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 /* BEGIN CSTYLED */
32 /*
33 * __k_cosl( long double x; long double y )
34 * kernel cos 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 cos(-x) = cos(x), we may replace x by |x|
40 * 2. if x < 25/128 = [0x3ffc4000, 0] = 0.15625 , then
41 * if x < 2^-57 (hx < 0x3fc60000 0), return 1.0 with inexact if x != 0
42 * z = x*x;
43 * if x <= 1/128 = 2**-7 = 0.0078125
44 * cos(x)=1.0+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))))
45 * else
46 * cos(x)=1.0+z*(q1+ ... z*q8)
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 * cos(t+x')
54 * = cos(t)cos(x')-sin(t)sin(x')
55 * = cos(t)(1+z*(qq1+z*qq2))-[sin(t)]*x*(1+z*(pp1+z*pp2))
56 * = cos(t) + [cos(t)]*(z*(qq1+z*qq2))-
57 * [sin(t)]*x*(1+z*(pp1+z*pp2))
58 *
59 * Thus,
60 * let a= _TBL_cos_hi[i], b = _TBL_cos_lo[i], c= _TBL_sin_hi[i],
61 * x = (x-t)+y
62 * z = x*x;
63 * cos(t+x) = a+(b+ (-c*x*(1+z*(pp1+z*pp2))+a*(z*(qq1+z*qq2)))
64 */
65 /* END CSTYLED */
66
67 #include "libm.h"
68
69 #include <sys/isa_defs.h>
70
71 extern const long double _TBL_cosl_hi[], _TBL_cosl_lo[], _TBL_sinl_hi[];
72 static const long double one = 1.0;
73
74 /*
75 * |sin(x) - (x+pp1*x^3+...+ pp5*x^11 )| <= 2^-122.32 for |x|<1/64
76 */
77 static const long double
78 pp1 = -1.666666666666666666666666666586782940810e-0001L,
79 pp2 = 8.333333333333333333333003723660929317540e-0003L,
80 pp3 = -1.984126984126984076045903483778337804470e-0004L,
81 pp4 = 2.755731922361906641319723106210900949413e-0006L,
82 pp5 = -2.505198398570947019093998469135012057673e-0008L;
83
84 /*
85 *
86 * |cos(x) - (1+q1*x^2+...+q8*x^16)| <= 2^-117.11 for |x|<= 0.15625
87 */
88 static const long double
89 q1 = -4.999999999999999999999999999999756416975e-0001L,
90 q2 = 4.166666666666666666666666664006066577258e-0002L,
91 q3 = -1.388888888888888888888877700363937169637e-0003L,
92 q4 = 2.480158730158730158494468463031814083559e-0005L,
93 q5 = -2.755731922398586276322819250356005542871e-0007L,
94 q6 = 2.087675698767424261441959760729854017855e-0009L,
95 q7 = -1.147074481239662089072452129010790774761e-0011L,
96 q8 = 4.777761647399651599730663422263531034782e-0014L;
97
98 /*
99 *
100 * |cos(x) - (1+qq1*x^2+...+ qq5*x^10)| <= 2^-123.84 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_cosl(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 = 1.0;
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 < 0x3ffc4000) {
126 if (ix < 0x3fc60000)
127 if ((i = (int)x) == 0)
128 return (one);
129
130 /* generate inexact */
131 z = x * x;
132
133 if (ix < 0x3ff80000) /* 0.0078125 */
134 return (one + z * (qq1 + z * (qq2 + z * (qq3 + z *
135 (qq4 + z * qq5)))));
136 else
137 return (one + z * (q1 + z * (q2 + z * (q3 + z * (q4 +
138 z * (q5 + z * (q6 + z * (q7 + z * q8))))))));
139 }
140
141 j = (ix + 0x400) & 0x7ffff800;
142 i = (j - 0x3ffc4000) >> 11;
143 #if defined(__i386) || defined(__amd64)
144 ITOX(j, pt);
145 #else
146 pt[0] = j;
147 #endif
148
149 if (hx > 0)
150 x = y - (t - x);
151 else
152 x = (-y) - (t + x);
153
154 a = _TBL_cosl_hi[i];
155 z = x * x;
156 t = z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5))));
157 w = x * (one + z * (pp1 + z * (pp2 + z * (pp3 + z * (pp4 + z * pp5)))));
158 t = _TBL_cosl_lo[i] - (_TBL_sinl_hi[i] * w - a * t);
159 return (a + t);
160 }