kc3-lang/libtommath/etc/tune.c

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• Hash : db76bed2
  Author :
  Date : 2019-05-04T18:57:07
  

  added autotuning functionality for the Toom-Cook cut-offs

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• etc/tune.c

• /* Tune the Karatsuba parameters
   *
   * Tom St Denis, tstdenis82@gmail.com
   */
  #include "../tommath.h"
  #include "../tommath_private.h"
  #include <stdint.h>
  #include <time.h>
  #include <inttypes.h>
  #include <limits.h>
  #include <errno.h>
  
  static uint64_t s_ranval(void);
  static void s_raninit(uint64_t seed);
  static int s_mp_random(mp_int *a, int limbs);
  static uint64_t s_timer_function(void);
  static void s_timer_start(void);
  static uint64_t s_timer_stop(void);
  static uint64_t s_time_mul(int size);
  static uint64_t s_time_sqr(int size);
  static void s_usage(char *s);
  
  /*
     Please take in mind that both multiplicands are of the same size. The balancing
     mechanism in mp_balance works well but has some overhead itself. You can test
     the behaviour of it with the option "-o" followed by a (small) positive number 'x'
     to generate ratios of the form 1:x.
  */
  
  /* Bob Jenkins' http://burtleburtle.net/bob/rand/smallprng.html */
  /* Chosen for speed and a good "mix" */
  typedef struct ranctx {
     uint64_t a;
     uint64_t b;
     uint64_t c;
     uint64_t d;
  } ranctx;
  
  static ranctx burtle_x;
  
  #   define rot(x,k) (((x)<<(k))|((x)>>(64-(k))))
  static uint64_t s_ranval(void)
  {
     uint64_t e = burtle_x.a - rot(burtle_x.b, 7);
     burtle_x.a = burtle_x.b ^ rot(burtle_x.c, 13);
     burtle_x.b = burtle_x.c + rot(burtle_x.d, 37);
     burtle_x.c = burtle_x.d + e;
     burtle_x.d = e + burtle_x.a;
     return burtle_x.d;
  }
  
  static void s_raninit(uint64_t seed)
  {
     uint64_t i;
     burtle_x.a = 0xf1ea5eed;
     burtle_x.b = burtle_x.c = burtle_x.d = seed;
     for (i = 0; i < 20; ++i) {
        (void) s_ranval();
     }
  }
  
  /*
     The original used LTM's mp_rand which uses the cryptographically secure
     source of the OS for its purpose. That is too expensive, too slow and
     most important for a benchmark: it is not repeatable.
  */
  static int s_mp_random(mp_int *a, int limbs)
  {
     int e = MP_OKAY;
     if ((e = mp_grow(a, limbs + 1)) != MP_OKAY) {
        goto LTM_ERR;
     }
     a->used = limbs--;
     do {
        a->dp[limbs] = (mp_digit)(s_ranval() & MP_MASK);
     } while (limbs--);
     mp_clamp(a);
  LTM_ERR:
     return e;
  }
  
  static uint64_t s_timer_function(void)
  {
  #if _POSIX_C_SOURCE >= 199309L
  #define LTM_BILLION 1000000000
     struct timespec ts;
  
     /* TODO: Sets errno in case of error. Use? */
     clock_gettime(CLOCK_MONOTONIC, &ts);
     return (((uint64_t)ts.tv_sec) * LTM_BILLION + (uint64_t)ts.tv_nsec);
  #else
     clock_t t;
     t = clock();
     if (t < (clock_t)(0)) {
        return (uint64_t)(0);
     }
     return (uint64_t)(t);
  #endif
  }
  
  /* generic ISO C timer */
  static uint64_t s_timer_tmp;
  static void s_timer_start(void)
  {
     s_timer_tmp = s_timer_function();
  }
  static uint64_t s_timer_stop(void)
  {
     return s_timer_function() - s_timer_tmp;
  }
  
  
  static int s_check_result;
  static int s_number_of_test_loops;
  static int s_stabilization_extra;
  static int s_offset = 1;
  
