aboutsummaryrefslogtreecommitdiff
path: root/sysdeps/libm-ieee754/s_exp2.c
diff options
context:
space:
mode:
Diffstat (limited to 'sysdeps/libm-ieee754/s_exp2.c')
-rw-r--r--sysdeps/libm-ieee754/s_exp2.c128
1 files changed, 128 insertions, 0 deletions
diff --git a/sysdeps/libm-ieee754/s_exp2.c b/sysdeps/libm-ieee754/s_exp2.c
new file mode 100644
index 0000000000..e10fae5492
--- /dev/null
+++ b/sysdeps/libm-ieee754/s_exp2.c
@@ -0,0 +1,128 @@
+/* Double-precision floating point 2^x.
+ Copyright (C) 1997 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. */
+
+/* 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.
+ It has been slightly modified to compute 2^x instead of e^x.
+ */
+#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>
+
+#include "t_exp2.h"
+
+static const volatile double TWO1000 = 1.071508607186267320948e+301;
+static const volatile double TWOM1000 = 9.3326361850321887899e-302;
+
+double
+__ieee754_exp2 (double x)
+{
+ static const uint32_t a_inf = 0x7f800000;
+ /* Check for usual case. */
+ if (isless (x, (double) DBL_MAX_EXP)
+ && isgreater (x, (double) (DBL_MIN_EXP - 1)))
+ {
+ static const float TWO43 = 8796093022208.0;
+ int tval;
+ double rx, x22;
+ union ieee754_double ex2_u;
+ fenv_t oldenv;
+
+ feholdexcept (&oldenv);
+ fesetround (FE_TONEAREST);
+
+ /* 1. Argument reduction.
+ Choose integers ex, -256 <= t < 256, and some real
+ -1/1024 <= x1 <= 1024 so that
+ x = ex + t/512 + x1.
+
+ First, calculate rx = ex + t/512. */
+ if (x >= 0)
+ {
+ rx = x + TWO43;
+ rx -= TWO43;
+ }
+ else
+ {
+ rx = x - TWO43;
+ rx += TWO43;
+ }
+ x -= rx; /* Compute x=x1. */
+ /* Compute tval = (ex*512 + t)+256.
+ Now, t = (tval mod 512)-256 and ex=tval/512 [that's mod, NOT %; and
+ /-round-to-nearest not the usual c integer /]. */
+ tval = (int) (rx * 512.0 + 256.0);
+
+ /* 2. Adjust for accurate table entry.
+ Find e so that
+ x = ex + t/512 + e + x2
+ where -1e6 < e < 1e6, and
+ (double)(2^(t/512+e))
+ is accurate to one part in 2^-64. */
+
+ /* 'tval & 511' is the same as 'tval%512' except that it's always
+ positive.
+ Compute x = x2. */
+ x -= exp2_deltatable[tval & 511];
+
+ /* 3. Compute ex2 = 2^(t/512+e+ex). */
+ ex2_u.d = exp2_accuratetable[tval & 511];
+ ex2_u.ieee.exponent += tval >> 9;
+
+ /* 4. Approximate 2^x2 - 1, using a fourth-degree polynomial,
+ 2^x2 ~= sum(k=0..4 | (x2 * ln(2))^k / k! ) +
+ so
+ 2^x2 - 1 ~= sum(k=1..4 | (x2 * ln(2))^k / k! )
+ with error less than 2^(1/1024) * (x2 * ln(2))^5 / 5! < 1.2e-18. */
+
+ x22 = (((.0096181291076284772
+ * x + .055504108664821580)
+ * x + .240226506959100712)
+ * x + .69314718055994531) * ex2_u.d;
+
+ /* 5. Return (2^x2-1) * 2^(t/512+e+ex) + 2^(t/512+e+ex). */
+ fesetenv (&oldenv);
+
+ /* Need to check: does this set FE_INEXACT correctly? */
+ return x22 * x + ex2_u.d;
+ }
+ /* 2^inf == inf, with no error. */
+ else if (x == *(const float *) &a_inf)
+ return x;
+ /* Check for overflow. */
+ else if (isgreaterequal (x, (double) DBL_MAX_EXP))
+ return TWO1000 * TWO1000;
+ /* And underflow (including -inf). */
+ else if (isless (x, (double) (DBL_MIN_EXP - DBL_MANT_DIG)))
+ return TWOM1000 * TWOM1000;
+ /* Maybe the result needs to be a denormalised number... */
+ else if (!isnan (x))
+ return __ieee754_exp2 (x + 1000.0) * TWOM1000;
+ else /* isnan(x) */
+ return x + x;
+}