1 /* mpn_fib2_ui -- calculate Fibonacci numbers.
2
3 THE FUNCTIONS IN THIS FILE ARE FOR INTERNAL USE ONLY. THEY'RE ALMOST
4 CERTAIN TO BE SUBJECT TO INCOMPATIBLE CHANGES OR DISAPPEAR COMPLETELY IN
5 FUTURE GNU MP RELEASES.
6
7 Copyright 2001, 2002, 2005, 2009, 2018 Free Software Foundation, Inc.
8
9 This file is part of the GNU MP Library.
10
11 The GNU MP Library is free software; you can redistribute it and/or modify
12 it under the terms of either:
13
14 * the GNU Lesser General Public License as published by the Free
15 Software Foundation; either version 3 of the License, or (at your
16 option) any later version.
17
18 or
19
20 * the GNU General Public License as published by the Free Software
21 Foundation; either version 2 of the License, or (at your option) any
22 later version.
23
24 or both in parallel, as here.
25
26 The GNU MP Library is distributed in the hope that it will be useful, but
27 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
28 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
29 for more details.
30
31 You should have received copies of the GNU General Public License and the
32 GNU Lesser General Public License along with the GNU MP Library. If not,
33 see https://www.gnu.org/licenses/. */
34
35 #include <stdio.h>
36 #include "gmp-impl.h"
37
38 /* change this to "#define TRACE(x) x" for diagnostics */
39 #define TRACE(x)
40
41
42 /* Store F[n] at fp and F[n-1] at f1p. fp and f1p should have room for
43 MPN_FIB2_SIZE(n) limbs.
44
45 The return value is the actual number of limbs stored, this will be at
46 least 1. fp[size-1] will be non-zero, except when n==0, in which case
47 fp[0] is 0 and f1p[0] is 1. f1p[size-1] can be zero, since F[n-1]<F[n]
48 (for n>0).
49
50 Notes: F[2k+1] = 4*F[k]^2 - F[k-1]^2 + 2*(-1)^k.
51
52 In F[2k+1] with k even, +2 is applied to 4*F[k]^2 just by ORing into the
53 low limb.
54
55 In F[2k+1] with k odd, -2 is applied to F[k-1]^2 just by ORing into the
56 low limb.
57 */
58
59 mp_size_t
60 mpn_fib2_ui (mp_ptr fp, mp_ptr f1p, unsigned long int n)
61 {
62 mp_size_t size;
63 unsigned long nfirst, mask;
64
65 TRACE (printf ("mpn_fib2_ui n=%lu\n", n));
66
67 ASSERT (! MPN_OVERLAP_P (fp, MPN_FIB2_SIZE(n), f1p, MPN_FIB2_SIZE(n)));
68
69 /* Take a starting pair from the table. */
70 mask = 1;
71 for (nfirst = n; nfirst > FIB_TABLE_LIMIT; nfirst /= 2)
72 mask <<= 1;
73 TRACE (printf ("nfirst=%lu mask=0x%lX\n", nfirst, mask));
74
75 f1p[0] = FIB_TABLE ((int) nfirst - 1);
76 fp[0] = FIB_TABLE (nfirst);
77 size = 1;
78
79 /* Skip to the end if the table lookup gives the final answer. */
80 if (mask != 1)
81 {
82 mp_size_t alloc;
83 mp_ptr xp;
84 TMP_DECL;
85
86 TMP_MARK;
87 alloc = MPN_FIB2_SIZE (n);
88 xp = TMP_ALLOC_LIMBS (alloc);
89
90 do
91 {
92 /* Here fp==F[k] and f1p==F[k-1], with k being the bits of n from
93 n&mask upwards.
94
95 The next bit of n is n&(mask>>1) and we'll double to the pair
96 fp==F[2k],f1p==F[2k-1] or fp==F[2k+1],f1p==F[2k], according as
97 that bit is 0 or 1 respectively. */
98
99 TRACE (printf ("k=%lu mask=0x%lX size=%ld alloc=%ld\n",
100 n >> refmpn_count_trailing_zeros(mask),
101 mask, size, alloc);
102 mpn_trace ("fp ", fp, size);
103 mpn_trace ("f1p", f1p, size));
104
105 /* fp normalized, f1p at most one high zero */
106 ASSERT (fp[size-1] != 0);
107 ASSERT (f1p[size-1] != 0 || f1p[size-2] != 0);
108
109 /* f1p[size-1] might be zero, but this occurs rarely, so it's not
110 worth bothering checking for it */
111 ASSERT (alloc >= 2*size);
112 mpn_sqr (xp, fp, size);
113 mpn_sqr (fp, f1p, size);
114 size *= 2;
115
116 /* Shrink if possible. Since fp was normalized there'll be at
117 most one high zero on xp (and if there is then there's one on
118 yp too). */
119 ASSERT (xp[size-1] != 0 || fp[size-1] == 0);
120 size -= (xp[size-1] == 0);
121 ASSERT (xp[size-1] != 0); /* only one xp high zero */
122
123 /* Calculate F[2k-1] = F[k]^2 + F[k-1]^2. */
124 f1p[size] = mpn_add_n (f1p, xp, fp, size);
125
126 /* Calculate F[2k+1] = 4*F[k]^2 - F[k-1]^2 + 2*(-1)^k.
127 n&mask is the low bit of our implied k. */
128
129 ASSERT ((fp[0] & 2) == 0);
130 /* fp is F[k-1]^2 == 0 or 1 mod 4, like all squares. */
131 fp[0] |= (n & mask ? 2 : 0); /* possible -2 */
132 #if HAVE_NATIVE_mpn_rsblsh2_n
133 fp[size] = mpn_rsblsh2_n (fp, fp, xp, size);
134 MPN_INCR_U(fp, size + 1, (n & mask ? 0 : 2)); /* possible +2 */
135 #else
136 {
137 mp_limb_t c;
138
139 c = mpn_lshift (xp, xp, size, 2);
140 xp[0] |= (n & mask ? 0 : 2); /* possible +2 */
141 c -= mpn_sub_n (fp, xp, fp, size);
142 fp[size] = c;
143 }
144 #endif
145 ASSERT (alloc >= size+1);
146 size += (fp[size] != 0);
147
148 /* now n&mask is the new bit of n being considered */
149 mask >>= 1;
150
151 /* Calculate F[2k] = F[2k+1] - F[2k-1], replacing the unwanted one of
152 F[2k+1] and F[2k-1]. */
153 if (n & mask)
154 ASSERT_NOCARRY (mpn_sub_n (f1p, fp, f1p, size));
155 else {
156 ASSERT_NOCARRY (mpn_sub_n ( fp, fp, f1p, size));
157
158 /* Can have a high zero after replacing F[2k+1] with F[2k].
159 f1p will have a high zero if fp does. */
160 ASSERT (fp[size-1] != 0 || f1p[size-1] == 0);
161 size -= (fp[size-1] == 0);
162 }
163 }
164 while (mask != 1);
165
166 TMP_FREE;
167 }
168
169 TRACE (printf ("done size=%ld\n", size);
170 mpn_trace ("fp ", fp, size);
171 mpn_trace ("f1p", f1p, size));
172
173 return size;
174 }