mp_limb_t mpn_dcpi1_div_qr_n (mp_ptr qp, mp_ptr np, mp_srcptr dp, mp_size_t n, gmp_pi1_t *dinv, 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_sbpi1_div_qr (qp + lo, np + 2 * lo, 2 * hi, dp + lo, hi, dinv->inv32); else qh = mpn_dcpi1_div_qr_n (qp + lo, np + 2 * lo, dp + lo, hi, dinv, 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_DIV_QR_THRESHOLD)) ql = mpn_sbpi1_div_qr (qp, np + hi, 2 * lo, dp + hi, lo, dinv->inv32); else ql = mpn_dcpi1_div_qr_n (qp, np + hi, dp + hi, lo, dinv, tp); mpn_mul (tp, dp, hi, qp, lo); cy = mpn_sub_n (np, np, tp, n); if (ql != 0) cy += mpn_sub_n (np + lo, np + lo, dp, hi); while (cy != 0) { mpn_sub_1 (qp, qp, lo, 1); cy -= mpn_add_n (np, np, dp, n); } return qh; }
mp_limb_t mpn_dcpi1_divappr_q (mp_ptr qp, mp_ptr np, mp_size_t nn, mp_srcptr dp, mp_size_t dn, gmp_pi1_t *dinv) { mp_size_t qn; mp_limb_t qh, cy, qsave; mp_ptr tp; TMP_DECL; TMP_MARK; ASSERT (dn >= 6); ASSERT (nn > dn); ASSERT (dp[dn-1] & GMP_NUMB_HIGHBIT); 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 */ tp = TMP_SALLOC_LIMBS (dn); /* Perform the typically smaller block first. */ if (qn == 1) { mp_limb_t q, n2, n1, n0, d1, d0; /* 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]; 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 { udiv_qr_3by2 (q, n1, n0, n2, n1, n0, d1, d0, dinv->inv32); 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 { if (qn == 2) qh = mpn_divrem_2 (qp, 0L, np - 2, 4, dp - 2); else if (BELOW_THRESHOLD (qn, DC_DIV_QR_THRESHOLD)) qh = mpn_sbpi1_div_qr (qp, np - qn, 2 * qn, dp - qn, qn, dinv->inv32); else qh = mpn_dcpi1_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 + 1; while (qn > dn) { qp -= dn; np -= dn; mpn_dcpi1_div_qr_n (qp, np - dn, dp - dn, dn, dinv, 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_dcpi1_divappr_q_n (qp, np - dn, dp - dn, dn, dinv, tp); MPN_COPY_INCR (qp, qp + 1, qn); qp[qn] = qsave; } else /* (qn < dn) */ { mp_ptr q2p; #if 0 /* not possible since we demand nn > dn */ 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; } #endif qp -= qn; /* point at low limb of next quotient block */ np -= qn; /* point in the middle of partial remainder */ q2p = TMP_SALLOC_LIMBS (qn + 1); /* Should we at all check DC_DIVAPPR_Q_THRESHOLD here, or reply on callers not to be silly? */ if (BELOW_THRESHOLD (qn, DC_DIVAPPR_Q_THRESHOLD)) { qh = mpn_sbpi1_divappr_q (q2p, np - qn - 2, 2 * (qn + 1), dp - (qn + 1), qn + 1, dinv->inv32); } else { /* It is tempting to use qp for recursive scratch and put quotient in tp, but the recursive scratch needs one limb too many. */ tp = TMP_SALLOC_LIMBS (qn + 1); qh = mpn_dcpi1_divappr_q_n (q2p, np - qn - 2, dp - (qn + 1), qn + 1, dinv, tp); } MPN_COPY (qp, q2p + 1, qn); } TMP_FREE; return qh; }
mp_limb_t mpn_dcpi1_div_qr (mp_ptr qp, mp_ptr np, mp_size_t nn, mp_srcptr dp, mp_size_t dn, gmp_pi1_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_sbpi1_div_qr's limits */ ASSERT (nn - dn >= 3); /* to adhere to mpn_sbpi1_div_qr's limits */ ASSERT (dp[dn-1] & GMP_NUMB_HIGHBIT); tp = TMP_SALLOC_LIMBS (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; /* 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]; 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 { udiv_qr_3by2 (q, n1, n0, n2, n1, n0, d1, d0, dinv->inv32); 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_sbpi1_div_qr (qp, np - qn, 2 * qn, dp - qn, qn, dinv->inv32); else qh = mpn_dcpi1_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; mpn_dcpi1_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_sbpi1_div_qr (qp, np - qn, 2 * qn, dp - qn, qn, dinv->inv32); else qh = mpn_dcpi1_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; }