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/* from: FreeBSD: head/lib/msun/src/e_acosh.c 176451 2008-02-22 02:30:36Z das */
/* @(#)e_acosh.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
/*
* See e_acosh.c for complete comments.
*
* Converted to long double by David Schultz <das@FreeBSD.ORG> and
* Bruce D. Evans.
*/
#include <float.h>
#ifdef __i386__
#include <ieeefp.h>
#endif
#include "fpmath.h"
#include "math.h"
#include "math_private.h"
/* EXP_LARGE is the threshold above which we use acosh(x) ~= log(2x). */
#if LDBL_MANT_DIG == 64
#define EXP_LARGE 34
#elif LDBL_MANT_DIG == 113
#define EXP_LARGE 58
#else
#error "Unsupported long double format"
#endif
#if LDBL_MAX_EXP != 0x4000
/* We also require the usual expsign encoding. */
#error "Unsupported long double format"
#endif
#define BIAS (LDBL_MAX_EXP - 1)
static const double
one = 1.0;
#if LDBL_MANT_DIG == 64
static const union IEEEl2bits
u_ln2 = LD80C(0xb17217f7d1cf79ac, -1, 6.93147180559945309417e-1L);
#define ln2 u_ln2.e
#elif LDBL_MANT_DIG == 113
static const long double
ln2 = 6.93147180559945309417232121458176568e-1L; /* 0x162e42fefa39ef35793c7673007e6.0p-113 */
#else
#error "Unsupported long double format"
#endif
long double
acoshl(long double x)
{
long double t;
int16_t hx;
ENTERI();
GET_LDBL_EXPSIGN(hx, x);
if (hx < 0x3fff) { /* x < 1, or misnormal */
RETURNI((x-x)/(x-x));
} else if (hx >= BIAS + EXP_LARGE) { /* x >= LARGE */
if (hx >= 0x7fff) { /* x is inf, NaN or misnormal */
RETURNI(x+x);
} else
RETURNI(logl(x)+ln2); /* acosh(huge)=log(2x), or misnormal */
} else if (hx == 0x3fff && x == 1) {
RETURNI(0.0); /* acosh(1) = 0 */
} else if (hx >= 0x4000) { /* LARGE > x >= 2, or misnormal */
t=x*x;
RETURNI(logl(2.0*x-one/(x+sqrtl(t-one))));
} else { /* 1<x<2 */
t = x-one;
RETURNI(log1pl(t+sqrtl(2.0*t+t*t)));
}
}
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