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--- old/usr/src/lib/libm/common/LD/__sinl.c
+++ new/usr/src/lib/libm/common/LD/__sinl.c
1 1 /*
2 2 * CDDL HEADER START
3 3 *
4 4 * The contents of this file are subject to the terms of the
5 5 * Common Development and Distribution License (the "License").
6 6 * You may not use this file except in compliance with the License.
7 7 *
8 8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
9 9 * or http://www.opensolaris.org/os/licensing.
10 10 * See the License for the specific language governing permissions
11 11 * and limitations under the License.
12 12 *
13 13 * When distributing Covered Code, include this CDDL HEADER in each
14 14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
15 15 * If applicable, add the following below this CDDL HEADER, with the
16 16 * fields enclosed by brackets "[]" replaced with your own identifying
17 17 * information: Portions Copyright [yyyy] [name of copyright owner]
18 18 *
19 19 * CDDL HEADER END
20 20 */
21 21
22 22 /*
23 23 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
24 24 */
25 25 /*
26 26 * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
27 27 * Use is subject to license terms.
28 28 */
29 29
30 30 /* INDENT OFF */
31 31 /*
32 32 * __k_sinl( long double x; long double y )
33 33 * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.785398164
34 34 * Input x is assumed to be bounded by ~pi/4 in magnitude.
35 35 * Input y is the tail of x.
36 36 *
37 37 * Table look up algorithm
38 38 * 1. by sin(-x) = -sin(x), need only to consider positive x
39 39 * 2. if x < 25/128 = [0x3ffc9000,0,0,0] = 0.1953125 , then
40 40 * if x < 2^-57 (hx < 0x3fc60000,0,0,0), return x (inexact if x!= 0)
41 41 * z = x*x;
42 42 * if x <= 1/64 = 2**-6
43 43 * sin(x) = x + (y+(x*z)*(p1 + z*p2))
44 44 * else
45 45 * sin(x) = x + (y+(x*z)*(p1 + z*(p2 + z*(p3 + z*p4))))
46 46 * 3. else
47 47 * ht = (hx + 0x400)&0x7ffff800 (round x to a break point t)
48 48 * lt = 0
49 49 * i = (hy-0x3ffc4000)>>11; (i<=64)
50 50 * x' = (x - t)+y (|x'| ~<= 2^-7
51 51 * By
52 52 * sin(t+x')
53 53 * = sin(t)cos(x')+cos(t)sin(x')
54 54 * = sin(t)(1+z*(qq1+z*qq2))+[cos(t)]*x*(1+z*(pp1+z*pp2))
55 55 * = sin(t) + [sin(t)]*(z*(qq1+z*qq2))+
56 56 * [cos(t)]*x*(1+z*(pp1+z*pp2))
57 57 *
58 58 * Thus,
59 59 * let a= _TBL_sin_hi[i], b = _TBL_sin_lo[i], c= _TBL_cos_hi[i],
60 60 * x = (x-t)+y
61 61 * z = x*x;
62 62 * sin(t+x) = a+(b+ ((c*x)*(1+z*(pp1+z*pp2))+a*(z*(qq1+z*qq2)))
63 63 */
64 64
65 65 #include "libm.h"
66 66
67 67 #include <sys/isa_defs.h>
68 68
69 69 extern const long double _TBL_sinl_hi[], _TBL_sinl_lo[], _TBL_cosl_hi[];
70 70 static const long double
71 71 one = 1.0,
72 72 /*
73 73 * |sin(x) - (x+pp1*x^3+...+ pp5*x^11)| <= 2^-122.32 for |x|<1/64
74 74 */
75 75 pp1 = -1.666666666666666666666666666586782940810e-0001L,
76 76 pp2 = 8.333333333333333333333003723660929317540e-0003L,
77 77 pp3 = -1.984126984126984076045903483778337804470e-0004L,
78 78 pp4 = 2.755731922361906641319723106210900949413e-0006L,
79 79 pp5 = -2.505198398570947019093998469135012057673e-0008L,
80 80 /*
81 81 * |(sin(x) - (x+p1*x^3+...+p8*x^17)|
82 82 * |------------------------------- | <= 2^-116.17 for |x|<0.1953125
83 83 * | x |
84 84 */
85 85 p1 = -1.666666666666666666666666666666211262297e-0001L,
86 86 p2 = 8.333333333333333333333333301497876908541e-0003L,
87 87 p3 = -1.984126984126984126984041302881180621922e-0004L,
88 88 p4 = 2.755731922398589064100587351307269621093e-0006L,
89 89 p5 = -2.505210838544163129378906953765595393873e-0008L,
90 90 p6 = 1.605904383643244375050998243778534074273e-0010L,
91 91 p7 = -7.647162722800685516901456114270824622699e-0013L,
92 92 p8 = 2.810046428661902961725428841068844462603e-0015L,
93 93 /*
94 94 * 2 10 -123.84
95 95 * |cos(x) - (1+qq1*x +...+ qq5*x )| <= 2 for |x|<=1/128
96 96 */
97 97 qq1 = -4.999999999999999999999999999999378373641e-0001L,
98 98 qq2 = 4.166666666666666666666665478399327703130e-0002L,
99 99 qq3 = -1.388888888888888888058211230618051613494e-0003L,
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99 lines elided |
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100 100 qq4 = 2.480158730156105377771585658905303111866e-0005L,
101 101 qq5 = -2.755728099762526325736488376695157008736e-0007L;
102 102 /* INDENT ON */
103 103 long double
104 104 __k_sinl(long double x, long double y) {
105 105 long double a, t, z, w;
106 106 int *pt = (int *) &t, *px = (int *) &x;
107 107 int i, j, hx, ix;
108 108
109 109 t = 1.0L;
110 -#if defined(_BIG_ENDIAN)
111 - hx = px[0];
112 -#else
110 +#if defined(__i386) || defined(__amd64)
113 111 XTOI(px, hx);
112 +#else
113 + hx = px[0];
114 114 #endif
115 115 ix = hx & 0x7fffffff;
116 116 if (ix < 0x3ffc9000) {
117 117 if (ix < 0x3fc60000)
118 118 if (((int) x) == 0)
119 119 return (x); /* generate inexact */
120 120 z = x * x;
121 121 t = z * (p1 + z * (p2 + z * (p3 + z * (p4 + z * (p5 + z *
122 122 (p6 + z * (p7 + z * p8)))))));
123 123 t = y + x * t;
124 124 return (x + t);
125 125 }
126 126 j = (ix + 0x400) & 0x7ffff800;
127 127 i = (j - 0x3ffc4000) >> 11;
128 -#if defined(_BIG_ENDIAN)
129 - pt[0] = j;
130 -#else
128 +#if defined(__i386) || defined(__amd64)
131 129 ITOX(j, pt);
130 +#else
131 + pt[0] = j;
132 132 #endif
133 133 if (hx > 0)
134 134 x = y - (t - x);
135 135 else
136 136 x = (-y) - (t + x);
137 137 a = _TBL_sinl_hi[i];
138 138 z = x * x;
139 139 t = z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5))));
140 140 w = x * (one + z * (pp1 + z * (pp2 + z * (pp3 + z * (pp4 + z *
141 141 pp5)))));
142 142 t = _TBL_cosl_hi[i] * w + a * t;
143 143 t += _TBL_sinl_lo[i];
144 144 if (hx < 0)
145 145 return (-a - t);
146 146 else
147 147 return (a + t);
148 148 }
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