#include <inttypes.h>
#include "shared.h"
#define S_MP_RAND_JENKINS_C
#include "s_mp_rand_jenkins.c"
static long rand_long(void)
{
long x;
if (s_mp_rand_jenkins(&x, sizeof(x)) != MP_OKAY) {
fprintf(stderr, "s_mp_rand_source failed\n");
exit(EXIT_FAILURE);
}
return x;
}
static unsigned int rand_uint(void)
{
unsigned int x;
if (s_mp_rand_jenkins(&x, sizeof(x)) != MP_OKAY) {
fprintf(stderr, "s_mp_rand_source failed\n");
exit(EXIT_FAILURE);
}
return x;
}
static int rand_int(void)
{
return (int)rand_uint();
}
static int32_t rand_int32(void)
{
int32_t x;
if (s_mp_rand_jenkins(&x, sizeof(x)) != MP_OKAY) {
fprintf(stderr, "s_mp_rand_source failed\n");
exit(EXIT_FAILURE);
}
return x;
}
static int64_t rand_int64(void)
{
int64_t x;
if (s_mp_rand_jenkins(&x, sizeof(x)) != MP_OKAY) {
fprintf(stderr, "s_mp_rand_source failed\n");
exit(EXIT_FAILURE);
}
return x;
}
static uint32_t uabs32(int32_t x)
{
return (x > 0) ? (uint32_t)x : -(uint32_t)x;
}
static uint64_t uabs64(int64_t x)
{
return (x > 0) ? (uint64_t)x : -(uint64_t)x;
}
/* This function prototype is needed
* to test dead code elimination
* which is used for feature detection.
*
* If the feature detection does not
* work as desired we will get a linker error.
*/
void does_not_exist(void);
static int test_feature_detection(void)
{
#define TEST_FEATURE1_C
if (!MP_HAS(TEST_FEATURE1)) {
does_not_exist();
return EXIT_FAILURE;
}
#define TEST_FEATURE2_C 1
if (MP_HAS(TEST_FEATURE2)) {
does_not_exist();
return EXIT_FAILURE;
}
#define TEST_FEATURE3_C 0
if (MP_HAS(TEST_FEATURE3)) {
does_not_exist();
return EXIT_FAILURE;
}
#define TEST_FEATURE4_C something
if (MP_HAS(TEST_FEATURE4)) {
does_not_exist();
return EXIT_FAILURE;
}
if (MP_HAS(TEST_FEATURE5)) {
does_not_exist();
return EXIT_FAILURE;
}
return EXIT_SUCCESS;
}
static int test_trivial_stuff(void)
{
mp_int a, b, c, d;
DOR(mp_init_multi(&a, &b, &c, &d, NULL));
EXPECT(mp_error_to_string(MP_OKAY) != NULL);
/* a: 0->5 */
mp_set(&a, 5u);
/* a: 5-> b: -5 */
DO(mp_neg(&a, &b));
EXPECT(mp_cmp(&a, &b) == MP_GT);
EXPECT(mp_cmp(&b, &a) == MP_LT);
EXPECT(mp_isneg(&b));
/* a: 5-> a: -5 */
DO(mp_neg(&a, &a));
EXPECT(mp_cmp(&b, &a) == MP_EQ);
EXPECT(mp_isneg(&a));
/* a: -5-> b: 5 */
DO(mp_abs(&a, &b));
EXPECT(!mp_isneg(&b));
/* a: -5-> b: -4 */
DO(mp_add_d(&a, 1u, &b));
EXPECT(mp_isneg(&b));
EXPECT(mp_get_i32(&b) == -4);
EXPECT(mp_get_u32(&b) == (uint32_t)-4);
EXPECT(mp_get_mag_u32(&b) == 4);
/* a: -5-> b: 1 */
DO(mp_add_d(&a, 6u, &b));
EXPECT(mp_get_u32(&b) == 1);
/* a: -5-> a: 1 */
DO(mp_add_d(&a, 6u, &a));
EXPECT(mp_get_u32(&a) == 1);
mp_zero(&a);
/* a: 0-> a: 6 */
DO(mp_add_d(&a, 6u, &a));
EXPECT(mp_get_u32(&a) == 6);
mp_set(&a, 42u);
mp_set(&b, 1u);
DO(mp_neg(&b, &b));
mp_set(&c, 1u);
DO(mp_exptmod(&a, &b, &c, &d));
mp_set(&c, 7u);
/* same here */
EXPECT(mp_exptmod(&a, &b, &c, &d) != MP_OKAY);
EXPECT(mp_iseven(&a) != mp_isodd(&a));
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_mp_hash(void)
{
mp_int a;
mp_hval hash;
int i;
int len = 5;
const char *input[] = {
"0",
"///////////////////////////////////////////////////////////////////",
"4n9cbk886QtLQmofprid3l2Q0GD8Yv979Lh8BdZkFE8g2pDUUSMBET/+M/YFyVZ3mBp",
"5NlgzHhmIX05O5YoW5yW5reAlVNtRAlIcN2dfoATnNdc1Cw5lHZUTwNthmK6/ZLKfY6",
"3gweiHDX+ji5utraSe46IJX+uuh7iggs63xIpMP5MriU4Np+LpHI5are8RzS9pKh9xP"
};
const mp_hval hvals[] = {
#if (MP_DIGIT_BIT == 15)
0x50c5d1f,
0x51b3ba04,
0xf83febd7,
0x2dc8624c,
0xf5c2996b
#elif (MP_DIGIT_BIT == 60)
0xaf63bd4c8601b7df,
0xdb090f8a5cd75210,
0xabae35c7872c107d,
0xfec74888bcef5fcd,
0x27ba96030abceda5
#elif (MP_DIGIT_BIT == 31)
0xaf63bd4c8601b7df,
0xec1be1c4749a7b86,
0x138ac13639116f2e,
0xdd317b32ac9dd90f,
0x6f87eaac03140738
#else
0xaf63bd4c8601b7df,
0x7e868fbf541faf44,
0x420cca3a4cb623bb,
0x16636d996304ee7f,
0x33afc9f1b274fa67
#endif
};
DOR(mp_init(&a));
for (i = 0; i < len; ++i) {
DO(mp_read_radix(&a, input[i], 64));
DO(mp_hash(&a, &hash));
EXPECT(hash == hvals[i]);
}
mp_clear(&a);
return EXIT_SUCCESS;
LBL_ERR:
mp_clear(&a);
return EXIT_FAILURE;
}
static int check_get_set_i32(mp_int *a, int32_t b)
{
mp_clear(a);
DO(mp_shrink(a));
mp_set_i32(a, b);
DO(mp_shrink(a));
EXPECT(mp_get_i32(a) == b);
EXPECT(mp_get_u32(a) == (uint32_t)b);
EXPECT(mp_get_mag_u32(a) == uabs32(b));
mp_set_u32(a, (uint32_t)b);
EXPECT(mp_get_u32(a) == (uint32_t)b);
EXPECT(mp_get_i32(a) == (int32_t)(uint32_t)b);
return EXIT_SUCCESS;
LBL_ERR:
return EXIT_FAILURE;
}
static int test_mp_get_set_i32(void)
{
int i;
mp_int a;
DOR(mp_init(&a));
check_get_set_i32(&a, 0);
check_get_set_i32(&a, -1);
check_get_set_i32(&a, 1);
check_get_set_i32(&a, INT32_MIN);
check_get_set_i32(&a, INT32_MAX);
for (i = 0; i < 1000; ++i) {
int32_t b = rand_int32();
EXPECT(check_get_set_i32(&a, b) == EXIT_SUCCESS);
}
mp_clear(&a);
return EXIT_SUCCESS;
LBL_ERR:
mp_clear(&a);
return EXIT_FAILURE;
}
static int check_get_set_i64(mp_int *a, int64_t b)
{
mp_clear(a);
if (mp_shrink(a) != MP_OKAY) return EXIT_FAILURE;
mp_set_i64(a, b);
if (mp_shrink(a) != MP_OKAY) return EXIT_FAILURE;
if (mp_get_i64(a) != b) return EXIT_FAILURE;
if (mp_get_u64(a) != (uint64_t)b) return EXIT_FAILURE;
if (mp_get_mag_u64(a) != uabs64(b)) return EXIT_FAILURE;
mp_set_u64(a, (uint64_t)b);
if (mp_get_u64(a) != (uint64_t)b) return EXIT_FAILURE;
if (mp_get_i64(a) != (int64_t)(uint64_t)b) return EXIT_FAILURE;
return EXIT_SUCCESS;
}
static int test_mp_get_set_i64(void)
{
int i;
mp_int a;
DOR(mp_init(&a));
check_get_set_i64(&a, 0);
check_get_set_i64(&a, -1);
check_get_set_i64(&a, 1);
check_get_set_i64(&a, INT64_MIN);
check_get_set_i64(&a, INT64_MAX);
for (i = 0; i < 1000; ++i) {
int64_t b = rand_int64();
if (check_get_set_i64(&a, b) != EXIT_SUCCESS) {
goto LBL_ERR;
}
}
mp_clear(&a);
return EXIT_SUCCESS;
LBL_ERR:
mp_clear(&a);
return EXIT_FAILURE;
}
static int test_mp_fread_fwrite(void)
{
mp_int a, b;
FILE *tmp = NULL;
DOR(mp_init_multi(&a, &b, NULL));
mp_set_ul(&a, 123456uL);
tmp = tmpfile();
DO(mp_fwrite(&a, 64, tmp));
rewind(tmp);
DO(mp_fread(&b, 64, tmp));
EXPECT(mp_get_u32(&b) == 123456uL);
fclose(tmp);
mp_clear_multi(&a, &b, NULL);
return EXIT_SUCCESS;
LBL_ERR:
if (tmp != NULL) fclose(tmp);
mp_clear_multi(&a, &b, NULL);
return EXIT_FAILURE;
}
static mp_err very_random_source(void *out, size_t size)
{
memset(out, 0xff, size);
return MP_OKAY;
}
static int test_mp_rand(void)
{
mp_int a, b;
int n;
mp_err e = MP_OKAY;
DOR(mp_init_multi(&a, &b, NULL));
mp_rand_source(very_random_source);
for (n = 1; n < 1024; ++n) {
DO(mp_rand(&a, n));
DO(mp_incr(&a));
DO(mp_div_2d(&a, n * MP_DIGIT_BIT, &b, NULL));
if (mp_cmp_d(&b, 1u) != MP_EQ) {
ndraw(&a, "mp_rand() a");
ndraw(&b, "mp_rand() b");
e = MP_ERR;
break;
}
}
LBL_ERR:
mp_rand_source(s_mp_rand_jenkins);
mp_clear_multi(&a, &b, NULL);
return (e == MP_OKAY) ? EXIT_SUCCESS : EXIT_FAILURE;
}
static int test_mp_kronecker(void)
{
struct mp_kronecker_st {
long n;
int c[21];
};
static struct mp_kronecker_st kronecker[] = {
/*-10, -9, -8, -7,-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10*/
{ -10, { 0, -1, 0, -1, 0, 0, 0, 1, 0, -1, 0, 1, 0, -1, 0, 0, 0, 1, 0, 1, 0 } },
{ -9, { -1, 0, -1, 1, 0, -1, -1, 0, -1, -1, 0, 1, 1, 0, 1, 1, 0, -1, 1, 0, 1 } },
{ -8, { 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0 } },
{ -7, { 1, -1, -1, 0, 1, 1, -1, 1, -1, -1, 0, 1, 1, -1, 1, -1, -1, 0, 1, 1, -1 } },
{ -6, { 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0 } },
{ -5, { 0, -1, 1, -1, 1, 0, -1, -1, 1, -1, 0, 1, -1, 1, 1, 0, -1, 1, -1, 1, 0 } },
{ -4, { 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0 } },
{ -3, { -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1 } },
{ -2, { 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0 } },
{ -1, { -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1 } },
{ 0, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 } },
{ 1, { 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 } },
{ 2, { 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0 } },
{ 3, { 1, 0, -1, -1, 0, -1, 1, 0, -1, 1, 0, 1, -1, 0, 1, -1, 0, -1, -1, 0, 1 } },
{ 4, { 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0 } },
