Line data Source code
1 : /* Copyright (C) 2016 The PARI group.
2 :
3 : This file is part of the PARI/GP package.
4 :
5 : PARI/GP is free software; you can redistribute it and/or modify it under the
6 : terms of the GNU General Public License as published by the Free Software
7 : Foundation; either version 2 of the License, or (at your option) any later
8 : version. It is distributed in the hope that it will be useful, but WITHOUT
9 : ANY WARRANTY WHATSOEVER.
10 :
11 : Check the License for details. You should have received a copy of it, along
12 : with the package; see the file 'COPYING'. If not, write to the Free Software
13 : Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. */
14 :
15 : #include "pari.h"
16 : #include "paripriv.h"
17 :
18 : /**********************************************************************/
19 : /*** ***/
20 : /*** Public prime table ***/
21 : /*** ***/
22 : /**********************************************************************/
23 :
24 : static ulong _maxprimelim = 0;
25 : static GEN _prodprimes,_prodprimes_addr;
26 : typedef unsigned char *byteptr;
27 :
28 : /* Build/Rebuild table of prime differences. The actual work is done by the
29 : * following two subroutines; the user entry point is the function
30 : * initprimes() below; initprimes1() is the basecase, called when
31 : * maxnum (size) is moderate. Must be called after pari_init_stack() )*/
32 : static void
33 1841 : initprimes1(ulong size, long *lenp, pari_prime *p1)
34 : {
35 1841 : pari_sp av = avma;
36 : long k;
37 1841 : byteptr q, r, s, p = (byteptr)stack_calloc(size+2), fin = p + size;
38 : pari_prime *re;
39 :
40 22092 : for (r=q=p,k=1; r<=fin; )
41 : {
42 33138 : do { r+=k; k+=2; r+=k; } while (*++q);
43 889203 : for (s=r; s<=fin; s+=k) *s = 1;
44 : }
45 1841 : re = p1; *re++ = 2; *re++ = 3; /* 2 and 3 */
46 1841 : for (s=q=p+1; ; s=q)
47 : {
48 940751 : do q++; while (*q);
49 314811 : if (q > fin) break;
50 312970 : *re++ = (pari_prime) 2*(q-p)+1;
51 : }
52 1841 : *re++ = 0;
53 1841 : *lenp = re - p1;
54 1841 : set_avma(av);
55 1841 : }
56 :
57 : /* Timing in ms (Athlon/850; reports 512K of secondary cache; looks
58 : like there is 64K of quickier cache too).
59 :
60 : arena| 30m 100m 300m 1000m 2000m <-- primelimit
61 : =================================================
62 : 16K 1.1053 1.1407 1.2589 1.4368 1.6086
63 : 24K 1.0000 1.0625 1.1320 1.2443 1.3095
64 : 32K 1.0000 1.0469 1.0761 1.1336 1.1776
65 : 48K 1.0000 1.0000 1.0254 1.0445 1.0546
66 : 50K 1.0000 1.0000 1.0152 1.0345 1.0464
67 : 52K 1.0000 1.0000 1.0203 1.0273 1.0362
68 : 54K 1.0000 1.0000 1.0812 1.0216 1.0281
69 : 56K 1.0526 1.0000 1.0051 1.0144 1.0205
70 : 58K 1.0000 1.0000 1.0000 1.0086 1.0123
71 : 60K 0.9473 0.9844 1.0051 1.0014 1.0055
72 : 62K 1.0000 0.9844 0.9949 0.9971 0.9993
73 : 64K 1.0000 1.0000 1.0000 1.0000 1.0000
74 : 66K 1.2632 1.2187 1.2183 1.2055 1.1953
75 : 68K 1.4211 1.4844 1.4721 1.4425 1.4188
76 : 70K 1.7368 1.7188 1.7107 1.6767 1.6421
77 : 72K 1.9474 1.9531 1.9594 1.9023 1.8573
78 : 74K 2.2105 2.1875 2.1827 2.1207 2.0650
79 : 76K 2.4211 2.4219 2.4010 2.3305 2.2644
80 : 78K 2.5789 2.6250 2.6091 2.5330 2.4571
81 : 80K 2.8421 2.8125 2.8223 2.7213 2.6380
82 : 84K 3.1053 3.1875 3.1776 3.0819 2.9802
83 : 88K 3.5263 3.5312 3.5228 3.4124 3.2992
84 : 92K 3.7895 3.8438 3.8375 3.7213 3.5971
85 : 96K 4.0000 4.1093 4.1218 3.9986 3.9659
86 : 112K 4.3684 4.5781 4.5787 4.4583 4.6115
87 : 128K 4.7368 4.8750 4.9188 4.8075 4.8997
88 : 192K 5.5263 5.7188 5.8020 5.6911 5.7064
89 : 256K 6.0000 6.2187 6.3045 6.1954 6.1033
90 : 384K 6.7368 6.9531 7.0405 6.9181 6.7912
91 : 512K 7.3158 7.5156 7.6294 7.5000 7.4654
92 : 768K 9.1579 9.4531 9.6395 9.5014 9.1075
93 : 1024K 10.368 10.7497 10.9999 10.878 10.8201
94 : 1536K 12.579 13.3124 13.7660 13.747 13.4739
95 : 2048K 13.737 14.4839 15.0509 15.151 15.1282
96 : 3076K 14.789 15.5780 16.2993 16.513 16.3365
97 :
98 : Now the same number relative to the model
99 :
100 : (1 + 0.36*sqrt(primelimit)/arena) * (arena <= 64 ? 1.05 : (arena-64)**0.38)
101 :
102 : [SLOW2_IN_ROOTS = 0.36, ALPHA = 0.38]
103 :
104 : arena| 30m 100m 300m 1000m 2000m <-- primelimit
105 : =================================================
106 : 16K 1.014 0.9835 0.9942 0.9889 1.004
107 : 24K 0.9526 0.9758 0.9861 0.9942 0.981
108 : 32K 0.971 0.9939 0.9884 0.9849 0.9806
109 : 48K 0.9902 0.9825 0.996 0.9945 0.9885
110 : 50K 0.9917 0.9853 0.9906 0.9926 0.9907
111 : 52K 0.9932 0.9878 0.9999 0.9928 0.9903
112 : 54K 0.9945 0.9902 1.064 0.9939 0.9913
113 : 56K 1.048 0.9924 0.9925 0.993 0.9921
114 : 58K 0.9969 0.9945 0.9909 0.9932 0.9918
115 : 60K 0.9455 0.9809 0.9992 0.9915 0.9923
116 : 62K 0.9991 0.9827 0.9921 0.9924 0.9929
117 : 64K 1 1 1 1 1
118 : 66K 1.02 0.9849 0.9857 0.9772 0.9704
119 : 68K 0.8827 0.9232 0.9176 0.9025 0.8903
120 : 70K 0.9255 0.9177 0.9162 0.9029 0.8881
121 : 72K 0.9309 0.936 0.9429 0.9219 0.9052
122 : 74K 0.9715 0.9644 0.967 0.9477 0.9292
123 : 76K 0.9935 0.9975 0.9946 0.9751 0.9552
124 : 78K 0.9987 1.021 1.021 1.003 0.9819
125 : 80K 1.047 1.041 1.052 1.027 1.006
126 : 84K 1.052 1.086 1.092 1.075 1.053
127 : 88K 1.116 1.125 1.133 1.117 1.096
128 : 92K 1.132 1.156 1.167 1.155 1.134
129 : 96K 1.137 1.177 1.195 1.185 1.196
130 : 112K 1.067 1.13 1.148 1.15 1.217
131 : 128K 1.04 1.083 1.113 1.124 1.178
132 : 192K 0.9368 0.985 1.025 1.051 1.095
133 : 256K 0.8741 0.9224 0.9619 0.995 1.024
134 : 384K 0.8103 0.8533 0.8917 0.9282 0.9568
135 : 512K 0.7753 0.8135 0.8537 0.892 0.935
136 : 768K 0.8184 0.8638 0.9121 0.9586 0.9705
137 : 1024K 0.8241 0.8741 0.927 0.979 1.03
138 : 1536K 0.8505 0.9212 0.9882 1.056 1.096
139 : 2048K 0.8294 0.8954 0.9655 1.041 1.102
140 :
141 : */
142 :
143 : #ifndef SLOW2_IN_ROOTS
144 : /* SLOW2_IN_ROOTS below 3: some slowdown starts to be noticable
145 : * when things fit into the cache on Sparc.
