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authorUlrich Drepper <drepper@redhat.com>1999-07-14 00:54:57 +0000
committerUlrich Drepper <drepper@redhat.com>1999-07-14 00:54:57 +0000
commitabfbdde177c3a7155070dda1b2cdc8292054cc26 (patch)
treee021306b596381fbf8311d2b7eb294e918ff17c8 /sysdeps/ieee754/dbl-64/e_exp.c
parent86421aa57ecfd70963ae66848bd6a6dd3b8e0fe6 (diff)
downloadglibc-abfbdde177c3a7155070dda1b2cdc8292054cc26.tar.gz
Update.
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+/* 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;
+}