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 } 175
Indexes created Sat Feb 28 05:31:39 UTC 2026