1 /*
2 * CDDL HEADER START
3 *
4 * The contents of this file are subject to the terms of the
5 * Common Development and Distribution License (the "License").
6 * You may not use this file except in compliance with the License.
7 *
8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
9 * or http://www.opensolaris.org/os/licensing.
10 * See the License for the specific language governing permissions
11 * and limitations under the License.
12 *
13 * When distributing Covered Code, include this CDDL HEADER in each
14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
15 * If applicable, add the following below this CDDL HEADER, with the
16 * fields enclosed by brackets "[]" replaced with your own identifying
17 * information: Portions Copyright [yyyy] [name of copyright owner]
18 *
19 * CDDL HEADER END
20 */
21 /*
22 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
23 */
24 /*
25 * Copyright 2005 Sun Microsystems, Inc. All rights reserved.
26 * Use is subject to license terms.
27 */
28
29 #pragma weak __cos = cos
30
31 /* INDENT OFF */
32 /*
33 * cos(x)
34 * Accurate Table look-up algorithm by K.C. Ng, May, 1995.
35 *
36 * Algorithm: see sincos.c
37 */
38
39 #include "libm.h"
40
41 static const double sc[] = {
42 /* ONE = */ 1.0,
43 /* NONE = */ -1.0,
44 /*
45 * |sin(x) - (x+pp1*x^3+pp2*x^5)| <= 2^-58.79 for |x| < 0.008
46 */
47 /* PP1 = */ -0.166666666666316558867252052378889521480627858683055567,
48 /* PP2 = */ .008333315652997472323564894248466758248475374977974017927,
49 /*
50 * |(sin(x) - (x+p1*x^3+...+p4*x^9)|
51 * |------------------------------ | <= 2^-57.63 for |x| < 0.1953125
52 * | x |
53 */
54 /* P1 = */ -1.666666666666629669805215138920301589656e-0001,
55 /* P2 = */ 8.333333332390951295683993455280336376663e-0003,
56 /* P3 = */ -1.984126237997976692791551778230098403960e-0004,
57 /* P4 = */ 2.753403624854277237649987622848330351110e-0006,
58 /*
59 * |cos(x) - (1+qq1*x^2+qq2*x^4)| <= 2^-55.99 for |x| <= 0.008 (0x3f80624d)
60 */
61 /* QQ1 = */ -0.4999999999975492381842911981948418542742729,
62 /* QQ2 = */ 0.041666542904352059294545209158357640398771740,
63 /* Q1 = */ -0.5,
64 /* Q2 = */ 4.166666666500350703680945520860748617445e-0002,
65 /* Q3 = */ -1.388888596436972210694266290577848696006e-0003,
66 /* Q4 = */ 2.478563078858589473679519517892953492192e-0005,
67 /* PIO2_H = */ 1.570796326794896557999,
68 /* PIO2_L = */ 6.123233995736765886130e-17,
69 /* PIO2_L0 = */ 6.123233995727922165564e-17,
70 /* PIO2_L1 = */ 8.843720566135701120255e-29,
71 /* PI3O2_H = */ 4.712388980384689673997,
72 /* PI3O2_L = */ 1.836970198721029765839e-16,
73 /* PI3O2_L0 = */ 1.836970198720396133587e-16,
74 /* PI3O2_L1 = */ 6.336322524749201142226e-29,
75 /* PI5O2_H = */ 7.853981633974482789995,
76 /* PI5O2_L = */ 3.061616997868382943065e-16,
77 /* PI5O2_L0 = */ 3.061616997861941598865e-16,
78 /* PI5O2_L1 = */ 6.441344200433640781982e-28,
79 };
80 /* INDENT ON */
81
82 #define ONE sc[0]
83 #define PP1 sc[2]
84 #define PP2 sc[3]
85 #define P1 sc[4]
86 #define P2 sc[5]
87 #define P3 sc[6]
88 #define P4 sc[7]
89 #define QQ1 sc[8]
90 #define QQ2 sc[9]
91 #define Q1 sc[10]
92 #define Q2 sc[11]
93 #define Q3 sc[12]
94 #define Q4 sc[13]
95 #define PIO2_H sc[14]
96 #define PIO2_L sc[15]
97 #define PIO2_L0 sc[16]
98 #define PIO2_L1 sc[17]
99 #define PI3O2_H sc[18]