146 : * The choice of 2.6 gives a slowdown of 1-2% on UltraSparcII,
147 : * but makes calculations for "maximum" of 436273009
148 : * fit into 256K cache (still common for some architectures).
149 : *
150 : * One may change it when small caches become uncommon, but the gain
151 : * is not going to be very noticable... */
152 : # ifdef i386 /* gcc defines this? */
153 : # define SLOW2_IN_ROOTS 0.36
154 : # else
155 : # define SLOW2_IN_ROOTS 2.6
156 : # endif
157 : #endif
158 : #ifndef CACHE_ARENA
159 : # ifdef i386 /* gcc defines this? */
160 : /* Due to smaller SLOW2_IN_ROOTS, smaller arena is OK; fit L1 cache */
161 : # define CACHE_ARENA (63 * 1024UL) /* No slowdown even with 64K L1 cache */
162 : # else
163 : # define CACHE_ARENA (200 * 1024UL) /* No slowdown even with 256K L2 cache */
164 : # endif
165 : #endif
166 :
167 : #define CACHE_ALPHA (0.38) /* Cache performance model parameter */
168 : #define CACHE_CUTOFF (0.018) /* Cache performance not smooth here */
169 :
170 : static double slow2_in_roots = SLOW2_IN_ROOTS;
171 :
172 : typedef struct {
173 : ulong arena;
174 : double power;
175 : double cutoff;
176 : } cache_model_t;
177 :
178 : static cache_model_t cache_model = { CACHE_ARENA, CACHE_ALPHA, CACHE_CUTOFF };
179 :
180 : /* Assume that some calculation requires a chunk of memory to be
181 : accessed often in more or less random fashion (as in sieving).
182 : Assume that the calculation can be done in steps by subdividing the
183 : chunk into smaller subchunks (arenas) and treating them
184 : separately. Assume that the overhead of subdivision is equivalent
185 : to the number of arenas.
186 :
187 : Find an optimal size of the arena taking into account the overhead
188 : of subdivision, and the overhead of arena not fitting into the
189 : cache. Assume that arenas of size slow2_in_roots slows down the
190 : calculation 2x (comparing to very big arenas; when cache hits do
191 : not matter). Since cache performance varies wildly with
192 : architecture, load, and wheather (especially with cache coloring
193 : enabled), use an idealized cache model based on benchmarks above.
194 :
195 : Assume that an independent region of FIXED_TO_CACHE bytes is accessed
196 : very often concurrently with the arena access.
197 : */
198 : static ulong
199 1841 : good_arena_size(ulong slow2_size, ulong total, ulong fixed_to_cache,
200 : cache_model_t *cache_model)
201 : {
202 1841 : ulong asize, cache_arena = cache_model->arena;
203 : double Xmin, Xmax, A, B, C1, C2, D, V;
204 1841 : double alpha = cache_model->power, cut_off = cache_model->cutoff;
205 :
206 : /* Estimated relative slowdown,
207 : with overhead = max((fixed_to_cache+arena)/cache_arena - 1, 0):
208 :
209 : 1 + slow2_size/arena due to initialization overhead;
210 :
211 : max(1, 4.63 * overhead^0.38 ) due to footprint > cache size.
212 :
213 : [The latter is hard to substantiate theoretically, but this
214 : function describes benchmarks pretty close; it does not hurt that
215 : one can minimize it explicitly too ;-). The switch between
216 : different choices of max() happens when overhead=0.018.]
217 :
218 : Thus the problem is minimizing (1 + slow2_size/arena)*overhead**0.29.
219 : This boils down to F=((X+A)/(X+B))X^alpha, X=overhead,
220 : B = (1 - fixed_to_cache/cache_arena), A = B + slow2_size/cache_arena,
221 : alpha = 0.38, and X>=0.018, X>-B.
222 :
223 : We need to find the rightmost root of (X+A)*(X+B) - alpha(A-B)X to the
224 : right of 0.018 (if such exists and is below Xmax). Then we manually
225 : check the remaining region [0, 0.018].
226 :
227 : Since we cannot trust the purely-experimental cache-hit slowdown
228 : function, as a sanity check always prefer fitting into the
229 : cache (or "almost fitting") if F-law predicts that the larger
230 : value of the arena provides less than 10% speedup.
231 : */
232 :
233 : /* The simplest case: we fit into cache */
234 1841 : asize = cache_arena - fixed_to_cache;
235 1841 : if (total <= asize) return total;
236 : /* The simple case: fitting into cache doesn't slow us down more than 10% */
237 1841 : if (asize > 10 * slow2_size) return asize;
238 : /* Slowdown of not fitting into cache is significant. Try to optimize.
