/* Check divide and conquer division routine. */
void
check_dc_div_qr_n (void)
{
mp_limb_t np[2*MAX_LIMBS];
mp_limb_t np2[2*MAX_LIMBS];
mp_limb_t rp[2*MAX_LIMBS+1];
mp_limb_t dp[MAX_LIMBS];
mp_limb_t qp[2*MAX_LIMBS];
mp_limb_t tp[DC_DIVAPPR_Q_N_ITCH(MAX_LIMBS)];
mp_limb_t dip, cy;
mp_size_t rn, dn, qn;
gmp_randstate_t rands;
int i, j, s;
gmp_randinit_default(rands);
for (i = 0; i < ITERS; i++)
{
dn = (random() % (MAX_LIMBS - 5)) + 6;
mpn_rrandom (np, rands, 2*dn);
mpn_rrandom (dp, rands, dn);
dp[dn-1] |= GMP_LIMB_HIGHBIT;
MPN_COPY(np2, np, 2*dn);
invert_1(dip, dp[dn - 1], dp[dn - 2]);
qn = dn + 1;
qp[qn - 1] = mpn_dc_div_qr_n(qp, np, dp, dn, dip, tp);
MPN_NORMALIZE(qp, qn);
if (qn)
{
if (qn >= dn) mpn_mul(rp, qp, qn, dp, dn);
else mpn_mul(rp, dp, dn, qp, qn);
rn = dn + qn;
MPN_NORMALIZE(rp, rn);
if (rn > 2*dn)
{
printf("failed: q*d has too many limbs\n");
abort();
}
if (mpn_cmp(rp, np2, 2*dn) > 0)
{
printf("failed: remainder negative\n");
abort();
}
mpn_sub(rp, np2, 2*dn, rp, rn);
rn = 2*dn;
MPN_NORMALIZE(rp, rn);
} else
{
rn = 2*dn;
MPN_COPY(rp, np, 2*dn);
}
s = (rn < dn) ? -1 : (rn > dn) ? 1 : mpn_cmp(rp, dp, dn);
if (s >= 0)
{
printf ("failed:\n");
printf ("dn = %lu, qn = %lu, rn = %lu\n\n", dn, qn, rn);
gmp_printf (" np: %Nx\n\n", np2, 2*dn);
gmp_printf (" dp: %Nx\n\n", dp, dn);
gmp_printf (" qp: %Nx\n\n", qp, qn);
gmp_printf (" rp: %Nx\n\n", rp, rn);
abort ();
}
if (mpn_cmp(rp, np, rn) != 0)
{
printf("failed: remainder does not match\n");
gmp_printf (" np: %Nx\n\n", np2, 2*dn);
gmp_printf (" dp: %Nx\n\n", dp, dn);
gmp_printf (" qp: %Nx\n\n", qp, qn);
gmp_printf (" rp: %Nx\n\n", rp, rn);
gmp_printf (" rp2: %Nx\n\n", np, rn);
}
}
gmp_randclear(rands);
}
mp_limb_t
mpn_dc_div_qr (mp_ptr qp,
mp_ptr np, mp_size_t nn,
mp_srcptr dp, mp_size_t dn,
mp_limb_t dinv)
{
mp_size_t qn;
mp_limb_t qh, cy;
mp_ptr tp;
TMP_DECL;
TMP_MARK;
ASSERT (dn >= 6); /* to adhere to mpn_sb_div_qr's limits */
ASSERT (nn - dn >= 3); /* to adhere to mpn_sb_div_qr's limits */
ASSERT (dp[dn-1] & GMP_NUMB_HIGHBIT);
tp = TMP_ALLOC_LIMBS (DC_DIVAPPR_Q_N_ITCH(dn));
qn = nn - dn;
qp += qn;
np += nn;
dp += dn;
if (qn > dn)
{
/* Reduce qn mod dn without division, optimizing small operations. */
do
qn -= dn;
while (qn > dn);
qp -= qn; /* point at low limb of next quotient block */
np -= qn; /* point in the middle of partial remainder */
/* Perform the typically smaller block first. */
if (qn == 1)
{
mp_limb_t q, n2, n1, n0, d1, d0, d11, d01;
/* Handle qh up front, for simplicity. */
qh = mpn_cmp (np - dn + 1, dp - dn, dn) >= 0;
if (qh)
ASSERT_NOCARRY (mpn_sub_n (np - dn + 1, np - dn + 1, dp - dn, dn));
/* A single iteration of schoolbook: One 3/2 division,
followed by the bignum update and adjustment. */
n2 = np[0];
n1 = np[-1];
n0 = np[-2];
d1 = dp[-1];
d0 = dp[-2];
d01 = d0 + 1;
d11 = d1 + (d01 < d0);
ASSERT (n2 < d1 || (n2 == d1 && n1 <= d0));
if (UNLIKELY (n2 == d1) && n1 == d0)
{
q = GMP_NUMB_MASK;
cy = mpn_submul_1 (np - dn, dp - dn, dn, q);
ASSERT (cy == n2);
}
else
{
mpir_divrem32_preinv2 (q, n1, n0, n2, n1, n0, d11, d01, d1, d0, dinv);
if (dn > 2)
{
mp_limb_t cy, cy1;
cy = mpn_submul_1 (np - dn, dp - dn, dn - 2, q);
cy1 = n0 < cy;