100 #define PI3O2_L sc[19]
101 #define PI3O2_L0 sc[20]
102 #define PI3O2_L1 sc[21]
103 #define PI5O2_H sc[22]
104 #define PI5O2_L sc[23]
105 #define PI5O2_L0 sc[24]
106 #define PI5O2_L1 sc[25]
107
108 extern const double _TBL_sincos[], _TBL_sincosx[];
109
110 double
111 cos(double x) {
112 double z, y[2], w, s, v, p, q;
113 int i, j, n, hx, ix, lx;
114
115 hx = ((int *)&x)[HIWORD];
116 lx = ((int *)&x)[LOWORD];
117 ix = hx & ~0x80000000;
118
119 if (ix <= 0x3fc50000) { /* |x| < 10.5/64 = 0.164062500 */
120 if (ix < 0x3e400000) { /* |x| < 2**-27 */
121 if ((int)x == 0)
122 return (ONE);
123 }
124 z = x * x;
125 if (ix < 0x3f800000) /* |x| < 0.008 */
126 w = z * (QQ1 + z * QQ2);
127 else
128 w = z * ((Q1 + z * Q2) + (z * z) * (Q3 + z * Q4));
129 return (ONE + w);
130 }
131
132 /* for 0.164062500 < x < M, */
133 n = ix >> 20;
134 if (n < 0x402) { /* x < 8 */
135 i = (((ix >> 12) & 0xff) | 0x100) >> (0x401 - n);
136 j = i - 10;
137 x = fabs(x);
138 v = x - _TBL_sincosx[j];
139 if (((j - 81) ^ (j - 101)) < 0) {
140 /* near pi/2, cos(pi/2-x)=sin(x) */
141 p = PIO2_H - x;
142 i = ix - 0x3ff921fb;
143 x = p + PIO2_L;
144 if ((i | ((lx - 0x54442D00) & 0xffffff00)) == 0) {
145 /* very close to pi/2 */
146 x = p + PIO2_L0;
147 return (x + PIO2_L1);
148 }
149 z = x * x;
150 if (((ix - 0x3ff92000) >> 12) == 0) {
151 /* |pi/2-x|<2**-8 */
152 w = PIO2_L + (z * x) * (PP1 + z * PP2);
153 } else {
154 w = PIO2_L + (z * x) * ((P1 + z * P2) +
155 (z * z) * (P3 + z * P4));
156 }
157 return (p + w);
158 }
159 s = v * v;
160 if (((j - 282) ^ (j - 302)) < 0) {
161 /* near 3/2pi, cos(x-3/2pi)=sin(x) */
162 p = x - PI3O2_H;
163 i = ix - 0x4012D97C;
164 x = p - PI3O2_L;
165 if ((i | ((lx - 0x7f332100) & 0xffffff00)) == 0) {
166 /* very close to 3/2pi */
167 x = p - PI3O2_L0;
168 return (x - PI3O2_L1);
169 }
170 z = x * x;
171 if (((ix - 0x4012D800) >> 9) == 0) {
172 /* |x-3/2pi|<2**-8 */
173 w = (z * x) * (PP1 + z * PP2) - PI3O2_L;
174 } else {
175 w = (z * x) * ((P1 + z * P2) + (z * z)
176 * (P3 + z * P4)) - PI3O2_L;
177 }
178 return (p + w);
179 }
180 if (((j - 483) ^ (j - 503)) < 0) {
181 /* near 5pi/2, cos(5pi/2-x)=sin(x) */
182 p = PI5O2_H - x;
183 i = ix - 0x401F6A7A;
184 x = p + PI5O2_L;
185 if ((i | ((lx - 0x29553800) & 0xffffff00)) == 0) {
186 /* very close to pi/2 */
187 x = p + PI5O2_L0;
188 return (x + PI5O2_L1);
189 }
190 z = x * x;
191 if (((ix - 0x401F6A7A) >> 7) == 0) {
192 /* |pi/2-x|<2**-8 */
193 w = PI5O2_L + (z * x) * (PP1 + z * PP2);
194 } else {
195 w = PI5O2_L + (z * x) * ((P1 + z * P2) +
196 (z * z) * (P3 + z * P4));
197 }
198 return (p + w);
199 }
200 j <<= 1;
201 w = _TBL_sincos[j];
202 z = _TBL_sincos[j+1];
203 p = v + (v * s) * (PP1 + s * PP2);
204 q = s * (QQ1 + s * QQ2);
205 return (z - (w * p - z * q));
206 }
207
208 if (ix >= 0x7ff00000) /* cos(Inf or NaN) is NaN */
209 return (x / x);
210
211 /* argument reduction needed */
212 n = __rem_pio2(x, y);
213 switch (n & 3) {
214 case 0:
215 return (__k_cos(y[0], y[1]));
216 case 1:
217 return (-__k_sin(y[0], y[1]));
218 case 2:
219 return (-__k_cos(y[0], y[1]));
220 default:
221 return (__k_sin(y[0], y[1]));
222 }
223 }
|
1 /*
2 * CDDL HEADER START
3 *
4 * The contents of this file are subject to the terms of the
5 * Common Development and Distribution License (the "License").
