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Diffstat (limited to 'vendor/gmp-6.3.0/mpz/fib_ui.c')
| -rw-r--r-- | vendor/gmp-6.3.0/mpz/fib_ui.c | 158 |
1 files changed, 158 insertions, 0 deletions
diff --git a/vendor/gmp-6.3.0/mpz/fib_ui.c b/vendor/gmp-6.3.0/mpz/fib_ui.c new file mode 100644 index 0000000..a65f3c9 --- /dev/null +++ b/vendor/gmp-6.3.0/mpz/fib_ui.c @@ -0,0 +1,158 @@ +/* mpz_fib_ui -- calculate Fibonacci numbers. + +Copyright 2000-2002, 2005, 2012, 2014, 2015 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 either: + + * 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. + +or + + * the GNU General Public License as published by the Free Software + Foundation; either version 2 of the License, or (at your option) any + later version. + +or both in parallel, as here. + +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 General Public License +for more details. + +You should have received copies of the GNU General Public License and the +GNU Lesser General Public License along with the GNU MP Library. If not, +see https://www.gnu.org/licenses/. */ + +#include <stdio.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; + TMP_DECL; + + if (n <= FIB_TABLE_LIMIT) + { + MPZ_NEWALLOC (fn, 1)[0] = FIB_TABLE (n); + SIZ(fn) = (n != 0); /* F[0]==0, others are !=0 */ + return; + } + + n2 = n/2; + xalloc = MPN_FIB2_SIZE (n2) + 1; + fp = MPZ_NEWALLOC (fn, 2 * xalloc); + + 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_add_n_sub_n + xp[size] = mpn_lshift (xp, xp, size, 1); + yp[size] = 0; + ASSERT_NOCARRY (mpn_add_n_sub_n (xp, yp, xp, yp, size+1)); + xsize = size + (xp[size] != 0); + ASSERT (yp[size] <= 1); + ysize = size + yp[size]; +#else + mp_limb_t c2; + + 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; +#if HAVE_NATIVE_mpn_addlsh1_n + c = mpn_addlsh1_n (yp, xp, yp, size); +#else + c = mpn_lshift (yp, yp, size, 1); + c += mpn_add_n (yp, yp, xp, size); +#endif + 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; +} |