1 /* $NetBSD: fpu_hyperb.c,v 1.17 2016/12/05 15:31:01 isaki Exp $ */
2
3 /*
4 * Copyright (c) 1995 Ken Nakata
5 * All rights reserved.
6 *
7 * Redistribution and use in source and binary forms, with or without
8 * modification, are permitted provided that the following conditions
9 * are met:
10 * 1. Redistributions of source code must retain the above copyright
11 * notice, this list of conditions and the following disclaimer.
12 * 2. Redistributions in binary form must reproduce the above copyright
13 * notice, this list of conditions and the following disclaimer in the
14 * documentation and/or other materials provided with the distribution.
15 * 3. Neither the name of the author nor the names of its contributors
16 * may be used to endorse or promote products derived from this software
17 * without specific prior written permission.
18 *
19 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
20 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
21 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
22 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
23 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
24 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
25 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
26 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
27 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
28 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
29 * SUCH DAMAGE.
30 *
31 * @(#)fpu_hyperb.c 10/24/95
32 */
33
34 /*
35 * Copyright (c) 2011 Tetsuya Isaki. All rights reserved.
36 *
37 * Redistribution and use in source and binary forms, with or without
38 * modification, are permitted provided that the following conditions
39 * are met:
40 * 1. Redistributions of source code must retain the above copyright
41 * notice, this list of conditions and the following disclaimer.
42 * 2. Redistributions in binary form must reproduce the above copyright
43 * notice, this list of conditions and the following disclaimer in the
44 * documentation and/or other materials provided with the distribution.
45 *
46 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
47 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
48 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
49 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
50 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
51 * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
52 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
53 * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
54 * OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
55 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
56 * SUCH DAMAGE.
57 */
58
59 #include <sys/cdefs.h>
60 __KERNEL_RCSID(0, "$NetBSD: fpu_hyperb.c,v 1.17 2016/12/05 15:31:01 isaki Exp $");
61
62 #include <machine/ieee.h>
63
64 #include "fpu_emulate.h"
65
66 /*
67 * fpu_hyperb.c: defines the following functions
68 *
69 * fpu_atanh(), fpu_cosh(), fpu_sinh(), and fpu_tanh()
70 */
71
72 /*
73 * 1 1 + x
74 * atanh(x) = ---*log(-------)
75 * 2 1 - x
76 */
77 struct fpn *
fpu_atanh(struct fpemu * fe)78 fpu_atanh(struct fpemu *fe)
79 {
80 struct fpn x;
81 struct fpn t;
82 struct fpn *r;
83
84 if (ISNAN(&fe->fe_f2))
85 return &fe->fe_f2;
