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Diffstat (limited to 'sysdeps/ieee754/flt-32/e_expf.c')
| -rw-r--r-- | sysdeps/ieee754/flt-32/e_expf.c | 140 |
1 files changed, 140 insertions, 0 deletions
diff --git a/sysdeps/ieee754/flt-32/e_expf.c b/sysdeps/ieee754/flt-32/e_expf.c new file mode 100644 index 0000000000..e8a9c9d874 --- /dev/null +++ b/sysdeps/ieee754/flt-32/e_expf.c @@ -0,0 +1,140 @@ +/* Single-precision floating point e^x. + Copyright (C) 1997, 1998 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Geoffrey Keating <geoffk@ozemail.com.au> + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Library General Public License as + published by the Free Software Foundation; either version 2 of the + License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Library General Public License for more details. + + You should have received a copy of the GNU Library General Public + License along with the GNU C Library; see the file COPYING.LIB. If not, + write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, + Boston, MA 02111-1307, USA. */ + +/* How this works: + + The input value, x, is written as + + x = n * ln(2) + t/512 + delta[t] + x; + + where: + - n is an integer, 127 >= n >= -150; + - t is an integer, 177 >= t >= -177 + - delta is based on a table entry, delta[t] < 2^-28 + - x is whatever is left, |x| < 2^-10 + + Then e^x is approximated as + + e^x = 2^n ( e^(t/512 + delta[t]) + + ( e^(t/512 + delta[t]) + * ( p(x + delta[t] + n * ln(2)) - delta ) ) ) + + where + - p(x) is a polynomial approximating e(x)-1; + - e^(t/512 + delta[t]) is obtained from a table. + + The table used is the same one as for the double precision version; + since we have the table, we might as well use it. + + It turns out to be faster to do calculations in double precision than + to perform an 'accurate table method' expf, because of the range reduction + overhead (compare exp2f). + */ +#ifndef _GNU_SOURCE +#define _GNU_SOURCE +#endif +#include <float.h> +#include <ieee754.h> +#include <math.h> +#include <fenv.h> +#include <inttypes.h> +#include <math_private.h> + +extern const float __exp_deltatable[178]; +extern const double __exp_atable[355] /* __attribute__((mode(DF))) */; + +static const volatile float TWOM100 = 7.88860905e-31; +static const volatile float TWO127 = 1.7014118346e+38; + +float +__ieee754_expf (float x) +{ + static const float himark = 88.72283935546875; + static const float lomark = -103.972084045410; + /* Check for usual case. */ + if (isless (x, himark) && isgreater (x, lomark)) + { + static const float THREEp42 = 13194139533312.0; + static const float THREEp22 = 12582912.0; + /* 1/ln(2). */ +#undef M_1_LN2 + static const float M_1_LN2 = 1.44269502163f; + /* ln(2) */ +#undef M_LN2 + static const double M_LN2 = .6931471805599452862; + + int tval; + double x22, t, result, dx; + float n, delta; + union ieee754_double ex2_u; + fenv_t oldenv; + + feholdexcept (&oldenv); +#ifdef FE_TONEAREST + fesetround (FE_TONEAREST); +#endif + + /* Calculate n. */ + n = x * M_1_LN2 + THREEp22; + n -= THREEp22; + dx = x - n*M_LN2; + + /* Calculate t/512. */ + t = dx + THREEp42; + t -= THREEp42; + dx -= t; + + /* Compute tval = t. */ + tval = (int) (t * 512.0); + + if (t >= 0) + delta = - __exp_deltatable[tval]; + else + delta = __exp_deltatable[-tval]; + + /* Compute ex2 = 2^n e^(t/512+delta[t]). */ + ex2_u.d = __exp_atable[tval+177]; + ex2_u.ieee.exponent += (int) n; + + /* Approximate e^(dx+delta) - 1, using a second-degree polynomial, + with maximum error in [-2^-10-2^-28,2^-10+2^-28] + less than 5e-11. */ + x22 = (0.5000000496709180453 * dx + 1.0000001192102037084) * dx + delta; + + /* Return result. */ + fesetenv (&oldenv); + + result = x22 * ex2_u.d + ex2_u.d; + return (float) result; + } + /* Exceptional cases: */ + else if (isless (x, himark)) + { + if (__isinff (x)) + /* e^-inf == 0, with no error. */ + return 0; + else + /* Underflow */ + return TWOM100 * TWOM100; + } + else + /* Return x, if x is a NaN or Inf; or overflow, otherwise. */ + return TWO127*x; +} |