  #define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1)
  static uint64_t s_time_mul(int size)
  {
     int x, e;
     mp_int  a, b, c, d;
     uint64_t t1;
  
     if ((e = mp_init_multi(&a, &b, &c, &d, NULL)) != MP_OKAY) {
        t1 = UINT64_MAX;
        goto LTM_ERR;
     }
  
     if ((e = s_mp_random(&a, size * s_offset)) != MP_OKAY) {
        t1 = UINT64_MAX;
        goto LTM_ERR;
     }
     if ((e = s_mp_random(&b, size)) != MP_OKAY) {
        t1 = UINT64_MAX;
        goto LTM_ERR;
     }
  
     s_timer_start();
     for (x = 0; x < s_number_of_test_loops; x++) {
        if ((e = mp_mul(&a,&b,&c)) != MP_OKAY) {
           t1 = UINT64_MAX;
           goto LTM_ERR;
        }
        if (s_check_result == 1) {
           if ((e = s_mp_mul(&a,&b,&d)) != MP_OKAY) {
              t1 = UINT64_MAX;
              goto LTM_ERR;
           }
           if (mp_cmp(&c, &d) != MP_EQ) {
              /* Time of 0 cannot happen (famous last words?) */
              t1 = 0uLL;
              goto LTM_ERR;
           }
        }
     }
  
     t1 = s_timer_stop();
  LTM_ERR:
     mp_clear_multi(&a, &b, &c, &d, NULL);
     return t1;
  }
  
  static uint64_t s_time_sqr(int size)
  {
     int x, e;
     mp_int  a, b, c;
     uint64_t t1;
  
     if ((e = mp_init_multi(&a, &b, &c, NULL)) != MP_OKAY) {
        t1 = UINT64_MAX;
        goto LTM_ERR;
     }
  
     if ((e = s_mp_random(&a, size)) != MP_OKAY) {
        t1 = UINT64_MAX;
        goto LTM_ERR;
     }
  
     s_timer_start();
     for (x = 0; x < s_number_of_test_loops; x++) {
        if ((e = mp_sqr(&a,&b)) != MP_OKAY) {
           t1 = UINT64_MAX;
           goto LTM_ERR;
        }
        if (s_check_result == 1) {
           if ((e = s_mp_sqr(&a,&c)) != MP_OKAY) {
              t1 = UINT64_MAX;
              goto LTM_ERR;
           }
           if (mp_cmp(&c, &b) != MP_EQ) {
              t1 = 0uLL;
              goto LTM_ERR;
           }
        }
     }
  
     t1 = s_timer_stop();
  LTM_ERR:
     mp_clear_multi(&a, &b, &c, NULL);
     return t1;
  }
  
  static void s_usage(char *s)
  {
     fprintf(stderr,"Usage: %s [TvcpGbtrSLFfMmosh]\n",s);
     fprintf(stderr,"          -T testmode, for use with testme.sh\n");
     fprintf(stderr,"          -v verbose, print all timings\n");
     fprintf(stderr,"          -c check results\n");
     fprintf(stderr,"          -p print benchmark of final cutoffs in files \"multiplying\"\n");
     fprintf(stderr,"             and \"squaring\"\n");
     fprintf(stderr,"          -G [string] suffix for the filenames listed above\n");
     fprintf(stderr,"             Implies '-p'\n");
     fprintf(stderr,"          -b print benchmark of bncore.c\n");
     fprintf(stderr,"          -t prints comma separated results\n");
     fprintf(stderr,"          -r [64] number of rounds\n");
     fprintf(stderr,"          -S [0xdeadbeef] seed for PRNG\n");
     fprintf(stderr,"          -L [3] number of negative values accumulated until the result is accepted\n");
     fprintf(stderr,"          -M [3000] upper limit of T-C tests/prints\n");
     fprintf(stderr,"          -m [1] increment of T-C tests/prints\n");
     fprintf(stderr,"          -o [1] multiplier for the second multiplicand\n");
     fprintf(stderr,"             (Not for computing the cut-offs!)\n");
     fprintf(stderr,"          -s 'preset' use values in 'preset' for printing.\n");
     fprintf(stderr,"             'preset' is a comma separated string with cut-offs for\n");
     fprintf(stderr,"             ksm, kss, tc3m, tc3s in that order\n");
     fprintf(stderr,"             ksm  = karatsuba multiplication\n");
     fprintf(stderr,"             kss  = karatsuba squaring\n");
     fprintf(stderr,"             tc3m = Toom-Cook 3-way multiplication\n");
     fprintf(stderr,"             tc3s = Toom-Cook 3-way squaring\n");
     fprintf(stderr,"             Implies '-p'\n");
     fprintf(stderr,"          -h this message\n");
  }
  
