| 1/* from: FreeBSD: head/lib/msun/src/e_atanh.c 176451 2008-02-22 02:30:36Z das */
|
1
2/* @(#)e_atanh.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_atanh.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_atanh.c 176451 2008-02-22 02:30:36Z das $");
| 17__FBSDID("$FreeBSD: head/lib/msun/src/e_atanhl.c 251599 2013-06-10 06:04:58Z das $");
|
17
| 18
|
18/* __ieee754_atanh(x)
19 * Method :
20 * 1.Reduced x to positive by atanh(-x) = -atanh(x)
21 * 2.For x>=0.5
22 * 1 2x x
23 * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
24 * 2 1 - x 1 - x
25 *
26 * For x<0.5
27 * atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
| 19/*
20 * See e_atanh.c for complete comments.
|
28 *
| 21 *
|
29 * Special cases:
30 * atanh(x) is NaN if |x| > 1 with signal;
31 * atanh(NaN) is that NaN with no signal;
32 * atanh(+-1) is +-INF with signal.
33 *
| 22 * Converted to long double by David Schultz <das@FreeBSD.ORG> and
23 * Bruce D. Evans.
|
34 */
35
| 24 */
25
|
| 26#include <float.h>
27#ifdef __i386__
28#include <ieeefp.h>
29#endif
30
31#include "fpmath.h"
|
36#include "math.h"
37#include "math_private.h"
38
| 32#include "math.h"
33#include "math_private.h"
34
|
| 35/* EXP_TINY is the threshold below which we use atanh(x) ~= x. */
36#if LDBL_MANT_DIG == 64
37#define EXP_TINY -34
38#elif LDBL_MANT_DIG == 113
39#define EXP_TINY -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
|
39static const double one = 1.0, huge = 1e300;
40static const double zero = 0.0;
41
| 51static const double one = 1.0, huge = 1e300;
52static const double zero = 0.0;
53
|
42double
43__ieee754_atanh(double x)
| 54long double
55atanhl(long double x)
|
44{
| 56{
|
45 double t;
46 int32_t hx,ix;
47 u_int32_t lx;
48 EXTRACT_WORDS(hx,lx,x);
49 ix = hx&0x7fffffff;
50 if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
51 return (x-x)/(x-x);
52 if(ix==0x3ff00000)
53 return x/zero;
54 if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */
55 SET_HIGH_WORD(x,ix);
56 if(ix<0x3fe00000) { /* x < 0.5 */
| 57 long double t;
58 uint16_t hx, ix;
59
60 ENTERI();
61 GET_LDBL_EXPSIGN(hx, x);
62 ix = hx & 0x7fff;
63 if (ix >= 0x3fff) /* |x| >= 1, or NaN or misnormal */
64 RETURNI(fabsl(x) == 1 ? x / zero : (x - x) / (x - x));
65 if (ix < BIAS + EXP_TINY && (huge + x) > zero)
66 RETURNI(x); /* x is tiny */
67 SET_LDBL_EXPSIGN(x, ix);
68 if (ix < 0x3ffe) { /* |x| < 0.5, or misnormal */
|
57 t = x+x;
| 69 t = x+x;
|
58 t = 0.5*log1p(t+t*x/(one-x));
| 70 t = 0.5*log1pl(t+t*x/(one-x));
|
59 } else
| 71 } else
|
60 t = 0.5*log1p((x+x)/(one-x));
61 if(hx>=0) return t; else return -t;
| 72 t = 0.5*log1pl((x+x)/(one-x));
73 RETURNI((hx & 0x8000) == 0 ? t : -t);
|
62}
| 74}
|