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/* @(#)s_asinh.c 5.1 93/09/24 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */
 
/*
FUNCTION
        <<asinh>>, <<asinhf>>---inverse hyperbolic sine
 
INDEX
        asinh
INDEX
        asinhf
 
ANSI_SYNOPSIS
        #include <math.h>
        double asinh(double <[x]>);
        float asinhf(float <[x]>);
 
TRAD_SYNOPSIS
        #include <math.h>
        double asinh(<[x]>)
        double <[x]>;
 
        float asinhf(<[x]>)
        float <[x]>;
 
DESCRIPTION
<<asinh>> calculates the inverse hyperbolic sine of <[x]>.
<<asinh>> is defined as
@ifinfo
. sgn(<[x]>) * log(abs(<[x]>) + sqrt(1+<[x]>*<[x]>))
@end ifinfo
@tex
$$sign(x) \times ln\Bigl(|x| + \sqrt{1+x^2}\Bigr)$$
@end tex
 
<<asinhf>> is identical, other than taking and returning floats.
 
RETURNS
<<asinh>> and <<asinhf>> return the calculated value.
 
PORTABILITY
Neither <<asinh>> nor <<asinhf>> are ANSI C.
 
*/
 
/* asinh(x)
 * Method :
 *      Based on
 *              asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
 *      we have
 *      asinh(x) := x  if  1+x*x=1,
 *               := sign(x)*(log(x)+ln2)) for large |x|, else
 *               := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
 *               := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
 */
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
static const double
#else
static double
#endif
one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
ln2 =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
huge=  1.00000000000000000000e+300;
 
#ifdef __STDC__
        double asinh(double x)
#else
        double asinh(x)
        double x;
#endif
{
        double t,w;
        __int32_t hx,ix;
        GET_HIGH_WORD(hx,x);
        ix = hx&0x7fffffff;
        if(ix>=0x7ff00000) return x+x;  /* x is inf or NaN */
        if(ix< 0x3e300000) {    /* |x|<2**-28 */
            if(huge+x>one) return x;    /* return x inexact except 0 */
        }
        if(ix>0x41b00000) {     /* |x| > 2**28 */
            w = __ieee754_log(fabs(x))+ln2;
        } else if (ix>0x40000000) {     /* 2**28 > |x| > 2.0 */
            t = fabs(x);
            w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t));
        } else {                /* 2.0 > |x| > 2**-28 */
            t = x*x;
            w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t)));
        }
        if(hx>0) return w; else return -w;
}
 
#endif /* _DOUBLE_IS_32BITS */

Line No.	Rev	Author	Line
1	39	lampret
2			`/* @(#)s_asinh.c 5.1 93/09/24 */`
3			`/*`
4			`* ====================================================`
5			`* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.`
6			`*`
7			`* Developed at SunPro, a Sun Microsystems, Inc. business.`
8			`* Permission to use, copy, modify, and distribute this`
9			`* software is freely granted, provided that this notice`
10			`* is preserved.`
11			`* ====================================================`
12			`*/`
13
14			`/*`
15			`FUNCTION`
16			`<<asinh>>, <<asinhf>>---inverse hyperbolic sine`
17
18			`INDEX`
19			`asinh`
20			`INDEX`
21			`asinhf`
22
23			`ANSI_SYNOPSIS`
24			`#include <math.h>`
25			`double asinh(double <[x]>);`
26			`float asinhf(float <[x]>);`
27
28			`TRAD_SYNOPSIS`
29			`#include <math.h>`
30			`double asinh(<[x]>)`
31			`double <[x]>;`
32
33			`float asinhf(<[x]>)`
34			`float <[x]>;`
35
36			`DESCRIPTION`
37			`<<asinh>> calculates the inverse hyperbolic sine of <[x]>.`
38			`<<asinh>> is defined as`
39			`@ifinfo`
40			`. sgn(<[x]>) * log(abs(<[x]>) + sqrt(1+<[x]>*<[x]>))`
41			`@end ifinfo`
42			`@tex`
43			`$$sign(x) \times ln\Bigl(\|x\| + \sqrt{1+x^2}\Bigr)$$`
44			`@end tex`
45
46			`<<asinhf>> is identical, other than taking and returning floats.`
47
48			`RETURNS`
49			`<<asinh>> and <<asinhf>> return the calculated value.`
50
51			`PORTABILITY`
52			`Neither <<asinh>> nor <<asinhf>> are ANSI C.`
53
54			`*/`
55
56			`/* asinh(x)`
57			`* Method :`
58			`* Based on`
59			`* asinh(x) = sign(x) * log [ \|x\| + sqrt(x*x+1) ]`
60			`* we have`
61			`* asinh(x) := x if 1+x*x=1,`
62			`* := sign(x)*(log(x)+ln2)) for large \|x\|, else`
63			`* := sign(x)log(2\|x\|+1/(\|x\|+sqrt(xx+1))) if\|x\|>2, else`
64			`* := sign(x)*log1p(\|x\| + x^2/(1 + sqrt(1+x^2)))`
65			`*/`
66
67			`#include "fdlibm.h"`
68
69			`#ifndef _DOUBLE_IS_32BITS`
70
71			`#ifdef __STDC__`
72			`static const double`
73			`#else`
74			`static double`
75			`#endif`
76			`one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */`
77			`ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */`
78			`huge= 1.00000000000000000000e+300;`
79
80			`#ifdef __STDC__`
81			`double asinh(double x)`
82			`#else`
83			`double asinh(x)`
84			`double x;`
85			`#endif`
86			`{`
87			`double t,w;`
88			`__int32_t hx,ix;`
89			`GET_HIGH_WORD(hx,x);`
90			`ix = hx&0x7fffffff;`
91			`if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */`
92			`if(ix< 0x3e300000) { /* \|x\|<2*-28 /`
93			`if(huge+x>one) return x; /* return x inexact except 0 */`
94			`}`
95			`if(ix>0x41b00000) { /* \|x\| > 2*28 /`
96			`w = __ieee754_log(fabs(x))+ln2;`
97			`} else if (ix>0x40000000) { /* 2*28 > \|x\| > 2.0 /`
98			`t = fabs(x);`
99			`w = __ieee754_log(2.0t+one/(__ieee754_sqrt(xx+one)+t));`
100			`} else { /* 2.0 > \|x\| > 2*-28 /`
101			`t = x*x;`
102			`w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t)));`
103			`}`
104			`if(hx>0) return w; else return -w;`
105			`}`
106
107			`#endif /* _DOUBLE_IS_32BITS */`

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