1 /* mpn_bz_divrem_n and auxilliary routines.
3 THE FUNCTIONS IN THIS FILE ARE INTERNAL FUNCTIONS WITH MUTABLE
4 INTERFACES. IT IS ONLY SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES.
5 IN FACT, IT IS ALMOST GUARANTEED THAT THEY'LL CHANGE OR DISAPPEAR IN A
9 Copyright (C) 2000 Free Software Foundation, Inc.
10 Contributed by Paul Zimmermann.
12 This file is part of the GNU MP Library.
14 The GNU MP Library is free software; you can redistribute it and/or modify
15 it under the terms of the GNU Lesser General Public License as published by
16 the Free Software Foundation; either version 2.1 of the License, or (at your
17 option) any later version.
19 The GNU MP Library is distributed in the hope that it will be useful, but
20 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
21 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
22 License for more details.
24 You should have received a copy of the GNU Lesser General Public License
25 along with the GNU MP Library; see the file COPYING.LIB. If not, write to
26 the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
27 MA 02111-1307, USA. */
33 [1] Fast Recursive Division, by Christoph Burnikel and Joachim Ziegler,
34 Technical report MPI-I-98-1-022, october 1998.
35 http://www.mpi-sb.mpg.de/~ziegler/TechRep.ps.gz
38 static mp_limb_t mpn_bz_div_3_halves_by_2
39 _PROTO ((mp_ptr qp, mp_ptr np, mp_srcptr dp, mp_size_t n));
42 /* mpn_bz_divrem_n(n) calls 2*mul(n/2)+2*div(n/2), thus to be faster than
43 div(n) = 4*div(n/2), we need mul(n/2) to be faster than the classic way,
44 i.e. n/2 >= KARATSUBA_MUL_THRESHOLD */
46 #define BZ_THRESHOLD (7 * KARATSUBA_MUL_THRESHOLD)
51 unused_mpn_divrem (qp, qxn, np, nn, dp, dn)
59 /* This might be useful: */
63 mp_ptr tp = alloca ((nn + qxn) * BYTES_PER_MP_LIMB);
64 MPN_COPY (tp + qxn - nn, np, nn);
66 c = mpn_divrem (qp, 0L, tp, nn + qxn, dp, dn);
67 /* Maybe copy proper part of tp to np? Documentation is unclear about
68 the returned np value when qxn != 0 */
75 /* mpn_bz_divrem_n - Implements algorithm of page 8 in [1]: divides (np,2n)
76 by (dp,n) and puts the quotient in (qp,n), the remainder in (np,n).
77 Returns most significant limb of the quotient, which is 0 or 1.
78 Requires that the most significant bit of the divisor is set. */
82 mpn_bz_divrem_n (mp_ptr qp, mp_ptr np, mp_srcptr dp, mp_size_t n)
84 mpn_bz_divrem_n (qp, np, dp, n)
95 qhl = mpn_bz_divrem_n (qp + 1, np + 2, dp + 1, n - 1);
96 cc = mpn_submul_1 (np + 1, qp + 1, n - 1, dp[0]);
97 cc = mpn_sub_1 (np + n, np + n, 1, cc);
98 if (qhl) cc += mpn_sub_1 (np + n, np + n, 1, dp[0]);
101 qhl -= mpn_sub_1 (qp + 1, qp + 1, n - 1, (mp_limb_t) 1);
102 cc -= mpn_add_n (np + 1, np + 1, dp, n);
104 qhl += mpn_add_1 (qp + 1, qp + 1, n - 1,
105 mpn_sb_divrem_mn (qp, np, n + 1, dp, n));
110 qhl = mpn_bz_div_3_halves_by_2 (qp + n2, np + n2, dp, n2);
111 qhl += mpn_add_1 (qp + n2, qp + n2, n2,
112 mpn_bz_div_3_halves_by_2 (qp, np, dp, n2));
118 /* divides (np, 3n) by (dp, 2n) and puts the quotient in (qp, n),
119 the remainder in (np, 2n) */
123 mpn_bz_div_3_halves_by_2 (mp_ptr qp, mp_ptr np, mp_srcptr dp, mp_size_t n)
125 mpn_bz_div_3_halves_by_2 (qp, np, dp, n)
132 mp_size_t twon = n + n;
138 if (n < BZ_THRESHOLD)
139 qhl = mpn_sb_divrem_mn (qp, np + n, twon, dp + n, n);
141 qhl = mpn_bz_divrem_n (qp, np + n, dp + n, n);
142 tmp = (mp_ptr) TMP_ALLOC (twon * BYTES_PER_MP_LIMB);
143 mpn_mul_n (tmp, qp, dp, n);
144 cc = mpn_sub_n (np, np, tmp, twon);
146 if (qhl) cc += mpn_sub_n (np + n, np + n, dp, n);
149 qhl -= mpn_sub_1 (qp, qp, n, (mp_limb_t) 1);
150 cc -= mpn_add_n (np, np, dp, twon);