0, two=2.0, tiny = 1.0e-4900L;
|
|
#else
|
|
static long double one=1.0, two=2.0, tiny = 1.0e-4900L;
|
|
#endif
|
|
|
|
#ifdef __STDC__
|
|
long double __tanhl(long double x)
|
|
#else
|
|
long double __tanhl(x)
|
|
long double x;
|
|
#endif
|
|
{
|
|
long double t,z;
|
|
int32_t se;
|
|
u_int32_t j0,j1,ix;
|
|
|
|
/* High word of |x|. */
|
|
GET_LDOUBLE_WORDS(se,j0,j1,x);
|
|
ix = se&0x7fff;
|
|
|
|
/* x is INF or NaN */
|
|
if(ix==0x7fff) {
|
|
/* for NaN it's not important which branch: tanhl(NaN) = NaN */
|
|
if (se&0x8000) return one/x-one; /* tanhl(-inf)= -1; */
|
|
else return one/x+one; /* tanhl(+inf)=+1 */
|
|
}
|
|
|
|
/* |x| < 23 */
|
|
if (ix < 0x4003 || (ix == 0x4003 && j0 < 0xb8000000u)) {/* |x|<23 */
|
|
if ((ix|j0|j1) == 0)
|
|
return x; /* x == +- 0 */
|
|
if (ix<0x3fc8) /* |x|<2**-55 */
|
|
return x*(one+tiny); /* tanh(small) = small */
|
|
if (ix>=0x3fff) { /* |x|>=1 */
|
|
t = __expm1l(two*fabsl(x));
|
|
z = one - two/(t+two);
|
|
} else {
|
|
t = __expm1l(-two*fabsl(x));
|
|
z= -t/(t+two);
|
|
}
|
|
/* |x| > 23, return +-1 */
|
|
} else {
|
|
z = one - tiny; /* raised inexact flag */
|
|
}
|
|
return (se&0x8000)? -z: z;
|
|
}
|
|
weak_alias (__tanhl, tanhl)
|