{ 5, { 0, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0 } },
{ 6, { 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0 } },
{ 7, { -1, 1, 1, 0, 1, -1, 1, 1, 1, 1, 0, 1, 1, 1, 1, -1, 1, 0, 1, 1, -1 } },
{ 8, { 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0 } },
{ 9, { 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1 } },
{ 10, { 0, 1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, -1, 0, 1, 0 } }
};
long k, m;
int i, cnt;
mp_int a, b;
DOR(mp_init_multi(&a, &b, NULL));
mp_set_ul(&a, 0uL);
mp_set_ul(&b, 1uL);
DO(mp_kronecker(&a, &b, &i));
EXPECT(i == 1);
for (cnt = 0; cnt < (int)(sizeof(kronecker)/sizeof(kronecker[0])); ++cnt) {
k = kronecker[cnt].n;
mp_set_l(&a, k);
/* only test positive values of a */
for (m = -10; m <= 10; m++) {
mp_set_l(&b, m);
DO(mp_kronecker(&a, &b, &i));
EXPECT(i == kronecker[cnt].c[m + 10]);
}
}
mp_clear_multi(&a, &b, NULL);
return EXIT_SUCCESS;
LBL_ERR:
mp_clear_multi(&a, &b, NULL);
return EXIT_FAILURE;
}
static int test_mp_complement(void)
{
int i;
mp_int a, b, c;
DOR(mp_init_multi(&a, &b, &c, NULL));
for (i = 0; i < 1000; ++i) {
long l = rand_long();
mp_set_l(&a, l);
DO(mp_complement(&a, &b));
l = ~l;
mp_set_l(&c, l);
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;
}
static int test_mp_signed_rsh(void)
{
int i;
mp_int a, b, d;
DOR(mp_init_multi(&a, &b, &d, NULL));
for (i = 0; i < 1000; ++i) {
long l;
int em;
l = rand_long();
mp_set_l(&a, l);
em = rand_uint() % 32;
mp_set_l(&d, l >> em);
DO(mp_signed_rsh(&a, em, &b));
EXPECT(mp_cmp(&b, &d) == MP_EQ);
}
mp_clear_multi(&a, &b, &d, NULL);
return EXIT_SUCCESS;
LBL_ERR:
mp_clear_multi(&a, &b, &d, NULL);
return EXIT_FAILURE;
}
static int test_mp_xor(void)
{
int i;
mp_int a, b, c, d;
DOR(mp_init_multi(&a, &b, &c, &d, NULL));
for (i = 0; i < 1000; ++i) {
long l, em;
l = rand_long();
mp_set_l(&a,l);
em = rand_long();
mp_set_l(&b, em);
mp_set_l(&d, l ^ em);
DO(mp_xor(&a, &b, &c));
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_mp_or(void)
{
int i;
mp_int a, b, c, d;
DOR(mp_init_multi(&a, &b, &c, &d, NULL));
for (i = 0; i < 1000; ++i) {
long l, em;
l = rand_long();
mp_set_l(&a, l);
em = rand_long();
mp_set_l(&b, em);
mp_set_l(&d, l | em);
DO(mp_or(&a, &b, &c));
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_mp_and(void)
{
int i;
mp_int a, b, c, d;
DOR(mp_init_multi(&a, &b, &c, &d, NULL));
for (i = 0; i < 1000; ++i) {
long l, em;
l = rand_long();
mp_set_l(&a, l);
em = rand_long();
mp_set_l(&b, em);
mp_set_l(&d, l & em);
DO(mp_and(&a, &b, &c));
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_mp_invmod(void)
{
mp_int a, b, c, d;
int i, j, k;
int e;
int results[21][21] =
/* Table generated with Pari/GP
for(i=-10,10,
k=0;
d=0;
printf(" {");
for(j=-10,10,
iferr(
printf(lift(Mod(1/i, j)) ", "),
k,
printf("-1, "))
);
print("},")
)
Changes to the output: replaced j < 1 with -1 for now and added the result of 0^(-1) mod (1)
j = -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 */
{
{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, 8, -1 }, /* i = -10 */
{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 3, 1, -1, 3, 7, -1, 1 }, /* -9 */
{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 3, -1, 6, -1, 1, -1 }, /* -8 */
{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 2, 1, 2, 5, -1, 1, 5, 7 }, /* -7 */
{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, -1, 1, -1, -1, -1 }, /* -6 */
{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 3, -1, 1, 4, 3, 7, -1 }, /* -5 */
{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 1, -1, 5, -1, 2, -1 }, /* -4 */
{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 3, -1, 2, 5, -1, 3 }, /* -3 */
{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 2, -1, 3, -1, 4, -1 }, /* -2 */
{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 2, 3, 4, 5, 6, 7, 8, 9 }, /* -1 */
{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, /* 0 */
{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1 }, /* 1 */
{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, -1, 2, -1, 3, -1, 4, -1, 5, -1 }, /* 2 */
{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 1, -1, 3, 2, -1, 5, 3, -1, 7 }, /* 3 */
{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, -1, 1, -1, 4, -1, 2, -1, 7, -1 }, /* 4 */
{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 1, 2, 1, -1, 5, 3, 5, 2, -1 }, /* 5 */
{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, -1, -1, -1, 1, -1, 6, -1, -1, -1 }, /* 6 */
{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 1, 1, 3, 3, 1, -1, 7, 4, 3 }, /* 7 */
{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, -1, 2, -1, 2, -1, 1, -1, 8, -1 }, /* 8 */
{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 1, -1, 1, 4, -1, 4, 1, -1, 9 }, /* 9 */
{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, -1, 1, -1, -1, -1, 5, -1, 1, -1 } /* 10 */
};
DOR(mp_init_multi(&a, &b, &c, &d, NULL));
/* mp_invmod corner-case of https://github.com/libtom/libtommath/issues/118 */
{
const char *a_ = "47182BB8DF0FFE9F61B1F269BACC066B48BA145D35137D426328DC3F88A5EA44";
const char *b_ = "FFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFF";
const char *should_ = "0521A82E10376F8E4FDEF9A32A427AC2A0FFF686E00290D39E3E4B5522409596";
DO(mp_read_radix(&a, a_, 16));
DO(mp_read_radix(&b, b_, 16));
DO(mp_read_radix(&c, should_, 16));
DO(mp_invmod(&a, &b, &d));
EXPECT(mp_cmp(&c, &d) == MP_EQ);
}
/* Some small general tests https://github.com/libtom/libtommath/issues/534 */
for (i = -10; i < 11; i++) {
for (j = -10; j < 11; j++) {
mp_set_i32(&a, i);
mp_set_i32(&b, j);
e = mp_invmod(&a, &b, &c);
if (e != MP_OKAY) {
if (results[i+10][j+10] != -1) {
printf("error = %s from ", mp_error_to_string(e));
printf("error at i = %d, j =%d should be an error but gave ",i,j);
e = mp_fwrite(&c,10,stdout);
printf("\n");
goto LBL_ERR;
}
} else {
k = mp_get_i32(&c);
if (k != results[i+10][j+10]) {
printf("result at i = %d, j =%d is %d but should be %d \n", i,j,k,results[i+10][j+10]);
goto LBL_ERR;
}
}
}
}
mp_clear_multi(&a, &b, &c, &d, NULL);
return EXIT_SUCCESS;
LBL_ERR:
mp_clear_multi(&a, &b, &c, &d, NULL);
return EXIT_FAILURE;
}
#if defined(MP_HAS_SET_DOUBLE)
#ifdef _MSC_VER
#pragma warning(push)
#pragma warning(disable: 4723) /* potential divide by 0 */
#endif
static int test_mp_set_double(void)
{
int i;
double dbl_zero = 0.0;
mp_int a, b;
DOR(mp_init_multi(&a, &b, NULL));
/* test mp_get_double/mp_set_double */
EXPECT(mp_set_double(&a, +1.0/dbl_zero) == MP_VAL);
EXPECT(mp_set_double(&a, -1.0/dbl_zero) == MP_VAL);
EXPECT(mp_set_double(&a, +0.0/dbl_zero) == MP_VAL);
EXPECT(mp_set_double(&a, -0.0/dbl_zero) == MP_VAL);
for (i = 0; i < 1000; ++i) {
int tmp = rand_int();
double dbl = (double)tmp * rand_int() + 1;
DO(mp_set_double(&a, dbl));
EXPECT(dbl == mp_get_double(&a));
DO(mp_set_double(&a, -dbl));
EXPECT(-dbl == mp_get_double(&a));
}
mp_clear_multi(&a, &b, NULL);
return EXIT_SUCCESS;
LBL_ERR:
mp_clear_multi(&a, &b, NULL);
return EXIT_FAILURE;
}
#ifdef _MSC_VER
#pragma warning(pop)
#endif
#endif
static int test_mp_get_u32(void)
{
uint32_t t;
int i;
mp_int a, b;
DOR(mp_init_multi(&a, &b, NULL));
for (i = 0; i < 1000; ++i) {
t = (uint32_t)rand_long();
mp_set_ul(&a, t);
EXPECT(t == mp_get_u32(&a));
}
mp_set_ul(&a, 0uL);
EXPECT(mp_get_u32(&a) == 0);
mp_set_ul(&a, UINT32_MAX);
EXPECT(mp_get_u32(&a) == UINT32_MAX);
mp_clear_multi(&a, &b, NULL);
return EXIT_SUCCESS;
LBL_ERR:
mp_clear_multi(&a, &b, NULL);
return EXIT_FAILURE;
}
static int test_mp_get_ul(void)
{
unsigned long s, t;
int i;
mp_int a, b;
DOR(mp_init_multi(&a, &b, NULL));
for (i = 0; i < ((int)MP_SIZEOF_BITS(unsigned long) - 1); ++i) {
t = (1UL << (i+1)) - 1;
if (!t)
t = ~0UL;
printf(" t = 0x%lx i = %d\r", t, i);
do {
mp_set_ul(&a, t);
s = mp_get_ul(&a);
EXPECT(s == t);
t <<= 1;
} while (t != 0uL);
}
mp_clear_multi(&a, &b, NULL);
return EXIT_SUCCESS;
LBL_ERR:
mp_clear_multi(&a, &b, NULL);
return EXIT_FAILURE;
}
static int test_mp_get_u64(void)
{
uint64_t q, r;
int i;
mp_int a, b;
DOR(mp_init_multi(&a, &b, NULL));
for (i = 0; i < (int)(MP_SIZEOF_BITS(uint64_t) - 1); ++i) {
r = ((uint64_t)1 << (i+1)) - 1;
