1/*	$NetBSD: bn_mp_div.c,v 1.2 2017/01/28 21:31:47 christos Exp $	*/
2
3#include <tommath.h>
4#ifdef BN_MP_DIV_C
5/* LibTomMath, multiple-precision integer library -- Tom St Denis
6 *
7 * LibTomMath is a library that provides multiple-precision
8 * integer arithmetic as well as number theoretic functionality.
9 *
10 * The library was designed directly after the MPI library by
11 * Michael Fromberger but has been written from scratch with
12 * additional optimizations in place.
13 *
14 * The library is free for all purposes without any express
15 * guarantee it works.
16 *
17 * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
18 */
19
20#ifdef BN_MP_DIV_SMALL
21
22/* slower bit-bang division... also smaller */
23int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
24{
25   mp_int ta, tb, tq, q;
26   int    res, n, n2;
27
28  /* is divisor zero ? */
29  if (mp_iszero (b) == 1) {
30    return MP_VAL;
31  }
32
33  /* if a < b then q=0, r = a */
34  if (mp_cmp_mag (a, b) == MP_LT) {
35    if (d != NULL) {
36      res = mp_copy (a, d);
37    } else {
38      res = MP_OKAY;
39    }
40    if (c != NULL) {
41      mp_zero (c);
42    }
43    return res;
44  }
45
46  /* init our temps */
47  if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL) != MP_OKAY)) {
48     return res;
49  }
50
51
52  mp_set(&tq, 1);
53  n = mp_count_bits(a) - mp_count_bits(b);
54  if (((res = mp_abs(a, &ta)) != MP_OKAY) ||
55      ((res = mp_abs(b, &tb)) != MP_OKAY) ||
56      ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) ||
57      ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) {
58      goto LBL_ERR;
59  }
60
61  while (n-- >= 0) {
62     if (mp_cmp(&tb, &ta) != MP_GT) {
63        if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) ||
64            ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) {
65           goto LBL_ERR;
66        }
67     }
68     if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) ||
69         ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) {
70           goto LBL_ERR;
71     }
72  }
73
74  /* now q == quotient and ta == remainder */
75  n  = a->sign;
76  n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG);
77  if (c != NULL) {
78     mp_exch(c, &q);
79     c->sign  = (mp_iszero(c) == MP_YES) ? MP_ZPOS : n2;
80  }
81  if (d != NULL) {
82     mp_exch(d, &ta);
83     d->sign = (mp_iszero(d) == MP_YES) ? MP_ZPOS : n;
84  }
85LBL_ERR:
86   mp_clear_multi(&ta, &tb, &tq, &q, NULL);
87   return res;
88}
89
90#else
91
92/* integer signed division.
93 * c*b + d == a [e.g. a/b, c=quotient, d=remainder]
94 * HAC pp.598 Algorithm 14.20
95 *
96 * Note that the description in HAC is horribly
97 * incomplete.  For example, it doesn't consider
98 * the case where digits are removed from 'x' in
99 * the inner loop.  It also doesn't consider the
100 * case that y has fewer than three digits, etc..
101 *
102 * The overall algorithm is as described as
103 * 14.20 from HAC but fixed to treat these cases.
104*/
105int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
106{
107  mp_int  q, x, y, t1, t2;
108  int     res, n, t, i, norm, neg;
109
110  /* is divisor zero ? */
111  if (mp_iszero (b) == 1) {
112    return MP_VAL;
113  }
114
115  /* if a < b then q=0, r = a */
116  if (mp_cmp_mag (a, b) == MP_LT) {
117    if (d != NULL) {
118      res = mp_copy (a, d);
119    } else {
120      res = MP_OKAY;
121    }
122    if (c != NULL) {
123      mp_zero (c);
124    }
125    return res;
126  }
127
128  if ((res = mp_init_size (&q, a->used + 2)) != MP_OKAY) {
129    return res;
130  }
131  q.used = a->used + 2;
132
133  if ((res = mp_init (&t1)) != MP_OKAY) {
134    goto LBL_Q;
135  }
136
137  if ((res = mp_init (&t2)) != MP_OKAY) {
138    goto LBL_T1;
139  }
140
141  if ((res = mp_init_copy (&x, a)) != MP_OKAY) {
142    goto LBL_T2;
143  }
144
145  if ((res = mp_init_copy (&y, b)) != MP_OKAY) {
146    goto LBL_X;
147  }
148
149  /* fix the sign */
150  neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
