Annotation of OpenXM_contrib/gmp/mpz/lucnum_ui.c, Revision 1.1.1.1
1.1 ohara 1: /* mpz_lucnum_ui -- calculate Lucas number.
2:
3: Copyright 2001 Free Software Foundation, Inc.
4:
5: This file is part of the GNU MP Library.
6:
7: The GNU MP Library is free software; you can redistribute it and/or modify
8: it under the terms of the GNU Lesser General Public License as published by
9: the Free Software Foundation; either version 2.1 of the License, or (at your
10: option) any later version.
11:
12: The GNU MP Library is distributed in the hope that it will be useful, but
13: WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
14: or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
15: License for more details.
16:
17: You should have received a copy of the GNU Lesser General Public License
18: along with the GNU MP Library; see the file COPYING.LIB. If not, write to
19: the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
20: MA 02111-1307, USA. */
21:
22: #include <stdio.h>
23: #include "gmp.h"
24: #include "gmp-impl.h"
25:
26:
27: /* change this to "#define TRACE(x) x" for diagnostics */
28: #define TRACE(x)
29:
30:
31: /* Notes:
32:
33: For the +4 in L[2k+1] when k is even, all L[4m+3] == 4, 5 or 7 mod 8, so
34: there can't be an overflow applying +4 to just the low limb (since that
35: would leave 0, 1, 2 or 3 mod 8).
36:
37: For the -4 in L[2k+1] when k is even, it seems (no proof) that
38: L[3*2^(b-2)-3] == -4 mod 2^b, so for instance with a 32-bit limb
39: L[0xBFFFFFFD] == 0xFFFFFFFC mod 2^32, and this implies a borrow from the
40: low limb. Obviously L[0xBFFFFFFD] is a huge number, but it's at least
41: conceivable to calculate it, so it probably should be handled.
42:
43: For the -2 in L[2k] with k even, it seems (no proof) L[2^(b-1)] == -1 mod
44: 2^b, so for instance in 32-bits L[0x80000000] has a low limb of
45: 0xFFFFFFFF so there would have been a borrow. Again L[0x80000000] is
46: obviously huge, but probably should be made to work. */
47:
48: void
49: mpz_lucnum_ui (mpz_ptr ln, unsigned long n)
50: {
51: mp_size_t lalloc, xalloc, lsize, xsize;
52: mp_ptr lp, xp;
53: mp_limb_t c;
54: int zeros;
55: TMP_DECL (marker);
56:
57: TRACE (printf ("mpn_lucnum_ui n=%lu\n", n));
58:
59: if (n <= FIB_TABLE_LUCNUM_LIMIT)
60: {
61: /* L[n] = F[n] + 2F[n-1] */
62: PTR(ln)[0] = FIB_TABLE(n) + 2 * FIB_TABLE ((int) n - 1);
63: SIZ(ln) = 1;
64: return;
65: }
66:
67: /* +1 since L[n]=F[n]+2F[n-1] might be 1 limb bigger than F[n], further +1
68: since square or mul used below might need an extra limb over the true
69: size */
70: lalloc = MPN_FIB2_SIZE (n) + 2;
71: MPZ_REALLOC (ln, lalloc);
72: lp = PTR (ln);
73:
74: TMP_MARK (marker);
75: xalloc = lalloc;
76: xp = TMP_ALLOC_LIMBS (xalloc);
77:
78: /* Strip trailing zeros from n, until either an odd number is reached
79: where the L[2k+1] formula can be used, or until n fits within the