n0 = (n0 - cy) & GMP_NUMB_MASK;
cy = n1 < cy1;
n1 = (n1 - cy1) & GMP_NUMB_MASK;
np[-2] = n0;
if (UNLIKELY (cy != 0))
{
n1 += d1 + mpn_add_n (np - dn, np - dn, dp - dn, dn - 1);
qh -= (q == 0);
q = (q - 1) & GMP_NUMB_MASK;
}
}
else
np[-2] = n0;
np[-1] = n1;
}
qp[0] = q;
}
else
{
/* Do a 2qn / qn division */
if (qn == 2)
qh = mpn_divrem_2 (qp, 0L, np - 2, 4, dp - 2); /* FIXME: obsolete function. Use 5/3 division? */
else if (BELOW_THRESHOLD (qn, DC_DIV_QR_THRESHOLD))
qh = mpn_sb_div_qr (qp, np - qn, 2 * qn, dp - qn, qn, dinv);
else
qh = mpn_dc_div_qr_n (qp, np - qn, dp - qn, qn, dinv, tp);
if (qn != dn)
{
if (qn > dn - qn)
mpn_mul (tp, qp, qn, dp - dn, dn - qn);
else
mpn_mul (tp, dp - dn, dn - qn, qp, qn);
cy = mpn_sub_n (np - dn, np - dn, tp, dn);
if (qh != 0)
cy += mpn_sub_n (np - dn + qn, np - dn + qn, dp - dn, dn - qn);
while (cy != 0)
{
qh -= mpn_sub_1 (qp, qp, qn, 1);
cy -= mpn_add_n (np - dn, np - dn, dp - dn, dn);
}
}
}
qn = nn - dn - qn;
do
{
qp -= dn;
np -= dn;
ASSERT_NOCARRY(mpn_dc_div_qr_n (qp, np - dn, dp - dn, dn, dinv, tp));
qn -= dn;
}
while (qn > 0);
}
else
{
qp -= qn; /* point at low limb of next quotient block */
np -= qn; /* point in the middle of partial remainder */
if (BELOW_THRESHOLD (qn, DC_DIV_QR_THRESHOLD))
qh = mpn_sb_div_qr (qp, np - qn, 2 * qn, dp - qn, qn, dinv);
else
qh = mpn_dc_div_qr_n (qp, np - qn, dp - qn, qn, dinv, tp);
if (qn != dn)
{
if (qn > dn - qn)
mpn_mul (tp, qp, qn, dp - dn, dn - qn);
else
mpn_mul (tp, dp - dn, dn - qn, qp, qn);
cy = mpn_sub_n (np - dn, np - dn, tp, dn);
if (qh != 0)
cy += mpn_sub_n (np - dn + qn, np - dn + qn, dp - dn, dn - qn);
while (cy != 0)
{
qh -= mpn_sub_1 (qp, qp, qn, 1);
cy -= mpn_add_n (np - dn, np - dn, dp - dn, dn);
}
}
}
TMP_FREE;
return qh;
}
/* Check divide and conquer division routine. */
void
check_dc_divappr_q_n (void)
{
mp_limb_t tp[DC_DIVAPPR_Q_N_ITCH(MAX_LIMBS)];
mp_limb_t np[2*MAX_LIMBS];
mp_limb_t np2[2*MAX_LIMBS];
mp_limb_t rp[2*MAX_LIMBS];
mp_limb_t dp[MAX_LIMBS];
mp_limb_t qp[MAX_LIMBS];
mp_limb_t dip;
mp_size_t nn, rn, dn, qn;
gmp_randstate_t rands;
int i, j, s;
gmp_randinit_default(rands);
for (i = 0; i < ITERS; i++)
{
dn = (random() % (MAX_LIMBS - 6)) + 6;
nn = 2*dn;
mpn_rrandom (np, rands, nn);
mpn_rrandom (dp, rands, dn);
dp[dn-1] |= GMP_LIMB_HIGHBIT;
MPN_COPY(np2, np, nn);
invert_1(dip, dp[dn - 1], dp[dn - 2]);
qn = nn - dn + 1;
qp[qn - 1] = mpn_dc_divappr_q_n(qp, np, dp, dn, dip, tp);
MPN_NORMALIZE(qp, qn);
if (qn)
{
if (qn >= dn) mpn_mul(rp, qp, qn, dp, dn);
else mpn_mul(rp, dp, dn, qp, qn);
rn = dn + qn;
MPN_NORMALIZE(rp, rn);
s = (rn < nn) ? -1 : (rn > nn) ? 1 : mpn_cmp(rp, np2, nn);
if (s <= 0)
{
mpn_sub(rp, np2, nn, rp, rn);
rn = nn;
MPN_NORMALIZE(rp, rn);
} else
{
mpn_sub(rp, rp, rn, np2, nn);
MPN_NORMALIZE(rp, rn);
}
} else
{
rn = nn;
MPN_COPY(rp, np, nn);
}
s = (rn < dn) ? -1 : (rn > dn) ? 1 : mpn_cmp(rp, dp, dn);
if (s >= 0)
{
printf ("failed:\n");
printf ("nn = %lu, dn = %lu, qn = %lu, rn = %lu\n\n", nn, dn, qn, rn);
gmp_printf (" np: %Nx\n\n", np2, nn);
gmp_printf (" dp: %Nx\n\n", dp, dn);
gmp_printf (" qp: %Nx\n\n", qp, qn);
gmp_printf (" rp: %Nx\n\n", rp, rn);
abort ();
}
}
gmp_randclear(rands);
}