1/* from: FreeBSD: head/lib/msun/src/s_tanhl.c XXX */
2
3/*
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 *
7 * Developed at SunPro, 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 * See s_tanh.c for complete comments.
16 *
17 * Converted to long double by Bruce D. Evans.
18 */
19
20#include <float.h>
21#ifdef __i386__
22#include <ieeefp.h>
23#endif
24
25#include "math.h"
26#include "math_private.h"
27#include "fpmath.h"
28#include "k_expl.h"
29
30#if LDBL_MAX_EXP != 0x4000
31/* We also require the usual expsign encoding. */
32#error "Unsupported long double format"
33#endif
34
35#define	BIAS	(LDBL_MAX_EXP - 1)
36
37static const volatile double tiny = 1.0e-300;
38static const double one = 1.0;
39#if LDBL_MANT_DIG == 64
40/*
41 * Domain [-0.25, 0.25], range ~[-1.6304e-22, 1.6304e-22]:
42 * |tanh(x)/x - t(x)| < 2**-72.3
43 */
44static const union IEEEl2bits
45T3u = LD80C(0xaaaaaaaaaaaaaa9f, -2, -3.33333333333333333017e-1L);
46#define	T3	T3u.e
47static const double
48T5  =  1.3333333333333314e-1,		/*  0x1111111111110a.0p-55 */
49T7  = -5.3968253968210485e-2,		/* -0x1ba1ba1ba1a1a1.0p-57 */
50T9  =  2.1869488531393817e-2,		/*  0x1664f488172022.0p-58 */
51T11 = -8.8632352345964591e-3,		/* -0x1226e34bc138d5.0p-59 */
52T13 =  3.5921169709993771e-3,		/*  0x1d6d371d3e400f.0p-61 */
53T15 = -1.4555786415756001e-3,		/* -0x17d923aa63814d.0p-62 */
54T17 =  5.8645267876296793e-4,		/*  0x13378589b85aa7.0p-63 */
55T19 = -2.1121033571392224e-4;		/* -0x1baf0af80c4090.0p-65 */
56#elif LDBL_MANT_DIG == 113
57/*
58 * Domain [-0.25, 0.25], range ~[-2.4211e-37, 2.4211e-37]:
59 * |tanh(x)/x - t(x)| < 2**121.6
60 */
61static const long double
62T3 = -3.33333333333333333333333333333332980e-1L,	/* -0x1555555555555555555555555554e.0p-114L */
63T5  =  1.33333333333333333333333333332707260e-1L,	/*  0x1111111111111111111111110ab7b.0p-115L */
64T7  = -5.39682539682539682539682535723482314e-2L,	/* -0x1ba1ba1ba1ba1ba1ba1ba17b5fc98.0p-117L */
65T9  =  2.18694885361552028218693591149061717e-2L,	/*  0x1664f4882c10f9f32d6b1a12a25e5.0p-118L */
66T11 = -8.86323552990219656883762347736381851e-3L,	/* -0x1226e355e6c23c8f5a5a0f386cb4d.0p-119L */
67T13 =  3.59212803657248101358314398220822722e-3L,	/*  0x1d6d3d0e157ddfb403ad3637442c6.0p-121L */
68T15 = -1.45583438705131796512568010348874662e-3L;	/* -0x17da36452b75e150c44cc34253b34.0p-122L */
69static const double
70T17 =  5.9002744094556621e-4,		/*  0x1355824803668e.0p-63 */
71T19 = -2.3912911424260516e-4,		/* -0x1f57d7734c8dde.0p-65 */
72T21 =  9.6915379535512898e-5,		/*  0x1967e18ad6a6ca.0p-66 */
73T23 = -3.9278322983156353e-5,		/* -0x1497d8e6b75729.0p-67 */