239 : Do not be afraid to spend some time on optimization - in trivial
240 : cases we do not reach this point; any gain we get should
241 : compensate the time spent on optimization. */
242 :
243 0 : B = (1 - ((double)fixed_to_cache)/cache_arena);
244 0 : A = B + ((double)slow2_size)/cache_arena;
245 0 : C2 = A*B;
246 0 : C1 = (A + B - 1/alpha*(A - B))/2;
247 0 : D = C1*C1 - C2;
248 0 : if (D > 0)
249 0 : V = cut_off*cut_off + 2*C1*cut_off + C2; /* Value at CUT_OFF */
250 : else
251 0 : V = 0; /* Peacify the warning */
252 0 : Xmin = cut_off;
253 0 : Xmax = ((double)total - fixed_to_cache)/cache_arena; /* Two candidates */
254 :
255 0 : if ( D <= 0 || (V >= 0 && C1 + cut_off >= 0) ) /* slowdown increasing */
256 0 : Xmax = cut_off; /* Only one candidate */
257 0 : else if (V >= 0 && /* slowdown concave down */
258 0 : ((Xmax + C1) <= 0 || (Xmax*Xmax + 2*C1*Xmax + C2) <= 0))
259 : /* DO NOTHING */; /* Keep both candidates */
260 0 : else if (V <= 0 && (Xmax*Xmax + 2*C1*Xmax + C2) <= 0) /*slowdown decreasing*/
261 0 : Xmin = cut_off; /* Only one candidate */
262 : else /* Now we know: 2 roots, the largest is in CUT_OFF..Xmax */
263 0 : Xmax = sqrt(D) - C1;
264 0 : if (Xmax != Xmin) { /* Xmin == CUT_OFF; Check which one is better */
265 0 : double v1 = (cut_off + A)/(cut_off + B);
266 0 : double v2 = 2.33 * (Xmax + A)/(Xmax + B) * pow(Xmax, alpha);
267 :
268 0 : if (1.1 * v2 >= v1) /* Prefer fitting into the cache if slowdown < 10% */
269 0 : V = v1;
270 : else
271 0 : { Xmin = Xmax; V = v2; }
272 0 : } else if (B > 0) /* We need V */
273 0 : V = 2.33 * (Xmin + A)/(Xmin + B) * pow(Xmin, alpha);
274 0 : if (B > 0 && 1.1 * V > A/B) /* Now Xmin is the minumum. Compare with 0 */
275 0 : Xmin = 0;
276 :
277 0 : asize = (ulong)((1 + Xmin)*cache_arena - fixed_to_cache);
278 0 : if (asize > total) asize = total; /* May happen due to approximations */
279 0 : return asize;
280 : }
281 :
282 : /* Use as in
283 : install(set_optimize,lLDG) \\ Through some M too?
284 : set_optimize(2,1) \\ disable dependence on limit
285 : \\ 1: how much cache usable, 2: slowdown of setup, 3: alpha, 4: cutoff
286 : \\ 2,3,4 are in units of 0.001
287 :
288 : { time_primes_arena(ar,limit) = \\ ar = arena size in K
289 : set_optimize(1,floor(ar*1024));
290 : default(primelimit, 200 000); \\ 100000 results in *larger* malloc()!
291 : gettime;
292 : default(primelimit, floor(limit));
293 : if(ar >= 1, ar=floor(ar));
294 : print("arena "ar"K => "gettime"ms");
295 : }
296 : */
297 : long
298 0 : set_optimize(long what, GEN g)
299 : {
300 0 : long ret = 0;
301 :
302 0 : switch (what) {
303 0 : case 1:
304 0 : ret = (long)cache_model.arena;
305 0 : break;
306 0 : case 2:
307 0 : ret = (long)(slow2_in_roots * 1000);
308 0 : break;
309 0 : case 3:
310 0 : ret = (long)(cache_model.power * 1000);
311 0 : break;
312 0 : case 4:
313 0 : ret = (long)(cache_model.cutoff * 1000);
314 0 : break;
315 0 : default:
316 0 : pari_err_BUG("set_optimize");
317 0 : break;
318 : }
319 0 : if (g != NULL) {
320 0 : ulong val = itou(g);
321 :
322 0 : switch (what) {
323 0 : case 1: cache_model.arena = val; break;
324 0 : case 2: slow2_in_roots = (double)val / 1000.; break;
325 0 : case 3: cache_model.power = (double)val / 1000.; break;
326 0 : case 4: cache_model.cutoff = (double)val / 1000.; break;
327 : }
328 : }
329 0 : return ret;
330 : }
331 :
332 : /* s is odd; prime (starting from 3 = known_primes[2]), terminated by a 0 byte.
333 : * Checks n odd numbers starting at 'start', setting bytes to 0 (composite)
334 : * or 1 (prime), starting at data */
335 : static void
336 7053 : sieve_chunk(pari_prime *known_primes, ulong s, byteptr data, ulong n)
337 : {
338 7053 : ulong p, cnt = n-1, start = s;
339 : pari_prime *q;
340 :
341 7053 : memset(data, 0, n);
342 7053 : start >>= 1; /* (start - 1)/2 */
343 7053 : start += n; /* Corresponds to the end */
344 : /* data corresponds to start, q runs over primediffs */
345 1013244 : for (q = known_primes + 1, p = 3; p; p = *++q)
346 : { /* first odd number >= start > p and divisible by p
347 : = last odd number <= start + 2p - 2 and 0 (mod p)
348 : = p + last number <= start + p - 2 and 0 (mod 2p)
349 : = p + start+p-2 - (start+p-2) % 2p
350 : = start + 2(p - 1 - ((start-1)/2 + (p-1)/2) % p). */
351 1006191 : long off = cnt - ((start+(p>>1)) % p);
352 1607084161 : while (off >= 0) { data[off] = 1; off -= p; }
353 : }
354 7053 : }
355 :
356 : static void
357 1841 : set_prodprimes(void)
358 : {
359 1841 : pari_sp ltop = avma, av;
360 1841 : ulong b = 1UL << 8, M = minuu(maxprime(), GP_DATA->factorlimit);
361 1841 : GEN W, w, v = primes_interval_zv(3, M);
362 1841 : long s, u, j, jold, l = lg(v);
363 :
364 1841 : W = cgetg(64+1, t_VEC);
365 151008025 : for (jold = j = u = 1; j < l; j++)
366 151006184 : if (uel(v,j) >= b)
367 : {
368 23933 : long lw = (j == l-1? l: j) - jold + 1;
369 23933 : w = v+jold-1; w[0] = evaltyp(t_VECSMALL) | _evallg(lw);
370 23933 : gel(W,u++) = zv_prod_Z(w); /* p_jold ... p_{j-1} */
371 23933 : jold = j; b *= 2;
372 23933 : if (b > M) b = M; /* truncate last run */
373 : }
374 1841 : setlg(W, u);
375 23933 : for (j = 2; j < u; j++) gel(W,j) = mulii(gel(W,j-1), gel(W,j));
376 1841 : s = gsizeword(W);
377 1841 : w = (GEN)pari_malloc(s*sizeof(long));
378 1841 : av = (pari_sp)(w + s);
379 1841 : _prodprimes_addr = w;
380 1841 : _prodprimes = gcopy_avma(W, &av);
381 1841 : set_avma(ltop);
382 1841 : }
383 :
384 : static void
385 1841 : initprimes0(ulong maxnum, long *lenp, pari_prime *p1)
386 : {
387 1841 : pari_sp av = avma, bot = pari_mainstack->bot;