80: FIB_TABLE data. The table is preferred of course. */
81: zeros = 0;
82: for (;;)
83: {
84: if (n & 1)
85: {
86: /* L[2k+1] = 5*F[k-1]*(2*F[k]+F[k-1]) - 4*(-1)^k */
87:
88: mp_size_t yalloc, ysize;
89: mp_ptr yp;
90:
91: TRACE (printf (" initial odd n=%lu\n", n));
92:
93: yalloc = MPN_FIB2_SIZE (n/2);
94: yp = TMP_ALLOC_LIMBS (yalloc);
95: ASSERT (xalloc >= yalloc);
96:
97: xsize = mpn_fib2_ui (xp, yp, n/2);
98:
99: /* possible high zero on F[k-1] */
100: ysize = xsize;
101: ysize -= (yp[ysize-1] == 0);
102: ASSERT (yp[ysize-1] != 0);
103:
104: /* xp = 2*F[k] + F[k-1] */
105: c = mpn_lshift (xp, xp, xsize, 1);
106: c += mpn_add_n (xp, xp, yp, xsize);
107: ASSERT (xalloc >= xsize+1);
108: xp[xsize] = c;
109: xsize += (c != 0);
110: ASSERT (xp[xsize-1] != 0);
111:
112: ASSERT (lalloc >= xsize + ysize);
113: c = mpn_mul (lp, xp, xsize, yp, ysize);
114: lsize = xsize + ysize;
115: lsize -= (c == 0);
116:
117: /* lp = 5*lp */
118: #if HAVE_NATIVE_mpn_addlshift
119: c = mpn_addlshift (lp, lp, lsize, 2);
120: #else
121: c = mpn_lshift (xp, lp, lsize, 2);
122: c += mpn_add_n (lp, lp, xp, lsize);
123: #endif
124: ASSERT (lalloc >= lsize+1);
125: lp[lsize] = c;
126: lsize += (c != 0);
127:
128: /* lp = lp - 4*(-1)^k */
129: if (n & 2)
130: {
131: /* no overflow, see comments above */
132: ASSERT (lp[0] <= MP_LIMB_T_MAX-4);
133: lp[0] += 4;
134: }
135: else
136: {
137: /* won't go negative */
138: MPN_DECR_U (lp, lsize, CNST_LIMB(4));
139: }
140:
141: TRACE (mpn_trace (" l",lp, lsize));
142: break;
143: }
144:
145: MP_PTR_SWAP (xp, lp); /* balance the swaps wanted in the L[2k] below */
146: zeros++;
147: n /= 2;
148:
149: if (n <= FIB_TABLE_LUCNUM_LIMIT)
150: {
151: /* L[n] = F[n] + 2F[n-1] */
152: lp[0] = FIB_TABLE (n) + 2 * FIB_TABLE ((int) n - 1);
153: lsize = 1;
154:
155: TRACE (printf (" initial small n=%lu\n", n);
156: mpn_trace (" l",lp, lsize));
157: break;
158: }
159: }
160:
161: for ( ; zeros != 0; zeros--)
162: {
163: /* L[2k] = L[k]^2 + 2*(-1)^k */
164:
165: TRACE (printf (" zeros=%d\n", zeros));
166:
167: ASSERT (xalloc >= 2*lsize);
168: mpn_sqr_n (xp, lp, lsize);
169: lsize *= 2;
170: lsize -= (xp[lsize-1] == 0);
171:
172: /* First time around the loop k==n determines (-1)^k, after that k is
173: always even and we set n=0 to indicate that. */
174: if (n & 1)
175: {
176: /* L[n]^2 == 0 or 1 mod 4, like all squares, so +2 gives no carry */
177: ASSERT (xp[0] <= MP_LIMB_T_MAX-2);
178: xp[0] += 2;
179: n = 0;
180: }
181: else
182: {
183: /* won't go negative */
184: MPN_DECR_U (xp, lsize, CNST_LIMB(2));
185: }
186:
187: MP_PTR_SWAP (xp, lp);
188: ASSERT (lp[lsize-1] != 0);
189: }
190:
191: /* should end up in the right spot after all the xp/lp swaps */
192: ASSERT (lp == PTR(ln));
193: SIZ(ln) = lsize;
194:
195: TMP_FREE (marker);
196: }
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