| 1/* from: FreeBSD: head/lib/msun/src/e_acosh.c 176451 2008-02-22 02:30:36Z das */
2
|
1/* @(#)s_asinh.c 5.1 93/09/24 */
2/*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
9 * is preserved.
10 * ====================================================
11 */
12
13#include <sys/cdefs.h>
| 3/* @(#)s_asinh.c 5.1 93/09/24 */
4/*
5 * ====================================================
6 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
7 *
8 * Developed at SunPro, 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#include <sys/cdefs.h>
|
14__FBSDID("$FreeBSD: head/lib/msun/src/s_asinh.c 176451 2008-02-22 02:30:36Z das $");
| 16__FBSDID("$FreeBSD: head/lib/msun/src/s_asinhl.c 251599 2013-06-10 06:04:58Z das $");
|
15
| 17
|
16/* asinh(x)
17 * Method :
18 * Based on
19 * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
20 * we have
21 * asinh(x) := x if 1+x*x=1,
22 * := sign(x)*(log(x)+ln2)) for large |x|, else
23 * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
24 * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
| 18/*
19 * See s_asinh.c for complete comments.
20 *
21 * Converted to long double by David Schultz <das@FreeBSD.ORG> and
22 * Bruce D. Evans.
|
25 */
26
| 23 */
24
|
| 25#include <float.h>
26#ifdef __i386__
27#include <ieeefp.h>
28#endif
29
30#include "fpmath.h"
|
27#include "math.h"
28#include "math_private.h"
29
| 31#include "math.h"
32#include "math_private.h"
33
|
| 34/* EXP_LARGE is the threshold above which we use asinh(x) ~= log(2x). */
35/* EXP_TINY is the threshold below which we use asinh(x) ~= x. */
36#if LDBL_MANT_DIG == 64
37#define EXP_LARGE 34
38#define EXP_TINY -34
39#elif LDBL_MANT_DIG == 113
40#define EXP_LARGE 58
41#define EXP_TINY -58
42#else
43#error "Unsupported long double format"
44#endif
45
46#if LDBL_MAX_EXP != 0x4000
47/* We also require the usual expsign encoding. */
48#error "Unsupported long double format"
49#endif
50
51#define BIAS (LDBL_MAX_EXP - 1)
52
|
30static const double
31one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
| 53static const double
54one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
|
32ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
| |
33huge= 1.00000000000000000000e+300;
34
| 55huge= 1.00000000000000000000e+300;
56
|
35double
36asinh(double x)
| 57#if LDBL_MANT_DIG == 64
58static const union IEEEl2bits
59u_ln2 = LD80C(0xb17217f7d1cf79ac, -1, 6.93147180559945309417e-1L);
60#define ln2 u_ln2.e
61#elif LDBL_MANT_DIG == 113
62static const long double
63ln2 = 6.93147180559945309417232121458176568e-1L; /* 0x162e42fefa39ef35793c7673007e6.0p-113 */
64#else
65#error "Unsupported long double format"
66#endif
67
68long double
69asinhl(long double x)
|
37{
| 70{
|
38 double t,w;
39 int32_t hx,ix;
40 GET_HIGH_WORD(hx,x);
41 ix = hx&0x7fffffff;
42 if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */
43 if(ix< 0x3e300000) { /* |x|<2**-28 */
44 if(huge+x>one) return x; /* return x inexact except 0 */
| 71 long double t, w;
72 uint16_t hx, ix;
73
74 ENTERI();
75 GET_LDBL_EXPSIGN(hx, x);
76 ix = hx & 0x7fff;
77 if (ix >= 0x7fff) RETURNI(x+x); /* x is inf, NaN or misnormal */
78 if (ix < BIAS + EXP_TINY) { /* |x| < TINY, or misnormal */
79 if (huge + x > one) RETURNI(x); /* return x inexact except 0 */
|
45 }
| 80 }
|
46 if(ix>0x41b00000) { /* |x| > 2**28 */
47 w = __ieee754_log(fabs(x))+ln2;
48 } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */
49 t = fabs(x);
50 w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t));
51 } else { /* 2.0 > |x| > 2**-28 */
| 81 if (ix >= BIAS + EXP_LARGE) { /* |x| >= LARGE, or misnormal */
82 w = logl(fabsl(x))+ln2;
83 } else if (ix >= 0x4000) { /* LARGE > |x| >= 2.0, or misnormal */
84 t = fabsl(x);
85 w = logl(2.0*t+one/(sqrtl(x*x+one)+t));
86 } else { /* 2.0 > |x| >= TINY, or misnormal */
|
52 t = x*x;
| 87 t = x*x;
|
53 w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t)));
| 88 w =log1pl(fabsl(x)+t/(one+sqrtl(one+t)));
|
54 }
| 89 }
|
55 if(hx>0) return w; else return -w;
| 90 RETURNI((hx & 0x8000) == 0 ? w : -w);
|
56}
| 91}
|