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b59549574e
The dbl-64 and flt-32 implementations of exp2 functions produce spurious underflow exceptions. The underlying reason is the same in both cases: the computation works as (2^a - 1)*2^b + 2^b for suitably chosen a and b, where a has small magnitude so 2^a - 1 can be computed with a low-degree polynomial approximation, and (2^a - 1)*2^b can underflow even when the final result does not. This patch fixes this by adjusting the threshold for when scaling is used to avoid intermediate underflow so it works for any possible value of a where the final result would not underflow. Tested for x86_64 and x86. [BZ #18219] * sysdeps/ieee754/dbl-64/e_exp2.c (__ieee754_exp2): Reduce threshold on absolute value of exponent for which scaling is used. * sysdeps/ieee754/flt-32/e_exp2f.c (__ieee754_exp2f): Likewise. * math/auto-libm-test-in: Add more tests of exp2. * math/auto-libm-test-out: Regenerated.
129 lines
3.8 KiB
C
129 lines
3.8 KiB
C
/* Single-precision floating point 2^x.
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Copyright (C) 1997-2015 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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Contributed by Geoffrey Keating <geoffk@ozemail.com.au>
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The GNU C 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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The GNU C 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 the GNU C Library; if not, see
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<http://www.gnu.org/licenses/>. */
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/* The basic design here is from
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Shmuel Gal and Boris Bachelis, "An Accurate Elementary Mathematical
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Library for the IEEE Floating Point Standard", ACM Trans. Math. Soft.,
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17 (1), March 1991, pp. 26-45.
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It has been slightly modified to compute 2^x instead of e^x, and for
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single-precision.
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*/
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#ifndef _GNU_SOURCE
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# define _GNU_SOURCE
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#endif
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#include <stdlib.h>
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#include <float.h>
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#include <ieee754.h>
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#include <math.h>
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#include <fenv.h>
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#include <inttypes.h>
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#include <math_private.h>
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#include "t_exp2f.h"
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static const volatile float TWOM100 = 7.88860905e-31;
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static const volatile float TWO127 = 1.7014118346e+38;
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float
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__ieee754_exp2f (float x)
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{
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static const float himark = (float) FLT_MAX_EXP;
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static const float lomark = (float) (FLT_MIN_EXP - FLT_MANT_DIG - 1);
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/* Check for usual case. */
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if (isless (x, himark) && isgreaterequal (x, lomark))
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{
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static const float THREEp14 = 49152.0;
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int tval, unsafe;
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float rx, x22, result;
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union ieee754_float ex2_u, scale_u;
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if (fabsf (x) < FLT_EPSILON / 4.0f)
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return 1.0f + x;
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{
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SET_RESTORE_ROUND_NOEXF (FE_TONEAREST);
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/* 1. Argument reduction.
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Choose integers ex, -128 <= t < 128, and some real
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-1/512 <= x1 <= 1/512 so that
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x = ex + t/512 + x1.
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First, calculate rx = ex + t/256. */
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rx = x + THREEp14;
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rx -= THREEp14;
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x -= rx; /* Compute x=x1. */
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/* Compute tval = (ex*256 + t)+128.
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Now, t = (tval mod 256)-128 and ex=tval/256 [that's mod, NOT %;
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and /-round-to-nearest not the usual c integer /]. */
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tval = (int) (rx * 256.0f + 128.0f);
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/* 2. Adjust for accurate table entry.
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Find e so that
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x = ex + t/256 + e + x2
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where -7e-4 < e < 7e-4, and
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(float)(2^(t/256+e))
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is accurate to one part in 2^-64. */
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/* 'tval & 255' is the same as 'tval%256' except that it's always
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positive.
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Compute x = x2. */
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x -= __exp2f_deltatable[tval & 255];
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/* 3. Compute ex2 = 2^(t/255+e+ex). */
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ex2_u.f = __exp2f_atable[tval & 255];
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tval >>= 8;
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/* x2 is an integer multiple of 2^-30; avoid intermediate
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underflow from the calculation of x22 * x. */
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unsafe = abs(tval) >= -FLT_MIN_EXP - 32;
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ex2_u.ieee.exponent += tval >> unsafe;
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scale_u.f = 1.0;
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scale_u.ieee.exponent += tval - (tval >> unsafe);
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/* 4. Approximate 2^x2 - 1, using a second-degree polynomial,
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with maximum error in [-2^-9 - 2^-14, 2^-9 + 2^-14]
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less than 1.3e-10. */
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x22 = (.24022656679f * x + .69314736128f) * ex2_u.f;
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}
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/* 5. Return (2^x2-1) * 2^(t/512+e+ex) + 2^(t/512+e+ex). */
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result = x22 * x + ex2_u.f;
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if (!unsafe)
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return result;
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else
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return result * scale_u.f;
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}
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/* Exceptional cases: */
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else if (isless (x, himark))
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{
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if (__isinf_nsf (x))
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/* e^-inf == 0, with no error. */
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return 0;
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else
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/* Underflow */
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return TWOM100 * TWOM100;
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}
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else
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/* Return x, if x is a NaN or Inf; or overflow, otherwise. */
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return TWO127*x;
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}
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strong_alias (__ieee754_exp2f, __exp2f_finite)
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