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11210 libm should be cstyle(1ONBLD) clean
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--- old/usr/src/lib/libm/common/C/__rem_pio2m.c
+++ new/usr/src/lib/libm/common/C/__rem_pio2m.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
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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 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
23 24 */
25 +
24 26 /*
25 27 * Copyright 2005 Sun Microsystems, Inc. All rights reserved.
26 28 * Use is subject to license terms.
27 29 */
28 30
29 31 /*
30 32 * int __rem_pio2m(x,y,e0,nx,prec,ipio2)
31 33 * double x[],y[]; int e0,nx,prec; const int ipio2[];
32 34 *
33 35 * __rem_pio2m return the last three digits of N with
34 36 * y = x - N*pi/2
35 37 * so that |y| < pi/4.
36 38 *
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37 39 * The method is to compute the integer (mod 8) and fraction parts of
38 40 * (2/pi)*x without doing the full multiplication. In general we
39 41 * skip the part of the product that are known to be a huge integer (
40 42 * more accurately, = 0 mod 8 ). Thus the number of operations are
41 43 * independent of the exponent of the input.
42 44 *
43 45 * (2/PI) is represented by an array of 24-bit integers in ipio2[].
44 46 * Here PI could as well be a machine value pi.
45 47 *
46 48 * Input parameters:
47 - * x[] The input value (must be positive) is broken into nx
49 + * x[] The input value (must be positive) is broken into nx
48 50 * pieces of 24-bit integers in double precision format.
49 51 * x[i] will be the i-th 24 bit of x. The scaled exponent
50 52 * of x[0] is given in input parameter e0 (i.e., x[0]*2^e0
51 53 * match x's up to 24 bits.
52 54 *
53 55 * Example of breaking a double z into x[0]+x[1]+x[2]:
54 56 * e0 = ilogb(z)-23
55 57 * z = scalbn(z,-e0)
56 58 * for i = 0,1,2
57 59 * x[i] = floor(z)
58 60 * z = (z-x[i])*2**24
59 61 *
60 62 *
61 63 * y[] ouput result in an array of double precision numbers.
62 64 * The dimension of y[] is:
63 65 * 24-bit precision 1
64 66 * 53-bit precision 2
65 67 * 64-bit precision 2
66 68 * 113-bit precision 3
67 69 * The actual value is the sum of them. Thus for 113-bit
68 70 * precsion, one may have to do something like:
69 71 *
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70 72 * long double t,w,r_head, r_tail;
71 73 * t = (long double)y[2] + (long double)y[1];
72 74 * w = (long double)y[0];
73 75 * r_head = t+w;
74 76 * r_tail = w - (r_head - t);
75 77 *
76 78 * e0 The exponent of x[0]
77 79 *
78 80 * nx dimension of x[]
79 81 *
80 - * prec an interger indicating the precision:
82 + * prec an interger indicating the precision:
81 83 * 0 24 bits (single)
82 84 * 1 53 bits (double)
83 85 * 2 64 bits (extended)
84 86 * 3 113 bits (quad)
85 87 *
86 88 * ipio2[]
87 89 * integer array, contains the (24*i)-th to (24*i+23)-th
88 90 * bit of 2/pi or 2/PI after binary point. The corresponding
89 91 * floating value is
90 92 *
91 93 * ipio2[i] * 2^(-24(i+1)).
92 94 *
93 95 * External function:
94 96 * double scalbn( ), floor( );
95 97 *
96 98 *
97 99 * Here is the description of some local variables:
98 100 *
99 - * jk jk+1 is the initial number of terms of ipio2[] needed
101 + * jk jk+1 is the initial number of terms of ipio2[] needed
100 102 * in the computation. The recommended value is 3,4,4,
101 103 * 6 for single, double, extended,and quad.
102 104 *
103 - * jz local integer variable indicating the number of
105 + * jz local integer variable indicating the number of
104 106 * terms of ipio2[] used.
