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/* Racing SQUFOF, based in part on Ben Buhrow's code. */
#include <math.h>
#include "ptypes.h"
#include "small_factor.h"
/* Return 0 if n is not a perfect square. Set sqrtn to int(sqrt(n)) if so.
* See Math::Prime::Util factor.c for more info on this.
*/
static int is_perfect_square(UV n, UV* sqrtn)
{
UV m; /* lm */
m = n & 127;
if ((m*0x8bc40d7d) & (m*0xa1e2f5d1) & 0x14020a) return 0;
/* Faster with just the first test on x86
m = n % 63;
if ((m*0x3d491df7) & (m*0xc824a9f9) & 0x10f14008) return 0;
*/
m = sqrt(n);
if (n != (m*m))
return 0;
if (sqrtn != 0) *sqrtn = m;
return 1;
}
static UV gcd_ui(UV x, UV y) {
UV t;
if (y < x) { t = x; x = y; y = t; }
while (y > 0) {
t = y; y = x % y; x = t; /* y1 <- x0 % y0 ; x1 <- y0 */
}
return x;
}
typedef struct
{
UV mult;
UV valid;
UV P;
UV bn;
UV Qn;
UV Q0;
UV b0;
UV it;
UV imax;
} mult_t;
/* N < 2^63 (or 2^31). *f == 1 if no factor found */
static void squfof_unit(UV n, mult_t* mult_save, UV* f)
{
UV imax,i,Q0,b0,Qn,bn,P,bbn,Ro,S,So,t1,t2;
int j;
*f = 0;
P = mult_save->P;
bn = mult_save->bn;
Qn = mult_save->Qn;
Q0 = mult_save->Q0;
b0 = mult_save->b0;
i = mult_save->it;
imax = i + mult_save->imax;
#define SQUARE_SEARCH_ITERATION \
t1 = P; \
P = bn*Qn - P; \
t2 = Qn; \
Qn = Q0 + bn*(t1-P); \
Q0 = t2; \
bn = (b0 + P) / Qn; \
i++;
while (1) {
j = 0;
if (i & 0x1) {
SQUARE_SEARCH_ITERATION;
}
/* i is now even */
while (1) {
/* We need to know P, bn, Qn, Q0, iteration count, i from prev */
if (i >= imax) {
/* save state and try another multiplier */
mult_save->P = P;
mult_save->bn = bn;
mult_save->Qn = Qn;
mult_save->Q0 = Q0;
mult_save->it = i;
*f = 0;
return;
}
SQUARE_SEARCH_ITERATION;
/* Even iteration. Check for square: Qn = S*S */
if (is_perfect_square( Qn, &S ))
break;
/* Odd iteration */
SQUARE_SEARCH_ITERATION;
}
/* printf("found square %lu after %lu iterations with mult %d\n", Qn, i, mult_save->mult); */
/* Reduce to G0 */
Ro = P + S*((b0 - P)/S);
t1 = Ro;
So = (n - t1*t1)/S;
bbn = (b0+Ro)/So;
/* Search for symmetry point */
#define SYMMETRY_POINT_ITERATION \
t1 = Ro; \
Ro = bbn*So - Ro; \
t2 = So; \
So = S + bbn*(t1-Ro); \
S = t2; \
bbn = (b0+Ro)/So; \
if (Ro == t1) break;
j = 0;
while (1) {
SYMMETRY_POINT_ITERATION;
SYMMETRY_POINT_ITERATION;
SYMMETRY_POINT_ITERATION;
SYMMETRY_POINT_ITERATION;
if (j++ > 2000000) {
mult_save->valid = 0;
*f = 0;
return;
}
}
*f = gcd_ui(Ro, n);
if (*f > 1)
return;
}
}
#define NSQUFOF_MULT (sizeof(multipliers)/sizeof(multipliers[0]))
int racing_squfof_factor(UV n, UV *factors, UV rounds)
{
const UV multipliers[] = {
3*5*7*11, 3*5*7, 3*5*11, 3*5, 3*7*11, 3*7, 5*7*11, 5*7,
3*11, 3, 5*11, 5, 7*11, 7, 11, 1 };
const UV big2 = UV_MAX >> 2;
mult_t mult_save[NSQUFOF_MULT];
int i, still_racing;
UV nn64, mult, f64;
UV rounds_done = 0;
/* Caller should have handled these trivial cases */
MPUassert( (n >= 3) && ((n%2) != 0) , "bad n in racing_squfof_factor");
/* Too big */
if (n > big2) {
factors[0] = n; return 1;
}
for (i = 0; i < (int)NSQUFOF_MULT; i++) {
mult = multipliers[i];
nn64 = n * mult;
mult_save[i].mult = mult;
if ((big2 / mult) < n) {
mult_save[i].valid = 0; /* This multiplier would overflow 64-bit */
continue;
}
mult_save[i].valid = 1;
mult_save[i].b0 = sqrt( (double)nn64 );
mult_save[i].imax = sqrt( (double)mult_save[i].b0 ) / 3;
if (mult_save[i].imax < 20) mult_save[i].imax = 20;
if (mult_save[i].imax > rounds) mult_save[i].imax = rounds;
mult_save[i].Q0 = 1;
mult_save[i].P = mult_save[i].b0;
mult_save[i].Qn = nn64 - (mult_save[i].b0 * mult_save[i].b0);
if (mult_save[i].Qn == 0) {
factors[0] = mult_save[i].b0;
factors[1] = n / mult_save[i].b0;
MPUassert( factors[0] * factors[1] == n , "incorrect factoring");
return 2;
}
mult_save[i].bn = (mult_save[i].b0 + mult_save[i].P) / mult_save[i].Qn;
mult_save[i].it = 0;
}
/* Process the multipliers a little at a time: 0.33*(n*mult)^1/4: 20-20k */
do {
still_racing = 0;
for (i = 0; i < (int)NSQUFOF_MULT; i++) {
if (!mult_save[i].valid)
continue;
nn64 = n * (UV)multipliers[i];
squfof_unit(nn64, &mult_save[i], &f64);
if (f64 > 1) {
if (f64 != multipliers[i]) {
f64 /= gcd_ui(f64, multipliers[i]);
if (f64 != 1) {
factors[0] = f64;
factors[1] = n / f64;
MPUassert( factors[0] * factors[1] == n , "incorrect factoring");
return 2;
}
}
/* Found trivial factor. Quit working with this multiplier. */
mult_save[i].valid = 0;
}
if (mult_save[i].valid == 1)
still_racing = 1;
rounds_done += mult_save[i].imax;
if (rounds_done >= rounds)
break;
}
} while (still_racing && rounds_done < rounds);
/* No factors found */
factors[0] = n;
return 1;
}
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