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/* @(#)e_acosh.c 5.1 93/09/24 */
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/* @(#)e_acosh.c 5.1 93/09/24 */
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/*
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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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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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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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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* software is freely granted, provided that this notice
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* is preserved.
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* is preserved.
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* ====================================================
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* ====================================================
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*
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*
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*/
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*/
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/* __ieee754_acosh(x)
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/* __ieee754_acosh(x)
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* Method :
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* Method :
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* Based on
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* Based on
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* acosh(x) = log [ x + sqrt(x*x-1) ]
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* acosh(x) = log [ x + sqrt(x*x-1) ]
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* we have
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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(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) := 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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* acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
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*
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*
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* Special cases:
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* Special cases:
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* acosh(x) is NaN with signal if x<1.
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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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* acosh(NaN) is NaN without signal.
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*/
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*/
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#include "fdlibm.h"
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#include "fdlibm.h"
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#ifndef _DOUBLE_IS_32BITS
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#ifndef _DOUBLE_IS_32BITS
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#ifdef __STDC__
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#ifdef __STDC__
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static const double
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static const double
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#else
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#else
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static double
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static double
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#endif
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#endif
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one = 1.0,
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one = 1.0,
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ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */
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ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */
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#ifdef __STDC__
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#ifdef __STDC__
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double __ieee754_acosh(double x)
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double __ieee754_acosh(double x)
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#else
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#else
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double __ieee754_acosh(x)
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double __ieee754_acosh(x)
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double x;
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double x;
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#endif
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#endif
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{
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{
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double t;
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double t;
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__int32_t hx;
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__int32_t hx;
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__uint32_t lx;
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__uint32_t lx;
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EXTRACT_WORDS(hx,lx,x);
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EXTRACT_WORDS(hx,lx,x);
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if(hx<0x3ff00000) { /* x < 1 */
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if(hx<0x3ff00000) { /* x < 1 */
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return (x-x)/(x-x);
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return (x-x)/(x-x);
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} else if(hx >=0x41b00000) { /* x > 2**28 */
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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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if(hx >=0x7ff00000) { /* x is inf of NaN */
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return x+x;
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return x+x;
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} else
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} else
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return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */
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return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */
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} else if(((hx-0x3ff00000)|lx)==0) {
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} else if(((hx-0x3ff00000)|lx)==0) {
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return 0.0; /* acosh(1) = 0 */
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return 0.0; /* acosh(1) = 0 */
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} else if (hx > 0x40000000) { /* 2**28 > x > 2 */
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} else if (hx > 0x40000000) { /* 2**28 > x > 2 */
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t=x*x;
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t=x*x;
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return __ieee754_log(2.0*x-one/(x+__ieee754_sqrt(t-one)));
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return __ieee754_log(2.0*x-one/(x+__ieee754_sqrt(t-one)));
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} else { /* 1<x<2 */
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} else { /* 1<x<2 */
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t = x-one;
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t = x-one;
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return log1p(t+__ieee754_sqrt(2.0*t+t*t));
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return log1p(t+__ieee754_sqrt(2.0*t+t*t));
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}
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}
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}
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}
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#endif /* defined(_DOUBLE_IS_32BITS) */
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#endif /* defined(_DOUBLE_IS_32BITS) */
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