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/* @(#)e_acosh.c 5.1 93/09/24 */
 
/*
FUNCTION
<<acosh>>, <<acoshf>>---inverse hyperbolic cosine
 
INDEX
acosh
INDEX
acoshf
 
ANSI_SYNOPSIS
        #include <math.h>
        double acosh(double <[x]>);
        float acoshf(float <[x]>);
 
TRAD_SYNOPSIS
        #include <math.h>
        double acosh(<[x]>)
        double <[x]>;
 
        float acoshf(<[x]>)
        float <[x]>;
 
DESCRIPTION
<<acosh>> calculates the inverse hyperbolic cosine of <[x]>.
<<acosh>> is defined as
@ifinfo
. log(<[x]> + sqrt(<[x]>*<[x]>-1))
@end ifinfo
@tex
$$ln\Bigl(x + \sqrt{x^2-1}\Bigr)$$
@end tex
 
<[x]> must be a number greater than or equal to 1.
 
<<acoshf>> is identical, other than taking and returning floats.
 
RETURNS
<<acosh>> and <<acoshf>> return the calculated value.  If <[x]>
less than 1, the return value is NaN and <<errno>> is set to <<EDOM>>.
 
You can change the error-handling behavior with the non-ANSI
<<matherr>> function.
 
PORTABILITY
Neither <<acosh>> nor <<acoshf>> are ANSI C.  They are not recommended
for portable programs.
 
 
QUICKREF ANSI SVID POSIX RENTRANT
 acos    n,n,n,m
 acosf   n,n,n,m
 
MATHREF
 acosh, NAN,   arg,DOMAIN,EDOM
 acosh, < 1.0, NAN,DOMAIN,EDOM
 acosh, >=1.0, acosh(arg),,,
 
MATHREF
 acoshf, NAN,   arg,DOMAIN,EDOM
 acoshf, < 1.0, NAN,DOMAIN,EDOM
 acoshf, >=1.0, acosh(arg),,,
 
*/
 
/*
 * ====================================================
 * 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.
 * ====================================================
 *
 */
 
/* acosh(x)
 * Method :
 *      Based on
 *              acosh(x) = log [ x + sqrt(x*x-1) ]
 *      we have
 *              acosh(x) := log(x)+ln2, if x is large; else
 *              acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
 *              acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
 *
 * Special cases:
 *      acosh(x) is NaN with signal if x<1.
 *      acosh(NaN) is NaN without signal.
 */
 
#include "fdlibm.h"
 
#ifndef _DOUBLE_IS_32BITS
 
#ifdef __STDC__
static const double
#else
static double
#endif
one     = 1.0,
ln2     = 6.93147180559945286227e-01;  /* 0x3FE62E42, 0xFEFA39EF */
 
#ifdef __STDC__
        double acosh(double x)
#else
        double acosh(x)
        double x;
#endif
{
        double t;
        __int32_t hx;
        __uint32_t lx;
        EXTRACT_WORDS(hx,lx,x);
        if(hx<0x3ff00000) {             /* x < 1 */
            return (x-x)/(x-x);
        } else if(hx >=0x41b00000) {    /* x > 2**28 */
            if(hx >=0x7ff00000) {       /* x is inf of NaN */
                return x+x;
            } else
                return log(x)+ln2;      /* acosh(huge)=log(2x) */
        } else if(((hx-0x3ff00000)|lx)==0) {
            return 0.0;                 /* acosh(1) = 0 */
        } else if (hx > 0x40000000) {   /* 2**28 > x > 2 */
            t=x*x;
            return log(2.0*x-one/(x+sqrt(t-one)));
        } else {                        /* 1<x<2 */
            t = x-one;
            return log1p(t+sqrt(2.0*t+t*t));
        }
}
 