105 107 *
106 108 * jx nx - 1
107 109 *
108 110 * jv index for pointing to the suitable ipio2[] for the
109 111 * computation. In general, we want
110 112 * ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8
111 113 * is an integer. Thus
112 114 * e0-3-24*jv >= 0 or (e0-3)/24 >= jv
113 115 * Hence jv = max(0,(e0-3)/24).
114 116 *
115 117 * jp jp+1 is the number of terms in pio2[] needed, jp = jk.
116 118 *
117 - * q[] double array with integral value, representing the
119 + * q[] double array with integral value, representing the
118 120 * 24-bits chunk of the product of x and 2/pi.
119 121 *
120 122 * q0 the corresponding exponent of q[0]. Note that the
121 123 * exponent for q[i] would be q0-24*i.
122 124 *
123 125 * pio2[] double precision array, obtained by cutting pi/2
124 126 * into 24 bits chunks.
125 127 *
126 128 * f[] ipio2[] in floating point
127 129 *
128 130 * iq[] integer array by breaking up q[] in 24-bits chunk.
129 131 *
130 132 * fq[] final product of x*(2/pi) in fq[0],..,fq[jk]
131 133 *
132 134 * ih integer. If >0 it indicats q[] is >= 0.5, hence
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133 135 * it also indicates the *sign* of the result.
134 136 *
135 137 */
136 138
137 139 #include "libm.h"
138 140
139 141 #if defined(__i386) && !defined(__amd64)
140 142 extern int __swapRP(int);
141 143 #endif
142 144
143 -static const int init_jk[] = { 3, 4, 4, 6 }; /* initial value for jk */
144 -
145 +static const int init_jk[] = { 3, 4, 4, 6 }; /* initial value for jk */
145 146 static const double pio2[] = {
146 - 1.57079625129699707031e+00,
147 - 7.54978941586159635335e-08,
148 - 5.39030252995776476554e-15,
149 - 3.28200341580791294123e-22,
150 - 1.27065575308067607349e-29,
151 - 1.22933308981111328932e-36,
152 - 2.73370053816464559624e-44,
153 - 2.16741683877804819444e-51,
147 + 1.57079625129699707031e+00, 7.54978941586159635335e-08,
148 + 5.39030252995776476554e-15, 3.28200341580791294123e-22,
149 + 1.27065575308067607349e-29, 1.22933308981111328932e-36,
150 + 2.73370053816464559624e-44, 2.16741683877804819444e-51,
154 151 };
155 152
156 -static const double
157 - zero = 0.0,
158 - one = 1.0,
159 - half = 0.5,
160 - eight = 8.0,
161 - eighth = 0.125,
162 - two24 = 16777216.0,
163 - twon24 = 5.960464477539062500E-8;
153 +static const double zero = 0.0,
154 + one = 1.0,
155 + half = 0.5,
156 + eight = 8.0,
157 + eighth = 0.125,
158 + two24 = 16777216.0,
159 + twon24 = 5.960464477539062500E-8;
164 160
165 161 int
166 162 __rem_pio2m(double *x, double *y, int e0, int nx, int prec, const int *ipio2)
167 163 {
168 - int jz, jx, jv, jp, jk, carry, n, iq[20];
169 - int i, j, k, m, q0, ih;
170 - double z, fw, f[20], fq[20], q[20];
164 + int jz, jx, jv, jp, jk, carry, n, iq[20];
165 + int i, j, k, m, q0, ih;
166 + double z, fw, f[20], fq[20], q[20];
167 +
171 168 #if defined(__i386) && !defined(__amd64)
172 - int rp;
