mp_limb_t
mpn_dc_divappr_q_n (mp_ptr qp, mp_ptr np, mp_srcptr dp, mp_size_t n,
mp_srcptr dip, mp_ptr tp)
{
mp_size_t lo, hi;
mp_limb_t cy, qh, ql;
lo = n >> 1; /* floor(n/2) */
hi = n - lo; /* ceil(n/2) */
if (BELOW_THRESHOLD (hi, DC_DIV_QR_THRESHOLD))
qh = mpn_sb_div_qr (qp + lo, np + 2 * lo, 2 * hi, dp + lo, hi, dip);
else
qh = mpn_dc_div_qr_n (qp + lo, np + 2 * lo, dp + lo, hi, dip, tp);
mpn_mul (tp, qp + lo, hi, dp, lo);
cy = mpn_sub_n (np + lo, np + lo, tp, n);
if (qh != 0)
cy += mpn_sub_n (np + n, np + n, dp, lo);
while (cy != 0)
{
qh -= mpn_sub_1 (qp + lo, qp + lo, hi, 1);
cy -= mpn_add_n (np + lo, np + lo, dp, n);
}
if (BELOW_THRESHOLD (lo, DC_DIVAPPR_Q_THRESHOLD))
ql = mpn_sb_divappr_q (qp, np + hi, 2 * lo, dp + hi, lo, dip);
else
ql = mpn_dc_divappr_q_n (qp, np + hi, dp + hi, lo, dip, tp);
if (UNLIKELY (ql != 0))
{
mp_size_t i;
for (i = 0; i < lo; i++)
qp[i] = GMP_NUMB_MASK;
}
return qh;
}
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;
}
mp_limb_t
mpn_preinv_dc_divappr_q (mp_ptr qp,
mp_ptr np, mp_size_t nn,
mp_srcptr dp, mp_size_t dn,
mp_srcptr dip)
{
mp_size_t qn;
mp_limb_t qh, cy, qsave;
mp_ptr tp;
TMP_DECL;
TMP_MARK;
tp = TMP_SALLOC_LIMBS (dn+1);
qn = nn - dn;
qp += qn;
np += nn;
dp += dn;
if (qn > dn)
{
qn++; /* pretend we'll need an extra limb */
/* 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 (BELOW_THRESHOLD (qn, DC_DIV_QR_THRESHOLD))
qh = mpn_sb_div_qr (qp, np - qn, 2 * qn, dp - qn, qn, dip);
else
qh = mpn_dc_div_qr_n (qp, np - qn, dp - qn, qn, dip, 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 + 1;
while (qn > dn)
{
qp -= dn;
np -= dn;
mpn_dc_div_qr_n (qp, np - dn, dp - dn, dn, dip, tp);
qn -= dn;
}
/* Since we pretended we'd need an extra quotient limb before, we now
have made sure the code above left just dn-1=qn quotient limbs to
develop. Develop that plus a guard limb. */
qn--;
qp -= qn;
np -= dn;
qsave = qp[qn];
mpn_dc_divappr_q_n (qp, np - dn, dp - dn, dn, dip, tp);
MPN_COPY_INCR (qp, qp + 1, qn);
qp[qn] = qsave;
}
else
{
if (qn == 0)
{
qh = mpn_cmp (np - dn, dp - dn, dn) >= 0;
if (qh)
mpn_sub_n (np - dn, np - dn, dp - dn, dn);
TMP_FREE;
return qh;
}
qp -= qn; /* point at low limb of next quotient block */
np -= qn; /* point in the middle of partial remainder */
if (BELOW_THRESHOLD (qn, DC_DIVAPPR_Q_THRESHOLD))
/* Full precision. Optimal? */
qh = mpn_sb_divappr_q (qp, np - dn, nn, dp - dn, dn, dip);
else
{
/* Put quotient in tp, use qp as temporary, since qp lacks a limb. */
qh = mpn_dc_divappr_q_n (tp, np - qn - 2, dp - (qn + 1), qn + 1, dip, qp);
MPN_COPY (qp, tp + 1, qn);
}
}
TMP_FREE;
return qh;
}
int main(void)
{
mp_limb_t r1, r2, dinv1, dinv2, a1[80], a2[80], b[40], q1[80], q2[80];
mp_size_t limbs = 10;
long i, j;
for (i = 0; i < 1000; i++)
{
mpn_random(a1, 2*limbs);
mpn_random(b, limbs);
mpn_copyi(a2, a1, 2*limbs);
b[limbs - 1] |= GMP_NUMB_HIGHBIT; /* normalise b */
#if (TIME == MPIR) || TEST
invert_1(dinv1, b[limbs - 1], b[limbs - 2]);
#endif
#if (TIME == THIS) || TEST
dinv2 = div_preinv1(b[limbs - 1], b[limbs - 2]);
#endif
#if TEST
r1 = mpn_sb_div_qr(q1, a1, 2*limbs, b, limbs, dinv1);
r2 = div_basecase(q2, a2, 2*limbs, b, limbs, dinv2);
#endif
#if TIME
for (j = 0; j < 1000; j++)
{
#if TIME == MPIR
