mirror of
https://git.planet-casio.com/Lephenixnoir/OpenLibm.git
synced 2024-12-29 13:03:42 +01:00
06dbb6e72b
Put external headers before internal ones. While there, replace a lot of occurences of "openlibm.h" with <openlibm.h>. It should be thought of as an external header, as it is installed along with the library.
83 lines
2.3 KiB
C
83 lines
2.3 KiB
C
/* @(#)e_cosh.c 5.1 93/09/24 */
|
|
/*
|
|
* ====================================================
|
|
* 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.
|
|
* ====================================================
|
|
*/
|
|
|
|
/* 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.h>
|
|
|
|
#include "math_private.h"
|
|
|
|
static const long double one = 1.0, half=0.5, huge = 1.0e4900L;
|
|
|
|
long double
|
|
coshl(long double x)
|
|
{
|
|
long double t,w;
|
|
int32_t ex;
|
|
u_int32_t mx,lx;
|
|
|
|
/* High word of |x|. */
|
|
GET_LDOUBLE_WORDS(ex,mx,lx,x);
|
|
ex &= 0x7fff;
|
|
|
|
/* x is INF or NaN */
|
|
if(ex==0x7fff) return x*x;
|
|
|
|
/* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */
|
|
if(ex < 0x3ffd || (ex == 0x3ffd && mx < 0xb17217f7u)) {
|
|
t = expm1l(fabsl(x));
|
|
w = one+t;
|
|
if (ex<0x3fbc) return w; /* cosh(tiny) = 1 */
|
|
return one+(t*t)/(w+w);
|
|
}
|
|
|
|
/* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
|
|
if (ex < 0x4003 || (ex == 0x4003 && mx < 0xb0000000u)) {
|
|
t = expl(fabsl(x));
|
|
return half*t+half/t;
|
|
}
|
|
|
|
/* |x| in [22, ln(maxdouble)] return half*exp(|x|) */
|
|
if (ex < 0x400c || (ex == 0x400c && mx < 0xb1700000u))
|
|
return half*expl(fabsl(x));
|
|
|
|
/* |x| in [log(maxdouble), log(2*maxdouble)) */
|
|
if (ex == 0x400c && (mx < 0xb174ddc0u
|
|
|| (mx == 0xb174ddc0u && lx < 0x31aec0ebu)))
|
|
{
|
|
w = expl(half*fabsl(x));
|
|
t = half*w;
|
|
return t*w;
|
|
}
|
|
|
|
/* |x| >= log(2*maxdouble), cosh(x) overflow */
|
|
return huge*huge;
|
|
}
|