if (!r)
r = UINT64_MAX;
printf(" r = 0x%" PRIx64 " i = %d\r", r, i);
do {
mp_set_u64(&a, r);
q = mp_get_u64(&a);
EXPECT(q == r);
r <<= 1;
} while (r != 0u);
}
mp_clear_multi(&a, &b, NULL);
return EXIT_SUCCESS;
LBL_ERR:
mp_clear_multi(&a, &b, NULL);
return EXIT_FAILURE;
}
static int test_mp_sqrt(void)
{
int i, n;
mp_int a, b, c;
DOR(mp_init_multi(&a, &b, &c, NULL));
for (i = 0; i < 1000; ++i) {
printf("%6d\r", i);
fflush(stdout);
n = (rand_int() & 15) + 1;
DO(mp_rand(&a, n));
DO(mp_sqrt(&a, &b));
DO(mp_root_n(&a, 2, &c));
EXPECT(mp_cmp_mag(&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;
}
static int test_mp_is_square(void)
{
int i, n;
mp_int a, b;
bool res;
DOR(mp_init_multi(&a, &b, NULL));
/* Domain is {x \in \mathbb{Z} : x \le 0} */
mp_set_l(&a, -1);
EXPECT(mp_is_square(&a, &res) == MP_VAL);
EXPECT(!res);
/* Zero is a perfect square, too */
mp_zero(&a);
DO(mp_is_square(&a, &res));
EXPECT(res);
for (i = 0; i < 1000; ++i) {
printf("%6d\r", i);
fflush(stdout);
/* test mp_is_square false negatives */
n = (rand_int() & 7) + 1;
DO(mp_rand(&a, n));
DO(mp_sqr(&a, &a));
DO(mp_is_square(&a, &res));
EXPECT(res);
/* test for false positives */
DO(mp_add_d(&a, 1u, &a));
DO(mp_is_square(&a, &res));
EXPECT(!res);
}
mp_clear_multi(&a, &b, NULL);
return EXIT_SUCCESS;
LBL_ERR:
mp_clear_multi(&a, &b, NULL);
return EXIT_FAILURE;
}
static int test_mp_sqrtmod_prime(void)
{
struct mp_sqrtmod_prime_st {
unsigned long p;
unsigned long n;
mp_digit r;
};
static struct mp_sqrtmod_prime_st sqrtmod_prime[] = {
{ 5, 14, 3 }, /* 5 \cong 1 (mod 4) */
{ 7, 9, 4 }, /* 7 \cong 3 (mod 4) */
{ 113, 2, 62 } /* 113 \cong 1 (mod 4) */
};
int i;
mp_int a, b, c;
DOR(mp_init_multi(&a, &b, &c, NULL));
/* r^2 = n (mod p) */
for (i = 0; i < (int)(sizeof(sqrtmod_prime)/sizeof(sqrtmod_prime[0])); ++i) {
mp_set_ul(&a, sqrtmod_prime[i].p);
mp_set_ul(&b, sqrtmod_prime[i].n);
DO(mp_sqrtmod_prime(&b, &a, &c));
EXPECT(mp_cmp_d(&c, sqrtmod_prime[i].r) == MP_EQ);
}
/* Check handling of wrong input (here: modulus is square and cong. 1 mod 4,24 ) */
mp_set_ul(&a, 25);
mp_set_ul(&b, 2);
EXPECT(mp_sqrtmod_prime(&b, &a, &c) == MP_VAL);
/* b \cong 0 (mod a) */
mp_set_ul(&a, 45);
mp_set_ul(&b, 3);
EXPECT(mp_sqrtmod_prime(&b, &a, &c) == MP_VAL);
mp_clear_multi(&a, &b, &c, NULL);
return EXIT_SUCCESS;
LBL_ERR:
mp_clear_multi(&a, &b, &c, NULL);
return EXIT_FAILURE;
}
static int test_mp_prime_rand(void)
{
int ix;
mp_int a, b;
DOR(mp_init_multi(&a, &b, NULL));
/* test for size */
for (ix = 10; ix < 128; ix++) {
printf("Testing (not safe-prime): %9d bits \n", ix);
fflush(stdout);
DO(mp_prime_rand(&a, 8, ix, (rand_int() & 1) ? 0 : MP_PRIME_2MSB_ON));
EXPECT(mp_count_bits(&a) == ix);
}
mp_clear_multi(&a, &b, NULL);
return EXIT_SUCCESS;
LBL_ERR:
mp_clear_multi(&a, &b, NULL);
return EXIT_FAILURE;
}
static int test_mp_prime_is_prime(void)
{
int ix;
mp_err e;
bool cnt, fu;
mp_int a, b;
DOR(mp_init_multi(&a, &b, NULL));
/* strong Miller-Rabin pseudoprime to the first 200 primes (F. Arnault) */
printf("Testing mp_prime_is_prime() with Arnault's pseudoprime 803...901");
DO(mp_read_radix(&a,
"91xLNF3roobhzgTzoFIG6P13ZqhOVYSN60Fa7Cj2jVR1g0k89zdahO9/kAiRprpfO1VAp1aBHucLFV/qLKLFb+zonV7R2Vxp1K13ClwUXStpV0oxTNQVjwybmFb5NBEHImZ6V7P6+udRJuH8VbMEnS0H8/pSqQrg82OoQQ2fPpAk6G1hkjqoCv5s/Yr",
64));
DO(mp_prime_is_prime(&a, mp_prime_rabin_miller_trials(mp_count_bits(&a)), &cnt));
if (cnt) {
printf("Arnault's pseudoprime is not prime but mp_prime_is_prime says it is.\n");
goto LBL_ERR;
}
/* About the same size as Arnault's pseudoprime */
printf("\rTesting mp_prime_is_prime() with certified prime 2^1119 + 53 ");
mp_set(&a, 1u);
DO(mp_mul_2d(&a,1119,&a));
DO(mp_add_d(&a, 53u, &a));
e = mp_prime_is_prime(&a, mp_prime_rabin_miller_trials(mp_count_bits(&a)), &cnt);
/* small problem */
if (e != MP_OKAY) {
printf("\nfailed with error: %s\n", mp_error_to_string(e));
}
/* large problem */
if (!cnt) {
printf("A certified prime is a prime but mp_prime_is_prime says it is not.\n");
}
if ((e != MP_OKAY) || !cnt) {
printf("prime tested was: 0x");
DO(mp_fwrite(&a,16,stdout));
putchar('\n');
goto LBL_ERR;
}
printf("\r ");
for (ix = 16; ix < 128; ix++) {
printf("\rTesting ( safe-prime): %9d bits ", ix);
fflush(stdout);
DO(mp_prime_rand(&a, 8, ix, ((rand_int() & 1) ? 0 : MP_PRIME_2MSB_ON) | MP_PRIME_SAFE));
EXPECT(mp_count_bits(&a) == ix);
/* let's see if it's really a safe prime */
DO(mp_sub_d(&a, 1u, &b));
DO(mp_div_2(&b, &b));
DO(mp_prime_is_prime(&b, mp_prime_rabin_miller_trials(mp_count_bits(&b)), &cnt));
/* large problem */
EXPECT(cnt);
DO(mp_prime_frobenius_underwood(&b, &fu));
EXPECT(fu);
if ((e != MP_OKAY) || !cnt) {
printf("prime tested was: 0x");
DO(mp_fwrite(&a,16,stdout));
putchar('\n');
printf("sub tested was: 0x");
DO(mp_fwrite(&b,16,stdout));
putchar('\n');
goto LBL_ERR;
}
}
/* Check regarding problem #143 */
DO(mp_read_radix(&a,
"FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD129024E088A67CC74020BBEA63B139B22514A08798E3404DDEF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245E485B576625E7EC6F44C42E9A63A3620FFFFFFFFFFFFFFFF",
16));
DO(mp_prime_strong_lucas_selfridge(&a, &cnt));
/* large problem */
EXPECT(cnt);
if ((e != MP_OKAY) || !cnt) {
printf("prime tested was: 0x");
DO(mp_fwrite(&a,16,stdout));
putchar('\n');
goto LBL_ERR;
}
mp_clear_multi(&a, &b, NULL);
return EXIT_SUCCESS;
LBL_ERR:
mp_clear_multi(&a, &b, NULL);
return EXIT_FAILURE;
}
static int test_mp_prime_next_prime(void)
{
mp_int a, b, c;
DOR(mp_init_multi(&a, &b, &c, NULL));
/* edge cases */
mp_set(&a, 0u);
DO(mp_prime_next_prime(&a, 5, false));
if (mp_cmp_d(&a, 2u) != MP_EQ) {
printf("mp_prime_next_prime: output should have been 2 but was: ");
DO(mp_fwrite(&a,10,stdout));
putchar('\n');
goto LBL_ERR;
}
mp_set(&a, 0u);
DO(mp_prime_next_prime(&a, 5, true));
if (mp_cmp_d(&a, 3u) != MP_EQ) {
printf("mp_prime_next_prime: output should have been 3 but was: ");
DO(mp_fwrite(&a,10,stdout));
putchar('\n');
goto LBL_ERR;
}
mp_set(&a, 2u);
DO(mp_prime_next_prime(&a, 5, false));
if (mp_cmp_d(&a, 3u) != MP_EQ) {
printf("mp_prime_next_prime: output should have been 3 but was: ");
DO(mp_fwrite(&a,10,stdout));
putchar('\n');
goto LBL_ERR;
}
mp_set(&a, 2u);
DO(mp_prime_next_prime(&a, 5, true));
if (mp_cmp_d(&a, 3u) != MP_EQ) {
printf("mp_prime_next_prime: output should have been 3 but was: ");
DO(mp_fwrite(&a,10,stdout));
putchar('\n');
goto LBL_ERR;
}
mp_set(&a, 8u);
DO(mp_prime_next_prime(&a, 5, true));
if (mp_cmp_d(&a, 11u) != MP_EQ) {
printf("mp_prime_next_prime: output should have been 11 but was: ");
DO(mp_fwrite(&a,10,stdout));
putchar('\n');
goto LBL_ERR;
}
/* 2^300 + 157 is a 300 bit large prime to guarantee a multi-limb bigint */
DO(mp_2expt(&a, 300));
mp_set_u32(&b, 157);
DO(mp_add(&a, &b, &a));
DO(mp_copy(&a, &b));
/* 2^300 + 385 is the next prime */
mp_set_u32(&c, 228);
DO(mp_add(&b, &c, &b));
DO(mp_prime_next_prime(&a, 5, false));
if (mp_cmp(&a, &b) != MP_EQ) {
printf("mp_prime_next_prime: output should have been\n");
DO(mp_fwrite(&b,10,stdout));
putchar('\n');
printf("but was:\n");
DO(mp_fwrite(&a,10,stdout));
putchar('\n');
goto LBL_ERR;
}
/* Use another temporary variable or recompute? Mmh... */
DO(mp_2expt(&a, 300));
mp_set_u32(&b, 157);
DO(mp_add(&a, &b, &a));
DO(mp_copy(&a, &b));
/* 2^300 + 631 is the next prime congruent to 3 mod 4*/
mp_set_u32(&c, 474);
DO(mp_add(&b, &c, &b));
DO(mp_prime_next_prime(&a, 5, true));
if (mp_cmp(&a, &b) != MP_EQ) {
printf("mp_prime_next_prime (bbs): output should have been\n");
DO(mp_fwrite(&b,10,stdout));
putchar('\n');
printf("but was:\n");
DO(mp_fwrite(&a,10,stdout));
putchar('\n');
goto LBL_ERR;
}
mp_clear_multi(&a, &b, &c, NULL);
return EXIT_SUCCESS;
LBL_ERR:
mp_clear_multi(&a, &b, &c, NULL);
return EXIT_FAILURE;
}
static int test_mp_montgomery_reduce(void)
{
mp_digit mp;
int ix, n;
unsigned int i;
char buf[4096];
/* size_t written; */
mp_int a, b, c, d, e;
DOR(mp_init_multi(&a, &b, &c, &d, &e, NULL));
/* test montgomery */
for (i = 1; i <= 10; i++) {
if (i == 10)
i = 1000;
printf(" digit size: %2d\r", i);
fflush(stdout);
for (n = 0; n < 1000; n++) {