6 * You may not use this file except in compliance with the License.
7 *
8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
9 * or http://www.opensolaris.org/os/licensing.
10 * See the License for the specific language governing permissions
11 * and limitations under the License.
12 *
13 * When distributing Covered Code, include this CDDL HEADER in each
14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
15 * If applicable, add the following below this CDDL HEADER, with the
16 * fields enclosed by brackets "[]" replaced with your own identifying
17 * information: Portions Copyright [yyyy] [name of copyright owner]
18 *
19 * CDDL HEADER END
20 */
21
22 /*
23 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
24 */
25
26 /*
27 * Copyright 2005 Sun Microsystems, Inc. All rights reserved.
28 * Use is subject to license terms.
29 */
30
31 #pragma weak __cos = cos
32
33
34 /*
35 * cos(x)
36 * Accurate Table look-up algorithm by K.C. Ng, May, 1995.
37 *
38 * Algorithm: see sincos.c
39 */
40
41 #include "libm.h"
42
43 static const double sc[] = {
44 /* ONE = */
45 1.0,
46 /* NONE = */ -1.0,
47
48 /*
49 * |sin(x) - (x+pp1*x^3+pp2*x^5)| <= 2^-58.79 for |x| < 0.008
50 */
51 /* PP1 = */-0.166666666666316558867252052378889521480627858683055567,
52 /* PP2 = */.008333315652997472323564894248466758248475374977974017927,
53
54 /*
55 * |(sin(x) - (x+p1*x^3+...+p4*x^9)|
56 * |------------------------------ | <= 2^-57.63 for |x| < 0.1953125
57 * | x |
58 */
59 /* P1 = */ -1.666666666666629669805215138920301589656e-0001,
60 /* P2 = */ 8.333333332390951295683993455280336376663e-0003,
61 /* P3 = */ -1.984126237997976692791551778230098403960e-0004,
62 /* P4 = */ 2.753403624854277237649987622848330351110e-0006,
63
64 /*
65 * |cos(x) - (1+qq1*x^2+qq2*x^4)| <= 2^-55.99 for |x| <= 0.008 (0x3f80624d)
66 */
67 /* QQ1 = */-0.4999999999975492381842911981948418542742729,
68 /* QQ2 = */0.041666542904352059294545209158357640398771740,
69 /* Q1 = */ -0.5,
70 /* Q2 = */ 4.166666666500350703680945520860748617445e-0002,
71 /* Q3 = */ -1.388888596436972210694266290577848696006e-0003,
72 /* Q4 = */ 2.478563078858589473679519517892953492192e-0005,
73 /* PIO2_H = */ 1.570796326794896557999,
74 /* PIO2_L = */ 6.123233995736765886130e-17,
75 /* PIO2_L0 = */ 6.123233995727922165564e-17,
76 /* PIO2_L1 = */ 8.843720566135701120255e-29,
77 /* PI3O2_H = */ 4.712388980384689673997,
78 /* PI3O2_L = */ 1.836970198721029765839e-16,
79 /* PI3O2_L0 = */ 1.836970198720396133587e-16,
80 /* PI3O2_L1 = */ 6.336322524749201142226e-29,
81 /* PI5O2_H = */ 7.853981633974482789995,
82 /* PI5O2_L = */ 3.061616997868382943065e-16,
83 /* PI5O2_L0 = */ 3.061616997861941598865e-16,
84 /* PI5O2_L1 = */ 6.441344200433640781982e-28,
85 };
86
87
88 #define ONE sc[0]
89 #define PP1 sc[2]
90 #define PP2 sc[3]
91 #define P1 sc[4]
92 #define P2 sc[5]
93 #define P3 sc[6]
94 #define P4 sc[7]
95 #define QQ1 sc[8]
96 #define QQ2 sc[9]
97 #define Q1 sc[10]
98 #define Q2 sc[11]
99 #define Q3 sc[12]
100 #define Q4 sc[13]
101 #define PIO2_H sc[14]
102 #define PIO2_L sc[15]
103 #define PIO2_L0 sc[16]
104 #define PIO2_L1 sc[17]
105 #define PI3O2_H sc[18]
106 #define PI3O2_L sc[19]
107 #define PI3O2_L0 sc[20]
