/**
* This is a general function to count divisors. It will work
* for any integer.
*
* We can optimise. If sqrt(num) is also a divisor, there are
* an odd number of divisors.
* All divisors have pairs so we only need to check half of them.
* ie. up to sqrt(num)
*/
int mpz_count_divisors(const mpz_t num) {
int count=0;
mpz_t div;
mpz_t sqt;
mpz_init(sqt);
mpz_init(div);
mpz_sqrtrem(sqt,div,num);
if(!mpz_cmp_ui(div,0)){
count--;
if(/*div not num*/1) {}
}
mpz_set(div,sqt);
do {
if(mpz_divisible_p(num,div)){
count++;count++;
}
mpz_sub_ui(div,div,1);
} while(mpz_cmp_ui(div,0));
mpz_clear(div);
mpz_clear(sqt);
return count;
}
static Variant HHVM_FUNCTION(gmp_sqrtrem,
const Variant& data) {
mpz_t gmpData, gmpSquareRoot, gmpRemainder;
if (!variantToGMPData(cs_GMP_FUNC_NAME_GMP_SQRTREM, gmpData, data)) {
return false;
}
if (mpz_sgn(gmpData) < 0) {
raise_warning(cs_GMP_INVALID_NUMBER_IS_NEGATIVE,
cs_GMP_FUNC_NAME_GMP_SQRTREM);
return false;
}
mpz_init(gmpSquareRoot);
mpz_init(gmpRemainder);
mpz_sqrtrem(gmpSquareRoot, gmpRemainder, gmpData);
ArrayInit returnArray(2, ArrayInit::Map{});
returnArray.set(0, NEWOBJ(GMPResource)(gmpSquareRoot));
returnArray.set(1, NEWOBJ(GMPResource)(gmpRemainder));
mpz_clear(gmpData);
mpz_clear(gmpSquareRoot);
mpz_clear(gmpRemainder);
return returnArray.toVariant();
}
static PyObject *
GMPy_MPZ_Function_IsqrtRem(PyObject *self, PyObject *other)
{
MPZ_Object *root = NULL, *rem = NULL, *temp = NULL;
PyObject *result;
if (!(temp = GMPy_MPZ_From_Integer(other, NULL))) {
TYPE_ERROR("isqrt_rem() requires 'mpz' argument");
return NULL;
}
if (mpz_sgn(temp->z) < 0) {
VALUE_ERROR("isqrt_rem() of negative number");
Py_DECREF((PyObject*)temp);
return NULL;
}
if (!(result = PyTuple_New(2)) ||
!(root = GMPy_MPZ_New(NULL)) ||
!(rem = GMPy_MPZ_New(NULL))) {
/* LCOV_EXCL_START */
Py_DECREF((PyObject*)temp);
Py_XDECREF(result);
Py_XDECREF((PyObject*)root);
Py_XDECREF((PyObject*)rem);
return NULL;
/* LCOV_EXCL_STOP */
}
mpz_sqrtrem(root->z, rem->z, temp->z);
Py_DECREF((PyObject*)temp);
PyTuple_SET_ITEM(result, 0, (PyObject*)root);
PyTuple_SET_ITEM(result, 1, (PyObject*)rem);
return result;
}
int executeSumCalculation(mpz_t num)
{
mpz_t sum, squareRoot, sqrtRem, st;
mpz_t range, rem;
int i;
pthread_mutex_t mutex;
pthread_cond_t cond;
unsigned long long termCount;
int err;
SUM_THREAD_CONTEXT contexts[SUM_THREADS_PER_CALC];
mpz_init(squareRoot);
mpz_init(sqrtRem);
mpz_init(range);
mpz_init(rem);
pthread_mutex_init(&mutex, NULL);
pthread_cond_init(&cond, NULL);
termCount = 0;
//The sum starts at 1 because 1 is a factor of any number
mpz_init_set_ui(sum, 1);
//We know that exactly 1 factor of every pair of factors will
//appear before the square root.
mpz_sqrtrem(squareRoot, sqrtRem, num);
//Check if the the number is a square
if (mpz_cmp_ui(sqrtRem, 0) != 0)
{
//Emulate ceil
mpz_add_ui(squareRoot, squareRoot, 1);
}
//Factor starts at 2
mpz_init_set_ui(st, 2);
//Compute range
mpz_mod_ui(rem, squareRoot, SUM_THREADS_PER_CALC);
mpz_sub(squareRoot, squareRoot, rem);
mpz_divexact_ui(range, squareRoot, SUM_THREADS_PER_CALC);
for (i = 0; i < SUM_THREADS_PER_CALC; i++)
{
mpz_init_set(contexts[i].st, st);
mpz_init_set(contexts[i].factor, st);
mpz_init(contexts[i].otherfactor);
mpz_add(st, st, range);
if (i == 0)
{
mpz_sub_ui(st, st, 2);
}
mpz_init_set(contexts[i].end, st);
if (i == 0)
{
mpz_add(contexts[i].end, contexts[i].end, rem);
mpz_add(st, st, rem);
}
mpz_init_set(contexts[i].num, num);
contexts[i].sum = ∑
contexts[i].termCount = &termCount;
contexts[i].termMutex = &mutex;
contexts[i].termVar = &cond;
printf("Assigning work to sum thread %d\n", i);
err = pthread_create(&contexts[i].id, NULL, SumThread, &contexts[i]);
if (err != 0)
return -1;
}
fflush(stdout);
for (;;)
{
pthread_mutex_lock(&mutex);
printf("%llu sum threads complete\n", termCount);
fflush(stdout);
if (termCount == SUM_THREADS_PER_CALC)
{
pthread_mutex_unlock(&mutex);
break;
}
if (mpz_cmp(sum, num) > 0)
{
printf("sum is too large; terminating children\n");
fflush(stdout);
pthread_mutex_unlock(&mutex);
break;
}
pthread_cond_wait(&cond, &mutex);
pthread_mutex_unlock(&mutex);
}
for (i = 0; i < SUM_THREADS_PER_CALC; i++)
{
void *ret;
pthread_cancel(contexts[i].id);
pthread_join(contexts[i].id, &ret);
mpz_clear(contexts[i].st);
mpz_clear(contexts[i].num);
mpz_clear(contexts[i].factor);
mpz_clear(contexts[i].end);
mpz_clear(contexts[i].otherfactor);
}
mpz_clear(squareRoot);
mpz_clear(sqrtRem);
mpz_clear(range);
mpz_clear(rem);
mpz_clear(st);
if (mpz_cmp(sum, num) == 0)
{
mpz_clear(sum);
return 1;
}
else
{
mpz_clear(sum);
return 0;
}
}
int main(int argc, char **argv) {
gettimeofday(&start_global, NULL);
print_lib_version();
mpz_init(N);
mpz_t B;
mpz_init(B);
unsigned long int uBase;
int64_t nb_primes;
modular_root_t *modular_roots;
uint64_t i, j;
if (mpz_init_set_str(N, argv[1], 10) == -1) {
printf("Cannot load N %s\n", argv[1]);
exit(2);
}
mpz_t sqrtN, rem;
mpz_init(sqrtN);
mpz_init(rem);
mpz_sqrtrem(sqrtN, rem, N);
if (mpz_cmp_ui(rem, 0) != 0) /* if not perfect square, calculate the ceiling */
mpz_add_ui(sqrtN, sqrtN, 1);
else /* N is a perfect square, factored! */
{
printf("\n<<<[FACTOR]>>> %s\n", mpz_get_str(NULL, 10, sqrtN));
return 0;
}
if (mpz_probab_prime_p(N, 10) > 0) /* don't bother factoring */
{
printf("N:%s is prime\n", mpz_get_str(NULL, 10, N));
exit(0);
}
OPEN_LOG_FILE("freq");
//--------------------------------------------------------
// calculate the smoothness base for the given N
//--------------------------------------------------------
get_smoothness_base(B, N); /* if N is too small, the program will surely fail, please consider a pen and paper instead */
uBase = mpz_get_ui(B);
printf("n: %s\tBase: %s\n", mpz_get_str(NULL, 10, N),
mpz_get_str(NULL, 10, B));
//--------------------------------------------------------
// sieve primes that are less than the smoothness base using Eratosthenes sieve
//--------------------------------------------------------
START_TIMER();
nb_primes = sieve_primes_up_to((int64_t) (uBase));
printf("\nPrimes found %" PRId64 " [Smoothness Base %lu]\n", nb_primes,
uBase);
STOP_TIMER_PRINT_TIME("\tEratosthenes Sieving done");
//--------------------------------------------------------
// fill the primes array with primes to which n is a quadratic residue
//--------------------------------------------------------
START_TIMER();
primes = calloc(nb_primes, sizeof(int64_t));
nb_qr_primes = fill_primes_with_quadratic_residue(primes, N);
/*for(i=0; i<nb_qr_primes; i++)
printf("%" PRId64 "\n", primes[i]);*/
printf("\nN-Quadratic primes found %" PRId64 "\n", nb_qr_primes);
STOP_TIMER_PRINT_TIME("\tQuadratic prime filtering done");
//--------------------------------------------------------
// calculate modular roots
//--------------------------------------------------------
START_TIMER();
modular_roots = calloc(nb_qr_primes, sizeof(modular_root_t));
mpz_t tmp, r1, r2;
mpz_init(tmp);
mpz_init(r1);
mpz_init(r2);
for (i = 0; i < nb_qr_primes; i++) {
mpz_set_ui(tmp, (unsigned long) primes[i]);
