| 1/* from: FreeBSD: head/lib/msun/src/e_acosh.c 176451 2008-02-22 02:30:36Z das */
|
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>
| 2
3/* @(#)e_acosh.c 1.3 95/01/18 */
4/*
5 * ====================================================
6 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
7 *
8 * Developed at SunSoft, a Sun Microsystems, Inc. business.
9 * Permission to use, copy, modify, and distribute this
10 * software is freely granted, provided that this notice
11 * is preserved.
12 * ====================================================
13 *
14 */
15
16#include <sys/cdefs.h>
|
16__FBSDID("$FreeBSD: head/lib/msun/src/e_acosh.c 176451 2008-02-22 02:30:36Z das $");
| 17__FBSDID("$FreeBSD: head/lib/msun/src/e_acoshl.c 251599 2013-06-10 06:04:58Z das $");
|
17
| 18
|
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.
| 19/*
20 * See e_acosh.c for complete comments.
|
26 *
| 21 *
|
27 * Special cases:
28 * acosh(x) is NaN with signal if x<1.
29 * acosh(NaN) is NaN without signal.
| 22 * Converted to long double by David Schultz <das@FreeBSD.ORG> and
23 * Bruce D. Evans.
|
30 */
31
| 24 */
25
|
| 26#include <float.h>
27#ifdef __i386__
28#include <ieeefp.h>
29#endif
30
31#include "fpmath.h"
|
32#include "math.h"
33#include "math_private.h"
34
| 32#include "math.h"
33#include "math_private.h"
34
|
| 35/* EXP_LARGE is the threshold above which we use acosh(x) ~= log(2x). */
36#if LDBL_MANT_DIG == 64
37#define EXP_LARGE 34
38#elif LDBL_MANT_DIG == 113
39#define EXP_LARGE 58
40#else
41#error "Unsupported long double format"
42#endif
43
44#if LDBL_MAX_EXP != 0x4000
45/* We also require the usual expsign encoding. */
46#error "Unsupported long double format"
47#endif
48
49#define BIAS (LDBL_MAX_EXP - 1)
50
|
35static const double
| 51static const double
|
36one = 1.0,
37ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */
| 52one = 1.0;
|
38
| 53
|
39double
40__ieee754_acosh(double x)
| 54#if LDBL_MANT_DIG == 64
55static const union IEEEl2bits
56u_ln2 = LD80C(0xb17217f7d1cf79ac, -1, 6.93147180559945309417e-1L);
57#define ln2 u_ln2.e
58#elif LDBL_MANT_DIG == 113
59static const long double
60ln2 = 6.93147180559945309417232121458176568e-1L; /* 0x162e42fefa39ef35793c7673007e6.0p-113 */
61#else
62#error "Unsupported long double format"
63#endif
64
65long double
66acoshl(long double x)
|
41{
| 67{
|
42 double t;
43 int32_t hx;
44 u_int32_t lx;
45 EXTRACT_WORDS(hx,lx,x);
46 if(hx<0x3ff00000) { /* x < 1 */
47 return (x-x)/(x-x);
48 } else if(hx >=0x41b00000) { /* x > 2**28 */
49 if(hx >=0x7ff00000) { /* x is inf of NaN */
50 return x+x;
| 68 long double t;
69 int16_t hx;
70
71 ENTERI();
72 GET_LDBL_EXPSIGN(hx, x);
73 if (hx < 0x3fff) { /* x < 1, or misnormal */
74 RETURNI((x-x)/(x-x));
75 } else if (hx >= BIAS + EXP_LARGE) { /* x >= LARGE */
76 if (hx >= 0x7fff) { /* x is inf, NaN or misnormal */
77 RETURNI(x+x);
|
51 } else
| 78 } else
|
52 return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */
53 } else if(((hx-0x3ff00000)|lx)==0) {
54 return 0.0; /* acosh(1) = 0 */
55 } else if (hx > 0x40000000) { /* 2**28 > x > 2 */
| 79 RETURNI(logl(x)+ln2); /* acosh(huge)=log(2x), or misnormal */
80 } else if (hx == 0x3fff && x == 1) {
81 RETURNI(0.0); /* acosh(1) = 0 */
82 } else if (hx >= 0x4000) { /* LARGE > x >= 2, or misnormal */
|
56 t=x*x;
| 83 t=x*x;
|
57 return __ieee754_log(2.0*x-one/(x+sqrt(t-one)));
| 84 RETURNI(logl(2.0*x-one/(x+sqrtl(t-one))));
|
58 } else { /* 1<x<2 */
59 t = x-one;
| 85 } else { /* 1<x<2 */
86 t = x-one;
|
60 return log1p(t+sqrt(2.0*t+t*t));
| 87 RETURNI(log1pl(t+sqrtl(2.0*t+t*t)));
|
61 }
62}
| 88 }
89}
|