source: trunk/gcc/libjava/java/lang/k_rem_pio2.c@ 3103

Last change on this file since 3103 was 2, checked in by bird, 23 years ago

Initial revision
  • Property cvs2svn:cvs-rev set to 1.1
  • Property svn:eol-style set to native
  • Property svn:executable set to *
File size: 8.4 KB
Line 
1
2/* @(#)k_rem_pio2.c 5.1 93/09/24 */
3/*
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 *
7 * Developed at SunPro, a Sun Microsystems, Inc. business.
8 * Permission to use, copy, modify, and distribute this
9 * software is freely granted, provided that this notice
10 * is preserved.
11 * ====================================================
12 */
13
14/*
15 * __kernel_rem_pio2(x,y,e0,nx,prec,ipio2)
16 * double x[],y[]; int e0,nx,prec; int ipio2[];
17 *
18 * __kernel_rem_pio2 return the last three digits of N with
19 * y = x - N*pi/2
20 * so that |y| < pi/2.
21 *
22 * The method is to compute the integer (mod 8) and fraction parts of
23 * (2/pi)*x without doing the full multiplication. In general we
24 * skip the part of the product that are known to be a huge integer (
25 * more accurately, = 0 mod 8 ). Thus the number of operations are
26 * independent of the exponent of the input.
27 *
28 * (2/pi) is represented by an array of 24-bit integers in ipio2[].
29 *
30 * Input parameters:
31 * x[] The input value (must be positive) is broken into nx
32 * pieces of 24-bit integers in double precision format.
33 * x[i] will be the i-th 24 bit of x. The scaled exponent
34 * of x[0] is given in input parameter e0 (i.e., x[0]*2^e0
35 * match x's up to 24 bits.
36 *
37 * Example of breaking a double positive z into x[0]+x[1]+x[2]:
38 * e0 = ilogb(z)-23
39 * z = scalbn(z,-e0)
40 * for i = 0,1,2
41 * x[i] = floor(z)
42 * z = (z-x[i])*2**24
43 *
44 *
45 * y[] ouput result in an array of double precision numbers.
46 * The dimension of y[] is:
47 * 24-bit precision 1
48 * 53-bit precision 2
49 * 64-bit precision 2
50 * 113-bit precision 3
51 * The actual value is the sum of them. Thus for 113-bit
52 * precison, one may have to do something like:
53 *
54 * long double t,w,r_head, r_tail;
55 * t = (long double)y[2] + (long double)y[1];
56 * w = (long double)y[0];
57 * r_head = t+w;
58 * r_tail = w - (r_head - t);
59 *
60 * e0 The exponent of x[0]
61 *
62 * nx dimension of x[]
63 *
64 * prec an integer indicating the precision:
65 * 0 24 bits (single)
66 * 1 53 bits (double)
67 * 2 64 bits (extended)
68 * 3 113 bits (quad)
69 *
70 * ipio2[]
71 * integer array, contains the (24*i)-th to (24*i+23)-th
72 * bit of 2/pi after binary point. The corresponding
73 * floating value is
74 *
75 * ipio2[i] * 2^(-24(i+1)).
76 *
77 * External function:
78 * double scalbn(), floor();
79 *
80 *
81 * Here is the description of some local variables:
82 *
83 * jk jk+1 is the initial number of terms of ipio2[] needed
84 * in the computation. The recommended value is 2,3,4,
85 * 6 for single, double, extended,and quad.
86 *
87 * jz local integer variable indicating the number of
88 * terms of ipio2[] used.
89 *
90 * jx nx - 1
91 *
92 * jv index for pointing to the suitable ipio2[] for the
93 * computation. In general, we want
94 * ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8
95 * is an integer. Thus
96 * e0-3-24*jv >= 0 or (e0-3)/24 >= jv
97 * Hence jv = max(0,(e0-3)/24).
98 *
99 * jp jp+1 is the number of terms in PIo2[] needed, jp = jk.
100 *
101 * q[] double array with integral value, representing the
102 * 24-bits chunk of the product of x and 2/pi.
103 *
104 * q0 the corresponding exponent of q[0]. Note that the
105 * exponent for q[i] would be q0-24*i.
106 *
107 * PIo2[] double precision array, obtained by cutting pi/2
108 * into 24 bits chunks.
109 *
110 * f[] ipio2[] in floating point
111 *
112 * iq[] integer array by breaking up q[] in 24-bits chunk.
113 *
114 * fq[] final product of x*(2/pi) in fq[0],..,fq[jk]
115 *
116 * ih integer. If >0 it indicates q[] is >= 0.5, hence
117 * it also indicates the *sign* of the result.
118 *
119 */
120
121
122/*
123 * Constants:
124 * The hexadecimal values are the intended ones for the following
125 * constants. The decimal values may be used, provided that the
126 * compiler will convert from decimal to binary accurately enough
127 * to produce the hexadecimal values shown.