mpz_sqrtm(r1, N, tmp); /* calculate the modular root */
mpz_neg(r2, r1); /* -q mod n */
mpz_mod(r2, r2, tmp);
modular_roots[i].root1 = mpz_get_ui(r1);
modular_roots[i].root2 = mpz_get_ui(r2);
}
mpz_clear(tmp);
mpz_clear(r1);
mpz_clear(r2);
STOP_TIMER_PRINT_TIME("\nModular roots calculation done");
/*for(i=0; i<nb_qr_primes; i++)
{
printf("[%10" PRId64 "-> roots: %10u - %10u]\n", primes[i], modular_roots[i].root1, modular_roots[i].root2);
}*/
//--------------------------------------------------------
// ***** initialize the matrix *****
//--------------------------------------------------------
START_TIMER();
init_matrix(&matrix, nb_qr_primes + NB_VECTORS_OFFSET, nb_qr_primes);
mpz_init2(tmp_matrix_row, nb_qr_primes);
STOP_TIMER_PRINT_TIME("\nMatrix initialized");
//--------------------------------------------------------
// [Sieving]
//--------------------------------------------------------
START_TIMER();
mpz_t x, sieving_index, next_sieving_index;
unsigned long ui_index, SIEVING_STEP = 50000; /* we sieve for 50000 elements at each loop */
uint64_t p_pow;
smooth_number_t *x_squared;
x_squared = calloc(SIEVING_STEP, sizeof(smooth_number_t));
smooth_numbers = calloc(nb_qr_primes + NB_VECTORS_OFFSET,
sizeof(smooth_number_t));
mpz_init_set(x, sqrtN);
mpz_init_set(sieving_index, x);
mpz_init_set(next_sieving_index, x);
mpz_t p;
mpz_init(p);
mpz_t str;
mpz_init_set(str, sieving_index);
printf("\nSieving ...\n");
//--------------------------------------------------------
// Init before sieving
//--------------------------------------------------------
for (i = 0; i < SIEVING_STEP; i++) {
mpz_init(x_squared[i].value_x);
mpz_init(x_squared[i].value_x_squared);
/* the factors_exp array is used to keep track of exponents */
//x_squared[i].factors_exp = calloc(nb_qr_primes, sizeof(uint64_t));
/* we use directly the exponents vector modulo 2 to preserve space */mpz_init2(
x_squared[i].factors_vect, nb_qr_primes);
mpz_add_ui(x, x, 1);
}
int nb_smooth_per_round = 0;
char s[512];
//--------------------------------------------------------
// WHILE smooth numbers found less than the primes in the smooth base + NB_VECTORS_OFFSET
//--------------------------------------------------------
while (nb_smooth_numbers_found < nb_qr_primes + NB_VECTORS_OFFSET) {
nb_smooth_per_round = 0;
mpz_set(x, next_sieving_index); /* sieve numbers from sieving_index to sieving_index + sieving_step */
mpz_set(sieving_index, next_sieving_index);
printf("\r");
printf(
"\t\tSieving at: %s30 <--> Smooth numbers found: %" PRId64 "/%" PRId64 "",
mpz_get_str(NULL, 10, sieving_index), nb_smooth_numbers_found,
nb_qr_primes);
fflush(stdout);
for (i = 0; i < SIEVING_STEP; i++) {
mpz_set(x_squared[i].value_x, x);
mpz_pow_ui(x_squared[i].value_x_squared, x, 2); /* calculate value_x_squared <- x²-n */
mpz_sub(x_squared[i].value_x_squared, x_squared[i].value_x_squared,
N);
mpz_clear(x_squared[i].factors_vect);
mpz_init2(x_squared[i].factors_vect, nb_qr_primes); /* reconstruct a new fresh 0ed vector of size nb_qr_primes bits */
mpz_add_ui(x, x, 1);
}
mpz_set(next_sieving_index, x);
//--------------------------------------------------------
// eliminate factors in the x_squared array, those who are 'destructed' to 1 are smooth
//--------------------------------------------------------
for (i = 0; i < nb_qr_primes; i++) {
mpz_set_ui(p, (unsigned long) primes[i]);
mpz_set(x, sieving_index);
/* get the first multiple of p that is directly larger that sieving_index
* Quadratic SIEVING: all elements from this number and in positions multiples of root1 and root2
* are also multiples of p */
get_sieving_start_index(x, x, p, modular_roots[i].root1);
mpz_set(str, x);
mpz_sub(x, x, sieving_index); /* x contains index of first number that is divisible by p */
for (j = mpz_get_ui(x); j < SIEVING_STEP; j += primes[i]) {
p_pow = mpz_remove(x_squared[j].value_x_squared,
x_squared[j].value_x_squared, p); /* eliminate all factors of p */
if (p_pow & 1) /* mark bit if odd power of p exists in this x_squared[j] */
{
mpz_setbit(x_squared[j].factors_vect, i);
}
if (mpz_cmp_ui(x_squared[j].value_x_squared, 1) == 0) {
save_smooth_number(x_squared[j]);
nb_smooth_per_round++;
}
/* sieve next element located p steps from here */
}
/* same goes for root2 */
if (modular_roots[i].root2 == modular_roots[i].root1)
continue;
mpz_set(x, sieving_index);
get_sieving_start_index(x, x, p, modular_roots[i].root2);
mpz_set(str, x);
mpz_sub(x, x, sieving_index);
for (j = mpz_get_ui(x); j < SIEVING_STEP; j += primes[i]) {
p_pow = mpz_remove(x_squared[j].value_x_squared,
x_squared[j].value_x_squared, p);
if (p_pow & 1) {
mpz_setbit(x_squared[j].factors_vect, i);
}
if (mpz_cmp_ui(x_squared[j].value_x_squared, 1) == 0) {
save_smooth_number(x_squared[j]);
nb_smooth_per_round++;
}
}
}
//printf("\tSmooth numbers found %" PRId64 "\n", nb_smooth_numbers_found);
/*sprintf(s, "[start: %s - end: %s - step: %" PRId64 "] nb_smooth_per_round: %d",
mpz_get_str(NULL, 10, sieving_index),
mpz_get_str(NULL, 10, next_sieving_index),
SIEVING_STEP,
nb_smooth_per_round);
APPEND_TO_LOG_FILE(s);*/
}
STOP_TIMER_PRINT_TIME("\nSieving DONE");
uint64_t t = 0;
//--------------------------------------------------------
//the matrix ready, start Gauss elimination. The Matrix is filled on the call of save_smooth_number()
//--------------------------------------------------------
START_TIMER();
gauss_elimination(&matrix);
STOP_TIMER_PRINT_TIME("\nGauss elimination done");
//print_matrix_matrix(&matrix);
//print_matrix_identity(&matrix);
uint64_t row_index = nb_qr_primes + NB_VECTORS_OFFSET - 1; /* last row in the matrix */
int nb_linear_relations = 0;
mpz_t linear_relation_z, solution_z;
mpz_init(linear_relation_z);
mpz_init(solution_z);
get_matrix_row(linear_relation_z, &matrix, row_index--); /* get the last few rows in the Gauss eliminated matrix*/
while (mpz_cmp_ui(linear_relation_z, 0) == 0) {
nb_linear_relations++;
get_matrix_row(linear_relation_z, &matrix, row_index--);
}
printf("\tLinear dependent relations found : %d\n", nb_linear_relations);
//--------------------------------------------------------
// Factor
//--------------------------------------------------------
//We use the last linear relation to reconstruct our solution
START_TIMER();
printf("\nFactorizing..\n");
mpz_t solution_X, solution_Y;
mpz_init(solution_X);
mpz_init(solution_Y);
/* we start testing from the first linear relation encountered in the matrix */
for (j = nb_linear_relations; j > 0; j--) {
printf("Trying %d..\n", nb_linear_relations - j + 1);
mpz_set_ui(solution_X, 1);
mpz_set_ui(solution_Y, 1);
get_identity_row(solution_z, &matrix,
nb_qr_primes + NB_VECTORS_OFFSET - j + 1);
for (i = 0; i < nb_qr_primes; i++) {
if (mpz_tstbit(solution_z, i)) {
mpz_mul(solution_X, solution_X, smooth_numbers[i].value_x);
mpz_mod(solution_X, solution_X, N); /* reduce x to modulo N */
mpz_mul(solution_Y, solution_Y,
smooth_numbers[i].value_x_squared);
/*TODO: handling huge stuff here, there is no modulo N like in the solution_X case!
