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_sinl(long double x, long double y);
32 * kernel sin 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 *
36 * Table look up algorithm
37 * 1. by sin(-x) = -sin(x), need only to consider positive x
38 * 2. if x < 25/128 = [0x3ffc9000,0,0,0] = 0.1953125 , then
39 * if x < 2^-57 (hx < 0x3fc60000,0,0,0), return x (inexact if x!= 0)
40 * z = x*x;
41 * if x <= 1/64 = 2**-6
42 * sin(x) = x + (y+(x*z)*(p1 + z*p2))
43 * else
44 * sin(x) = x + (y+(x*z)*(p1 + z*(p2 + z*(p3 + z*p4))))
45 * 3. else
46 * ht = (hx + 0x400)&0x7ffff800 (round x to a break point t)
47 * lt = 0
48 * i = (hy-0x3ffc4000)>>11; (i<=64)
49 * x' = (x - t)+y (|x'| ~<= 2^-7
50 * By
51 * sin(t+x')
52 * = sin(t)cos(x')+cos(t)sin(x')
53 * = sin(t)(1+z*(qq1+z*qq2))+[cos(t)]*x*(1+z*(pp1+z*pp2))
54 * = sin(t) + [sin(t)]*(z*(qq1+z*qq2))+
55 * [cos(t)]*x*(1+z*(pp1+z*pp2))
56 *
57 * Thus,
58 * let a= _TBL_sin_hi[i], b = _TBL_sin_lo[i], c= _TBL_cos_hi[i],
59 * x = (x-t)+y
60 * z = x*x;
61 * sin(t+x) = a+(b+ ((c*x)*(1+z*(pp1+z*pp2))+a*(z*(qq1+z*qq2)))
62 */
63
64 #include "libm.h"
65
66 extern const long double _TBL_sinl_hi[], _TBL_sinl_lo[], _TBL_cosl_hi[];
67 static const long double
68 one = 1.0L,
69 /*
70 * 3 11 -122.32
71 * |sin(x) - (x+pp1*x +...+ pp5*x )| <= 2 for |x|<1/64
72 */
73 pp1 = -1.666666666666666666666666666586782940810e-0001L,
74 pp2 = +8.333333333333333333333003723660929317540e-0003L,
75 pp3 = -1.984126984126984076045903483778337804470e-0004L,
76 pp4 = +2.755731922361906641319723106210900949413e-0006L,
77 pp5 = -2.505198398570947019093998469135012057673e-0008L,
78 /*
79 * |(sin(x) - (x+p1*x^3+...+p8*x^17)|
80 * |------------------------------- | <= 2^-116.17 for |x|<0.1953125
81 * | x |
82 */
83 p1 = -1.666666666666666666666666666666211262297e-0001L,
84 p2 = +8.333333333333333333333333301497876908541e-0003L,
85 p3 = -1.984126984126984126984041302881180621922e-0004L,
86 p4 = +2.755731922398589064100587351307269621093e-0006L,
87 p5 = -2.505210838544163129378906953765595393873e-0008L,
88 p6 = +1.605904383643244375050998243778534074273e-0010L,
89 p7 = -7.647162722800685516901456114270824622699e-0013L,
90 p8 = +2.810046428661902961725428841068844462603e-0015L,
91 /*
92 * 2 10 -123.84
93 * |cos(x) - (1+qq1*x +...+ qq5*x )| <= 2 for |x|<=1/128
94 */
95 qq1 = -4.999999999999999999999999999999378373641e-0001L,
96 qq2 = +4.166666666666666666666665478399327703130e-0002L,
97 qq3 = -1.388888888888888888058211230618051613494e-0003L,
98 qq4 = +2.480158730156105377771585658905303111866e-0005L,
99 qq5 = -2.755728099762526325736488376695157008736e-0007L;
100
101 #define i0 0
102
103 long double
104 __k_sinl(long double x, long double y) {
105 long double a, t, z, w;
106 int *pt = (int *) &t, *px = (int *) &x;
107 int i, j, hx, ix;
108
109 t = 1.0L;
110 hx = px[i0];
111 ix = hx & 0x7fffffff;
112 if (ix < 0x3ffc9000) {
113 *(3 - i0 + (int *) &t) = -1; /* one-ulp */
114 *(2 + (int *) &t) = -1; /* one-ulp */
115 *(1 + (int *) &t) = -1; /* one-ulp */
116 *(i0 + (int *) &t) -= 1; /* one-ulp */
117 if (ix < 0x3fc60000)
118 if (((int) (x * t)) < 1)
119 return (x); /* inexact and underflow */
120 z = x * x;
121 t = z * (p1 + z * (p2 + z * (p3 + z * (p4 + z * (p5 +
122 z * (p6 + z * (p7 + z * p8)))))));
123 t = y + x * t;
124 return (x + t);
125 }
126 j = (ix + 0x400) & 0x7ffff800;
127 i = (j - 0x3ffc4000) >> 11;
128 pt[i0] = j;
129 if (hx > 0)
130 x = y - (t - x);
131 else
132 x = (-y) - (t + x);
133 a = _TBL_sinl_hi[i];
134 z = x * x;
135 t = z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5))));
136 w = x * (one + z * (pp1 + z * (pp2 + z * (pp3 + z * (pp4 + z * pp5)))));
137 t = _TBL_cosl_hi[i] * w + a * t;
138 t += _TBL_sinl_lo[i];
139 if (hx < 0)
140 return (-a - t);
141 else
142 return (a + t);
143 }