388 : long alloced, psize;
389 : byteptr q, end, p;
390 : ulong remains, curlow, rootnum, asize, prime_above, last;
391 : pari_prime *end1, *curdiff, *p_prime_above;
392 :
393 1841 : if (!odd(maxnum)) maxnum--; /* make it odd. */
394 : /* base case */
395 1841 : if (maxnum < 1ul<<17) { initprimes1(maxnum>>1, lenp, p1); return; }
396 :
397 : /* Checked to be enough up to 40e6, attained at 155893 */
398 1841 : rootnum = usqrt(maxnum) | 1;
399 1841 : initprimes1(rootnum>>1, &psize, p1);
400 1841 : last = rootnum;
401 1841 : end1 = p1 + psize - 1;
402 1841 : remains = (maxnum - last) >> 1; /* number of odd numbers to check */
403 : /* we access primes array of psize too; but we access it consecutively,
404 : * thus we do not include it in fixed_to_cache */
405 1841 : asize = good_arena_size((ulong)(rootnum * slow2_in_roots), remains+1, 0,
406 : &cache_model) - 1;
407 : /* enough room on the stack ? */
408 1841 : alloced = (((byteptr)avma) <= ((byteptr)bot) + asize);
409 1841 : p = (byteptr)(alloced? pari_malloc(asize+1): stack_malloc(asize+1));
410 1841 : end = p + asize; /* the 0 sentinel goes at end. */
411 1841 : curlow = last + 2; /* First candidate: know primes up to last (odd). */
412 1841 : curdiff = end1;
413 :
414 : /* During each iteration p..end-1 represents a range of odd
415 : numbers. */
416 1841 : p_prime_above = p1 + 2;
417 1841 : prime_above = 3;
418 8894 : while (remains)
419 : { /* cycle over arenas; performance not crucial */
420 : pari_prime was_delta;
421 7053 : if (asize > remains) { asize = remains; end = p + asize; }
422 : /* Fake the upper limit appropriate for the given arena */
423 321864 : while (prime_above*prime_above <= curlow + (asize << 1) && *p_prime_above)
424 314811 : prime_above = *p_prime_above++;
425 7053 : was_delta = *p_prime_above;
426 7053 : *p_prime_above = 0; /* sentinel for sieve_chunk */
427 7053 : sieve_chunk(p1, curlow, p, asize);
428 7053 : *p_prime_above = was_delta; /* restore */
429 :
430 7053 : p[asize] = 0; /* sentinel */
431 7053 : for (q = p; ; q++)
432 : { /* q runs over addresses corresponding to primes */
433 964278669 : while (*q) q++; /* use sentinel at end */
434 150698426 : if (q >= end) break;
435 150691373 : *curdiff++ = (pari_prime) 2*(q-p) + curlow;
436 : }
437 7053 : remains -= asize;
438 7053 : curlow += (asize<<1);
439 : }
440 1841 : *curdiff++ = 0; /* sentinel */
441 1841 : *lenp = curdiff - p1;
442 1841 : if (alloced) pari_free(p); else set_avma(av);
443 : }
444 :
445 : ulong
446 44322027 : maxprime(void) { return pari_PRIMES? pari_PRIMES[pari_PRIMES[0]]: 0; }
447 : ulong
448 44282827 : maxprimelim(void) { return pari_PRIMES? _maxprimelim: 0; }
449 : ulong
450 196 : maxprimeN(void) { return pari_PRIMES? pari_PRIMES[0]: 0; }
451 : GEN
452 2686089 : prodprimes(void) { return pari_PRIMES? _prodprimes: NULL; }
453 : void
454 0 : maxprime_check(ulong c) { if (maxprime() < c) pari_err_MAXPRIME(c); }
455 :
456 : static pari_prime*
457 1841 : initprimes(ulong maxnum)
458 : {
459 : pari_prime *t;
460 : long len;
461 : ulong N;
462 1841 : if (maxnum < 65537)
463 : {
464 0 : maxnum = 65537;
465 0 : N = 6543;
466 : }
467 : else
468 1841 : N = (long) ceil(primepi_upper_bound((double)maxnum));
469 1841 : t = (pari_prime*) pari_malloc(sizeof(*t) * (N+2));
470 1841 : initprimes0(maxnum, &len, t+1); t[0] = (pari_prime)(len-1);
471 1841 : _maxprimelim = maxnum;
472 1841 : return (pari_prime*) pari_realloc(t, sizeof(*t) * (len+1));
473 : }
474 :
475 : void
476 1841 : initprimetable(ulong maxnum)
477 : {
478 1841 : pari_prime *old = pari_PRIMES;
479 1841 : pari_PRIMES = initprimes(maxnum);
480 1841 : if (old) free(old);
481 1841 : set_prodprimes();
482 1841 : }
483 :
484 : /**********************************************************************/
485 : /*** ***/
486 : /*** forprime ***/
487 : /*** ***/
488 : /**********************************************************************/
489 :
490 : /* return good chunk size for sieve, 16 | chunk + 2 */
491 : static ulong
492 7308200 : optimize_chunk(ulong a, ulong b)
493 : {
494 : /* TODO: Optimize size (surely < 512k to stay in L2 cache, but not so large
495 : * as to force recalculating too often). */
496 7308200 : ulong chunk = 0x80000UL;
497 7308200 : ulong tmp = (b - a) / chunk + 1;
498 :
499 7308200 : if (tmp == 1)
500 7 : chunk = b - a + 16;
501 : else
502 7308193 : chunk = (b - a) / tmp + 15;
503 : /* ensure 16 | chunk + 2 */
504 7308200 : return (((chunk + 2)>>4)<<4) - 2;
505 : }
506 : static void
507 7308187 : sieve_init(forprime_t *T, ulong a, ulong b)
508 : {
509 7308187 : T->sieveb = b;
510 7308187 : T->chunk = optimize_chunk(a, b);
511 : /* >> 1 [only odds] + 3 [convert from bits to bytes] */
512 7308209 : T->isieve = (unsigned char*)stack_malloc(((T->chunk+2) >> 4) + 1);
513 7308204 : T->cache[0] = 0;
514 7308204 : T->a = a;
515 7308204 : T->end = minuu(a + T->chunk, b);
516 7308197 : T->pos = T->maxpos = 0;
517 7308197 : }
518 :
519 : enum {PRST_none, PRST_diffptr, PRST_sieve, PRST_unextprime, PRST_nextprime};
520 :
521 : static void
522 12844020 : u_forprime_set_prime_table(forprime_t *T, ulong a)
523 : {
524 12844020 : T->strategy = PRST_diffptr;
525 12844020 : if (a < 3)
526 : {
527 1517818 : T->p = 0;
528 1517818 : T->n = 0;
529 : }
530 : else
531 : {
532 11326202 : long n = PRIMES_search(a - 1);
533 11329079 : if (n < 0) n = - n - 1;
534 11329079 : T->n = n;
535 11329079 : T->p = pari_PRIMES[n];
536 : }
537 12846897 : }
538 :
539 : /* Set p so that p + q the smallest integer = c (mod q) and > original p.
