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 * long double __k_sincos(long double x, long double y, long double *c);
33 * kernel sincosl function on [-pi/4, pi/4], pi/4 ~ 0.785398164
34 * Input x is assumed to be bounded by ~pi/4 in magnitude.
35 * Input y is the tail of x.
36 * return sinl(x) with *c = cosl(x)
37 *
38 * Table look up algorithm
39 * see __k_sinl and __k_cosl
40 */
41
42 #include "libm.h"
43
44 extern const long double _TBL_sinl_hi[], _TBL_sinl_lo[], _TBL_cosl_hi[],
45 _TBL_cosl_lo[];
46 static const long double one = 1.0L;
47
48 /*
49 * 3 11 -122.32
50 * |sin(x) - (x+pp1*x +...+ pp5*x )| <= 2 for |x|<1/64
51 */
52 static const long double
53 pp1 = -1.666666666666666666666666666586782940810e-0001L,
54 pp2 = +8.333333333333333333333003723660929317540e-0003L,
55 pp3 = -1.984126984126984076045903483778337804470e-0004L,
56 pp4 = +2.755731922361906641319723106210900949413e-0006L,
57 pp5 = -2.505198398570947019093998469135012057673e-0008L;
58
59 /*
60 * |(sin(x) - (x+p1*x^3+...+p8*x^17)|
61 * |------------------------------- | <= 2^-116.17 for |x|<0.1953125
62 * | x |
63 */
64 static const long double
65 p1 = -1.666666666666666666666666666666211262297e-0001L,
66 p2 = +8.333333333333333333333333301497876908541e-0003L,
67 p3 = -1.984126984126984126984041302881180621922e-0004L,
68 p4 = +2.755731922398589064100587351307269621093e-0006L,
69 p5 = -2.505210838544163129378906953765595393873e-0008L,
70 p6 = +1.605904383643244375050998243778534074273e-0010L,
71 p7 = -7.647162722800685516901456114270824622699e-0013L,
72 p8 = +2.810046428661902961725428841068844462603e-0015L;
73
74 /*
75 * 2 10 -123.84
76 * |cos(x) - (1+qq1*x +...+ qq5*x )| <= 2 for |x|<=1/128
77 */
78 static const long double
79 qq1 = -4.999999999999999999999999999999378373641e-0001L,
80 qq2 = +4.166666666666666666666665478399327703130e-0002L,
81 qq3 = -1.388888888888888888058211230618051613494e-0003L,
82 qq4 = +2.480158730156105377771585658905303111866e-0005L,
83 qq5 = -2.755728099762526325736488376695157008736e-0007L;
84
85 /*
86 * 2 16 -117.11
87 * |cos(x) - (1+q1*x + ... + q8*x )| <= 2 for |x|<= 0.15625
88 */
89 static const long double
90 q1 = -4.999999999999999999999999999999756416975e-0001L,
91 q2 = +4.166666666666666666666666664006066577258e-0002L,
92 q3 = -1.388888888888888888888877700363937169637e-0003L,
93 q4 = +2.480158730158730158494468463031814083559e-0005L,
94 q5 = -2.755731922398586276322819250356005542871e-0007L,
95 q6 = +2.087675698767424261441959760729854017855e-0009L,
96 q7 = -1.147074481239662089072452129010790774761e-0011L,
97 q8 = +4.777761647399651599730663422263531034782e-0014L;
98
99 #define i0 0
100
101 long double
102 __k_sincosl(long double x, long double y, long double *c)
103 {
104 long double a1, a2, t, t1, t2, z, w;
105 int *pt = (int *)&t, *px = (int *)&x;
106 int i, j, hx, ix;
107
108 t = 1.0L;
109 hx = px[i0];
110 ix = hx & 0x7fffffff;
111
112 if (ix < 0x3ffc4000) {
113 if (ix < 0x3fc60000) {
114 if (((int)x) == 0) {
115 *c = one;
116 return (x);
117 } /* generate inexact */
118 }
119
120 z = x * x;
121
122 if (ix < 0x3ff80000) {
123 *c = one + z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 +
124 z * qq5))));
125 t = z * (p1 + z * (p2 + z * (p3 + z * (p4 + z * (p5 +
126 z * p6)))));
127 } else {
128 *c = one + z * (q1 + z * (q2 + z * (q3 + z * (q4 + z *
129 (q5 + z * (q6 + z * (q7 + z * q8)))))));
130 t = z * (p1 + z * (p2 + z * (p3 + z * (p4 + z * (p5 +
131 z * (p6 + z * (p7 + z * p8)))))));
132 }
133
134 t = y + x * t;
135 return (x + t);
136 }
137
138 j = (ix + 0x400) & 0x7ffff800;
139 i = (j - 0x3ffc4000) >> 11;
140 pt[i0] = j;
141
142 if (hx > 0)
143 x = y - (t - x);
144 else
145 x = (-y) - (t + x);
146
147 a1 = _TBL_sinl_hi[i];
148 z = x * x;
149 t = z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5))));
150 w = x * (one + z * (pp1 + z * (pp2 + z * (pp3 + z * (pp4 + z * pp5)))));
151 a2 = _TBL_cosl_hi[i];
152 t2 = _TBL_cosl_lo[i] - (a1 * w - a2 * t);
153 *c = a2 + t2;
154 t1 = a2 * w + a1 * t;
155 t1 += _TBL_sinl_lo[i];
156
157 if (hx < 0)
158 return (-a1 - t1);
159 else
160 return (a1 + t1);
161 }