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Addition of 2,3,5 mixed radix NTT #613

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a3d42ad
Addition of 2,3,5 mixed radix NTT
Oct 15, 2026
63342f5
Repairs #1
Oct 16, 2026
5b3d80b
Repairs #2
Oct 16, 2026
85decc2
some style corrections
Oct 16, 2026
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69 changes: 68 additions & 1 deletion demo/test.c
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Original file line number Diff line number Diff line change
Expand Up @@ -2142,8 +2142,71 @@ static int test_s_mp_sqr_toom(void)
mp_clear_multi(&a, &b, &c, NULL);
return EXIT_FAILURE;
}
#if (MP_DIGIT_BIT > 16)
static int test_s_mp_mul_ntt(void)
{
mp_int a, b, c, d;
int size;

#if (MP_DIGIT_BIT == 60)
int tc_cutoff;
#endif

DOR(mp_init_multi(&a, &b, &c, &d, NULL));
/* This number construction is limb-size specific */
#if (MP_DIGIT_BIT == 60)
DO(mp_rand(&a, 1196));
DO(mp_mul_2d(&a,71787 - mp_count_bits(&a), &a));

DO(mp_rand(&b, 1338));
DO(mp_mul_2d(&b, 80318 - mp_count_bits(&b), &b));
DO(mp_mul_2d(&b, 6310, &b));
DO(mp_2expt(&c, 99000 - 1000));
DO(mp_add(&b, &c, &b));

tc_cutoff = MP_MUL_NTT_CUTOFF;
MP_MUL_NTT_CUTOFF = INT_MAX;
DO(mp_mul(&a, &b, &c));
MP_MUL_NTT_CUTOFF = tc_cutoff;
DO(mp_mul(&a, &b, &d));
EXPECT(mp_cmp(&c, &d) == MP_EQ);
#endif

for (size = MP_MUL_NTT_CUTOFF; size < (MP_MUL_NTT_CUTOFF + 20); size++) {
DO(mp_rand(&a, size));
DO(mp_rand(&b, size));
DO(s_mp_mul_ntt(&a, &b, &c));
DO(s_mp_mul_full(&a,&b,&d));
EXPECT(mp_cmp(&c, &d) == MP_EQ);
}

mp_clear_multi(&a, &b, &c, &d, NULL);
return EXIT_SUCCESS;
LBL_ERR:
mp_clear_multi(&a, &b, &c, &d, NULL);
return EXIT_FAILURE;
}

static int test_s_mp_sqr_ntt(void)
{
mp_int a, b, c;
int size;

DOR(mp_init_multi(&a, &b, &c, NULL));
for (size = MP_SQR_NTT_CUTOFF; size < (MP_SQR_NTT_CUTOFF + 20); size++) {
DO(mp_rand(&a, size));
DO(s_mp_sqr_ntt(&a, &b));
DO(s_mp_sqr(&a, &c));
EXPECT(mp_cmp(&b, &c) == MP_EQ);
}

mp_clear_multi(&a, &b, &c, NULL);
return EXIT_SUCCESS;
LBL_ERR:
mp_clear_multi(&a, &b, &c, NULL);
return EXIT_FAILURE;
}
#endif
static int test_mp_radix_size(void)
{
mp_int a;
Expand Down Expand Up @@ -2606,7 +2669,11 @@ static int unit_tests(int argc, char **argv)
T2(s_mp_mul_karatsuba, ONLY_PUBLIC_API, S_MP_MUL_KARATSUBA),
T2(s_mp_sqr_karatsuba, ONLY_PUBLIC_API, S_MP_SQR_KARATSUBA),
T2(s_mp_mul_toom, ONLY_PUBLIC_API, S_MP_MUL_TOOM),
T2(s_mp_sqr_toom, ONLY_PUBLIC_API, S_MP_SQR_TOOM)
T2(s_mp_sqr_toom, ONLY_PUBLIC_API, S_MP_SQR_TOOM),
#if (MP_DIGIT_BIT > 16)
T2(s_mp_mul_ntt, ONLY_PUBLIC_API, S_MP_MUL_NTT),
T2(s_mp_sqr_ntt, ONLY_PUBLIC_API, S_MP_SQR_NTT)
#endif
#undef T3
#undef T2
#undef T1
Expand Down
86 changes: 58 additions & 28 deletions etc/tune.c
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Original file line number Diff line number Diff line change
Expand Up @@ -20,8 +20,8 @@
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 uint64_t s_time_mul(int size, int increment);
static uint64_t s_time_sqr(int size, int increment);
static void s_usage(char *s);

static uint64_t s_timer_function(void)
Expand Down Expand Up @@ -61,7 +61,7 @@ static int s_stabilization_extra;
static int s_offset = 1;