128 */
129
130#include "fdlibm.h"
131
132#ifndef _DOUBLE_IS_32BITS
133
134#ifdef __STDC__
135static const int init_jk[] = {2,3,4,6}; /* initial value for jk */
136#else
137static int init_jk[] = {2,3,4,6};
138#endif
139
140#ifdef __STDC__
141static const double PIo2[] = {
142#else
143static double PIo2[] = {
144#endif
145 1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */
146 7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */
147 5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */
148 3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */
149 1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */
150 1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */
151 2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */
152 2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */
153};
154
155#ifdef __STDC__
156static const double
157#else
158static double
159#endif
160zero = 0.0,
161one = 1.0,
162two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
163twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */
164
165#ifdef __STDC__
166 int __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const int32_t *ipio2)
167#else
168 int __kernel_rem_pio2(x,y,e0,nx,prec,ipio2)
169 double x[], y[]; int e0,nx,prec; int32_t ipio2[];
170#endif
171{
172 int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
173 double z,fw,f[20],fq[20],q[20];
174
175 /* initialize jk*/
176 jk = init_jk[prec];
177 jp = jk;
178
179 /* determine jx,jv,q0, note that 3>q0 */
180 jx = nx-1;
181 jv = (e0-3)/24; if(jv<0) jv=0;
182 q0 = e0-24*(jv+1);
183
184 /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
185 j = jv-jx; m = jx+jk;
186 for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (double) ipio2[j];
187
188 /* compute q[0],q[1],...q[jk] */
189 for (i=0;i<=jk;i++) {
190 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
191 }
192
193 jz = jk;
194recompute:
195 /* distill q[] into iq[] reversingly */
196 for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
197 fw = (double)((int32_t)(twon24* z));
198 iq[i] = (int32_t)(z-two24*fw);
199 z = q[j-1]+fw;
200 }
201
202 /* compute n */
203 z = scalbn(z,(int)q0); /* actual value of z */
204 z -= 8.0*floor(z*0.125); /* trim off integer >= 8 */
205 n = (int32_t) z;
206 z -= (double)n;
207 ih = 0;
208 if(q0>0) { /* need iq[jz-1] to determine n */
209 i = (iq[jz-1]>>(24-q0)); n += i;
210 iq[jz-1] -= i<<(24-q0);
211 ih = iq[jz-1]>>(23-q0);
212 }
213 else if(q0==0) ih = iq[jz-1]>>23;
214 else if(z>=0.5) ih=2;
215
216 if(ih>0) { /* q > 0.5 */
217 n += 1; carry = 0;
218 for(i=0;i<jz ;i++) { /* compute 1-q */
219 j = iq[i];
220 if(carry==0) {
221 if(j!=0) {
222 carry = 1; iq[i] = 0x1000000- j;
223 }
224 } else iq[i] = 0xffffff - j;
225 }
226 if(q0>0) { /* rare case: chance is 1 in 12 */
227 switch(q0) {
228 case 1:
229 iq[jz-1] &= 0x7fffff; break;
230 case 2:
231 iq[jz-1] &= 0x3fffff; break;
232 }
233 }
234 if(ih==2) {
235 z = one - z;
236 if(carry!=0) z -= scalbn(one,(int)q0);
237 }
238 }
239
240 /* check if recomputation is needed */
241 if(z==zero) {
242 j = 0;
243 for (i=jz-1;i>=jk;i--) j |= iq[i];
244 if(j==0) { /* need recomputation */
245 for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */
246
247 for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */
248 f[jx+i] = (double) ipio2[jv+i];
249 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
250 q[i] = fw;
251 }
252 jz += k;
253 goto recompute;
254 }
255 }
256
257 /* chop off zero terms */
258 if(z==0.0) {
259 jz -= 1; q0 -= 24;
260 while(iq[jz]==0) { jz--; q0-=24;}
261 } else { /* break z into 24-bit if necessary */
262 z = scalbn(z,-(int)q0);
263 if(z>=two24) {
264 fw = (double)((int32_t)(twon24*z));
265 iq[jz] = (int32_t)(z-two24*fw);
266 jz += 1; q0 += 24;
267 iq[jz] = (int32_t) fw;
268 } else iq[jz] = (int32_t) z ;
269 }
270
271 /* convert integer "bit" chunk to floating-point value */
272 fw = scalbn(one,(int)q0);
273 for(i=jz;i>=0;i--) {
274 q[i] = fw*(double)iq[i]; fw*=twon24;
275 }
276
277 /* compute PIo2[0,...,jp]*q[jz,...,0] */
278 for(i=jz;i>=0;i--) {
279 for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
280 fq[jz-i] = fw;
281 }
282
283 /* compress fq[] into y[] */
284 switch(prec) {
285 case 0:
286 fw = 0.0;
287 for (i=jz;i>=0;i--) fw += fq[i];
288 y[0] = (ih==0)? fw: -fw;
289 break;
290 case 1:
291 case 2:
292 fw = 0.0;
293 for (i=jz;i>=0;i--) fw += fq[i];
294 y[0] = (ih==0)? fw: -fw;
295 fw = fq[0]-fw;
296 for (i=1;i<=jz;i++) fw += fq[i];
297 y[1] = (ih==0)? fw: -fw;
298 break;
299 case 3: /* painful */
300 for (i=jz;i>0;i--) {
301 fw = fq[i-1]+fq[i];
302 fq[i] += fq[i-1]-fw;
303 fq[i-1] = fw;
304 }
305 for (i=jz;i>1;i--) {
306 fw = fq[i-1]+fq[i];
307 fq[i] += fq[i-1]-fw;
308 fq[i-1] = fw;
309 }
310 for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
311 if(ih==0) {
312 y[0] = fq[0]; y[1] = fq[1]; y[2] = fw;
313 } else {
314 y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
315 }
316 }
317 return n&7;
318}
319
320#endif /* defined(_DOUBLE_IS_32BITS) */
Note: See TracBrowser for help on using the repository browser.