version 1.1.1.1, 2000/01/10 15:35:23 |
version 1.1.1.2, 2000/09/09 14:12:24 |
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/* mpn_divrem -- Divide natural numbers, producing both remainder and |
/* mpn_divrem -- Divide natural numbers, producing both remainder and |
quotient. |
quotient. This is now just a middle layer for calling the new |
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internal mpn_tdiv_qr. |
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Copyright (C) 1993, 1994, 1995, 1996 Free Software Foundation, Inc. |
Copyright (C) 1993, 1994, 1995, 1996, 1997, 1999, 2000 Free Software |
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Foundation, Inc. |
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This file is part of the GNU MP Library. |
This file is part of the GNU MP Library. |
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The GNU MP Library is free software; you can redistribute it and/or modify |
The GNU MP Library is free software; you can redistribute it and/or modify |
it under the terms of the GNU Library General Public License as published by |
it under the terms of the GNU Lesser General Public License as published by |
the Free Software Foundation; either version 2 of the License, or (at your |
the Free Software Foundation; either version 2.1 of the License, or (at your |
option) any later version. |
option) any later version. |
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The GNU MP Library is distributed in the hope that it will be useful, but |
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 |
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY |
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Library General Public |
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public |
License for more details. |
License for more details. |
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You should have received a copy of the GNU Library General Public License |
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 |
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, |
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
MA 02111-1307, USA. */ |
MA 02111-1307, USA. */ |
Line 24 MA 02111-1307, USA. */ |
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Line 26 MA 02111-1307, USA. */ |
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#include "gmp-impl.h" |
#include "gmp-impl.h" |
#include "longlong.h" |
#include "longlong.h" |
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/* Divide num (NP/NSIZE) by den (DP/DSIZE) and write |
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the NSIZE-DSIZE least significant quotient limbs at QP |
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and the DSIZE long remainder at NP. If QEXTRA_LIMBS is |
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non-zero, generate that many fraction bits and append them after the |
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other quotient limbs. |
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Return the most significant limb of the quotient, this is always 0 or 1. |
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Preconditions: |
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0. NSIZE >= DSIZE. |
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1. The most significant bit of the divisor must be set. |
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2. QP must either not overlap with the input operands at all, or |
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QP + DSIZE >= NP must hold true. (This means that it's |
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possible to put the quotient in the high part of NUM, right after the |
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remainder in NUM. |
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3. NSIZE >= DSIZE, even if QEXTRA_LIMBS is non-zero. */ |
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mp_limb_t |
mp_limb_t |
#if __STDC__ |
#if __STDC__ |
mpn_divrem (mp_ptr qp, mp_size_t qextra_limbs, |
mpn_divrem (mp_ptr qp, mp_size_t qxn, |
mp_ptr np, mp_size_t nsize, |
mp_ptr np, mp_size_t nn, |
mp_srcptr dp, mp_size_t dsize) |
mp_srcptr dp, mp_size_t dn) |
#else |
#else |
mpn_divrem (qp, qextra_limbs, np, nsize, dp, dsize) |
mpn_divrem (qp, qxn, np, nn, dp, dn) |
mp_ptr qp; |
mp_ptr qp; |
mp_size_t qextra_limbs; |
mp_size_t qxn; |
mp_ptr np; |
mp_ptr np; |
mp_size_t nsize; |
mp_size_t nn; |
mp_srcptr dp; |
mp_srcptr dp; |
mp_size_t dsize; |
mp_size_t dn; |
#endif |
#endif |
{ |
{ |
mp_limb_t most_significant_q_limb = 0; |
if (dn == 1) |
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switch (dsize) |
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{ |
{ |
case 0: |
mp_limb_t ret; |
/* We are asked to divide by zero, so go ahead and do it! (To make |
mp_ptr q2p; |
the compiler not remove this statement, return the value.) */ |
mp_size_t qn; |
return 1 / dsize; |
TMP_DECL (marker); |
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case 1: |
TMP_MARK (marker); |
{ |
q2p = (mp_ptr) TMP_ALLOC ((nn + qxn) * BYTES_PER_MP_LIMB); |
mp_size_t i; |
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mp_limb_t n1; |
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mp_limb_t d; |
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d = dp[0]; |
np[0] = mpn_divrem_1 (q2p, qxn, np, nn, dp[0]); |
n1 = np[nsize - 1]; |
qn = nn + qxn - 1; |
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MPN_COPY (qp, q2p, qn); |
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ret = q2p[qn]; |
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if (n1 >= d) |
TMP_FREE (marker); |
{ |
return ret; |
n1 -= d; |
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most_significant_q_limb = 1; |
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} |
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qp += qextra_limbs; |
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for (i = nsize - 2; i >= 0; i--) |
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udiv_qrnnd (qp[i], n1, n1, np[i], d); |
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qp -= qextra_limbs; |
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for (i = qextra_limbs - 1; i >= 0; i--) |
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udiv_qrnnd (qp[i], n1, n1, 0, d); |
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np[0] = n1; |
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} |
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break; |
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case 2: |
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{ |
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mp_size_t i; |
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mp_limb_t n1, n0, n2; |
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mp_limb_t d1, d0; |
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np += nsize - 2; |
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d1 = dp[1]; |
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d0 = dp[0]; |
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n1 = np[1]; |
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n0 = np[0]; |
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if (n1 >= d1 && (n1 > d1 || n0 >= d0)) |
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{ |
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sub_ddmmss (n1, n0, n1, n0, d1, d0); |
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most_significant_q_limb = 1; |
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} |
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for (i = qextra_limbs + nsize - 2 - 1; i >= 0; i--) |
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{ |
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mp_limb_t q; |
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mp_limb_t r; |
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if (i >= qextra_limbs) |
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np--; |
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else |
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np[0] = 0; |
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if (n1 == d1) |
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{ |
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/* Q should be either 111..111 or 111..110. Need special |
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treatment of this rare case as normal division would |
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give overflow. */ |
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q = ~(mp_limb_t) 0; |
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r = n0 + d1; |
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if (r < d1) /* Carry in the addition? */ |
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{ |
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add_ssaaaa (n1, n0, r - d0, np[0], 0, d0); |
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qp[i] = q; |
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continue; |
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} |
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n1 = d0 - (d0 != 0); |
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n0 = -d0; |
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} |
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else |
