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      1 /* Exercise mpz_fac_ui and mpz_bin_uiui.
      2 
      3 Copyright 2000-2002, 2012, 2013, 2017-2018 Free Software Foundation, Inc.
      4 
      5 This file is part of the GNU MP Library test suite.
      6 
      7 The GNU MP Library test suite is free software; you can redistribute it
      8 and/or modify it under the terms of the GNU General Public License as
      9 published by the Free Software Foundation; either version 3 of the License,
     10 or (at your option) any later version.
     11 
     12 The GNU MP Library test suite is distributed in the hope that it will be
     13 useful, but WITHOUT ANY WARRANTY; without even the implied warranty of
     14 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General
     15 Public License for more details.
     16 
     17 You should have received a copy of the GNU General Public License along with
     18 the GNU MP Library test suite.  If not, see https://www.gnu.org/licenses/.  */
     19 
     20 #include <stdio.h>
     21 #include <stdlib.h>
     22 
     23 #include "testutils.h"
     24 
     25 /* Usage: t-fac_ui [x|num]
     26 
     27    With no arguments testing goes up to the initial value of "limit" below.
     28    With a number argument tests are carried that far, or with a literal "x"
     29    tests are continued without limit (this being meant only for development
     30    purposes).  */
     31 
     32 void
     33 try_mpz_bin_uiui (mpz_srcptr want, unsigned long n, unsigned long k)
     34 {
     35   mpz_t  got;
     36 
     37   mpz_init (got);
     38   mpz_bin_uiui (got, n, k);
     39   if (mpz_cmp (got, want) != 0)
     40     {
     41       printf ("mpz_bin_uiui wrong\n");
     42       printf ("  n=%lu\n", n);
     43       printf ("  k=%lu\n", k);
     44       printf ("  got="); mpz_out_str (stdout, 10, got); printf ("\n");
     45       printf ("  want="); mpz_out_str (stdout, 10, want); printf ("\n");
     46       abort();
     47     }
     48   mpz_clear (got);
     49 }
     50 
     51 /* Test all bin(n,k) cases, with 0 <= k <= n + 1 <= count.  */
     52 void
     53 bin_smallexaustive (unsigned int count)
     54 {
     55   mpz_t          want;
     56   unsigned long  n, k;
     57 
     58   mpz_init (want);
     59 
     60   for (n = 0; n < count; n++)
     61     {
     62       mpz_set_ui (want, 1);
     63       for (k = 0; k <= n; k++)
     64 	{
     65 	  try_mpz_bin_uiui (want, n, k);
     66 	  mpz_mul_ui (want, want, n - k);
     67 	  mpz_fdiv_q_ui (want, want, k + 1);
     68 	}
     69       try_mpz_bin_uiui (want, n, k);
     70     }
     71 
     72   mpz_clear (want);
     73 }
     74 
     75 /* Test all fac(n) cases, with 0 <= n <= limit.  */
     76 void
     77 fac_smallexaustive (unsigned int limit)
     78 {
     79   mpz_t          f, r;
     80   unsigned long  n;
     81   mpz_init_set_si (f, 1);  /* 0! = 1 */
     82   mpz_init (r);
     83 
     84   for (n = 0; n < limit; n++)
     85     {
     86       mpz_fac_ui (r, n);
     87 
     88       if (mpz_cmp (f, r) != 0)
     89         {
     90           printf ("mpz_fac_ui(%lu) wrong\n", n);
     91           printf ("  got  "); mpz_out_str (stdout, 10, r); printf("\n");
     92           printf ("  want "); mpz_out_str (stdout, 10, f); printf("\n");
     93           abort ();
     94         }
     95 
     96       mpz_mul_ui (f, f, n+1);  /* (n+1)! = n! * (n+1) */
     97     }
     98 
     99   mpz_clear (f);
    100   mpz_clear (r);
    101 }
    102 
    103 void checkWilson (mpz_t f, unsigned long n)
    104 {
    105   unsigned long m, a;
    106 
    107   mpz_2fac_ui (f, 2 * n - 1);
    108 
    109   a = mpz_fdiv_q_ui (f, f, n);
    110   m = mpz_fdiv_ui (f, n);
    111   if ((m != n - 1) || (a != 0))
    112     {
    113       printf ("mpz_2fac_ui(%lu) wrong\n", 2 * n - 1);
    114       printf ("  Wilson's theorem not verified: got (%lu, %lu), expected (0, %lu).\n", a, m, n - 1);
    115       abort ();
    116     }
    117 
    118   mpz_fac_ui (f, n - 1);
    119   m = mpz_fdiv_ui (f, n);
    120   if ( m != n - 1)
    121     {
    122       printf ("mpz_fac_ui(%lu) wrong\n", n - 1);
    123       printf ("  Wilson's theorem not verified: got %lu, expected %lu.\n",m ,n - 1);
    124       abort ();
    125     }
    126 }
    127 
    128 void
    129 checkprimes (unsigned long p1, unsigned long p2, unsigned long p3)
    130 {
    131   mpz_t          b, f;
    132 
    133   if (p1 - 1 != p2 - 1 + p3 - 1)
    134     {
    135       printf ("checkprimes(%lu, %lu, %lu) wrong\n", p1, p2, p3);
    136       printf (" %lu - 1 != %lu - 1 + %lu - 1 \n", p1, p2, p3);
    137       abort ();
    138     }
    139 
    140   mpz_init (b);
    141   mpz_init (f);
    142 
    143   checkWilson (b, p1); /* b = (p1-1)! */
    144   checkWilson (f, p2); /* f = (p2-1)! */
    145   mpz_divexact (b, b, f);
    146   checkWilson (f, p3); /* f = (p3-1)! */
    147   mpz_divexact (b, b, f); /* b = (p1-1)!/((p2-1)!(p3-1)!) */
    148   mpz_bin_uiui (f, p1 - 1, p2 - 1);
    149   if (mpz_cmp (f, b) != 0)
    150     {
    151       printf ("checkprimes(%lu, %lu, %lu) wrong\n", p1, p2, p3);
    152       printf ("  got  "); mpz_out_str (stdout, 10, b); printf("\n");
    153       printf ("  want "); mpz_out_str (stdout, 10, f); printf("\n");
    154       abort ();
    155     }
    156 
    157   mpz_clear (b);
    158   mpz_clear (f);
    159 
    160 }
    161 
    162 void
    163 testmain (int argc, char *argv[])
    164 {
    165   unsigned long  limit = 128;
    166 
    167   if (argc > 1 && argv[1][0] == 'x')
    168     limit = ~ limit;
    169   else if (argc > 1)
    170     limit = atoi (argv[1]);
    171 
    172   checkprimes(1009, 733, 277);
    173   fac_smallexaustive (limit);
    174   bin_smallexaustive (limit);
    175 }
    176