* eliminate squares as long as you go*/
}
}
mpz_sqrt(solution_Y, solution_Y);
mpz_mod(solution_Y, solution_Y, N); /* y = sqrt(MUL(xi²-n)) mod N */
mpz_sub(solution_X, solution_X, solution_Y);
mpz_gcd(solution_X, solution_X, N);
if (mpz_cmp(solution_X, N) != 0 && mpz_cmp_ui(solution_X, 1) != 0) /* factor can be 1 or N, try another relation */
break;
}
mpz_cdiv_q(solution_Y, N, solution_X);
printf("\n>>>>>>>>>>> FACTORED %s =\n", mpz_get_str(NULL, 10, N));
printf("\tFactor 1: %s \n\tFactor 2: %s", mpz_get_str(NULL, 10, solution_X),
mpz_get_str(NULL, 10, solution_Y));
/*sprintf(s, "\n>>>>>>>>>>> FACTORED %s =\n", mpz_get_str(NULL, 10, N));
APPEND_TO_LOG_FILE(s);
sprintf(s, "\tFactor 1: %s \n\tFactor 2: %s", mpz_get_str(NULL, 10, solution_X), mpz_get_str(NULL, 10, solution_Y));
APPEND_TO_LOG_FILE(s);
gettimeofday(&end_global, NULL);
timersub(&end_global, &start_global, &elapsed);
sprintf(s, "****** TOTAL TIME: %.3f ms\n", elapsed.tv_sec * 1000 + elapsed.tv_usec / (double) 1000);
APPEND_TO_LOG_FILE(s);*/
STOP_TIMER_PRINT_TIME("\nFactorizing done");
printf("Cleaning memory..\n");
/********************** clear the x_squared array **********************/
for (i = 0; i < SIEVING_STEP; i++) {
mpz_clear(x_squared[i].value_x);
mpz_clear(x_squared[i].value_x_squared);
//free(x_squared[i].factors_exp);
mpz_clear(x_squared[i].factors_vect);
}
free(x_squared);
/********************** clear the x_squared array **********************/
free(modular_roots);
/********************** clear the smooth_numbers array **********************/
for (i = 0; i < nb_qr_primes + NB_VECTORS_OFFSET; i++) {
mpz_clear(smooth_numbers[i].value_x);
mpz_clear(smooth_numbers[i].value_x_squared);
//free(smooth_numbers[i].factors_exp);
}
free(smooth_numbers);
/********************** clear the smooth_numbers array **********************/
free(primes);
/********************** clear mpz _t **********************/mpz_clear(B);
mpz_clear(N);
sqrtN, rem;
mpz_clear(x);
mpz_clear(sieving_index);
mpz_clear(next_sieving_index);
mpz_clear(p);
mpz_clear(str);
/********************** clear mpz _t **********************/
free_matrix(&matrix);
gettimeofday(&end_global, NULL);
timersub(&end_global, &start_global, &elapsed);
printf("****** TOTAL TIME: %.3f ms\n",
elapsed.tv_sec * 1000 + elapsed.tv_usec / (double) 1000);
show_mem_usage();
return 0;
}
int
main (int argc, char **argv)
{
mpz_t x2;
mpz_t x, rem;
mpz_t temp, temp2;
mp_size_t x2_size;
int i;
int reps = 1000;
gmp_randstate_ptr rands;
mpz_t bs;
unsigned long size_range;
tests_start ();
TESTS_REPS (reps, argv, argc);
rands = RANDS;
mpz_init (bs);
mpz_init (x2);
mpz_init (x);
mpz_init (rem);
mpz_init (temp);
mpz_init (temp2);
for (i = 0; i < reps; i++)
{
mpz_urandomb (bs, rands, 32);
size_range = mpz_get_ui (bs) % 17 + 2; /* 0..262144 bit operands */
mpz_urandomb (bs, rands, size_range);
x2_size = mpz_get_ui (bs);
mpz_rrandomb (x2, rands, x2_size);
/* printf ("%ld\n", SIZ (x2)); */
mpz_sqrtrem (x, rem, x2);
MPZ_CHECK_FORMAT (x);
MPZ_CHECK_FORMAT (rem);
mpz_mul (temp, x, x);
/* Is square of result > argument? */
if (mpz_cmp (temp, x2) > 0)
dump_abort (x2, x, rem);
mpz_add_ui (temp2, x, 1);
mpz_mul (temp2, temp2, temp2);
/* Is square of (result + 1) <= argument? */
if (mpz_cmp (temp2, x2) <= 0)
dump_abort (x2, x, rem);
mpz_add (temp2, temp, rem);
/* Is the remainder wrong? */
if (mpz_cmp (x2, temp2) != 0)
dump_abort (x2, x, rem);
}
mpz_clear (bs);
mpz_clear (x2);
mpz_clear (x);
mpz_clear (rem);
mpz_clear (temp);
mpz_clear (temp2);
tests_end ();
exit (0);
}
int
main (int argc, char **argv)
{
mpz_t x2;
mpz_t x, rem;
mpz_t temp, temp2;
mp_size_t x2_size;
int i;
int reps = 20000;
gmp_randstate_t rands;
mpz_t bs;
unsigned long size_range;
tests_start ();
gmp_randinit_default(rands);
mpz_init (bs);
if (argc == 2)
reps = atoi (argv[1]);
mpz_init (x2);
mpz_init (x);
mpz_init (rem);
mpz_init (temp);
mpz_init (temp2);
for (i = 0; i < reps; i++)
{
mpz_urandomb (bs, rands, 32);
size_range = mpz_get_ui (bs) % 12 + 2; /* 0..8191 bit operands */
mpz_urandomb (bs, rands, size_range);
x2_size = mpz_get_ui (bs);
mpz_rrandomb (x2, rands, x2_size);
/* printf ("%ld\n", SIZ (x2)); */
mpz_sqrtrem (x, rem, x2);
mpz_mul (temp, x, x);
/* Is square of result > argument? */
if (mpz_cmp (temp, x2) > 0)
dump_abort (x2, x, rem);
mpz_add_ui (temp2, x, 1);
mpz_mul (temp2, temp2, temp2);
/* Is square of (result + 1) <= argument? */
if (mpz_cmp (temp2, x2) <= 0)
dump_abort (x2, x, rem);
mpz_add (temp2, temp, rem);
/* Is the remainder wrong? */
if (mpz_cmp (x2, temp2) != 0)
dump_abort (x2, x, rem);
}
mpz_clear (bs);
mpz_clear (x2);
mpz_clear (x);
mpz_clear (rem);
mpz_clear (temp);
mpz_clear (temp2);
gmp_randclear(rands);
tests_end ();
exit (0);
}
/* assuming slaves (workers)) are all homogenous, let them all do the calculations
regarding primes sieving, calculating the smoothness base and the modular roots */
int main(int argc, char **argv) {
MPI_Init(&argc, &argv);
MPI_Comm_rank(MPI_COMM_WORLD, &my_rank);
MPI_Comm_size(MPI_COMM_WORLD, &mpi_group_size);
int len;
MPI_Get_processor_name(processor_name, &len);
gettimeofday(&start_global, NULL);
print_lib_version();
mpz_init(N);
mpz_t B;
mpz_init(B);
unsigned long int uBase;
int64_t nb_primes;
modular_root_t *modular_roots;
uint64_t i, j;
if (argc < 2) {
PRINT(my_rank, "usage: %s Number_to_factorize\n", argv[0]);
exit(2);
}
if (mpz_init_set_str(N, argv[1], 10) == -1) {
PRINT(my_rank, "Cannot load N %s\n", argv[1]);
exit(2);
}
mpz_t sqrtN, rem;
