Optimized acosh for 64-bit platforms
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2012-01-11 Ulrich Drepper <drepper@gmail.com>
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* sysdeps/ieee754/dbl-64/wordsize-64/e_acosh.c: New file.
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* sysdeps/ieee754/dbl-64/s_scalbln.c: Add branch prediction.
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* sysdeps/ieee754/flt-32/s_scalblnf.c: Likewise.
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* sysdeps/ieee754/ldbl-96/s_scalblnl.c: Likewise.
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/* Optimized for 64-bit by Ulrich Drepper <drepper@gmail.com>, 2012 */
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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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int64_t hx;
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EXTRACT_WORDS64 (hx, x);
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if (hx > INT64_C (0x4000000000000000))
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{
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if (__builtin_expect (hx >= INT64_C (0x41b0000000000000), 0))
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{
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/* x > 2**28 */
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if (hx >= INT64_C (0x7ff0000000000000))
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/* x is inf of NaN */
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return x + x;
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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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/* 2**28 > x > 2 */
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double 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 if (__builtin_expect (hx > INT64_C (0x3ff0000000000000), 1))
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{
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/* 1<x<2 */
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double 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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else if (__builtin_expect (hx == INT64_C (0x3ff0000000000000), 1))
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return 0.0; /* acosh(1) = 0 */
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else /* x < 1 */
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return (x - x) / (x - x);
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}
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strong_alias (__ieee754_acosh, __acosh_finite)
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