/[jscoverage]/trunk/js/src/fdlibm/k_rem_pio2.c
ViewVC logotype

Contents of /trunk/js/src/fdlibm/k_rem_pio2.c

Parent Directory Parent Directory | Revision Log Revision Log


Revision 2 - (show annotations)
Wed Aug 1 13:51:53 2007 UTC (14 years, 9 months ago) by siliconforks
File MIME type: text/plain
File size: 10285 byte(s)
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 /* @(#)k_rem_pio2.c 1.3 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 * __kernel_rem_pio2(x,y,e0,nx,prec,ipio2)
54 * double x[],y[]; int e0,nx,prec; int ipio2[];
55 *
56 * __kernel_rem_pio2 return the last three digits of N with
57 * y = x - N*pi/2
58 * so that |y| < pi/2.
59 *
60 * The method is to compute the integer (mod 8) and fraction parts of
61 * (2/pi)*x without doing the full multiplication. In general we
62 * skip the part of the product that are known to be a huge integer (
63 * more accurately, = 0 mod 8 ). Thus the number of operations are
64 * independent of the exponent of the input.
65 *
66 * (2/pi) is represented by an array of 24-bit integers in ipio2[].
67 *
68 * Input parameters:
69 * x[] The input value (must be positive) is broken into nx
70 * pieces of 24-bit integers in double precision format.
71 * x[i] will be the i-th 24 bit of x. The scaled exponent
72 * of x[0] is given in input parameter e0 (i.e., x[0]*2^e0
73 * match x's up to 24 bits.
74 *
75 * Example of breaking a double positive z into x[0]+x[1]+x[2]:
76 * e0 = ilogb(z)-23
77 * z = scalbn(z,-e0)
78 * for i = 0,1,2
79 * x[i] = floor(z)
80 * z = (z-x[i])*2**24
81 *
82 *
83 * y[] ouput result in an array of double precision numbers.
84 * The dimension of y[] is:
85 * 24-bit precision 1
86 * 53-bit precision 2
87 * 64-bit precision 2
88 * 113-bit precision 3
89 * The actual value is the sum of them. Thus for 113-bit
90 * precison, one may have to do something like:
91 *
92 * long double t,w,r_head, r_tail;
93 * t = (long double)y[2] + (long double)y[1];
94 * w = (long double)y[0];
95 * r_head = t+w;
96 * r_tail = w - (r_head - t);
97 *
98 * e0 The exponent of x[0]
99 *
100 * nx dimension of x[]
101 *
102 * prec an integer indicating the precision:
103 * 0 24 bits (single)
104 * 1 53 bits (double)
105 * 2 64 bits (extended)
106 * 3 113 bits (quad)
107 *
108 * ipio2[]
109 * integer array, contains the (24*i)-th to (24*i+23)-th
110 * bit of 2/pi after binary point. The corresponding
111 * floating value is
112 *
113 * ipio2[i] * 2^(-24(i+1)).
114 *
115 * External function:
116 * double scalbn(), floor();
117 *
118 *
119 * Here is the description of some local variables:
120 *
121 * jk jk+1 is the initial number of terms of ipio2[] needed
122 * in the computation. The recommended value is 2,3,4,
123 * 6 for single, double, extended,and quad.
124 *
125 * jz local integer variable indicating the number of
126 * terms of ipio2[] used.
127 *
128 * jx nx - 1
129 *
130 * jv index for pointing to the suitable ipio2[] for the
131 * computation. In general, we want
132 * ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8
133 * is an integer. Thus
134 * e0-3-24*jv >= 0 or (e0-3)/24 >= jv
135 * Hence jv = max(0,(e0-3)/24).
136 *
137 * jp jp+1 is the number of terms in PIo2[] needed, jp = jk.
138 *
139 * q[] double array with integral value, representing the
140 * 24-bits chunk of the product of x and 2/pi.
141 *
142 * q0 the corresponding exponent of q[0]. Note that the
143 * exponent for q[i] would be q0-24*i.
144 *
145 * PIo2[] double precision array, obtained by cutting pi/2
146 * into 24 bits chunks.
147 *
148 * f[] ipio2[] in floating point
149 *
150 * iq[] integer array by breaking up q[] in 24-bits chunk.
151 *
152 * fq[] final product of x*(2/pi) in fq[0],..,fq[jk]
153 *
154 * ih integer. If >0 it indicates q[] is >= 0.5, hence
155 * it also indicates the *sign* of the result.
156 *
157 */
158
159
160 /*
161 * Constants:
162 * The hexadecimal values are the intended ones for the following
163 * constants. The decimal values may be used, provided that the
164 * compiler will convert from decimal to binary accurately enough
165 * to produce the hexadecimal values shown.
166 */
167
168 #include "fdlibm.h"
169
170 #ifdef __STDC__
171 static const int init_jk[] = {2,3,4,6}; /* initial value for jk */
172 #else
173 static int init_jk[] = {2,3,4,6};
174 #endif
175
176 #ifdef __STDC__
177 static const double PIo2[] = {
178 #else
179 static double PIo2[] = {
180 #endif
181 1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */
182 7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */
