Code coverage tests

This page documents the degree to which the PARI/GP source code is tested by our public test suite, distributed with the source distribution in directory src/test/. This is measured by the gcov utility; we then process gcov output using the lcov frond-end.

We test a few variants depending on Configure flags on the pari.math.u-bordeaux.fr machine (x86_64 architecture), and agregate them in the final report:

The target is to exceed 90% coverage for all mathematical modules (given that branches depending on DEBUGLEVEL or DEBUGMEM are not covered). This script is run to produce the results below.

LCOV - code coverage report
Current view: top level - language - forprime.c (source / functions) Hit Total Coverage
Test: PARI/GP v2.14.0 lcov report (development 27783-affec94c65) Lines: 407 482 84.4 %
Date: 2022-07-07 07:34:25 Functions: 34 39 87.2 %
Legend: Lines: hit not hit

          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 _maxprime = 0;
      25             : static ulong diffptrlen;
      26             : 
      27             : /* Building/Rebuilding the diffptr table. The actual work is done by the
      28             :  * following two subroutines;  the user entry point is the function
      29             :  * initprimes() below.  initprimes1() is the old algorithm, called when
      30             :  * maxnum (size) is moderate. Must be called after pari_init_stack() )*/
      31             : static void
      32        1792 : initprimes1(ulong size, long *lenp, ulong *lastp, byteptr p1)
      33             : {
      34        1792 :   pari_sp av = avma;
      35             :   long k;
      36        1792 :   byteptr q, r, s, p = (byteptr)stack_calloc(size+2), fin = p + size;
      37             : 
      38       17920 :   for (r=q=p,k=1; r<=fin; )
      39             :   {
      40       25088 :     do { r+=k; k+=2; r+=k; } while (*++q);
      41      569856 :     for (s=r; s<=fin; s+=k) *s = 1;
      42             :   }
      43        1792 :   r = p1; *r++ = 2; *r++ = 1; /* 2 and 3 */
      44        1792 :   for (s=q=p+1; ; s=q)
      45             :   {
      46      632576 :     do q++; while (*q);
      47      224000 :     if (q > fin) break;
      48      222208 :     *r++ = (unsigned char) ((q-s) << 1);
      49             :   }
      50        1792 :   *r++ = 0;
      51        1792 :   *lenp = r - p1;
      52        1792 :   *lastp = ((s - p) << 1) + 1;
      53        1792 :   set_avma(av);
      54        1792 : }
      55             : 
      56             : /*  Timing in ms (Athlon/850; reports 512K of secondary cache; looks
      57             :     like there is 64K of quickier cache too).
      58             : 
      59             :       arena|    30m     100m    300m    1000m    2000m  <-- primelimit
      60             :       =================================================
      61             :       16K       1.1053  1.1407  1.2589  1.4368   1.6086
      62             :       24K       1.0000  1.0625  1.1320  1.2443   1.3095
      63             :       32K       1.0000  1.0469  1.0761  1.1336   1.1776
      64             :       48K       1.0000  1.0000  1.0254  1.0445   1.0546
      65             :       50K       1.0000  1.0000  1.0152  1.0345   1.0464
      66             :       52K       1.0000  1.0000  1.0203  1.0273   1.0362
      67             :       54K       1.0000  1.0000  1.0812  1.0216   1.0281
      68             :       56K       1.0526  1.0000  1.0051  1.0144   1.0205
      69             :       58K       1.0000  1.0000  1.0000  1.0086   1.0123
      70             :       60K       0.9473  0.9844  1.0051  1.0014   1.0055
      71             :       62K       1.0000  0.9844  0.9949  0.9971   0.9993
      72             :       64K       1.0000  1.0000  1.0000  1.0000   1.0000
      73             :       66K       1.2632  1.2187  1.2183  1.2055   1.1953
      74             :       68K       1.4211  1.4844  1.4721  1.4425   1.4188
      75             :       70K       1.7368  1.7188  1.7107  1.6767   1.6421
      76             :       72K       1.9474  1.9531  1.9594  1.9023   1.8573
      77             :       74K       2.2105  2.1875  2.1827  2.1207   2.0650
      78             :       76K       2.4211  2.4219  2.4010  2.3305   2.2644
      79             :       78K       2.5789  2.6250  2.6091  2.5330   2.4571
      80             :       80K       2.8421  2.8125  2.8223  2.7213   2.6380
      81             :       84K       3.1053  3.1875  3.1776  3.0819   2.9802
      82             :       88K       3.5263  3.5312  3.5228  3.4124   3.2992
      83             :       92K       3.7895  3.8438  3.8375  3.7213   3.5971
      84             :       96K       4.0000  4.1093  4.1218  3.9986   3.9659
      85             :       112K      4.3684  4.5781  4.5787  4.4583   4.6115
      86             :       128K      4.7368  4.8750  4.9188  4.8075   4.8997
      87             :       192K      5.5263  5.7188  5.8020  5.6911   5.7064
      88             :       256K      6.0000  6.2187  6.3045  6.1954   6.1033
      89             :       384K      6.7368  6.9531  7.0405  6.9181   6.7912
      90             :       512K      7.3158  7.5156  7.6294  7.5000   7.4654
      91             :       768K      9.1579  9.4531  9.6395  9.5014   9.1075
      92             :       1024K    10.368  10.7497 10.9999 10.878   10.8201
      93             :       1536K    12.579  13.3124 13.7660 13.747   13.4739
      94             :       2048K    13.737  14.4839 15.0509 15.151   15.1282
      95             :       3076K    14.789  15.5780 16.2993 16.513   16.3365
      96             : 
      97             :     Now the same number relative to the model
      98             : 
      99             :     (1 + 0.36*sqrt(primelimit)/arena) * (arena <= 64 ? 1.05 : (arena-64)**0.38)
     100             : 
     101             :      [SLOW2_IN_ROOTS = 0.36, ALPHA = 0.38]
     102             : 
     103             :       arena|    30m     100m    300m    1000m    2000m  <-- primelimit
     104             :       =================================================
     105             :         16K    1.014    0.9835  0.9942  0.9889  1.004
     106             :         24K    0.9526   0.9758  0.9861  0.9942  0.981
     107             :         32K    0.971    0.9939  0.9884  0.9849  0.9806
     108             :         48K    0.9902   0.9825  0.996   0.9945  0.9885
     109             :         50K    0.9917   0.9853  0.9906  0.9926  0.9907
     110             :         52K    0.9932   0.9878  0.9999  0.9928  0.9903
     111             :         54K    0.9945   0.9902  1.064   0.9939  0.9913
     112             :         56K    1.048    0.9924  0.9925  0.993   0.9921
     113             :         58K    0.9969   0.9945  0.9909  0.9932  0.9918
     114             :         60K    0.9455   0.9809  0.9992  0.9915  0.9923
     115             :         62K    0.9991   0.9827  0.9921  0.9924  0.9929
     116             :         64K    1        1       1       1       1
     117             :         66K    1.02     0.9849  0.9857  0.9772  0.9704
     118             :         68K    0.8827   0.9232  0.9176  0.9025  0.8903
     119             :         70K    0.9255   0.9177  0.9162  0.9029  0.8881
     120             :         72K    0.9309   0.936   0.9429  0.9219  0.9052
     121             :         74K    0.9715   0.9644  0.967   0.9477  0.9292
     122             :         76K    0.9935   0.9975  0.9946  0.9751  0.9552
     123             :         78K    0.9987   1.021   1.021   1.003   0.9819
     124             :         80K    1.047    1.041   1.052   1.027   1.006
     125             :         84K    1.052    1.086   1.092   1.075   1.053
     126             :         88K    1.116    1.125   1.133   1.117   1.096
     127             :         92K    1.132    1.156   1.167   1.155   1.134
     128             :         96K    1.137    1.177   1.195   1.185   1.196
     129             :        112K    1.067    1.13    1.148   1.15    1.217
     130             :        128K    1.04     1.083   1.113   1.124   1.178
     131             :        192K    0.9368   0.985   1.025   1.051   1.095
     132             :        256K    0.8741   0.9224  0.9619  0.995   1.024
     133             :        384K    0.8103   0.8533  0.8917  0.9282  0.9568
     134             :        512K    0.7753   0.8135  0.8537  0.892   0.935
     135             :        768K    0.8184   0.8638  0.9121  0.9586  0.9705
     136             :       1024K    0.8241   0.8741  0.927   0.979   1.03
     137             :       1536K    0.8505   0.9212  0.9882  1.056   1.096
     138             :       2048K    0.8294   0.8954  0.9655  1.041   1.102
     139             : 
     140             : */
     141             : 
     142             : #ifndef SLOW2_IN_ROOTS
     143             :   /* SLOW2_IN_ROOTS below 3: some slowdown starts to be noticable
     144             :    * when things fit into the cache on Sparc.