DO(mp_rand(&a, (int)i));
a.dp[0] |= 1;
/* let's see if R is right */
DO(mp_montgomery_calc_normalization(&b, &a));
DO(mp_montgomery_setup(&a, &mp));
/* now test a random reduction */
for (ix = 0; ix < 100; ix++) {
DO(mp_rand(&c, 1 + (int)(rand_uint() % (2*i))));
DO(mp_copy(&c, &d));
DO(mp_copy(&c, &e));
DO(mp_mod(&d, &a, &d));
DO(mp_montgomery_reduce(&c, &a, mp));
DO(mp_mulmod(&c, &b, &a, &c));
if (mp_cmp(&c, &d) != MP_EQ) {
/* *INDENT-OFF* */
printf("d = e mod a, c = e MOD a\n");
DO(mp_to_decimal(&a, buf, sizeof(buf))); printf("a = %s\n", buf);
DO(mp_to_decimal(&e, buf, sizeof(buf))); printf("e = %s\n", buf);
DO(mp_to_decimal(&d, buf, sizeof(buf))); printf("d = %s\n", buf);
DO(mp_to_decimal(&c, buf, sizeof(buf))); printf("c = %s\n", buf);
printf("compare no compare!\n"); goto LBL_ERR;
/* *INDENT-ON* */
}
/* only one big montgomery reduction */
if (i > 10) {
n = 1000;
ix = 100;
}
}
}
}
mp_clear_multi(&a, &b, &c, &d, &e, NULL);
return EXIT_SUCCESS;
LBL_ERR:
mp_clear_multi(&a, &b, &c, &d, &e, NULL);
return EXIT_FAILURE;
}
static int test_mp_read_radix(void)
{
char buf[4096];
size_t written;
mp_int a;
DOR(mp_init_multi(&a, NULL));
DO(mp_read_radix(&a, "123456", 10));
DO(mp_to_radix(&a, buf, sizeof(buf), &written, 10));
printf(" '123456' a == %s, length = %zu", buf, written);
/* See comment in mp_to_radix.c */
/*
if( (err = mp_to_radix(&a, buf, 3u, &written, 10) ) != MP_OKAY) goto LBL_ERR;
printf(" '56' a == %s, length = %zu\n", buf, written);
if( (err = mp_to_radix(&a, buf, 4u, &written, 10) ) != MP_OKAY) goto LBL_ERR;
printf(" '456' a == %s, length = %zu\n", buf, written);
if( (err = mp_to_radix(&a, buf, 30u, &written, 10) ) != MP_OKAY) goto LBL_ERR;
printf(" '123456' a == %s, length = %zu, error = %s\n",
buf, written, mp_error_to_string(err));
*/
DO(mp_read_radix(&a, "-123456", 10));
DO(mp_to_radix(&a, buf, sizeof(buf), &written, 10));
printf("\r '-123456' a == %s, length = %zu", buf, written);
DO(mp_read_radix(&a, "0", 10));
DO(mp_to_radix(&a, buf, sizeof(buf), &written, 10));
printf("\r '0' a == %s, length = %zu", buf, written);
while (0) {
char *s = fgets(buf, sizeof(buf), stdin);
if (s != buf) break;
DO(mp_read_radix(&a, buf, 10));
DO(mp_prime_next_prime(&a, 5, true));
DO(mp_to_radix(&a, buf, sizeof(buf), NULL, 10));
printf("%s, %lu\n", buf, (unsigned long)a.dp[0] & 3uL);
}
mp_clear(&a);
return EXIT_SUCCESS;
LBL_ERR:
mp_clear(&a);
return EXIT_FAILURE;
}
static int test_mp_cnt_lsb(void)
{
int ix;
mp_int a, b;
DOR(mp_init_multi(&a, &b, NULL));
mp_set(&a, 1u);
for (ix = 0; ix < 1024; ix++) {
EXPECT(mp_cnt_lsb(&a) == ix);
DO(mp_mul_2(&a, &a));
}
mp_clear_multi(&a, &b, NULL);
return EXIT_SUCCESS;
LBL_ERR:
mp_clear_multi(&a, &b, NULL);
return EXIT_FAILURE;
}
static int test_mp_reduce_2k(void)
{
int ix, cnt;
mp_int a, b, c, d;
DOR(mp_init_multi(&a, &b, &c, &d, NULL));
/* test mp_reduce_2k */
for (cnt = 3; cnt <= 128; ++cnt) {
mp_digit tmp;
DO(mp_2expt(&a, cnt));
DO(mp_sub_d(&a, 2u, &a)); /* a = 2**cnt - 2 */
printf("\r %4d bits", cnt);
printf("(%d)", mp_reduce_is_2k(&a));
DO(mp_reduce_2k_setup(&a, &tmp));
printf("(%lu)", (unsigned long) tmp);
for (ix = 0; ix < 1000; ix++) {
if (!(ix & 127)) {
printf(".");
fflush(stdout);
}
DO(mp_rand(&b, ((cnt / MP_DIGIT_BIT) + 1) * 2));
DO(mp_copy(&c, &b));
DO(mp_mod(&c, &a, &c));
DO(mp_reduce_2k(&b, &a, 2u));
EXPECT(mp_cmp(&c, &b) == 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_div_3(void)
{
int cnt;
mp_int a, b, c, d, e;
DOR(mp_init_multi(&a, &b, &c, &d, &e, NULL));
/* test s_mp_div_3 */
mp_set(&d, 3u);
for (cnt = 0; cnt < 10000;) {
mp_digit r2;
if (!(++cnt & 127)) {
printf("\r %9d", cnt);
fflush(stdout);
}
DO(mp_rand(&a, (int)(rand_uint() % 128) + 1));
DO(mp_div(&a, &d, &b, &e));
DO(s_mp_div_3(&a, &c, &r2));
EXPECT(!mp_cmp(&b, &c) && !mp_cmp_d(&e, r2));
}
printf("... passed!");
mp_clear_multi(&a, &b, &c, &d, &e, NULL);
return EXIT_SUCCESS;
LBL_ERR:
mp_clear_multi(&a, &b, &c, &d, &e, NULL);
return EXIT_FAILURE;
}
static int test_mp_dr_reduce(void)
{
mp_digit mp;
int cnt;
unsigned rr;
int ix;
mp_int a, b, c;
DOR(mp_init_multi(&a, &b, &c, NULL));
/* test the DR reduction */
for (cnt = 2; cnt < 32; cnt++) {
printf("\r%d digit modulus", cnt);
DO(mp_grow(&a, cnt));
mp_zero(&a);
for (ix = 1; ix < cnt; ix++) {
a.dp[ix] = MP_MASK;
}
a.used = cnt;
a.dp[0] = 3;
DO(mp_rand(&b, cnt - 1));
DO(mp_copy(&b, &c));
rr = 0;
do {
if (!(rr & 127)) {
printf(".");
fflush(stdout);
}
DO(mp_sqr(&b, &b));
DO(mp_add_d(&b, 1u, &b));
DO(mp_copy(&b, &c));
DO(mp_mod(&b, &a, &b));
mp_dr_setup(&a, &mp);
DO(mp_dr_reduce(&c, &a, mp));
EXPECT(mp_cmp(&b, &c) == MP_EQ);
} while (++rr < 500);
printf(" passed");
fflush(stdout);
}
mp_clear_multi(&a, &b, &c, NULL);
return EXIT_SUCCESS;
LBL_ERR:
mp_clear_multi(&a, &b, &c, NULL);
return EXIT_FAILURE;
}
static int test_mp_reduce_2k_l(void)
{
# if LTM_DEMO_TEST_REDUCE_2K_L
mp_int a, b, c, d;
int cnt;
char buf[4096];
size_t length;
DOR(mp_init_multi(&a, &b, NULL));
/* test the mp_reduce_2k_l code */
# if LTM_DEMO_TEST_REDUCE_2K_L == 1
/* first load P with 2^1024 - 0x2A434 B9FDEC95 D8F9D550 FFFFFFFF FFFFFFFF */
DO(mp_2expt(&a, 1024));
DO(mp_read_radix(&b, "2A434B9FDEC95D8F9D550FFFFFFFFFFFFFFFF", 16));
DO(mp_sub(&a, &b, &a));
# elif LTM_DEMO_TEST_REDUCE_2K_L == 2
/* p = 2^2048 - 0x1 00000000 00000000 00000000 00000000 4945DDBF 8EA2A91D 5776399B B83E188F */
DO(mp_2expt(&a, 2048));
DO(mp_read_radix(&b,
"1000000000000000000000000000000004945DDBF8EA2A91D5776399BB83E188F",
16));
DO(mp_sub(&a, &b, &a));
# else
# error oops
# endif
DO(mp_to_radix(&a, buf, sizeof(buf), &length, 10));
printf("\n\np==%s, length = %zu\n", buf, length);
/* now mp_reduce_is_2k_l() should return */
EXPECT(mp_reduce_is_2k_l(&a) == 1);
DO(mp_reduce_2k_setup_l(&a, &d));
/* now do a million square+1 to see if it varies */
DO(mp_rand(&b, 64));
DO(mp_mod(&b, &a, &b));
DO(mp_copy(&b, &c));
printf("Testing: mp_reduce_2k_l...");
fflush(stdout);
for (cnt = 0; cnt < (int)(1uL << 20); cnt++) {
DO(mp_sqr(&b, &b));
DO(mp_add_d(&b, 1u, &b));
DO(mp_reduce_2k_l(&b, &a, &d));
DO(mp_sqr(&c, &c));
DO(mp_add_d(&c, 1u, &c));
DO(mp_mod(&c, &a, &c));
if (mp_cmp(&b, &c) != MP_EQ) {
printf("mp_reduce_2k_l() failed at step %d\n", cnt);
DO(mp_to_hex(&b, buf, sizeof(buf)));
printf("b == %s\n", buf);
DO(mp_to_hex(&c, buf, sizeof(buf)));
printf("c == %s\n", buf);
goto LBL_ERR;
}
}
mp_clear_multi(&a, &b, NULL);
return EXIT_SUCCESS;
LBL_ERR:
mp_clear_multi(&a, &b, NULL);
return EXIT_FAILURE;
#else
return EXIT_SUCCESS;
# endif /* LTM_DEMO_TEST_REDUCE_2K_L */
}
/* stripped down version of mp_radix_size. The faster version can be off by up to +3 */
static mp_err s_rs(const mp_int *a, int radix, int *size)
{
mp_err res;
int digs = 0u;
mp_int t;
mp_digit d;
*size = 0u;
if (mp_iszero(a)) {
*size = 2u;
return MP_OKAY;
}
if (radix == 2) {
*size = mp_count_bits(a) + 1;
return MP_OKAY;
}
DO_WHAT(mp_init_copy(&t, a), return MP_ERR);
t.sign = MP_ZPOS;
while (!mp_iszero(&t)) {
if ((res = mp_div_d(&t, (mp_digit)radix, &t, &d)) != MP_OKAY) {
mp_clear(&t);
return res;
}
++digs;
}
mp_clear(&t);
*size = digs + 1;
return MP_OKAY;
}
static int test_mp_log_n(void)
{
mp_int a;
mp_digit d;
int base, lb, size, i;
const int max_base = MP_MIN(INT_MAX, MP_DIGIT_MAX);
if (MP_HAS(S_MP_WORD_TOO_SMALL)) {
fprintf(stderr, "Testing mp_log_n with restricted size of mp_word.\n");
} else {
fprintf(stderr, "Testing mp_log_n with normal size of mp_word.\n");
}
DOR(mp_init(&a));
/*
base a result
0 x MP_VAL
1 x MP_VAL
*/
mp_set(&a, 42u);
base = 0u;
EXPECT(mp_log_n(&a, base, &lb) == MP_VAL);
base = 1u;
EXPECT(mp_log_n(&a, base, &lb) == MP_VAL);
/*
base a result
2 0 MP_VAL
2 1 0
2 2 1
2 3 1
*/
base = 2u;
mp_zero(&a);
EXPECT(mp_log_n(&a, base, &lb) == MP_VAL);
for (d = 1; d < 4; d++) {
mp_set(&a, d);
DO(mp_log_n(&a, base, &lb));
EXPECT(lb == ((d == 1)?0:1));
}
/*
base a result
3 0 MP_VAL
3 1 0
3 2 0
3 3 1
*/
base = 3u;
mp_zero(&a);
EXPECT(mp_log_n(&a, base, &lb) == MP_VAL);
for (d = 1; d < 4; d++) {
mp_set(&a, d);
DO(mp_log_n(&a, base, &lb));
EXPECT(lb == (((int)d < base)?0:1));
}
/*
bases 2..64 with "a" a random large constant.
