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dba466c344
. Fix the threshold for expl(x) where |x| is small.
. Also update the previously incorrect comment to match the
new threshold.
* ld128/s_expl.c:
. Re-order logic in exceptional cases to match the logic used in
other long double functions.
. Fix the threshold for expl(x) where is |x| is small.
. Also update the previously incorrect comment to match the
new threshold.
Submitted by: bde
Approved by: das (mentor)
262 lines
13 KiB
C
262 lines
13 KiB
C
/*-
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* Copyright (c) 2012 Steven G. Kargl
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice unmodified, this list of conditions, and the following
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* disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
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* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
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* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
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* IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
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* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
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* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
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* THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*/
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#include <sys/cdefs.h>
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__FBSDID("$FreeBSD$");
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/*
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* ld128 version of s_expl.c. See ../ld80/s_expl.c for most comments.
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*/
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#include <float.h>
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#include "fpmath.h"
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#include "math.h"
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#include "math_private.h"
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#define INTERVALS 128
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#define BIAS (LDBL_MAX_EXP - 1)
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static volatile const long double tiny = 0x1p-10000L;
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static const long double
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INV_L = 1.84664965233787316142070359168242182e+02L,
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L1 = 5.41521234812457272982212595914567508e-03L,
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L2 = -1.02536706388947310094527932552595546e-29L,
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huge = 0x1p10000L,
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o_threshold = 11356.523406294143949491931077970763428L,
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twom10000 = 0x1p-10000L,
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u_threshold = -11433.462743336297878837243843452621503L;
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static const long double
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P2 = 5.00000000000000000000000000000000000e-1L,
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P3 = 1.66666666666666666666666666666666972e-1L,
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P4 = 4.16666666666666666666666666653708268e-2L,
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P5 = 8.33333333333333333333333315069867254e-3L,
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P6 = 1.38888888888888888888996596213795377e-3L,
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P7 = 1.98412698412698412718821436278644414e-4L,
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P8 = 2.48015873015869681884882576649543128e-5L,
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P9 = 2.75573192240103867817876199544468806e-6L,
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P10 = 2.75573236172670046201884000197885520e-7L,
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P11 = 2.50517544183909126492878226167697856e-8L;
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static const struct {
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long double hi;
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long double lo;
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} s[INTERVALS] = {
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0x1p0L, 0x0p0L,
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0x1.f252b376bba974e8696fc2p0L, 0x1.6390d4c6ad5476b5162f40e1d9a9p-88L,
|
|
0x1.f50765b6e4540674f84b76p0L, 0x2.862baff99000dfc4352ba29b8908p-92L,
|
|
0x1.f7bfdad9cbe138913b4bfep0L, 0x7.2bd95c5ce7280fa4d2344a3f5618p-92L,
|
|
0x1.fa7c1819e90d82e90a7e74p0L, 0xb.263c1dc060c36f7650b4c0f233a8p-92L,
|
|
0x1.fd3c22b8f71f10975ba4b2p0L, 0x1.2bcf3a5e12d269d8ad7c1a4a8875p-88L
|
|
};
|
|
|
|
long double
|
|
expl(long double x)
|
|
{
|
|
union IEEEl2bits u, v;
|
|
long double fn, r, r1, r2, q, t, twopk, twopkp10000;
|
|
int k, n, n2;
|
|
uint32_t hx, ix;
|
|
|
|
/* Filter out exceptional cases. */
|
|
u.e = x;
|
|
hx = u.xbits.expsign;
|
|
ix = hx & 0x7fff;
|
|
if (ix >= BIAS + 13) { /* |x| >= 8192 or x is NaN */
|
|
if (ix == BIAS + LDBL_MAX_EXP) {
|
|
if (hx & 0x8000 && u.xbits.manh == 0 &&
|
|
u.xbits.manl == 0)
|
|
return (0.0L); /* x is -Inf */
|
|
return (x + x); /* x is +Inf or NaN */
|
|
}
|
|
if (x > o_threshold)
|
|
return (huge * huge);
|
|
if (x < u_threshold)
|
|
return (tiny * tiny);
|
|
} else if (ix < BIAS - 115) { /* |x| < 0x1p-115 */
|
|
if (huge + x > 1.0L) /* trigger inexact iff x != 0 */
|
|
return (1.0L + x);
|
|
}
|
|
|
|
/* Reduce x to (k*ln2 + midpoint[n2] + r1 + r2). */
|
|
fn = x * INV_L + 0x1.8p112 - 0x1.8p112;
|
|
n = (int)fn;
|
|
n2 = (unsigned)n % INTERVALS;
|
|
k = (n - n2) / INTERVALS;
|
|
r1 = x - fn * L1;
|
|
r2 = -fn * L2;
|
|
|
|
/* Prepare scale factors. */
|
|
v.xbits.manh = 0;
|
|
v.xbits.manl = 0;
|
|
if (k >= LDBL_MIN_EXP) {
|
|
v.xbits.expsign = BIAS + k;
|
|
twopk = v.e;
|
|
} else {
|
|
v.xbits.expsign = BIAS + k + 10000;
|
|
twopkp10000 = v.e;
|
|
}
|
|
|
|
r = r1 + r2;
|
|
q = r * r * (P2 + r * (P3 + r * (P4 + r * (P5 + r * (P6 + r * (P7 +
|
|
r * (P8 + r * (P9 + r * (P10 + r * P11)))))))));
|
|
t = s[n2].lo + s[n2].hi;
|
|
t = s[n2].hi + (s[n2].lo + t * (r2 + q + r1));
|
|
|
|
/* Scale by 2**k. */
|
|
if (k >= LDBL_MIN_EXP) {
|
|
if (k == LDBL_MAX_EXP)
|
|
return (t * 2.0L * 0x1p16383L);
|
|
return (t * twopk);
|
|
} else {
|
|
return (t * twopkp10000 * twom10000);
|
|
}
|
|
}
|