     145             :    * The choice of 2.6 gives a slowdown of 1-2% on UltraSparcII,
     146             :    * but makes calculations for "maximum" of 436273009
     147             :    * fit into 256K cache (still common for some architectures).
     148             :    *
     149             :    * One may change it when small caches become uncommon, but the gain
     150             :    * is not going to be very noticable... */
     151             : #  ifdef i386           /* gcc defines this? */
     152             : #    define SLOW2_IN_ROOTS      0.36
     153             : #  else
     154             : #    define SLOW2_IN_ROOTS      2.6
     155             : #  endif
     156             : #endif
     157             : #ifndef CACHE_ARENA
     158             : #  ifdef i386           /* gcc defines this? */
     159             :    /* Due to smaller SLOW2_IN_ROOTS, smaller arena is OK; fit L1 cache */
     160             : #    define CACHE_ARENA (63 * 1024UL) /* No slowdown even with 64K L1 cache */
     161             : #  else
     162             : #    define CACHE_ARENA (200 * 1024UL) /* No slowdown even with 256K L2 cache */
     163             : #  endif
     164             : #endif
     165             : 
     166             : #define CACHE_ALPHA     (0.38)          /* Cache performance model parameter */
     167             : #define CACHE_CUTOFF    (0.018)         /* Cache performance not smooth here */
     168             : 
     169             : static double slow2_in_roots = SLOW2_IN_ROOTS;
     170             : 
     171             : typedef struct {
     172             :     ulong arena;
     173             :     double power;
     174             :     double cutoff;
     175             : } cache_model_t;
     176             : 
     177             : static cache_model_t cache_model = { CACHE_ARENA, CACHE_ALPHA, CACHE_CUTOFF };
     178             : 
     179             : /* Assume that some calculation requires a chunk of memory to be
     180             :    accessed often in more or less random fashion (as in sieving).
     181             :    Assume that the calculation can be done in steps by subdividing the
     182             :    chunk into smaller subchunks (arenas) and treating them
     183             :    separately.  Assume that the overhead of subdivision is equivalent
     184             :    to the number of arenas.
     185             : 
     186             :    Find an optimal size of the arena taking into account the overhead
     187             :    of subdivision, and the overhead of arena not fitting into the
     188             :    cache.  Assume that arenas of size slow2_in_roots slows down the
     189             :    calculation 2x (comparing to very big arenas; when cache hits do
     190             :    not matter).  Since cache performance varies wildly with
     191             :    architecture, load, and wheather (especially with cache coloring
     192             :    enabled), use an idealized cache model based on benchmarks above.
     193             : 
     194             :    Assume that an independent region of FIXED_TO_CACHE bytes is accessed
     195             :    very often concurrently with the arena access.
     196             :  */
     197             : static ulong
     198        1792 : good_arena_size(ulong slow2_size, ulong total, ulong fixed_to_cache,
     199             :                 cache_model_t *cache_model)
     200             : {
     201        1792 :   ulong asize, cache_arena = cache_model->arena;
     202             :   double Xmin, Xmax, A, B, C1, C2, D, V;
     203        1792 :   double alpha = cache_model->power, cut_off = cache_model->cutoff;
     204             : 
     205             :   /* Estimated relative slowdown,
     206             :      with overhead = max((fixed_to_cache+arena)/cache_arena - 1, 0):
     207             : 
     208             :      1 + slow2_size/arena due to initialization overhead;
     209             : 
     210             :      max(1, 4.63 * overhead^0.38 ) due to footprint > cache size.
     211             : 
     212             :      [The latter is hard to substantiate theoretically, but this
     213             :      function describes benchmarks pretty close; it does not hurt that
     214             :      one can minimize it explicitly too ;-).  The switch between
     215             :      different choices of max() happens when overhead=0.018.]
     216             : 
     217             :      Thus the problem is minimizing (1 + slow2_size/arena)*overhead**0.29.
     218             :      This boils down to F=((X+A)/(X+B))X^alpha, X=overhead,
     219             :      B = (1 - fixed_to_cache/cache_arena), A = B + slow2_size/cache_arena,
     220             :      alpha = 0.38, and X>=0.018, X>-B.
     221             : 
     222             :      We need to find the rightmost root of (X+A)*(X+B) - alpha(A-B)X to the
     223             :      right of 0.018 (if such exists and is below Xmax).  Then we manually
     224             :      check the remaining region [0, 0.018].
     225             : 
     226             :      Since we cannot trust the purely-experimental cache-hit slowdown
     227             :      function, as a sanity check always prefer fitting into the
     228             :      cache (or "almost fitting") if F-law predicts that the larger
     229             :      value of the arena provides less than 10% speedup.
     230             :    */
     231             : 
     232             :   /* The simplest case: we fit into cache */
     233        1792 :   asize = cache_arena - fixed_to_cache;
     234        1792 :   if (total <= asize) return total;
     235             :   /* The simple case: fitting into cache doesn't slow us down more than 10% */
     236        1792 :   if (asize > 10 * slow2_size) return asize;
     237             :   /* Slowdown of not fitting into cache is significant.  Try to optimize.
