545 lines
16 KiB
C
545 lines
16 KiB
C
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/* Tune the Karatsuba parameters
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*
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* Tom St Denis, tstdenis82@gmail.com
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*/
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#include "tommath_private.h"
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#include <time.h>
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#include <inttypes.h>
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#include <errno.h>
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#define S_MP_RAND_JENKINS_C
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#include "../demo/s_mp_rand_jenkins.c"
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/*
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Please take in mind that both multiplicands are of the same size. The balancing
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mechanism in mp_balance works well but has some overhead itself. You can test
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the behaviour of it with the option "-o" followed by a (small) positive number 'x'
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to generate ratios of the form 1:x.
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*/
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static uint64_t s_timer_function(void);
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static void s_timer_start(void);
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static uint64_t s_timer_stop(void);
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static uint64_t s_time_mul(int size);
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static uint64_t s_time_sqr(int size);
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static void s_usage(char *s);
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static uint64_t s_timer_function(void)
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{
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#if _POSIX_C_SOURCE >= 199309L
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#define LTM_BILLION 1000000000
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struct timespec ts;
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/* TODO: Sets errno in case of error. Use? */
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clock_gettime(CLOCK_MONOTONIC, &ts);
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return (((uint64_t)ts.tv_sec) * LTM_BILLION + (uint64_t)ts.tv_nsec);
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#else
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clock_t t;
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t = clock();
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if (t < (clock_t)(0)) {
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return (uint64_t)(0);
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}
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return (uint64_t)(t);
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#endif
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}
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/* generic ISO C timer */
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static uint64_t s_timer_tmp;
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static void s_timer_start(void)
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{
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s_timer_tmp = s_timer_function();
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}
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static uint64_t s_timer_stop(void)
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{
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return s_timer_function() - s_timer_tmp;
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}
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static int s_check_result;
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static int s_number_of_test_loops;
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static int s_stabilization_extra;
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static int s_offset = 1;
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#define s_mp_mul_full(a, b, c) s_mp_mul(a, b, c, (a)->used + (b)->used + 1)
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static uint64_t s_time_mul(int size)
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{
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int x;
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mp_err e;
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mp_int a, b, c, d;
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uint64_t t1;
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if ((e = mp_init_multi(&a, &b, &c, &d, NULL)) != MP_OKAY) {
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t1 = UINT64_MAX;
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goto LBL_ERR;
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}
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if ((e = mp_rand(&a, size * s_offset)) != MP_OKAY) {
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t1 = UINT64_MAX;
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goto LBL_ERR;
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}
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if ((e = mp_rand(&b, size)) != MP_OKAY) {
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t1 = UINT64_MAX;
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goto LBL_ERR;
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}
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s_timer_start();
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for (x = 0; x < s_number_of_test_loops; x++) {
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if ((e = mp_mul(&a,&b,&c)) != MP_OKAY) {
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t1 = UINT64_MAX;
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goto LBL_ERR;
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}
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if (s_check_result == 1) {
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if ((e = s_mp_mul_full(&a,&b,&d)) != MP_OKAY) {
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t1 = UINT64_MAX;
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goto LBL_ERR;
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}
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if (mp_cmp(&c, &d) != MP_EQ) {
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/* Time of 0 cannot happen (famous last words?) */
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t1 = 0u;
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goto LBL_ERR;
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}
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}
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}
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t1 = s_timer_stop();
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LBL_ERR:
