127 lines
3.9 KiB
C
127 lines
3.9 KiB
C
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/* Single-precision floating point 2^x.
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Copyright (C) 1997 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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Contributed by Geoffrey Keating <geoffk@ozemail.com.au>
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Library General Public License as
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published by the Free Software Foundation; either version 2 of the
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License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Library General Public License for more details.
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You should have received a copy of the GNU Library General Public
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License along with the GNU C Library; see the file COPYING.LIB. If not,
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write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
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Boston, MA 02111-1307, USA. */
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/* The basic design here is from
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Shmuel Gal and Boris Bachelis, "An Accurate Elementary Mathematical
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Library for the IEEE Floating Point Standard", ACM Trans. Math. Soft.,
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17 (1), March 1991, pp. 26-45.
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It has been slightly modified to compute 2^x instead of e^x, and for
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single-precision.
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*/
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#define _GNU_SOURCE
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#include <float.h>
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#include <ieee754.h>
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#include <math.h>
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#include <fenv.h>
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#include <inttypes.h>
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#include <math_private.h>
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#include "t_exp2f.h"
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static const volatile float TWOM100 = 7.88860905e-31;
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static const volatile float huge = 1e+30;
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float
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__ieee754_exp2f (float x)
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{
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static const uint32_t a_inf = 0x7f800000;
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/* Check for usual case. */
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if (isless (x, (float) FLT_MAX_EXP)
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&& isgreater (x, (float) (FLT_MIN_EXP - 1)))
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{
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static const float TWO16 = 65536.0;
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int tval;
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float rx, x22;
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union ieee754_float ex2_u;
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fenv_t oldenv;
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feholdexcept (&oldenv);
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fesetround (FE_TONEAREST);
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/* 1. Argument reduction.
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Choose integers ex, -128 <= t < 128, and some real
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-1/512 <= x1 <= 1/512 so that
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x = ex + t/512 + x1.
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First, calculate rx = ex + t/256. */
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if (x >= 0)
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{
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rx = x + TWO16;
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rx -= TWO16;
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}
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else
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{
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rx = x - TWO16;
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rx += TWO16;
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}
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x -= rx; /* Compute x=x1. */
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/* Compute tval = (ex*256 + t)+128.
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Now, t = (tval mod 256)-128 and ex=tval/256 [that's mod, NOT %; and
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/-round-to-nearest not the usual c integer /]. */
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tval = (int) (rx * 256.0f + 128.0f);
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/* 2. Adjust for accurate table entry.
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Find e so that
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x = ex + t/256 + e + x2
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where -7e-4 < e < 7e-4, and
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(float)(2^(t/256+e))
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is accurate to one part in 2^-64. */
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/* 'tval & 255' is the same as 'tval%256' except that it's always
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positive.
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Compute x = x2. */
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x -= exp2_deltatable[tval & 255];
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/* 3. Compute ex2 = 2^(t/255+e+ex). */
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ex2_u.f = exp2_accuratetable[tval & 255];
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ex2_u.ieee.exponent += tval >> 8;
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/* 4. Approximate 2^x2 - 1, using a second-degree polynomial,
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2^x2 ~= sum(k=0..2 | (x2 * ln(2))^k / k! ) +
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so
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2^x2 - 1 ~= sum(k=1..4 | (x2 * ln(2))^k / k! )
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with error less than 2^(1/512+7e-4) * (x2 * ln(2))^3 / 3! < 1.2e-18. */
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x22 = (.240226507f * x + .6931471806f) * ex2_u.f;
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/* 5. Return (2^x2-1) * 2^(t/512+e+ex) + 2^(t/512+e+ex). */
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fesetenv (&oldenv);
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/* Need to check: does this set FE_INEXACT correctly? */
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return x22 * x + ex2_u.f;
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}
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/* 2^inf == inf, with no error. */
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else if (x == *(const float *)&a_inf)
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{
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return x;
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}
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/* Check for overflow. */
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else if (isgreaterequal (x, (float) FLT_MAX_EXP))
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return huge * huge;
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/* And underflow (including -inf). */
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else if (isless (x, (float) (FLT_MIN_EXP - FLT_MANT_DIF)))
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return TWOM100 * TWOM100;
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/* Maybe the result needs to be a denormalised number... */
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else if (!isnan (x))
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return __ieee754_exp2f (x + 100.0) * TWOM100;
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else /* isnan(x) */
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return x + x;
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}
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