     238             :      Do not be afraid to spend some time on optimization - in trivial
     239             :      cases we do not reach this point; any gain we get should
     240             :      compensate the time spent on optimization.  */
     241             : 
     242           0 :   B = (1 - ((double)fixed_to_cache)/cache_arena);
     243           0 :   A = B + ((double)slow2_size)/cache_arena;
     244           0 :   C2 = A*B;
     245           0 :   C1 = (A + B - 1/alpha*(A - B))/2;
     246           0 :   D = C1*C1 - C2;
     247           0 :   if (D > 0)
     248           0 :     V = cut_off*cut_off + 2*C1*cut_off + C2; /* Value at CUT_OFF */
     249             :   else
     250           0 :     V = 0; /* Peacify the warning */
     251           0 :   Xmin = cut_off;
     252           0 :   Xmax = ((double)total - fixed_to_cache)/cache_arena; /* Two candidates */
     253             : 
     254           0 :   if ( D <= 0 || (V >= 0 && C1 + cut_off >= 0) ) /* slowdown increasing */
     255           0 :     Xmax = cut_off; /* Only one candidate */
     256           0 :   else if (V >= 0 && /* slowdown concave down */
     257           0 :            ((Xmax + C1) <= 0 || (Xmax*Xmax + 2*C1*Xmax + C2) <= 0))
     258             :       /* DO NOTHING */;  /* Keep both candidates */
     259           0 :   else if (V <= 0 && (Xmax*Xmax + 2*C1*Xmax + C2) <= 0) /*slowdown decreasing*/
     260           0 :       Xmin = cut_off; /* Only one candidate */
     261             :   else /* Now we know: 2 roots, the largest is in CUT_OFF..Xmax */
     262           0 :       Xmax = sqrt(D) - C1;
     263           0 :   if (Xmax != Xmin) { /* Xmin == CUT_OFF; Check which one is better */
     264           0 :     double v1 = (cut_off + A)/(cut_off + B);
     265           0 :     double v2 = 2.33 * (Xmax + A)/(Xmax + B) * pow(Xmax, alpha);
     266             : 
     267           0 :     if (1.1 * v2 >= v1) /* Prefer fitting into the cache if slowdown < 10% */
     268           0 :       V = v1;
     269             :     else
     270           0 :     { Xmin = Xmax; V = v2; }
     271           0 :   } else if (B > 0) /* We need V */
     272           0 :     V = 2.33 * (Xmin + A)/(Xmin + B) * pow(Xmin, alpha);
     273           0 :   if (B > 0 && 1.1 * V > A/B)  /* Now Xmin is the minumum.  Compare with 0 */
     274           0 :     Xmin = 0;
     275             : 
     276           0 :   asize = (ulong)((1 + Xmin)*cache_arena - fixed_to_cache);
     277           0 :   if (asize > total) asize = total; /* May happen due to approximations */
     278           0 :   return asize;
     279             : }
     280             : 
     281             : /* Use as in
     282             :     install(set_optimize,lLDG)          \\ Through some M too?
     283             :     set_optimize(2,1) \\ disable dependence on limit
     284             :     \\ 1: how much cache usable, 2: slowdown of setup, 3: alpha, 4: cutoff
     285             :     \\ 2,3,4 are in units of 0.001
     286             : 
     287             :     { time_primes_arena(ar,limit) =     \\ ar = arena size in K
     288             :         set_optimize(1,floor(ar*1024));
     289             :         default(primelimit, 200 000);   \\ 100000 results in *larger* malloc()!
     290             :         gettime;
     291             :         default(primelimit, floor(limit));
     292             :         if(ar >= 1, ar=floor(ar));
     293             :         print("arena "ar"K => "gettime"ms");
     294             :     }
     295             : */
     296             : long
     297           0 : set_optimize(long what, GEN g)
     298             : {
     299           0 :   long ret = 0;
     300             : 
     301           0 :   switch (what) {
     302           0 :   case 1:
     303           0 :     ret = (long)cache_model.arena;
     304           0 :     break;
     305           0 :   case 2:
     306           0 :     ret = (long)(slow2_in_roots * 1000);
     307           0 :     break;
     308           0 :   case 3:
     309           0 :     ret = (long)(cache_model.power * 1000);
     310           0 :     break;
     311           0 :   case 4:
     312           0 :     ret = (long)(cache_model.cutoff * 1000);
     313           0 :     break;
     314           0 :   default:
     315           0 :     pari_err_BUG("set_optimize");
     316           0 :     break;
     317             :   }
     318           0 :   if (g != NULL) {
     319           0 :     ulong val = itou(g);
     320             : 
     321           0 :     switch (what) {
     322           0 :     case 1: cache_model.arena = val; break;
     323           0 :     case 2: slow2_in_roots     = (double)val / 1000.; break;
     324           0 :     case 3: cache_model.power  = (double)val / 1000.; break;
     325           0 :     case 4: cache_model.cutoff = (double)val / 1000.; break;
     326             :     }
     327           0 :   }
     328           0 :   return ret;
     329             : }
     330             : 
     331             : /* s is odd; prime differences (starting from 5-3=2) start at known_primes[2],
     332             :   terminated by a 0 byte. Checks n odd numbers starting at 'start', setting
     333             :   bytes starting at data to 0 (composite) or 1 (prime) */
     334             : static void
     335        4080 : sieve_chunk(byteptr known_primes, ulong s, byteptr data, ulong n)
     336             : {
     337        4080 :   ulong p, cnt = n-1, start = s, delta = 1;
     338             :   byteptr q;
     339             : 
     340        4080 :   memset(data, 0, n);
     341        4080 :   start >>= 1;  /* (start - 1)/2 */
     342        4080 :   start += n; /* Corresponds to the end */
     343             :   /* data corresponds to start, q runs over primediffs */
     344      477368 :   for (q = known_primes + 1, p = 3; delta; delta = *++q, p += delta)
     345             :   { /* first odd number >= start > p and divisible by p
     346             :        = last odd number <= start + 2p - 2 and 0 (mod p)
     347             :        = p + last number <= start + p - 2 and 0 (mod 2p)
     348             :        = p + start+p-2 - (start+p-2) % 2p
     349             :        = start + 2(p - 1 - ((start-1)/2 + (p-1)/2) % p). */
     350      473288 :     long off = cnt - ((start+(p>>1)) % p);
     351   730593864 :     while (off >= 0) { data[off] = 1; off -= p; }
     352             :   }
     353        4080 : }
     354             : 
     355             : /* assume maxnum <= 436273289 < 2^29 */
     356             : static void
     357        1792 : initprimes0(ulong maxnum, long *lenp, ulong *lastp, byteptr p1)
     358             : {
     359        1792 :   pari_sp av = avma, bot = pari_mainstack->bot;
     360             :   long alloced, psize;
     361             :   byteptr q, end, p, end1, plast, curdiff;
     362             :   ulong last, remains, curlow, rootnum, asize;
     363             :   ulong prime_above;
     364             :   byteptr p_prime_above;
     365             : 
     366        1792 :   maxnum |= 1; /* make it odd. */
     367             :   /* base case */
     368        1792 :   if (maxnum < 1ul<<17) { initprimes1(maxnum>>1, lenp, lastp, p1); return; }
     369             : 
     370             :   /* Checked to be enough up to 40e6, attained at 155893 */
     371        1792 :   rootnum = usqrt(maxnum) | 1;
     372        1792 :   initprimes1(rootnum>>1, &psize, &last, p1);
     373        1792 :   end1 = p1 + psize - 1;
     374        1792 :   remains = (maxnum - last) >> 1; /* number of odd numbers to check */
     375             : 
     376             :   /* we access primes array of psize too; but we access it consecutively,
     377             :    * thus we do not include it in fixed_to_cache */
     378        1792 :   asize = good_arena_size((ulong)(rootnum * slow2_in_roots), remains+1, 0,
     379             :                           &cache_model) - 1;
     380             :   /* enough room on the stack ? */
     381        1792 :   alloced = (((byteptr)avma) <= ((byteptr)bot) + asize);
     382        1792 :   if (alloced)
     383           0 :     p = (byteptr)pari_malloc(asize+1);
     384             :   else
     385        1792 :     p = (byteptr)stack_malloc(asize+1);
     386        1792 :   end = p + asize; /* the 0 sentinel goes at end. */