#define s_mp_mul_full(a, b, c) s_mp_mul(a, b, c, (a)->used + (b)->used + 1)
static uint64_t s_time_mul(int size)
static uint64_t s_time_mul(int size, int increment)
{
int x;
mp_err e;
Expand All @@ -83,7 +83,7 @@ static uint64_t s_time_mul(int size)
}

s_timer_start();
for (x = 0; x < s_number_of_test_loops; x++) {
for (x = 0; x < s_number_of_test_loops; x += increment) {
if ((e = mp_mul(&a,&b,&c)) != MP_OKAY) {
t1 = UINT64_MAX;
goto LBL_ERR;
Expand All @@ -107,7 +107,7 @@ static uint64_t s_time_mul(int size)
return t1;
}

static uint64_t s_time_sqr(int size)
static uint64_t s_time_sqr(int size, int increment)
{
int x;
mp_err e;
Expand All @@ -125,7 +125,7 @@ static uint64_t s_time_sqr(int size)
}

s_timer_start();
for (x = 0; x < s_number_of_test_loops; x++) {
for (x = 0; x < s_number_of_test_loops; x+=increment) {
if ((e = mp_sqr(&a,&b)) != MP_OKAY) {
t1 = UINT64_MAX;
goto LBL_ERR;
Expand Down Expand Up @@ -158,7 +158,7 @@ struct tune_args {
int increment_print;
} args;

static void s_run(const char *name, uint64_t (*op)(int size), int *cutoff)
static void s_run(const char *name, uint64_t (*op)(int size, int increment), int *cutoff, int increment)
{
int x, count = 0;
uint64_t t1, t2;
Expand All @@ -167,14 +167,14 @@ static void s_run(const char *name, uint64_t (*op)(int size), int *cutoff)
}
for (x = 8; x < args.upper_limit_print; x += args.increment_print) {
*cutoff = INT_MAX;
t1 = op(x);
t1 = op(x, increment);
if ((t1 == 0u) || (t1 == UINT64_MAX)) {
fprintf(stderr,"%s failed at x = INT_MAX (%s)\n", name,
(t1 == 0u)?"wrong result":"internal error");
exit(EXIT_FAILURE);
}
*cutoff = x;
t2 = op(x);
t2 = op(x, increment);
if ((t2 == 0u) || (t2 == UINT64_MAX)) {
fprintf(stderr,"%s failed (%s)\n", name,
(t2 == 0u)?"wrong result":"internal error");
Expand Down Expand Up @@ -243,6 +243,8 @@ static void s_usage(char *s)
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," nttm = NTT multiplication\n");
fprintf(stderr," ntts = NTT squaring\n");
fprintf(stderr," Implies '-p'\n");
fprintf(stderr," -h this message\n");
exit(s_exit_code);
Expand All @@ -251,17 +253,20 @@ static void s_usage(char *s)
struct cutoffs {
int MUL_KARATSUBA, SQR_KARATSUBA;
int MUL_TOOM, SQR_TOOM;
int MUL_NTT, SQR_NTT;
};

const struct cutoffs max_cutoffs =
{ INT_MAX, INT_MAX, INT_MAX, INT_MAX };
{ INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX, INT_MAX};

static void set_cutoffs(const struct cutoffs *c)
{
MP_MUL_KARATSUBA_CUTOFF = c->MUL_KARATSUBA;
MP_SQR_KARATSUBA_CUTOFF = c->SQR_KARATSUBA;
MP_MUL_TOOM_CUTOFF = c->MUL_TOOM;
MP_SQR_TOOM_CUTOFF = c->SQR_TOOM;
MP_MUL_NTT_CUTOFF = c->MUL_NTT;
MP_SQR_NTT_CUTOFF = c->SQR_NTT;
}

static void get_cutoffs(struct cutoffs *c)
Expand All @@ -270,7 +275,8 @@ static void get_cutoffs(struct cutoffs *c)
c->SQR_KARATSUBA = MP_SQR_KARATSUBA_CUTOFF;
c->MUL_TOOM = MP_MUL_TOOM_CUTOFF;
c->SQR_TOOM = MP_SQR_TOOM_CUTOFF;

c->MUL_NTT = MP_MUL_NTT_CUTOFF;
c->SQR_NTT = MP_SQR_NTT_CUTOFF;
}

int main(int argc, char **argv)
Expand Down Expand Up @@ -302,7 +308,7 @@ int main(int argc, char **argv)
args.bncore = 0;
args.terse = 0;

args.upper_limit_print = 3000;
args.upper_limit_print = 20000;
args.increment_print = 1;