The range of bases tested allows to check with
radix_size.
*/
DO(mp_rand(&a, 10));
for (base = 2; base < 65; base++) {
DO(mp_log_n(&a, base, &lb));
DO(s_rs(&a,base, &size));
/* radix_size includes the memory needed for '\0', too*/
size -= 2;
EXPECT(lb == size);
}
/*
bases 2..64 with "a" a small constant and a small exponent "n" to test
in the range a^n - 10 .. a^n + 10. That will check the correction loops
and the test for perfect power.
For simplicity a = base and n = 23 (64^23 == 2^138 > 2^128)
*/
for (base = 2; base < 65; base++) {
mp_set(&a,(mp_digit)base);
DO(mp_expt_n(&a, 23, &a));
DO(mp_sub_d(&a, 10u, &a));
for (i = 0; i < 20; i++) {
DO(mp_log_n(&a, base, &lb));
DO(s_rs(&a, base, &size));
size -= 2;
EXPECT(lb == size);
DO(mp_add_d(&a, 1u, &a));
}
}
/*Test base upper edgecase with base = UINT32_MAX and number = (UINT32_MAX/2)*UINT32_MAX^10 */
mp_set(&a, max_base);
DO(mp_expt_n(&a, 10uL, &a));
DO(mp_add_d(&a, max_base / 2, &a));
DO(mp_log_n(&a, max_base, &lb));
EXPECT(lb == 10u);
mp_clear(&a);
return EXIT_SUCCESS;
LBL_ERR:
mp_clear(&a);
return EXIT_FAILURE;
}
static int test_mp_log(void)
{
mp_int a, base, bn, t;
int lb, lb2, i, j;
if (MP_HAS(S_MP_WORD_TOO_SMALL)) {
fprintf(stdout, "Testing mp_log with restricted size of mp_word.\n");
} else {
fprintf(stdout, "Testing mp_log with normal size of mp_word.\n");
}
DOR(mp_init_multi(&a, &base, &bn, &t, NULL));
/*
The small values got tested above for mp_log_n already, leaving the big stuff
with bases larger than INT_MAX.
*/
/* Edgecases a^b and -1+a^b (floor(log_2(256^129)) = 1032) */
for (i = 2; i < 256; i++) {
mp_set_i32(&a,i);
for (j = 2; j < ((i/2)+1); j++) {
DO(mp_expt_n(&a, j, &bn));
mp_set_i32(&base,j);
/* i^j a perfect power */
DO(mp_log(&bn, &a, &lb));
DO(mp_expt_n(&a, lb, &t));
if (mp_cmp(&t, &bn) != MP_EQ) {
fprintf(stderr,"FAILURE mp_log for perf. power at i = %d, j = %d\n", i, j);
goto LBL_ERR;
}
/* -1 + i^j */
DO(mp_decr(&bn));
DO(mp_log(&bn, &a, &lb2));
if (lb != (lb2+1)) {
fprintf(stderr,"FAILURE mp_log for -1 + i^j at i = %d, j = %d\n", i, j);
goto LBL_ERR;
}
}
}
/* Random a, base */
for (i = 1; i < 256; i++) {
do {
DO(mp_rand(&a, i));
} while (mp_cmp_d(&a,2u) == MP_LT);
for (j = 1; j < ((i/2)+1); j++) {
do {
DO(mp_rand(&base, j));
} while (mp_cmp_d(&base,2u) == MP_LT);
DO(mp_log(&a, &base, &lb));
DO(mp_expt_n(&base, lb, &bn));
/* "bn" must be smaller than or equal to "a" at this point. */
if (mp_cmp(&bn, &a) == MP_GT) {
fprintf(stderr,"FAILURE mp_log random in GT check");
goto LBL_ERR;
}
DO(mp_mul(&bn, &base, &bn));
/* "bn" must be bigger than "a" at this point. */
if (mp_cmp(&bn, &a) != MP_GT) {
fprintf(stderr,"FAILURE mp_log random in NOT GT check");
goto LBL_ERR;
}
}
}
mp_clear_multi(&a, &base, &bn, &t, NULL);
return EXIT_SUCCESS;
LBL_ERR:
mp_clear_multi(&a, &base, &bn, &t, NULL);
return EXIT_FAILURE;
}
static int test_mp_incr(void)
{
mp_int a, b;
DOR(mp_init_multi(&a, &b, NULL));
/* Does it increment inside the limits of a MP_xBIT limb? */
mp_set(&a, MP_MASK/2);
DO(mp_incr(&a));
EXPECT(mp_cmp_d(&a, (MP_MASK/2u) + 1u) == MP_EQ);
/* Does it increment outside of the limits of a MP_xBIT limb? */
mp_set(&a, MP_MASK);
mp_set(&b, MP_MASK);
DO(mp_incr(&a));
DO(mp_add_d(&b, 1u, &b));
EXPECT(mp_cmp(&a, &b) == MP_EQ);
/* Does it increment from -1 to 0? */
mp_set(&a, 1u);
a.sign = MP_NEG;
DO(mp_incr(&a));
EXPECT(mp_cmp_d(&a, 0u) == MP_EQ);
/* Does it increment from -(MP_MASK + 1) to -MP_MASK? */
mp_set(&a, MP_MASK);
DO(mp_add_d(&a, 1u, &a));
a.sign = MP_NEG;
DO(mp_incr(&a));
EXPECT(a.sign == MP_NEG);
a.sign = MP_ZPOS;
EXPECT(mp_cmp_d(&a, MP_MASK) == MP_EQ);
mp_clear_multi(&a, &b, NULL);
return EXIT_SUCCESS;
LBL_ERR:
mp_clear_multi(&a, &b, NULL);
return EXIT_FAILURE;
}
static int test_mp_decr(void)
{
mp_int a, b;
DOR(mp_init_multi(&a, &b, NULL));
/* Does it decrement inside the limits of a MP_xBIT limb? */
mp_set(&a, MP_MASK/2);
DO(mp_decr(&a));
EXPECT(mp_cmp_d(&a, (MP_MASK/2u) - 1u) == MP_EQ);
/* Does it decrement outside of the limits of a MP_xBIT limb? */
mp_set(&a, MP_MASK);
DO(mp_add_d(&a, 1u, &a));
DO(mp_decr(&a));
EXPECT(mp_cmp_d(&a, MP_MASK) == MP_EQ);
/* Does it decrement from 0 to -1? */
mp_zero(&a);
DO(mp_decr(&a));
if (a.sign == MP_NEG) {
a.sign = MP_ZPOS;
EXPECT(mp_cmp_d(&a, 1u) == MP_EQ);
} else {
goto LBL_ERR;
}
/* Does it decrement from -MP_MASK to -(MP_MASK + 1)? */
mp_set(&a, MP_MASK);
a.sign = MP_NEG;
mp_set(&b, MP_MASK);
b.sign = MP_NEG;
DO(mp_sub_d(&b, 1u, &b));
DO(mp_decr(&a));
EXPECT(mp_cmp(&a, &b) == MP_EQ);
mp_clear_multi(&a, &b, NULL);
return EXIT_SUCCESS;
LBL_ERR:
mp_clear_multi(&a, &b, NULL);
return EXIT_FAILURE;
}
/*
Cannot test mp_exp(_d) without mp_root_n and vice versa.
So one of the two has to be tested from scratch.
Numbers generated by
for i in {1..10}
do
seed=$(head -c 10000 /dev/urandom | tr -dc '[:digit:]' | head -c 120);
echo $seed;
convertbase $seed 10 64;
done
(The program "convertbase" uses libtommath's to/from_radix functions)
Roots were precalculated with Pari/GP
default(realprecision,1000);
for(n=3,100,r = floor(a^(1/n));printf("\"" r "\", "))
All numbers as strings to simplify things, especially for the
low-mp branch.
