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+/* Single-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, and for
+ single-precision.
+ */
+#define _GNU_SOURCE
+#include <float.h>
+#include <ieee754.h>
+#include <math.h>
+#include <fenv.h>
+#include <inttypes.h>
+#include <math_private.h>
+
+#include "t_exp2f.h"
+
+static const volatile float TWOM100 = 7.88860905e-31;
+static const volatile float huge = 1e+30;
+
+float
+__ieee754_exp2f (float x)
+{
+ static const uint32_t a_inf = 0x7f800000;
+ /* Check for usual case. */
+ if (isless (x, (float) FLT_MAX_EXP)
+ && isgreater (x, (float) (FLT_MIN_EXP - 1)))
+ {
+ static const float TWO16 = 65536.0;
+ int tval;
+ float rx, x22;
+ union ieee754_float ex2_u;
+ fenv_t oldenv;
+
+ feholdexcept (&oldenv);
+ fesetround (FE_TONEAREST);
+
+ /* 1. Argument reduction.
+ Choose integers ex, -128 <= t < 128, and some real
+ -1/512 <= x1 <= 1/512 so that
+ x = ex + t/512 + x1.
+
+ First, calculate rx = ex + t/256. */
+ if (x >= 0)
+ {
+ rx = x + TWO16;
+ rx -= TWO16;
+ }
+ else
+ {
+ rx = x - TWO16;
+ rx += TWO16;
+ }
+ x -= rx; /* Compute x=x1. */
+ /* Compute tval = (ex*256 + t)+128.
+ Now, t = (tval mod 256)-128 and ex=tval/256 [that's mod, NOT %; and
+ /-round-to-nearest not the usual c integer /]. */
+ tval = (int) (rx * 256.0f + 128.0f);
+
+ /* 2. Adjust for accurate table entry.
+ Find e so that
+ x = ex + t/256 + e + x2
+ where -7e-4 < e < 7e-4, and
+ (float)(2^(t/256+e))
+ is accurate to one part in 2^-64. */
+
+ /* 'tval & 255' is the same as 'tval%256' except that it's always
+ positive.
+ Compute x = x2. */
+ x -= exp2_deltatable[tval & 255];
+
+ /* 3. Compute ex2 = 2^(t/255+e+ex). */
+ ex2_u.f = exp2_accuratetable[tval & 255];
+ ex2_u.ieee.exponent += tval >> 8;
+
+ /* 4. Approximate 2^x2 - 1, using a second-degree polynomial,
+ 2^x2 ~= sum(k=0..2 | (x2 * ln(2))^k / k! ) +
+ so
+ 2^x2 - 1 ~= sum(k=1..4 | (x2 * ln(2))^k / k! )
+ with error less than 2^(1/512+7e-4) * (x2 * ln(2))^3 / 3! < 1.2e-18. */
+
+ x22 = (.240226507f * x + .6931471806f) * ex2_u.f;
+
+ /* 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.f;
+ }
+ /* 2^inf == inf, with no error. */
+ else if (x == *(const float *)&a_inf)
+ {
+ return x;
+ }
+ /* Check for overflow. */
+ else if (isgreaterequal (x, (float) FLT_MAX_EXP))
+ return huge * huge;
+ /* And underflow (including -inf). */
+ else if (isless (x, (float) (FLT_MIN_EXP - FLT_MANT_DIF)))
+ return TWOM100 * TWOM100;
+ /* Maybe the result needs to be a denormalised number... */
+ else if (!isnan (x))
+ return __ieee754_exp2f (x + 100.0) * TWOM100;
+ else /* isnan(x) */
+ return x + x;
+}