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134 lines
3.7 KiB
C
134 lines
3.7 KiB
C
/* Single-precision floating point e^x.
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Copyright (C) 1997-2013 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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/* How this works:
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The input value, x, is written as
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x = n * ln(2) + t/512 + delta[t] + x;
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where:
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- n is an integer, 127 >= n >= -150;
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- t is an integer, 177 >= t >= -177
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- delta is based on a table entry, delta[t] < 2^-28
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- x is whatever is left, |x| < 2^-10
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Then e^x is approximated as
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e^x = 2^n ( e^(t/512 + delta[t])
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+ ( e^(t/512 + delta[t])
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* ( p(x + delta[t] + n * ln(2)) - delta ) ) )
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where
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- p(x) is a polynomial approximating e(x)-1;
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- e^(t/512 + delta[t]) is obtained from a table.
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The table used is the same one as for the double precision version;
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since we have the table, we might as well use it.
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It turns out to be faster to do calculations in double precision than
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to perform an 'accurate table method' expf, because of the range reduction
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overhead (compare exp2f).
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*/
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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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extern const float __exp_deltatable[178];
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extern const double __exp_atable[355] /* __attribute__((mode(DF))) */;
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static const float TWOM100 = 7.88860905e-31;
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static const float TWO127 = 1.7014118346e+38;
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float
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__ieee754_expf (float x)
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{
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static const float himark = 88.72283935546875;
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static const float lomark = -103.972084045410;
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/* Check for usual case. */
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if (isless (x, himark) && isgreater (x, lomark))
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{
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static const float THREEp42 = 13194139533312.0;
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static const float THREEp22 = 12582912.0;
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/* 1/ln(2). */
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#undef M_1_LN2
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static const float M_1_LN2 = 1.44269502163f;
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/* ln(2) */
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#undef M_LN2
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static const double M_LN2 = .6931471805599452862;
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int tval;
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double x22, t, result, dx;
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float n, delta;
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union ieee754_double ex2_u;
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{
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SET_RESTORE_ROUND_NOEXF (FE_TONEAREST);
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/* Calculate n. */
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n = x * M_1_LN2 + THREEp22;
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n -= THREEp22;
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dx = x - n*M_LN2;
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/* Calculate t/512. */
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t = dx + THREEp42;
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t -= THREEp42;
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dx -= t;
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/* Compute tval = t. */
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tval = (int) (t * 512.0);
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if (t >= 0)
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delta = - __exp_deltatable[tval];
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else
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delta = __exp_deltatable[-tval];
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/* Compute ex2 = 2^n e^(t/512+delta[t]). */
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ex2_u.d = __exp_atable[tval+177];
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ex2_u.ieee.exponent += (int) n;
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/* Approximate e^(dx+delta) - 1, using a second-degree polynomial,
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with maximum error in [-2^-10-2^-28,2^-10+2^-28]
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less than 5e-11. */
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x22 = (0.5000000496709180453 * dx + 1.0000001192102037084) * dx + delta;
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}
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/* Return result. */
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result = x22 * ex2_u.d + ex2_u.d;
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return (float) result;
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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 (__isinff (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_expf, __expf_finite)
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