/*------------------------------------------------------------------------*/
static uint32
get_prime_roots(poly_coeff_t *c, uint32 p, uint32 *roots,
mpz_poly_t *tmp_poly)
{
/* find all nonzero roots of (N' - x^d) mod p, where
d is the desired polynomial degree and N' is the
transformed version of N modulo p. We throw out roots
of zero because a zero root implies p divides the
degree or the leading algebraic poly coefficient, and
neither of these is allowed in later stages */
uint32 i, high_coeff;
mpz_tdiv_r_ui(tmp_poly->coeff[0], c->trans_N, p);
if (mpz_cmp_ui(tmp_poly->coeff[0], 0) == 0) {
/* when p divides trans_N, only a root of zero
exists, so skip this p */
return 0;
}
for (i = 1; i < c->degree; i++)
mpz_set_ui(tmp_poly->coeff[i], 0);
tmp_poly->degree = i;
mpz_set_ui(tmp_poly->coeff[i], p - 1);
return poly_get_zeros(roots, tmp_poly, p, &high_coeff, 0);
}
int knuth(int mm,int *epr,mpz_t N,mpz_t D)
{
double dp, fks, top = -10.0;
char found = FALSE;
int i, j, bk=0, nk=0, kk, r, p;
static int K[]={0,1,2,3,5,6,7,10,11,13,14,15,17,0};// 这些是可能的multiplier
epr[0]=1;
epr[1]=2;
do
{
kk=K[++nk];
if(kk==0)
{
kk=K[bk];
found=TRUE;// 把最大的估计值对应的部分再进行一次求素数而不是直接return
}
mpz_mul_si(D, N, kk);
fks=log(2.0)/2.0;
r=mpz_tdiv_r_ui(TB, D, 8);
if(r==1) fks*=4.0;
if(r==5) fks*=2.0;
fks-=log((double)kk)/2.0;
i=0;
j=1;
while(j<mm)
{
p=qsieve->PRIMES[++i];
r=mpz_tdiv_r_ui(TB, D, p);
if(qsieve_powmod(r,(p-1)/2,p)<=1) // 求kk*N的前mm个质数，在这些质数下雅可比符号是0或1
{
epr[++j]=p;
dp=(double)p;
if(kk%p==0) fks+=log(dp)/dp; else fks+=2*log(dp)/(dp-1.0);// 每个素数对估价的贡献
}
}
if(fks>top)
{
top=fks;
bk=nk; // 最大的估价
}
} while(!found);
return kk;
}
int
main (int argc, char **argv)
{
mpz_t dividend;
mpz_t quotient, remainder;
mpz_t quotient2, remainder2;
mpz_t temp;
mp_size_t dividend_size;
unsigned long divisor;
int i;
int reps = 10000;
gmp_randstate_ptr rands;
mpz_t bs;
unsigned long bsi, size_range;
unsigned long r_rq, r_q, r_r, r;
tests_start ();
rands = RANDS;
mpz_init (bs);
if (argc == 2)
reps = atoi (argv[1]);
mpz_init (dividend);
mpz_init (quotient);
mpz_init (remainder);
mpz_init (quotient2);
mpz_init (remainder2);
mpz_init (temp);
for (i = 0; i < reps; i++)
{
mpz_urandomb (bs, rands, 32);
size_range = mpz_get_ui (bs) % 10 + 2; /* 0..2047 bit operands */
do
{
mpz_rrandomb (bs, rands, 64);
divisor = mpz_get_ui (bs);
}
while (divisor == 0);
mpz_urandomb (bs, rands, size_range);
dividend_size = mpz_get_ui (bs);
mpz_rrandomb (dividend, rands, dividend_size);
mpz_urandomb (bs, rands, 2);
bsi = mpz_get_ui (bs);
if ((bsi & 1) != 0)
mpz_neg (dividend, dividend);
/* printf ("%ld\n", SIZ (dividend)); */
r_rq = mpz_tdiv_qr_ui (quotient, remainder, dividend, divisor);
r_q = mpz_tdiv_q_ui (quotient2, dividend, divisor);
r_r = mpz_tdiv_r_ui (remainder2, dividend, divisor);
r = mpz_tdiv_ui (dividend, divisor);
/* First determine that the quotients and remainders computed
with different functions are equal. */
if (mpz_cmp (quotient, quotient2) != 0)
dump_abort ("quotients from mpz_tdiv_qr_ui and mpz_tdiv_q_ui differ",
dividend, divisor);
if (mpz_cmp (remainder, remainder2) != 0)
dump_abort ("remainders from mpz_tdiv_qr_ui and mpz_tdiv_r_ui differ",
dividend, divisor);
/* Check if the sign of the quotient is correct. */
if (mpz_cmp_ui (quotient, 0) != 0)
if ((mpz_cmp_ui (quotient, 0) < 0)
!= (mpz_cmp_ui (dividend, 0) < 0))
dump_abort ("quotient sign wrong", dividend, divisor);
/* Check if the remainder has the same sign as the dividend
(quotient rounded towards 0). */
if (mpz_cmp_ui (remainder, 0) != 0)
if ((mpz_cmp_ui (remainder, 0) < 0) != (mpz_cmp_ui (dividend, 0) < 0))
dump_abort ("remainder sign wrong", dividend, divisor);
mpz_mul_ui (temp, quotient, divisor);
mpz_add (temp, temp, remainder);
if (mpz_cmp (temp, dividend) != 0)
dump_abort ("n mod d != n - [n/d]*d", dividend, divisor);
mpz_abs (remainder, remainder);
if (mpz_cmp_ui (remainder, divisor) >= 0)
dump_abort ("remainder greater than divisor", dividend, divisor);
if (mpz_cmp_ui (remainder, r_rq) != 0)
dump_abort ("remainder returned from mpz_tdiv_qr_ui is wrong",
dividend, divisor);
if (mpz_cmp_ui (remainder, r_q) != 0)
dump_abort ("remainder returned from mpz_tdiv_q_ui is wrong",
dividend, divisor);
if (mpz_cmp_ui (remainder, r_r) != 0)
dump_abort ("remainder returned from mpz_tdiv_r_ui is wrong",
dividend, divisor);
if (mpz_cmp_ui (remainder, r) != 0)
dump_abort ("remainder returned from mpz_tdiv_ui is wrong",
dividend, divisor);
}
mpz_clear (bs);
mpz_clear (dividend);
mpz_clear (quotient);
mpz_clear (remainder);
mpz_clear (quotient2);
mpz_clear (remainder2);
mpz_clear (temp);
tests_end ();
exit (0);
}
