aboutsummaryrefslogtreecommitdiff
path: root/sysdeps/ieee754/flt-32/e_expf.c
diff options
context:
space:
mode:
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/flt-32/e_expf.c
parent86421aa57ecfd70963ae66848bd6a6dd3b8e0fe6 (diff)
downloadglibc-abfbdde177c3a7155070dda1b2cdc8292054cc26.tar
glibc-abfbdde177c3a7155070dda1b2cdc8292054cc26.tar.gz
glibc-abfbdde177c3a7155070dda1b2cdc8292054cc26.tar.bz2
glibc-abfbdde177c3a7155070dda1b2cdc8292054cc26.zip
Update.
Diffstat (limited to 'sysdeps/ieee754/flt-32/e_expf.c')
-rw-r--r--sysdeps/ieee754/flt-32/e_expf.c140
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;
+}