     387        1792 :   curlow = last + 2; /* First candidate: know primes up to last (odd). */
     388        1792 :   curdiff = end1;
     389             : 
     390             :   /* During each iteration p..end-1 represents a range of odd
     391             :      numbers.  plast is a pointer which represents the last prime seen,
     392             :      it may point before p..end-1. */
     393        1792 :   plast = p - 1;
     394        1792 :   p_prime_above = p1 + 2;
     395        1792 :   prime_above = 3;
     396        5872 :   while (remains)
     397             :   { /* cycle over arenas; performance not crucial */
     398             :     unsigned char was_delta;
     399        4080 :     if (asize > remains) { asize = remains; end = p + asize; }
     400             :     /* Fake the upper limit appropriate for the given arena */
     401      228080 :     while (prime_above*prime_above <= curlow + (asize << 1) && *p_prime_above)
     402      224000 :       prime_above += *p_prime_above++;
     403        4080 :     was_delta = *p_prime_above;
     404        4080 :     *p_prime_above = 0; /* sentinel for sieve_chunk */
     405        4080 :     sieve_chunk(p1, curlow, p, asize);
     406        4080 :     *p_prime_above = was_delta; /* restore */
     407             : 
     408        4080 :     p[asize] = 0; /* sentinel */
     409        4080 :     for (q = p; ; plast = q++)
     410             :     { /* q runs over addresses corresponding to primes */
     411   447376880 :       while (*q) q++; /* use sentinel at end */
     412    74214384 :       if (q >= end) break;
     413    74210304 :       *curdiff++ = (unsigned char)(q-plast) << 1; /* < 255 for q < 436273291 */
     414             :     }
     415        4080 :     plast -= asize;
     416        4080 :     remains -= asize;
     417        4080 :     curlow += (asize<<1);
     418             :   }
     419        1792 :   last = curlow - ((p - plast) << 1);
     420        1792 :   *curdiff++ = 0; /* sentinel */
     421        1792 :   *lenp = curdiff - p1;
     422        1792 :   *lastp = last;
     423        1792 :   if (alloced) pari_free(p); else set_avma(av);
     424             : }
     425             : 
     426             : ulong
     427    41977303 : maxprime(void) { return diffptr ? _maxprime : 0; }
     428             : ulong
     429         259 : maxprimeN(void) { return diffptr ? diffptrlen-1: 0; }
     430             : 
     431             : void
     432           0 : maxprime_check(ulong c) { if (_maxprime < c) pari_err_MAXPRIME(c); }
     433             : 
     434             : /* We ensure 65302 <= maxnum <= 436273289: the LHS ensures modular function
     435             :  * have enough fast primes to work, the RHS ensures that p_{n+1} - p_n < 255
     436             :  * (N.B. RHS would be incorrect since initprimes0 would make it odd, thereby
     437             :  * increasing it by 1) */
     438             : byteptr
     439        1792 : initprimes(ulong maxnum, long *lenp, ulong *lastp)
     440             : {
     441             :   byteptr t;
     442        1792 :   if (maxnum < 65537)
     443           0 :     maxnum = 65537;
     444        1792 :   else if (maxnum > 436273289)
     445           0 :     maxnum = 436273289;
     446        1792 :   t = (byteptr)pari_malloc((size_t) (1.09 * maxnum/log((double)maxnum)) + 146);
     447        1792 :   initprimes0(maxnum, lenp, lastp, t);
     448        1792 :   return (byteptr)pari_realloc(t, *lenp);
     449             : }
     450             : 
     451             : void
     452        1792 : initprimetable(ulong maxnum)
     453             : {
     454             :   long len;
     455             :   ulong last;
     456        1792 :   byteptr p = initprimes(maxnum, &len, &last), old = diffptr;
     457        1792 :   diffptrlen = minss(diffptrlen, len);
     458        1792 :   _maxprime  = minss(_maxprime,last); /*Protect against ^C*/
     459        1792 :   diffptr = p; diffptrlen = len; _maxprime = last;
     460        1792 :   if (old) free(old);
     461        1792 : }
     462             : 
     463             : /* all init_primepointer_xx routines set *ptr to the corresponding place
     464             :  * in prime table */
     465             : /* smallest p >= a */
     466             : ulong
     467           0 : init_primepointer_geq(ulong a, byteptr *pd)
     468             : {
     469             :   ulong n, p;
     470           0 :   prime_table_next_p(a, pd, &p, &n);
     471           0 :   return p;
     472             : }
     473             : /* largest p < a */
     474             : ulong
     475    15875967 : init_primepointer_lt(ulong a, byteptr *pd)
     476             : {
     477             :   ulong n, p;
     478    15875967 :   prime_table_next_p(a, pd, &p, &n);
     479    15875332 :   PREC_PRIME_VIADIFF(p, *pd);
     480    15875332 :   return p;
     481             : }
     482             : /* largest p <= a */
     483             : ulong
     484           0 : init_primepointer_leq(ulong a, byteptr *pd)
     485             : {
     486             :   ulong n, p;
     487           0 :   prime_table_next_p(a, pd, &p, &n);
     488           0 :   if (p != a) PREC_PRIME_VIADIFF(p, *pd);
     489           0 :   return p;
     490             : }
     491             : /* smallest p > a */
     492             : ulong
     493           0 : init_primepointer_gt(ulong a, byteptr *pd)
     494             : {
     495             :   ulong n, p;
     496           0 :   prime_table_next_p(a, pd, &p, &n);
     497           0 :   if (p == a) NEXT_PRIME_VIADIFF(p, *pd);
     498           0 :   return p;
     499             : }
     500             : 
     501             : /**********************************************************************/
     502             : /***                                                                ***/
     503             : /***                     forprime                                   ***/
     504             : /***                                                                ***/
     505             : /**********************************************************************/
     506             : 
     507             : /* return good chunk size for sieve, 16 | chunk + 2 */
     508             : static ulong
     509     2981393 : optimize_chunk(ulong a, ulong b)
     510             : {
     511             :   /* TODO: Optimize size (surely < 512k to stay in L2 cache, but not so large
     512             :    * as to force recalculating too often). */
     513     2981393 :   ulong chunk = 0x80000UL;
     514     2981393 :   ulong tmp = (b - a) / chunk + 1;
     515             : 
     516     2981393 :   if (tmp == 1)
     517       41143 :     chunk = b - a + 16;
     518             :   else
     519     2940250 :     chunk = (b - a) / tmp + 15;
     520             :   /* ensure 16 | chunk + 2 */
     521     2981393 :   return (((chunk + 2)>>4)<<4) - 2;
     522             : }
     523             : static void
     524     2981383 : sieve_init(forprime_t *T, ulong a, ulong b)
     525             : {
     526     2981383 :   T->sieveb = b;
     527     2981383 :   T->chunk = optimize_chunk(a, b);
     528             :   /* >> 1 [only odds] + 3 [convert from bits to bytes] */
     529     2981408 :   T->isieve = (unsigned char*)stack_malloc(((T->chunk+2) >> 4) + 1);
     530     2981401 :   T->cache[0] = 0;
     531     2981401 :   T->a = a;
     532     2981401 :   T->end = minuu(a + T->chunk, b);
     533     2981396 :   T->pos = T->maxpos = 0;
     534     2981396 : }
     535             : 
     536             : enum {PRST_none, PRST_diffptr, PRST_sieve, PRST_unextprime, PRST_nextprime};
     537             : 
     538             : static void
     539    17274402 : u_forprime_set_prime_table(forprime_t *T, ulong a)
     540             : {
     541    17274402 :   T->strategy = PRST_diffptr;
     542    17274402 :   if (a < 3)
     543             :   {
     544     1398595 :     T->p = 0;
     545     1398595 :     T->d = diffptr;
     546             :   }
     547             :   else
     548    15875807 :     T->p = init_primepointer_lt(a, &T->d);
     549    17273982 : }
     550             : 
     551             : /* Set p so that p + q the smallest integer = c (mod q) and > original p.
