xref: /freebsd/lib/msun/src/s_tanhl.c (revision 1c05a6ea6b849ff95e539c31adea887c644a6a01)
1 /* from: FreeBSD: head/lib/msun/src/s_tanhl.c XXX */
2 
3 /* @(#)s_tanh.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>
16 __FBSDID("$FreeBSD$");
17 
18 /*
19  * See s_tanh.c for complete comments.
20  *
21  * Converted to long double by Bruce D. Evans.
22  */
23 
24 #include <float.h>
25 #ifdef __i386__
26 #include <ieeefp.h>
27 #endif
28 
29 #include "math.h"
30 #include "math_private.h"
31 #include "fpmath.h"
32 #include "k_expl.h"
33 
34 #if LDBL_MAX_EXP != 0x4000
35 /* We also require the usual expsign encoding. */
36 #error "Unsupported long double format"
37 #endif
38 
39 #define	BIAS	(LDBL_MAX_EXP - 1)
40 
41 static const volatile double tiny = 1.0e-300;
42 static const double one = 1.0;
43 #if LDBL_MANT_DIG == 64
44 /*
45  * Domain [-0.25, 0.25], range ~[-1.6304e-22, 1.6304e-22]:
46  * |tanh(x)/x - t(x)| < 2**-72.3
47  */
48 static const union IEEEl2bits
49 T3u = LD80C(0xaaaaaaaaaaaaaa9f, -2, -3.33333333333333333017e-1L);
50 #define	T3	T3u.e
51 static const double
52 T5  =  1.3333333333333314e-1,		/*  0x1111111111110a.0p-55 */
53 T7  = -5.3968253968210485e-2,		/* -0x1ba1ba1ba1a1a1.0p-57 */
54 T9  =  2.1869488531393817e-2,		/*  0x1664f488172022.0p-58 */
55 T11 = -8.8632352345964591e-3,		/* -0x1226e34bc138d5.0p-59 */
56 T13 =  3.5921169709993771e-3,		/*  0x1d6d371d3e400f.0p-61 */
57 T15 = -1.4555786415756001e-3,		/* -0x17d923aa63814d.0p-62 */
58 T17 =  5.8645267876296793e-4,		/*  0x13378589b85aa7.0p-63 */
59 T19 = -2.1121033571392224e-4;		/* -0x1baf0af80c4090.0p-65 */
60 #elif LDBL_MANT_DIG == 113
61 /*
62  * Domain [-0.25, 0.25], range ~[-2.4211e-37, 2.4211e-37]:
63  * |tanh(x)/x - t(x)| < 2**121.6
64  */
65 static const long double
66 T3 = -3.33333333333333333333333333333332980e-1L,	/* -0x1555555555555555555555555554e.0p-114L */
67 T5  =  1.33333333333333333333333333332707260e-1L,	/*  0x1111111111111111111111110ab7b.0p-115L */
68 T7  = -5.39682539682539682539682535723482314e-2L,	/* -0x1ba1ba1ba1ba1ba1ba1ba17b5fc98.0p-117L */
69 T9  =  2.18694885361552028218693591149061717e-2L,	/*  0x1664f4882c10f9f32d6b1a12a25e5.0p-118L */
70 T11 = -8.86323552990219656883762347736381851e-3L,	/* -0x1226e355e6c23c8f5a5a0f386cb4d.0p-119L */
71 T13 =  3.59212803657248101358314398220822722e-3L,	/*  0x1d6d3d0e157ddfb403ad3637442c6.0p-121L */
72 T15 = -1.45583438705131796512568010348874662e-3L;	/* -0x17da36452b75e150c44cc34253b34.0p-122L */
73 static const double
74 T17 =  5.9002744094556621e-4,		/*  0x1355824803668e.0p-63 */
75 T19 = -2.3912911424260516e-4,		/* -0x1f57d7734c8dde.0p-65 */
76 T21 =  9.6915379535512898e-5,		/*  0x1967e18ad6a6ca.0p-66 */
77 T23 = -3.9278322983156353e-5,		/* -0x1497d8e6b75729.0p-67 */
