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// =================================================================== //
// Copyright(c)'2021 by The Givaro group
// This file is part of Givaro.
// Givaro is governed by the CeCILL-B license under French law
// and abiding by the rules of distribution of free software.
// see the COPYRIGHT file for more details.
// Time-stamp: <07 Jun 21 18:57:12 Jean-Guillaume.Dumas@imag.fr>
//
// Fibonacci numbers /////////////////////////
// =================================================================== //
/*! @file examples/Integer/Fibonacci.C
* @ingroup examples
* @ingroup integers
* @example examples/Integer/Fibonacci.C
* @brief NO DOC
*/
#include <iostream>
#include <stdlib.h>
#include <stdio.h>
#include <givaro/givinteger.h>
#define GMPFIBTABLESIZE 93
#define GMPCNSTUINT(C) ((uint64_t) C##u)
const uint64_t givfibtable[GMPFIBTABLESIZE+2] {
GMPCNSTUINT (0x1), /* -1 */
GMPCNSTUINT (0x0), /* 0 */
GMPCNSTUINT (0x1), /* 1 */
GMPCNSTUINT (0x1), /* 2 */
GMPCNSTUINT (0x2), /* 3 */
GMPCNSTUINT (0x3), /* 4 */
GMPCNSTUINT (0x5), /* 5 */
GMPCNSTUINT (0x8), /* 6 */
GMPCNSTUINT (0xd), /* 7 */
GMPCNSTUINT (0x15), /* 8 */
GMPCNSTUINT (0x22), /* 9 */
GMPCNSTUINT (0x37), /* 10 */
GMPCNSTUINT (0x59), /* 11 */
GMPCNSTUINT (0x90), /* 12 */
GMPCNSTUINT (0xe9), /* 13 */
GMPCNSTUINT (0x179), /* 14 */
GMPCNSTUINT (0x262), /* 15 */
GMPCNSTUINT (0x3db), /* 16 */
GMPCNSTUINT (0x63d), /* 17 */
GMPCNSTUINT (0xa18), /* 18 */
GMPCNSTUINT (0x1055), /* 19 */
GMPCNSTUINT (0x1a6d), /* 20 */
GMPCNSTUINT (0x2ac2), /* 21 */
GMPCNSTUINT (0x452f), /* 22 */
GMPCNSTUINT (0x6ff1), /* 23 */
GMPCNSTUINT (0xb520), /* 24 */
GMPCNSTUINT (0x12511), /* 25 */
GMPCNSTUINT (0x1da31), /* 26 */
GMPCNSTUINT (0x2ff42), /* 27 */
GMPCNSTUINT (0x4d973), /* 28 */
GMPCNSTUINT (0x7d8b5), /* 29 */
GMPCNSTUINT (0xcb228), /* 30 */
GMPCNSTUINT (0x148add), /* 31 */
GMPCNSTUINT (0x213d05), /* 32 */
GMPCNSTUINT (0x35c7e2), /* 33 */
GMPCNSTUINT (0x5704e7), /* 34 */
GMPCNSTUINT (0x8cccc9), /* 35 */
GMPCNSTUINT (0xe3d1b0), /* 36 */
GMPCNSTUINT (0x1709e79), /* 37 */
GMPCNSTUINT (0x2547029), /* 38 */
GMPCNSTUINT (0x3c50ea2), /* 39 */
GMPCNSTUINT (0x6197ecb), /* 40 */
GMPCNSTUINT (0x9de8d6d), /* 41 */
GMPCNSTUINT (0xff80c38), /* 42 */
GMPCNSTUINT (0x19d699a5), /* 43 */
GMPCNSTUINT (0x29cea5dd), /* 44 */
GMPCNSTUINT (0x43a53f82), /* 45 */
GMPCNSTUINT (0x6d73e55f), /* 46 */
GMPCNSTUINT (0xb11924e1), /* 47 */
GMPCNSTUINT (0x11e8d0a40), /* 48 */
GMPCNSTUINT (0x1cfa62f21), /* 49 */
GMPCNSTUINT (0x2ee333961), /* 50 */
GMPCNSTUINT (0x4bdd96882), /* 51 */
GMPCNSTUINT (0x7ac0ca1e3), /* 52 */
GMPCNSTUINT (0xc69e60a65), /* 53 */
GMPCNSTUINT (0x1415f2ac48), /* 54 */
GMPCNSTUINT (0x207fd8b6ad), /* 55 */
GMPCNSTUINT (0x3495cb62f5), /* 56 */
GMPCNSTUINT (0x5515a419a2), /* 57 */
GMPCNSTUINT (0x89ab6f7c97), /* 58 */
GMPCNSTUINT (0xdec1139639), /* 59 */
