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 * __k_cosl(long double x, long double y)
32 * kernel cos 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 cos(-x) = cos(x), we may replace x by |x|
38 * 2. if x < 25/128 = [0x3ffc4000, 0] = 0.15625 , then
39 * if x < 2^-57 (hx < 0x3fc60000 0), return 1.0 with inexact if x != 0
40 * z = x*x;
41 * if x <= 1/128 = 2**-7 = 0.0078125
42 * cos(x)=1.0+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))))
43 * else
44 * cos(x)=1.0+z*(q1+ ... z*q8)
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 * cos(t+x')
52 * = cos(t)cos(x')-sin(t)sin(x')
53 * = cos(t)(1+z*(qq1+z*qq2))-[sin(t)]*x*(1+z*(pp1+z*pp2))
54 * = cos(t) + [cos(t)]*(z*(qq1+z*qq2))-
55 * [sin(t)]*x*(1+z*(pp1+z*pp2))
56 *
57 * Thus,
58 * let a= _TBL_cos_hi[i], b = _TBL_cos_lo[i], c= _TBL_sin_hi[i],
59 * x = (x-t)+y
60 * z = x*x;
61 * cos(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_cosl_hi[], _TBL_cosl_lo[], _TBL_sinl_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 * 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 * 2 10 -123.84
92 * |cos(x) - (1+qq1*x +...+ qq5*x )| <= 2 for |x|<=1/128
93 */
94 qq1 = -4.999999999999999999999999999999378373641e-0001L,
95 qq2 = +4.166666666666666666666665478399327703130e-0002L,
96 qq3 = -1.388888888888888888058211230618051613494e-0003L,
97 qq4 = +2.480158730156105377771585658905303111866e-0005L,
98 qq5 = -2.755728099762526325736488376695157008736e-0007L;
99
100 #define i0 0
101
102 long double
103 __k_cosl(long double x, long double y) {
104 long double a, t, 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 if (ix < 0x3ffc4000) {
112 if (ix < 0x3fc60000)
113 if ((i = (int) x) == 0)
114 return (one); /* generate inexact */
115 z = x * x;
116
117 if (ix < 0x3ff80000) /* 0.0078125 */
118 return one + z * (qq1 + z * (qq2 + z * (qq3 +
119 z * (qq4 + z * qq5))));
120 else
121 return one + z * (q1 + z * (q2 + z * (q3 +
122 z * (q4 + z * (q5 + z * (q6 + z * (q7 +
123 z * q8)))))));
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 a = _TBL_cosl_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 t = _TBL_cosl_lo[i] - (_TBL_sinl_hi[i] * w - a * t);
137 return (a + t);
138 }