151  x.sign = y.sign = MP_ZPOS;
152
153  /* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */
154  norm = mp_count_bits(&y) % DIGIT_BIT;
155  if (norm < (int)(DIGIT_BIT-1)) {
156     norm = (DIGIT_BIT-1) - norm;
157     if ((res = mp_mul_2d (&x, norm, &x)) != MP_OKAY) {
158       goto LBL_Y;
159     }
160     if ((res = mp_mul_2d (&y, norm, &y)) != MP_OKAY) {
161       goto LBL_Y;
162     }
163  } else {
164     norm = 0;
165  }
166
167  /* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */
168  n = x.used - 1;
169  t = y.used - 1;
170
171  /* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */
172  if ((res = mp_lshd (&y, n - t)) != MP_OKAY) { /* y = y*b**{n-t} */
173    goto LBL_Y;
174  }
175
176  while (mp_cmp (&x, &y) != MP_LT) {
177    ++(q.dp[n - t]);
178    if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) {
179      goto LBL_Y;
180    }
181  }
182
183  /* reset y by shifting it back down */
184  mp_rshd (&y, n - t);
185
186  /* step 3. for i from n down to (t + 1) */
187  for (i = n; i >= (t + 1); i--) {
188    if (i > x.used) {
189      continue;
190    }
191
192    /* step 3.1 if xi == yt then set q{i-t-1} to b-1,
193     * otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */
194    if (x.dp[i] == y.dp[t]) {
195      q.dp[i - t - 1] = ((((mp_digit)1) << DIGIT_BIT) - 1);
196    } else {
197      mp_word tmp;
198      tmp = ((mp_word) x.dp[i]) << ((mp_word) DIGIT_BIT);
199      tmp |= ((mp_word) x.dp[i - 1]);
200      tmp /= ((mp_word) y.dp[t]);
201      if (tmp > (mp_word) MP_MASK)
202        tmp = MP_MASK;
203      q.dp[i - t - 1] = (mp_digit) (tmp & (mp_word) (MP_MASK));
204    }
205
206    /* while (q{i-t-1} * (yt * b + y{t-1})) >
207             xi * b**2 + xi-1 * b + xi-2
208
209       do q{i-t-1} -= 1;
210    */
211    q.dp[i - t - 1] = (q.dp[i - t - 1] + 1) & MP_MASK;
212    do {
213      q.dp[i - t - 1] = (q.dp[i - t - 1] - 1) & MP_MASK;
214
215      /* find left hand */
216      mp_zero (&t1);
217      t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1];
218      t1.dp[1] = y.dp[t];
219      t1.used = 2;
220      if ((res = mp_mul_d (&t1, q.dp[i - t - 1], &t1)) != MP_OKAY) {
221        goto LBL_Y;
222      }
223
224      /* find right hand */
225      t2.dp[0] = (i - 2 < 0) ? 0 : x.dp[i - 2];
226      t2.dp[1] = (i - 1 < 0) ? 0 : x.dp[i - 1];
227      t2.dp[2] = x.dp[i];
228      t2.used = 3;
229    } while (mp_cmp_mag(&t1, &t2) == MP_GT);
230
231    /* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */
232    if ((res = mp_mul_d (&y, q.dp[i - t - 1], &t1)) != MP_OKAY) {
233      goto LBL_Y;
234    }
235
236    if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
237      goto LBL_Y;
238    }
239
240    if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) {
241      goto LBL_Y;
242    }
243
244    /* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */
245    if (x.sign == MP_NEG) {
246      if ((res = mp_copy (&y, &t1)) != MP_OKAY) {
247        goto LBL_Y;
248      }
249      if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
250        goto LBL_Y;
251      }
252      if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) {
253        goto LBL_Y;
254      }
255
256      q.dp[i - t - 1] = (q.dp[i - t - 1] - 1UL) & MP_MASK;
257    }
258  }
259
260  /* now q is the quotient and x is the remainder
261   * [which we have to normalize]
262   */
263
264  /* get sign before writing to c */
265  x.sign = x.used == 0 ? MP_ZPOS : a->sign;
266
267  if (c != NULL) {
268    mp_clamp (&q);
269    mp_exch (&q, c);
270    c->sign = neg;
271  }
272
273  if (d != NULL) {
274    mp_div_2d (&x, norm, &x, NULL);
275    mp_exch (&x, d);
276  }
277
278  res = MP_OKAY;
279
280LBL_Y:mp_clear (&y);
281LBL_X:mp_clear (&x);
282LBL_T2:mp_clear (&t2);
283LBL_T1:mp_clear (&t1);
284LBL_Q:mp_clear (&q);
285  return res;
286}
287
288#endif
289
290#endif
291
292/* Source: /cvs/libtom/libtommath/bn_mp_div.c,v  */
293/* Revision: 1.4  */
294/* Date: 2006/12/28 01:25:13  */
295