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70 lines
1.8 KiB
C
70 lines
1.8 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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/* __ieee754_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 <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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__ieee754_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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if (hx < 0x3ff00000) /* x < 1 */
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{
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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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{
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if (hx >= 0x7ff00000) /* x is inf of NaN */
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{
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return x + x;
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}
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else
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return __ieee754_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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{
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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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{
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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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}
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else /* 1<x<2 */
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{
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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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}
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}
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strong_alias (__ieee754_acosh, __acosh_finite)
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