183 5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */
184 3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */
185 1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */
186 1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */
187 2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */
188 2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */
189 };
190
191 #ifdef __STDC__
192 static const double
193 #else
194 static double
195 #endif
196 zero = 0.0,
197 one = 1.0,
198 two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
199 twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */
200
201 #ifdef __STDC__
202 int __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const int *ipio2)
203 #else
204 int __kernel_rem_pio2(x,y,e0,nx,prec,ipio2)
205 double x[], y[]; int e0,nx,prec; int ipio2[];
206 #endif
207 {
208 int jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
209 double z,fw,f[20],fq[20],q[20];
210
211 /* initialize jk*/
212 jk = init_jk[prec];
213 jp = jk;
214
215 /* determine jx,jv,q0, note that 3>q0 */
216 jx = nx-1;
217 jv = (e0-3)/24; if(jv<0) jv=0;
218 q0 = e0-24*(jv+1);
219
220 /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
221 j = jv-jx; m = jx+jk;
222 for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (double) ipio2[j];
223
224 /* compute q[0],q[1],...q[jk] */
225 for (i=0;i<=jk;i++) {
226 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
227 }
228
229 jz = jk;
230 recompute:
231 /* distill q[] into iq[] reversingly */
232 for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
233 fw = (double)((int)(twon24* z));
234 iq[i] = (int)(z-two24*fw);
235 z = q[j-1]+fw;
236 }
237
238 /* compute n */
239 z = fd_scalbn(z,q0); /* actual value of z */
240 z -= 8.0*fd_floor(z*0.125); /* trim off integer >= 8 */
241 n = (int) z;
242 z -= (double)n;
243 ih = 0;
244 if(q0>0) { /* need iq[jz-1] to determine n */
245 i = (iq[jz-1]>>(24-q0)); n += i;
246 iq[jz-1] -= i<<(24-q0);
247 ih = iq[jz-1]>>(23-q0);
248 }
249 else if(q0==0) ih = iq[jz-1]>>23;
250 else if(z>=0.5) ih=2;
251
252 if(ih>0) { /* q > 0.5 */
253 n += 1; carry = 0;
254 for(i=0;i<jz ;i++) { /* compute 1-q */
255 j = iq[i];
256 if(carry==0) {
257 if(j!=0) {
258 carry = 1; iq[i] = 0x1000000- j;
259 }
260 } else iq[i] = 0xffffff - j;
261 }
262 if(q0>0) { /* rare case: chance is 1 in 12 */
263 switch(q0) {
264 case 1:
265 iq[jz-1] &= 0x7fffff; break;
266 case 2:
267 iq[jz-1] &= 0x3fffff; break;
268 }
269 }
270 if(ih==2) {
271 z = one - z;
272 if(carry!=0) z -= fd_scalbn(one,q0);
273 }
274 }
275
276 /* check if recomputation is needed */
277 if(z==zero) {
278 j = 0;
279 for (i=jz-1;i>=jk;i--) j |= iq[i];
280 if(j==0) { /* need recomputation */
281 for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */
282
283 for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */
284 f[jx+i] = (double) ipio2[jv+i];
285 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
286 q[i] = fw;
287 }
288 jz += k;
289 goto recompute;
290 }
291 }
292
293 /* chop off zero terms */
294 if(z==0.0) {
295 jz -= 1; q0 -= 24;
296 while(iq[jz]==0) { jz--; q0-=24;}
297 } else { /* break z into 24-bit if necessary */
298 z = fd_scalbn(z,-q0);
299 if(z>=two24) {
300 fw = (double)((int)(twon24*z));
301 iq[jz] = (int)(z-two24*fw);
302 jz += 1; q0 += 24;
303 iq[jz] = (int) fw;
304 } else iq[jz] = (int) z ;
305 }
306
307 /* convert integer "bit" chunk to floating-point value */
308 fw = fd_scalbn(one,q0);
309 for(i=jz;i>=0;i--) {
310 q[i] = fw*(double)iq[i]; fw*=twon24;
311 }
312
313 /* compute PIo2[0,...,jp]*q[jz,...,0] */
314 for(i=jz;i>=0;i--) {
315 for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
316 fq[jz-i] = fw;
317 }
318
319 /* compress fq[] into y[] */
320 switch(prec) {
321 case 0:
322 fw = 0.0;
323 for (i=jz;i>=0;i--) fw += fq[i];
324 y[0] = (ih==0)? fw: -fw;
325 break;
326 case 1:
327 case 2:
328 fw = 0.0;
329 for (i=jz;i>=0;i--) fw += fq[i];
330 y[0] = (ih==0)? fw: -fw;
331 fw = fq[0]-fw;
332 for (i=1;i<=jz;i++) fw += fq[i];
333 y[1] = (ih==0)? fw: -fw;
334 break;
335 case 3: /* painful */
336 for (i=jz;i>0;i--) {
337 fw = fq[i-1]+fq[i];
338 fq[i] += fq[i-1]-fw;
339 fq[i-1] = fw;
340 }
341 for (i=jz;i>1;i--) {
342 fw = fq[i-1]+fq[i];
343 fq[i] += fq[i-1]-fw;
344 fq[i-1] = fw;
345 }
346 for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
347 if(ih==0) {
348 y[0] = fq[0]; y[1] = fq[1]; y[2] = fw;
349 } else {
350 y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
351 }
352 }
353 return n&7;
354 }

  ViewVC Help
Powered by ViewVC 1.1.24