  
  
  int main(int argc, char **argv)
  {
     uint64_t t1, t2;
     int x, i, j;
     int count = 0;
  
     int testmode = 0;
     int verbose = 0;
     int print = 0;
     int bncore = 0;
     int terse = 0;
  
     int upper_limit_print = 3000;
     int increment_print = 1;
  
     int printpreset = 0;
     /*int preset[8];*/
     int base = 10;
     char *endptr, *str;
     long val;
  
     uint64_t seed = 0xdeadbeef;
  
     int opt;
     int ksm, kss, tc3m, tc3s;
  
     FILE *squaring, *multiplying;
     char mullog[256] = "multiplying";
     char sqrlog[256] = "squaring";
     s_number_of_test_loops = 64;
     s_stabilization_extra = 3;
  
     /* Very simple option parser, please treat it nicely. */
     if (argc != 1) {
        for (opt = 1; (opt < argc) && (argv[opt][0] == '-'); opt++) {
           switch (argv[opt][1]) {
           case 'T':
              testmode = 1;
              s_check_result = 1;
              upper_limit_print = 1000;
              increment_print = 11;
              s_number_of_test_loops = 1;
              s_stabilization_extra = 1;
              s_offset = 1;
              break;
           case 'v':
              verbose = 1;
              break;
           case 'c':
              s_check_result = 1;
              break;
           case 'p':
              print = 1;
              break;
           case 'G':
              print = 1;
              opt++;
              if (opt >= argc) {
                 s_usage(argv[0]);
              }
              /* manual strcat() */
              for (i = 0; i < 255; i++) {
                 if (mullog[i] == '\0') {
                    break;
                 }
              }
              for (j = 0; i < 255; j++, i++) {
                 mullog[i] = argv[opt][j];
                 if (argv[opt][j] == '\0') {
                    break;
                 }
              }
              for (i = 0; i < 255; i++) {
                 if (sqrlog[i] == '\0') {
                    break;
                 }
              }
              for (j = 0; i < 255; j++, i++) {
                 sqrlog[i] = argv[opt][j];
                 if (argv[opt][j] == '\0') {
                    break;
                 }
              }
              break;
           case 'b':
              bncore = 1;
              break;
           case 't':
              terse = 1;
              break;
           case 'S':
              opt++;
              if (opt >= argc) {
                 s_usage(argv[0]);
              }
              str = argv[opt];
              errno = 0;
              val = strtol(str, &endptr, base);
              if ((errno == ERANGE && (val == LONG_MAX || val == LONG_MIN))
                  || (errno != 0 && val == 0)) {
                 fprintf(stderr,"Seed %s not usable\n", argv[opt]);
                 exit(EXIT_FAILURE);
              }
              if (endptr == str) {
                 fprintf(stderr, "No seed given?\n");
                 exit(EXIT_FAILURE);
              }
              seed = (uint64_t)val;
              break;
           case 'L':
              opt++;
              if (opt >= argc) {
                 s_usage(argv[0]);
              }
              str = argv[opt];
              errno = 0;
              val = strtol(str, &endptr, base);
              if ((val > INT_MAX || val < 0) || (errno != 0)) {
                 fprintf(stderr,"Value %s not usable\n", argv[opt]);
                 exit(EXIT_FAILURE);
              }
              if (endptr == str) {
                 fprintf(stderr, "No value for option \"-L\"given\n");
                 exit(EXIT_FAILURE);
              }
              s_stabilization_extra = (int)val;
              break;
           case 'o':
              opt++;
              if (opt >= argc) {
                 s_usage(argv[0]);
              }
              str = argv[opt];
              errno = 0;
              val = strtol(str, &endptr, base);
              if ((val > INT_MAX || val < 0) || (errno != 0)) {
                 fprintf(stderr,"Value %s not usable as an offset\n", argv[opt]);
                 exit(EXIT_FAILURE);
              }
              if (endptr == str) {
                 fprintf(stderr, "No value for the offset given\n");
                 exit(EXIT_FAILURE);
              }
              s_offset = (int)val;
              break;
           case 'r':
              opt++;
              if (opt >= argc) {
                 s_usage(argv[0]);
              }
              str = argv[opt];
              errno = 0;
              val = strtol(str, &endptr, base);
              if ((val > INT_MAX || val < 0) || (errno != 0)) {
                 fprintf(stderr,"Value %s not usable as the number of rounds for \"-r\"\n", argv[opt]);
                 exit(EXIT_FAILURE);
              }
              if (endptr == str) {
                 fprintf(stderr, "No value for the number of rounds given\n");
                 exit(EXIT_FAILURE);
              }
              s_number_of_test_loops = (int)val;
              break;
  
