/*
* CDDL HEADER START
*
* The contents of this file are subject to the terms of the
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* You may not use this file except in compliance with the License.
*
* You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
* or http://www.opensolaris.org/os/licensing.
* See the License for the specific language governing permissions
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*
* When distributing Covered Code, include this CDDL HEADER in each
* file and include the License file at usr/src/OPENSOLARIS.LICENSE.
* If applicable, add the following below this CDDL HEADER, with the
* fields enclosed by brackets "[]" replaced with your own identifying
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*/
/*
* Copyright 2011 Nexenta Systems, Inc. All rights reserved.
*/
/*
* Copyright 2006 Sun Microsystems, Inc. All rights reserved.
* Use is subject to license terms.
*/
/*
* expl(x)
* Table driven method
* Written by K.C. Ng, November 1988.
* Algorithm :
* 1. Argument Reduction: given the input x, find r and integer k
* and j such that
* x = (32k+j)*ln2 + r, |r| <= (1/64)*ln2 .
*
* 2. expl(x) = 2^k * (2^(j/32) + 2^(j/32)*expm1(r))
* Note:
* a. expm1(r) = (2r)/(2-R), R = r - r^2*(t1 + t2*r^2)
* b. 2^(j/32) is represented as
* _TBL_expl_hi[j]+_TBL_expl_lo[j]
* where
* _TBL_expl_hi[j] = 2^(j/32) rounded
* _TBL_expl_lo[j] = 2^(j/32) - _TBL_expl_hi[j].
*
* Special cases:
* expl(INF) is INF, expl(NaN) is NaN;
* expl(-INF)= 0;
* for finite argument, only expl(0)=1 is exact.
*
* Accuracy:
* according to an error analysis, the error is always less than
* an ulp (unit in the last place).
*
* Misc. info.
* For 113 bit long double
* if x > 1.135652340629414394949193107797076342845e+4
* then expl(x) overflow;
* if x < -1.143346274333629787883724384345262150341e+4
* then expl(x) underflow
*
* Constants:
* Only decimal values are given. We assume that the compiler will convert
* from decimal to binary accurately enough to produce the correct
* hexadecimal values.
*/
#pragma weak __expl = expl
#include "libm.h"
extern const long double _TBL_expl_hi[], _TBL_expl_lo[];
static const long double
one = 1.0L,
two = 2.0L,
ln2_64 = 1.083042469624914545964425189778400898568e-2L,
ovflthreshold = 1.135652340629414394949193107797076342845e+4L,
unflthreshold = -1.143346274333629787883724384345262150341e+4L,
invln2_32 = 4.616624130844682903551758979206054839765e+1L,
ln2_32hi = 2.166084939249829091928849858592451515688e-2L,
ln2_32lo = 5.209643502595475652782654157501186731779e-27L;
/* rational approximation coeffs for [-(ln2)/64,(ln2)/64] */
static const long double
t1 = 1.666666666666666666666666666660876387437e-1L,
t2 = -2.777777777777777777777707812093173478756e-3L,
t3 = 6.613756613756613482074280932874221202424e-5L,
t4 = -1.653439153392139954169609822742235851120e-6L,
t5 = 4.175314851769539751387852116610973796053e-8L;
long double
expl(long double x) {
int *px = (int *) &x, ix, j, k, m;
long double t, r;
ix = px[0]; /* high word of x */
if (ix >= 0x7fff0000)
return (x + x); /* NaN of +inf */
if (((unsigned) ix) >= 0xffff0000)
return (-one / x); /* NaN or -inf */
if ((ix & 0x7fffffff) < 0x3fc30000) {
if ((int) x < 1)
return (one + x); /* |x|<2^-60 */
}
if (ix > 0) {
if (x > ovflthreshold)
return (scalbnl(x, 20000));
k = (int) (invln2_32 * (x + ln2_64));
} else {
if (x < unflthreshold)
return (scalbnl(-x, -40000));
k = (int) (invln2_32 * (x - ln2_64));
}
j = k&0x1f;
m = k>>5;
t = (long double) k;
x = (x - t * ln2_32hi) - t * ln2_32lo;
t = x * x;
r = (x - t * (t1 + t * (t2 + t * (t3 + t * (t4 + t * t5))))) - two;
x = _TBL_expl_hi[j] - ((_TBL_expl_hi[j] * (x + x)) / r -
_TBL_expl_lo[j]);
return (scalbnl(x, m));
}