| /* mpn_divrem -- Divide natural numbers, producing both remainder and |
| quotient. |
| |
| Copyright (C) 1993, 1994, 1995, 1996 Free Software Foundation, Inc. |
| |
| This file is part of the GNU MP Library. |
| |
| The GNU MP Library is free software; you can redistribute it and/or modify |
| it under the terms of the GNU Lesser General Public License as published by |
| the Free Software Foundation; either version 2.1 of the License, or (at your |
| option) any later version. |
| |
| The GNU MP Library is distributed in the hope that it will be useful, but |
| WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY |
| or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public |
| License for more details. |
| |
| You should have received a copy of the GNU Lesser General Public License |
| along with the GNU MP Library; see the file COPYING.LIB. If not, write to |
| the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
| MA 02111-1307, USA. */ |
| |
| #include <config.h> |
| #include "gmp-impl.h" |
| |
| /* Divide num (NP/NSIZE) by den (DP/DSIZE) and write |
| the NSIZE-DSIZE least significant quotient limbs at QP |
| and the DSIZE long remainder at NP. If QEXTRA_LIMBS is |
| non-zero, generate that many fraction bits and append them after the |
| other quotient limbs. |
| Return the most significant limb of the quotient, this is always 0 or 1. |
| |
| Preconditions: |
| 0. NSIZE >= DSIZE. |
| 1. The most significant bit of the divisor must be set. |
| 2. QP must either not overlap with the input operands at all, or |
| QP + DSIZE >= NP must hold true. (This means that it's |
| possible to put the quotient in the high part of NUM, right after the |
| remainder in NUM. |
| 3. NSIZE >= DSIZE, even if QEXTRA_LIMBS is non-zero. */ |
| |
| mp_limb_t |
| #if __STDC__ |
| mpn_divrem (mp_ptr qp, mp_size_t qextra_limbs, |
| mp_ptr np, mp_size_t nsize, |
| mp_srcptr dp, mp_size_t dsize) |
| #else |
| mpn_divrem (qp, qextra_limbs, np, nsize, dp, dsize) |
| mp_ptr qp; |
| mp_size_t qextra_limbs; |
| mp_ptr np; |
| mp_size_t nsize; |
| mp_srcptr dp; |
| mp_size_t dsize; |
| #endif |
| { |
| mp_limb_t most_significant_q_limb = 0; |
| |
| switch (dsize) |
| { |
| case 0: |
| /* We are asked to divide by zero, so go ahead and do it! (To make |
| the compiler not remove this statement, return the value.) */ |
| return 1 / dsize; |
| |
| case 1: |
| { |
| mp_size_t i; |
| mp_limb_t n1; |
| mp_limb_t d; |
| |
| d = dp[0]; |
| n1 = np[nsize - 1]; |
| |
| if (n1 >= d) |
| { |
| n1 -= d; |
| most_significant_q_limb = 1; |
| } |
| |
| qp += qextra_limbs; |
| for (i = nsize - 2; i >= 0; i--) |
| udiv_qrnnd (qp[i], n1, n1, np[i], d); |
| qp -= qextra_limbs; |
| |
| for (i = qextra_limbs - 1; i >= 0; i--) |
| udiv_qrnnd (qp[i], n1, n1, 0, d); |
| |
| np[0] = n1; |
| } |
| break; |
| |
| case 2: |
| { |
| mp_size_t i; |
| mp_limb_t n1, n0, n2; |
| mp_limb_t d1, d0; |
| |
| np += nsize - 2; |
| d1 = dp[1]; |
| d0 = dp[0]; |
| n1 = np[1]; |
| n0 = np[0]; |
| |
| if (n1 >= d1 && (n1 > d1 || n0 >= d0)) |
| { |
| sub_ddmmss (n1, n0, n1, n0, d1, d0); |
| most_significant_q_limb = 1; |
| } |
| |
| for (i = qextra_limbs + nsize - 2 - 1; i >= 0; i--) |
| { |
| mp_limb_t q; |
| mp_limb_t r; |
| |
| if (i >= qextra_limbs) |
| np--; |
| else |
| np[0] = 0; |
| |
| if (n1 == d1) |
| { |
| /* Q should be either 111..111 or 111..110. Need special |
| treatment of this rare case as normal division would |
| give overflow. */ |
| q = ~(mp_limb_t) 0; |
| |
| r = n0 + d1; |
| if (r < d1) /* Carry in the addition? */ |
| { |
| add_ssaaaa (n1, n0, r - d0, np[0], 0, d0); |
| qp[i] = q; |
| continue; |
| } |
| n1 = d0 - (d0 != 0); |
| n0 = -d0; |
| } |
| else |
| { |
| udiv_qrnnd (q, r, n1, n0, d1); |
| umul_ppmm (n1, n0, d0, q); |
| } |
| |
| n2 = np[0]; |
| q_test: |
| if (n1 > r || (n1 == r && n0 > n2)) |
| { |
| /* The estimated Q was too large. */ |
| q--; |
| |
| sub_ddmmss (n1, n0, n1, n0, 0, d0); |
| r += d1; |
| if (r >= d1) /* If not carry, test Q again. */ |
| goto q_test; |
| } |
| |
| qp[i] = q; |
| sub_ddmmss (n1, n0, r, n2, n1, n0); |
| } |
| np[1] = n1; |
| np[0] = n0; |
| } |
| break; |
| |
| default: |
| { |
| mp_size_t i; |
| mp_limb_t dX, d1, n0; |
| |
| np += nsize - dsize; |
| dX = dp[dsize - 1]; |
| d1 = dp[dsize - 2]; |
| n0 = np[dsize - 1]; |
| |
| if (n0 >= dX) |
| { |
| if (n0 > dX || mpn_cmp (np, dp, dsize - 1) >= 0) |
| { |
| mpn_sub_n (np, np, dp, dsize); |
| n0 = np[dsize - 1]; |
| most_significant_q_limb = 1; |
| } |
| } |
| |
| for (i = qextra_limbs + nsize - dsize - 1; i >= 0; i--) |
| { |
| mp_limb_t q; |
| mp_limb_t n1, n2; |
| mp_limb_t cy_limb; |
| |
| if (i >= qextra_limbs) |
| { |
| np--; |
| n2 = np[dsize]; |
| } |
| else |
| { |
| n2 = np[dsize - 1]; |
| MPN_COPY_DECR (np + 1, np, dsize); |
| np[0] = 0; |
| } |
| |
| if (n0 == dX) |
| /* This might over-estimate q, but it's probably not worth |
| the extra code here to find out. */ |
| q = ~(mp_limb_t) 0; |
| else |
| { |
| mp_limb_t r; |
| |
| udiv_qrnnd (q, r, n0, np[dsize - 1], dX); |
| umul_ppmm (n1, n0, d1, q); |
| |
| while (n1 > r || (n1 == r && n0 > np[dsize - 2])) |
| { |
| q--; |
| r += dX; |
| if (r < dX) /* I.e. "carry in previous addition?" */ |
| break; |
| n1 -= n0 < d1; |
| n0 -= d1; |
| } |
| } |
| |
| /* Possible optimization: We already have (q * n0) and (1 * n1) |
| after the calculation of q. Taking advantage of that, we |
| could make this loop make two iterations less. */ |
| |
| cy_limb = mpn_submul_1 (np, dp, dsize, q); |
| |
| if (n2 != cy_limb) |
| { |
| mpn_add_n (np, np, dp, dsize); |
| q--; |
| } |
| |
| qp[i] = q; |
| n0 = np[dsize - 1]; |
| } |
| } |
| } |
| |
| return most_significant_q_limb; |
| } |