/* Very simple option parser, please treat it nicely. */
Expand Down Expand Up @@ -423,6 +429,10 @@ int main(int argc, char **argv)
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");
str = endptr + 1;
MP_MUL_NTT_CUTOFF = (int)s_strtol(str, &endptr, "[3/4] No value for MP_MUL_NTT_CUTOFF given");
str = endptr + 1;
MP_SQR_NTT_CUTOFF = (int)s_strtol(str, &endptr, "[4/4] No value for MP_SQR_NTT_CUTOFF given");
break;
case 'h':
s_exit_code = EXIT_SUCCESS;
Expand All @@ -448,7 +458,7 @@ int main(int argc, char **argv)
struct {
const char *name;
int *cutoff, *update;
uint64_t (*fn)(int size);
uint64_t (*fn)(int size, int increment);
} test[] = {
#define T_MUL_SQR(n, o, f) { #n, &MP_##o##_CUTOFF, &(updated.o), MP_HAS(S_MP_##o) ? f : NULL }
/*
Expand All @@ -457,33 +467,49 @@ int main(int argc, char **argv)
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),
T_MUL_SQR("Karatsuba multiplication", MUL_KARATSUBA, s_time_mul), /* 0 */
T_MUL_SQR("Karatsuba squaring", SQR_KARATSUBA, s_time_sqr), /* 1 */
T_MUL_SQR("Toom-Cook 3-way multiplying", MUL_TOOM, s_time_mul), /* 2 */
T_MUL_SQR("Toom-Cook 3-way squaring", SQR_TOOM, s_time_sqr), /* 3 */
T_MUL_SQR("NTT multiplying", MUL_NTT, s_time_mul), /* 4 */
T_MUL_SQR("NTT squaring", SQR_NTT, s_time_sqr), /* 5 */
#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) {
for (n = 0; n < 4; ++n) {
if (test[n].fn != NULL) {
s_run(test[n].name, test[n].fn, test[n].cutoff, 1);
*test[n].update = *test[n].cutoff;
/* *test[n].cutoff = INT_MAX; */
}
}
for (n = 4; n < 6; ++n) {
if (test[n].fn != NULL) {
s_run(test[n].name, test[n].fn, test[n].cutoff);
s_run(test[n].name, test[n].fn, test[n].cutoff, 53);
*test[n].update = *test[n].cutoff;
*test[n].cutoff = INT_MAX;
/* Only test Karatsuba against school,
test the rest against the cutoff one lower */
/* *test[n].cutoff = INT_MAX; */
}
}
}
if (args.terse == 1) {
printf("%d %d %d %d\n",
printf("%d %d %d %d %d %d\n",
updated.MUL_KARATSUBA,
updated.SQR_KARATSUBA,
updated.MUL_TOOM,
updated.SQR_TOOM);
updated.SQR_TOOM,
updated.MUL_NTT,
updated.SQR_NTT);

} 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);
printf("MUL_NTT_CUTOFF = %d\n", updated.MUL_NTT);
printf("SQR_NTT_CUTOFF = %d\n", updated.SQR_NTT);
}

if (args.print == 1) {
Expand All @@ -503,19 +529,19 @@ int main(int argc, char **argv)

