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Diffstat (limited to 'sysdeps/ieee754/dbl-64/e_exp.c')
| -rw-r--r-- | sysdeps/ieee754/dbl-64/e_exp.c | 162 |
1 files changed, 162 insertions, 0 deletions
diff --git a/sysdeps/ieee754/dbl-64/e_exp.c b/sysdeps/ieee754/dbl-64/e_exp.c new file mode 100644 index 0000000..ee0b22f --- /dev/null +++ b/sysdeps/ieee754/dbl-64/e_exp.c @@ -0,0 +1,162 @@ +/* Double-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 basic design here is from + Shmuel Gal and Boris Bachelis, "An Accurate Elementary Mathematical + Library for the IEEE Floating Point Standard", ACM Trans. Math. Soft., + 17 (1), March 1991, pp. 26-45. + + The input value, x, is written as + + x = n * ln(2)_0 + t/512 + delta[t] + x + n * ln(2)_1 + + where: + - n is an integer, 1024 >= n >= -1075; + - ln(2)_0 is the first 43 bits of ln(2), and ln(2)_1 is the remainder, so + that |ln(2)_1| < 2^-32; + - 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_1 ( 2^n_0 e^(t/512 + delta[t]) + + ( 2^n_0 e^(t/512 + delta[t]) + * ( p(x + n * ln(2)_1) + - n*ln(2)_1 + - n*ln(2)_1 * p(x + n * ln(2)_1) ) ) ) + + where + - p(x) is a polynomial approximating e(x)-1; + - e^(t/512 + delta[t]) is obtained from a table; + - n_1 + n_0 = n, so that |n_0| < DBL_MIN_EXP-1. + + If it happens that n_1 == 0 (this is the usual case), that multiplication + is omitted. + */ +#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 double TWO1023 = 8.988465674311579539e+307; +static const volatile double TWOM1000 = 9.3326361850321887899e-302; + +double +__ieee754_exp (double x) +{ + static const double himark = 709.7827128933840868; + static const double lomark = -745.1332191019412221; + /* Check for usual case. */ + if (isless (x, himark) && isgreater (x, lomark)) + { + static const double THREEp42 = 13194139533312.0; + static const double THREEp51 = 6755399441055744.0; + /* 1/ln(2). */ + static const double M_1_LN2 = 1.442695040888963387; + /* ln(2), part 1 */ + static const double M_LN2_0 = .6931471805598903302; + /* ln(2), part 2 */ + static const double M_LN2_1 = 5.497923018708371155e-14; + + int tval, unsafe, n_i; + double x22, n, t, dely, result; + union ieee754_double ex2_u, scale_u; + fenv_t oldenv; + + feholdexcept (&oldenv); +#ifdef FE_TONEAREST + fesetround (FE_TONEAREST); +#endif + + /* Calculate n. */ + n = x * M_1_LN2 + THREEp51; + n -= THREEp51; + x = x - n*M_LN2_0; + + /* Calculate t/512. */ + t = x + THREEp42; + t -= THREEp42; + x -= t; + + /* Compute tval = t. */ + tval = (int) (t * 512.0); + + if (t >= 0) + x -= __exp_deltatable[tval]; + else + x += __exp_deltatable[-tval]; + + /* Now, the variable x contains x + n*ln(2)_1. */ + dely = n*M_LN2_1; + + /* Compute ex2 = 2^n_0 e^(t/512+delta[t]). */ + ex2_u.d = __exp_atable[tval+177]; + n_i = (int)n; + /* 'unsafe' is 1 iff n_1 != 0. */ + unsafe = abs(n_i) >= -DBL_MIN_EXP - 1; + ex2_u.ieee.exponent += n_i >> unsafe; + + /* Compute scale = 2^n_1. */ + scale_u.d = 1.0; + scale_u.ieee.exponent += n_i - (n_i >> unsafe); + + /* Approximate e^x2 - 1, using a fourth-degree polynomial, + with maximum error in [-2^-10-2^-28,2^-10+2^-28] + less than 4.9e-19. */ + x22 = (((0.04166666898464281565 + * x + 0.1666666766008501610) + * x + 0.499999999999990008) + * x + 0.9999999999999976685) * x; + /* Allow for impact of dely. */ + x22 -= dely + dely*x22; + + /* Return result. */ + fesetenv (&oldenv); + + result = x22 * ex2_u.d + ex2_u.d; + if (!unsafe) + return result; + else + return result * scale_u.d; + } + /* Exceptional cases: */ + else if (isless (x, himark)) + { + if (__isinf (x)) + /* e^-inf == 0, with no error. */ + return 0; + else + /* Underflow */ + return TWOM1000 * TWOM1000; + } + else + /* Return x, if x is a NaN or Inf; or overflow, otherwise. */ + return TWO1023*x; +} |