78 T25 =  1.5918887220143869e-5,		/*  0x10b1319998cafa.0p-68 */
79 T27 = -6.4514295231630956e-6,		/* -0x1b0f2b71b218eb.0p-70 */
80 T29 =  2.6120754043964365e-6,		/*  0x15e963a3cf3a39.0p-71 */
81 T31 = -1.0407567231003314e-6,		/* -0x1176041e656869.0p-72 */
82 T33 =  3.4744117554063574e-7;		/*  0x1750fe732cab9c.0p-74 */
83 #endif /* LDBL_MANT_DIG == 64 */
84 
85 static inline long double
86 divl(long double a, long double b, long double c, long double d,
87     long double e, long double f)
88 {
89 	long double inv, r;
90 	float fr, fw;
91 
92 	_2sumF(a, c);
93 	b = b + c;
94 	_2sumF(d, f);
95 	e = e + f;
96 
97 	inv = 1 / (d + e);
98 
99 	r = (a + b) * inv;
100 	fr = r;
101 	r = fr;
102 
103 	fw = d + e;
104 	e = d - fw + e;
105 	d = fw;
106 
107 	r = r + (a - d * r + b - e * r) * inv;
108 
109 	return r;
110 }
111 
112 long double
113 tanhl(long double x)
114 {
115 	long double hi,lo,s,x2,x4,z;
116 #if LDBL_MANT_DIG == 113
117 	double dx2;
118 #endif
119 	int16_t jx,ix;
120 
121 	GET_LDBL_EXPSIGN(jx,x);
122 	ix = jx&0x7fff;
123 
124     /* x is INF or NaN */
125 	if(ix>=0x7fff) {
126 	    if (jx>=0) return one/x+one;    /* tanh(+-inf)=+-1 */
127 	    else       return one/x-one;    /* tanh(NaN) = NaN */
128 	}
129 
130 	ENTERI();
131 
132     /* |x| < 40 */
133 	if (ix < 0x4004 || fabsl(x) < 40) {	/* |x|<40 */
134 	    if (__predict_false(ix<BIAS-(LDBL_MANT_DIG+1)/2)) {	/* |x|<TINY */
135 		/* tanh(+-0) = +0; tanh(tiny) = tiny(-+) with inexact: */
136 		return (x == 0 ? x : (0x1p200 * x - x) * 0x1p-200);
137 	    }
138 	    if (ix<0x3ffd) {		/* |x|<0.25 */
139 		x2 = x*x;
140 #if LDBL_MANT_DIG == 64
141 		x4 = x2*x2;
142 		RETURNI(((T19*x2 + T17)*x4 + (T15*x2 + T13))*(x2*x*x2*x4*x4) +
143 		    ((T11*x2 + T9)*x4 + (T7*x2 + T5))*(x2*x*x2) +
144 		    T3*(x2*x) + x);
145 #elif LDBL_MANT_DIG == 113
146 		dx2 = x2;
147 #if 0
148 		RETURNI(((((((((((((((T33*dx2 + T31)*dx2 + T29)*dx2 + T27)*dx2 +
149 		    T25)*x2 + T23)*x2 + T21)*x2 + T19)*x2 + T17)*x2 +
150 		    T15)*x2 + T13)*x2 + T11)*x2 + T9)*x2 + T7)*x2 + T5)*
151 		    (x2*x*x2) +
152 		    T3*(x2*x) + x);
153 #else
154 		long double q = ((((((((((((((T33*dx2 + T31)*dx2 + T29)*dx2 + T27)*dx2 +
155 		    T25)*x2 + T23)*x2 + T21)*x2 + T19)*x2 + T17)*x2 +
156 		    T15)*x2 + T13)*x2 + T11)*x2 + T9)*x2 + T7)*x2 + T5)*
157 		    (x2*x*x2);
158 		RETURNI(q + T3*(x2*x) + x);
159 #endif
160 #endif
161 	    }
162 	    k_hexpl(2*fabsl(x), &hi, &lo);
163 	    if (ix<0x4001 && fabsl(x) < 1.5)	/* |x|<1.5 */
164 		z = divl(hi, lo, -0.5, hi, lo, 0.5);
165 	    else
166 		z = one - one/(lo+0.5+hi);
167     /* |x| >= 40, return +-1 */
168 	} else {
169 	    z = one - tiny;		/* raise inexact flag */
170 	}
171 	s = 1;
172 	if (jx<0) s = -1;
173 	RETURNI(s*z);
174 }
175