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e_acosh.c (176451) e_acosh.c (251599)
1
2/* @(#)e_acosh.c 1.3 95/01/18 */
3/*
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 *
7 * Developed at SunSoft, 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#include <sys/cdefs.h>
1
2/* @(#)e_acosh.c 1.3 95/01/18 */
3/*
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 *
7 * Developed at SunSoft, 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#include <sys/cdefs.h>
16__FBSDID("$FreeBSD: head/lib/msun/src/e_acosh.c 176451 2008-02-22 02:30:36Z das $");
16__FBSDID("$FreeBSD: head/lib/msun/src/e_acosh.c 251599 2013-06-10 06:04:58Z das $");
17
18/* __ieee754_acosh(x)
19 * Method :
20 * Based on
21 * acosh(x) = log [ x + sqrt(x*x-1) ]
22 * we have
23 * acosh(x) := log(x)+ln2, if x is large; else
24 * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
25 * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
26 *
27 * Special cases:
28 * acosh(x) is NaN with signal if x<1.
29 * acosh(NaN) is NaN without signal.
30 */
31
17
18/* __ieee754_acosh(x)
19 * Method :
20 * Based on
21 * acosh(x) = log [ x + sqrt(x*x-1) ]
22 * we have
23 * acosh(x) := log(x)+ln2, if x is large; else
24 * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
25 * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
26 *
27 * Special cases:
28 * acosh(x) is NaN with signal if x<1.
29 * acosh(NaN) is NaN without signal.
30 */
31
32#include <float.h>
33
32#include "math.h"
33#include "math_private.h"
34
35static const double
36one = 1.0,
37ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */
38
39double

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55 } else if (hx > 0x40000000) { /* 2**28 > x > 2 */
56 t=x*x;
57 return __ieee754_log(2.0*x-one/(x+sqrt(t-one)));
58 } else { /* 1<x<2 */
59 t = x-one;
60 return log1p(t+sqrt(2.0*t+t*t));
61 }
62}
34#include "math.h"
35#include "math_private.h"
36
37static const double
38one = 1.0,
39ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */
40
41double

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57 } else if (hx > 0x40000000) { /* 2**28 > x > 2 */
58 t=x*x;
59 return __ieee754_log(2.0*x-one/(x+sqrt(t-one)));
60 } else { /* 1<x<2 */
61 t = x-one;
62 return log1p(t+sqrt(2.0*t+t*t));
63 }
64}
65
66#if LDBL_MANT_DIG == 53
67__weak_reference(acosh, acoshl);
68#endif