     552             :  * Assume 0 < c < q. Set p = 0 on overflow */
     553             : static void
     554        3602 : arith_set(forprime_t *T)
     555             : {
     556        3602 :   ulong r = T->p % T->q; /* 0 <= r <= min(p, q-1) */
     557        3602 :   pari_sp av = avma;
     558        3602 :   GEN d = adduu(T->p - r, T->c);
     559        3602 :   if (T->c > r) d = subiu(d, T->q);
     560             :   /* d = c mod q,  d = c > r? p-r+c-q: p-r+c, so that
     561             :    *  d <= p  and  d+q = c>r? p-r+c  : p-r+c+q > p */
     562        3602 :   T->p = itou_or_0(d); set_avma(av); /* d = 0 is impossible */
     563        3602 : }
     564             : 
     565             : /* run through primes in arithmetic progression = c (mod q) */
     566             : static int
     567    26083105 : u_forprime_sieve_arith_init(forprime_t *T, struct pari_sieve *psieve,
     568             :                             ulong a, ulong b, ulong c, ulong q)
     569             : {
     570             :   ulong maxp, maxp2;
     571    26083105 :   if (!odd(b) && b > 2) b--;
     572    26083720 :   if (a > b || b < 2)
     573             :   {
     574      875381 :     T->strategy = PRST_diffptr; /* paranoia */
     575      875381 :     T->p = 0; /* empty */
     576      875381 :     T->b = 0; /* empty */
     577      875381 :     T->d = diffptr;
     578      875381 :     return 0;
     579             :   }
     580    25208339 :   maxp = maxprime();
     581    25206721 :   if (q != 1)
     582             :   {
     583      363242 :     c %= q;
     584      363242 :     if (ugcd(c,q) != 1) { a = maxuu(a,c); b = minuu(b,c); }
     585      363256 :     if (odd(q) && (a > 2 || c != 2))
     586             :     { /* only *odd* primes. If a <= c = 2, then p = 2 must be included :-( */
     587      295995 :       if (!odd(c)) c += q;
     588      296207 :       q <<= 1;
     589             :     }
     590             :   }
     591    25206912 :   T->q = q;
     592    25206912 :   T->c = c;
     593    25206912 :   T->strategy = PRST_none; /* unknown */
     594    25206912 :   T->psieve = psieve; /* unused for now */
     595    25206912 :   T->isieve = NULL; /* unused for now */
     596    25206912 :   T->b = b;
     597    25206912 :   if (maxp >= b) { /* [a,b] \subset prime table */
     598    15253763 :     u_forprime_set_prime_table(T, a);
     599    15251284 :     return 1;
     600             :   }
     601             :   /* b > maxp */
     602     9953149 :   if (a >= maxp)
     603             :   {
     604     7931445 :     T->p = a - 1;
     605     7931445 :     if (T->q > 1) arith_set(T);
     606             :   }
     607             :   else
     608     2021704 :     u_forprime_set_prime_table(T, a);
     609             : 
     610     9953400 :   maxp2 = (maxp & HIGHMASK)? 0 : maxp*maxp;
     611             :   /* FIXME: should sieve as well if q != 1, adapt sieve code */
     612     9953400 :   if (q != 1 || (maxp2 && maxp2 <= a)
     613     3164936 :              || T->b - maxuu(a,maxp) < maxp / expu(b))
     614     6972137 :   { if (T->strategy==PRST_none) T->strategy = PRST_unextprime; }
     615             :   else
     616             :   { /* worth sieving */
     617             : #ifdef LONG_IS_64BIT
     618     1633823 :     const ulong UPRIME_MAX = 18446744073709551557UL;
     619             : #else
     620     1347564 :     const ulong UPRIME_MAX = 4294967291UL;
     621             : #endif
     622             :     ulong sieveb;
     623     2981387 :     if (b > UPRIME_MAX) b = UPRIME_MAX;
     624     2981387 :     sieveb = b;
     625     2981387 :     if (maxp2 && maxp2 < b) sieveb = maxp2;
     626     2981387 :     if (T->strategy==PRST_none) T->strategy = PRST_sieve;
     627     2981387 :     sieve_init(T, maxuu(maxp+2, a), sieveb);
     628             :   }
     629     9953385 :   return 1;
     630             : }
     631             : 
     632             : int
     633    24579711 : u_forprime_arith_init(forprime_t *T, ulong a, ulong b, ulong c, ulong q)
     634    24579711 : { return u_forprime_sieve_arith_init(T, NULL, a, b, c, q); }
     635             : 
     636             : /* will run through primes in [a,b] */
     637             : int
     638    24213384 : u_forprime_init(forprime_t *T, ulong a, ulong b)
     639    24213384 : { return u_forprime_arith_init(T, a,b, 0,1); }
     640             : 
     641             : /* will run through primes in [a,b] */
     642             : static int
     643     1497057 : u_forprime_sieve_init(forprime_t *T, struct pari_sieve *s, ulong b)
     644     1497057 : { return u_forprime_sieve_arith_init(T, s, s->start, b, s->c, s->q); }
     645             : 
     646             : /* now only run through primes <= c; assume c <= b above */
     647             : void
     648          63 : u_forprime_restrict(forprime_t *T, ulong c) { T->b = c; }
     649             : 
     650             : /* b = NULL: loop forever */
     651             : int
     652        1999 : forprimestep_init(forprime_t *T, GEN a, GEN b, GEN q)
     653             : {
     654             :   long lb;
     655        1999 :   a = gceil(a); if (typ(a) != t_INT) pari_err_TYPE("forprime_init",a);
     656        1999 :   if (signe(a) <= 0) a = gen_1;
     657        1999 :   if (b && typ(b) != t_INFINITY)
     658             :   {
     659         711 :     b = gfloor(b);
     660         711 :     if (typ(b) != t_INT) pari_err_TYPE("forprime_init",b);
     661         711 :     if (signe(b) < 0 || cmpii(a,b) > 0)
     662             :     {
     663           7 :       T->strategy = PRST_nextprime; /* paranoia */
     664           7 :       T->bb = T->pp = gen_0; return 0;
     665             :     }
     666         704 :     lb = lgefint(b);