540 : * Assume 0 < c < q. */
541 : static void
542 101975 : arith_set(forprime_t *T)
543 : {
544 101975 : ulong r = T->p % T->q; /* 0 <= r <= min(p, q-1) */
545 101975 : pari_sp av = avma;
546 101975 : GEN d = adduu(T->p - r, T->c); /* = c mod q */
547 101975 : if (T->c > r) d = subiu(d, T->q);
548 : /* d = c mod q, d = c > r? p-r+c-q: p-r+c, so that
549 : * d <= p and d+q = c>r? p-r+c : p-r+c+q > p */
550 101975 : if (signe(d) <= 0)
551 : {
552 20 : T->p = 0;
553 20 : T->strategy = PRST_nextprime;
554 20 : affii(d, T->pp);
555 : }
556 : else
557 101955 : T->p = itou_or_0(d);
558 101975 : set_avma(av);
559 101975 : }
560 :
561 : /* run through primes in arithmetic progression = c (mod q) */
562 : static int
563 26355090 : u_forprime_sieve_arith_init(forprime_t *T, struct pari_sieve *psieve,
564 : ulong a, ulong b, ulong c, ulong q)
565 : {
566 : ulong maxp, maxp2;
567 26355090 : if (!odd(b) && b > 2) b--;
568 26353419 : if (a > b || b < 2)
569 : {
570 882916 : T->strategy = PRST_diffptr; /* paranoia */
571 882916 : T->p = 0; /* empty */
572 882916 : T->b = 0; /* empty */
573 882916 : T->n = 0;
574 882916 : return 0;
575 : }
576 25470503 : maxp = maxprime();
577 25469673 : if (q != 1)
578 : {
579 : ulong D;
580 587449 : c %= q; D = ugcd(c, q);
581 587426 : if (D != 1) { a = maxuu(a,D); b = minuu(b,D); }
582 587426 : if (odd(q) && (a > 2 || c != 2))
583 : { /* only *odd* primes. If a <= c = 2, then p = 2 must be included :-( */
584 508757 : if (!odd(c)) c += q;
585 510074 : q <<= 1;
586 : }
587 : }
588 25470930 : T->q = q;
589 25470930 : T->c = c;
590 25470930 : T->strategy = PRST_none; /* unknown */
591 25470930 : T->psieve = psieve; /* unused for now */
592 25470930 : T->isieve = NULL; /* unused for now */
593 25470930 : T->b = b;
594 25470930 : if (maxp >= b) { /* [a,b] \subset prime table */
595 10124558 : u_forprime_set_prime_table(T, a);
596 10127562 : return 1;
597 : }
598 : /* b > maxp */
599 15346372 : if (a >= maxp)
600 : {
601 12627646 : T->p = a - 1;
602 12627646 : if (T->q != 1) arith_set(T);
603 : }
604 : else
605 2718726 : u_forprime_set_prime_table(T, a);
606 :
607 15346348 : maxp2 = (maxp & HIGHMASK)? 0 : maxp*maxp;
608 : /* FIXME: should sieve as well if q != 1, adapt sieve code */
609 15346348 : if (q != 1 || (maxp2 && maxp2 <= a)
610 7309390 : || T->b - maxuu(a,maxp) < maxp / expu(b))
611 8038264 : { if (T->strategy==PRST_none) T->strategy = PRST_unextprime; }
612 : else
613 : { /* worth sieving */
614 : #ifdef LONG_IS_64BIT
615 5195445 : const ulong UPRIME_MAX = 18446744073709551557UL;
616 : #else
617 2112750 : const ulong UPRIME_MAX = 4294967291UL;
618 : #endif
619 : ulong sieveb;
620 7308195 : if (b > UPRIME_MAX) b = UPRIME_MAX;
621 7308195 : sieveb = b;
622 7308195 : if (maxp2 && maxp2 < b) sieveb = maxp2;
623 7308195 : if (T->strategy==PRST_none) T->strategy = PRST_sieve;
624 7308195 : sieve_init(T, maxuu(maxp+2, a), sieveb);
625 : }
626 15346335 : return 1;
627 : }
628 :
629 : int
630 21275153 : u_forprime_arith_init(forprime_t *T, ulong a, ulong b, ulong c, ulong q)
631 21275153 : { return u_forprime_sieve_arith_init(T, NULL, a, b, c, q); }
632 :
633 : /* will run through primes in [a,b] */
634 : int
635 20684272 : u_forprime_init(forprime_t *T, ulong a, ulong b)
636 20684272 : { return u_forprime_arith_init(T, a,b, 0,1); }
637 :
638 : /* will run through primes in [a,b] */
639 : static int
640 5072861 : u_forprime_sieve_init(forprime_t *T, struct pari_sieve *s, ulong b)
641 5072861 : { return u_forprime_sieve_arith_init(T, s, s->start, b, s->c, s->q); }
642 :
643 : /* now only run through primes <= c; assume c <= b above */
644 : void
645 63 : u_forprime_restrict(forprime_t *T, ulong c) { T->b = c; }
646 :
647 : /* b = NULL: loop forever */
648 : int
649 2182 : forprimestep_init(forprime_t *T, GEN a, GEN b, GEN q)
650 : {
651 2182 : GEN c = NULL;
652 : long lb;
653 :
654 2182 : a = gceil(a); if (typ(a) != t_INT) pari_err_TYPE("forprime_init",a);
655 2182 : T->qq = NULL; T->q = 1; T->c = 0;
656 2182 : if (q)
657 : {
658 133 : switch(typ(q))
659 : {
660 56 : case t_INT:
661 56 : c = a; break;
662 77 : case t_INTMOD:
663 77 : c = gel(q,2); q = gel(q,1);
664 : /* first int >= initial a which is = c (mod q) */
