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4648909d56
This patch fixes bug 16354, spurious underflows from cosh when a tiny argument is passed to expm1 and expm1 correctly underflows although the final result of cosh should be 1. As noted in that bug, some cases are latent because of expm1 implementations not raising underflow (bug 16353), but all the implementations are fixed similarly. They already contained checks for tiny arguments, but the checks were too late to avoid underflow from expm1 (although they would avoid underflow from subsequent squaring of the result of expm1); they are moved before the expm1 calls. The thresholds used for considering arguments tiny are not particularly consistent in how they relate to the precision of the floating-point format in question. They are, however, all sufficient to ensure that the round-to-nearest result of cosh is indeed 1 below the threshold (although sometimes they are smaller than necessary). But the previous logic did not return 1, but the previously computed 1 + expm1(abs(x)) value. And the thresholds in the ldbl-128 and ldbl-128ibm code (0x1p-71L - I suspect 0x3f8b was intended in the code instead of 0x3fb8 - and (roughly) 0x1p-55L) are not sufficient for that value to be 1. So by moving the test for tiny arguments, and consequently returning 1 directly now the expm1 value hasn't been computed by that point, this patch also fixes bug 17061, the (large number of ulps) inaccuracy for small arguments in those implementations. Tests for that bug are duly added. Tested x86_64 and x86 and ulps updated accordingly. Also tested for mips64 and powerpc32 to validate the ldbl-128 and ldbl-128ibm changes. [BZ #16354] [BZ #17061] * sysdeps/ieee754/dbl-64/e_cosh.c (__ieee754_cosh): Check for small arguments before calling __expm1. * sysdeps/ieee754/flt-32/e_coshf.c (__ieee754_coshf): Check for small arguments before calling __expm1f. * sysdeps/ieee754/ldbl-128/e_coshl.c (__ieee754_coshl): Check for small arguments before calling __expm1l. * sysdeps/ieee754/ldbl-128ibm/e_coshl.c (__ieee754_coshl): Likewise. * sysdeps/ieee754/ldbl-96/e_coshl.c (__ieee754_coshl): Likewise. * math/auto-libm-test-in: Add more cosh tests. Do not allow spurious underflow for some cosh tests. * math/auto-libm-test-out: Regenerated. * sysdeps/i386/fpu/libm-test-ulps: Update.
111 lines
3.6 KiB
C
111 lines
3.6 KiB
C
/*
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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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/* Changes for 128-bit long double are
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Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
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and are incorporated herein by permission of the author. The author
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reserves the right to distribute this material elsewhere under different
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copying permissions. These modifications are distributed here under
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the following terms:
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This library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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This library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with this library; if not, see
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<http://www.gnu.org/licenses/>. */
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/* __ieee754_coshl(x)
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* Method :
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* mathematically coshl(x) if defined to be (exp(x)+exp(-x))/2
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* 1. Replace x by |x| (coshl(x) = coshl(-x)).
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* 2.
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* [ exp(x) - 1 ]^2
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* 0 <= x <= ln2/2 : coshl(x) := 1 + -------------------
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* 2*exp(x)
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*
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* exp(x) + 1/exp(x)
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* ln2/2 <= x <= 22 : coshl(x) := -------------------
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* 2
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* 22 <= x <= lnovft : coshl(x) := expl(x)/2
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* lnovft <= x <= ln2ovft: coshl(x) := expl(x/2)/2 * expl(x/2)
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* ln2ovft < x : coshl(x) := huge*huge (overflow)
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*
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* Special cases:
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* coshl(x) is |x| if x is +INF, -INF, or NaN.
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* only coshl(0)=1 is exact for finite x.
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*/
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#include <math.h>
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#include <math_private.h>
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static const long double one = 1.0, half = 0.5, huge = 1.0e4900L,
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ovf_thresh = 1.1357216553474703894801348310092223067821E4L;
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long double
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__ieee754_coshl (long double x)
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{
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long double t, w;
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int32_t ex;
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ieee854_long_double_shape_type u;
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u.value = x;
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ex = u.parts32.w0 & 0x7fffffff;
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/* Absolute value of x. */
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u.parts32.w0 = ex;
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/* x is INF or NaN */
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if (ex >= 0x7fff0000)
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return x * x;
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/* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */
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if (ex < 0x3ffd62e4) /* 0.3465728759765625 */
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{
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if (ex < 0x3fb80000) /* |x| < 2^-116 */
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return one; /* cosh(tiny) = 1 */
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t = __expm1l (u.value);
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w = one + t;
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return one + (t * t) / (w + w);
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}
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/* |x| in [0.5*ln2,40], return (exp(|x|)+1/exp(|x|)/2; */
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if (ex < 0x40044000)
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{
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t = __ieee754_expl (u.value);
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return half * t + half / t;
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}
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/* |x| in [22, ln(maxdouble)] return half*exp(|x|) */
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if (ex <= 0x400c62e3) /* 11356.375 */
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return half * __ieee754_expl (u.value);
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/* |x| in [log(maxdouble), overflowthresold] */
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if (u.value <= ovf_thresh)
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{
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w = __ieee754_expl (half * u.value);
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t = half * w;
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return t * w;
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}
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/* |x| > overflowthresold, cosh(x) overflow */
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return huge * huge;
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}
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strong_alias (__ieee754_coshl, __coshl_finite)
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