           case 'M':
              opt++;
              if (opt >= argc) {
                 s_usage(argv[0]);
              }
              str = argv[opt];
              errno = 0;
              val = strtol(str, &endptr, base);
              if ((val > INT_MAX || val < 0) || (errno != 0)) {
                 fprintf(stderr,"Value %s not usable as the upper limit of T-C tests (\"-M\")\n", argv[opt]);
                 exit(EXIT_FAILURE);
              }
              if (endptr == str) {
                 fprintf(stderr, "No value for the upper limit of T-C tests given\n");
                 exit(EXIT_FAILURE);
              }
              upper_limit_print = (int)val;
              break;
           case 'm':
              opt++;
              if (opt >= argc) {
                 s_usage(argv[0]);
              }
              str = argv[opt];
              errno = 0;
              val = strtol(str, &endptr, base);
              if ((val > INT_MAX || val < 0) || (errno != 0)) {
                 fprintf(stderr,"Value %s not usable as the increment for the T-C tests (\"-m\")\n", argv[opt]);
                 exit(EXIT_FAILURE);
              }
              if (endptr == str) {
                 fprintf(stderr, "No value for the increment for the T-C tests given\n");
                 exit(EXIT_FAILURE);
              }
              increment_print = (int)val;
              break;
           case 's':
              printpreset = 1;
              print = 1;
              opt++;
              if (opt >= argc) {
                 s_usage(argv[0]);
              }
              str = argv[opt];
              i = 0;
              /* Only the most basic checks */
              errno = 0;
              val = strtol(str, &endptr, base);
              if ((val > INT_MAX || val < 0) || (errno != 0)) {
                 fprintf(stderr,"input #%d wrong\n", i+1);
                 exit(EXIT_FAILURE);
              }
              if (endptr == str) {
                 fprintf(stderr, "No input for #%d?\n", i+1);
                 exit(EXIT_FAILURE);
              }
              i++;
              str = endptr + 1;
              KARATSUBA_MUL_CUTOFF = (int)val;
              errno = 0;
              val = strtol(str, &endptr, base);
              if ((val > INT_MAX || val < 0) || (errno != 0)) {
                 fprintf(stderr,"input #%d wrong\n", i+1);
                 exit(EXIT_FAILURE);
              }
              if (endptr == str) {
                 fprintf(stderr, "No input for #%d?\n", i+1);
                 exit(EXIT_FAILURE);
              }
              i++;
              str = endptr + 1;
              KARATSUBA_SQR_CUTOFF = (int)val;
              errno = 0;
              val = strtol(str, &endptr, base);
              if ((val > INT_MAX || val < 0) || (errno != 0)) {
                 fprintf(stderr,"input #%d wrong\n", i+1);
                 exit(EXIT_FAILURE);
              }
              if (endptr == str) {
                 fprintf(stderr, "No input for #%d?\n", i+1);
                 exit(EXIT_FAILURE);
              }
              i++;
              str = endptr + 1;
              TOOM_MUL_CUTOFF = (int)val;
              errno = 0;
              val = strtol(str, &endptr, base);
              if ((val > INT_MAX || val < 0) || (errno != 0)) {
                 fprintf(stderr,"input #%d wrong\n", i+1);
                 exit(EXIT_FAILURE);
              }
              if (endptr == str) {
                 fprintf(stderr, "No input for #%d?\n", i+1);
                 exit(EXIT_FAILURE);
              }
              i++;
              str = endptr + 1;
              TOOM_SQR_CUTOFF = (int)val;
           case 'h':
           default:
              s_usage(argv[0]);
              exit(EXIT_FAILURE);
           }
        }
     }
  
