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clean up __expo2.c, use a slightly better k constant

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nsz 2012-03-13 16:38:22 +01:00
commit df8b3e5aef
2 changed files with 14 additions and 84 deletions
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49
src/math/__expo2.c
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@ -1,51 +1,16 @@
/* origin: FreeBSD /usr/src/lib/msun/src/k_exp.c */
/*-
* Copyright (c) 2011 David Schultz <das@FreeBSD.ORG>
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*/
#include "libm.h" #include "libm.h"
/* /* k is such that k*ln2 has minimal relative error and x - kln2 > log(DBL_MIN) */
* We use exp(x) = exp(x - kln2) * 2**k, static const int k = 2043;
* k is carefully chosen to minimize |exp(kln2) - 2**k| static const double kln2 = 0x1.62066151add8bp+10;
*/
static const uint32_t k = 1799;
static const double kln2 = 1246.97177782734161156;
/* exp(x)/2 when x is huge */ /* exp(x)/2 for x >= log(DBL_MAX), slightly better than 0.5*exp(x/2)*exp(x/2) */
double __expo2(double x) double __expo2(double x)
{ {
double scale; double scale;
int n;
/* /* note that k is odd and scale*scale overflows */
* efficient scalbn(y, k-1): INSERT_WORDS(scale, (uint32_t)(0x3ff + k/2) << 20, 0);
* 2**(k-1) cannot be represented /* exp(x - k ln2) * 2**(k-1) */
* so we use that k-1 is even and scale in two steps
*/
n = (k - 1)/2;
INSERT_WORDS(scale, (0x3ff + n) << 20, 0);
return exp(x - kln2) * scale * scale; return exp(x - kln2) * scale * scale;
} }

49
src/math/__expo2f.c
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@ -1,51 +1,16 @@
/* origin: FreeBSD /usr/src/lib/msun/src/k_expf.c */
/*-
* Copyright (c) 2011 David Schultz <das@FreeBSD.ORG>
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*/
#include "libm.h" #include "libm.h"
/* /* k is such that k*ln2 has minimal relative error and x - kln2 > log(FLT_MIN) */
* We use exp(x) = exp(x - kln2) * 2**k, static const int k = 235;
* k is carefully chosen to minimize |exp(kln2) - 2**k| static const float kln2 = 0x1.45c778p+7f;
*/
static const uint32_t k = 235;
static const float kln2 = 162.88958740f;
/* expf(x)/2 when x is huge */ /* expf(x)/2 for x >= log(FLT_MAX), slightly better than 0.5f*expf(x/2)*expf(x/2) */
float __expo2f(float x) float __expo2f(float x)
{ {
float scale; float scale;
int n;
/* /* note that k is odd and scale*scale overflows */
* efficient scalbnf(y, k-1): SET_FLOAT_WORD(scale, (uint32_t)(0x7f + k/2) << 23);
* 2**(k-1) cannot be represented /* exp(x - k ln2) * 2**(k-1) */
* so we use that k-1 is even and scale in two steps
*/
n = (k - 1)/2;
SET_FLOAT_WORD(scale, (0x7f + n) << 23);
return expf(x - kln2) * scale * scale; return expf(x - kln2) * scale * scale;
} }