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authortege <tege@gmplib.org>1999-03-08 03:25:29 +0100
committertege <tege@gmplib.org>1999-03-08 03:25:29 +0100
commit9a33b56398813b081ca80c97626c69d95c97bdfb (patch)
tree97f154d8adc9e6663492001c0f0e22478658f90a /mpz
parent7b29202b995a83ebfe4b5028b837e1b72e0c9404 (diff)
downloadgmp-9a33b56398813b081ca80c97626c69d95c97bdfb.tar.gz
*** empty log message ***
Diffstat (limited to 'mpz')
-rw-r--r--mpz/fib_ui.c125
1 files changed, 125 insertions, 0 deletions
diff --git a/mpz/fib_ui.c b/mpz/fib_ui.c
new file mode 100644
index 000000000..9ef42a462
--- /dev/null
+++ b/mpz/fib_ui.c
@@ -0,0 +1,125 @@
+/* mpz_fib_ui(result, n) -- Set RESULT to the Nth Fibonacci number.
+
+Copyright (C) 1998 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 Library General Public License as published by
+the Free Software Foundation; either version 2 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 Library General Public
+License for more details.
+
+You should have received a copy of the GNU Library General Public License
+along with the GNU MP Library; see the file COPYING.LIB. If not, write to
+the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+MA 02111-1307, USA. */
+
+#include "gmp.h"
+#include "gmp-impl.h"
+
+/* This is fast, but could be made somewhat faster and neater.
+ The timing is somewhat fluctuating for even/odd sizes because
+ of the extra hair used to save variables and operations. Here
+ are a few things one might want to address:
+ 1. Avoid using 4 intermediate variables in mpz_fib_bigcase.
+ 2. Call mpn functions directly. Straightforward for these functions.
+ 3. Merge the three functions into one.
+*/
+
+/* Determine the needed storage for Fib(n). */
+#define FIB_SIZE(n) (((mp_size_t) ((n)*0.695)) / BITS_PER_MP_LIMB + 2)
+
+static void mpz_fib_bigcase (mpz_t, mpz_t, unsigned long int);
+static void mpz_fib_basecase (mpz_t, mpz_t, unsigned long int);
+
+#define FIB_THRES 60
+
+void
+mpz_fib_ui (mpz_t r, unsigned long int n)
+{
+ if (n == 0)
+ mpz_set_ui (r, 0);
+ else
+ {
+ mpz_t t1;
+ mpz_init (t1);
+ if (n < FIB_THRES)
+ mpz_fib_basecase (t1, r, n);
+ else
+ mpz_fib_bigcase (t1, r, n);
+ mpz_clear (t1);
+ }
+}
+
+static void
+mpz_fib_basecase (mpz_t t1, mpz_t t2, unsigned long int n)
+{
+ unsigned long int m, i;
+
+ mpz_set_ui (t1, 0);
+ mpz_set_ui (t2, 1);
+ m = n/2;
+ for (i = 0; i < m; i++)
+ {
+ mpz_add (t1, t1, t2);
+ mpz_add (t2, t1, t2);
+ }
+ if ((n & 1) == 0)
+ {
+ mpz_sub (t1, t2, t1);
+ mpz_sub (t2, t2, t1); /* trick: recover t1 value just overwritten */
+ }
+}
+
+static void
+mpz_fib_bigcase (mpz_t t1, mpz_t t2, unsigned long int n)
+{
+ unsigned long int n2;
+ int ni, i;
+ mpz_t x1, x2, u1, u2;
+
+ ni = 0;
+ for (n2 = n; n2 > FIB_THRES; n2 /= 2)
+ ni++;
+
+ mpz_fib_basecase (t1, t2, n2);
+
+ mpz_init (x1);
+ mpz_init (x2);
+ mpz_init (u1);
+ mpz_init (u2);
+
+ for (i = ni - 1; i >= 0; i--)
+ {
+ mpz_mul_2exp (x1, t1, 1);
+ mpz_mul_2exp (x2, t2, 1);
+
+ mpz_add (x1, x1, t2);
+ mpz_sub (x2, x2, t1);
+
+ mpz_mul (u1, t2, x1);
+ mpz_mul (u2, t1, x2);
+
+ if (((n >> i) & 1) == 0)
+ {
+ mpz_sub (t1, u1, u2);
+ mpz_set (t2, u1);
+ }
+ else
+ {
+ mpz_set (t1, u1);
+ mpz_mul_2exp (t2, u1, 1);
+ mpz_sub (t2, t2, u2);
+ }
+ }
+
+ mpz_clear (x1);
+ mpz_clear (x2);
+ mpz_clear (u1);
+ mpz_clear (u2);
+}