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 * __k_sinl( long double x; long double y )
34 * kernel sin 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 *
38 * Table look up algorithm
39 * 1. by sin(-x) = -sin(x), need only to consider positive x
40 * 2. if x < 25/128 = [0x3ffc9000,0,0,0] = 0.1953125 , then
41 * if x < 2^-57 (hx < 0x3fc60000,0,0,0), return x (inexact if x != 0)
42 * z = x*x;
43 * if x <= 1/64 = 2**-6
44 * sin(x) = x + (y+(x*z)*(p1 + z*p2))
45 * else
46 * sin(x) = x + (y+(x*z)*(p1 + z*(p2 + z*(p3 + z*p4))))
47 * 3. else
48 * ht = (hx + 0x400)&0x7ffff800 (round x to a break point t)
49 * lt = 0
50 * i = (hy-0x3ffc4000)>>11; (i<=64)
51 * x' = (x - t)+y (|x'| ~<= 2^-7
52 * By
53 * sin(t+x')
54 * = sin(t)cos(x')+cos(t)sin(x')
55 * = sin(t)(1+z*(qq1+z*qq2))+[cos(t)]*x*(1+z*(pp1+z*pp2))
56 * = sin(t) + [sin(t)]*(z*(qq1+z*qq2))+
57 * [cos(t)]*x*(1+z*(pp1+z*pp2))
58 *
59 * Thus,
60 * let a= _TBL_sin_hi[i], b = _TBL_sin_lo[i], c= _TBL_cos_hi[i],
61 * x = (x-t)+y
62 * z = x*x;
63 * sin(t+x) = a+(b+ ((c*x)*(1+z*(pp1+z*pp2))+a*(z*(qq1+z*qq2)))
64 */
65
66 #include "libm.h"
67
68 #include <sys/isa_defs.h>
69
70 extern const long double _TBL_sinl_hi[], _TBL_sinl_lo[], _TBL_cosl_hi[];
71 static const long double one = 1.0;
72
73 /*
74 * |sin(x) - (x+pp1*x^3+...+ pp5*x^11)| <= 2^-122.32 for |x|<1/64
75 */
76 static const long double
77 pp1 = -1.666666666666666666666666666586782940810e-0001L,
78 pp2 = 8.333333333333333333333003723660929317540e-0003L,
79 pp3 = -1.984126984126984076045903483778337804470e-0004L,
80 pp4 = 2.755731922361906641319723106210900949413e-0006L,
81 pp5 = -2.505198398570947019093998469135012057673e-0008L;
82
83 /*
84 * |(sin(x) - (x+p1*x^3+...+p8*x^17)|
85 * |------------------------------- | <= 2^-116.17 for |x|<0.1953125
86 * | x |
87 */
88 static const long double
89 p1 = -1.666666666666666666666666666666211262297e-0001L,
90 p2 = 8.333333333333333333333333301497876908541e-0003L,
91 p3 = -1.984126984126984126984041302881180621922e-0004L,
92 p4 = 2.755731922398589064100587351307269621093e-0006L,
93 p5 = -2.505210838544163129378906953765595393873e-0008L,
94 p6 = 1.605904383643244375050998243778534074273e-0010L,
95 p7 = -7.647162722800685516901456114270824622699e-0013L,
96 p8 = 2.810046428661902961725428841068844462603e-0015L;
97
98 /*
99 * 2 10 -123.84
100 * |cos(x) - (1+qq1*x +...+ qq5*x )| <= 2 for |x|<=1/128
101 */
102 static const long double
103 qq1 = -4.999999999999999999999999999999378373641e-0001L,
104 qq2 = 4.166666666666666666666665478399327703130e-0002L,
105 qq3 = -1.388888888888888888058211230618051613494e-0003L,
106 qq4 = 2.480158730156105377771585658905303111866e-0005L,
107 qq5 = -2.755728099762526325736488376695157008736e-0007L;
108
109
110 long double
111 __k_sinl(long double x, long double y)
112 {
113 long double a, t, z, w;
114 int *pt = (int *)&t, *px = (int *)&x;
115 int i, j, hx, ix;
116
117 t = 1.0L;
118 #if defined(__i386) || defined(__amd64)
119 XTOI(px, hx);
120 #else
121 hx = px[0];
122 #endif
123 ix = hx & 0x7fffffff;
124
125 if (ix < 0x3ffc9000) {
126 if (ix < 0x3fc60000)
127 if (((int)x) == 0)
128 return (x);
129
130 /* generate inexact */
131 z = x * x;
132 t = z * (p1 + z * (p2 + z * (p3 + z * (p4 + z * (p5 + z * (p6 +
133 z * (p7 + z * p8)))))));
134 t = y + x * t;
135 return (x + t);
136 }
137
138 j = (ix + 0x400) & 0x7ffff800;
139 i = (j - 0x3ffc4000) >> 11;
140 #if defined(__i386) || defined(__amd64)
141 ITOX(j, pt);
142 #else
143 pt[0] = j;
144 #endif
145
146 if (hx > 0)
147 x = y - (t - x);
148 else
149 x = (-y) - (t + x);
150
151 a = _TBL_sinl_hi[i];
152 z = x * x;
153 t = z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5))));
154 w = x * (one + z * (pp1 + z * (pp2 + z * (pp3 + z * (pp4 + z * pp5)))));
155 t = _TBL_cosl_hi[i] * w + a * t;
156 t += _TBL_sinl_lo[i];
157
158 if (hx < 0)
159 return (-a - t);
160 else
161 return (a + t);
162 }