     667         704 :     T->bb = b;
     668             :   }
     669        1288 :   else if (!b || inf_get_sign(b) > 0)
     670             :   {
     671        1288 :     lb = lgefint(a) + 4;
     672        1288 :     T->bb = NULL;
     673             :   }
     674             :   else /* b == -oo */
     675             :   {
     676           0 :     T->strategy = PRST_nextprime; /* paranoia */
     677           0 :     T->bb = T->pp = gen_0; return 0;
     678             :   }
     679        1992 :   T->pp = cgeti(lb);
     680        1992 :   T->c = 0;
     681        1992 :   T->q = 1;
     682             :   /* a, b are positive integers, a <= b */
     683        1992 :   if (q)
     684             :   {
     685          91 :     switch(typ(q))
     686             :     {
     687          21 :       case t_INT: break;
     688          70 :       case t_INTMOD: a = addii(a, modii(subii(gel(q,2),a), gel(q,1)));
     689          70 :                      q = gel(q,1); break;
     690           0 :       default: pari_err_TYPE("forprimestep_init",q);
     691             :     }
     692          91 :     if (signe(q) <= 0) pari_err_TYPE("forprimestep_init (q <= 0)",q);
     693          91 :     if (equali1(q)) q = NULL;
     694             :     else
     695             :     {
     696          91 :       T->q = itou(q);
     697          91 :       T->c = umodiu(a, T->q);
     698             :     }
     699             :   }
     700        1992 :   if (lgefint(a) == 3) /* lb == 3 implies b != NULL */
     701        1858 :     return u_forprime_arith_init(T, uel(a,2), lb == 3? uel(b,2): ULONG_MAX,
     702             :                                     T->c, T->q);
     703         134 :   T->strategy = PRST_nextprime;
     704         134 :   affii(subiu(a,T->q), T->pp);
     705         134 :   return 1;
     706             : }
     707             : int
     708        1258 : forprime_init(forprime_t *T, GEN a, GEN b)
     709        1258 : { return forprimestep_init(T,a,b,NULL); }
     710             : 
     711             : /* assume a <= b <= maxprime()^2, a,b odd, sieve[n] corresponds to
     712             :  *   a+16*n, a+16*n+2, ..., a+16*n+14 (bits 0 to 7)
     713             :  * maxpos = index of last sieve cell.
     714             :  * b-a+2 must be divisible by 16 for use by u_forprime_next */
     715             : static void
     716        5600 : sieve_block(ulong a, ulong b, ulong maxpos, unsigned char* sieve)
     717             : {
     718        5600 :   ulong p = 2, lim = usqrt(b), sz = (b-a) >> 1;
     719        5600 :   byteptr d = diffptr+1;
     720        5600 :   (void)memset(sieve, 0, maxpos+1);
     721             :   for (;;)
     722    18132037 :   { /* p is odd */
     723             :     ulong k, r;
     724    18137637 :     NEXT_PRIME_VIADIFF(p, d); /* starts at p = 3 */
     725    18137637 :     if (p > lim) break;
     726             : 
     727             :     /* solve a + 2k = 0 (mod p) */
     728    18132037 :     r = a % p;
     729    18132037 :     if (r == 0)
     730        9030 :       k = 0;
     731             :     else
     732             :     {
     733    18123007 :       k = p - r;
     734    18123007 :       if (odd(k)) k += p;
     735    18123007 :       k >>= 1;
     736             :     }
     737             :     /* m = a + 2k is the smallest odd m >= a, p | m */
     738             :     /* position n (corresponds to a+2n) is sieve[n>>3], bit n&7 */
     739  3925578946 :     while (k <= sz) { sieve[k>>3] |= 1 << (k&7); k += p; /* 2k += 2p */ }
     740             :   }
     741        5600 : }
     742             : 
     743             : static void
     744        1792 : pari_sieve_init(struct pari_sieve *s, ulong a, ulong b)
     745             : {
     746        1792 :   ulong maxpos= (b - a) >> 4;
     747        1792 :   s->start = a; s->end = b;
     748        1792 :   s->sieve = (unsigned char*) pari_malloc(maxpos+1);
     749        1792 :   s->c = 0; s->q = 1;
     750        1792 :   sieve_block(a, b, maxpos, s->sieve);
     751        1792 :   s->maxpos = maxpos; /* must be last in case of SIGINT */
     752        1792 : }
     753             : 
     754             : static struct pari_sieve pari_sieve_modular;
     755             : 
     756             : #ifdef LONG_IS_64BIT
     757             : #define PARI_MODULAR_BASE ((1UL<<((BITS_IN_LONG-2)>>1))+1)
     758             : #else
     759             : #define PARI_MODULAR_BASE ((1UL<<(BITS_IN_LONG-1))+1)
     760             : #endif
     761             : 
     762             : void
     763        1792 : pari_init_primes(ulong maxprime)
     764             : {
     765        1792 :   ulong a = PARI_MODULAR_BASE, b = a + (1UL<<20)-2;
     766        1792 :   initprimetable(maxprime);
     767        1792 :   pari_sieve_init(&pari_sieve_modular, a, b);
     768        1792 : }
     769             : 
     770             : void
     771        1792 : pari_close_primes(void)
     772             : {
     773        1792 :   pari_free(diffptr);
     774        1792 :   pari_free(pari_sieve_modular.sieve);
     775        1792 : }
     776             : 
     777             : void
     778      492025 : init_modular_small(forprime_t *S)
     779             : {
     780             : #ifdef LONG_IS_64BIT
     781      421713 :   u_forprime_sieve_init(S, &pari_sieve_modular, ULONG_MAX);
     782             : #else
     783       70312 :   ulong a = (1UL<<((BITS_IN_LONG-2)>>1))+1;
     784       70312 :   u_forprime_init(S, a, ULONG_MAX);
     785             : #endif
     786      492022 : }
     787             : 
     788             : void
     789     7500303 : init_modular_big(forprime_t *S)
     790             : {
     791             : #ifdef LONG_IS_64BIT
