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Wed Aug 1 13:51:53 2007 UTC (14 years, 9 months ago) by siliconforks
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Initial import.

1 /* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
2 *
3 * ***** BEGIN LICENSE BLOCK *****
4 * Version: MPL 1.1/GPL 2.0/LGPL 2.1
5 *
6 * The contents of this file are subject to the Mozilla Public License Version
7 * 1.1 (the "License"); you may not use this file except in compliance with
8 * the License. You may obtain a copy of the License at
9 * http://www.mozilla.org/MPL/
10 *
11 * Software distributed under the License is distributed on an "AS IS" basis,
12 * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
13 * for the specific language governing rights and limitations under the
14 * License.
15 *
16 * The Original Code is Mozilla Communicator client code, released
17 * March 31, 1998.
18 *
19 * The Initial Developer of the Original Code is
20 * Sun Microsystems, Inc.
21 * Portions created by the Initial Developer are Copyright (C) 1998
22 * the Initial Developer. All Rights Reserved.
23 *
24 * Contributor(s):
25 *
26 * Alternatively, the contents of this file may be used under the terms of
27 * either of the GNU General Public License Version 2 or later (the "GPL"),
28 * or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
29 * in which case the provisions of the GPL or the LGPL are applicable instead
30 * of those above. If you wish to allow use of your version of this file only
31 * under the terms of either the GPL or the LGPL, and not to allow others to
32 * use your version of this file under the terms of the MPL, indicate your
33 * decision by deleting the provisions above and replace them with the notice
34 * and other provisions required by the GPL or the LGPL. If you do not delete
35 * the provisions above, a recipient may use your version of this file under
36 * the terms of any one of the MPL, the GPL or the LGPL.
37 *
38 * ***** END LICENSE BLOCK ***** */
39
40 /* @(#)e_rem_pio2.c 1.4 95/01/18 */
41 /*
42 * ====================================================
43 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
44 *
45 * Developed at SunSoft, a Sun Microsystems, Inc. business.
46 * Permission to use, copy, modify, and distribute this
47 * software is freely granted, provided that this notice
48 * is preserved.
49 * ====================================================
50 *
51 */
52
53 /* __ieee754_rem_pio2(x,y)
54 *
55 * return the remainder of x rem pi/2 in y[0]+y[1]
56 * use __kernel_rem_pio2()
57 */
58
59 #include "fdlibm.h"
60
61 /*
62 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
63 */
64 #ifdef __STDC__
65 static const int two_over_pi[] = {
66 #else
67 static int two_over_pi[] = {
68 #endif
69 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
70 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
71 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
72 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
73 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
74 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
75 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
76 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
77 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
78 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
79 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
80 };
81
82 #ifdef __STDC__
83 static const int npio2_hw[] = {
84 #else
85 static int npio2_hw[] = {
86 #endif
87 0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
88 0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
89 0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
90 0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
91 0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
92 0x404858EB, 0x404921FB,
93 };
94
95 /*
96 * invpio2: 53 bits of 2/pi
97 * pio2_1: first 33 bit of pi/2
98 * pio2_1t: pi/2 - pio2_1
99 * pio2_2: second 33 bit of pi/2
100 * pio2_2t: pi/2 - (pio2_1+pio2_2)
101 * pio2_3: third 33 bit of pi/2
102 * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
103 */
104
105 #ifdef __STDC__
106 static const double
107 #else
108 static double
109 #endif
110 zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
111 half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
112 two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
113 invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
114 pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
115 pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
116 pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
117 pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
118 pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
119 pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
120
121 #ifdef __STDC__
122 int __ieee754_rem_pio2(double x, double *y)
123 #else
124 int __ieee754_rem_pio2(x,y)
125 double x,y[];
126 #endif
127 {
128 fd_twoints u, ux, uz;
129 double z = 0;
130 double w,t,r,fn;
131 double tx[3];
132 int e0,i,j,nx,n,ix,hx;
133
134 u.d = x;
135 hx = __HI(u); /* high word of x */
136 ix = hx&0x7fffffff;
137 if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */
138 {y[0] = x; y[1] = 0; return 0;}
139 if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */
140 if(hx>0) {
141 z = x - pio2_1;
142 if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
143 y[0] = z - pio2_1t;
144 y[1] = (z-y[0])-pio2_1t;
145 } else { /* near pi/2, use 33+33+53 bit pi */
146 z -= pio2_2;
147 y[0] = z - pio2_2t;
148 y[1] = (z-y[0])-pio2_2t;
149 }
150 return 1;
151 } else { /* negative x */
152 z = x + pio2_1;
153 if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
154 y[0] = z + pio2_1t;
155 y[1] = (z-y[0])+pio2_1t;
156 } else { /* near pi/2, use 33+33+53 bit pi */
157 z += pio2_2;
158 y[0] = z + pio2_2t;
159 y[1] = (z-y[0])+pio2_2t;
160 }
161 return -1;
162 }
163 }
164 if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
165 t = fd_fabs(x);
166 n = (int) (t*invpio2+half);
167 fn = (double)n;
168 r = t-fn*pio2_1;
169 w = fn*pio2_1t; /* 1st round good to 85 bit */
170 if(n<32&&ix!=npio2_hw[n-1]) {
171 y[0] = r-w; /* quick check no cancellation */
172 } else {
173 j = ix>>20;
174 y[0] = r-w;
175 u.d = y[0];
176 i = j-(((__HI(u))>>20)&0x7ff);
177 if(i>16) { /* 2nd iteration needed, good to 118 */
178 t = r;
179 w = fn*pio2_2;
180 r = t-w;
181 w = fn*pio2_2t-((t-r)-w);
182 y[0] = r-w;
183 u.d = y[0];
184 i = j-(((__HI(u))>>20)&0x7ff);
185 if(i>49) { /* 3rd iteration need, 151 bits acc */
186 t = r; /* will cover all possible cases */
187 w = fn*pio2_3;
188 r = t-w;
189 w = fn*pio2_3t-((t-r)-w);
190 y[0] = r-w;
191 }
192 }
193 }
194 y[1] = (r-y[0])-w;
195 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
196 else return n;
197 }
198 /*
199 * all other (large) arguments
200 */
201 if(ix>=0x7ff00000) { /* x is inf or NaN */
202 y[0]=y[1]=x-x; return 0;
203 }
204 /* set z = scalbn(|x|,ilogb(x)-23) */
205 ux.d = x; uz.d = z;
206 __LO(uz) = __LO(ux);
207 z = uz.d;
208 e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */
209 uz.d = z;
210 __HI(uz) = ix - (e0<<20);
211 z = uz.d;
212 for(i=0;i<2;i++) {
213 tx[i] = (double)((int)(z));
214 z = (z-tx[i])*two24;
215 }
216 tx[2] = z;
217 nx = 3;
218 while(tx[nx-1]==zero) nx--; /* skip zero term */
219 n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);
220 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
221 return n;
222 }

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