92 lines
2.4 KiB
C
92 lines
2.4 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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/* @(#)s_asinh.c 5.1 93/09/24 */
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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 SunPro, 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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#include <sys/cdefs.h>
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__FBSDID("$FreeBSD$");
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/*
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* See s_asinh.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 asinh(x) ~= log(2x). */
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/* EXP_TINY is the threshold below which we use asinh(x) ~= x. */
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#if LDBL_MANT_DIG == 64
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#define EXP_LARGE 34
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#define EXP_TINY -34
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#elif LDBL_MANT_DIG == 113
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#define EXP_LARGE 58
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#define EXP_TINY -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 = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
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huge= 1.00000000000000000000e+300;
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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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asinhl(long double x)
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{
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long double t, w;
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uint16_t hx, ix;
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ENTERI();
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GET_LDBL_EXPSIGN(hx, x);
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ix = hx & 0x7fff;
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if (ix >= 0x7fff) RETURNI(x+x); /* x is inf, NaN or misnormal */
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if (ix < BIAS + EXP_TINY) { /* |x| < TINY, or misnormal */
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if (huge + x > one) RETURNI(x); /* return x inexact except 0 */
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}
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if (ix >= BIAS + EXP_LARGE) { /* |x| >= LARGE, or misnormal */
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w = logl(fabsl(x))+ln2;
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} else if (ix >= 0x4000) { /* LARGE > |x| >= 2.0, or misnormal */
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t = fabsl(x);
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w = logl(2.0*t+one/(sqrtl(x*x+one)+t));
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} else { /* 2.0 > |x| >= TINY, or misnormal */
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t = x*x;
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w =log1pl(fabsl(x)+t/(one+sqrtl(one+t)));
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}
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RETURNI((hx & 0x8000) == 0 ? w : -w);
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}
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