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math: long double trigonometric cleanup (cosl, sinl, sincosl, tanl)

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ld128 support was added to internal kernel functions (__cosl, __sinl,
__tanl, __rem_pio2l) from freebsd (not tested, but should be a good
start for when ld128 arch arrives)

__rem_pio2l had some code cleanup, the freebsd ld128 code seems to
gather the results of a large reduction with precision loss (fixed
the bug but a todo comment was added for later investigation)

the old copyright was removed from the non-kernel wrapper functions
(cosl, sinl, sincosl, tanl) since these are trivial and the interesting
parts and comments had been already rewritten.
This commit is contained in:
Szabolcs Nagy
2013-09-03 18:50:58 +00:00
parent bcd797a5ba
commit ea9bb95a5b
8 changed files with 228 additions and 236 deletions
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70
src/math/cosl.c
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@ -1,34 +1,3 @@
/* origin: FreeBSD /usr/src/lib/msun/src/s_cosl.c */
/*-
* Copyright (c) 2007 Steven G. Kargl
* 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 unmodified, 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 ``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 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.
*/
/*
* Limited testing on pseudorandom numbers drawn within [-2e8:4e8] shows
* an accuracy of <= 0.7412 ULP.
*/
#include "libm.h"
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
@ -38,44 +7,33 @@ long double cosl(long double x) {
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
long double cosl(long double x)
{
union IEEEl2bits z;
union ldshape u = {x};
unsigned n;
long double y[2];
long double hi, lo;
long double y[2], hi, lo;
z.e = x;
z.bits.sign = 0;
/* If x = NaN or Inf, then cos(x) = NaN. */
if (z.bits.exp == 0x7fff)
return (x - x) / (x - x);
/* |x| < (double)pi/4 */
if (z.e < M_PI_4) {
/* |x| < 0x1p-64 */
if (z.bits.exp < 0x3fff - 64)
u.i.se &= 0x7fff;
if (u.i.se == 0x7fff)
return x - x;
x = u.f;
if (x < M_PI_4) {
if (u.i.se < 0x3fff - LDBL_MANT_DIG)
/* raise inexact if x!=0 */
return 1.0 + x;
return __cosl(z.e, 0);
return __cosl(x, 0);
}
n = __rem_pio2l(x, y);
hi = y[0];
lo = y[1];
switch (n & 3) {
case 0:
hi = __cosl(hi, lo);
break;
return __cosl(hi, lo);
case 1:
hi = -__sinl(hi, lo, 1);
break;
return -__sinl(hi, lo, 1);
case 2:
hi = -__cosl(hi, lo);
break;
return -__cosl(hi, lo);
case 3:
hi = __sinl(hi, lo, 1);
break;
default:
return __sinl(hi, lo, 1);
}
return hi;
}
#endif