86 if (ISINF(&fe->fe_f2))
87 return fpu_newnan(fe);
88
89 /* if x is +0/-0, return +0/-0 */
90 if (ISZERO(&fe->fe_f2))
91 return &fe->fe_f2;
92
93 /*
94 * -INF if x == -1
95 * +INF if x == 1
96 */
97 r = &fe->fe_f2;
98 if (r->fp_exp == 0 && r->fp_mant[0] == FP_1 &&
99 r->fp_mant[1] == 0 && r->fp_mant[2] == 0) {
100 r->fp_class = FPC_INF;
101 return r;
102 }
103
104 /* NAN if |x| > 1 */
105 if (fe->fe_f2.fp_exp >= 0)
106 return fpu_newnan(fe);
107
108 CPYFPN(&x, &fe->fe_f2);
109
110 /* t := 1 - x */
111 fpu_const(&fe->fe_f1, FPU_CONST_1);
112 fe->fe_f2.fp_sign = !fe->fe_f2.fp_sign;
113 r = fpu_add(fe);
114 CPYFPN(&t, r);
115
116 /* r := 1 + x */
117 fpu_const(&fe->fe_f1, FPU_CONST_1);
118 CPYFPN(&fe->fe_f2, &x);
119 r = fpu_add(fe);
120
121 /* (1-x)/(1+x) */
122 CPYFPN(&fe->fe_f1, r);
123 CPYFPN(&fe->fe_f2, &t);
124 r = fpu_div(fe);
125
126 /* log((1-x)/(1+x)) */
127 CPYFPN(&fe->fe_f2, r);
128 r = fpu_logn(fe);
129
130 /* r /= 2 */
131 r->fp_exp--;
132
133 return r;
134 }
135
136 /*
137 * exp(x) + exp(-x)
138 * cosh(x) = ------------------
139 * 2
140 */
141 struct fpn *
fpu_cosh(struct fpemu * fe)142 fpu_cosh(struct fpemu *fe)
143 {
144 struct fpn x, *fp;
145
146 if (ISNAN(&fe->fe_f2))
147 return &fe->fe_f2;
148
149 if (ISINF(&fe->fe_f2)) {
150 fe->fe_f2.fp_sign = 0;
151 return &fe->fe_f2;
152 }
153
154 /* if x is +0/-0, return 1 */ /* XXX is this necessary? */
155 if (ISZERO(&fe->fe_f2)) {
156 fpu_const(&fe->fe_f2, FPU_CONST_1);
157 return &fe->fe_f2;
158 }
159
160 fp = fpu_etox(fe);
161 CPYFPN(&x, fp);
162
163 fpu_const(&fe->fe_f1, FPU_CONST_1);
164 CPYFPN(&fe->fe_f2, fp);
165 fp = fpu_div(fe);
166
167 CPYFPN(&fe->fe_f1, fp);
168 CPYFPN(&fe->fe_f2, &x);
169 fp = fpu_add(fe);
170
171 fp->fp_exp--;
172
173 return fp;
174 }
175
176 /*
177 * exp(x) - exp(-x)
178 * sinh(x) = ------------------
179 * 2
180 */
181 struct fpn *
fpu_sinh(struct fpemu * fe)182 fpu_sinh(struct fpemu *fe)
183 {
184 struct fpn x, *fp;
185
186 if (ISNAN(&fe->fe_f2))
187 return &fe->fe_f2;
188 if (ISINF(&fe->fe_f2))
189 return &fe->fe_f2;
190
191 /* if x is +0/-0, return +0/-0 */
192 if (ISZERO(&fe->fe_f2))
193 return &fe->fe_f2;
194
195 fp = fpu_etox(fe);
196 CPYFPN(&x, fp);
197
198 fpu_const(&fe->fe_f1, FPU_CONST_1);
199 CPYFPN(&fe->fe_f2, fp);
200 fp = fpu_div(fe);
201
202 fp->fp_sign = 1;
203 CPYFPN(&fe->fe_f1, fp);
204 CPYFPN(&fe->fe_f2, &x);
205 fp = fpu_add(fe);
206
207 fp->fp_exp--;
208
209 return fp;
210 }
211
212 /*
213 * sinh(x)
214 * tanh(x) = ---------
215 * cosh(x)
216 */
217 struct fpn *
fpu_tanh(struct fpemu * fe)218 fpu_tanh(struct fpemu *fe)
219 {
220 struct fpn x;
221 struct fpn s;
222 struct fpn *r;
223 int sign;
224
225 if (ISNAN(&fe->fe_f2))
226 return &fe->fe_f2;
227
228 /* if x is +0/-0, return +0/-0 */
229 if (ISZERO(&fe->fe_f2))
230 return &fe->fe_f2;
231
232 if (ISINF(&fe->fe_f2)) {
233 sign = fe->fe_f2.fp_sign;
234 fpu_const(&fe->fe_f2, FPU_CONST_1);
235 fe->fe_f2.fp_sign = sign;
236 return &fe->fe_f2;
237 }
238
239 CPYFPN(&x, &fe->fe_f2);
240
241 /* sinh(x) */
242 CPYFPN(&fe->fe_f2, &x);
243 r = fpu_sinh(fe);
244 CPYFPN(&s, r);
245
246 /* cosh(x) */
247 CPYFPN(&fe->fe_f2, &x);
248 r = fpu_cosh(fe);
249 CPYFPN(&fe->fe_f2, r);
250
251 CPYFPN(&fe->fe_f1, &s);
252 r = fpu_div(fe);
253
254 return r;
255 }
256