*/
static int test_mp_root_n(void)
{
mp_int a, c, r;
int i, j;
const char *input[] = {
"4n9cbk886QtLQmofprid3l2Q0GD8Yv979Lh8BdZkFE8g2pDUUSMBET/+M/YFyVZ3mBp",
"5NlgzHhmIX05O5YoW5yW5reAlVNtRAlIcN2dfoATnNdc1Cw5lHZUTwNthmK6/ZLKfY6",
"3gweiHDX+ji5utraSe46IJX+uuh7iggs63xIpMP5MriU4Np+LpHI5are8RzS9pKh9xP",
"5QOJUSKMrfe7LkeyJOlupS8h7bjT+TXmZkDzOjZtfj7mdA7cbg0lRX3CuafhjIrpK8S",
"4HtYFldVkyVbrlg/s7kmaA7j45PvLQm+1bbn6ehgP8tVoBmGbv2yDQI1iQQze4AlHyN",
"3bwCUx79NAR7c68OPSp5ZabhZ9aBEr7rWNTO2oMY7zhbbbw7p6shSMxqE9K9nrTNucf",
"4j5RGb78TfuYSzrXn0z6tiAoWiRI81hGY3el9AEa9S+gN4x/AmzotHT2Hvj6lyBpE7q",
"4lwg30SXqZhEHNsl5LIXdyu7UNt0VTWebP3m7+WUL+hsnFW9xJe7UnzYngZsvWh14IE",
"1+tcqFeRuGqjRADRoRUJ8gL4UUSFQVrVVoV6JpwVcKsuBq5G0pABn0dLcQQQMViiVRj",
"hXwxuFySNSFcmbrs/coz4FUAaUYaOEt+l4V5V8vY71KyBvQPxRq/6lsSrG2FHvWDax"
};
/* roots 3-100 of the above */
const char *root[10][100] = {
{
"9163694094944489658600517465135586130944",
"936597377180979771960755204040", "948947857956884030956907",
"95727185767390496595", "133844854039712620", "967779611885360",
"20926191452627", "974139547476", "79203891950", "9784027073",
"1667309744", "365848129", "98268452", "31109156", "11275351",
"4574515", "2040800", "986985", "511525", "281431", "163096",
"98914", "62437", "40832", "27556", "19127", "13614", "9913",
"7367", "5577", "4294", "3357", "2662", "2138", "1738", "1428",
"1185", "993", "839", "715", "613", "530", "461", "403", "355",
"314", "279", "249", "224", "202", "182", "166", "151", "138",
"126", "116", "107", "99", "92", "85", "79", "74", "69", "65", "61",
"57", "54", "51", "48", "46", "43", "41", "39", "37", "36", "34",
"32", "31", "30", "28", "27", "26", "25", "24", "23", "23", "22",
"21", "20", "20", "19", "18", "18", "17", "17", "16", "16", "15"
}, {
"9534798256755061606359588498764080011382",
"964902943621813525741417593772", "971822399862464674540423",
"97646291566833512831", "136141536090599560", "982294733581430",
"21204945933335", "985810529393", "80066084985", "9881613813",
"1682654547", "368973625", "99051783", "31341581", "11354620",
"4604882", "2053633", "992879", "514434", "282959", "163942",
"99406", "62736", "41020", "27678", "19208", "13670", "9952",
"7395", "5598", "4310", "3369", "2671", "2145", "1744", "1433",
"1189", "996", "842", "717", "615", "531", "462", "404", "356",
"315", "280", "250", "224", "202", "183", "166", "151", "138",
"127", "116", "107", "99", "92", "85", "80", "74", "70", "65", "61",
"58", "54", "51", "48", "46", "43", "41", "39", "37", "36", "34",
"32", "31", "30", "29", "27", "26", "25", "24", "23", "23", "22",
"21", "20", "20", "19", "18", "18", "17", "17", "16", "16", "15"
}, {
"8398539113202579297642815367509019445624",
"877309458945432597462853440936", "900579899458998599215071",
"91643543761699761637", "128935656335800903", "936647990947203",
"20326748623514", "948988882684", "77342677787", "9573063447",
"1634096832", "359076114", "96569670", "30604705", "11103188",
"4508519", "2012897", "974160", "505193", "278105", "161251",
"97842", "61788", "40423", "27291", "18949", "13492", "9826",
"7305", "5532", "4260", "3332", "2642", "2123", "1726", "1418",
"1177", "986", "834", "710", "610", "527", "458", "401", "353",
"312", "278", "248", "223", "201", "181", "165", "150", "137",
"126", "116", "107", "99", "91", "85", "79", "74", "69", "65", "61",
"57", "54", "51", "48", "46", "43", "41", "39", "37", "35", "34",
"32", "31", "30", "28", "27", "26", "25", "24", "23", "22", "22",
"21", "20", "20", "19", "18", "18", "17", "17", "16", "16", "15"
}, {
"9559098494021810340217797724866627755195",
"966746709063325235560830083787", "973307706084821682248292",
"97770642291138756434", "136290128605981259", "983232784778520",
"21222944848922", "986563584410", "80121684894", "9887903837",
"1683643206", "369174929", "99102220", "31356542", "11359721",
"4606836", "2054458", "993259", "514621", "283057", "163997",
"99437", "62755", "41032", "27686", "19213", "13674", "9955",
"7397", "5599", "4311", "3370", "2672", "2146", "1744", "1433",
"1189", "996", "842", "717", "615", "532", "462", "404", "356",
"315", "280", "250", "224", "202", "183", "166", "151", "138",
"127", "116", "107", "99", "92", "86", "80", "74", "70", "65", "61",
"58", "54", "51", "48", "46", "43", "41", "39", "37", "36", "34",
"32", "31", "30", "29", "27", "26", "25", "24", "23", "23", "22",
"21", "20", "20", "19", "18", "18", "17", "17", "16", "16", "15"
}, {
"8839202025813295923132694443541993309220",
"911611499784863252820288596270", "928640961450376817534853",
"94017030509441723821", "131792686685970629", "954783483196511",
"20676214073400", "963660189823", "78428929840", "9696237956",
"1653495486", "363032624", "97562430", "30899570", "11203842",
"4547110", "2029216", "981661", "508897", "280051", "162331",
"98469", "62168", "40663", "27446", "19053", "13563", "9877",
"7341", "5558", "4280", "3347", "2654", "2132", "1733", "1424",
"1182", "990", "837", "713", "612", "529", "460", "402", "354",
"313", "279", "249", "223", "201", "182", "165", "150", "138",
"126", "116", "107", "99", "92", "85", "79", "74", "69", "65", "61",
"57", "54", "51", "48", "46", "43", "41", "39", "37", "36", "34",
"32", "31", "30", "28", "27", "26", "25", "24", "23", "23", "22",
"21", "20", "20", "19", "18", "18", "17", "17", "16", "16", "15"
}, {
"8338442683973420410660145045849076963795",
"872596990706967613912664152945", "896707843885562730147307",
"91315073695274540969", "128539440806486007", "934129001105825",
"20278149285734", "946946589774", "77191347471", "9555892093",
"1631391010", "358523975", "96431070", "30563524", "11089126",
"4503126", "2010616", "973111", "504675", "277833", "161100",
"97754", "61734", "40390", "27269", "18934", "13482", "9819",
"7300", "5528", "4257", "3330", "2641", "2122", "1725", "1417",
"1177", "986", "833", "710", "609", "527", "458", "401", "353",
"312", "278", "248", "222", "200", "181", "165", "150", "137",
"126", "116", "107", "99", "91", "85", "79", "74", "69", "65", "61",
"57", "54", "51", "48", "46", "43", "41", "39", "37", "35", "34",
"32", "31", "30", "28", "27", "26", "25", "24", "23", "22", "22",
"21", "20", "20", "19", "18", "18", "17", "17", "16", "16", "15"
}, {
"9122818552483814953977703257848970704164",
"933462289569511464780529972314", "946405863353935713909178",
"95513446972056321834", "133588658082928446",
"966158521967027", "20895030642048", "972833934108",
"79107381638", "9773098125", "1665590516", "365497822",
"98180628", "31083090", "11266459", "4571108", "2039360",
"986323", "511198", "281260", "163001", "98858",
"62404", "40811", "27543", "19117", "13608", "9908",
"7363", "5575", "4292", "3356", "2661", "2138",
"1737", "1428", "1185", "993", "839", "714", "613",
"530", "461", "403", "355", "314", "279", "249",
"224", "202", "182", "165", "151", "138", "126",
"116", "107", "99", "92", "85", "79", "74", "69",
"65", "61", "57", "54", "51", "48", "46", "43",
"41", "39", "37", "36", "34", "32", "31", "30",
"28", "27", "26", "25", "24", "23", "23", "22",
"21", "20", "20", "19", "18", "18", "17", "17",
"16", "16", "15"
}, {
"9151329724083804100369546479681933027521",
"935649419557299174433860420387", "948179413831316112751907",
"95662582675170358900", "133767426788182384",
"967289728859610", "20916775466497", "973745045600",
"79174731802", "9780725058", "1666790321", "365742295",
"98241919", "31101281", "11272665", "4573486", "2040365",
"986785", "511426", "281380", "163067", "98897",
"62427", "40826", "27552", "19124", "13612", "9911",
"7366", "5576", "4294", "3357", "2662", "2138",
"1738", "1428", "1185", "993", "839", "715", "613",
"530", "461", "403", "355", "314", "279", "249",
"224", "202", "182", "165", "151", "138", "126",
"116", "107", "99", "92", "85", "79", "74", "69",
"65", "61", "57", "54", "51", "48", "46", "43",
"41", "39", "37", "36", "34", "32", "31", "30",
"28", "27", "26", "25", "24", "23", "23", "22",
"21", "20", "20", "19", "18", "18", "17", "17",
"16", "16", "15"
}, {
"6839396355168045468586008471269923213531",
"752078770083218822016981965090", "796178899357307807726034",