74T25 =  1.5918887220143869e-5,		/*  0x10b1319998cafa.0p-68 */
75T27 = -6.4514295231630956e-6,		/* -0x1b0f2b71b218eb.0p-70 */
76T29 =  2.6120754043964365e-6,		/*  0x15e963a3cf3a39.0p-71 */
77T31 = -1.0407567231003314e-6,		/* -0x1176041e656869.0p-72 */
78T33 =  3.4744117554063574e-7;		/*  0x1750fe732cab9c.0p-74 */
79#endif /* LDBL_MANT_DIG == 64 */
80
81static inline long double
82divl(long double a, long double b, long double c, long double d,
83    long double e, long double f)
84{
85	long double inv, r;
86	float fr, fw;
87
88	_2sumF(a, c);
89	b = b + c;
90	_2sumF(d, f);
91	e = e + f;
92
93	inv = 1 / (d + e);
94
95	r = (a + b) * inv;
96	fr = r;
97	r = fr;
98
99	fw = d + e;
100	e = d - fw + e;
101	d = fw;
102
103	r = r + (a - d * r + b - e * r) * inv;
104
105	return r;
106}
107
108long double
109tanhl(long double x)
110{
111	long double hi,lo,s,x2,x4,z;
112#if LDBL_MANT_DIG == 113
113	double dx2;
114#endif
115	int16_t jx,ix;
116
117	GET_LDBL_EXPSIGN(jx,x);
118	ix = jx&0x7fff;
119
120    /* x is INF or NaN */
121	if(ix>=0x7fff) {
122	    if (jx>=0) return one/x+one;    /* tanh(+-inf)=+-1 */
123	    else       return one/x-one;    /* tanh(NaN) = NaN */
124	}
125
126	ENTERI();
127
128    /* |x| < 40 */
129	if (ix < 0x4004 || fabsl(x) < 40) {	/* |x|<40 */
130	    if (__predict_false(ix<BIAS-(LDBL_MANT_DIG+1)/2)) {	/* |x|<TINY */
131		/* tanh(+-0) = +0; tanh(tiny) = tiny(-+) with inexact: */
132		return (x == 0 ? x : (0x1p200 * x - x) * 0x1p-200);
133	    }
134	    if (ix<0x3ffd) {		/* |x|<0.25 */
135		x2 = x*x;
136#if LDBL_MANT_DIG == 64
137		x4 = x2*x2;
138		RETURNI(((T19*x2 + T17)*x4 + (T15*x2 + T13))*(x2*x*x2*x4*x4) +
139		    ((T11*x2 + T9)*x4 + (T7*x2 + T5))*(x2*x*x2) +
140		    T3*(x2*x) + x);
141#elif LDBL_MANT_DIG == 113
142		dx2 = x2;
143#if 0
144		RETURNI(((((((((((((((T33*dx2 + T31)*dx2 + T29)*dx2 + T27)*dx2 +
145		    T25)*x2 + T23)*x2 + T21)*x2 + T19)*x2 + T17)*x2 +
146		    T15)*x2 + T13)*x2 + T11)*x2 + T9)*x2 + T7)*x2 + T5)*
147		    (x2*x*x2) +
148		    T3*(x2*x) + x);
149#else
150		long double q = ((((((((((((((T33*dx2 + T31)*dx2 + T29)*dx2 + T27)*dx2 +
151		    T25)*x2 + T23)*x2 + T21)*x2 + T19)*x2 + T17)*x2 +
152		    T15)*x2 + T13)*x2 + T11)*x2 + T9)*x2 + T7)*x2 + T5)*
153		    (x2*x*x2);
154		RETURNI(q + T3*(x2*x) + x);
155#endif
156#endif
157	    }
158	    k_hexpl(2*fabsl(x), &hi, &lo);
159	    if (ix<0x4001 && fabsl(x) < 1.5)	/* |x|<1.5 */
160		z = divl(hi, lo, -0.5, hi, lo, 0.5);
161	    else
162		z = one - one/(lo+0.5+hi);
163    /* |x| >= 40, return +-1 */
164	} else {
165	    z = one - tiny;		/* raise inexact flag */
166	}
167	s = 1;
168	if (jx<0) s = -1;
169	RETURNI(s*z);
170}
171