59 lines
1.5 KiB
C
59 lines
1.5 KiB
C
/* @(#)e_acosh.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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/* acoshl(x)
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* Method :
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* Based on
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* acoshl(x) = logl [ x + sqrtl(x*x-1) ]
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* we have
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* acoshl(x) := logl(x)+ln2, if x is large; else
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* acoshl(x) := logl(2x-1/(sqrtl(x*x-1)+x)) if x>2; else
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* acoshl(x) := log1pl(t+sqrtl(2.0*t+t*t)); where t=x-1.
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*
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* Special cases:
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* acoshl(x) is NaN with signal if x<1.
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* acoshl(NaN) is NaN without signal.
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*/
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#include <openlibm_math.h>
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#include "math_private.h"
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static const long double
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one = 1.0,
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ln2 = 0.6931471805599453094172321214581766L;
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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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u_int64_t lx;
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int64_t hx;
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GET_LDOUBLE_WORDS64(hx,lx,x);
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if(hx<0x3fff000000000000LL) { /* x < 1 */
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return (x-x)/(x-x);
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} else if(hx >=0x4035000000000000LL) { /* x > 2**54 */
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if(hx >=0x7fff000000000000LL) { /* x is inf of NaN */
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return x+x;
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} else
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return logl(x)+ln2; /* acoshl(huge)=logl(2x) */
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} else if(((hx-0x3fff000000000000LL)|lx)==0) {
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return 0.0L; /* acosh(1) = 0 */
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} else if (hx > 0x4000000000000000LL) { /* 2**28 > x > 2 */
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t=x*x;
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return logl(2.0L*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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return log1pl(t+sqrtl(2.0L*t+t*t));
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}
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}
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