mpz_init(sqrtN);
mpz_init(rem);
mpz_sqrtrem(sqrtN, rem, N);
if (mpz_cmp_ui(rem, 0) != 0) /* if not perfect square, calculate the ceiling */
mpz_add_ui(sqrtN, sqrtN, 1);
else /* N is a perfect square, factored! */
{
PRINT(my_rank, "\n<<<[FACTOR]>>> %s\n", mpz_get_str(NULL, 10, sqrtN));
return 0;
}
if (mpz_probab_prime_p(N, 10) > 0) /* don't bother factoring */
{
PRINT(my_rank, "N:%s is prime\n", mpz_get_str(NULL, 10, N));
exit(0);
}
OPEN_LOG_FILE("freq");
//--------------------------------------------------------
// calculate the smoothness base for the given N
//--------------------------------------------------------
get_smoothness_base(B, N); /* if N is too small, the program will surely fail, please consider a pen and paper instead */
uBase = mpz_get_ui(B);
PRINT(my_rank, "n: %s\tBase: %s\n",
mpz_get_str(NULL, 10, N), mpz_get_str(NULL, 10, B));
//--------------------------------------------------------
// sieve primes that are less than the smoothness base using Eratosthenes sieve
//--------------------------------------------------------
START_TIMER();
nb_primes = sieve_primes_up_to((int64_t) (uBase));
PRINT(my_rank, "\tPrimes found %" PRId64 " [Smoothness Base %lu]\n",
nb_primes, uBase);
STOP_TIMER_PRINT_TIME("\tEratosthenes Sieving done");
//--------------------------------------------------------
// fill the primes array with primes to which n is a quadratic residue
//--------------------------------------------------------
START_TIMER();
primes = calloc(nb_primes, sizeof(int64_t));
nb_qr_primes = fill_primes_with_quadratic_residue(primes, N);
/*for(i=0; i<nb_qr_primes; i++)
PRINT(my_rank, "%" PRId64 "\n", primes[i]);*/
PRINT(my_rank, "\tN-Quadratic primes found %" PRId64 "\n", nb_qr_primes);
STOP_TIMER_PRINT_TIME("\tQuadratic prime filtering done");
//--------------------------------------------------------
// calculate modular roots
//--------------------------------------------------------
START_TIMER();
modular_roots = calloc(nb_qr_primes, sizeof(modular_root_t));
mpz_t tmp, r1, r2;
mpz_init(tmp);
mpz_init(r1);
mpz_init(r2);
for (i = 0; i < nb_qr_primes; i++) {
mpz_set_ui(tmp, (unsigned long) primes[i]);
mpz_sqrtm(r1, N, tmp); /* calculate the modular root */
mpz_neg(r2, r1); /* -q mod n */
mpz_mod(r2, r2, tmp);
modular_roots[i].root1 = mpz_get_ui(r1);
modular_roots[i].root2 = mpz_get_ui(r2);
}
mpz_clear(tmp);
mpz_clear(r1);
mpz_clear(r2);
STOP_TIMER_PRINT_TIME("Modular roots calculation done");
//--------------------------------------------------------
// ***** initialize the matrix *****
//--------------------------------------------------------
if (my_rank == 0) /* only the master have the matrix */
{
START_TIMER();
init_matrix(&matrix, nb_qr_primes + NB_VECTORS_OFFSET, nb_qr_primes);
mpz_init2(tmp_matrix_row, nb_qr_primes);
STOP_TIMER_PRINT_TIME("Matrix initialized");
}
//--------------------------------------------------------
// [Sieving] - everyones sieves including the master
//--------------------------------------------------------
START_TIMER();
mpz_t x, sieving_index, next_sieving_index, relative_start, global_step;
unsigned long ui_index, SIEVING_STEP = 50000; /* we sieve for 50000 elements at each loop */
int LOCAL_SIEVING_ROUNDS = 10; /* number of iterations a worker sieves before communicating results to the master */
unsigned long sieving_round = 0;
unsigned long nb_big_rounds = 0;
uint64_t p_pow;
smooth_number_t *x_squared;
x_squared = calloc(SIEVING_STEP, sizeof(smooth_number_t));
if (my_rank == 0)
smooth_numbers = calloc(nb_qr_primes + NB_VECTORS_OFFSET,
sizeof(smooth_number_t));
else
temp_slaves_smooth_numbers = calloc(500, sizeof(smooth_number_t));
/* TODO: this is not properly correct, using a linkedlist is better to keep track of temporary
* smooth numbers at the slaves nodes however it's pretty rare to find 500 smooth numbers in
* 50000 * 10 interval. */
mpz_init_set(x, sqrtN);
mpz_init(global_step);
mpz_init(relative_start);
mpz_init(sieving_index);
mpz_init(next_sieving_index);
mpz_t p;
mpz_init(p);
mpz_t str;
mpz_init_set(str, sieving_index);
PRINT(my_rank, "\n[%s] Sieving ...\n", processor_name);
//--------------------------------------------------------
// Init before sieving
//--------------------------------------------------------
for (i = 0; i < SIEVING_STEP; i++) {
mpz_init(x_squared[i].value_x);
mpz_init(x_squared[i].value_x_squared);
mpz_init2(x_squared[i].factors_vect, nb_qr_primes);
mpz_add_ui(x, x, 1);
}
int nb_smooth_per_round = 0;
char s[512];
//--------------------------------------------------------
// WHILE smooth numbers found less than the primes in the smooth base + NB_VECTORS_OFFSET for master
// Or master asked for more smooth numbers from slaves
//--------------------------------------------------------
while (1) {
mpz_set_ui(global_step, nb_big_rounds); /* calculates the coordinate where the workers start sieving from */
mpz_mul_ui(global_step, global_step, (unsigned long) mpi_group_size);
mpz_mul_ui(global_step, global_step, SIEVING_STEP);
mpz_mul_ui(global_step, global_step, LOCAL_SIEVING_ROUNDS);
mpz_add(global_step, global_step, sqrtN);
mpz_set_ui(relative_start, SIEVING_STEP);
mpz_mul_ui(relative_start, relative_start, LOCAL_SIEVING_ROUNDS);
mpz_mul_ui(relative_start, relative_start, (unsigned long) my_rank);
mpz_add(relative_start, relative_start, global_step);
mpz_set(sieving_index, relative_start);
mpz_set(next_sieving_index, relative_start);