169 + int rp;
173 170
174 171 rp = __swapRP(fp_extended);
175 172 #endif
176 173
177 174 /* initialize jk */
178 175 jp = jk = init_jk[prec];
179 176
180 177 /* determine jx,jv,q0, note that 3>q0 */
181 178 jx = nx - 1;
182 179 jv = (e0 - 3) / 24;
180 +
183 181 if (jv < 0)
184 182 jv = 0;
183 +
185 184 q0 = e0 - 24 * (jv + 1);
186 185
187 186 /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
188 187 j = jv - jx;
189 188 m = jx + jk;
189 +
190 190 for (i = 0; i <= m; i++, j++)
191 - f[i] = (j < 0)? zero : (double)ipio2[j];
191 + f[i] = (j < 0) ? zero : (double)ipio2[j];
192 192
193 193 /* compute q[0],q[1],...q[jk] */
194 194 for (i = 0; i <= jk; i++) {
195 195 for (j = 0, fw = zero; j <= jx; j++)
196 - fw += x[j] * f[jx+i-j];
196 + fw += x[j] * f[jx + i - j];
197 +
197 198 q[i] = fw;
198 199 }
199 200
200 201 jz = jk;
202 +
201 203 recompute:
202 204 /* distill q[] into iq[] reversingly */
203 205 for (i = 0, j = jz, z = q[jz]; j > 0; i++, j--) {
204 206 fw = (double)((int)(twon24 * z));
205 207 iq[i] = (int)(z - two24 * fw);
206 - z = q[j-1] + fw;
208 + z = q[j - 1] + fw;
207 209 }
208 210
209 211 /* compute n */
210 212 z = scalbn(z, q0); /* actual value of z */
211 213 z -= eight * floor(z * eighth); /* trim off integer >= 8 */
212 214 n = (int)z;
213 215 z -= (double)n;
214 216 ih = 0;
217 +
215 218 if (q0 > 0) { /* need iq[jz-1] to determine n */
216 - i = (iq[jz-1] >> (24 - q0));
219 + i = (iq[jz - 1] >> (24 - q0));
217 220 n += i;
218 - iq[jz-1] -= i << (24 - q0);
219 - ih = iq[jz-1] >> (23 - q0);
221 + iq[jz - 1] -= i << (24 - q0);
222 + ih = iq[jz - 1] >> (23 - q0);
220 223 } else if (q0 == 0) {
221 - ih = iq[jz-1] >> 23;
224 + ih = iq[jz - 1] >> 23;
222 225 } else if (z >= half) {
223 226 ih = 2;
224 227 }
225 228
226 - if (ih > 0) { /* q > 0.5 */
229 + if (ih > 0) { /* q > 0.5 */
227 230 n += 1;
228 231 carry = 0;
232 +
229 233 for (i = 0; i < jz; i++) { /* compute 1-q */
230 234 j = iq[i];
235 +
231 236 if (carry == 0) {
232 237 if (j != 0) {
233 238 carry = 1;
234 239 iq[i] = 0x1000000 - j;
235 240 }
236 241 } else {
237 242 iq[i] = 0xffffff - j;
238 243 }
239 244 }
245 +
240 246 if (q0 > 0) { /* rare case: chance is 1 in 12 */
241 247 switch (q0) {
242 248 case 1:
243 - iq[jz-1] &= 0x7fffff;
249 + iq[jz - 1] &= 0x7fffff;
244 250 break;
245 251 case 2:
246 - iq[jz-1] &= 0x3fffff;
252 + iq[jz - 1] &= 0x3fffff;
247 253 break;
248 254 }
249 255 }
256 +
250 257 if (ih == 2) {
251 258 z = one - z;
259 +
252 260 if (carry != 0)
253 261 z -= scalbn(one, q0);
254 262 }
255 263 }
256 264
257 265 /* check if recomputation is needed */
258 266 if (z == zero) {
259 267 j = 0;
268 +
260 269 for (i = jz - 1; i >= jk; i--)
261 270 j |= iq[i];
262 - if (j == 0) { /* need recomputation */
271 +
272 + if (j == 0) { /* need recomputation */
263 273 /* set k to no. of terms needed */
264 - for (k = 1; iq[jk-k] == 0; k++)
