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 * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
27 * Use is subject to license terms.
28 */
29
30 /*
31 * long double __k_sincos(long double x, long double y, long double *c);
32 * kernel sincosl function on [-pi/4, pi/4], pi/4 ~ 0.785398164
33 * Input x is assumed to be bounded by ~pi/4 in magnitude.
34 * Input y is the tail of x.
35 * return sinl(x) with *c = cosl(x)
36 *
37 * Table look up algorithm
38 * see __k_sinl and __k_cosl
39 */
40
41 #include "libm.h"
42
43 extern const long double _TBL_sinl_hi[], _TBL_sinl_lo[],
44 _TBL_cosl_hi[], _TBL_cosl_lo[];
45 static const long double
46 one = 1.0L,
47 /*
48 * 3 11 -122.32
49 * |sin(x) - (x+pp1*x +...+ pp5*x )| <= 2 for |x|<1/64
50 */
51 pp1 = -1.666666666666666666666666666586782940810e-0001L,
52 pp2 = +8.333333333333333333333003723660929317540e-0003L,
53 pp3 = -1.984126984126984076045903483778337804470e-0004L,
54 pp4 = +2.755731922361906641319723106210900949413e-0006L,
55 pp5 = -2.505198398570947019093998469135012057673e-0008L,
56 /*
57 * |(sin(x) - (x+p1*x^3+...+p8*x^17)|
58 * |------------------------------- | <= 2^-116.17 for |x|<0.1953125
59 * | x |
60 */
61 p1 = -1.666666666666666666666666666666211262297e-0001L,
62 p2 = +8.333333333333333333333333301497876908541e-0003L,
63 p3 = -1.984126984126984126984041302881180621922e-0004L,
64 p4 = +2.755731922398589064100587351307269621093e-0006L,
65 p5 = -2.505210838544163129378906953765595393873e-0008L,
66 p6 = +1.605904383643244375050998243778534074273e-0010L,
67 p7 = -7.647162722800685516901456114270824622699e-0013L,
68 p8 = +2.810046428661902961725428841068844462603e-0015L,
69 /*
70 * 2 10 -123.84
71 * |cos(x) - (1+qq1*x +...+ qq5*x )| <= 2 for |x|<=1/128
72 */
73 qq1 = -4.999999999999999999999999999999378373641e-0001L,
74 qq2 = +4.166666666666666666666665478399327703130e-0002L,
75 qq3 = -1.388888888888888888058211230618051613494e-0003L,
76 qq4 = +2.480158730156105377771585658905303111866e-0005L,
77 qq5 = -2.755728099762526325736488376695157008736e-0007L,
78 /*
79 * 2 16 -117.11
80 * |cos(x) - (1+q1*x + ... + q8*x )| <= 2 for |x|<= 0.15625
81 */
82 q1 = -4.999999999999999999999999999999756416975e-0001L,
83 q2 = +4.166666666666666666666666664006066577258e-0002L,
84 q3 = -1.388888888888888888888877700363937169637e-0003L,
85 q4 = +2.480158730158730158494468463031814083559e-0005L,
86 q5 = -2.755731922398586276322819250356005542871e-0007L,
87 q6 = +2.087675698767424261441959760729854017855e-0009L,
88 q7 = -1.147074481239662089072452129010790774761e-0011L,
89 q8 = +4.777761647399651599730663422263531034782e-0014L;
90
91 #define i0 0
92
93 long double
94 __k_sincosl(long double x, long double y, long double *c) {
95 long double a1, a2, t, t1, t2, z, w;
96 int *pt = (int *) &t, *px = (int *) &x;
97 int i, j, hx, ix;
98
99 t = 1.0L;
100 hx = px[i0];
101 ix = hx & 0x7fffffff;
102 if (ix < 0x3ffc4000) {
103 if (ix < 0x3fc60000)
104 if (((int) x) == 0) {
105 *c = one;
106 return (x);
107 } /* generate inexact */
108 z = x * x;
109
110 if (ix < 0x3ff80000) {
111 *c = one + z * (qq1 + z * (qq2 + z * (qq3 +
112 z * (qq4 + z * qq5))));
113 t = z * (p1 + z * (p2 + z * (p3 + z * (p4 +
114 z * (p5 + z * p6)))));
115 } else {
116 *c = one + z * (q1 + z * (q2 + z * (q3 + z * (q4 +
117 z * (q5 + z * (q6 + z * (q7 + z * q8)))))));
118 t = z * (p1 + z * (p2 + z * (p3 + z * (p4 + z * (p5 +
119 z * (p6 + z * (p7 + z * p8)))))));
120 }
121
122 t = y + x * t;
123 return (x + t);
124 }
125 j = (ix + 0x400) & 0x7ffff800;
126 i = (j - 0x3ffc4000) >> 11;
127 pt[i0] = j;
128 if (hx > 0)
129 x = y - (t - x);
130 else
131 x = (-y) - (t + x);
132 a1 = _TBL_sinl_hi[i];
133 z = x * x;
134 t = z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5))));
135 w = x * (one + z * (pp1 + z * (pp2 + z * (pp3 + z * (pp4 + z * pp5)))));
136 a2 = _TBL_cosl_hi[i];
137 t2 = _TBL_cosl_lo[i] - (a1 * w - a2 * t);
138 *c = a2 + t2;
139 t1 = a2 * w + a1 * t;
140 t1 += _TBL_sinl_lo[i];
141 if (hx < 0)
142 return (-a1 - t1);
143 else
144 return (a1 + t1);
145 }