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mp_clear_multi(&a, &b, &c, &d, NULL);
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return t1;
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}
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static uint64_t s_time_sqr(int size)
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{
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int x;
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mp_err e;
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mp_int a, b, c;
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uint64_t t1;
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if ((e = mp_init_multi(&a, &b, &c, NULL)) != MP_OKAY) {
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t1 = UINT64_MAX;
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goto LBL_ERR;
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}
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if ((e = mp_rand(&a, size)) != MP_OKAY) {
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t1 = UINT64_MAX;
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goto LBL_ERR;
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}
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s_timer_start();
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for (x = 0; x < s_number_of_test_loops; x++) {
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if ((e = mp_sqr(&a,&b)) != MP_OKAY) {
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t1 = UINT64_MAX;
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goto LBL_ERR;
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}
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if (s_check_result == 1) {
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if ((e = s_mp_sqr(&a,&c)) != MP_OKAY) {
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t1 = UINT64_MAX;
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goto LBL_ERR;
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}
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if (mp_cmp(&c, &b) != MP_EQ) {
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t1 = 0u;
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goto LBL_ERR;
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}
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}
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}
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t1 = s_timer_stop();
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LBL_ERR:
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mp_clear_multi(&a, &b, &c, NULL);
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return t1;
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}
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struct tune_args {
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int testmode;
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int verbose;
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int print;
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int bncore;
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int terse;
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int upper_limit_print;
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int increment_print;
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} args;
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static void s_run(const char *name, uint64_t (*op)(int size), int *cutoff)
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{
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int x, count = 0;
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uint64_t t1, t2;
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if ((args.verbose == 1) || (args.testmode == 1)) {
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printf("# %s.\n", name);
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}
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for (x = 8; x < args.upper_limit_print; x += args.increment_print) {
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*cutoff = INT_MAX;
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t1 = op(x);
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if ((t1 == 0u) || (t1 == UINT64_MAX)) {
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fprintf(stderr,"%s failed at x = INT_MAX (%s)\n", name,
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(t1 == 0u)?"wrong result":"internal error");
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exit(EXIT_FAILURE);
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}
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*cutoff = x;
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t2 = op(x);
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if ((t2 == 0u) || (t2 == UINT64_MAX)) {
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fprintf(stderr,"%s failed (%s)\n", name,
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(t2 == 0u)?"wrong result":"internal error");
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exit(EXIT_FAILURE);
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}
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if (args.verbose == 1) {
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printf("%d: %9" PRIu64 " %9" PRIu64 ", %9" PRIi64 "\n", x, t1, t2, (int64_t)t2 - (int64_t)t1);
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}
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if (t2 < t1) {
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if (count == s_stabilization_extra) {
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count = 0;
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break;
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} else if (count < s_stabilization_extra) {
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count++;
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}
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} else if (count > 0) {
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count--;
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}
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}
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*cutoff = x - s_stabilization_extra * args.increment_print;
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}
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static long s_strtol(const char *str, char **endptr, const char *err)
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{
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const int base = 10;
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char *_endptr;
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long val;
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errno = 0;
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val = strtol(str, &_endptr, base);
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if ((val > INT_MAX || val < 0) || (errno != 0)) {
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fprintf(stderr, "Value %s not usable\n", str);