for (sieving_round = 0; sieving_round < LOCAL_SIEVING_ROUNDS; /* each slave sieves for LOCAL_SIEVING_ROUNDS rounds */
sieving_round++) {
nb_smooth_per_round = 0;
mpz_set(x, next_sieving_index); /* sieve numbers from sieving_index to sieving_index + sieving_step */
mpz_set(sieving_index, next_sieving_index);
if (my_rank == 0) {
printf("\r");
printf(
"\t\tSieving at: %s30 <--> Smooth numbers found: %" PRId64 "/%" PRId64 "",
mpz_get_str(NULL, 10, sieving_index),
nb_global_smooth_numbers_found, nb_qr_primes);
fflush(stdout);
}
for (i = 0; i < SIEVING_STEP; i++) {
mpz_set(x_squared[i].value_x, x);
mpz_pow_ui(x_squared[i].value_x_squared, x, 2); /* calculate value_x_squared <- x²-n */
mpz_sub(x_squared[i].value_x_squared,
x_squared[i].value_x_squared, N);
mpz_clear(x_squared[i].factors_vect);
mpz_init2(x_squared[i].factors_vect, nb_qr_primes); /* reconstruct a new fresh 0ed vector of size nb_qr_primes bits */
mpz_add_ui(x, x, 1);
}
mpz_set(next_sieving_index, x);
//--------------------------------------------------------
// eliminate factors in the x_squared array, those who are 'destructed' to 1 are smooth
//--------------------------------------------------------
for (i = 0; i < nb_qr_primes; i++) {
mpz_set_ui(p, (unsigned long) primes[i]);
mpz_set(x, sieving_index);
/* get the first multiple of p that is directly larger that sieving_index
* Quadratic SIEVING: all elements from this number and in positions multiples of root1 and root2
* are also multiples of p */
get_sieving_start_index(x, x, p, modular_roots[i].root1);
mpz_set(str, x);
mpz_sub(x, x, sieving_index); /* x contains index of first number that is divisible by p */
for (j = mpz_get_ui(x); j < SIEVING_STEP; j += primes[i]) {
p_pow = mpz_remove(x_squared[j].value_x_squared,
x_squared[j].value_x_squared, p); /* eliminate all factors of p */
if (p_pow & 1) /* mark bit if odd power of p exists in this x_squared[j] */
{
mpz_setbit(x_squared[j].factors_vect, i);
}
if (mpz_cmp_ui(x_squared[j].value_x_squared, 1) == 0) {
save_smooth_number(x_squared[j]);
nb_smooth_per_round++;
}
/* sieve next element located p steps from here */
}
/* same goes for root2 */
if (modular_roots[i].root2 == modular_roots[i].root1)
continue;
mpz_set(x, sieving_index);
get_sieving_start_index(x, x, p, modular_roots[i].root2);
mpz_set(str, x);
mpz_sub(x, x, sieving_index);
for (j = mpz_get_ui(x); j < SIEVING_STEP; j += primes[i]) {
p_pow = mpz_remove(x_squared[j].value_x_squared,
x_squared[j].value_x_squared, p);
if (p_pow & 1) {
mpz_setbit(x_squared[j].factors_vect, i);
}
if (mpz_cmp_ui(x_squared[j].value_x_squared, 1) == 0) {
save_smooth_number(x_squared[j]);
nb_smooth_per_round++;
}
}
}
}
if (my_rank == 0) /* master gathers smooth numbers from slaves */
{
gather_smooth_numbers();
notify_slaves();
} else /* slaves send their smooth numbers to master */
{
send_smooth_numbers_to_master();
nb_global_smooth_numbers_found = get_server_notification();
}
if (nb_global_smooth_numbers_found >= nb_qr_primes + NB_VECTORS_OFFSET)
break;
nb_big_rounds++;
}
STOP_TIMER_PRINT_TIME("\nSieving DONE");
if (my_rank == 0) {
uint64_t t = 0;
//--------------------------------------------------------
//the matrix ready, start Gauss elimination. The Matrix is filled on the call of save_smooth_number()
//--------------------------------------------------------
START_TIMER();
gauss_elimination(&matrix);
STOP_TIMER_PRINT_TIME("\nGauss elimination done");
uint64_t row_index = nb_qr_primes + NB_VECTORS_OFFSET - 1; /* last row in the matrix */
int nb_linear_relations = 0;
mpz_t linear_relation_z, solution_z;
mpz_init(linear_relation_z);
mpz_init(solution_z);
get_matrix_row(linear_relation_z, &matrix, row_index--); /* get the last few rows in the Gauss eliminated matrix*/
while (mpz_cmp_ui(linear_relation_z, 0) == 0) {
nb_linear_relations++;
get_matrix_row(linear_relation_z, &matrix, row_index--);
}
PRINT(my_rank, "\tLinear dependent relations found : %d\n",
nb_linear_relations);
//--------------------------------------------------------
// Factor
//--------------------------------------------------------
//We use the last linear relation to reconstruct our solution
START_TIMER();
PRINT(my_rank, "%s", "\nFactorizing..\n");
mpz_t solution_X, solution_Y;
mpz_init(solution_X);
mpz_init(solution_Y);
/* we start testing from the first linear relation encountered in the matrix */
for (j = nb_linear_relations; j > 0; j--) {
PRINT(my_rank, "Trying %d..\n", nb_linear_relations - j + 1);
mpz_set_ui(solution_X, 1);
mpz_set_ui(solution_Y, 1);
get_identity_row(solution_z, &matrix,
nb_qr_primes + NB_VECTORS_OFFSET - j + 1);
for (i = 0; i < nb_qr_primes; i++) {
if (mpz_tstbit(solution_z, i)) {
mpz_mul(solution_X, solution_X, smooth_numbers[i].value_x);
mpz_mod(solution_X, solution_X, N); /* reduce x to modulo N */
mpz_mul(solution_Y, solution_Y,
smooth_numbers[i].value_x_squared);
/*TODO: handling huge stuff here, there is no modulo N like in the solution_X case!
* eliminate squares as long as you go*/
}
}
mpz_sqrt(solution_Y, solution_Y);
mpz_mod(solution_Y, solution_Y, N); /* y = sqrt(MUL(xi²-n)) mod N */
mpz_sub(solution_X, solution_X, solution_Y);
mpz_gcd(solution_X, solution_X, N);
if (mpz_cmp(solution_X, N) != 0 && mpz_cmp_ui(solution_X, 1) != 0) /* factor can be 1 or N, try another relation */
break;
}
mpz_cdiv_q(solution_Y, N, solution_X);
PRINT(my_rank, "\n>>>>>>>>>>> FACTORED %s =\n",
mpz_get_str(NULL, 10, N));
PRINT(
my_rank,
"\tFactor 1: %s \n\tFactor 2: %s",