     s_raninit(seed);
  
     ksm  = KARATSUBA_MUL_CUTOFF;
     kss  = KARATSUBA_SQR_CUTOFF;
     tc3m = TOOM_MUL_CUTOFF;
     tc3s = TOOM_SQR_CUTOFF;
  
     if ((bncore == 0) && (printpreset == 0)) {
        /* Turn all limits from bncore.c to the max */
        KARATSUBA_MUL_CUTOFF = INT_MAX;
        KARATSUBA_SQR_CUTOFF = INT_MAX;
        TOOM_MUL_CUTOFF = INT_MAX;
        TOOM_SQR_CUTOFF = INT_MAX;
  #ifdef BN_S_MP_KARATSUBA_MUL_C
        /*
           The influence of the Comba multiplication cannot be
           eradicated programmatically. It depends on the size
           of the macro MP_WPARRAY in tommath.h which needs to
           be changed manually (to 0 (zero)).
         */
        if ((verbose == 1) || (testmode == 1)) {
           puts("# Karatsuba multiplication.");
        }
        for (x = 8; x < upper_limit_print; x += increment_print) {
           KARATSUBA_MUL_CUTOFF = INT_MAX;
           t1 = s_time_mul(x);
           if ((t1 == 0uLL) || (t1 == UINT64_MAX)) {
              fprintf(stderr,"Karatsuba multiplication  failed at x = INT_MAX (%s)\n",
                      (t1 == 0uLL)?"wrong result":"internal error");
              exit(EXIT_FAILURE);
           }
           KARATSUBA_MUL_CUTOFF = x;
           t2 = s_time_mul(x);
           if ((t2 == 0uLL) || (t2 == UINT64_MAX)) {
              fprintf(stderr,"Karatsuba multiplication failed (%s)\n",
                      (t2 == 0uLL)?"wrong result":"internal error");
              exit(EXIT_FAILURE);
           }
           if (verbose == 1) {
              printf("%d: %9"PRIu64" %9"PRIu64", %9"PRIi64"\n", x, t1, t2, (int64_t)t2 - (int64_t)t1);
           }
           if (t2 < t1) {
              if (count == s_stabilization_extra) {
                 count = 0;
                 break;
              } else if (count < s_stabilization_extra) {
                 count++;
              }
           } else if (count > 0) {
              count--;
           }
        }
        KARATSUBA_MUL_CUTOFF = x - s_stabilization_extra * increment_print;
  #endif
  #ifdef BN_S_MP_KARATSUBA_SQR_C
        if ((verbose == 1) || (testmode == 1)) {
           puts("# Karatsuba squaring.");
        }
        for (x = 8; x < upper_limit_print; x += increment_print) {
           KARATSUBA_SQR_CUTOFF = INT_MAX;
           t1 = s_time_sqr(x);
           if ((t1 == 0uLL) || (t1 == UINT64_MAX)) {
              fprintf(stderr,"Karatsuba squaring failed at x = INT_MAX (%s)\n",
                      (t1 == 0uLL)?"wrong result":"internal error");
              exit(EXIT_FAILURE);
           }
           KARATSUBA_SQR_CUTOFF = x;
           t2 = s_time_sqr(x);
           if ((t2 == 0uLL) || (t2 == UINT64_MAX)) {
              fprintf(stderr,"Karatsuba squaring failed (%s)\n",
                      (t2 == 0uLL)?"wrong result":"internal error");
              exit(EXIT_FAILURE);
           }
           if (verbose == 1) {
              printf("%d: %9"PRIu64" %9"PRIu64", %9"PRIi64"\n", x, t1, t2, (int64_t)t2 - (int64_t)t1);
           }
           if (t2 < t1) {
              if (count == s_stabilization_extra) {
                 count = 0;
                 break;
              } else if (count < s_stabilization_extra) {
                 count++;
              }
           } else if (count > 0) {
              count--;
           }
