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