mirror of
https://git.planet-casio.com/Lephenixnoir/OpenLibm.git
synced 2024-12-29 13:03:42 +01:00
7e5585aaca
This is a bit more consistent with the naming of the other header files (openlibm_complex.h and openlibm_fenv.h). Re-add an openlibm.h header that includes all of the public headers as a shorthand. Fix up all of the source files to include <openlibm_math.h> instead of <openlibm.h>. While there, fix ordering of the includes.
105 lines
3.3 KiB
C
105 lines
3.3 KiB
C
/*
|
|
* ====================================================
|
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
*
|
|
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
|
* Permission to use, copy, modify, and distribute this
|
|
* software is freely granted, provided that this notice
|
|
* is preserved.
|
|
* ====================================================
|
|
*/
|
|
|
|
/*
|
|
* Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
|
|
*
|
|
* Permission to use, copy, modify, and distribute this software for any
|
|
* purpose with or without fee is hereby granted, provided that the above
|
|
* copyright notice and this permission notice appear in all copies.
|
|
*
|
|
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
|
|
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
|
|
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
|
|
* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
|
|
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
|
|
* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
|
|
* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
|
|
*/
|
|
|
|
/* coshl(x)
|
|
* Method :
|
|
* mathematically coshl(x) if defined to be (exp(x)+exp(-x))/2
|
|
* 1. Replace x by |x| (coshl(x) = coshl(-x)).
|
|
* 2.
|
|
* [ exp(x) - 1 ]^2
|
|
* 0 <= x <= ln2/2 : coshl(x) := 1 + -------------------
|
|
* 2*exp(x)
|
|
*
|
|
* exp(x) + 1/exp(x)
|
|
* ln2/2 <= x <= 22 : coshl(x) := -------------------
|
|
* 2
|
|
* 22 <= x <= lnovft : coshl(x) := expl(x)/2
|
|
* lnovft <= x <= ln2ovft: coshl(x) := expl(x/2)/2 * expl(x/2)
|
|
* ln2ovft < x : coshl(x) := huge*huge (overflow)
|
|
*
|
|
* Special cases:
|
|
* coshl(x) is |x| if x is +INF, -INF, or NaN.
|
|
* only coshl(0)=1 is exact for finite x.
|
|
*/
|
|
|
|
#include <openlibm_math.h>
|
|
|
|
#include "math_private.h"
|
|
|
|
static const long double one = 1.0, half = 0.5, huge = 1.0e4900L,
|
|
ovf_thresh = 1.1357216553474703894801348310092223067821E4L;
|
|
|
|
long double
|
|
coshl(long double x)
|
|
{
|
|
long double t, w;
|
|
int32_t ex;
|
|
ieee_quad_shape_type u;
|
|
|
|
u.value = x;
|
|
ex = u.parts32.mswhi & 0x7fffffff;
|
|
|
|
/* Absolute value of x. */
|
|
u.parts32.mswhi = ex;
|
|
|
|
/* x is INF or NaN */
|
|
if (ex >= 0x7fff0000)
|
|
return x * x;
|
|
|
|
/* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */
|
|
if (ex < 0x3ffd62e4) /* 0.3465728759765625 */
|
|
{
|
|
t = expm1l (u.value);
|
|
w = one + t;
|
|
if (ex < 0x3fb80000) /* |x| < 2^-116 */
|
|
return w; /* cosh(tiny) = 1 */
|
|
|
|
return one + (t * t) / (w + w);
|
|
}
|
|
|
|
/* |x| in [0.5*ln2,40], return (exp(|x|)+1/exp(|x|)/2; */
|
|
if (ex < 0x40044000)
|
|
{
|
|
t = expl (u.value);
|
|
return half * t + half / t;
|
|
}
|
|
|
|
/* |x| in [22, ln(maxdouble)] return half*exp(|x|) */
|
|
if (ex <= 0x400c62e3) /* 11356.375 */
|
|
return half * expl (u.value);
|
|
|
|
/* |x| in [log(maxdouble), overflowthresold] */
|
|
if (u.value <= ovf_thresh)
|
|
{
|
|
w = expl (half * u.value);
|
|
t = half * w;
|
|
return t * w;
|
|
}
|
|
|
|
/* |x| > overflowthresold, cosh(x) overflow */
|
|
return huge * huge;
|
|
}
|