1 /* mpn/bdivmod.c: mpn_bdivmod for computing U/V mod 2^d.
2
3 Copyright 1991, 1993, 1994, 1995, 1996, 1999, 2000, 2001, 2002 Free Software
4 Foundation, Inc.
5
6 This file is part of the GNU MP Library.
7
8 The GNU MP Library is free software; you can redistribute it and/or modify
9 it under the terms of the GNU Lesser General Public License as published by
10 the Free Software Foundation; either version 2.1 of the License, or (at your
11 option) any later version.
12
13 The GNU MP Library is distributed in the hope that it will be useful, but
14 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
15 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
16 License for more details.
17
18 You should have received a copy of the GNU Lesser General Public License
19 along with the GNU MP Library; see the file COPYING.LIB. If not, write to
20 the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
21 MA 02110-1301, USA. */
22
23 /* q_high = mpn_bdivmod (qp, up, usize, vp, vsize, d).
24
25 Puts the low d/BITS_PER_MP_LIMB limbs of Q = U / V mod 2^d at qp, and
26 returns the high d%BITS_PER_MP_LIMB bits of Q as the result.
27
28 Also, U - Q * V mod 2^(usize*BITS_PER_MP_LIMB) is placed at up. Since the
29 low d/BITS_PER_MP_LIMB limbs of this difference are zero, the code allows
30 the limb vectors at qp to overwrite the low limbs at up, provided qp <= up.
31
32 Preconditions:
33 1. V is odd.
34 2. usize * BITS_PER_MP_LIMB >= d.
35 3. If Q and U overlap, qp <= up.
36
37 Ken Weber (kweber@mat.ufrgs.br, kweber@mcs.kent.edu)
38
39 Funding for this work has been partially provided by Conselho Nacional
40 de Desenvolvimento Cienti'fico e Tecnolo'gico (CNPq) do Brazil, Grant
41 301314194-2, and was done while I was a visiting reseacher in the Instituto
42 de Matema'tica at Universidade Federal do Rio Grande do Sul (UFRGS).
43
44 References:
45 T. Jebelean, An algorithm for exact division, Journal of Symbolic
46 Computation, v. 15, 1993, pp. 169-180.
47
48 K. Weber, The accelerated integer GCD algorithm, ACM Transactions on
49 Mathematical Software, v. 21 (March), 1995, pp. 111-122. */
50
51 #include "mpir.h"
52 #include "gmp-impl.h"
53 #include "longlong.h"
54
55
56 mp_limb_t
mpn_bdivmod(mp_ptr qp,mp_ptr up,mp_size_t usize,mp_srcptr vp,mp_size_t vsize,mpir_ui d)57 mpn_bdivmod (mp_ptr qp, mp_ptr up, mp_size_t usize,
58 mp_srcptr vp, mp_size_t vsize, mpir_ui d)
59 {
60 mp_limb_t v_inv;
61
62 ASSERT (usize >= 1);
63 ASSERT (vsize >= 1);
64 ASSERT (usize * GMP_NUMB_BITS >= d);
65 ASSERT (! MPN_OVERLAP_P (up, usize, vp, vsize));
66 ASSERT (! MPN_OVERLAP_P (qp, d/GMP_NUMB_BITS, vp, vsize));
67 ASSERT (MPN_SAME_OR_INCR2_P (qp, d/GMP_NUMB_BITS, up, usize));
68 ASSERT_MPN (up, usize);
69 ASSERT_MPN (vp, vsize);
70
71 /* 1/V mod 2^GMP_NUMB_BITS. */
72 modlimb_invert (v_inv, vp[0]);
73
74 /* Fast code for two cases previously used by the accel part of mpn_gcd.
75 (Could probably remove this now it's inlined there.) */
76 if (usize == 2 && vsize == 2 &&
77 (d == GMP_NUMB_BITS || d == 2*GMP_NUMB_BITS))
78 {
79 mp_limb_t hi, lo;
80 mp_limb_t q = (up[0] * v_inv) & GMP_NUMB_MASK;
81 umul_ppmm (hi, lo, q, vp[0] << GMP_NAIL_BITS);
82 up[0] = 0;
83 up[1] -= hi + q*vp[1];
84 qp[0] = q;
85 if (d == 2*GMP_NUMB_BITS)
86 {
87 q = (up[1] * v_inv) & GMP_NUMB_MASK;
88 up[1] = 0;
89 qp[1] = q;
90 }
91 return 0;
92 }
93
94 /* Main loop. */
95 while (d >= GMP_NUMB_BITS)
96 {
97 mp_limb_t q = (up[0] * v_inv) & GMP_NUMB_MASK;
98 mp_limb_t b = mpn_submul_1 (up, vp, MIN (usize, vsize), q);
99 if (usize > vsize)
100 mpn_sub_1 (up + vsize, up + vsize, usize - vsize, b);
101 d -= GMP_NUMB_BITS;
102 up += 1, usize -= 1;
103 *qp++ = q;
104 }
105
106 if (d)
107 {
108 mp_limb_t b;
109 mp_limb_t q = (up[0] * v_inv) & (((mp_limb_t)1<<d) - 1);
110 if (q <= 1)
111 {
112 if (q == 0)
113 return 0;
114 else
115 b = mpn_sub_n (up, up, vp, MIN (usize, vsize));
116 }
117 else
118 b = mpn_submul_1 (up, vp, MIN (usize, vsize), q);
119
120 if (usize > vsize)
121 mpn_sub_1 (up + vsize, up + vsize, usize - vsize, b);
122 return q;
123 }
124
125 return 0;
126 }
127