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1.1 maekawa 1: /* mpn_divrem -- Divide natural numbers, producing both remainder and
2: quotient.
3:
4: Copyright (C) 1993, 1994, 1995, 1996 Free Software 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 Library General Public License as published by
10: the Free Software Foundation; either version 2 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 Library General Public
16: License for more details.
17:
18: You should have received a copy of the GNU Library 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., 59 Temple Place - Suite 330, Boston,
21: MA 02111-1307, USA. */
22:
23: #include "gmp.h"
24: #include "gmp-impl.h"
25: #include "longlong.h"
26:
27: /* Divide num (NP/NSIZE) by den (DP/DSIZE) and write
28: the NSIZE-DSIZE least significant quotient limbs at QP
29: and the DSIZE long remainder at NP. If QEXTRA_LIMBS is
30: non-zero, generate that many fraction bits and append them after the
31: other quotient limbs.
32: Return the most significant limb of the quotient, this is always 0 or 1.
33:
34: Preconditions:
35: 0. NSIZE >= DSIZE.
36: 1. The most significant bit of the divisor must be set.
37: 2. QP must either not overlap with the input operands at all, or
38: QP + DSIZE >= NP must hold true. (This means that it's
39: possible to put the quotient in the high part of NUM, right after the
40: remainder in NUM.
41: 3. NSIZE >= DSIZE, even if QEXTRA_LIMBS is non-zero. */
42:
43: mp_limb_t
44: #if __STDC__
45: mpn_divrem (mp_ptr qp, mp_size_t qextra_limbs,
46: mp_ptr np, mp_size_t nsize,
47: mp_srcptr dp, mp_size_t dsize)
48: #else
49: mpn_divrem (qp, qextra_limbs, np, nsize, dp, dsize)
50: mp_ptr qp;
51: mp_size_t qextra_limbs;
52: mp_ptr np;
53: mp_size_t nsize;
54: mp_srcptr dp;
55: mp_size_t dsize;
56: #endif
57: {
58: mp_limb_t most_significant_q_limb = 0;
59:
60: switch (dsize)
61: {
62: case 0:
63: /* We are asked to divide by zero, so go ahead and do it! (To make
64: the compiler not remove this statement, return the value.) */
65: return 1 / dsize;
66:
67: case 1:
68: {
69: mp_size_t i;
70: mp_limb_t n1;
71: mp_limb_t d;
72:
73: d = dp[0];
74: n1 = np[nsize - 1];
75:
76: if (n1 >= d)
77: {
78: n1 -= d;
79: most_significant_q_limb = 1;
80: }
81:
82: qp += qextra_limbs;
83: for (i = nsize - 2; i >= 0; i--)
84: udiv_qrnnd (qp[i], n1, n1, np[i], d);
85: qp -= qextra_limbs;
86:
87: for (i = qextra_limbs - 1; i >= 0; i--)
88: udiv_qrnnd (qp[i], n1, n1, 0, d);
89:
90: np[0] = n1;
91: }
92: break;
93:
94: case 2:
95: {
96: mp_size_t i;
97: mp_limb_t n1, n0, n2;
98: mp_limb_t d1, d0;
99:
100: np += nsize - 2;
101: d1 = dp[1];
102: d0 = dp[0];
103: n1 = np[1];
104: n0 = np[0];
105:
106: if (n1 >= d1 && (n1 > d1 || n0 >= d0))
107: {
108: sub_ddmmss (n1, n0, n1, n0, d1, d0);
109: most_significant_q_limb = 1;
110: }
111:
112: for (i = qextra_limbs + nsize - 2 - 1; i >= 0; i--)
113: {
114: mp_limb_t q;
115: mp_limb_t r;
116:
117: if (i >= qextra_limbs)
118: np--;
119: else
120: np[0] = 0;
121:
122: if (n1 == d1)
123: {
124: /* Q should be either 111..111 or 111..110. Need special
125: treatment of this rare case as normal division would
126: give overflow. */
127: q = ~(mp_limb_t) 0;
128:
129: r = n0 + d1;
130: if (r < d1) /* Carry in the addition? */
131: {
132: add_ssaaaa (n1, n0, r - d0, np[0], 0, d0);
133: qp[i] = q;
134: continue;
135: }
136: n1 = d0 - (d0 != 0);
137: n0 = -d0;
138: }
139: else
140: {
141: udiv_qrnnd (q, r, n1, n0, d1);
142: umul_ppmm (n1, n0, d0, q);
143: }
144:
145: n2 = np[0];
146: q_test:
147: if (n1 > r || (n1 == r && n0 > n2))
148: {
149: /* The estimated Q was too large. */
150: q--;
151:
152: sub_ddmmss (n1, n0, n1, n0, 0, d0);
153: r += d1;
154: if (r >= d1) /* If not carry, test Q again. */
155: goto q_test;
156: }
157:
158: qp[i] = q;
159: sub_ddmmss (n1, n0, r, n2, n1, n0);
160: }
161: np[1] = n1;
162: np[0] = n0;
163: }
164: break;
165:
166: default:
167: {
168: mp_size_t i;
169: mp_limb_t dX, d1, n0;
170:
171: np += nsize - dsize;
172: dX = dp[dsize - 1];
173: d1 = dp[dsize - 2];
174: n0 = np[dsize - 1];
175:
176: if (n0 >= dX)
177: {
178: if (n0 > dX || mpn_cmp (np, dp, dsize - 1) >= 0)
179: {
180: mpn_sub_n (np, np, dp, dsize);
181: n0 = np[dsize - 1];
182: most_significant_q_limb = 1;
183: }
184: }
185:
186: for (i = qextra_limbs + nsize - dsize - 1; i >= 0; i--)
187: {
188: mp_limb_t q;
189: mp_limb_t n1, n2;
190: mp_limb_t cy_limb;
191:
192: if (i >= qextra_limbs)
193: {
194: np--;
195: n2 = np[dsize];
196: }
197: else
198: {
199: n2 = np[dsize - 1];
200: MPN_COPY_DECR (np + 1, np, dsize);
201: np[0] = 0;
202: }
203:
204: if (n0 == dX)
205: /* This might over-estimate q, but it's probably not worth
206: the extra code here to find out. */
207: q = ~(mp_limb_t) 0;
208: else
209: {
210: mp_limb_t r;
211:
212: udiv_qrnnd (q, r, n0, np[dsize - 1], dX);
213: umul_ppmm (n1, n0, d1, q);
214:
215: while (n1 > r || (n1 == r && n0 > np[dsize - 2]))
216: {
217: q--;
218: r += dX;
219: if (r < dX) /* I.e. "carry in previous addition?" */
220: break;
221: n1 -= n0 < d1;
222: n0 -= d1;
223: }
224: }
225:
226: /* Possible optimization: We already have (q * n0) and (1 * n1)
227: after the calculation of q. Taking advantage of that, we
228: could make this loop make two iterations less. */
229:
230: cy_limb = mpn_submul_1 (np, dp, dsize, q);
231:
232: if (n2 != cy_limb)
233: {
234: mpn_add_n (np, np, dp, dsize);
235: q--;
236: }
237:
238: qp[i] = q;
239: n0 = np[dsize - 1];
240: }
241: }
242: }
243:
244: return most_significant_q_limb;
245: }