/*
* pr_fact - print the factors of a number
*
* If the number is 0 or 1, then print the number and return.
* If the number is < 0, print -1, negate the number and continue
* processing.
*
* Print the factors of the number, from the lowest to the highest.
* A factor will be printed numtiple times if it divides the value
* multiple times.
*
* Factors are printed with leading tabs.
*/
static void
pr_fact(BIGNUM *val)
{
const ubig *fact; /* The factor found. */
/* Firewall - catch 0 and 1. */
if (BN_is_zero(val) || BN_is_one(val))
errx(1, "numbers <= 1 aren't permitted.");
/* Factor value. */
BN_print_dec_fp(stdout, val);
putchar(':');
for (fact = &prime[0]; !BN_is_one(val); ++fact) {
/* Look for the smallest factor. */
while (fact <= pr_limit) {
if (BN_mod_word(val, (BN_ULONG)*fact) == 0)
break;
fact++;
}
/* Watch for primes larger than the table. */
if (fact > pr_limit) {
#ifdef HAVE_OPENSSL
BIGNUM *bnfact;
bnfact = BN_new();
BN_set_word(bnfact, (BN_ULONG)*(fact - 1));
BN_sqr(bnfact, bnfact, ctx);
if (BN_cmp(bnfact, val) > 0
|| BN_is_prime(val, PRIME_CHECKS, NULL, NULL,
NULL) == 1) {
putchar(' ');
BN_print_dec_fp(stdout, val);
} else
pollard_rho(val);
#else
printf(" %s", BN_bn2dec(val));
#endif
break;
}
/* Divide factor out until none are left. */
do {
printf(" %lu", *fact);
BN_div_word(val, (BN_ULONG)*fact);
} while (BN_mod_word(val, (BN_ULONG)*fact) == 0);
/* Let the user know we're doing something. */
fflush(stdout);
}
putchar('\n');
}
/*
* pr_fact - print the factors of a number
*
* Print the factors of the number, from the lowest to the highest.
* A factor will be printed multiple times if it divides the value
* multiple times.
*
* Factors are printed with leading tabs.
*/
static void
pr_fact(BIGNUM *val)
{
const ubig *fact; /* The factor found. */
/* Firewall - catch 0 and 1. */
if (BN_is_zero(val)) /* Historical practice; 0 just exits. */
exit(0);
if (BN_is_one(val)) {
printf("1: 1\n");
return;
}
/* Factor value. */
if (hflag) {
fputs("0x", stdout);
BN_print_fp(stdout, val);
} else
BN_print_dec_fp(stdout, val);
putchar(':');
for (fact = &prime[0]; !BN_is_one(val); ++fact) {
/* Look for the smallest factor. */
do {
if (BN_mod_word(val, (BN_ULONG)*fact) == 0)
break;
} while (++fact <= pr_limit);
/* Watch for primes larger than the table. */
if (fact > pr_limit) {
#ifdef HAVE_OPENSSL
BIGNUM *bnfact;
bnfact = BN_new();
BN_set_word(bnfact, *(fact - 1));
if (!BN_sqr(bnfact, bnfact, ctx))
errx(1, "error in BN_sqr()");
if (BN_cmp(bnfact, val) > 0 ||
BN_is_prime(val, PRIME_CHECKS,
NULL, NULL, NULL) == 1)
pr_print(val);
else
pollard_pminus1(val);
#else
pr_print(val);
#endif
break;
}
/* Divide factor out until none are left. */
do {
printf(hflag ? " 0x%lx" : " %lu", *fact);
BN_div_word(val, (BN_ULONG)*fact);
} while (BN_mod_word(val, (BN_ULONG)*fact) == 0);
/* Let the user know we're doing something. */
fflush(stdout);
}
putchar('\n');
}
static void
pr_print(BIGNUM *val)
{
if (hflag) {
fputs(" 0x", stdout);
BN_print_fp(stdout, val);
} else {
putchar(' ');
BN_print_dec_fp(stdout, val);
}
}
static void
pollard_rho(BIGNUM *val)
{
BIGNUM *x, *y, *tmp, *num;
BN_ULONG a;
unsigned int steps_taken, steps_limit;
x = BN_new();
y = BN_new();
tmp = BN_new();
num = BN_new();
a = 1;
restart:
steps_taken = 0;
steps_limit = 2;
BN_set_word(x, 1);
BN_copy(y, x);
for (;;) {
BN_sqr(tmp, x, ctx);
BN_add_word(tmp, a);
BN_mod(x, tmp, val, ctx);
BN_sub(tmp, x, y);
if (BN_is_zero(tmp)) {
#ifdef DEBUG
printf(" (loop)");
#endif
a++;
goto restart;
}
BN_gcd(tmp, tmp, val, ctx);
if (!BN_is_one(tmp)) {
if (BN_is_prime(tmp, PRIME_CHECKS, NULL, NULL,
NULL) == 1) {
putchar(' ');
BN_print_dec_fp(stdout, tmp);
} else {
#ifdef DEBUG
printf(" (recurse for ");
BN_print_dec_fp(stdout, tmp);
putchar(')');
#endif
pollard_rho(BN_dup(tmp));
#ifdef DEBUG
printf(" (back)");
#endif
}
fflush(stdout);
BN_div(num, NULL, val, tmp, ctx);
if (BN_is_one(num))
return;
if (BN_is_prime(num, PRIME_CHECKS, NULL, NULL,
NULL) == 1) {
putchar(' ');
BN_print_dec_fp(stdout, num);
fflush(stdout);
return;
}
BN_copy(val, num);
goto restart;
}
steps_taken++;
if (steps_taken == steps_limit) {
BN_copy(y, x); /* teleport the turtle */
steps_taken = 0;
steps_limit *= 2;
if (steps_limit == 0) {
#ifdef DEBUG
printf(" (overflow)");
#endif
a++;
goto restart;
}
}
}
}