665 77 : a = addii(a, modii(subii(c,a), q)); break;
666 0 : default: pari_err_TYPE("forprimestep_init",q);
667 : }
668 133 : if (signe(q) <= 0) pari_err_TYPE("forprimestep_init (q <= 0)",q);
669 133 : if (equali1(q)) c = q = NULL;
670 : else
671 : {
672 133 : GEN D = gcdii(c, q);
673 133 : if (!is_pm1(D))
674 : { /* at most one prime: c */
675 42 : if (cmpii(a, D) < 0) a = D;
676 42 : if (gcmp(b, D) > 0) b = D;
677 : }
678 133 : if ((T->q = itou_or_0(q)))
679 125 : T->c = umodiu(c, T->q);
680 : else
681 8 : T->qq = q;
682 : }
683 : }
684 2182 : if (signe(a) <= 0) a = q? modii(a, q): gen_1;
685 2182 : if (b && typ(b) != t_INFINITY)
686 : {
687 789 : b = gfloor(b);
688 789 : if (typ(b) != t_INT) pari_err_TYPE("forprime_init",b);
689 789 : if (signe(b) < 0 || cmpii(a,b) > 0)
690 : {
691 21 : T->strategy = PRST_nextprime; /* paranoia */
692 21 : T->bb = T->pp = gen_0; return 0;
693 : }
694 768 : lb = lgefint(b);
695 768 : T->bb = b;
696 : }
697 1393 : else if (!b || inf_get_sign(b) > 0)
698 : {
699 1393 : lb = lgefint(a) + 4;
700 1393 : T->bb = NULL;
701 : }
702 : else /* b == -oo */
703 : {
704 0 : T->strategy = PRST_nextprime; /* paranoia */
705 0 : T->bb = T->pp = gen_0; return 0;
706 : }
707 2161 : T->pp = cgeti(T->qq? maxuu(lb, lgefint(T->qq)): lb);
708 : /* a, b are positive integers, a <= b */
709 2161 : if (!T->qq && lgefint(a) == 3) /* lb == 3 implies b != NULL */
710 2018 : return u_forprime_arith_init(T, uel(a,2), lb == 3? uel(b,2): ULONG_MAX,
711 : T->c, T->q);
712 143 : T->strategy = PRST_nextprime;
713 143 : affii(T->qq? subii(a,T->qq): subiu(a,T->q), T->pp); return 1;
714 : }
715 : int
716 1301 : forprime_init(forprime_t *T, GEN a, GEN b)
717 1301 : { return forprimestep_init(T,a,b,NULL); }
718 :
719 : /* assume a <= b <= maxprime()^2, a,b odd, sieve[n] corresponds to
720 : * a+16*n, a+16*n+2, ..., a+16*n+14 (bits 0 to 7)
721 : * maxpos = index of last sieve cell.
722 : * b-a+2 must be divisible by 16 for use by u_forprime_next */
723 : static void
724 8954 : sieve_block(ulong a, ulong b, ulong maxpos, unsigned char* sieve)
725 : {
726 8954 : ulong i, lim = usqrt(b), sz = (b-a) >> 1;
727 8954 : (void)memset(sieve, 0, maxpos+1);
728 8954 : for (i = 2;; i++)
729 24344387 : { /* p is odd */
730 24353341 : ulong k, r, p = pari_PRIMES[i]; /* starts at p = 3 */
731 24353341 : if (p > lim) break;
732 :
733 : /* solve a + 2k = 0 (mod p) */
734 24344387 : r = a % p;
735 24344387 : if (r == 0)
736 16114 : k = 0;
737 : else
738 : {
739 24328273 : k = p - r;
740 24328273 : if (odd(k)) k += p;
741 24328273 : k >>= 1;
742 : }
743 : /* m = a + 2k is the smallest odd m >= a, p | m */
744 : /* position n (corresponds to a+2n) is sieve[n>>3], bit n&7 */
745 5705915113 : while (k <= sz) { sieve[k>>3] |= 1 << (k&7); k += p; /* 2k += 2p */ }
746 : }
747 8954 : }
748 :
749 : static void
750 1841 : pari_sieve_init(struct pari_sieve *s, ulong a, ulong b)
751 : {
752 1841 : ulong maxpos= (b - a) >> 4;
753 1841 : s->start = a; s->end = b;
754 1841 : s->sieve = (unsigned char*) pari_malloc(maxpos+1);
755 1841 : s->c = 0; s->q = 1;
756 1841 : sieve_block(a, b, maxpos, s->sieve);
757 1841 : s->maxpos = maxpos; /* must be last in case of SIGINT */
758 1841 : }
759 :
760 : static struct pari_sieve pari_sieve_modular;
761 :
762 : #ifdef LONG_IS_64BIT
763 : #define PARI_MODULAR_BASE ((1UL<<((BITS_IN_LONG-2)>>1))+1)
764 : #else
765 : #define PARI_MODULAR_BASE ((1UL<<(BITS_IN_LONG-1))+1)
766 : #endif
767 :
768 : void
769 1841 : pari_init_primes(ulong maxprime)
770 : {
771 1841 : ulong a = PARI_MODULAR_BASE, b = a + (1UL<<20)-2;
772 1841 : initprimetable(maxprime);
773 1841 : pari_sieve_init(&pari_sieve_modular, a, b);
774 1841 : }
775 :
776 : void
777 1841 : pari_close_primes(void)
778 : {
779 1841 : if (pari_PRIMES)
780 : {
781 1841 : pari_free(pari_PRIMES);
782 1841 : pari_free(_prodprimes_addr);
783 : }
784 1841 : pari_free(pari_sieve_modular.sieve);
785 1841 : }
786 :
787 : void
788 4464464 : init_modular_small(forprime_t *S)
789 : {
790 : #ifdef LONG_IS_64BIT
791 3826397 : u_forprime_sieve_init(S, &pari_sieve_modular, ULONG_MAX);
792 : #else
793 638067 : ulong a = (1UL<<((BITS_IN_LONG-2)>>1))+1;