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exit(EXIT_FAILURE);
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}
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if (_endptr == str) {
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fprintf(stderr, "%s\n", err);
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exit(EXIT_FAILURE);
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}
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if (endptr != NULL) *endptr = _endptr;
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return val;
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}
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static int s_exit_code = EXIT_FAILURE;
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static void s_usage(char *s)
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{
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fprintf(stderr,"Usage: %s [TvcpGbtrSLFfMmosh]\n",s);
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fprintf(stderr," -T testmode, for use with testme.sh\n");
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fprintf(stderr," -v verbose, print all timings\n");
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fprintf(stderr," -c check results\n");
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fprintf(stderr," -p print benchmark of final cutoffs in files \"multiplying\"\n");
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fprintf(stderr," and \"squaring\"\n");
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fprintf(stderr," -G [string] suffix for the filenames listed above\n");
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fprintf(stderr," Implies '-p'\n");
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fprintf(stderr," -b print benchmark of bncore.c\n");
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fprintf(stderr," -t prints space (0x20) separated results\n");
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fprintf(stderr," -r [64] number of rounds\n");
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fprintf(stderr," -S [0xdeadbeef] seed for PRNG\n");
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fprintf(stderr," -L [3] number of negative values accumulated until the result is accepted\n");
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fprintf(stderr," -M [3000] upper limit of T-C tests/prints\n");
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fprintf(stderr," -m [1] increment of T-C tests/prints\n");
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fprintf(stderr," -o [1] multiplier for the second multiplicand\n");
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fprintf(stderr," (Not for computing the cut-offs!)\n");
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fprintf(stderr," -s 'preset' use values in 'preset' for printing.\n");
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fprintf(stderr," 'preset' is a comma separated string with cut-offs for\n");
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fprintf(stderr," ksm, kss, tc3m, tc3s in that order\n");
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fprintf(stderr," ksm = karatsuba multiplication\n");
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fprintf(stderr," kss = karatsuba squaring\n");
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fprintf(stderr," tc3m = Toom-Cook 3-way multiplication\n");
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fprintf(stderr," tc3s = Toom-Cook 3-way squaring\n");
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fprintf(stderr," Implies '-p'\n");
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fprintf(stderr," -h this message\n");
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exit(s_exit_code);
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}
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struct cutoffs {
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int MUL_KARATSUBA, SQR_KARATSUBA;
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int MUL_TOOM, SQR_TOOM;
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};
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const struct cutoffs max_cutoffs =
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{ INT_MAX, INT_MAX, INT_MAX, INT_MAX };
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static void set_cutoffs(const struct cutoffs *c)
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{
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MP_MUL_KARATSUBA_CUTOFF = c->MUL_KARATSUBA;
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MP_SQR_KARATSUBA_CUTOFF = c->SQR_KARATSUBA;
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MP_MUL_TOOM_CUTOFF = c->MUL_TOOM;
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MP_SQR_TOOM_CUTOFF = c->SQR_TOOM;
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}
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static void get_cutoffs(struct cutoffs *c)
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{
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c->MUL_KARATSUBA = MP_MUL_KARATSUBA_CUTOFF;
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c->SQR_KARATSUBA = MP_SQR_KARATSUBA_CUTOFF;
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c->MUL_TOOM = MP_MUL_TOOM_CUTOFF;
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c->SQR_TOOM = MP_SQR_TOOM_CUTOFF;
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}
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int main(int argc, char **argv)
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{
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uint64_t t1, t2;
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int x, i, j;
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size_t n;
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int printpreset = 0;
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/*int preset[8];*/
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char *endptr, *str;
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uint64_t seed = 0xdeadbeefULL;
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int opt;
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struct cutoffs orig, updated;
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FILE *squaring, *multiplying;
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char mullog[256] = "multiplying";
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char sqrlog[256] = "squaring";
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s_number_of_test_loops = 64;
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s_stabilization_extra = 3;
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s_mp_zero_buf(&args, sizeof(args));
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args.testmode = 0;
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args.verbose = 0;
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args.print = 0;
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args.bncore = 0;
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args.terse = 0;
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args.upper_limit_print = 3000;
