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 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
23 */
24 /*
25 * Copyright 2005 Sun Microsystems, Inc. All rights reserved.
26 * Use is subject to license terms.
27 */
28
29 /*
30 * __rem_pio2(x, y) passes back a better-than-double-precision
31 * approximation to x mod pi/2 in y[0]+y[1] and returns an integer
32 * congruent mod 8 to the integer part of x/(pi/2).
33 *
34 * This implementation tacitly assumes that x is finite and at
35 * least about pi/4 in magnitude.
36 */
37
38 #include "libm.h"
39
40 extern const int _TBL_ipio2_inf[];
41
42 /* INDENT OFF */
43 /*
44 * invpio2: 53 bits of 2/pi
45 * pio2_1: first 33 bit of pi/2
46 * pio2_1t: pi/2 - pio2_1
47 * pio2_2: second 33 bit of pi/2
48 * pio2_2t: pi/2 - pio2_2
49 * pio2_3: third 33 bit of pi/2
50 * pio2_3t: pi/2 - pio2_3
51 */
52 static const double
53 half = 0.5,
54 invpio2 = 0.636619772367581343075535, /* 2^ -1 * 1.45F306DC9C883 */
55 pio2_1 = 1.570796326734125614166, /* 2^ 0 * 1.921FB54400000 */
56 pio2_1t = 6.077100506506192601475e-11, /* 2^-34 * 1.0B4611A626331 */
57 pio2_2 = 6.077100506303965976596e-11, /* 2^-34 * 1.0B4611A600000 */
58 pio2_2t = 2.022266248795950732400e-21, /* 2^-69 * 1.3198A2E037073 */
59 pio2_3 = 2.022266248711166455796e-21, /* 2^-69 * 1.3198A2E000000 */
60 pio2_3t = 8.478427660368899643959e-32; /* 2^-104 * 1.B839A252049C1 */
61 /* INDENT ON */
62
63 int
64 __rem_pio2(double x, double *y) {
65 double w, t, r, fn;
66 double tx[3];
67 int e0, i, j, nx, n, ix, hx, lx;
68
69 hx = ((int *)&x)[HIWORD];
70 ix = hx & 0x7fffffff;
71
72 if (ix < 0x4002d97c) {
73 /* |x| < 3pi/4, special case with n=1 */
74 t = fabs(x) - pio2_1;
75 if (ix != 0x3ff921fb) { /* 33+53 bit pi is good enough */
76 y[0] = t - pio2_1t;
77 y[1] = (t - y[0]) - pio2_1t;
78 } else { /* near pi/2, use 33+33+53 bit pi */
79 t -= pio2_2;
80 y[0] = t - pio2_2t;
81 y[1] = (t - y[0]) - pio2_2t;
82 }
83 if (hx < 0) {
84 y[0] = -y[0];
85 y[1] = -y[1];
86 return (-1);
87 }
88 return (1);
89 }
90
91 if (ix <= 0x413921fb) {
92 /* |x| <= 2^19 pi */
93 t = fabs(x);
94 n = (int)(t * invpio2 + half);
95 fn = (double)n;
96 r = t - fn * pio2_1;
97 j = ix >> 20;
98 w = fn * pio2_1t; /* 1st round good to 85 bit */
99 y[0] = r - w;
100 i = j - ((((int *)y)[HIWORD] >> 20) & 0x7ff);
101 if (i > 16) { /* 2nd iteration (rare) */
102 /* 2nd round good to 118 bit */
103 if (i < 35) {
104 t = r; /* r-fn*pio2_2 may not be exact */
105 w = fn * pio2_2;
106 r = t - w;
107 w = fn * pio2_2t - ((t - r) - w);
108 y[0] = r - w;
109 } else {
110 r -= fn * pio2_2;
111 w = fn * pio2_2t;
112 y[0] = r - w;
113 i = j - ((((int *)y)[HIWORD] >> 20) & 0x7ff);
114 if (i > 49) {
115 /* 3rd iteration (extremely rare) */
116 if (i < 68) {
117 t = r;
118 w = fn * pio2_3;
119 r = t - w;
120 w = fn * pio2_3t -
121 ((t - r) - w);
122 y[0] = r - w;
123 } else {
124 /*
125 * 3rd round good to 151 bits;
126 * covered all possible cases
127 */
128 r -= fn * pio2_3;
129 w = fn * pio2_3t;
130 y[0] = r - w;
131 }
132 }
133 }
134 }
135 y[1] = (r - y[0]) - w;
136 if (hx < 0) {
137 y[0] = -y[0];
138 y[1] = -y[1];
139 return (-n);
140 }
141 return (n);
142 }
143
144 e0 = (ix >> 20) - 1046; /* e0 = ilogb(x)-23; */
145
146 /* break x into three 24 bit pieces */
147 lx = ((int *)&x)[LOWORD];
148 i = (lx & 0x1f) << 19;
149 tx[2] = (double)i;
150 j = (lx >> 5) & 0xffffff;
151 tx[1] = (double)j;
152 tx[0] = (double)((((ix & 0xfffff) | 0x100000) << 3) |
153 ((unsigned)lx >> 29));
154 nx = 3;
155 if (i == 0) {
156 /* skip zero term */
157 nx--;
158 if (j == 0)
159 nx--;
160 }
161 n = __rem_pio2m(tx, y, e0, nx, 2, _TBL_ipio2_inf);
162 if (hx < 0) {
163 y[0] = -y[0];
164 y[1] = -y[1];
165 return (-n);
166 }
167 return (n);
168 }