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 2006 Sun Microsystems, Inc. All rights reserved.
28 * Use is subject to license terms.
29 */
30
31
32 /*
33 * long double __k_sincos( long double x, long double y, long double *c )
34 * kernel sincosl 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 sinl(x) with *c = cosl(x)
38 *
39 * Table look up algorithm
40 * see __k_sinl() and __k_cosl()
41 */
42
43 #include "libm.h"
44
45 #include <sys/isa_defs.h>
46
47 extern const long double _TBL_sinl_hi[], _TBL_sinl_lo[], _TBL_cosl_hi[],
48 _TBL_cosl_lo[];
49 static const long double one = 1.0;
50
51 /*
52 * |sin(x) - (x+pp1*x^3+...+pp5*x^11)| <= 2^-122.32 for |x|<1/64
53 */
54 static const long double
55 pp1 = -1.666666666666666666666666666586782940810e-0001L,
56 pp2 = 8.333333333333333333333003723660929317540e-0003L,
57 pp3 = -1.984126984126984076045903483778337804470e-0004L,
58 pp4 = 2.755731922361906641319723106210900949413e-0006L,
59 pp5 = -2.505198398570947019093998469135012057673e-0008L;
60
61 /*
62 * |(sin(x) - (x+p1*x^3+...+p8*x^17)|
63 * |------------------------------- | <= 2^-116.17 for |x|<0.1953125
64 * | x |
65 */
66 static const long double
67 p1 = -1.666666666666666666666666666666211262297e-0001L,
68 p2 = 8.333333333333333333333333301497876908541e-0003L,
69 p3 = -1.984126984126984126984041302881180621922e-0004L,
70 p4 = 2.755731922398589064100587351307269621093e-0006L,
71 p5 = -2.505210838544163129378906953765595393873e-0008L,
72 p6 = 1.605904383643244375050998243778534074273e-0010L,
73 p7 = -7.647162722800685516901456114270824622699e-0013L,
74 p8 = 2.810046428661902961725428841068844462603e-0015L;
75
76 /*
77 *
78 * |cos(x) - (1+qq1*x^2+...+ qq5*x^10)| <= 2^-123.84 for |x|<=1/128
79 */
80 static const long double
81 qq1 = -4.999999999999999999999999999999378373641e-0001L,
82 qq2 = 4.166666666666666666666665478399327703130e-0002L,
83 qq3 = -1.388888888888888888058211230618051613494e-0003L,
84 qq4 = 2.480158730156105377771585658905303111866e-0005L,
85 qq5 = -2.755728099762526325736488376695157008736e-0007L;
86
87 /*
88 *
89 * |cos(x) - (1+q1*x^2+...+ q8*x^16)| <= 2^-117.11 for |x|<= 0.15625
90 */
91 static const long double
92 q1 = -4.999999999999999999999999999999756416975e-0001L,
93 q2 = 4.166666666666666666666666664006066577258e-0002L,
94 q3 = -1.388888888888888888888877700363937169637e-0003L,
95 q4 = 2.480158730158730158494468463031814083559e-0005L,
96 q5 = -2.755731922398586276322819250356005542871e-0007L,
97 q6 = 2.087675698767424261441959760729854017855e-0009L,
98 q7 = -1.147074481239662089072452129010790774761e-0011L,
99 q8 = 4.777761647399651599730663422263531034782e-0014L;
100
101
102 long double
103 __k_sincosl(long double x, long double y, long double *c)
104 {
105 long double a1, a2, t, t1, t2, z, w;
106 int *pt = (int *)&t, *px = (int *)&x;
107 int i, j, hx, ix;
108
109 t = 1.0;
110 #if defined(__i386) || defined(__amd64)
111 XTOI(px, hx);
112 #else
113 hx = px[0];
114 #endif
115 ix = hx & 0x7fffffff;
116
117 if (ix < 0x3ffc4000) {
118 if (ix < 0x3fc60000) {
119 if (((int)x) == 0) {
120 *c = one;
121 return (x);
122 } /* generate inexact */
123 }
124
125 z = x * x;
126
127 if (ix < 0x3ff80000) {
128 *c = one + z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 +
129 z * qq5))));
130 t = z * (p1 + z * (p2 + z * (p3 + z * (p4 + z * (p5 +
131 z * p6)))));
132 } else {
133 *c = one + z * (q1 + z * (q2 + z * (q3 + z * (q4 + z *
134 (q5 + z * (q6 + z * (q7 + z * q8)))))));
135 t = z * (p1 + z * (p2 + z * (p3 + z * (p4 + z * (p5 +
136 z * (p6 + z * (p7 + z * p8)))))));
137 }
138
139 t = y + x * t;
140 return (x + t);
141 }
142
143 j = (ix + 0x400) & 0x7ffff800;
144 i = (j - 0x3ffc4000) >> 11;
145 #if defined(__i386) || defined(__amd64)
146 ITOX(j, pt);
147 #else
148 pt[0] = j;
149 #endif
150
151 if (hx > 0)
152 x = y - (t - x);
153 else
154 x = (-y) - (t + x);
155
156 a1 = _TBL_sinl_hi[i];
157 z = x * x;
158 t = z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5))));
159 w = x * (one + z * (pp1 + z * (pp2 + z * (pp3 + z * (pp4 + z * pp5)))));
160 a2 = _TBL_cosl_hi[i];
161 t2 = _TBL_cosl_lo[i] - (a1 * w - a2 * t);
162 *c = a2 + t2;
163 t1 = a2 * w + a1 * t;
164 t1 += _TBL_sinl_lo[i];
165
166 if (hx < 0)
167 return (-a1 - t1);
168 else
169 return (a1 + t1);
170 }