        }
        KARATSUBA_SQR_CUTOFF = x - s_stabilization_extra * increment_print;
  #endif
  #ifdef BN_S_MP_TOOM_MUL_C
        if ((verbose == 1) || (testmode == 1)) {
           puts("# Toom-Cook 3-way multiplying.");
        }
        for (x = 8; x < upper_limit_print; x += increment_print) {
           TOOM_MUL_CUTOFF = INT_MAX;
           t1 = s_time_mul(x);
           if ((t1 == 0uLL) || (t1 == UINT64_MAX)) {
              fprintf(stderr,"Toom-Cook 3-way multiplying failed at x = INT_MAX (%s)\n",
                      (t1 == 0uLL)?"wrong result":"internal error");
              exit(EXIT_FAILURE);
           }
           TOOM_MUL_CUTOFF = x;
           t2 = s_time_mul(x);
           if ((t2 == 0uLL) || (t2 == UINT64_MAX)) {
              fprintf(stderr,"Toom-Cook 3-way multiplication failed (%s)\n",
                      (t2 == 0uLL)?"wrong result":"internal error");
              exit(EXIT_FAILURE);
           }
           if (verbose == 1) {
              printf("%d: %9"PRIu64" %9"PRIu64", %9"PRIi64"\n", x, t1, t2, (int64_t)t2 - (int64_t)t1);
           }
           if (t2 < t1) {
              if (count == s_stabilization_extra) {
                 count = 0;
                 break;
              } else if (count < s_stabilization_extra) {
                 count++;
              }
           } else if (count > 0) {
              count--;
           }
        }
        TOOM_MUL_CUTOFF = x - s_stabilization_extra * increment_print;
  #endif
  #ifdef BN_S_MP_TOOM_SQR_C
        if ((verbose == 1) || (testmode == 1)) {
           puts("# Toom-Cook 3-way squaring.");
        }
        for (x = 8; x < upper_limit_print; x += increment_print) {
           TOOM_SQR_CUTOFF = INT_MAX;
           t1 = s_time_sqr(x);
           if ((t1 == 0uLL) || (t1 == UINT64_MAX)) {
              fprintf(stderr,"Toom-Cook 3-way squaring failed at x = INT_MAX (%s)\n",
                      (t1 == 0uLL)?"wrong result":"internal error");
              exit(EXIT_FAILURE);
           }
           TOOM_SQR_CUTOFF = x;
           t2 = s_time_sqr(x);
           if ((t2 == 0uLL) || (t2 == UINT64_MAX)) {
              fprintf(stderr,"Toom-Cook 3-way squaring failed (%s)\n",
                      (t2 == 0uLL)?"wrong result":"internal error");
              exit(EXIT_FAILURE);
           }
           if (verbose == 1) {
              printf("%d: %9"PRIu64" %9"PRIu64", %9"PRIi64"\n", x, t1, t2, (int64_t)t2 - (int64_t)t1);
           }
           if (t2 < t1) {
              if (count == s_stabilization_extra) {
                 count = 0;
                 break;
              } else if (count < s_stabilization_extra) {
                 count++;
              }
           } else if (count > 0) {
              count--;
           }
        }
        TOOM_SQR_CUTOFF = x - s_stabilization_extra * increment_print;
  #endif
     }
     if (terse == 1) {
        printf("%d %d %d %d\n",
               KARATSUBA_MUL_CUTOFF,
               KARATSUBA_SQR_CUTOFF,
               TOOM_MUL_CUTOFF,
               TOOM_SQR_CUTOFF);
     } else {
        printf("KARATSUBA_MUL_CUTOFF = %d\n", KARATSUBA_MUL_CUTOFF);
        printf("KARATSUBA_SQR_CUTOFF = %d\n", KARATSUBA_SQR_CUTOFF);
        printf("TOOM_MUL_CUTOFF = %d\n", TOOM_MUL_CUTOFF);
        printf("TOOM_SQR_CUTOFF = %d\n", TOOM_SQR_CUTOFF);
     }
  