794 638067 : u_forprime_init(S, a, ULONG_MAX);
795 : #endif
796 4464447 : }
797 :
798 : void
799 8696089 : init_modular_big(forprime_t *S)
800 : {
801 : #ifdef LONG_IS_64BIT
802 7449621 : u_forprime_init(S, HIGHBIT + 1, ULONG_MAX);
803 : #else
804 1246468 : u_forprime_sieve_init(S, &pari_sieve_modular, ULONG_MAX);
805 : #endif
806 8696048 : }
807 :
808 : /* T->cache is a 0-terminated list of primes, return the first one and
809 : * remove it from list. Most of the time the list contains a single prime */
810 : static ulong
811 129453693 : shift_cache(forprime_t *T)
812 : {
813 : long i;
814 129453693 : T->p = T->cache[0];
815 173119335 : for (i = 1;; i++) /* remove one prime from cache */
816 173119335 : if (! (T->cache[i-1] = T->cache[i]) ) break;
817 129453693 : return T->p;
818 : }
819 :
820 : ulong
821 202917968 : u_forprime_next(forprime_t *T)
822 : {
823 202917968 : if (T->strategy == PRST_diffptr)
824 : {
825 : for(;;)
826 : {
827 218319639 : if (++T->n <= pari_PRIMES[0])
828 : {
829 218319485 : T->p = pari_PRIMES[T->n];
830 218319485 : if (T->p > T->b) return 0;
831 218132825 : if (T->q == 1 || T->p % T->q == T->c) return T->p;
832 : }
833 : else
834 : { /* beyond the table */
835 154 : T->strategy = T->isieve? PRST_sieve: PRST_unextprime;
836 154 : if (T->q != 1) { arith_set(T); if (!T->p) return 0; }
837 : /* T->p possibly not a prime if q != 1 */
838 154 : break;
839 : }
840 : }
841 : }
842 142732515 : if (T->strategy == PRST_sieve)
843 : {
844 : ulong n;
845 129453922 : if (T->cache[0]) return shift_cache(T);
846 92520242 : NEXT_CHUNK:
847 92527356 : if (T->psieve)
848 : {
849 5072842 : T->sieve = T->psieve->sieve;
850 5072842 : T->end = T->psieve->end;
851 5072842 : if (T->end > T->sieveb) T->end = T->sieveb;
852 5072842 : T->maxpos = T->psieve->maxpos;
853 5072842 : T->pos = 0;
854 5072842 : T->psieve = NULL;
855 : }
856 140235121 : for (n = T->pos; n < T->maxpos; n++)
857 140225180 : if (T->sieve[n] != 0xFF)
858 : {
859 92517415 : unsigned char mask = T->sieve[n];
860 92517415 : ulong p = T->a + (n<<4);
861 92517415 : long i = 0;
862 92517415 : T->pos = n;
863 92517415 : if (!(mask & 1)) T->cache[i++] = p;
864 92517415 : if (!(mask & 2)) T->cache[i++] = p+2;
865 92517415 : if (!(mask & 4)) T->cache[i++] = p+4;
866 92517415 : if (!(mask & 8)) T->cache[i++] = p+6;
867 92517415 : if (!(mask & 16)) T->cache[i++] = p+8;
868 92517415 : if (!(mask & 32)) T->cache[i++] = p+10;
869 92517415 : if (!(mask & 64)) T->cache[i++] = p+12;
870 92517415 : if (!(mask &128)) T->cache[i++] = p+14;
871 92517415 : T->cache[i] = 0;
872 92517415 : T->pos = n+1;
873 92517415 : return shift_cache(T);
874 : }
875 : /* n = T->maxpos, last cell: check p <= b */
876 9941 : if (T->maxpos && n == T->maxpos && T->sieve[n] != 0xFF)
877 : {
878 2752 : unsigned char mask = T->sieve[n];
879 2752 : ulong p = T->a + (n<<4);
880 2752 : long i = 0;
881 2752 : T->pos = n;
882 2752 : if (!(mask & 1) && p <= T->sieveb) T->cache[i++] = p;
883 2752 : if (!(mask & 2) && p <= T->sieveb-2) T->cache[i++] = p+2;
884 2752 : if (!(mask & 4) && p <= T->sieveb-4) T->cache[i++] = p+4;
885 2752 : if (!(mask & 8) && p <= T->sieveb-6) T->cache[i++] = p+6;
886 2752 : if (!(mask & 16) && p <= T->sieveb-8) T->cache[i++] = p+8;
887 2752 : if (!(mask & 32) && p <= T->sieveb-10) T->cache[i++] = p+10;
888 2752 : if (!(mask & 64) && p <= T->sieveb-12) T->cache[i++] = p+12;
889 2752 : if (!(mask &128) && p <= T->sieveb-14) T->cache[i++] = p+14;
890 2752 : if (i)
891 : {
892 2598 : T->cache[i] = 0;
893 2598 : T->pos = n+1;
894 2598 : return shift_cache(T);
895 : }
896 : }
897 :
898 7343 : if (T->maxpos && T->end >= T->sieveb) /* done with sieves ? */
899 : {
900 230 : if (T->sieveb == T->b && T->b != ULONG_MAX) return 0;
901 1 : T->strategy = PRST_unextprime;
902 : }
903 : else
904 : { /* initialize next chunk */
905 7113 : T->sieve = T->isieve;
906 7113 : if (T->maxpos == 0)
907 3177 : T->a |= 1; /* first time; ensure odd */
908 : else
909 3936 : T->a = (T->end + 2) | 1;
910 7113 : T->end = T->a + T->chunk; /* may overflow */
911 7113 : if (T->end < T->a || T->end > T->sieveb) T->end = T->sieveb;
912 : /* end and a are odd; sieve[k] contains the a + 8*2k + (0,2,...,14).
