1 /* mpn_divrem_2 -- Divide natural numbers, producing both remainder and
2 quotient. The divisor is two limbs.
3
4 THIS FILE CONTAINS INTERNAL FUNCTIONS WITH MUTABLE INTERFACES. IT IS
5 ONLY SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS
6 ALMOST GUARANTEED THAT THEY'LL CHANGE OR DISAPPEAR IN A FUTURE GNU MP
7 RELEASE.
8
9
10 Copyright 1993, 1994, 1995, 1996, 1999, 2000, 2001, 2002 Free Software
11 Foundation, Inc.
12
13 This file is part of the GNU MP Library.
14
15 The GNU MP Library is free software; you can redistribute it and/or modify
16 it under the terms of the GNU Lesser General Public License as published by
17 the Free Software Foundation; either version 3 of the License, or (at your
18 option) any later version.
19
20 The GNU MP Library is distributed in the hope that it will be useful, but
21 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
22 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
23 License for more details.
24
25 You should have received a copy of the GNU Lesser General Public License
26 along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */
27
28 #include "gmp.h"
29 #include "gmp-impl.h"
30 #include "longlong.h"
31
32
33 /* The size where udiv_qrnnd_preinv should be used rather than udiv_qrnnd,
34 meaning the quotient size where that should happen, the quotient size
35 being how many udiv divisions will be done.
36
37 The default is to use preinv always, CPUs where this doesn't suit have
38 tuned thresholds. Note in particular that preinv should certainly be
39 used if that's the only division available (USE_PREINV_ALWAYS). */
40
41 #ifndef DIVREM_2_THRESHOLD
42 #define DIVREM_2_THRESHOLD 0
43 #endif
44
45
46 /* Divide num (NP/NSIZE) by den (DP/2) and write
47 the NSIZE-2 least significant quotient limbs at QP
48 and the 2 long remainder at NP. If QEXTRA_LIMBS is
49 non-zero, generate that many fraction bits and append them after the
50 other quotient limbs.
51 Return the most significant limb of the quotient, this is always 0 or 1.
52
53 Preconditions:
54 0. NSIZE >= 2.
55 1. The most significant bit of the divisor must be set.
56 2. QP must either not overlap with the input operands at all, or
57 QP + 2 >= NP must hold true. (This means that it's
58 possible to put the quotient in the high part of NUM, right after the
59 remainder in NUM.
60 3. NSIZE >= 2, even if QEXTRA_LIMBS is non-zero. */
61
62 mp_limb_t
mpn_divrem_2(mp_ptr qp,mp_size_t qxn,mp_ptr np,mp_size_t nn,mp_srcptr dp)63 mpn_divrem_2 (mp_ptr qp, mp_size_t qxn,
64 mp_ptr np, mp_size_t nn,
65 mp_srcptr dp)
66 {
67 mp_limb_t most_significant_q_limb = 0;
68 mp_size_t i;
69 mp_limb_t n1, n0, n2;
70 mp_limb_t d1, d0;
71 mp_limb_t d1inv;
72 int use_preinv;
73
74 ASSERT (nn >= 2);
75 ASSERT (qxn >= 0);
76 ASSERT (dp[1] & GMP_NUMB_HIGHBIT);
77 ASSERT (! MPN_OVERLAP_P (qp, nn-2+qxn, np, nn) || qp+2 >= np);
78 ASSERT_MPN (np, nn);
79 ASSERT_MPN (dp, 2);
80
81 np += nn - 2;
82 d1 = dp[1];
83 d0 = dp[0];
84 n1 = np[1];
85 n0 = np[0];
86
87 if (n1 >= d1 && (n1 > d1 || n0 >= d0))
88 {
89 #if GMP_NAIL_BITS == 0
90 sub_ddmmss (n1, n0, n1, n0, d1, d0);
91 #else
92 n0 = n0 - d0;
93 n1 = n1 - d1 - (n0 >> GMP_LIMB_BITS - 1);
94 n0 &= GMP_NUMB_MASK;
95 #endif
96 most_significant_q_limb = 1;
97 }
98
99 use_preinv = ABOVE_THRESHOLD (qxn + nn - 2, DIVREM_2_THRESHOLD);
100 if (use_preinv)
101 invert_limb (d1inv, d1);
102
103 for (i = qxn + nn - 2 - 1; i >= 0; i--)
104 {
105 mp_limb_t q;
106 mp_limb_t r;
107
108 if (i >= qxn)
109 np--;
110 else
111 np[0] = 0;
112
113 if (n1 == d1)
114 {
115 /* Q should be either 111..111 or 111..110. Need special handling
116 of this rare case as normal division would give overflow. */
117 q = GMP_NUMB_MASK;
118
119 r = (n0 + d1) & GMP_NUMB_MASK;
120 if (r < d1) /* Carry in the addition? */
121 {
122 #if GMP_NAIL_BITS == 0
123 add_ssaaaa (n1, n0, r - d0, np[0], 0, d0);
124 #else
125 n0 = np[0] + d0;
126 n1 = (r - d0 + (n0 >> GMP_NUMB_BITS)) & GMP_NUMB_MASK;
127 n0 &= GMP_NUMB_MASK;
128 #endif
129 qp[i] = q;
130 continue;
131 }
132 n1 = d0 - (d0 != 0);
133 n0 = -d0 & GMP_NUMB_MASK;
134 }
135 else
136 {
137 if (use_preinv)
138 udiv_qrnnd_preinv (q, r, n1, n0, d1, d1inv);
139 else
140 udiv_qrnnd (q, r, n1, n0 << GMP_NAIL_BITS, d1 << GMP_NAIL_BITS);
141 r >>= GMP_NAIL_BITS;
142 umul_ppmm (n1, n0, d0, q << GMP_NAIL_BITS);
143 n0 >>= GMP_NAIL_BITS;
144 }
145
146 n2 = np[0];
147
148 q_test:
149 if (n1 > r || (n1 == r && n0 > n2))
150 {
151 /* The estimated Q was too large. */
152 q--;
153
154 #if GMP_NAIL_BITS == 0
155 sub_ddmmss (n1, n0, n1, n0, 0, d0);
156 #else
157 n0 = n0 - d0;
158 n1 = n1 - (n0 >> GMP_LIMB_BITS - 1);
159 n0 &= GMP_NUMB_MASK;
160 #endif
161 r += d1;
162 if (r >= d1) /* If not carry, test Q again. */
163 goto q_test;
164 }
165
166 qp[i] = q;
167 #if GMP_NAIL_BITS == 0
168 sub_ddmmss (n1, n0, r, n2, n1, n0);
169 #else
170 n0 = n2 - n0;
171 n1 = r - n1 - (n0 >> GMP_LIMB_BITS - 1);
172 n0 &= GMP_NUMB_MASK;
173 #endif
174 }
175 np[1] = n1;
176 np[0] = n0;
177
178 return most_significant_q_limb;
179 }
180