mpz_get_str(NULL, 10, solution_X), mpz_get_str(NULL, 10, solution_Y));
sprintf(s, "\n>>>>>>>>>>> FACTORED %s =\n", mpz_get_str(NULL, 10, N));
APPEND_TO_LOG_FILE(s);
sprintf(s, "\tFactor 1: %s \n\tFactor 2: %s",
mpz_get_str(NULL, 10, solution_X),
mpz_get_str(NULL, 10, solution_Y));
APPEND_TO_LOG_FILE(s);
gettimeofday(&end_global, NULL);
timersub(&end_global, &start_global, &elapsed);
sprintf(s, "****** TOTAL TIME: %.3f ms\n",
elapsed.tv_sec * 1000 + elapsed.tv_usec / (double) 1000);
APPEND_TO_LOG_FILE(s);
STOP_TIMER_PRINT_TIME("\nFactorizing done");
}
PRINT(my_rank, "%s", "\nCleaning memory..\n");
/********************** clear the x_squared array **********************/
for (i = 0; i < SIEVING_STEP; i++) {
mpz_clear(x_squared[i].value_x);
mpz_clear(x_squared[i].value_x_squared);
//free(x_squared[i].factors_exp);
mpz_clear(x_squared[i].factors_vect);
}
free(x_squared);
/********************** clear the x_squared array **********************/
free(modular_roots);
/********************** clear the smooth_numbers array **********************/
if (my_rank == 0) {
for (i = 0; i < nb_qr_primes + NB_VECTORS_OFFSET; i++) {
mpz_clear(smooth_numbers[i].value_x);
mpz_clear(smooth_numbers[i].value_x_squared);
mpz_clear(smooth_numbers[i].factors_vect);
//free(smooth_numbers[i].factors_exp);
}
free(smooth_numbers);
} else {
for (i = 0; i < 500; i++) {
mpz_clear(temp_slaves_smooth_numbers[i].value_x);
mpz_clear(temp_slaves_smooth_numbers[i].value_x_squared);
mpz_clear(temp_slaves_smooth_numbers[i].factors_vect);
}
free(temp_slaves_smooth_numbers);
}
/********************** clear the smooth_numbers array **********************/
free(primes);
/********************** clear mpz _t **********************/mpz_clear(B);
mpz_clear(N);
sqrtN, rem;
mpz_clear(x);
mpz_clear(sieving_index);
mpz_clear(next_sieving_index);
mpz_clear(p);
mpz_clear(str);
/********************** clear mpz _t **********************/
free_matrix(&matrix);
gettimeofday(&end_global, NULL);
timersub(&end_global, &start_global, &elapsed);
PRINT(my_rank, "****** TOTAL TIME: %.3f ms\n",
elapsed.tv_sec * 1000 + elapsed.tv_usec / (double) 1000);
show_mem_usage();
MPI_Finalize();
return 0;
}
int
main() {
const int urfd = open("/dev/urandom", O_RDONLY);
mpz_t p, q, n;
fprintf(stderr, "Generating group...\n");
init_random_prime(p, urfd, 512, 3);
init_random_prime(q, urfd, 512, 7);
print(" p:", p);
print(" q:", q);
mpz_init(n);
mpz_mul(n, p, q);
print(" n:", n);
fprintf(stderr, "Performing extended Euclid...\n");
mpz_t u, v;
xgcd(u, v, p, q);
mpz_mul(u, u, p);
mpz_mul(v, v, q);
print (" u:", u);
print (" v:", v);
fprintf(stderr, "Picking random element...\n");
mpz_t e;
random_element(e, urfd, 1024, n);
print(" e:", e);
fprintf(stderr, "Tweaking...\n");
int a = is_quadratic_residue(e, p);
int b = is_quadratic_residue(e, q);
fprintf(stderr, " residue state: [%d, %d]\n", a, b);
int mul_2 = 0, negate = 0;
if (a ^ b) {
mul_2 = 1;
a ^= 1;
}
if (!a) {
negate = 1;
a ^= 1;
b ^= 1;
}
fprintf(stderr, " tweaks: 2:%d -:%d\n", mul_2, negate);
if (negate) {
mpz_neg(e, e);
}
if (mul_2) {
mpz_mul_ui(e, e, 2);
}
if (negate || mul_2)
mpz_mod(e, e, n);
print(" tweaked e:", e);
uint8_t root;
read(urfd, &root, 1);
root &= 3;
fprintf(stderr, "Calculating root %d...\n", root);
mpz_t pp1over4, qp1over4;
mpz_init_set(pp1over4, p);
mpz_add_ui(pp1over4, pp1over4, 1);
mpz_cdiv_q_2exp(pp1over4, pp1over4, 2);
mpz_init_set(qp1over4, q);
mpz_add_ui(qp1over4, qp1over4, 1);
mpz_cdiv_q_2exp(qp1over4, qp1over4, 2);
mpz_t proot, qroot;
mpz_init_set(proot, e);
mpz_powm(proot, e, pp1over4, p);
mpz_init_set(qroot, e);
mpz_powm(qroot, e, qp1over4, q);
if (root & 1)
mpz_neg(proot, proot);
if (root & 2)
mpz_neg(qroot, qroot);
mpz_mul(proot, proot, v);
mpz_mul(qroot, qroot, u);
mpz_add(proot, proot, qroot);
mpz_mod(proot, proot, n);
print(" sig:", proot);
fprintf(stderr, "Compressing signature...\n");
mpz_t zsig;
mpz_t ncopy;
mpz_init_set(ncopy, n);
signature_compress(zsig, proot, ncopy);
print(" zsig:", zsig);
mpz_t zsigcopy, t, t2;
mpz_init(t);
mpz_init(t2);
mpz_init(zsigcopy);
fprintf(stderr, "Performing 1000000 verifications\n");
const uint64_t start_time = time_now();
unsigned i;
for (i = 0; i < 1000000; ++i) {
mpz_set(zsigcopy, zsig);
mpz_mul(zsigcopy, zsigcopy, zsigcopy);
mpz_mul(zsigcopy, zsigcopy, e);
mpz_mod(zsigcopy, zsigcopy, n);
if (0 == mpz_sgn(zsigcopy))
abort();
mpz_sqrtrem(t, t2, zsigcopy);
if (mpz_sgn(t2))
abort();
}
const uint64_t end_time = time_now();
fprintf(stderr, "verify time: %f\n", ((double) (end_time - start_time)) / 1000000);
return 0;
}
int
main (int argc, char **argv)
{
int i;
int pass, reps = 400;
mpz_t in1, in2, in3;
unsigned long int in2i;
mp_size_t size;
mpz_t res1, res2, res3;
mpz_t ref1, ref2, ref3;
mpz_t t;
unsigned long int r1, r2;
gmp_randstate_ptr rands;
mpz_t bs;
unsigned long bsi, size_range;
tests_start ();
TESTS_REPS (reps, argv, argc);
rands = RANDS;
mpz_init (bs);
mpz_init (in1);
mpz_init (in2);
mpz_init (in3);
mpz_init (ref1);
mpz_init (ref2);
mpz_init (ref3);
mpz_init (res1);
mpz_init (res2);
mpz_init (res3);
mpz_init (t);
for (pass = 1; pass <= reps; pass++)
{
if (isatty (fileno (stdout)))
{
printf ("\r%d/%d passes", pass, reps);
fflush (stdout);
}
mpz_urandomb (bs, rands, 32);
size_range = mpz_get_ui (bs) % 21 + 2;
if ((pass & 1) == 0)
{
/* Make all input operands have quite different sizes */
mpz_urandomb (bs, rands, 32);
size = mpz_get_ui (bs) % size_range;
mpz_rrandomb (in1, rands, size);
mpz_urandomb (bs, rands, 32);