913 : * The largest k is (end-a) >> 4 */
914 7113 : T->pos = 0;
915 7113 : T->maxpos = (T->end - T->a) >> 4;
916 7113 : sieve_block(T->a, T->end, T->maxpos, T->sieve);
917 7114 : goto NEXT_CHUNK;
918 : }
919 : }
920 13278594 : if (T->strategy == PRST_unextprime)
921 : {
922 13274710 : if (T->q == 1)
923 : {
924 : #ifdef LONG_IS_64BIT
925 13121589 : switch(T->p)
926 : {
927 : #define retp(x) return T->p = (HIGHBIT+x <= T->b)? HIGHBIT+x: 0
928 7449562 : case HIGHBIT: retp(29);
929 3158893 : case HIGHBIT + 29: retp(99);
930 334745 : case HIGHBIT + 99: retp(123);
931 186465 : case HIGHBIT +123: retp(131);
932 128184 : case HIGHBIT +131: retp(155);
933 107415 : case HIGHBIT +155: retp(255);
934 86173 : case HIGHBIT +255: retp(269);
935 76702 : case HIGHBIT +269: retp(359);
936 62394 : case HIGHBIT +359: retp(435);
937 54974 : case HIGHBIT +435: retp(449);
938 48276 : case HIGHBIT +449: retp(453);
939 45410 : case HIGHBIT +453: retp(485);
940 39417 : case HIGHBIT +485: retp(491);
941 36324 : case HIGHBIT +491: retp(543);
942 33943 : case HIGHBIT +543: retp(585);
943 31368 : case HIGHBIT +585: retp(599);
944 27401 : case HIGHBIT +599: retp(753);
945 26627 : case HIGHBIT +753: retp(849);
946 25673 : case HIGHBIT +849: retp(879);
947 24095 : case HIGHBIT +879: retp(885);
948 23405 : case HIGHBIT +885: retp(903);
949 22925 : case HIGHBIT +903: retp(995);
950 : #undef retp
951 : }
952 : #endif
953 1091286 : T->p = unextprime(T->p + 1);
954 1093222 : if (T->p > T->b) return 0;
955 : }
956 : else do {
957 2798464 : T->p += T->q;
958 2798464 : if (T->p < T->q || T->p > T->b) { T->p = 0; break; } /* overflow */
959 2798438 : } while (!uisprime(T->p));
960 1246043 : if (T->p && T->p <= T->b) return T->p;
961 : /* overflow ulong, switch to GEN */
962 66 : T->strategy = PRST_nextprime;
963 : }
964 3950 : return 0; /* overflow */
965 : }
966 :
967 : GEN
968 45113960 : forprime_next(forprime_t *T)
969 : {
970 : pari_sp av;
971 : GEN p;
972 45113960 : if (T->strategy != PRST_nextprime)
973 : {
974 45106081 : ulong u = u_forprime_next(T);
975 45106081 : if (u) { affui(u, T->pp); return T->pp; }
976 : /* failure */
977 590 : if (T->strategy != PRST_nextprime) return NULL; /* we're done */
978 : /* overflow ulong, switch to GEN */
979 48 : u = ULONG_MAX;
980 48 : if (T->q > 1) u -= (ULONG_MAX-T->c) % T->q;
981 48 : affui(u, T->pp);
982 : }
983 7927 : av = avma; p = T->pp;
984 7927 : if (T->q == 1)
985 : {
986 7749 : p = nextprime(addiu(p, 1));
987 7749 : if (T->bb && abscmpii(p, T->bb) > 0) return gc_NULL(av);
988 : } else do {
989 3341 : p = T->qq? addii(p, T->qq): addiu(p, T->q);
990 3341 : if (T->bb && abscmpii(p, T->bb) > 0) return gc_NULL(av);
991 3285 : } while (!BPSW_psp(p));
992 7744 : affii(p, T->pp); return gc_const(av, T->pp);
993 : }
994 :
995 : void
996 861 : forprimestep(GEN a, GEN b, GEN q, GEN code)
997 : {
998 861 : pari_sp av = avma;
999 : forprime_t T;
1000 :
1001 861 : if (!forprimestep_init(&T, a,b,q)) { set_avma(av); return; }
1002 :
1003 847 : push_lex(T.pp,code);
1004 37823 : while(forprime_next(&T))
1005 : {
1006 37403 : closure_evalvoid(code); if (loop_break()) break;
1007 : /* p changed in 'code', complain */
1008 36983 : if (get_lex(-1) != T.pp)
1009 7 : pari_err(e_MISC,"prime index read-only: was changed to %Ps", get_lex(-1));
1010 : }
1011 840 : pop_lex(1); set_avma(av);
1012 : }
1013 : void
1014 735 : forprime(GEN a, GEN b, GEN code) { return forprimestep(a,b,NULL,code); }
1015 :
1016 : int
1017 70 : forcomposite_init(forcomposite_t *C, GEN a, GEN b)
1018 : {
1019 70 : pari_sp av = avma;
1020 70 : a = gceil(a);
1021 70 : if (typ(a)!=t_INT) pari_err_TYPE("forcomposite",a);
1022 70 : if (b) {
1023 63 : if (typ(b) == t_INFINITY) b = NULL;
1024 : else
1025 : {
1026 56 : b = gfloor(b);
1027 56 : if (typ(b)!=t_INT) pari_err_TYPE("forcomposite",b);
1028 : }
1029 : }
1030 70 : if (signe(a) < 0) pari_err_DOMAIN("forcomposite", "a", "<", gen_0, a);
1031 70 : if (abscmpiu(a, 4) < 0) a = utoipos(4);
1032 70 : C->first = 1;
1033 70 : if (!forprime_init(&C->T, a,b) && cmpii(a,b) > 0)
1034 : {
1035 7 : C->n = gen_1; /* in case caller forgets to check the return value */
1036 7 : C->b = gen_0; return gc_bool(av,0);
1037 : }
1038 63 : C->n = setloop(a);
1039 63 : C->b = b;
1040 63 : C->p = NULL; return 1;
1041 : }
1042 :
1043 : GEN
1044 238 : forcomposite_next(forcomposite_t *C)
1045 : {
1046 238 : if (C->first) /* first call ever */
1047 : {
1048 63 : C->first = 0;
1049 63 : C->p = forprime_next(&C->T);
1050 : }
1051 : else
1052 175 : C->n = incloop(C->n);
1053 238 : if (C->p)
1054 : {
1055 161 : if (cmpii(C->n, C->p) < 0) return C->n;
1056 77 : C->n = incloop(C->n);
1057 : /* n = p+1 */
1058 77 : C->p = forprime_next(&C->T); /* nextprime(p) > n */
1059 77 : if (C->p) return C->n;
1060 : }
1061 105 : if (!C->b || cmpii(C->n, C->b) <= 0) return C->n;
1062 42 : return NULL;
1063 : }
1064 :
1065 : void
1066 70 : forcomposite(GEN a, GEN b, GEN code)
1067 : {
1068 70 : pari_sp av = avma;
1069 : forcomposite_t T;
1070 : GEN n;
1071 70 : if (!forcomposite_init(&T,a,b)) return;
1072 63 : push_lex(T.n,code);
1073 238 : while((n = forcomposite_next(&T)))
1074 : {
1075 196 : closure_evalvoid(code); if (loop_break()) break;
1076 : /* n changed in 'code', complain */
1077 182 : if (get_lex(-1) != n)
1078 7 : pari_err(e_MISC,"index read-only: was changed to %Ps", get_lex(-1));
1079 : }
1080 56 : pop_lex(1); set_avma(av);
1081 : }
|