for (x = 8; x < args.upper_limit_print; x += args.increment_print) {
set_cutoffs(&max_cutoffs);
t1 = s_time_mul(x);
t1 = s_time_mul(x,1);
set_cutoffs(&orig);
t2 = s_time_mul(x);
t2 = s_time_mul(x,1);
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);
t1 = s_time_sqr(x,1);
set_cutoffs(&orig);
t2 = s_time_sqr(x);
t2 = s_time_sqr(x,1);
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) {
Expand All @@ -527,16 +553,20 @@ int main(int argc, char **argv)
if (args.verbose == 1) {
set_cutoffs(&orig);
if (args.terse == 1) {
printf("%d %d %d %d\n",
printf("%d %d %d %d %d %d\n",
MP_MUL_KARATSUBA_CUTOFF,
MP_SQR_KARATSUBA_CUTOFF,
MP_MUL_TOOM_CUTOFF,
MP_SQR_TOOM_CUTOFF);
MP_SQR_TOOM_CUTOFF,
MP_MUL_NTT_CUTOFF,
MP_SQR_NTT_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);
printf("MUL_NTT_CUTOFF = %d\n", MP_MUL_NTT_CUTOFF);
printf("SQR_NTT_CUTOFF = %d\n", MP_SQR_NTT_CUTOFF);
}
}
}
Expand Down
26 changes: 22 additions & 4 deletions etc/tune_it.sh
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Original file line number Diff line number Diff line change
Expand Up @@ -33,10 +33,12 @@ RNUM=0
# test are running if you do not have enough memory to avoid page faults. #
#############################################################################

# TODO: Because of NTT the defaults of LIMIT is down from 100, RLOOPS down from 10
# and LAG is up from 3
# Number of rounds overall.
LIMIT=100
LIMIT=10
# Number of loops for each input.
RLOOPS=10
RLOOPS=3
# Offset ( > 0 ) . Runs tests with asymmetric input of the form 1:OFFSET
# Please use another destination for TOMMATH_CUTOFFS_H if you change OFFSET, because the numbers
# with an offset different from 1 (one) are not usable as the general cut-off values
Expand All @@ -45,7 +47,7 @@ OFFSET=1
# Number ( >= 3 ) of positive results (TC-is-faster) accumulated until it is accepted.
# Due to the algorithm used to compute the median in this Posix compliant shell script
# the value needs to be 3 (three), not less, to keep the variation small.
LAG=3
LAG=100
# Keep the temporary file $FILE_NAME. Set to 0 (zero) to remove it at the end.
# The file is in a format fit to feed into R directly. If you do it and find the median
# of this program to be off by more than a couple: please contact the authors and report
Expand All @@ -56,7 +58,7 @@ KEEP_TEMP=1
echo "You might like to watch the numbers go up to $LIMIT but it will take a long time!"

# Might not have sufficient rights or disc full.
echo "km ks tc3m tc3s" > $FILE_NAME || die "Writing header to $FILE_NAME" $?
echo "km ks tc3m tc3s nttm ntts" > $FILE_NAME || die "Writing header to $FILE_NAME" $?
i=1
while [ $i -le $LIMIT ]; do
RNUM=$(LCG)
Expand Down Expand Up @@ -104,3 +106,19 @@ echo "#define MP_DEFAULT_MUL_TOOM_CUTOFF $TMP" >> $TOMMATH_CUTOFFS_H || die
TMP=$(median $FILE_NAME 4 $i)
echo "#define MP_DEFAULT_SQR_TOOM_CUTOFF $TMP"
echo "#define MP_DEFAULT_SQR_TOOM_CUTOFF $TMP" >> $TOMMATH_CUTOFFS_H || die "(tc3s) Appending to $TOMMATH_CUTOFFS_H" $?
TMP=$(median $FILE_NAME 5 $i)
echo "#define MP_DEFAULT_MUL_NTT_CUTOFF $TMP"
echo "#define MP_DEFAULT_MUL_NTT_CUTOFF $TMP" >> $TOMMATH_CUTOFFS_H || die "(nttm) Appending to $TOMMATH_CUTOFFS_H" $?
TMP=$(median $FILE_NAME 6 $i)
echo "#define MP_DEFAULT_SQR_NTT_CUTOFF $TMP"
echo "#define MP_DEFAULT_SQR_NTT_CUTOFF $TMP" >> $TOMMATH_CUTOFFS_H || die "(ntts) Appending to $TOMMATH_CUTOFFS_H" $?










2 changes: 2 additions & 0 deletions helper.pl
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -480,6 +480,8 @@ sub generate_def {
MP_SQR_KARATSUBA_CUTOFF
MP_MUL_TOOM_CUTOFF
MP_SQR_TOOM_CUTOFF
MP_MUL_NTT_CUTOFF
MP_SQR_NTT_CUTOFF
";
return 0;
}
Expand Down
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