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
32 /*
33 * double __k_sincos(double x, double y, double *c);
34 * kernel sincos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
35 * Input x is assumed to be bounded by ~pi/4 in magnitude.
36 * Input y is the tail of x.
37 * return sin(x) with *c = cos(x)
38 *
39 * Accurate Table look-up algorithm by K.C. Ng, May, 1995.
40 *
41 * 1. Reduce x to x>0 by sin(-x)=-sin(x),cos(-x)=cos(x).
42 * 2. For 0<= x < pi/4, let i = (64*x chopped)-10. Let d = x - a[i], where
43 * a[i] is a double that is close to (i+10.5)/64 and such that
44 * sin(a[i]) and cos(a[i]) is close to a double (with error less
45 * than 2**-8 ulp). Then
46 * cos(x) = cos(a[i]+d) = cos(a[i])cos(d) - sin(a[i])*sin(d)
47 * = TBL_cos_a[i]*(1+QQ1*d^2+QQ2*d^4) -
48 * TBL_sin_a[i]*(d+PP1*d^3+PP2*d^5)
49 * = TBL_cos_a[i] + (TBL_cos_a[i]*d^2*(QQ1+QQ2*d^2) -
50 * TBL_sin_a[i]*(d+PP1*d^3+PP2*d^5))
51 * sin(x) = sin(a[i]+d) = sin(a[i])cos(d) + cos(a[i])*sin(d)
52 * = TBL_sin_a[i]*(1+QQ1*d^2+QQ2*d^4) +
53 * TBL_cos_a[i]*(d+PP1*d^3+PP2*d^5)
54 * = TBL_sin_a[i] + (TBL_sin_a[i]*d^2*(QQ1+QQ2*d^2) +
55 * TBL_cos_a[i]*(d+PP1*d^3+PP2*d^5))
56 *
57 * For |y| less than 10.5/64 = 0.1640625, use
58 * sin(y) = y + y^3*(p1+y^2*(p2+y^2*(p3+y^2*p4)))
59 * cos(y) = 1 + y^2*(q1+y^2*(q2+y^2*(q3+y^2*q4)))
60 *
61 * For |y| less than 0.008, use
62 * sin(y) = y + y^3*(pp1+y^2*pp2)
63 * cos(y) = 1 + y^2*(qq1+y^2*qq2)
64 *
65 * Accuracy:
66 * TRIG(x) returns trig(x) nearly rounded (less than 1 ulp)
67 */
68
69 #include "libm.h"
70
71 static const double sc[] = {
72 /* ONE = */
73 1.0,
74 /* NONE = */ -1.0,
75
76 /*
77 * |sin(x) - (x+pp1*x^3+pp2*x^5)| <= 2^-58.79 for |x| < 0.008
78 */
79 /* PP1 = */-0.166666666666316558867252052378889521480627858683055567,
80 /* PP2 = */.008333315652997472323564894248466758248475374977974017927,
81
82 /*
83 * |(sin(x) - (x+p1*x^3+...+p4*x^9)|
84 * |------------------------------ | <= 2^-57.63 for |x| < 0.1953125
85 * | x |
86 */
87 /* P1 = */ -1.666666666666629669805215138920301589656e-0001,
88 /* P2 = */ 8.333333332390951295683993455280336376663e-0003,
89 /* P3 = */ -1.984126237997976692791551778230098403960e-0004,
90 /* P4 = */ 2.753403624854277237649987622848330351110e-0006,
91
92 /*
93 * |cos(x) - (1+qq1*x^2+qq2*x^4)| <= 2^-55.99 for |x| <= 0.008 (0x3f80624d)
94 */
95 /* QQ1 = */-0.4999999999975492381842911981948418542742729,
96 /* QQ2 = */0.041666542904352059294545209158357640398771740,
97
98 /*
99 * |cos(x) - (1+q1*x^2+...+q4*x^8)| <= 2^-55.86 for |x| <= 0.1640625 (10.5/64)
100 */
101 /* Q1 = */ -0.5,
102 /* Q2 = */ 4.166666666500350703680945520860748617445e-0002,
103 /* Q3 = */ -1.388888596436972210694266290577848696006e-0003,
104 /* Q4 = */ 2.478563078858589473679519517892953492192e-0005,
105 };
106
107
108 #define ONE sc[0]
109 #define NONE sc[1]
110 #define PP1 sc[2]
111 #define PP2 sc[3]
112 #define P1 sc[4]
113 #define P2 sc[5]
114 #define P3 sc[6]
115 #define P4 sc[7]
116 #define QQ1 sc[8]
117 #define QQ2 sc[9]
118 #define Q1 sc[10]
119 #define Q2 sc[11]
120 #define Q3 sc[12]
121 #define Q4 sc[13]
122
123 extern const double _TBL_sincos[], _TBL_sincosx[];
124
125 double
126 __k_sincos(double x, double y, double *c)
127 {
128 double z, w, s, v, p, q;
129 int i, j, n, hx, ix;
130
131 hx = ((int *)&x)[HIWORD];
132 ix = hx & ~0x80000000;
133
134 if (ix <= 0x3fc50000) { /* |x| < 10.5/64 = 0.164062500 */
135 if (ix < 0x3e400000) { /* |x| < 2**-27 */
136 if ((int)x == 0)
137 *c = ONE;
138
139 return (x + y);
140 } else {
141 z = x * x;
142
143 if (ix < 0x3f800000) { /* |x| < 0.008 */
144 q = z * (QQ1 + z * QQ2);
145 p = (x * z) * (PP1 + z * PP2) + y;
146 } else {
147 q = z * ((Q1 + z * Q2) + (z * z) * (Q3 + z *
148 Q4));
149 p = (x * z) * ((P1 + z * P2) + (z * z) * (P3 +
150 z * P4)) + y;
151 }
152
153 *c = ONE + q;
154 return (x + p);
155 }
156 } else { /* 0.164062500 < |x| < ~pi/4 */
157 n = ix >> 20;
158 i = (((ix >> 12) & 0xff) | 0x100) >> (0x401 - n);
159 j = i - 10;
160
161 if (hx < 0)
162 v = -y - (_TBL_sincosx[j] + x);
163 else
164 v = y - (_TBL_sincosx[j] - x);
165
166 s = v * v;
167 j <<= 1;
168 w = _TBL_sincos[j];
169 z = _TBL_sincos[j + 1];
170 p = s * (PP1 + s * PP2);
171 q = s * (QQ1 + s * QQ2);
172 p = v + v * p;
173 *c = z - (w * p - z * q);
174 s = w * q + z * p;
175 return ((hx >= 0) ? w + s : -(w + s));
176 }
177 }