--- /dev/null
+/* mpn_fib2_ui -- calculate Fibonacci numbers.
+
+ THE FUNCTIONS IN THIS FILE ARE FOR INTERNAL USE ONLY. THEY'RE ALMOST
+ CERTAIN TO BE SUBJECT TO INCOMPATIBLE CHANGES OR DISAPPEAR COMPLETELY IN
+ FUTURE GNU MP RELEASES.
+
+Copyright 2001, 2002, 2005 Free Software Foundation, Inc.
+
+This file is part of the GNU MP Library.
+
+The GNU MP Library is free software; you can redistribute it and/or modify
+it under the terms of the GNU Lesser General Public License as published by
+the Free Software Foundation; either version 3 of the License, or (at your
+option) any later version.
+
+The GNU MP Library is distributed in the hope that it will be useful, but
+WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
+License for more details.
+
+You should have received a copy of the GNU Lesser General Public License
+along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */
+
+#include <stdio.h>
+#include "gmp.h"
+#include "gmp-impl.h"
+#include "longlong.h"
+
+
+/* change this to "#define TRACE(x) x" for diagnostics */
+#define TRACE(x)
+
+
+/* Store F[n] at fp and F[n-1] at f1p. fp and f1p should have room for
+ MPN_FIB2_SIZE(n) limbs.
+
+ The return value is the actual number of limbs stored, this will be at
+ least 1. fp[size-1] will be non-zero, except when n==0, in which case
+ fp[0] is 0 and f1p[0] is 1. f1p[size-1] can be zero, since F[n-1]<F[n]
+ (for n>0).
+
+ Notes:
+
+ In F[2k+1] with k even, +2 is applied to 4*F[k]^2 just by ORing into the
+ low limb.
+
+ In F[2k+1] with k odd, -2 is applied to the low limb of 4*F[k]^2 -
+ F[k-1]^2. This F[2k+1] is an F[4m+3] and such numbers are congruent to
+ 1, 2 or 5 mod 8, which means no underflow reaching it with a -2 (since
+ that would leave 6 or 7 mod 8).
+
+ This property of F[4m+3] can be verified by induction on F[4m+3] =
+ 7*F[4m-1] - F[4m-5], that formula being a standard lucas sequence
+ identity U[i+j] = U[i]*V[j] - U[i-j]*Q^j.
+
+ Enhancements:
+
+ If there was an mpn_addlshift, it'd be possible to eliminate the yp
+ temporary, using xp=F[k]^2, fp=F[k-1]^2, f1p=xp+fp, fp+=4*fp, fp-=f1p,
+ fp+=2*(-1)^n, etc. */
+
+mp_size_t
+mpn_fib2_ui (mp_ptr fp, mp_ptr f1p, unsigned long int n)
+{
+ mp_ptr xp, yp;
+ mp_size_t size;
+ unsigned long nfirst, mask;
+ TMP_DECL;
+
+ TRACE (printf ("mpn_fib2_ui n=%lu\n", n));
+
+ ASSERT (! MPN_OVERLAP_P (fp, MPN_FIB2_SIZE(n), f1p, MPN_FIB2_SIZE(n)));
+
+ /* Take a starting pair from the table. */
+ mask = 1;
+ for (nfirst = n; nfirst > FIB_TABLE_LIMIT; nfirst /= 2)
+ mask <<= 1;
+ TRACE (printf ("nfirst=%lu mask=0x%lX\n", nfirst, mask));
+
+ f1p[0] = FIB_TABLE ((int) nfirst - 1);
+ fp[0] = FIB_TABLE (nfirst);
+ size = 1;
+
+ /* Skip to the end if the table lookup gives the final answer. */
+ if (mask != 1)
+ {
+ mp_size_t alloc;
+
+ TMP_MARK;
+ alloc = MPN_FIB2_SIZE (n);
+ TMP_ALLOC_LIMBS_2 (xp,alloc, yp,alloc);
+
+ do
+ {
+ mp_limb_t c;
+
+ /* Here fp==F[k] and f1p==F[k-1], with k being the bits of n from
+ n&mask upwards.
+
+ The next bit of n is n&(mask>>1) and we'll double to the pair
+ fp==F[2k],f1p==F[2k-1] or fp==F[2k+1],f1p==F[2k], according as
+ that bit is 0 or 1 respectively. */
+
+ TRACE (printf ("k=%lu mask=0x%lX size=%ld alloc=%ld\n",
+ n >> refmpn_count_trailing_zeros(mask),
+ mask, size, alloc);
+ mpn_trace ("fp ", fp, size);
+ mpn_trace ("f1p", f1p, size));
+
+ /* fp normalized, f1p at most one high zero */
+ ASSERT (fp[size-1] != 0);
+ ASSERT (f1p[size-1] != 0 || f1p[size-2] != 0);
+
+ /* f1p[size-1] might be zero, but this occurs rarely, so it's not
+ worth bothering checking for it */
+ ASSERT (alloc >= 2*size);
+ mpn_sqr_n (xp, fp, size);
+ mpn_sqr_n (yp, f1p, size);
+ size *= 2;
+
+ /* Shrink if possible. Since fp was normalized there'll be at
+ most one high zero on xp (and if there is then there's one on
+ yp too). */
+ ASSERT (xp[size-1] != 0 || yp[size-1] == 0);
+ size -= (xp[size-1] == 0);
+ ASSERT (xp[size-1] != 0); /* only one xp high zero */
+
+ /* Calculate F[2k+1] = 4*F[k]^2 - F[k-1]^2 + 2*(-1)^k.
+ n&mask is the low bit of our implied k. */
+ c = mpn_lshift (fp, xp, size, 2);
+ fp[0] |= (n & mask ? 0 : 2); /* possible +2 */
+ c -= mpn_sub_n (fp, fp, yp, size);
+ ASSERT (n & (mask << 1) ? fp[0] != 0 && fp[0] != 1 : 1);
+ fp[0] -= (n & mask ? 2 : 0); /* possible -2 */
+ ASSERT (alloc >= size+1);
+ xp[size] = 0;
+ yp[size] = 0;
+ fp[size] = c;
+ size += (c != 0);
+
+ /* Calculate F[2k-1] = F[k]^2 + F[k-1]^2.
+ F[2k-1]<F[2k+1] so no carry out of "size" limbs. */
+ ASSERT_NOCARRY (mpn_add_n (f1p, xp, yp, size));
+
+ /* now n&mask is the new bit of n being considered */
+ mask >>= 1;
+
+ /* Calculate F[2k] = F[2k+1] - F[2k-1], replacing the unwanted one of
+ F[2k+1] and F[2k-1]. */
+ ASSERT_NOCARRY (mpn_sub_n ((n & mask ? f1p : fp), fp, f1p, size));
+
+ /* Can have a high zero after replacing F[2k+1] with F[2k].
+ f1p will have a high zero if fp does. */
+ ASSERT (fp[size-1] != 0 || f1p[size-1] == 0);
+ size -= (fp[size-1] == 0);
+ }
+ while (mask != 1);
+
+ TMP_FREE;
+ }
+
+ TRACE (printf ("done size=%ld\n", size);
+ mpn_trace ("fp ", fp, size);
+ mpn_trace ("f1p", f1p, size));
+
+ return size;
+}
projects / msp430-gcc.git / blobdiff