     if (print == 1) {
        printf("Printing data for graphing to \"%s\" and \"%s\"\n",mullog, sqrlog);
  
        multiplying = fopen(mullog, "w+");
        if (multiplying == NULL) {
           fprintf(stderr, "Opening file \"%s\" failed\n", mullog);
           exit(EXIT_FAILURE);
        }
  
        squaring = fopen(sqrlog, "w+");
        if (squaring == NULL) {
           fprintf(stderr, "Opening file \"%s\" failed\n",sqrlog);
           exit(EXIT_FAILURE);
        }
  
        for (x = 8; x < upper_limit_print; x += increment_print) {
           KARATSUBA_MUL_CUTOFF = INT_MAX;
           KARATSUBA_SQR_CUTOFF = INT_MAX;
           TOOM_MUL_CUTOFF = INT_MAX;
           TOOM_SQR_CUTOFF = INT_MAX;
           t1 = s_time_mul(x);
           KARATSUBA_MUL_CUTOFF = kss;
           KARATSUBA_SQR_CUTOFF = ksm;
           TOOM_MUL_CUTOFF = tc3m;
           TOOM_SQR_CUTOFF = tc3s;
           t2 = s_time_mul(x);
           fprintf(multiplying, "%d: %9"PRIu64" %9"PRIu64", %9"PRIi64"\n", x, t1, t2, (int64_t)t2 - (int64_t)t1);
           fflush(multiplying);
           if (verbose == 1) {
              printf("MUL %d: %9"PRIu64" %9"PRIu64", %9"PRIi64"\n", x, t1, t2, (int64_t)t2 - (int64_t)t1);
              fflush(stdout);
           }
           KARATSUBA_MUL_CUTOFF = INT_MAX;
           KARATSUBA_SQR_CUTOFF = INT_MAX;
           TOOM_MUL_CUTOFF = INT_MAX;
           TOOM_SQR_CUTOFF = INT_MAX;
           t1 = s_time_sqr(x);
           KARATSUBA_MUL_CUTOFF = kss;
           KARATSUBA_SQR_CUTOFF = ksm;
           TOOM_MUL_CUTOFF = tc3m;
           TOOM_SQR_CUTOFF = tc3s;
           t2 = s_time_sqr(x);
           fprintf(squaring,"%d: %9"PRIu64" %9"PRIu64", %9"PRIi64"\n", x, t1, t2, (int64_t)t2 - (int64_t)t1);
           fflush(squaring);
           if (verbose == 1) {
              printf("SQR %d: %9"PRIu64" %9"PRIu64", %9"PRIi64"\n", x, t1, t2, (int64_t)t2 - (int64_t)t1);
              fflush(stdout);
           }
        }
        printf("Finished. Data for graphing in \"%s\" and \"%s\"\n",mullog, sqrlog);
        if (verbose == 1) {
           KARATSUBA_MUL_CUTOFF = kss;
           KARATSUBA_SQR_CUTOFF = ksm;
           TOOM_MUL_CUTOFF = tc3m;
           TOOM_SQR_CUTOFF = tc3s;
           if (terse == 1) {
              printf("%d %d %d %d\n",
                     KARATSUBA_MUL_CUTOFF,
                     KARATSUBA_SQR_CUTOFF,
                     TOOM_MUL_CUTOFF,
                     TOOM_SQR_CUTOFF);
           } else {
              printf("KARATSUBA_MUL_CUTOFF = %d\n", KARATSUBA_MUL_CUTOFF);
              printf("KARATSUBA_SQR_CUTOFF = %d\n", KARATSUBA_SQR_CUTOFF);
              printf("TOOM_MUL_CUTOFF = %d\n", TOOM_MUL_CUTOFF);
              printf("TOOM_SQR_CUTOFF = %d\n", TOOM_SQR_CUTOFF);
           }
        }
     }
     exit(EXIT_SUCCESS);
  }
  

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