1*05a0b428SJohn Marino /* @(#)s_asinh.c 5.1 93/09/24 */
2*05a0b428SJohn Marino /*
3*05a0b428SJohn Marino * ====================================================
4*05a0b428SJohn Marino * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5*05a0b428SJohn Marino *
6*05a0b428SJohn Marino * Developed at SunPro, a Sun Microsystems, Inc. business.
7*05a0b428SJohn Marino * Permission to use, copy, modify, and distribute this
8*05a0b428SJohn Marino * software is freely granted, provided that this notice
9*05a0b428SJohn Marino * is preserved.
10*05a0b428SJohn Marino * ====================================================
11*05a0b428SJohn Marino */
12*05a0b428SJohn Marino
13*05a0b428SJohn Marino /* asinh(x)
14*05a0b428SJohn Marino * Method :
15*05a0b428SJohn Marino * Based on
16*05a0b428SJohn Marino * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
17*05a0b428SJohn Marino * we have
18*05a0b428SJohn Marino * asinh(x) := x if 1+x*x=1,
19*05a0b428SJohn Marino * := sign(x)*(log(x)+ln2)) for large |x|, else
20*05a0b428SJohn Marino * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
21*05a0b428SJohn Marino * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
22*05a0b428SJohn Marino */
23*05a0b428SJohn Marino
24*05a0b428SJohn Marino #include <float.h>
25*05a0b428SJohn Marino #include <math.h>
26*05a0b428SJohn Marino
27*05a0b428SJohn Marino #include "math_private.h"
28*05a0b428SJohn Marino
29*05a0b428SJohn Marino static const double
30*05a0b428SJohn Marino one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
31*05a0b428SJohn Marino ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
32*05a0b428SJohn Marino huge= 1.00000000000000000000e+300;
33*05a0b428SJohn Marino
34*05a0b428SJohn Marino double
asinh(double x)35*05a0b428SJohn Marino asinh(double x)
36*05a0b428SJohn Marino {
37*05a0b428SJohn Marino double t,w;
38*05a0b428SJohn Marino int32_t hx,ix;
39*05a0b428SJohn Marino GET_HIGH_WORD(hx,x);
40*05a0b428SJohn Marino ix = hx&0x7fffffff;
41*05a0b428SJohn Marino if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */
42*05a0b428SJohn Marino if(ix< 0x3e300000) { /* |x|<2**-28 */
43*05a0b428SJohn Marino if(huge+x>one) return x; /* return x inexact except 0 */
44*05a0b428SJohn Marino }
45*05a0b428SJohn Marino if(ix>0x41b00000) { /* |x| > 2**28 */
46*05a0b428SJohn Marino w = log(fabs(x))+ln2;
47*05a0b428SJohn Marino } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */
48*05a0b428SJohn Marino t = fabs(x);
49*05a0b428SJohn Marino w = log(2.0*t+one/(sqrt(x*x+one)+t));
50*05a0b428SJohn Marino } else { /* 2.0 > |x| > 2**-28 */
51*05a0b428SJohn Marino t = x*x;
52*05a0b428SJohn Marino w =log1p(fabs(x)+t/(one+sqrt(one+t)));
53*05a0b428SJohn Marino }
54*05a0b428SJohn Marino if(hx>0) return w; else return -w;
55*05a0b428SJohn Marino }
56*05a0b428SJohn Marino
57*05a0b428SJohn Marino #if LDBL_MANT_DIG == DBL_MANT_DIG
58*05a0b428SJohn Marino __strong_alias(asinhl, asinh);
59*05a0b428SJohn Marino #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */
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