--- /dev/null
+/* mpz_fib_ui -- calculate Fibonacci numbers.
+
+Copyright 2000, 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 to "#define TRACE(x) x" to get some traces */
+#define TRACE(x)
+
+
+/* In the F[2k+1] below for k odd, the -2 won't give a borrow from the low
+ limb because the result F[2k+1] is an F[4m+3] and such numbers are always
+ == 1, 2 or 5 mod 8, whereas an underflow would leave 6 or 7. (This is
+ the same as in mpn_fib2_ui.)
+
+ In the F[2k+1] for k even, the +2 won't give a carry out of the low limb
+ in normal circumstances. This is an F[4m+1] and we claim that F[3*2^b+1]
+ == 1 mod 2^b is the first F[4m+1] congruent to 0 or 1 mod 2^b, and hence
+ if n < 2^GMP_NUMB_BITS then F[n] cannot have a low limb of 0 or 1. No
+ proof for this claim, but it's been verified up to b==32 and has such a
+ nice pattern it must be true :-). Of interest is that F[3*2^b] == 0 mod
+ 2^(b+1) seems to hold too.
+
+ When n >= 2^GMP_NUMB_BITS, which can arise in a nails build, then the low
+ limb of F[4m+1] can certainly be 1, and an mpn_add_1 must be used. */
+
+void
+mpz_fib_ui (mpz_ptr fn, unsigned long n)
+{
+ mp_ptr fp, xp, yp;
+ mp_size_t size, xalloc;
+ unsigned long n2;
+ mp_limb_t c, c2;
+ TMP_DECL;
+
+ if (n <= FIB_TABLE_LIMIT)
+ {
+ PTR(fn)[0] = FIB_TABLE (n);
+ SIZ(fn) = (n != 0); /* F[0]==0, others are !=0 */
+ return;
+ }
+
+ n2 = n/2;
+ xalloc = MPN_FIB2_SIZE (n2) + 1;
+ MPZ_REALLOC (fn, 2*xalloc+1);
+ fp = PTR (fn);
+
+ TMP_MARK;
+ TMP_ALLOC_LIMBS_2 (xp,xalloc, yp,xalloc);
+ size = mpn_fib2_ui (xp, yp, n2);
+
+ TRACE (printf ("mpz_fib_ui last step n=%lu size=%ld bit=%lu\n",
+ n >> 1, size, n&1);
+ mpn_trace ("xp", xp, size);
+ mpn_trace ("yp", yp, size));
+
+ if (n & 1)
+ {
+ /* F[2k+1] = (2F[k]+F[k-1])*(2F[k]-F[k-1]) + 2*(-1)^k */
+ mp_size_t xsize, ysize;
+
+#if HAVE_NATIVE_mpn_addsub_n
+ xp[size] = mpn_lshift (xp, xp, size, 1);
+ yp[size] = 0;
+ ASSERT_NOCARRY (mpn_addsub_n (xp, yp, xp, yp, size+1));
+ xsize = size + (xp[size] != 0);
+ ysize = size + (yp[size] != 0);
+#else
+ c2 = mpn_lshift (fp, xp, size, 1);
+ c = c2 + mpn_add_n (xp, fp, yp, size);
+ xp[size] = c;
+ xsize = size + (c != 0);
+ c2 -= mpn_sub_n (yp, fp, yp, size);
+ yp[size] = c2;
+ ASSERT (c2 <= 1);
+ ysize = size + c2;
+#endif
+
+ size = xsize + ysize;
+ c = mpn_mul (fp, xp, xsize, yp, ysize);
+
+#if GMP_NUMB_BITS >= BITS_PER_ULONG
+ /* no overflow, see comments above */
+ ASSERT (n & 2 ? fp[0] >= 2 : fp[0] <= GMP_NUMB_MAX-2);
+ fp[0] += (n & 2 ? -CNST_LIMB(2) : CNST_LIMB(2));
+#else
+ if (n & 2)
+ {
+ ASSERT (fp[0] >= 2);
+ fp[0] -= 2;
+ }
+ else
+ {
+ ASSERT (c != GMP_NUMB_MAX); /* because it's the high of a mul */
+ c += mpn_add_1 (fp, fp, size-1, CNST_LIMB(2));
+ fp[size-1] = c;
+ }
+#endif
+ }
+ else
+ {
+ /* F[2k] = F[k]*(F[k]+2F[k-1]) */
+
+ mp_size_t xsize, ysize;
+ c = mpn_lshift (yp, yp, size, 1);
+ c += mpn_add_n (yp, yp, xp, size);
+ yp[size] = c;
+ xsize = size;
+ ysize = size + (c != 0);
+ size += ysize;
+ c = mpn_mul (fp, yp, ysize, xp, xsize);
+ }
+
+ /* one or two high zeros */
+ size -= (c == 0);
+ size -= (fp[size-1] == 0);
+ SIZ(fn) = size;
+
+ TRACE (printf ("done special, size=%ld\n", size);
+ mpn_trace ("fp ", fp, size));
+
+ TMP_FREE;
+}
projects / msp430-gcc.git / blobdiff