size = mpz_get_ui (bs) % size_range;
mpz_rrandomb (in2, rands, size);
mpz_urandomb (bs, rands, 32);
size = mpz_get_ui (bs) % size_range;
mpz_rrandomb (in3, rands, size);
}
else
{
/* Make all input operands have about the same size */
mpz_urandomb (bs, rands, size_range);
size = mpz_get_ui (bs);
mpz_rrandomb (in1, rands, size);
mpz_urandomb (bs, rands, size_range);
size = mpz_get_ui (bs);
mpz_rrandomb (in2, rands, size);
mpz_urandomb (bs, rands, size_range);
size = mpz_get_ui (bs);
mpz_rrandomb (in3, rands, size);
}
mpz_urandomb (bs, rands, 3);
bsi = mpz_get_ui (bs);
if ((bsi & 1) != 0)
mpz_neg (in1, in1);
if ((bsi & 2) != 0)
mpz_neg (in2, in2);
if ((bsi & 4) != 0)
mpz_neg (in3, in3);
for (i = 0; i < numberof (dss); i++)
{
if (dss[i].isdivision && mpz_sgn (in2) == 0)
continue;
if (dss[i].isslow && size_range > 19)
continue;
(dss[i].fptr) (ref1, in1, in2);
MPZ_CHECK_FORMAT (ref1);
mpz_set (res1, in1);
INVOKE_RSS (dss[i], res1, res1, in2);
MPZ_CHECK_FORMAT (res1);
if (mpz_cmp (ref1, res1) != 0)
FAIL (dss, i, in1, in2, NULL);
mpz_set (res1, in2);
INVOKE_RSS (dss[i], res1, in1, res1);
MPZ_CHECK_FORMAT (res1);
if (mpz_cmp (ref1, res1) != 0)
FAIL (dss, i, in1, in2, NULL);
}
for (i = 0; i < numberof (ddss_div); i++)
{
if (mpz_sgn (in2) == 0)
continue;
(ddss_div[i].fptr) (ref1, ref2, in1, in2);
MPZ_CHECK_FORMAT (ref1);
MPZ_CHECK_FORMAT (ref2);
mpz_set (res1, in1);
INVOKE_RRSS (ddss_div[i], res1, res2, res1, in2);
MPZ_CHECK_FORMAT (res1);
MPZ_CHECK_FORMAT (res2);
if (mpz_cmp (ref1, res1) != 0 || mpz_cmp (ref2, res2) != 0)
FAIL (ddss_div, i, in1, in2, NULL);
mpz_set (res2, in1);
INVOKE_RRSS (ddss_div[i], res1, res2, res2, in2);
MPZ_CHECK_FORMAT (res1);
MPZ_CHECK_FORMAT (res2);
if (mpz_cmp (ref1, res1) != 0 || mpz_cmp (ref2, res2) != 0)
FAIL (ddss_div, i, in1, in2, NULL);
mpz_set (res1, in2);
INVOKE_RRSS (ddss_div[i], res1, res2, in1, res1);
MPZ_CHECK_FORMAT (res1);
MPZ_CHECK_FORMAT (res2);
if (mpz_cmp (ref1, res1) != 0 || mpz_cmp (ref2, res2) != 0)
FAIL (ddss_div, i, in1, in2, NULL);
mpz_set (res2, in2);
INVOKE_RRSS (ddss_div[i], res1, res2, in1, res2);
MPZ_CHECK_FORMAT (res1);
MPZ_CHECK_FORMAT (res2);
if (mpz_cmp (ref1, res1) != 0 || mpz_cmp (ref2, res2) != 0)
FAIL (ddss_div, i, in1, in2, NULL);
}
for (i = 0; i < numberof (ds); i++)
{
if (ds[i].nonneg && mpz_sgn (in1) < 0)
continue;
(ds[i].fptr) (ref1, in1);
MPZ_CHECK_FORMAT (ref1);
mpz_set (res1, in1);
INVOKE_RS (ds[i], res1, res1);
MPZ_CHECK_FORMAT (res1);
if (mpz_cmp (ref1, res1) != 0)
FAIL (ds, i, in1, in2, NULL);
}
in2i = mpz_get_ui (in2);
for (i = 0; i < numberof (dsi); i++)
{
if (dsi[i].mod != 0)
in2i = mpz_get_ui (in2) % dsi[i].mod;
(dsi[i].fptr) (ref1, in1, in2i);
MPZ_CHECK_FORMAT (ref1);
mpz_set (res1, in1);
INVOKE_RRS (dsi[i], res1, res1, in2i);
MPZ_CHECK_FORMAT (res1);
if (mpz_cmp (ref1, res1) != 0)
FAIL (dsi, i, in1, in2, NULL);
}
if (in2i != 0) /* Don't divide by 0. */
{
for (i = 0; i < numberof (dsi_div); i++)
{
r1 = (dsi_div[i].fptr) (ref1, in1, in2i);
MPZ_CHECK_FORMAT (ref1);
mpz_set (res1, in1);
r2 = (dsi_div[i].fptr) (res1, res1, in2i);
MPZ_CHECK_FORMAT (res1);
if (mpz_cmp (ref1, res1) != 0 || r1 != r2)
FAIL (dsi_div, i, in1, in2, NULL);
}
for (i = 0; i < numberof (ddsi_div); i++)
{
r1 = (ddsi_div[i].fptr) (ref1, ref2, in1, in2i);
MPZ_CHECK_FORMAT (ref1);
mpz_set (res1, in1);
r2 = (ddsi_div[i].fptr) (res1, res2, res1, in2i);
MPZ_CHECK_FORMAT (res1);
if (mpz_cmp (ref1, res1) != 0 || mpz_cmp (ref2, res2) != 0 || r1 != r2)
FAIL (ddsi_div, i, in1, in2, NULL);
mpz_set (res2, in1);
(ddsi_div[i].fptr) (res1, res2, res2, in2i);
MPZ_CHECK_FORMAT (res1);
if (mpz_cmp (ref1, res1) != 0 || mpz_cmp (ref2, res2) != 0 || r1 != r2)
FAIL (ddsi_div, i, in1, in2, NULL);
}
}
if (mpz_sgn (in1) >= 0)
{
mpz_sqrtrem (ref1, ref2, in1);
MPZ_CHECK_FORMAT (ref1);
MPZ_CHECK_FORMAT (ref2);
mpz_set (res1, in1);
mpz_sqrtrem (res1, res2, res1);
MPZ_CHECK_FORMAT (res1);
MPZ_CHECK_FORMAT (res2);
if (mpz_cmp (ref1, res1) != 0 || mpz_cmp (ref2, res2) != 0)
FAIL2 (mpz_sqrtrem, in1, NULL, NULL);
mpz_set (res2, in1);
mpz_sqrtrem (res1, res2, res2);
MPZ_CHECK_FORMAT (res1);
MPZ_CHECK_FORMAT (res2);
if (mpz_cmp (ref1, res1) != 0 || mpz_cmp (ref2, res2) != 0)
FAIL2 (mpz_sqrtrem, in1, NULL, NULL);
mpz_set (res1, in1);
mpz_sqrtrem (res1, res1, res1);
MPZ_CHECK_FORMAT (res1);
if (mpz_cmp (ref2, res1) != 0)
FAIL2 (mpz_sqrtrem, in1, NULL, NULL);
}
if (mpz_sgn (in1) >= 0)
{
mpz_root (ref1, in1, in2i % 0x100 + 1);
MPZ_CHECK_FORMAT (ref1);
mpz_set (res1, in1);
mpz_root (res1, res1, in2i % 0x100 + 1);
MPZ_CHECK_FORMAT (res1);
if (mpz_cmp (ref1, res1) != 0)
FAIL2 (mpz_root, in1, in2, NULL);
}
if (mpz_sgn (in1) >= 0)
{
mpz_rootrem (ref1, ref2, in1, in2i % 0x100 + 1);
MPZ_CHECK_FORMAT (ref1);
MPZ_CHECK_FORMAT (ref2);
mpz_set (res1, in1);
mpz_rootrem (res1, res2, res1, in2i % 0x100 + 1);
MPZ_CHECK_FORMAT (res1);
MPZ_CHECK_FORMAT (res2);
if (mpz_cmp (ref1, res1) != 0 || mpz_cmp (ref2, res2) != 0)
FAIL2 (mpz_rootrem, in1, in2, NULL);
mpz_set (res2, in1);
mpz_rootrem (res1, res2, res2, in2i % 0x100 + 1);
MPZ_CHECK_FORMAT (res1);
MPZ_CHECK_FORMAT (res2);
if (mpz_cmp (ref1, res1) != 0 || mpz_cmp (ref2, res2) != 0)
FAIL2 (mpz_rootrem, in1, in2, NULL);
}
if (size_range < 18) /* run fewer tests since gcdext lots of time */
{
mpz_gcdext (ref1, ref2, ref3, in1, in2);
MPZ_CHECK_FORMAT (ref1);
MPZ_CHECK_FORMAT (ref2);
MPZ_CHECK_FORMAT (ref3);
mpz_set (res1, in1);
mpz_gcdext (res1, res2, res3, res1, in2);
MPZ_CHECK_FORMAT (res1);
MPZ_CHECK_FORMAT (res2);
