70 lines
1.7 KiB
C
70 lines
1.7 KiB
C
/* @(#)s_asinh.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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/* asinhl(x)
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* Method :
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* Based on
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* asinhl(x) = signl(x) * logl [ |x| + sqrtl(x*x+1) ]
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* we have
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* asinhl(x) := x if 1+x*x=1,
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* := signl(x)*(logl(x)+ln2)) for large |x|, else
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* := signl(x)*logl(2|x|+1/(|x|+sqrtl(x*x+1))) if|x|>2, else
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* := signl(x)*log1pl(|x| + x^2/(1 + sqrtl(1+x^2)))
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*/
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#include <openlibm_math.h>
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#include "math_private.h"
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static const long double
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one = 1.0L,
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ln2 = 6.931471805599453094172321214581765681e-1L,
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huge = 1.0e+4900L;
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long double
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asinhl(long double x)
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{
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long double t, w;
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int32_t ix, sign;
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ieee_quad_shape_type u;
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u.value = x;
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sign = u.parts32.mswhi;
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ix = sign & 0x7fffffff;
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if (ix == 0x7fff0000)
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return x + x; /* x is inf or NaN */
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if (ix < 0x3fc70000)
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{ /* |x| < 2^ -56 */
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if (huge + x > one)
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return x; /* return x inexact except 0 */
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}
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u.parts32.mswhi = ix;
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if (ix > 0x40350000)
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{ /* |x| > 2 ^ 54 */
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w = logl (u.value) + ln2;
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}
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else if (ix >0x40000000)
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{ /* 2^ 54 > |x| > 2.0 */
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t = u.value;
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w = logl (2.0 * t + one / (sqrtl (x * x + one) + t));
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}
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else
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{ /* 2.0 > |x| > 2 ^ -56 */
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t = x * x;
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w = log1pl (u.value + t / (one + sqrtl (one + t)));
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}
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if (sign & 0x80000000)
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return -w;
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else
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return w;
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}
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