108 #define PI3O2_L1 sc[21]
109 #define PI5O2_H sc[22]
110 #define PI5O2_L sc[23]
111 #define PI5O2_L0 sc[24]
112 #define PI5O2_L1 sc[25]
113
114 extern const double _TBL_sincos[], _TBL_sincosx[];
115
116 double
117 cos(double x)
118 {
119 double z, y[2], w, s, v, p, q;
120 int i, j, n, hx, ix, lx;
121
122 hx = ((int *)&x)[HIWORD];
123 lx = ((int *)&x)[LOWORD];
124 ix = hx & ~0x80000000;
125
126 if (ix <= 0x3fc50000) { /* |x| < 10.5/64 = 0.164062500 */
127 if (ix < 0x3e400000) { /* |x| < 2**-27 */
128 if ((int)x == 0)
129 return (ONE);
130 }
131
132 z = x * x;
133
134 if (ix < 0x3f800000) /* |x| < 0.008 */
135 w = z * (QQ1 + z * QQ2);
136 else
137 w = z * ((Q1 + z * Q2) + (z * z) * (Q3 + z * Q4));
138
139 return (ONE + w);
140 }
141
142 /* for 0.164062500 < x < M, */
143 n = ix >> 20;
144
145 if (n < 0x402) { /* x < 8 */
146 i = (((ix >> 12) & 0xff) | 0x100) >> (0x401 - n);
147 j = i - 10;
148 x = fabs(x);
149 v = x - _TBL_sincosx[j];
150
151 if (((j - 81) ^ (j - 101)) < 0) {
152 /* near pi/2, cos(pi/2-x)=sin(x) */
153 p = PIO2_H - x;
154 i = ix - 0x3ff921fb;
155 x = p + PIO2_L;
156
157 if ((i | ((lx - 0x54442D00) & 0xffffff00)) == 0) {
158 /* very close to pi/2 */
159 x = p + PIO2_L0;
160 return (x + PIO2_L1);
161 }
162
163 z = x * x;
164
165 if (((ix - 0x3ff92000) >> 12) == 0) {
166 /* |pi/2-x|<2**-8 */
167 w = PIO2_L + (z * x) * (PP1 + z * PP2);
168 } else {
169 w = PIO2_L + (z * x) * ((P1 + z * P2) + (z *
170 z) * (P3 + z * P4));
171 }
172
173 return (p + w);
174 }
175
176 s = v * v;
177
178 if (((j - 282) ^ (j - 302)) < 0) {
179 /* near 3/2pi, cos(x-3/2pi)=sin(x) */
180 p = x - PI3O2_H;
181 i = ix - 0x4012D97C;
182 x = p - PI3O2_L;
183
184 if ((i | ((lx - 0x7f332100) & 0xffffff00)) == 0) {
185 /* very close to 3/2pi */
186 x = p - PI3O2_L0;
187 return (x - PI3O2_L1);
188 }
189
190 z = x * x;
191
192 if (((ix - 0x4012D800) >> 9) == 0) {
193 /* |x-3/2pi|<2**-8 */
194 w = (z * x) * (PP1 + z * PP2) - PI3O2_L;
195 } else {
196 w = (z * x) * ((P1 + z * P2) + (z * z) * (P3 +
197 z * P4)) - PI3O2_L;
198 }
199
200 return (p + w);
201 }
202
203 if (((j - 483) ^ (j - 503)) < 0) {
204 /* near 5pi/2, cos(5pi/2-x)=sin(x) */
205 p = PI5O2_H - x;
206 i = ix - 0x401F6A7A;
207 x = p + PI5O2_L;
208
209 if ((i | ((lx - 0x29553800) & 0xffffff00)) == 0) {
210 /* very close to pi/2 */
211 x = p + PI5O2_L0;
212 return (x + PI5O2_L1);
213 }
214
215 z = x * x;
216
217 if (((ix - 0x401F6A7A) >> 7) == 0) {
218 /* |pi/2-x|<2**-8 */
219 w = PI5O2_L + (z * x) * (PP1 + z * PP2);
220 } else {
221 w = PI5O2_L + (z * x) * ((P1 + z * P2) + (z *
222 z) * (P3 + z * P4));
223 }
224
225 return (p + w);
226 }
227
228 j <<= 1;
229 w = _TBL_sincos[j];
230 z = _TBL_sincos[j + 1];
231 p = v + (v * s) * (PP1 + s * PP2);
232 q = s * (QQ1 + s * QQ2);
233 return (z - (w * p - z * q));
234 }
235
236 if (ix >= 0x7ff00000) /* cos(Inf or NaN) is NaN */
237 return (x / x);
238
239 /* argument reduction needed */
240 n = __rem_pio2(x, y);
241
242 switch (n & 3) {
243 case 0:
244 return (__k_cos(y[0], y[1]));
245 case 1:
246 return (-__k_sin(y[0], y[1]));
247 case 2:
248 return (-__k_cos(y[0], y[1]));
249 default:
250 return (__k_sin(y[0], y[1]));
251 }
252 }
|