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/* @(#)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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/* acosh(x) |
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* Method : |
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* Based on |
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* acosh(x) = log [ x + sqrt(x*x-1) ] |
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* we have |
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* acosh(x) := log(x)+ln2, if x is large; else |
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* acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else |
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* acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. |
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* |
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* Special cases: |
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* acosh(x) is NaN with signal if x<1. |
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* acosh(NaN) is NaN without signal. |
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*/ |
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#include <float.h> |
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#include <math.h> |
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#include "math_private.h" |
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static const double |
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one = 1.0, |
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ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ |
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double |
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acosh(double x) |
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{ |
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double t; |
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int32_t hx; |
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u_int32_t lx; |
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EXTRACT_WORDS(hx,lx,x); |
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✗✓ |
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if(hx<0x3ff00000) { /* x < 1 */ |
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return (x-x)/(x-x); |
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✗✓ |
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} else if(hx >=0x41b00000) { /* x > 2**28 */ |
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if(hx >=0x7ff00000) { /* x is inf of NaN */ |
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return x+x; |
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} else |
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return log(x)+ln2; /* acosh(huge)=log(2x) */ |
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✗✓ |
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} else if(((hx-0x3ff00000)|lx)==0) { |
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return 0.0; /* acosh(1) = 0 */ |
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✓✓ |
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} else if (hx > 0x40000000) { /* 2**28 > x > 2 */ |
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t=x*x; |
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return log(2.0*x-one/(x+sqrt(t-one))); |
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} else { /* 1<x<2 */ |
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t = x-one; |
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return log1p(t+sqrt(2.0*t+t*t)); |
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} |
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} |
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DEF_STD(acosh); |
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LDBL_MAYBE_UNUSED_CLONE(acosh); |