#endif /* defined(_DOUBLE_IS_32BITS) */

Line No.	Rev	Author	Line
1	1010	ivang
2			`/* @(#)e_acosh.c 5.1 93/09/24 */`
3
4			`/*`
5			`FUNCTION`
6			`<<acosh>>, <<acoshf>>---inverse hyperbolic cosine`
7
8			`INDEX`
9			`acosh`
10			`INDEX`
11			`acoshf`
12
13			`ANSI_SYNOPSIS`
14			`#include <math.h>`
15			`double acosh(double <[x]>);`
16			`float acoshf(float <[x]>);`
17
18			`TRAD_SYNOPSIS`
19			`#include <math.h>`
20			`double acosh(<[x]>)`
21			`double <[x]>;`
22
23			`float acoshf(<[x]>)`
24			`float <[x]>;`
25
26			`DESCRIPTION`
27			`<<acosh>> calculates the inverse hyperbolic cosine of <[x]>.`
28			`<<acosh>> is defined as`
29			`@ifinfo`
30			`. log(<[x]> + sqrt(<[x]>*<[x]>-1))`
31			`@end ifinfo`
32			`@tex`
33			`$$ln\Bigl(x + \sqrt{x^2-1}\Bigr)$$`
34			`@end tex`
35
36			`<[x]> must be a number greater than or equal to 1.`
37
38			`<<acoshf>> is identical, other than taking and returning floats.`
39
40			`RETURNS`
41			`<<acosh>> and <<acoshf>> return the calculated value. If <[x]>`
42			`less than 1, the return value is NaN and <<errno>> is set to <<EDOM>>.`
43
44			`You can change the error-handling behavior with the non-ANSI`
45			`<<matherr>> function.`
46
47			`PORTABILITY`
48			`Neither <<acosh>> nor <<acoshf>> are ANSI C. They are not recommended`
49			`for portable programs.`
50
51
52			`QUICKREF ANSI SVID POSIX RENTRANT`
53			`acos n,n,n,m`
54			`acosf n,n,n,m`
55
56			`MATHREF`
57			`acosh, NAN, arg,DOMAIN,EDOM`
58			`acosh, < 1.0, NAN,DOMAIN,EDOM`
59			`acosh, >=1.0, acosh(arg),,,`
60
61			`MATHREF`
62			`acoshf, NAN, arg,DOMAIN,EDOM`
63			`acoshf, < 1.0, NAN,DOMAIN,EDOM`
64			`acoshf, >=1.0, acosh(arg),,,`
65
66			`*/`
67
68			`/*`
69			`* ====================================================`
70			`* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.`
71			`*`
72			`* Developed at SunPro, a Sun Microsystems, Inc. business.`
73			`* Permission to use, copy, modify, and distribute this`
74			`* software is freely granted, provided that this notice`
75			`* is preserved.`
76			`* ====================================================`
77			`*`
78			`*/`
79
80			`/* acosh(x)`
81			`* Method :`
82			`* Based on`
83			`* acosh(x) = log [ x + sqrt(x*x-1) ]`
84			`* we have`
85			`* acosh(x) := log(x)+ln2, if x is large; else`
86			`* acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else`
87			`* acosh(x) := log1p(t+sqrt(2.0t+tt)); where t=x-1.`
88			`*`
89			`* Special cases:`
90			`* acosh(x) is NaN with signal if x<1.`
91			`* acosh(NaN) is NaN without signal.`
92			`*/`
93
94			`#include "fdlibm.h"`
95
96			`#ifndef _DOUBLE_IS_32BITS`
97
98			`#ifdef __STDC__`
99			`static const double`
100			`#else`
101			`static double`
102			`#endif`
103			`one = 1.0,`
104			`ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */`
105
106			`#ifdef __STDC__`
107			`double acosh(double x)`
108			`#else`
109			`double acosh(x)`
110			`double x;`
111			`#endif`
112			`{`
113			`double t;`
114			`__int32_t hx;`
115			`__uint32_t lx;`
116			`EXTRACT_WORDS(hx,lx,x);`
117			`if(hx<0x3ff00000) { /* x < 1 */`
118			`return (x-x)/(x-x);`
119			`} else if(hx >=0x41b00000) { /* x > 2*28 /`
120			`if(hx >=0x7ff00000) { /* x is inf of NaN */`
121			`return x+x;`
122			`} else`
123			`return log(x)+ln2; /* acosh(huge)=log(2x) */`
124			`} else if(((hx-0x3ff00000)\|lx)==0) {`
125			`return 0.0; /* acosh(1) = 0 */`
126			`} else if (hx > 0x40000000) { /* 2*28 > x > 2 /`
127			`t=x*x;`
128			`return log(2.0*x-one/(x+sqrt(t-one)));`
129			`} else { /* 1<x<2 */`
130			`t = x-one;`
131			`return log1p(t+sqrt(2.0t+tt));`
132			`}`
133			`}`
134
135			`#endif /* defined(_DOUBLE_IS_32BITS) */`

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[/] [or1k/] [trunk/] [newlib-1.10.0/] [newlib/] [libm/] [mathfp/] [e_acosh.c] - Blame information for rev 1010