"82700643015444840424", "118072966296549115",
"867224751770392", "18981881485802", "892288574037",
"73130030771", "9093989389", "1558462688", "343617470",
"92683740", "29448679", "10708016", "4356820", "1948676",
"944610", "490587", "270425", "156989", "95362",
"60284", "39477", "26675", "18536", "13208", "9627",
"7161", "5426", "4181", "3272", "2596", "2087",
"1697", "1395", "1159", "971", "821", "700", "601",
"520", "452", "396", "348", "308", "274", "245",
"220", "198", "179", "163", "148", "136", "124",
"114", "106", "98", "91", "84", "78", "73", "68",
"64", "60", "57", "53", "50", "48", "45", "43",
"41", "39", "37", "35", "34", "32", "31", "29",
"28", "27", "26", "25", "24", "23", "22", "22",
"21", "20", "19", "19", "18", "18", "17", "17",
"16", "16", "15"
}, {
"4788090721380022347683138981782307670424",
"575601315594614059890185238256", "642831903229558719812840",
"69196031110028430211", "101340693763170691",
"758683936560287", "16854690815260", "801767985909",
"66353290503", "8318415180", "1435359033", "318340531",
"86304307", "27544217", "10054988", "4105446", "1841996",
"895414", "466223", "257591", "149855", "91205",
"57758", "37886", "25639", "17842", "12730", "9290",
"6918", "5248", "4048", "3170", "2518", "2026",
"1649", "1357", "1128", "946", "800", "682", "586",
"507", "441", "387", "341", "302", "268", "240",
"215", "194", "176", "160", "146", "133", "122",
"112", "104", "96", "89", "83", "77", "72", "67",
"63", "59", "56", "53", "50", "47", "45", "42",
"40", "38", "36", "35", "33", "32", "30", "29",
"28", "27", "26", "25", "24", "23", "22", "21",
"21", "20", "19", "19", "18", "17", "17", "16",
"16", "15", "15"
}
};
DOR(mp_init_multi(&a, &c, &r, NULL));
for (i = 0; i < 10; i++) {
DO(mp_read_radix(&a, input[i], 64));
for (j = 3; j < 100; j++) {
DO(mp_root_n(&a, j, &c));
DO(mp_read_radix(&r, root[i][j-3], 10));
EXPECT(mp_cmp(&r, &c) == MP_EQ);
}
}
mp_clear_multi(&a, &c, &r, NULL);
return EXIT_SUCCESS;
LBL_ERR:
mp_clear_multi(&a, &c, &r, NULL);
return EXIT_FAILURE;
}
/* Less error-prone than -1 + 2^n with mp_2expt */
static mp_err s_fill_with_ones(mp_int *a, int size)
{
int i;
mp_err err = MP_OKAY;
mp_zero(a);
if ((err = mp_grow(a, size)) != MP_OKAY) goto LTM_ERR;
for (i = 0; i < size; i++) {
a->dp[i] = (mp_digit)MP_MASK;
a->used++;
}
LTM_ERR:
return err;
}
static int test_s_mp_sqr(void)
{
mp_int a, b, c;
int i;
DOR(mp_init_multi(&a, &b, &c, NULL));
/* s_mp_mul() has a hardcoded branch to s_mul_comba if s_mul_comba is available,
so test another 10 just in case. */
for (i = 1; i < MP_MAX_COMBA + 10; i++) {
DO(s_fill_with_ones(&a, i));
DO(s_mp_sqr(&a, &b));
DO(s_mp_mul(&a, &a, &c, 2*i + 1));
EXPECT(mp_cmp(&b, &c) == MP_EQ);
DO(mp_rand(&a, i));
DO(s_mp_sqr(&a, &b));
DO(s_mp_mul(&a, &a, &c, 2*i + 1));
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;
}
static int test_s_mp_sqr_comba(void)
{
mp_int a, r1, r2;
int i, j;
DOR(mp_init_multi(&a, &r1, &r2, NULL));
for (i = 1; i <= MP_MAX_COMBA; i++) {
DO(s_fill_with_ones(&a, i));
DO(s_mp_sqr_comba(&a, &r1));
DO(s_mp_sqr(&a, &r2));
EXPECT(mp_cmp(&r1, &r2) == MP_EQ);
for (j = 0; j < 20; j++) {
DO(mp_rand(&a, i));
DO(s_mp_sqr_comba(&a, &r1));
DO(s_mp_sqr(&a, &r2));
EXPECT(mp_cmp(&r1, &r2) == MP_EQ);
}
}
mp_clear_multi(&a, &r1, &r2, NULL);
return EXIT_SUCCESS;
LBL_ERR:
mp_clear_multi(&a, &r1, &r2, NULL);
return EXIT_FAILURE;
}
static int test_s_mp_mul_balance(void)
{
mp_int a, b, c;
const char *na =
"4b0I5uMTujCysw+1OOuOyH2FX2WymrHUqi8BBDb7XpkV/4i7vXTbEYUy/kdIfCKu5jT5JEqYkdmnn3jAYo8XShPzNLxZx9yoLjxYRyptSuOI2B1DspvbIVYXY12sxPZ4/HCJ4Usm2MU5lO/006KnDMxuxiv1rm6YZJZ0eZU";
const char *nb = "3x9vs0yVi4hIq7poAeVcggC3WoRt0zRLKO";
const char *nc =
"HzrSq9WVt1jDTVlwUxSKqxctu2GVD+N8+SVGaPFRqdxyld6IxDBbj27BPJzYUdR96k3sWpkO8XnDBvupGPnehpQe4KlO/KmN1PjFov/UTZYM+LYzkFcBPyV6hkkL8ePC1rlFLAHzgJMBCXVp4mRqtkQrDsZXXlcqlbTFu69wF6zDEysiX2cAtn/kP9ldblJiwYPCD8hG";
DOR(mp_init_multi(&a, &b, &c, NULL));
DO(mp_read_radix(&a, na, 64));
DO(mp_read_radix(&b, nb, 64));
DO(s_mp_mul_balance(&a, &b, &c));
DO(mp_read_radix(&b, nc, 64));
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;
}
#define s_mp_mul_full(a, b, c) s_mp_mul(a, b, c, (a)->used + (b)->used + 1)
static int test_s_mp_mul_karatsuba(void)
{
mp_int a, b, c, d;
int size;
DOR(mp_init_multi(&a, &b, &c, &d, NULL));
for (size = MP_MUL_KARATSUBA_CUTOFF; size < (MP_MUL_KARATSUBA_CUTOFF + 20); size++) {
DO(mp_rand(&a, size));
DO(mp_rand(&b, size));
DO(s_mp_mul_karatsuba(&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_karatsuba(void)
{
mp_int a, b, c;
int size;
DOR(mp_init_multi(&a, &b, &c, NULL));
for (size = MP_SQR_KARATSUBA_CUTOFF; size < (MP_SQR_KARATSUBA_CUTOFF + 20); size++) {
DO(mp_rand(&a, size));
DO(s_mp_sqr_karatsuba(&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;
}
static int test_s_mp_mul_toom(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_TOOM_CUTOFF;
MP_MUL_TOOM_CUTOFF = INT_MAX;
DO(mp_mul(&a, &b, &c));
MP_MUL_TOOM_CUTOFF = tc_cutoff;
DO(mp_mul(&a, &b, &d));
EXPECT(mp_cmp(&c, &d) == MP_EQ);
#endif
for (size = MP_MUL_TOOM_CUTOFF; size < (MP_MUL_TOOM_CUTOFF + 20); size++) {
DO(mp_rand(&a, size));
DO(mp_rand(&b, size));
DO(s_mp_mul_toom(&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_toom(void)
{
mp_int a, b, c;
int size;
DOR(mp_init_multi(&a, &b, &c, NULL));
for (size = MP_SQR_TOOM_CUTOFF; size < (MP_SQR_TOOM_CUTOFF + 20); size++) {
DO(mp_rand(&a, size));
DO(s_mp_sqr_toom(&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;
}
static int test_mp_radix_size(void)
{
mp_int a;
int radix;
size_t size;
/* *INDENT-OFF* */
size_t results[65] = {
0, 0, 1627, 1027, 814, 702, 630, 581, 543,
514, 491, 471, 455, 441, 428, 418, 408, 399,
391, 384, 378, 372, 366, 361, 356, 352, 347,
343, 340, 336, 333, 330, 327, 324, 321, 318,
316, 314, 311, 309, 307, 305, 303, 301, 299,
298, 296, 294, 293, 291, 290, 288, 287, 285,
284, 283, 281, 280, 279, 278, 277, 276, 275,
273, 272
};
/* *INDENT-ON* */
DOR(mp_init(&a));
/* number to result in a different size for every base: 67^(4 * 67) */
mp_set(&a, 67);
DO(mp_expt_n(&a, 268, &a));
for (radix = 2; radix < 65; radix++) {
DO(mp_radix_size(&a, radix, &size));
EXPECT(size == results[radix]);
a.sign = MP_NEG;
DO(mp_radix_size(&a, radix, &size));
EXPECT(size == (results[radix] + 1));
a.sign = MP_ZPOS;
}
mp_clear(&a);
return EXIT_SUCCESS;
LBL_ERR:
mp_clear(&a);
return EXIT_FAILURE;
}
#define PRINTERR_V(...)
/* Some larger values to test the fast division algorithm */
static int test_s_mp_div_recursive(void)
{
mp_int a, b, c_q, c_r, d_q, d_r;
int size;
DOR(mp_init_multi(&a, &b, &c_q, &c_r, &d_q, &d_r, NULL));
for (size = MP_MUL_KARATSUBA_CUTOFF; size < (3 * MP_MUL_KARATSUBA_CUTOFF); size += 10) {
printf("\rsizes = %d / %d", 10 * size, size);
/* Relation 10:1 */
DO(mp_rand(&a, 10 * size));
DO(mp_rand(&b, size));
DO(s_mp_div_recursive(&a, &b, &c_q, &c_r));
DO(s_mp_div_school(&a, &b, &d_q, &d_r));
EXPECT(mp_cmp(&c_q, &d_q) == MP_EQ);
EXPECT(mp_cmp(&c_r, &d_r) == MP_EQ);
printf("\rsizes = %d / %d", 2 * size, size);
/* Relation 10:1 negative numerator*/
DO(mp_rand(&a, 10 * size));
DO(mp_neg(&a, &a));
DO(mp_rand(&b, size));
DO(s_mp_div_recursive(&a, &b, &c_q, &c_r));
DO(s_mp_div_school(&a, &b, &d_q, &d_r));
EXPECT(mp_cmp(&c_q, &d_q) == MP_EQ);
EXPECT(mp_cmp(&c_r, &d_r) == MP_EQ);
printf("\rsizes = %d / %d, negative numerator", 2 * size, size);
/* Relation 10:1 negative denominator*/
DO(mp_rand(&a, 10 * size));
DO(mp_rand(&b, size));
DO(mp_neg(&b, &b));
DO(s_mp_div_recursive(&a, &b, &c_q, &c_r));
DO(s_mp_div_school(&a, &b, &d_q, &d_r));
EXPECT(mp_cmp(&c_q, &d_q) == MP_EQ);
EXPECT(mp_cmp(&c_r, &d_r) == MP_EQ);
printf("\rsizes = %d / %d, negative denominator", 2 * size, size);
/* Relation 2:1 */
DO(mp_rand(&a, 2 * size));
DO(mp_rand(&b, size));
DO(s_mp_div_recursive(&a, &b, &c_q, &c_r));
DO(s_mp_div_school(&a, &b, &d_q, &d_r));
EXPECT(mp_cmp(&c_q, &d_q) == MP_EQ);
EXPECT(mp_cmp(&c_r, &d_r) == MP_EQ);
printf("\rsizes = %d / %d", 3 * size, 2 * size);
/* Upper limit 3:2 */
DO(mp_rand(&a, 3 * size));
