114 lines
3.2 KiB
C
114 lines
3.2 KiB
C
/* inv_div_qr_n - quotient and remainder using a precomputed inverse
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Copyright 2010 William Hart
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This file is part of the MPIR Library.
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The MPIR Library is free software; you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as published by
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the Free Software Foundation; either version 2.1 of the License, or (at your
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option) any later version.
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The MPIR Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
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License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with the MPIR Library; see the file COPYING.LIB. If not, write to
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the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
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MA 02110-1301, USA. */
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#include <mpir.h>
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#include "gmp-impl.h"
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#include "longlong.h"
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/*
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Computes the quotient and remainder of { np, 2*dn } by { dp, dn }.
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We require dp to be normalised and inv to be a precomputed inverse
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of { dp, dn } given by mpn_invert.
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*/
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mp_limb_t
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mpn_inv_div_qr_n(mp_ptr qp, mp_ptr np,
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mp_srcptr dp, mp_size_t dn, mp_srcptr inv)
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{
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mp_limb_t cy, lo, ret = 0, ret2 = 0;
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mp_size_t m, i;
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mp_ptr tp;
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TMP_DECL;
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TMP_MARK;
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ASSERT(mpn_is_invert(inv, dp, dn));
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if (mpn_cmp(np + dn, dp, dn) >= 0)
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{
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ret2 = 1;
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mpn_sub_n(np + dn, np + dn, dp, dn);
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}
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tp = TMP_ALLOC_LIMBS(2*dn + 1);
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mpn_mul(tp, np + dn - 1, dn + 1, inv, dn);
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add_ssaaaa(cy, lo, 0, np[dn - 1], 0, tp[dn]);
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ret += mpn_add_n(qp, tp + dn + 1, np + dn, dn);
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ret += mpn_add_1(qp, qp, dn, cy);
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/*
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Let X = B^dn + inv, D = { dp, dn }, N = { np, 2*dn }, then
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DX < B^{2*dn} <= D(X+1), thus
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Let N' = { np + n - 1, n + 1 }
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N'X/B^{dn+1} < B^{dn-1}N'/D <= N'X/B^{dn+1} + N'/B^{dn+1} < N'X/B^{dn+1} + 1
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N'X/B^{dn+1} < N/D <= N'X/B^{dn+1} + 1 + 2/B
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There is either one integer in this range, or two. However, in the latter case
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the left hand bound is either an integer or < 2/B below one.
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*/
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if (UNLIKELY(ret == 1))
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{
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ret -= mpn_sub_1(qp, qp, dn, 1);
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ASSERT(ret == 0);
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}
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ret -= mpn_sub_1(qp, qp, dn, 1);
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if (UNLIKELY(ret == ~CNST_LIMB(0)))
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ret += mpn_add_1(qp, qp, dn, 1);
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/* ret is now guaranteed to be 0 or 1*/
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ASSERT(ret == 0);
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m = dn + 1;
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if ((dn <= MPN_FFT_MUL_N_MINSIZE) || (ret))
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{
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mpn_mul_n(tp, qp, dp, dn);
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} else
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{
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mp_limb_t cy, cy2;
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if (m >= FFT_MULMOD_2EXPP1_CUTOFF)
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m = mpir_fft_adjust_limbs (m);
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cy = mpn_mulmod_Bexpp1_fft (tp, m, qp, dn, dp, dn);
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/* cy, {tp, m} = qp * dp mod (B^m+1) */
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cy2 = mpn_add_n(tp, tp, np + m, 2*dn - m);
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mpn_add_1(tp + 2*dn - m, tp + 2*dn - m, 2*m - 2*dn, cy2);
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/* Make correction */
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mpn_sub_1(tp, tp, m, tp[0] - dp[0]*qp[0]);
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}
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mpn_sub_n(np, np, tp, m);
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MPN_ZERO(np + m, 2*dn - m);
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while (np[dn] || mpn_cmp(np, dp, dn) >= 0)
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{
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ret += mpn_add_1(qp, qp, dn, 1);
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np[dn] -= mpn_sub_n(np, np, dp, dn);
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}
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/* Not possible for ret == 2 as we have qp*dp <= np */
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ASSERT(ret + ret2 < 2);
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TMP_FREE;
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return ret + ret2;
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}
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