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{ |
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udiv_qrnnd (q, r, n1, n0, d1); |
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umul_ppmm (n1, n0, d0, q); |
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} |
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n2 = np[0]; |
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q_test: |
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if (n1 > r || (n1 == r && n0 > n2)) |
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{ |
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/* The estimated Q was too large. */ |
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q--; |
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sub_ddmmss (n1, n0, n1, n0, 0, d0); |
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r += d1; |
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if (r >= d1) /* If not carry, test Q again. */ |
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goto q_test; |
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} |
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qp[i] = q; |
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sub_ddmmss (n1, n0, r, n2, n1, n0); |
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} |
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np[1] = n1; |
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np[0] = n0; |
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} |
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break; |
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default: |
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{ |
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mp_size_t i; |
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mp_limb_t dX, d1, n0; |
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np += nsize - dsize; |
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dX = dp[dsize - 1]; |
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d1 = dp[dsize - 2]; |
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n0 = np[dsize - 1]; |
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if (n0 >= dX) |
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{ |
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if (n0 > dX || mpn_cmp (np, dp, dsize - 1) >= 0) |
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{ |
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mpn_sub_n (np, np, dp, dsize); |
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n0 = np[dsize - 1]; |
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most_significant_q_limb = 1; |
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} |
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} |
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for (i = qextra_limbs + nsize - dsize - 1; i >= 0; i--) |
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{ |
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mp_limb_t q; |
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mp_limb_t n1, n2; |
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mp_limb_t cy_limb; |
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if (i >= qextra_limbs) |
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{ |
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np--; |
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n2 = np[dsize]; |
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} |
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else |
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{ |
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n2 = np[dsize - 1]; |
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MPN_COPY_DECR (np + 1, np, dsize); |
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np[0] = 0; |
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} |
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if (n0 == dX) |
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/* This might over-estimate q, but it's probably not worth |
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the extra code here to find out. */ |
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q = ~(mp_limb_t) 0; |
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else |
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{ |
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mp_limb_t r; |
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udiv_qrnnd (q, r, n0, np[dsize - 1], dX); |
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umul_ppmm (n1, n0, d1, q); |
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while (n1 > r || (n1 == r && n0 > np[dsize - 2])) |
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{ |
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q--; |
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r += dX; |
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if (r < dX) /* I.e. "carry in previous addition?" */ |
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break; |
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n1 -= n0 < d1; |
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n0 -= d1; |
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} |
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} |
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/* Possible optimization: We already have (q * n0) and (1 * n1) |
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after the calculation of q. Taking advantage of that, we |
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could make this loop make two iterations less. */ |
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cy_limb = mpn_submul_1 (np, dp, dsize, q); |
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if (n2 != cy_limb) |
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{ |
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mpn_add_n (np, np, dp, dsize); |
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q--; |
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} |
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qp[i] = q; |
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n0 = np[dsize - 1]; |
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} |
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} |
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} |
} |
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else if (dn == 2) |
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{ |
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return mpn_divrem_2 (qp, qxn, np, nn, dp); |
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} |
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else |
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{ |
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mp_ptr rp, q2p; |
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mp_limb_t qhl; |
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mp_size_t qn; |
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TMP_DECL (marker); |
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return most_significant_q_limb; |
TMP_MARK (marker); |
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if (qxn != 0) |
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{ |
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mp_ptr n2p; |
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n2p = (mp_ptr) TMP_ALLOC ((nn + qxn) * BYTES_PER_MP_LIMB); |
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MPN_ZERO (n2p, qxn); |
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MPN_COPY (n2p + qxn, np, nn); |
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q2p = (mp_ptr) TMP_ALLOC ((nn - dn + qxn + 1) * BYTES_PER_MP_LIMB); |
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rp = (mp_ptr) TMP_ALLOC (dn * BYTES_PER_MP_LIMB); |
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mpn_tdiv_qr (q2p, rp, 0L, n2p, nn + qxn, dp, dn); |
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MPN_COPY (np, rp, dn); |
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qn = nn - dn + qxn; |
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MPN_COPY (qp, q2p, qn); |
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qhl = q2p[qn]; |
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} |
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else |
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{ |
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q2p = (mp_ptr) TMP_ALLOC ((nn - dn + 1) * BYTES_PER_MP_LIMB); |
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rp = (mp_ptr) TMP_ALLOC (dn * BYTES_PER_MP_LIMB); |
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mpn_tdiv_qr (q2p, rp, 0L, np, nn, dp, dn); |
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MPN_COPY (np, rp, dn); /* overwrite np area with remainder */ |
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qn = nn - dn; |
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MPN_COPY (qp, q2p, qn); |
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qhl = q2p[qn]; |
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} |
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TMP_FREE (marker); |
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return qhl; |
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} |
} |
} |