274 + for (k = 1; iq[jk - k] == 0; k++)
265 275 ;
266 276
267 277 /* add q[jz+1] to q[jz+k] */
268 278 for (i = jz + 1; i <= jz + k; i++) {
269 - f[jx+i] = (double)ipio2[jv+i];
279 + f[jx + i] = (double)ipio2[jv + i];
280 +
270 281 for (j = 0, fw = zero; j <= jx; j++)
271 - fw += x[j] * f[jx+i-j];
282 + fw += x[j] * f[jx + i - j];
283 +
272 284 q[i] = fw;
273 285 }
286 +
274 287 jz += k;
275 288 goto recompute;
276 289 }
277 290 }
278 291
279 292 /* cut out zero terms */
280 293 if (z == zero) {
281 294 jz -= 1;
282 295 q0 -= 24;
296 +
283 297 while (iq[jz] == 0) {
284 298 jz--;
285 299 q0 -= 24;
286 300 }
287 - } else { /* break z into 24-bit if neccessary */
301 + } else { /* break z into 24-bit if neccessary */
288 302 z = scalbn(z, -q0);
303 +
289 304 if (z >= two24) {
290 305 fw = (double)((int)(twon24 * z));
291 306 iq[jz] = (int)(z - two24 * fw);
292 307 jz += 1;
293 308 q0 += 24;
294 309 iq[jz] = (int)fw;
295 310 } else {
296 311 iq[jz] = (int)z;
297 312 }
298 313 }
299 314
300 315 /* convert integer "bit" chunk to floating-point value */
301 316 fw = scalbn(one, q0);
317 +
302 318 for (i = jz; i >= 0; i--) {
303 319 q[i] = fw * (double)iq[i];
304 320 fw *= twon24;
305 321 }
306 322
307 323 /* compute pio2[0,...,jp]*q[jz,...,0] */
308 324 for (i = jz; i >= 0; i--) {
309 325 for (fw = zero, k = 0; k <= jp && k <= jz - i; k++)
310 - fw += pio2[k] * q[i+k];
311 - fq[jz-i] = fw;
326 + fw += pio2[k] * q[i + k];
327 +
328 + fq[jz - i] = fw;
312 329 }
313 330
314 331 /* compress fq[] into y[] */
315 332 switch (prec) {
316 333 case 0:
317 334 fw = zero;
335 +
318 336 for (i = jz; i >= 0; i--)
319 337 fw += fq[i];
320 - y[0] = (ih == 0)? fw : -fw;
338 +
339 + y[0] = (ih == 0) ? fw : -fw;
321 340 break;
322 341
323 342 case 1:
324 343 case 2:
325 344 fw = zero;
345 +
326 346 for (i = jz; i >= 0; i--)
327 347 fw += fq[i];
328 - y[0] = (ih == 0)? fw : -fw;
348 +
349 + y[0] = (ih == 0) ? fw : -fw;
329 350 fw = fq[0] - fw;
351 +
330 352 for (i = 1; i <= jz; i++)
331 353 fw += fq[i];
332 - y[1] = (ih == 0)? fw : -fw;
354 +
355 + y[1] = (ih == 0) ? fw : -fw;
333 356 break;
334 357
335 358 default:
359 +
336 360 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;
361 + fw = fq[i - 1] + fq[i];
362 + fq[i] += fq[i - 1] - fw;
363 + fq[i - 1] = fw;
340 364 }
365 +
341 366 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;
367 + fw = fq[i - 1] + fq[i];
368 + fq[i] += fq[i - 1] - fw;
369 + fq[i - 1] = fw;
345 370 }
371 +
346 372 for (fw = zero, i = jz; i >= 2; i--)
347 373 fw += fq[i];
374 +
348 375 if (ih == 0) {
349 376 y[0] = fq[0];
350 377 y[1] = fq[1];
351 378 y[2] = fw;
352 379 } else {
353 380 y[0] = -fq[0];
354 381 y[1] = -fq[1];
355 382 y[2] = -fw;
356 383 }
357 384 }
358 385
359 386 #if defined(__i386) && !defined(__amd64)
360 387 (void) __swapRP(rp);
361 388 #endif
362 389 return (n & 7);
363 390 }
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