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args.increment_print = 1;
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/* Very simple option parser, please treat it nicely. */
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if (argc != 1) {
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for (opt = 1; (opt < argc) && (argv[opt][0] == '-'); opt++) {
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switch (argv[opt][1]) {
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case 'T':
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args.testmode = 1;
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s_check_result = 1;
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args.upper_limit_print = 1000;
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args.increment_print = 11;
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s_number_of_test_loops = 1;
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s_stabilization_extra = 1;
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s_offset = 1;
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break;
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case 'v':
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args.verbose = 1;
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break;
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case 'c':
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s_check_result = 1;
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break;
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case 'p':
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args.print = 1;
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break;
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case 'G':
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args.print = 1;
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opt++;
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if (opt >= argc) {
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s_usage(argv[0]);
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}
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/* manual strcat() */
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for (i = 0; i < 255; i++) {
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if (mullog[i] == '\0') {
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break;
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}
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}
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for (j = 0; i < 255; j++, i++) {
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mullog[i] = argv[opt][j];
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if (argv[opt][j] == '\0') {
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break;
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}
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}
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for (i = 0; i < 255; i++) {
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if (sqrlog[i] == '\0') {
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break;
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}
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}
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for (j = 0; i < 255; j++, i++) {
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sqrlog[i] = argv[opt][j];
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if (argv[opt][j] == '\0') {
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break;
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}
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}
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break;
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case 'b':
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args.bncore = 1;
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break;
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case 't':
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args.terse = 1;
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break;
|
||
|
|
case 'S':
|
||
|
|
opt++;
|
||
|
|
if (opt >= argc) {
|
||
|
|
s_usage(argv[0]);
|
||
|
|
}
|
||
|
|
str = argv[opt];
|
||
|
|
errno = 0;
|
||
|
|
seed = (uint64_t)s_strtol(argv[opt], NULL, "No seed given?\n");
|
||
|
|
break;
|
||
|
|
case 'L':
|
||
|
|
opt++;
|
||
|
|
if (opt >= argc) {
|
||
|
|
s_usage(argv[0]);
|
||
|
|
}
|
||
|
|
s_stabilization_extra = (int)s_strtol(argv[opt], NULL, "No value for option \"-L\"given");
|
||
|
|
break;
|
||
|
|
case 'o':
|
||
|
|
opt++;
|
||
|
|
if (opt >= argc) {
|
||
|
|
s_usage(argv[0]);
|
||
|
|
}
|
||
|
|
s_offset = (int)s_strtol(argv[opt], NULL, "No value for the offset given");
|
||
|
|
break;
|
||
|
|
case 'r':
|
||
|
|
opt++;
|
||
|
|
if (opt >= argc) {
|
||
|
|
s_usage(argv[0]);
|
||
|
|
}
|
||
|
|
s_number_of_test_loops = (int)s_strtol(argv[opt], NULL, "No value for the number of rounds given");
|
||
|
|
break;
|
||
|
|
|
||
|
|
case 'M':
|
||
|
|
opt++;
|
||
|
|
if (opt >= argc) {
|
||
|
|
s_usage(argv[0]);
|
||
|
|
}
|
||
|
|
args.upper_limit_print = (int)s_strtol(argv[opt], NULL, "No value for the upper limit of T-C tests given");
|
||
|
|
break;
|
||
|
|
case 'm':
|
||
|
|
opt++;
|
||
|
|
if (opt >= argc) {
|
||
|
|
s_usage(argv[0]);
|
||
|
|
}
|
||
|
|
args.increment_print = (int)s_strtol(argv[opt], NULL, "No value for the increment for the T-C tests given");
|
||
|
|
break;
|
||
|
|
case 's':
|
||
|
|
printpreset = 1;
|
||
|
|
args.print = 1;
|
||
|
|
opt++;
|
||
|
|
if (opt >= argc) {
|
||
|
|
s_usage(argv[0]);
|
||
|
|
}
|
||
|
|
str = argv[opt];
|
||
|
|
MP_MUL_KARATSUBA_CUTOFF = (int)s_strtol(str, &endptr, "[1/4] No value for MP_MUL_KARATSUBA_CUTOFF given");
|
||
|
|
str = endptr + 1;
|
||
|
|
MP_SQR_KARATSUBA_CUTOFF = (int)s_strtol(str, &endptr, "[2/4] No value for MP_SQR_KARATSUBA_CUTOFF given");
|
||
|
|
str = endptr + 1;
|
||
|
|
MP_MUL_TOOM_CUTOFF = (int)s_strtol(str, &endptr, "[3/4] No value for MP_MUL_TOOM_CUTOFF given");
|
||
|
|
str = endptr + 1;
|
||
|
|
MP_SQR_TOOM_CUTOFF = (int)s_strtol(str, &endptr, "[4/4] No value for MP_SQR_TOOM_CUTOFF given");
|
||
|
|
break;
|
||
|
|
case 'h':
|
||
|
|
s_exit_code = EXIT_SUCCESS;
|
||
|
|
/* FALLTHROUGH */
|
||
|
|
default:
|
||
|
|
s_usage(argv[0]);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/*
|
||
|
|
mp_rand uses the cryptographically secure
|
||
|
|
source of the OS by default. That is too expensive, too slow and
|
||
|
|
most important for a benchmark: it is not repeatable.
|
||
|
|
*/
|
||
|
|
s_mp_rand_jenkins_init(seed);
|
||
|
|
mp_rand_source(s_mp_rand_jenkins);
|
||
|
|
|
||
|
|
get_cutoffs(&orig);
|
||
|
|
|
||
|
|
updated = max_cutoffs;
|
||
|
|
if ((args.bncore == 0) && (printpreset == 0)) {
|
||
|
|
struct {
|
||
|
|
const char *name;
|
||
|
|
int *cutoff, *update;
|
||
|
|
uint64_t (*fn)(int size);
|
||
|
|
} test[] = {
|
||
|
|
#define T_MUL_SQR(n, o, f) { #n, &MP_##o##_CUTOFF, &(updated.o), MP_HAS(S_MP_##o) ? f : NULL }
|
||
|
|
/*
|
||
|
|
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)).
