2014-09-21 17:33:12 +00:00
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/* acoshq.c -- __float128 version of e_acosh.c.
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2012-03-27 23:13:14 +00:00
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* Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz.
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*/
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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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2014-09-21 17:33:12 +00:00
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/* acoshq(x)
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2012-03-27 23:13:14 +00:00
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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 "quadmath-imp.h"
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static const __float128
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one = 1.0Q,
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ln2 = 0.6931471805599453094172321214581766Q;
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__float128
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acoshq (__float128 x)
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{
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__float128 t;
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uint64_t lx;
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int64_t hx;
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GET_FLT128_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 logq(x)+ln2; /* acoshl(huge)=logl(2x) */
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} else if(((hx-0x3fff000000000000LL)|lx)==0) {
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return 0.0Q; /* 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 logq(2.0Q*x-one/(x+sqrtq(t-one)));
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} else { /* 1<x<2 */
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t = x-one;
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return log1pq(t+sqrtq(2.0Q*t+t*t));
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}
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}
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