/*
* CDDL HEADER START
*
* The contents of this file are subject to the terms of the
* Common Development and Distribution License (the "License").
* 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
* and limitations under the License.
*
* 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
* information: Portions Copyright [yyyy] [name of copyright owner]
*
* CDDL HEADER END
*/
/*
* Copyright 2011 Nexenta Systems, Inc. All rights reserved.
*/
/*
* Copyright 2006 Sun Microsystems, Inc. All rights reserved.
* Use is subject to license terms.
*/
#pragma weak __expm1l = expm1l
#if !defined(__sparc)
#error Unsupported architecture
#endif
/*
* expm1l(x)
*
* Table driven method
* Written by K.C. Ng, June 1995.
* Algorithm :
* 1. expm1(x) = x if x<2**-114
* 2. if |x| <= 0.0625 = 1/16, use approximation
* expm1(x) = x + x*P/(2-P)
* where
* P = x - z*(P1+z*(P2+z*(P3+z*(P4+z*(P5+z*P6+z*P7))))), z = x*x;
* (this formula is derived from
* 2-P+x = R = x*(exp(x)+1)/(exp(x)-1) ~ 2 + x*x/6 - x^4/360 + ...)
*
* P1 = 1.66666666666666666666666666666638500528074603030e-0001
* P2 = -2.77777777777777777777777759668391122822266551158e-0003
* P3 = 6.61375661375661375657437408890138814721051293054e-0005
* P4 = -1.65343915343915303310185228411892601606669528828e-0006
* P5 = 4.17535139755122945763580609663414647067443411178e-0008
* P6 = -1.05683795988668526689182102605260986731620026832e-0009
* P7 = 2.67544168821852702827123344217198187229611470514e-0011
*
* Accuracy: |R-x*(exp(x)+1)/(exp(x)-1)|<=2**-119.13
*
* 3. For 1/16 < |x| < 1.125, choose x(+-i) ~ +-(i+4.5)/64, i=0,..,67
* since
* exp(x) = exp(xi+(x-xi))= exp(xi)*exp((x-xi))
* we have
* expm1(x) = expm1(xi)+(exp(xi))*(expm1(x-xi))
* where
* |s=x-xi| <= 1/128
* and
* expm1(s)=2s/(2-R), R= s-s^2*(T1+s^2*(T2+s^2*(T3+s^2*(T4+s^2*T5))))
*
* T1 = 1.666666666666666666666666666660876387437e-1L,
* T2 = -2.777777777777777777777707812093173478756e-3L,
* T3 = 6.613756613756613482074280932874221202424e-5L,
* T4 = -1.653439153392139954169609822742235851120e-6L,
* T5 = 4.175314851769539751387852116610973796053e-8L;
*
* 4. For |x| >= 1.125, return exp(x)-1.
* (see algorithm for exp)
*
* Special cases:
* expm1l(INF) is INF, expm1l(NaN) is NaN;
* expm1l(-INF)= -1;
* for finite argument, only expm1l(0)=0 is exact.
*
* Accuracy:
* according to an error analysis, the error is always less than
* 2 ulp (unit in the last place).
*
* Misc. info.
* For 113 bit long double
* if x > 1.135652340629414394949193107797076342845e+4
* then expm1l(x) overflow;
*
* 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.
*/
#include "libm.h"
extern const long double _TBL_expl_hi[], _TBL_expl_lo[];
extern const long double _TBL_expm1lx[], _TBL_expm1l[];
static const long double
zero = +0.0L,
one = +1.0L,
two = +2.0L,
ln2_64 = +1.083042469624914545964425189778400898568e-2L,
ovflthreshold = +1.135652340629414394949193107797076342845e+4L,
invln2_32 = +4.616624130844682903551758979206054839765e+1L,
ln2_32hi = +2.166084939249829091928849858592451515688e-2L,
ln2_32lo = +5.209643502595475652782654157501186731779e-27L,
huge = +1.0e4000L,
tiny = +1.0e-4000L,
P1 = +1.66666666666666666666666666666638500528074603030e-0001L,
P2 = -2.77777777777777777777777759668391122822266551158e-0003L,
P3 = +6.61375661375661375657437408890138814721051293054e-0005L,
P4 = -1.65343915343915303310185228411892601606669528828e-0006L,
P5 = +4.17535139755122945763580609663414647067443411178e-0008L,
P6 = -1.05683795988668526689182102605260986731620026832e-0009L,
P7 = +2.67544168821852702827123344217198187229611470514e-0011L,
/* rational approximation coeffs for [-(ln2)/64,(ln2)/64] */
T1 = +1.666666666666666666666666666660876387437e-1L,
T2 = -2.777777777777777777777707812093173478756e-3L,
T3 = +6.613756613756613482074280932874221202424e-5L,
T4 = -1.653439153392139954169609822742235851120e-6L,
T5 = +4.175314851769539751387852116610973796053e-8L;
long double
expm1l(long double x) {
int hx, ix, j, k, m;
long double t, r, s, w;
hx = ((int *) &x)[HIXWORD];
ix = hx & ~0x80000000;
if (ix >= 0x7fff0000) {
if (x != x)
return (x + x); /* NaN */
if (x < zero)
return (-one); /* -inf */
return (x); /* +inf */
}
if (ix < 0x3fff4000) { /* |x| < 1.25 */
if (ix < 0x3ffb0000) { /* |x| < 0.0625 */
if (ix < 0x3f8d0000) {
if ((int) x == 0)
return (x); /* |x|<2^-114 */
}
t = x * x;
r = (x - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t *
(P5 + t * (P6 + t * P7)))))));
return (x + (x * r) / (two - r));
}
/* compute i = [64*x] */
m = 0x4009 - (ix >> 16);
j = ((ix & 0x0000ffff) | 0x10000) >> m; /* j=4,...,67 */
if (hx < 0)
j += 82; /* negative */
s = x - _TBL_expm1lx[j];
t = s * s;
r = s - t * (T1 + t * (T2 + t * (T3 + t * (T4 + t * T5))));
r = (s + s) / (two - r);
w = _TBL_expm1l[j];
return (w + (w + one) * r);
}
if (hx > 0) {
if (x > ovflthreshold)
return (huge * huge);
k = (int) (invln2_32 * (x + ln2_64));
} else {
if (x < -80.0)
return (tiny - x / x);
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) - one);
}