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765714cafc
http://sourceware.org/ml/libc-alpha/2013-08/msg00083.html Further replacement of ieee854 macros and unions. These files also have some optimisations for comparison against 0.0L, infinity and nan. Since the ABI specifies that the high double of an IBM long double pair is the value rounded to double, a high double of 0.0 means the low double must also be 0.0. The ABI also says that infinity and nan are encoded in the high double, with the low double unspecified. This means that tests for 0.0L, +/-Infinity and +/-NaN need only check the high double. * sysdeps/ieee754/ldbl-128ibm/e_atan2l.c (__ieee754_atan2l): Rewrite all uses of ieee854 long double macros and unions. Simplify tests for long doubles that are fully specified by the high double. * sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c (__ieee754_gammal_r): Likewise. * sysdeps/ieee754/ldbl-128ibm/e_ilogbl.c (__ieee754_ilogbl): Likewise. Remove dead code too. * sysdeps/ieee754/ldbl-128ibm/e_jnl.c (__ieee754_jnl): Likewise. (__ieee754_ynl): Likewise. * sysdeps/ieee754/ldbl-128ibm/e_log10l.c (__ieee754_log10l): Likewise. * sysdeps/ieee754/ldbl-128ibm/e_logl.c (__ieee754_logl): Likewise. * sysdeps/ieee754/ldbl-128ibm/e_powl.c (__ieee754_powl): Likewise. Remove dead code too. * sysdeps/ieee754/ldbl-128ibm/k_tanl.c (__kernel_tanl): Likewise. * sysdeps/ieee754/ldbl-128ibm/s_expm1l.c (__expm1l): Likewise. * sysdeps/ieee754/ldbl-128ibm/s_frexpl.c (__frexpl): Likewise. * sysdeps/ieee754/ldbl-128ibm/s_isinf_nsl.c (__isinf_nsl): Likewise. Simplify. * sysdeps/ieee754/ldbl-128ibm/s_isinfl.c (___isinfl): Likewise. Simplify. * sysdeps/ieee754/ldbl-128ibm/s_log1pl.c (__log1pl): Likewise. * sysdeps/ieee754/ldbl-128ibm/s_modfl.c (__modfl): Likewise. * sysdeps/ieee754/ldbl-128ibm/s_nextafterl.c (__nextafterl): Likewise. Comment on variable precision. * sysdeps/ieee754/ldbl-128ibm/s_nexttoward.c (__nexttoward): Likewise. * sysdeps/ieee754/ldbl-128ibm/s_nexttowardf.c (__nexttowardf): Likewise. * sysdeps/ieee754/ldbl-128ibm/s_remquol.c (__remquol): Likewise. * sysdeps/ieee754/ldbl-128ibm/s_scalblnl.c (__scalblnl): Likewise. * sysdeps/ieee754/ldbl-128ibm/s_scalbnl.c (__scalbnl): Likewise. * sysdeps/ieee754/ldbl-128ibm/s_tanhl.c (__tanhl): Likewise. * sysdeps/powerpc/fpu/libm-test-ulps: Adjust tan_towardzero ulps.
84 lines
2.2 KiB
C
84 lines
2.2 KiB
C
/* @(#)s_tanh.c 5.1 93/09/24 */
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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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#if defined(LIBM_SCCS) && !defined(lint)
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static char rcsid[] = "$NetBSD: s_tanh.c,v 1.7 1995/05/10 20:48:22 jtc Exp $";
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#endif
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/* Tanh(x)
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* Return the Hyperbolic Tangent of x
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*
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* Method :
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* x -x
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* e - e
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* 0. tanh(x) is defined to be -----------
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* x -x
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* e + e
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* 1. reduce x to non-negative by tanh(-x) = -tanh(x).
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* 2. 0 <= x <= 2**-57 : tanh(x) := x*(one+x)
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* -t
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* 2**-57 < x <= 1 : tanh(x) := -----; t = expm1(-2x)
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* t + 2
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* 2
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* 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x)
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* t + 2
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* 22.0 < x <= INF : tanh(x) := 1.
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*
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* Special cases:
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* tanh(NaN) is NaN;
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* only tanh(0)=0 is exact for finite argument.
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*/
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#include <math.h>
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#include <math_private.h>
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#include <math_ldbl_opt.h>
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static const long double one=1.0L, two=2.0L, tiny = 1.0e-300L;
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long double __tanhl(long double x)
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{
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long double t,z;
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int64_t jx,ix;
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double xhi;
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/* High word of |x|. */
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xhi = ldbl_high (x);
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EXTRACT_WORDS64 (jx, xhi);
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ix = jx&0x7fffffffffffffffLL;
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/* x is INF or NaN */
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if(ix>=0x7ff0000000000000LL) {
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if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */
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else return one/x-one; /* tanh(NaN) = NaN */
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}
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/* |x| < 22 */
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if (ix < 0x4036000000000000LL) { /* |x|<22 */
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if (ix == 0)
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return x; /* x == +-0 */
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if (ix<0x3c60000000000000LL) /* |x|<2**-57 */
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return x*(one+x); /* tanh(small) = small */
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if (ix>=0x3ff0000000000000LL) { /* |x|>=1 */
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t = __expm1l(two*fabsl(x));
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z = one - two/(t+two);
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} else {
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t = __expm1l(-two*fabsl(x));
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z= -t/(t+two);
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}
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/* |x| > 22, return +-1 */
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} else {
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z = one - tiny; /* raised inexact flag */
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}
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return (jx>=0)? z: -z;
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}
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long_double_symbol (libm, __tanhl, tanhl);
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