/* Check schoolboy division routine. */ void check_sb_div_q (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 dip, cy; 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 - 2)) + 3; nn = (random() % MAX_LIMBS) + dn; mpn_rrandom (np, rands, nn); mpn_rrandom (dp, rands, dn); dp[dn-1] |= GMP_LIMB_HIGHBIT; MPN_COPY(np2, np, nn); mpir_invert_pi2(dip, dp[dn - 1], dp[dn - 2]); qn = nn - dn + 1; qp[qn - 1] = mpn_sb_div_q(qp, np, nn, dp, dn, dip); 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 > nn) { printf("failed: q*d has too many limbs\n"); abort(); } if (mpn_cmp(rp, np2, nn) > 0) { printf("failed: remainder negative\n"); abort(); } mpn_sub(rp, np2, nn, rp, rn); rn = 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); }
void mpn_tdiv_q (mp_ptr qp, mp_srcptr np, mp_size_t nn, mp_srcptr dp, mp_size_t dn) { mp_ptr new_dp, new_np, tp, rp, scratch; mp_limb_t cy, dh, qh; mp_size_t new_nn, qn; mp_limb_t dinv; int cnt; TMP_DECL; TMP_MARK; ASSERT (nn >= dn); ASSERT (dn > 0); ASSERT (dp[dn - 1] != 0); ASSERT (! MPN_OVERLAP_P (qp, nn - dn + 1, np, nn)); ASSERT (! MPN_OVERLAP_P (qp, nn - dn + 1, dp, dn)); ASSERT_ALWAYS (FUDGE >= 2); if (dn == 1) { mpn_divrem_1 (qp, 0L, np, nn, dp[dn - 1]); return; } scratch = TMP_ALLOC_LIMBS(nn + 1); qn = nn - dn + 1; /* Quotient size, high limb might be zero */ if (qn + FUDGE >= dn) { /* |________________________| |_______| */ new_np = scratch; dh = dp[dn - 1]; if (LIKELY ((dh & GMP_NUMB_HIGHBIT) == 0)) { count_leading_zeros (cnt, dh); cy = mpn_lshift (new_np, np, nn, cnt); new_np[nn] = cy; new_nn = nn + (cy != 0); new_dp = TMP_ALLOC_LIMBS (dn); mpn_lshift (new_dp, dp, dn, cnt); if (dn == 2) { qh = mpn_divrem_2 (qp, 0L, new_np, new_nn, new_dp); } else if (BELOW_THRESHOLD (dn, DC_DIV_Q_THRESHOLD) || BELOW_THRESHOLD (new_nn - dn, DC_DIV_Q_THRESHOLD)) { invert_1(dinv, new_dp[dn - 1], new_dp[dn - 2]); qh = mpn_sb_div_q (qp, new_np, new_nn, new_dp, dn, dinv); } else if (BELOW_THRESHOLD (dn, INV_DIV_Q_THRESHOLD) || BELOW_THRESHOLD (nn, 2 * INV_DIV_Q_THRESHOLD)) { invert_1(dinv, new_dp[dn - 1], new_dp[dn - 2]); qh = mpn_dc_div_q (qp, new_np, new_nn, new_dp, dn, dinv); } else { mp_ptr inv = TMP_ALLOC_LIMBS(dn); mpn_invert(inv, new_dp, dn); qh = mpn_inv_div_q (qp, new_np, new_nn, new_dp, dn, inv); } if (cy == 0) qp[qn - 1] = qh; else if (UNLIKELY (qh != 0)) { /* This happens only when the quotient is close to B^n and mpn_*_divappr_q returned B^n. */ mp_size_t i, n; n = new_nn - dn; for (i = 0; i < n; i++) qp[i] = GMP_NUMB_MAX; qh = 0; /* currently ignored */ } } else /* divisor is already normalised */ { if (new_np != np) MPN_COPY (new_np, np, nn); if (dn == 2) { qh = mpn_divrem_2 (qp, 0L, new_np, nn, dp); } else if (BELOW_THRESHOLD (dn, DC_DIV_Q_THRESHOLD) || BELOW_THRESHOLD (nn - dn, DC_DIV_Q_THRESHOLD)) { invert_1(dinv, dh, dp[dn - 2]); qh = mpn_sb_div_q (qp, new_np, nn, dp, dn, dinv); } else if (BELOW_THRESHOLD (dn, INV_DIV_Q_THRESHOLD) || BELOW_THRESHOLD (nn, 2 * INV_DIV_Q_THRESHOLD)) { invert_1(dinv, dh, dp[dn - 2]); qh = mpn_dc_div_q (qp, new_np, nn, dp, dn, dinv); } else { mp_ptr inv = TMP_ALLOC_LIMBS(dn); mpn_invert(inv, dp, dn); qh = mpn_inv_div_q (qp, new_np, nn, dp, dn, inv); } qp[nn - dn] = qh; } } else { /* |________________________| |_________________| */ tp = TMP_ALLOC_LIMBS (qn + 1); new_np = scratch; new_nn = 2 * qn + 1; if (new_np == np) /* We need {np,nn} to remain untouched until the final adjustment, so we need to allocate separate space for new_np. */ new_np = TMP_ALLOC_LIMBS (new_nn + 1); dh = dp[dn - 1]; if (LIKELY ((dh & GMP_NUMB_HIGHBIT) == 0)) { count_leading_zeros (cnt, dh); cy = mpn_lshift (new_np, np + nn - new_nn, new_nn, cnt); new_np[new_nn] = cy; new_nn += (cy != 0); new_dp = TMP_ALLOC_LIMBS (qn + 1); mpn_lshift (new_dp, dp + dn - (qn + 1), qn + 1, cnt); new_dp[0] |= dp[dn - (qn + 1) - 1] >> (GMP_NUMB_BITS - cnt); if (qn + 1 == 2) { qh = mpn_divrem_2 (tp, 0L, new_np, new_nn, new_dp); } else if (BELOW_THRESHOLD (qn - 1, DC_DIVAPPR_Q_THRESHOLD)) { invert_1(dinv, new_dp[qn], new_dp[qn - 1]); qh = mpn_sb_divappr_q (tp, new_np, new_nn, new_dp, qn + 1, dinv); } else if (BELOW_THRESHOLD (qn - 1, INV_DIVAPPR_Q_THRESHOLD)) { invert_1(dinv, new_dp[qn], new_dp[qn - 1]); qh = mpn_dc_divappr_q (tp, new_np, new_nn, new_dp, qn + 1, dinv); } else { mp_ptr inv = TMP_ALLOC_LIMBS(qn + 1); mpn_invert(inv, new_dp, qn + 1); qh = mpn_inv_divappr_q (tp, new_np, new_nn, new_dp, qn + 1, inv); } if (cy == 0) tp[qn] = qh; else if (UNLIKELY (qh != 0)) { /* This happens only when the quotient is close to B^n and mpn_*_divappr_q returned B^n. */ mp_size_t i, n; n = new_nn - (qn + 1); for (i = 0; i < n; i++) tp[i] = GMP_NUMB_MAX; qh = 0; /* currently ignored */ } } else /* divisor is already normalised */ {