r1 = mpn_sb_div_qr(q1, a1, 2*limbs, b, limbs, dinv1);
mpn_copyi(a1, a2, 2*limbs);
#endif
#if TIME == THIS
r2 = div_basecase(q2, a2, 2*limbs, b, limbs, dinv2);
mpn_copyi(a2, a1, 2*limbs);
#endif
}
#endif
#if TEST
if (r1 != r2)
{
printf("Error in most significant limb\n", j);
printf("%lu vs %lu\n", r1, r2);
abort();
}
for (j = 0; j < limbs; j++)
{
if (q1[limbs - j - 1] != q2[limbs - j - 1])
{
printf("Error in limb %ld of quotient\n", limbs - j - 1);
printf("%lu vs %lu\n", q1[limbs - j - 1], q2[limbs - j - 1]);
abort();
}
}
for (j = 0; j < limbs; j++)
{
if (a1[limbs - j - 1] != a2[limbs - j - 1])
{
printf("Error in limb %ld of remainder\n", limbs - j - 1);
printf("%lu vs %lu\n", a1[limbs - j - 1], a2[limbs - j - 1]);
abort();
}
}
#endif
}
printf("PASS\n");
return 0;
}
mp_limb_t
mpn_dc_divappr_q (mp_ptr qp, mp_ptr np, mp_size_t nn,
mp_srcptr dp, mp_size_t dn, mp_limb_t dinv)
{
mp_size_t q_orig, qn, sh, sl, i;
mp_limb_t qh, cy, cy2;
mp_ptr tp;
TMP_DECL;
ASSERT (dn >= 6);
ASSERT (nn >= dn + 3);
ASSERT (dp[dn-1] & GMP_NUMB_HIGHBIT);
qn = nn - dn;
if (qn + 1 < dn)
{
dp += dn - (qn + 1);
dn = qn + 1;
}
q_orig = qn;
qh = mpn_cmp(np + nn - dn, dp, dn) >= 0;
if (qh != 0)
mpn_sub_n(np + nn - dn, np + nn - dn, dp, dn);
np += nn - dn - qn;
nn = dn + qn;
/* Reduce until dn - 1 >= qn */
while (dn - 1 < qn)
{
sh = MIN(dn, qn - dn + 1);
if (sh <= DC_DIV_QR_THRESHOLD) cy2 = mpn_sb_div_qr(qp + qn - sh, np + nn - dn - sh, dn + sh, dp, dn, dinv);
else cy2 = mpn_dc_div_qr(qp + qn - sh, np + nn - dn - sh, dn + sh, dp, dn, dinv);
qn -= sh; nn -= sh;
}
cy = np[nn - 1];
/* split into two parts */
sh = qn/2; sl = qn - sh;
/* Rare case where truncation ruins normalisation */
if (cy > dp[dn - 1] || (cy == dp[dn - 1]
&& mpn_cmp(np + nn - qn, dp + dn - qn, qn - 1) >= 0))
{
__divappr_helper(qp, np + nn - qn - 2, dp + dn - qn - 1, qn);
return qh;
}
if (mpn_cmp(np + sl + dn - 1, dp + dn - sh - 1, sh + 1) >= 0)
__divappr_helper(qp + sl, np + dn + sl - 2, dp + dn - sh - 1, sh);
else
{
if (sh < SB_DIVAPPR_Q_CUTOFF)
mpn_sb_divappr_q(qp + sl, np + sl, dn + sh, dp, dn, dinv);
else
mpn_dc_divappr_q(qp + sl, np + sl, dn + sh, dp, dn, dinv);
}
cy = np[nn - sh];
TMP_MARK;
tp = TMP_ALLOC_LIMBS(sl + 2);
mpn_mulmid(tp, dp + dn - qn - 1, qn - 1, qp + sl, sh);
cy -= mpn_sub_n(np + nn - qn - 2, np + nn - qn - 2, tp, sl + 2);
TMP_FREE;
while ((mp_limb_signed_t) cy < 0)
{
qh -= mpn_sub_1(qp + sl, qp + sl, q_orig - sl, 1); /* ensure quotient is not too big */
/*
correct remainder, noting that "digits" of quotient aren't base B
but in base varying with truncation, thus correction needs fixup
*/
cy += mpn_add_n(np + nn - qn - 2, np + nn - qn - 2, dp + dn - sl - 2, sl + 2);
for (i = 0; i < sh - 1 && qp[sl + i] == ~CNST_LIMB(0); i++)
cy += mpn_add_1(np + nn - qn - 2, np + nn - qn - 2, sl + 2, dp[dn - sl - 3 - i]);
}
if (cy != 0) /* special case: unable to canonicalise */
__divappr_helper(qp, np + nn - qn - 2, dp + dn - sl - 1, sl);
else
{
if (mpn_cmp(np + dn - 1, dp + dn - sl - 1, sl + 1) >= 0)
__divappr_helper(qp, np + dn - 2, dp + dn - sl - 1, sl);
else
{
if (sl < SB_DIVAPPR_Q_CUTOFF)
mpn_sb_divappr_q(qp, np, dn + sl, dp, dn, dinv);
else
mpn_dc_divappr_q(qp, np, dn + sl, dp, dn, dinv);
}
}
return qh;
}