/* Tune the Karatsuba parameters
*
* Tom St Denis, tstdenis82@gmail.com
*/
#include "../tommath.h"
#include "../tommath_private.h"
#include <time.h>
#include <inttypes.h>
#include <errno.h>
/*
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.
*/
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);
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 = mp_rand(&a, size * s_offset)) != MP_OKAY) {
t1 = UINT64_MAX;
goto LTM_ERR;
}
if ((e = mp_rand(&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 = mp_rand(&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;
}
struct tune_args {
int testmode;
int verbose;
int print;
int bncore;
int terse;
int upper_limit_print;
int increment_print;
} args;
static void s_run(const char *name, uint64_t (*op)(int), int *cutoff)
{
int x, count = 0;
uint64_t t1, t2;
if ((args.verbose == 1) || (args.testmode == 1)) {
printf("# %s.\n", name);
}
for (x = 8; x < args.upper_limit_print; x += args.increment_print) {
*cutoff = INT_MAX;
t1 = op(x);
if ((t1 == 0uLL) || (t1 == UINT64_MAX)) {
fprintf(stderr,"%s failed at x = INT_MAX (%s)\n", name,
(t1 == 0uLL)?"wrong result":"internal error");
exit(EXIT_FAILURE);
}
*cutoff = x;
t2 = op(x);
if ((t2 == 0uLL) || (t2 == UINT64_MAX)) {
fprintf(stderr,"%s failed (%s)\n", name,
(t2 == 0uLL)?"wrong result":"internal error");
exit(EXIT_FAILURE);
}
if (args.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--;
}
}
*cutoff = x - s_stabilization_extra * args.increment_print;
}
static long s_strtol(const char *str, char **endptr, const char *err)
{
const int base = 10;
char *_endptr;
long val;
errno = 0;
val = strtol(str, &_endptr, base);
if ((val > INT_MAX || val < 0) || (errno != 0)) {
fprintf(stderr, "Value %s not usable\n", str);
exit(EXIT_FAILURE);
}
if (_endptr == str) {
fprintf(stderr, "%s\n", err);
exit(EXIT_FAILURE);
}
if (endptr) *endptr = _endptr;
return val;
}
static int s_exit_code = EXIT_FAILURE;
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 space (0x20) 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");
exit(s_exit_code);
}
struct cutoffs {
int KARATSUBA_MUL, KARATSUBA_SQR;
int TOOM_MUL, TOOM_SQR;
};
const struct cutoffs max_cutoffs =
{ INT_MAX, INT_MAX, INT_MAX, INT_MAX };
static void set_cutoffs(const struct cutoffs *c)
{
KARATSUBA_MUL_CUTOFF = c->KARATSUBA_MUL;
KARATSUBA_SQR_CUTOFF = c->KARATSUBA_SQR;
TOOM_MUL_CUTOFF = c->TOOM_MUL;
TOOM_SQR_CUTOFF = c->TOOM_SQR;
}
static void get_cutoffs(struct cutoffs *c)
{
c->KARATSUBA_MUL = KARATSUBA_MUL_CUTOFF;
c->KARATSUBA_SQR = KARATSUBA_SQR_CUTOFF;
c->TOOM_MUL = TOOM_MUL_CUTOFF;
c->TOOM_SQR = TOOM_SQR_CUTOFF;
}
int main(int argc, char **argv)
{
uint64_t t1, t2;
int x, i, j;
size_t n;
int printpreset = 0;
/*int preset[8];*/
char *endptr, *str;
uint64_t seed = 0xdeadbeef;
int opt;
struct cutoffs orig, updated;
FILE *squaring, *multiplying;
char mullog[256] = "multiplying";
char sqrlog[256] = "squaring";
s_number_of_test_loops = 64;
s_stabilization_extra = 3;
MP_ZERO_BUFFER(&args, sizeof(args));
args.testmode = 0;
args.verbose = 0;
args.print = 0;
args.bncore = 0;
args.terse = 0;
args.upper_limit_print = 3000;
args.increment_print = 1;
/* 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':
args.testmode = 1;
s_check_result = 1;
args.upper_limit_print = 1000;
args.increment_print = 11;
s_number_of_test_loops = 1;
s_stabilization_extra = 1;
s_offset = 1;
break;
case 'v':
args.verbose = 1;
break;
case 'c':
s_check_result = 1;
break;
case 'p':
args.print = 1;
break;
case 'G':
args.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':
args.bncore = 1;
break;
case 't':
args.terse = 1;
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];
KARATSUBA_MUL_CUTOFF = (int)s_strtol(str, &endptr, "[1/4] No value for KARATSUBA_MUL_CUTOFF given");
str = endptr + 1;
KARATSUBA_SQR_CUTOFF = (int)s_strtol(str, &endptr, "[2/4] No value for KARATSUBA_SQR_CUTOFF given");
str = endptr + 1;
TOOM_MUL_CUTOFF = (int)s_strtol(str, &endptr, "[3/4] No value for TOOM_MUL_CUTOFF given");
str = endptr + 1;
TOOM_SQR_CUTOFF = (int)s_strtol(str, &endptr, "[4/4] No value for TOOM_SQR_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);
} test[] = {
#define T_MUL_SQR(n, o, f) { #n, &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", KARATSUBA_MUL, s_time_mul),
T_MUL_SQR("Karatsuba squaring", KARATSUBA_SQR, s_time_sqr),
T_MUL_SQR("Toom-Cook 3-way multiplying", TOOM_MUL, s_time_mul),
T_MUL_SQR("Toom-Cook 3-way squaring", TOOM_SQR, 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) {
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.KARATSUBA_MUL,
updated.KARATSUBA_SQR,
updated.TOOM_MUL,
updated.TOOM_SQR);
} else {
printf("KARATSUBA_MUL_CUTOFF = %d\n", updated.KARATSUBA_MUL);
printf("KARATSUBA_SQR_CUTOFF = %d\n", updated.KARATSUBA_SQR);
printf("TOOM_MUL_CUTOFF = %d\n", updated.TOOM_MUL);
printf("TOOM_SQR_CUTOFF = %d\n", updated.TOOM_SQR);
}
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",
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);
}