|
||
|
|
*/
|
||
|
|
T_MUL_SQR("Karatsuba multiplication", MUL_KARATSUBA, s_time_mul),
|
||
|
|
T_MUL_SQR("Karatsuba squaring", SQR_KARATSUBA, s_time_sqr),
|
||
|
|
T_MUL_SQR("Toom-Cook 3-way multiplying", MUL_TOOM, s_time_mul),
|
||
|
|
T_MUL_SQR("Toom-Cook 3-way squaring", SQR_TOOM, s_time_sqr),
|
||
|
|
#undef T_MUL_SQR
|
||
|
|
};
|
||
|
|
/* Turn all limits from bncore.c to the max */
|
||
|
|
set_cutoffs(&max_cutoffs);
|
||
|
|
for (n = 0; n < sizeof(test)/sizeof(test[0]); ++n) {
|
||
|
|
if (test[n].fn != NULL) {
|
||
|
|
s_run(test[n].name, test[n].fn, test[n].cutoff);
|
||
|
|
*test[n].update = *test[n].cutoff;
|
||
|
|
*test[n].cutoff = INT_MAX;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
if (args.terse == 1) {
|
||
|
|
printf("%d %d %d %d\n",
|
||
|
|
updated.MUL_KARATSUBA,
|
||
|
|
updated.SQR_KARATSUBA,
|
||
|
|
updated.MUL_TOOM,
|
||
|
|
updated.SQR_TOOM);
|
||
|
|
} else {
|
||
|
|
printf("MUL_KARATSUBA_CUTOFF = %d\n", updated.MUL_KARATSUBA);
|
||
|
|
printf("SQR_KARATSUBA_CUTOFF = %d\n", updated.SQR_KARATSUBA);
|
||
|
|
printf("MUL_TOOM_CUTOFF = %d\n", updated.MUL_TOOM);
|
||
|
|
printf("SQR_TOOM_CUTOFF = %d\n", updated.SQR_TOOM);
|
||
|
|
}
|
||
|
|
|
||
|
|
if (args.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 < args.upper_limit_print; x += args.increment_print) {
|
||
|
|
set_cutoffs(&max_cutoffs);
|
||
|
|
t1 = s_time_mul(x);
|
||
|
|
set_cutoffs(&orig);
|
||
|
|
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 (args.verbose == 1) {
|
||
|
|
printf("MUL %d: %9" PRIu64 " %9" PRIu64 ", %9" PRIi64 "\n", x, t1, t2, (int64_t)t2 - (int64_t)t1);
|
||
|
|
fflush(stdout);
|
||
|
|
}
|
||
|
|
set_cutoffs(&max_cutoffs);
|
||
|
|
t1 = s_time_sqr(x);
|
||
|
|
set_cutoffs(&orig);
|
||
|
|
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 (args.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 (args.verbose == 1) {
|
||
|
|
set_cutoffs(&orig);
|
||
|
|
if (args.terse == 1) {
|
||
|
|
printf("%d %d %d %d\n",
|
||
|
|
MP_MUL_KARATSUBA_CUTOFF,
|
||
|
|
MP_SQR_KARATSUBA_CUTOFF,
|
||
|
|
MP_MUL_TOOM_CUTOFF,
|
||
|
|
MP_SQR_TOOM_CUTOFF);
|
||
|
|
} else {
|
||
|
|
printf("MUL_KARATSUBA_CUTOFF = %d\n", MP_MUL_KARATSUBA_CUTOFF);
|
||
|
|
printf("SQR_KARATSUBA_CUTOFF = %d\n", MP_SQR_KARATSUBA_CUTOFF);
|
||
|
|
printf("MUL_TOOM_CUTOFF = %d\n", MP_MUL_TOOM_CUTOFF);
|
||
|
|
printf("SQR_TOOM_CUTOFF = %d\n", MP_SQR_TOOM_CUTOFF);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
exit(EXIT_SUCCESS);
|
||
|
|
}
|