     792     6424959 :   u_forprime_init(S, HIGHBIT + 1, ULONG_MAX);
     793             : #else
     794     1075344 :   u_forprime_sieve_init(S, &pari_sieve_modular, ULONG_MAX);
     795             : #endif
     796     7500339 : }
     797             : 
     798             : /* T->cache is a 0-terminated list of primes, return the first one and
     799             :  * remove it from list. Most of the time the list contains a single prime */
     800             : static ulong
     801    86119470 : shift_cache(forprime_t *T)
     802             : {
     803             :   long i;
     804    86119470 :   T->p = T->cache[0];
     805    86119470 :   for (i = 1;; i++)  /* remove one prime from cache */
     806   114642586 :     if (! (T->cache[i-1] = T->cache[i]) ) break;
     807    86119470 :   return T->p;
     808             : }
     809             : 
     810             : ulong
     811   140154849 : u_forprime_next(forprime_t *T)
     812             : {
     813   140154849 :   if (T->strategy == PRST_diffptr)
     814             :   {
     815             :     for(;;)
     816             :     {
     817   193002221 :       if (!*(T->d))
     818             :       {
     819        8497 :         T->strategy = T->isieve? PRST_sieve: PRST_unextprime;
     820        8497 :         if (T->q != 1) { arith_set(T); if (!T->p) return 0; }
     821             :         /* T->p possibly not a prime if q != 1 */
     822        8497 :         break;
     823             :       }
     824             :       else
     825             :       {
     826   192993724 :         NEXT_PRIME_VIADIFF(T->p, T->d);
     827   192993724 :         if (T->p > T->b) return 0;
     828   192852354 :         if (T->q == 1 || T->p % T->q == T->c) return T->p;
     829             :       }
     830             :     }
     831             :   }
     832    97726939 :   if (T->strategy == PRST_sieve)
     833             :   {
     834             :     ulong n;
     835    86119697 :     if (T->cache[0]) return shift_cache(T);
     836    61865785 : NEXT_CHUNK:
     837    61869593 :     if (T->psieve)
     838             :     {
     839     1497052 :       T->sieve = T->psieve->sieve;
     840     1497052 :       T->end = T->psieve->end;
     841     1497052 :       if (T->end > T->sieveb) T->end = T->sieveb;
     842     1497052 :       T->maxpos = T->psieve->maxpos;
     843     1497052 :       T->pos = 0;
     844     1497052 :       T->psieve = NULL;
     845             :     }
     846    97645173 :     for (n = T->pos; n < T->maxpos; n++)
     847    97639303 :       if (T->sieve[n] != 0xFF)
     848             :       {
     849    61863723 :         unsigned char mask = T->sieve[n];
     850    61863723 :         ulong p = T->a + (n<<4);
     851    61863723 :         long i = 0;
     852    61863723 :         T->pos = n;
     853    61863723 :         if (!(mask &  1)) T->cache[i++] = p;
     854    61863723 :         if (!(mask &  2)) T->cache[i++] = p+2;
     855    61863723 :         if (!(mask &  4)) T->cache[i++] = p+4;
     856    61863723 :         if (!(mask &  8)) T->cache[i++] = p+6;
     857    61863723 :         if (!(mask & 16)) T->cache[i++] = p+8;
     858    61863723 :         if (!(mask & 32)) T->cache[i++] = p+10;
     859    61863723 :         if (!(mask & 64)) T->cache[i++] = p+12;
     860    61863723 :         if (!(mask &128)) T->cache[i++] = p+14;
     861    61863723 :         T->cache[i] = 0;
     862    61863723 :         T->pos = n+1;
     863    61863723 :         return shift_cache(T);
     864             :       }
     865             :     /* n = T->maxpos, last cell: check p <= b */
     866        5870 :     if (T->maxpos && n == T->maxpos && T->sieve[n] != 0xFF)
     867             :     {
     868        1946 :       unsigned char mask = T->sieve[n];
     869        1946 :       ulong p = T->a + (n<<4);
     870        1946 :       long i = 0;
     871        1946 :       T->pos = n;
     872        1946 :       if (!(mask &  1) && p <= T->sieveb) T->cache[i++] = p;
     873        1946 :       if (!(mask &  2) && p <= T->sieveb-2) T->cache[i++] = p+2;
     874        1946 :       if (!(mask &  4) && p <= T->sieveb-4) T->cache[i++] = p+4;
     875        1946 :       if (!(mask &  8) && p <= T->sieveb-6) T->cache[i++] = p+6;
     876        1946 :       if (!(mask & 16) && p <= T->sieveb-8) T->cache[i++] = p+8;
     877        1946 :       if (!(mask & 32) && p <= T->sieveb-10) T->cache[i++] = p+10;
     878        1946 :       if (!(mask & 64) && p <= T->sieveb-12) T->cache[i++] = p+12;
     879        1946 :       if (!(mask &128) && p <= T->sieveb-14) T->cache[i++] = p+14;
     880        1946 :       if (i)
     881             :       {
     882        1834 :         T->cache[i] = 0;
     883        1834 :         T->pos = n+1;
     884        1834 :         return shift_cache(T);
     885             :       }
     886             :     }
     887             : 
     888        4036 :     if (T->maxpos && T->end >= T->sieveb) /* done with sieves ? */
     889             :     {
     890         231 :       if (T->sieveb == T->b && T->b != ULONG_MAX) return 0;
     891           1 :       T->strategy = PRST_unextprime;
     892             :     }
     893             :     else
     894             :     { /* initialize next chunk */
     895        3805 :       T->sieve = T->isieve;
     896        3805 :       if (T->maxpos == 0)
     897        1043 :         T->a |= 1; /* first time; ensure odd */
     898             :       else
     899        2762 :         T->a = (T->end + 2) | 1;
     900        3805 :       T->end = T->a + T->chunk; /* may overflow */
     901        3805 :       if (T->end < T->a || T->end > T->sieveb) T->end = T->sieveb;
     902             :       /* end and a are odd; sieve[k] contains the a + 8*2k + (0,2,...,14).