GMPCNSTUINT (0x1686c8312d0), /* 60 */
GMPCNSTUINT (0x2472d96a909), /* 61 */
GMPCNSTUINT (0x3af9a19bbd9), /* 62 */
GMPCNSTUINT (0x5f6c7b064e2), /* 63 */
GMPCNSTUINT (0x9a661ca20bb), /* 64 */
GMPCNSTUINT (0xf9d297a859d), /* 65 */
GMPCNSTUINT (0x19438b44a658), /* 66 */
GMPCNSTUINT (0x28e0b4bf2bf5), /* 67 */
GMPCNSTUINT (0x42244003d24d), /* 68 */
GMPCNSTUINT (0x6b04f4c2fe42), /* 69 */
GMPCNSTUINT (0xad2934c6d08f), /* 70 */
GMPCNSTUINT (0x1182e2989ced1), /* 71 */
GMPCNSTUINT (0x1c5575e509f60), /* 72 */
GMPCNSTUINT (0x2dd8587da6e31), /* 73 */
GMPCNSTUINT (0x4a2dce62b0d91), /* 74 */
GMPCNSTUINT (0x780626e057bc2), /* 75 */
GMPCNSTUINT (0xc233f54308953), /* 76 */
GMPCNSTUINT (0x13a3a1c2360515), /* 77 */
GMPCNSTUINT (0x1fc6e116668e68), /* 78 */
GMPCNSTUINT (0x336a82d89c937d), /* 79 */
GMPCNSTUINT (0x533163ef0321e5), /* 80 */
GMPCNSTUINT (0x869be6c79fb562), /* 81 */
GMPCNSTUINT (0xd9cd4ab6a2d747), /* 82 */
GMPCNSTUINT (0x16069317e428ca9), /* 83 */
GMPCNSTUINT (0x23a367c34e563f0), /* 84 */
GMPCNSTUINT (0x39a9fadb327f099), /* 85 */
GMPCNSTUINT (0x5d4d629e80d5489), /* 86 */
GMPCNSTUINT (0x96f75d79b354522), /* 87 */
GMPCNSTUINT (0xf444c01834299ab), /* 88 */
GMPCNSTUINT (0x18b3c1d91e77decd), /* 89 */
GMPCNSTUINT (0x27f80ddaa1ba7878), /* 90 */
GMPCNSTUINT (0x40abcfb3c0325745), /* 91 */
GMPCNSTUINT (0x68a3dd8e61eccfbd), /* 92 */
GMPCNSTUINT (0xa94fad42221f2702), /* 93 */
};
namespace Givaro {
// Returns r=Fibo(n-1) & t=Fibo(n)
// b is temporary
// Assumes n>=0
Integer& Fibonacci(Integer& r, Integer& t,
const uint64_t n) {
if (n <= 93) {
uint64_t k(n);
r=givfibtable[k];
return t=givfibtable[++k];
}
uint64_t k(n); ++k; k >>=1 ;// n=2k-->k or n=2k+1--> k+1
Fibonacci(t,r,k); // n=2k-->k or n=2k+1--> k+1
if (n & 1u) {
Integer b(r);
r <<= 1;
r -= t;
r *= t; // r=t(2t-r)
t <<= 1;
t += b;
t *= b; // t=t(t-2t)
t -= r; // t=t^2+r^2
} else {
Integer b(t);
t <<= 1;
t += r;
t *= r; // t=r(r+2t)
r <<= 1;
Integer::sub(r,b,r); // r = t - r;
r *= b; // r=t(t-2r)
r += t; // r=t^2+r^2
}
return t;
}
// Assumes n>=0
// Avoids one of the last two (largest) multiplications
Integer& Fibonacci(Integer& t, const uint64_t n) {
Integer a;
if (n & 1u) {
uint64_t k(n); ++k; k >>=1 ;// n=2k-->k or n=2k+1--> k+1
// F[2k+1]=F[k]*(F[k+1]+2F[k]) +/- 1;
Fibonacci(t,a,k);
Integer b(t);
t <<= 1;
t += a;
t *= b;
return ( (k & 1u)? ++t : --t );
} else {
// F[2k]=F[k]*(F[k]+2F[k-1]);
Fibonacci(t,a, n>>1 );
t <<= 1;
t += a;
return t *= a;
}
}
}
int main (int argc, char * * argv) {
uint64_t n = argc > 1 ? (uint64_t)atoi(argv[1]) : 42u;
Givaro::Integer t;
Givaro::Timer tim; tim.start();
Givaro::Fibonacci(t,n);
tim.stop();
std::cout << t << std::endl;
std::clog << tim << std::endl;
return 0;
}
/* -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
// vim:sts=4:sw=4:ts=4:et:sr:cino=>s,f0,{0,g0,(0,\:0,t0,+0,=s
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