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Diffstat (limited to 'sysdeps/libm-ieee754/e_exp.c')
-rw-r--r-- | sysdeps/libm-ieee754/e_exp.c | 162 |
1 files changed, 0 insertions, 162 deletions
diff --git a/sysdeps/libm-ieee754/e_exp.c b/sysdeps/libm-ieee754/e_exp.c deleted file mode 100644 index ee0b22f6ae..0000000000 --- a/sysdeps/libm-ieee754/e_exp.c +++ /dev/null @@ -1,162 +0,0 @@ -/* 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; -} |