     903             :        * The largest k is (end-a) >> 4 */
     904        3805 :       T->pos = 0;
     905        3805 :       T->maxpos = (T->end - T->a) >> 4;
     906        3805 :       sieve_block(T->a, T->end, T->maxpos, T->sieve);
     907        3808 :       goto NEXT_CHUNK;
     908             :     }
     909             :   }
     910    11607243 :   if (T->strategy == PRST_unextprime)
     911             :   {
     912    11602825 :     if (T->q == 1)
     913             :     {
     914             : #ifdef LONG_IS_64BIT
     915    11586550 :       switch(T->p)
     916             :       {
     917             : #define retp(x) return T->p = (HIGHBIT+x <= T->b)? HIGHBIT+x: 0
     918     6424993 :         case HIGHBIT: retp(29);
     919     3092695 :         case HIGHBIT + 29: retp(99);
     920      302711 :         case HIGHBIT + 99: retp(123);
     921      165622 :         case HIGHBIT +123: retp(131);
     922      121546 :         case HIGHBIT +131: retp(155);
     923      100705 :         case HIGHBIT +155: retp(255);
     924       75888 :         case HIGHBIT +255: retp(269);
     925       66502 :         case HIGHBIT +269: retp(359);
     926       58070 :         case HIGHBIT +359: retp(435);
     927       50557 :         case HIGHBIT +435: retp(449);
     928       43331 :         case HIGHBIT +449: retp(453);
     929       39516 :         case HIGHBIT +453: retp(485);
     930       33271 :         case HIGHBIT +485: retp(491);
     931       29956 :         case HIGHBIT +491: retp(543);
     932       27138 :         case HIGHBIT +543: retp(585);
     933       24659 :         case HIGHBIT +585: retp(599);
     934       22627 :         case HIGHBIT +599: retp(753);
     935       21931 :         case HIGHBIT +753: retp(849);
     936       20965 :         case HIGHBIT +849: retp(879);
     937       19596 :         case HIGHBIT +879: retp(885);
     938       19105 :         case HIGHBIT +885: retp(903);
     939       18709 :         case HIGHBIT +903: retp(995);
     940             : #undef retp
     941             :       }
     942             : #endif
     943      817739 :       T->p = unextprime(T->p + 1);
     944             :     }
     945             :     else do {
     946       48417 :       T->p += T->q;
     947       48417 :       if (T->p < T->q || T->p > T->b) { T->p = 0; break; } /* overflow */
     948       48398 :     } while (!uisprime(T->p));
     949      822748 :     if (T->p && T->p <= T->b) return T->p;
     950             :     /* overflow ulong, switch to GEN */
     951       13241 :     T->strategy = PRST_nextprime;
     952             :   }
     953       17659 :   return 0; /* overflow */
     954             : }
     955             : 
     956             : GEN
     957     7891846 : forprime_next(forprime_t *T)
     958             : {
     959             :   pari_sp av;
     960             :   GEN p;
     961     7891846 :   if (T->strategy != PRST_nextprime)
     962             :   {
     963     7884098 :     ulong u = u_forprime_next(T);
     964     7884098 :     if (u) { affui(u, T->pp); return T->pp; }
     965             :     /* failure */
     966         527 :     if (T->strategy != PRST_nextprime) return NULL; /* we're done */
     967             :     /* overflow ulong, switch to GEN */
     968          40 :     u = ULONG_MAX;
     969          40 :     if (T->q > 1) u -= (ULONG_MAX-T->c) % T->q;
     970          40 :     affui(u, T->pp);
     971             :   }
     972        7788 :   av = avma; p = T->pp;
     973        7788 :   if (T->q == 1)
     974             :   {
     975        7694 :     p = nextprime(addiu(p, 1));
     976        7694 :     if (T->bb && abscmpii(p, T->bb) > 0) return gc_NULL(av);
     977             :   } else do {
     978        3055 :     p = addiu(p, T->q);
     979        3055 :     if (T->bb && abscmpii(p, T->bb) > 0) return gc_NULL(av);
     980        3034 :   } while (!BPSW_psp(p));
     981        7642 :   affii(p, T->pp); return gc_const(av, T->pp);
     982             : }
     983             : 
     984             : void
     985         721 : forprimestep(GEN a, GEN b, GEN q, GEN code)
     986             : {
     987         721 :   pari_sp av = avma;
     988             :   forprime_t T;
     989             : 
     990         721 :   if (!forprimestep_init(&T, a,b,q)) { set_avma(av); return; }
     991             : 
     992         714 :   push_lex(T.pp,code);
     993       43092 :   while(forprime_next(&T))
     994             :   {
     995       42721 :     closure_evalvoid(code); if (loop_break()) break;
     996             :     /* p changed in 'code', complain */
     997       42385 :     if (get_lex(-1) != T.pp)
     998           7 :       pari_err(e_MISC,"prime index read-only: was changed to %Ps", get_lex(-1));
     999             :   }
    1000         707 :   pop_lex(1); set_avma(av);
    1001             : }
    1002             : void
    1003         637 : forprime(GEN a, GEN b, GEN code) { return forprimestep(a,b,NULL,code); }
    1004             : 
    1005             : int
    1006          70 : forcomposite_init(forcomposite_t *C, GEN a, GEN b)
    1007             : {
    1008          70 :   pari_sp av = avma;
    1009          70 :   a = gceil(a);
    1010          70 :   if (typ(a)!=t_INT) pari_err_TYPE("forcomposite",a);
    1011          70 :   if (b) {
    1012          63 :     if (typ(b) == t_INFINITY) b = NULL;
    1013             :     else
    1014             :     {
    1015          56 :       b = gfloor(b);
    1016          56 :       if (typ(b)!=t_INT) pari_err_TYPE("forcomposite",b);
    1017             :     }
    1018             :   }
    1019          70 :   if (signe(a) < 0) pari_err_DOMAIN("forcomposite", "a", "<", gen_0, a);
    1020          70 :   if (abscmpiu(a, 4) < 0) a = utoipos(4);
    1021          70 :   C->first = 1;
    1022          70 :   if (!forprime_init(&C->T, a,b) && cmpii(a,b) > 0)
    1023             :   {
    1024           7 :     C->n = gen_1; /* in case caller forgets to check the return value */
    1025           7 :     C->b = gen_0; return gc_bool(av,0);
    1026             :   }
    1027          63 :   C->n = setloop(a);
    1028          63 :   C->b = b;
    1029          63 :   C->p = NULL; return 1;
    1030             : }
    1031             : 
    1032             : GEN
    1033         238 : forcomposite_next(forcomposite_t *C)
    1034             : {
    1035         238 :   if (C->first) /* first call ever */
    1036             :   {
    1037          63 :     C->first = 0;
    1038          63 :     C->p = forprime_next(&C->T);
    1039             :   }
    1040             :   else
    1041         175 :     C->n = incloop(C->n);
    1042         238 :   if (C->p)
    1043             :   {
    1044         161 :     if (cmpii(C->n, C->p) < 0) return C->n;
    1045          77 :     C->n = incloop(C->n);
    1046             :     /* n = p+1 */
    1047          77 :     C->p = forprime_next(&C->T); /* nextprime(p) > n */
    1048          77 :     if (C->p) return C->n;
    1049             :   }
    1050         105 :   if (!C->b || cmpii(C->n, C->b) <= 0) return C->n;
    1051          42 :   return NULL;
    1052             : }
    1053             : 
    1054             : void
    1055          70 : forcomposite(GEN a, GEN b, GEN code)
    1056             : {
    1057          70 :   pari_sp av = avma;
    1058             :   forcomposite_t T;
    1059             :   GEN n;
    1060          70 :   if (!forcomposite_init(&T,a,b)) return;
    1061          63 :   push_lex(T.n,code);
    1062         238 :   while((n = forcomposite_next(&T)))
    1063             :   {
    1064         196 :     closure_evalvoid(code); if (loop_break()) break;
    1065             :     /* n changed in 'code', complain */
    1066         182 :     if (get_lex(-1) != n)
    1067           7 :       pari_err(e_MISC,"index read-only: was changed to %Ps", get_lex(-1));
    1068             :   }
    1069          56 :   pop_lex(1); set_avma(av);
    1070             : }

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