DO(mp_rand(&b, 2 * size));
DO(s_mp_div_recursive(&a, &b, &c_q, &c_r));
DO(s_mp_div_school(&a, &b, &d_q, &d_r));
EXPECT(mp_cmp(&c_q, &d_q) == MP_EQ);
EXPECT(mp_cmp(&c_r, &d_r) == MP_EQ);
}
mp_clear_multi(&a, &b, &c_q, &c_r, &d_q, &d_r, NULL);
return EXIT_SUCCESS;
LBL_ERR:
mp_clear_multi(&a, &b, &c_q, &c_r, &d_q, &d_r, NULL);
return EXIT_FAILURE;
}
static int test_s_mp_div_small(void)
{
mp_int a, b, c_q, c_r, d_q, d_r;
int size;
DOR(mp_init_multi(&a, &b, &c_q, &c_r, &d_q, &d_r, NULL));
for (size = 1; size < MP_MUL_KARATSUBA_CUTOFF; size += 10) {
printf("\rsizes = %d / %d", 2 * size, size);
/* Relation 10:1 */
DO(mp_rand(&a, 2 * size));
DO(mp_rand(&b, size));
DO(s_mp_div_small(&a, &b, &c_q, &c_r));
DO(s_mp_div_school(&a, &b, &d_q, &d_r));
EXPECT(mp_cmp(&c_q, &d_q) == MP_EQ);
EXPECT(mp_cmp(&c_r, &d_r) == MP_EQ);
}
mp_clear_multi(&a, &b, &c_q, &c_r, &d_q, &d_r, NULL);
return EXIT_SUCCESS;
LBL_ERR:
mp_clear_multi(&a, &b, &c_q, &c_r, &d_q, &d_r, NULL);
return EXIT_FAILURE;
}
static int test_s_mp_radix_size_overestimate(void)
{
mp_int a;
int radix, n;
size_t size, size2;
/* *INDENT-OFF* */
size_t results[65] = {
0u, 0u, 1627u, 1027u, 814u, 702u, 630u, 581u, 543u,
514u, 491u, 471u, 455u, 441u, 428u, 418u, 408u, 399u,
391u, 384u, 378u, 372u, 366u, 361u, 356u, 352u, 347u,
343u, 340u, 336u, 333u, 330u, 327u, 324u, 321u, 318u,
316u, 314u, 311u, 309u, 307u, 305u, 303u, 301u, 299u,
298u, 296u, 294u, 293u, 291u, 290u, 288u, 287u, 285u,
284u, 283u, 281u, 280u, 279u, 278u, 277u, 276u, 275u,
273u, 272u
};
/* *INDENT-ON* */
DO(mp_init(&a));
/* number to result in a different size for every base: 67^(4 * 67) */
mp_set(&a, 67);
DO(mp_expt_n(&a, 268, &a));
for (radix = 2; radix < 65; radix++) {
DO(s_mp_radix_size_overestimate(&a, radix, &size));
EXPECT(size >= results[radix]);
EXPECT(size < results[radix] + 20); /* some error bound */
a.sign = MP_NEG;
DO(s_mp_radix_size_overestimate(&a, radix, &size));
EXPECT(size >= results[radix]);
EXPECT(size < results[radix] + 20); /* some error bound */
a.sign = MP_ZPOS;
}
/* randomized test */
for (n = 1; n < 1024; n += 1234) {
DO(mp_rand(&a, n));
for (radix = 2; radix < 65; radix++) {
DO(s_mp_radix_size_overestimate(&a, radix, &size));
DO(mp_radix_size(&a, radix, &size2));
EXPECT(size >= size2);
EXPECT(size < size2 + 20); /* some error bound */
a.sign = MP_NEG;
DO(s_mp_radix_size_overestimate(&a, radix, &size));
DO(mp_radix_size(&a, radix, &size2));
EXPECT(size >= size2);
EXPECT(size < size2 + 20); /* some error bound */
a.sign = MP_ZPOS;
}
}
mp_clear(&a);
return EXIT_SUCCESS;
LBL_ERR:
mp_clear(&a);
return EXIT_FAILURE;
}
static int test_mp_read_write_ubin(void)
{
mp_int a, b, c;
size_t size, len;
uint8_t *buf = NULL;
DOR(mp_init_multi(&a, &b, &c, NULL));
DO(mp_rand(&a, 15));
DO(mp_neg(&a, &b));
size = mp_ubin_size(&a);
printf("mp_to_ubin_size %zu - ", size);
buf = (uint8_t *)malloc(sizeof(*buf) * size);
if (buf == NULL) {
fprintf(stderr, "test_read_write_binaries (u) failed to allocate %zu bytes\n",
sizeof(*buf) * size);
goto LBL_ERR;
}
DO(mp_to_ubin(&a, buf, size, &len));
printf("mp_to_ubin len = %zu", len);
DO(mp_from_ubin(&c, buf, len));
if (mp_cmp(&a, &c) != MP_EQ) {
fprintf(stderr, "to/from ubin cycle failed\n");
goto LBL_ERR;
}
free(buf);
mp_clear_multi(&a, &b, &c, NULL);
return EXIT_SUCCESS;
LBL_ERR:
free(buf);
mp_clear_multi(&a, &b, &c, NULL);
return EXIT_FAILURE;
}
static int test_mp_read_write_sbin(void)
{
mp_int a, b, c;
size_t size, len;
uint8_t *buf = NULL;
DOR(mp_init_multi(&a, &b, &c, NULL));
DO(mp_rand(&a, 15));
DO(mp_neg(&a, &b));
size = mp_sbin_size(&a);
printf("mp_to_sbin_size %zu - ", size);
buf = (uint8_t *)malloc(sizeof(*buf) * size);
if (buf == NULL) {
fprintf(stderr, "test_read_write_binaries (s) failed to allocate %zu bytes\n",
sizeof(*buf) * size);
goto LBL_ERR;
}
DO(mp_to_sbin(&b, buf, size, &len));
printf("mp_to_sbin len = %zu", len);
DO(mp_from_sbin(&c, buf, len));
if (mp_cmp(&b, &c) != MP_EQ) {
fprintf(stderr, "to/from ubin cycle failed\n");
goto LBL_ERR;
}
free(buf);
mp_clear_multi(&a, &b, &c, NULL);
return EXIT_SUCCESS;
LBL_ERR:
free(buf);
mp_clear_multi(&a, &b, &c, NULL);
return EXIT_FAILURE;
}
static int test_mp_pack_unpack(void)
{
mp_int a, b;
size_t written, count;
uint8_t *buf = NULL;
mp_order order = MP_LSB_FIRST;
mp_endian endianness = MP_NATIVE_ENDIAN;
DOR(mp_init_multi(&a, &b, NULL));
DO(mp_rand(&a, 15));
count = mp_pack_count(&a, 0uL, 1uL);
buf = (uint8_t *)malloc(count);
if (buf == NULL) {
fprintf(stderr, "test_pack_unpack failed to allocate\n");
goto LBL_ERR;
}
DO(mp_pack((void *)buf, count, &written, order, 1uL,
endianness, 0uL, &a));
DO(mp_unpack(&b, count, order, 1uL,
endianness, 0uL, (const void *)buf));
if (mp_cmp(&a, &b) != MP_EQ) {
fprintf(stderr, "pack/unpack cycle failed\n");
goto LBL_ERR;
}
free(buf);
mp_clear_multi(&a, &b, NULL);
return EXIT_SUCCESS;
LBL_ERR:
free(buf);
mp_clear_multi(&a, &b, NULL);
return EXIT_FAILURE;
}
#ifndef LTM_TEST_DYNAMIC
#define ONLY_PUBLIC_API_C
#endif
static int unit_tests(int argc, char **argv)
{
static const struct {
const char *name;
int (*fn)(void);
} test[] = {
#define T0(n) { #n, test_##n }
#define T1(n, o) { #n, MP_HAS(o) ? test_##n : NULL }
#define T2(n, o1, o2) { #n, (MP_HAS(o1) && MP_HAS(o2)) ? test_##n : NULL }
#define T3(n, o1, o2, o3) { #n, (MP_HAS(o1) && MP_HAS(o2) && MP_HAS(o3)) ? test_##n : NULL }
T0(feature_detection),
T0(trivial_stuff),
T1(mp_hash, MP_HASH),
T2(mp_get_set_i32, MP_GET_I32, MP_GET_MAG_U32),
T2(mp_get_set_i64, MP_GET_I64, MP_GET_MAG_U64),
T1(mp_and, MP_AND),
T1(mp_cnt_lsb, MP_CNT_LSB),
T1(mp_complement, MP_COMPLEMENT),
T1(mp_decr, MP_SUB_D),
T2(s_mp_div_3, ONLY_PUBLIC_API, S_MP_DIV_3),
T1(mp_dr_reduce, MP_DR_REDUCE),
T2(mp_pack_unpack,MP_PACK, MP_UNPACK),
T2(mp_fread_fwrite, MP_FREAD, MP_FWRITE),
T1(mp_get_u32, MP_GET_I32),
T1(mp_get_u64, MP_GET_I64),
T1(mp_get_ul, MP_GET_L),
T1(mp_log_n, MP_LOG_N),
T1(mp_log, MP_LOG),
T1(mp_incr, MP_ADD_D),
T1(mp_invmod, MP_INVMOD),
T1(mp_is_square, MP_IS_SQUARE),
T1(mp_kronecker, MP_KRONECKER),
T1(mp_montgomery_reduce, MP_MONTGOMERY_REDUCE),
T1(mp_root_n, MP_ROOT_N),
T1(mp_or, MP_OR),
T1(mp_prime_is_prime, MP_PRIME_IS_PRIME),
T1(mp_prime_next_prime, MP_PRIME_NEXT_PRIME),
T1(mp_prime_rand, MP_PRIME_RAND),
T1(mp_rand, MP_RAND),
T1(mp_read_radix, MP_READ_RADIX),
T1(mp_read_write_ubin, MP_TO_UBIN),
T1(mp_read_write_sbin, MP_TO_SBIN),
T1(mp_reduce_2k, MP_REDUCE_2K),
T1(mp_reduce_2k_l, MP_REDUCE_2K_L),
T1(mp_radix_size, MP_RADIX_SIZE),
T2(s_mp_radix_size_overestimate, ONLY_PUBLIC_API, S_MP_RADIX_SIZE_OVERESTIMATE),
#if defined(MP_HAS_SET_DOUBLE)
T1(mp_set_double, MP_SET_DOUBLE),
#endif
T1(mp_signed_rsh, MP_SIGNED_RSH),
T2(mp_sqrt, MP_SQRT, MP_ROOT_N),
T1(mp_sqrtmod_prime, MP_SQRTMOD_PRIME),
T1(mp_xor, MP_XOR),
T3(s_mp_div_recursive, ONLY_PUBLIC_API, S_MP_DIV_RECURSIVE, S_MP_DIV_SCHOOL),
T3(s_mp_div_small, ONLY_PUBLIC_API, S_MP_DIV_SMALL, S_MP_DIV_SCHOOL),
T2(s_mp_sqr, ONLY_PUBLIC_API, S_MP_SQR),
/* s_mp_mul_comba not (yet) testable because s_mp_mul branches to s_mp_mul_comba automatically */
T2(s_mp_sqr_comba, ONLY_PUBLIC_API, S_MP_SQR_COMBA),
T2(s_mp_mul_balance, ONLY_PUBLIC_API, S_MP_MUL_BALANCE),
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)
#undef T3
#undef T2
#undef T1
};
unsigned long i, ok, fail, nop;
uint64_t t;
int j;
ok = fail = nop = 0;
t = (uint64_t)time(NULL);
printf("SEED: 0x%" PRIx64 "\n\n", t);
s_mp_rand_jenkins_init(t);
mp_rand_source(s_mp_rand_jenkins);
for (i = 0; i < (sizeof(test) / sizeof(test[0])); ++i) {
if (argc > 1) {
for (j = 1; j < argc; ++j) {
if (strstr(test[i].name, argv[j]) != NULL) {
break;
}
}
if (j == argc) continue;
}
printf("TEST %s\n", test[i].name);
if (test[i].fn == NULL) {
nop++;
printf("NOP %s\n\n", test[i].name);
} else if (test[i].fn() == EXIT_SUCCESS) {
ok++;
printf("\n");
} else {
fail++;
printf("\n\nFAIL %s\n\n", test[i].name);
}
}
fprintf(fail?stderr:stdout, "Tests OK/NOP/FAIL: %lu/%lu/%lu\n", ok, nop, fail);
if (fail != 0) return EXIT_FAILURE;
else return EXIT_SUCCESS;
}
int main(int argc, char **argv)
{
print_header();
return unit_tests(argc, argv);
}