MPZ_CHECK_FORMAT (res3);
if (mpz_cmp (ref1, res1) != 0 || mpz_cmp (ref2, res2) != 0
|| mpz_cmp (ref3, res3) != 0)
FAIL2 (mpz_gcdext, in1, in2, NULL);
mpz_set (res2, in1);
mpz_gcdext (res1, res2, res3, res2, in2);
MPZ_CHECK_FORMAT (res1);
MPZ_CHECK_FORMAT (res2);
MPZ_CHECK_FORMAT (res3);
if (mpz_cmp (ref1, res1) != 0 || mpz_cmp (ref2, res2) != 0
|| mpz_cmp (ref3, res3) != 0)
FAIL2 (mpz_gcdext, in1, in2, NULL);
mpz_set (res3, in1);
mpz_gcdext (res1, res2, res3, res3, in2);
MPZ_CHECK_FORMAT (res1);
MPZ_CHECK_FORMAT (res2);
MPZ_CHECK_FORMAT (res3);
if (mpz_cmp (ref1, res1) != 0 || mpz_cmp (ref2, res2) != 0
|| mpz_cmp (ref3, res3) != 0)
FAIL2 (mpz_gcdext, in1, in2, NULL);
mpz_set (res1, in2);
mpz_gcdext (res1, res2, res3, in1, res1);
MPZ_CHECK_FORMAT (res1);
MPZ_CHECK_FORMAT (res2);
MPZ_CHECK_FORMAT (res3);
if (mpz_cmp (ref1, res1) != 0 || mpz_cmp (ref2, res2) != 0
|| mpz_cmp (ref3, res3) != 0)
FAIL2 (mpz_gcdext, in1, in2, NULL);
mpz_set (res2, in2);
mpz_gcdext (res1, res2, res3, in1, res2);
MPZ_CHECK_FORMAT (res1);
MPZ_CHECK_FORMAT (res2);
MPZ_CHECK_FORMAT (res3);
if (mpz_cmp (ref1, res1) != 0 || mpz_cmp (ref2, res2) != 0
|| mpz_cmp (ref3, res3) != 0)
FAIL2 (mpz_gcdext, in1, in2, NULL);
mpz_set (res3, in2);
mpz_gcdext (res1, res2, res3, in1, res3);
MPZ_CHECK_FORMAT (res1);
MPZ_CHECK_FORMAT (res2);
MPZ_CHECK_FORMAT (res3);
if (mpz_cmp (ref1, res1) != 0 || mpz_cmp (ref2, res2) != 0
|| mpz_cmp (ref3, res3) != 0)
FAIL2 (mpz_gcdext, in1, in2, NULL);
mpz_set (res1, in1);
mpz_gcdext (res1, res2, NULL, res1, in2);
MPZ_CHECK_FORMAT (res1);
MPZ_CHECK_FORMAT (res2);
if (mpz_cmp (ref1, res1) != 0 || mpz_cmp (ref2, res2) != 0
|| mpz_cmp (ref3, res3) != 0)
FAIL2 (mpz_gcdext, in1, in2, NULL);
mpz_set (res2, in1);
mpz_gcdext (res1, res2, NULL, res2, in2);
MPZ_CHECK_FORMAT (res1);
MPZ_CHECK_FORMAT (res2);
if (mpz_cmp (ref1, res1) != 0 || mpz_cmp (ref2, res2) != 0
|| mpz_cmp (ref3, res3) != 0)
FAIL2 (mpz_gcdext, in1, in2, NULL);
mpz_set (res1, in2);
mpz_gcdext (res1, res2, NULL, in1, res1);
MPZ_CHECK_FORMAT (res1);
MPZ_CHECK_FORMAT (res2);
if (mpz_cmp (ref1, res1) != 0 || mpz_cmp (ref2, res2) != 0
|| mpz_cmp (ref3, res3) != 0)
FAIL2 (mpz_gcdext, in1, in2, NULL);
mpz_set (res2, in2);
mpz_gcdext (res1, res2, NULL, in1, res2);
MPZ_CHECK_FORMAT (res1);
MPZ_CHECK_FORMAT (res2);
if (mpz_cmp (ref1, res1) != 0 || mpz_cmp (ref2, res2) != 0
|| mpz_cmp (ref3, res3) != 0)
FAIL2 (mpz_gcdext, in1, in2, NULL);
}
/* Don't run mpz_powm for huge exponents or when undefined. */
if (size_range < 17 && mpz_sizeinbase (in2, 2) < 250 && mpz_sgn (in3) != 0
&& (mpz_sgn (in2) >= 0 || mpz_invert (t, in1, in3)))
{
mpz_powm (ref1, in1, in2, in3);
MPZ_CHECK_FORMAT (ref1);
mpz_set (res1, in1);
mpz_powm (res1, res1, in2, in3);
MPZ_CHECK_FORMAT (res1);
if (mpz_cmp (ref1, res1) != 0)
FAIL2 (mpz_powm, in1, in2, in3);
mpz_set (res1, in2);
mpz_powm (res1, in1, res1, in3);
MPZ_CHECK_FORMAT (res1);
if (mpz_cmp (ref1, res1) != 0)
FAIL2 (mpz_powm, in1, in2, in3);
mpz_set (res1, in3);
mpz_powm (res1, in1, in2, res1);
MPZ_CHECK_FORMAT (res1);
if (mpz_cmp (ref1, res1) != 0)
FAIL2 (mpz_powm, in1, in2, in3);
}
/* Don't run mpz_powm_ui when undefined. */
if (size_range < 17 && mpz_sgn (in3) != 0)
{
mpz_powm_ui (ref1, in1, in2i, in3);
MPZ_CHECK_FORMAT (ref1);
mpz_set (res1, in1);
mpz_powm_ui (res1, res1, in2i, in3);
MPZ_CHECK_FORMAT (res1);
if (mpz_cmp (ref1, res1) != 0)
FAIL2 (mpz_powm_ui, in1, in2, in3);
mpz_set (res1, in3);
mpz_powm_ui (res1, in1, in2i, res1);
MPZ_CHECK_FORMAT (res1);
if (mpz_cmp (ref1, res1) != 0)
FAIL2 (mpz_powm_ui, in1, in2, in3);
}
{
r1 = mpz_gcd_ui (ref1, in1, in2i);
MPZ_CHECK_FORMAT (ref1);
mpz_set (res1, in1);
r2 = mpz_gcd_ui (res1, res1, in2i);
MPZ_CHECK_FORMAT (res1);
if (mpz_cmp (ref1, res1) != 0)
FAIL2 (mpz_gcd_ui, in1, in2, NULL);
}
if (mpz_sgn (in2) != 0)
{
/* Test mpz_remove */
mp_bitcnt_t refretval, retval;
refretval = mpz_remove (ref1, in1, in2);
MPZ_CHECK_FORMAT (ref1);
mpz_set (res1, in1);
retval = mpz_remove (res1, res1, in2);
MPZ_CHECK_FORMAT (res1);
if (mpz_cmp (ref1, res1) != 0 || refretval != retval)
FAIL2 (mpz_remove, in1, in2, NULL);
mpz_set (res1, in2);
retval = mpz_remove (res1, in1, res1);
MPZ_CHECK_FORMAT (res1);
if (mpz_cmp (ref1, res1) != 0 || refretval != retval)
FAIL2 (mpz_remove, in1, in2, NULL);
}
if (mpz_sgn (in2) != 0)
{
/* Test mpz_divexact */
mpz_mul (t, in1, in2);
mpz_divexact (ref1, t, in2);
MPZ_CHECK_FORMAT (ref1);
mpz_set (res1, t);
mpz_divexact (res1, res1, in2);
MPZ_CHECK_FORMAT (res1);
if (mpz_cmp (ref1, res1) != 0)
FAIL2 (mpz_divexact, t, in2, NULL);
mpz_set (res1, in2);
mpz_divexact (res1, t, res1);
MPZ_CHECK_FORMAT (res1);
if (mpz_cmp (ref1, res1) != 0)
FAIL2 (mpz_divexact, t, in2, NULL);
}
if (mpz_sgn (in2) > 0)
{
/* Test mpz_divexact_gcd, same as mpz_divexact */
mpz_mul (t, in1, in2);
mpz_divexact_gcd (ref1, t, in2);
MPZ_CHECK_FORMAT (ref1);
mpz_set (res1, t);
mpz_divexact_gcd (res1, res1, in2);
MPZ_CHECK_FORMAT (res1);
if (mpz_cmp (ref1, res1) != 0)
FAIL2 (mpz_divexact_gcd, t, in2, NULL);
mpz_set (res1, in2);
mpz_divexact_gcd (res1, t, res1);
MPZ_CHECK_FORMAT (res1);
if (mpz_cmp (ref1, res1) != 0)
FAIL2 (mpz_divexact_gcd, t, in2, NULL);
}
}
if (isatty (fileno (stdout)))
printf ("\r%20s", "");
mpz_clear (bs);
mpz_clear (in1);
mpz_clear (in2);
mpz_clear (in3);
mpz_clear (ref1);
mpz_clear (ref2);
mpz_clear (ref3);
mpz_clear (res1);
mpz_clear (res2);
mpz_clear (res3);
mpz_clear (t);
if (isatty (fileno (stdout)))
printf ("\r");
tests_end ();
exit (0);
}
