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Don't speculate, benchmark: edit: I added my own matrix implementation using the optimized multiplication functions mentioned in my other answer. This resulted in a major speedup, but even the vanilla O(n^3) implementation of matrix multiplication with loops was faster than the Strassen algorithm. <pre><code><pre><script> var fib = {}; (function() { var sqrt_5 = Math.sqrt(5), phi = (1 + sqrt_5) / 2; fib.round = function(n) { return Math.floor(Math.pow(phi, n) / sqrt_5 + 0.5); }; })(); (function() { fib.loop = function(n) { var i = 0, j = 1; while(n--) { var tmp = i; i = j; j += tmp; } return i; }; })(); (function () { var cache = [0, 1]; fib.loop_cached = function(n) { if(n >= cache.length) { for(var i = cache.length; i <= n; ++i) cache[i] = cache[i - 1] + cache[i - 2]; } return cache[n]; }; })(); (function() { //Fibonacci sequence generator in JS //Cobbled together by Salty var m; var odd = [[1,1],[1,0]]; function matrix(a,b) { /* Matrix multiplication Strassen Algorithm Only works with 2x2 matrices. */ var c=[[0,0],[0,0]]; var m1=(a[0][0]+a[1][1])*(b[0][0]+b[1][1]); var m2=(a[1][0]+a[1][1])*b[0][0]; var m3=a[0][0]*(b[0][1]-b[1][1]); var m4=a[1][1]*(b[1][0]-b[0][0]); var m5=(a[0][0]+a[0][1])*b[1][1]; var m6=(a[1][0]-a[0][0])*(b[0][0]+b[0][1]); var m7=(a[0][1]-a[1][1])*(b[1][0]+b[1][1]); c[0][0]=m1+m4-m5+m7; c[0][1]=m3+m5; c[1][0]=m2+m4; c[1][1]=m1-m2+m3+m6; return c; } function mat(n) { if(n > 1) { mat(n/2); m = matrix(m,m); } m = (n%2<1) ? m : matrix(m,odd); } fib.matrix = function(n) { m = [[1,0],[0,1]]; mat(n-1); return m[0][0]; }; })(); (function() { var a; function square() { var a00 = a[0][0], a01 = a[0][1], a10 = a[1][0], a11 = a[1][1]; var a10_x_a01 = a10 * a01, a00_p_a11 = a00 + a11; a[0][0] = a10_x_a01 + a00 * a00; a[0][1] = a00_p_a11 * a01; a[1][0] = a00_p_a11 * a10; a[1][1] = a10_x_a01 + a11 * a11; } function powPlusPlus() { var a01 = a[0][1], a11 = a[1][1]; a[0][1] = a[0][0]; a[1][1] = a[1][0]; a[0][0] += a01; a[1][0] += a11; } function compute(n) { if(n > 1) { compute(n >> 1); square(); if(n & 1) powPlusPlus(); } } fib.matrix_optimised = function(n) { if(n == 0) return 0; a = [[1, 1], [1, 0]]; compute(n - 1); return a[0][0]; }; })(); (function() { var cache = {}; cache[0] = [[1, 0], [0, 1]]; cache[1] = [[1, 1], [1, 0]]; function mult(a, b) { return [ [a[0][0] * b[0][0] + a[0][1] * b[1][0], a[0][0] * b[0][1] + a[0][1] * b[1][1]], [a[1][0] * b[0][0] + a[1][1] * b[1][0], a[1][0] * b[0][1] + a[1][1] * b[1][1]] ]; } function compute(n) { if(!cache[n]) { var n_2 = n >> 1; compute(n_2); cache[n] = mult(cache[n_2], cache[n_2]); if(n & 1) cache[n] = mult(cache[1], cache[n]); } } fib.matrix_cached = function(n) { if(n == 0) return 0; compute(--n); return cache[n][0][0]; }; })(); function test(name, func, n, count) { var value; var start = Number(new Date); while(count--) value = func(n); var end = Number(new Date); return 'fib.' + name + '(' + n + ') = ' + value + ' [' + (end - start) + 'ms]'; } for(var func in fib) document.writeln(test(func, fib[func], 1450, 10000)); </script></pre> </code></pre> yields <pre><code>fib.round(1450) = 4.8149675025003456e+302 [20ms] fib.loop(1450) = 4.81496750250011e+302 [4035ms] fib.loop_cached(1450) = 4.81496750250011e+302 [8ms] fib.matrix(1450) = 4.814967502500118e+302 [2201ms] fib.matrix_optimised(1450) = 4.814967502500113e+302 [585ms] fib.matrix_cached(1450) = 4.814967502500113e+302 [12ms] </code></pre> Your algorithm is nearly as bad as uncached looping. Caching is your best bet, closely followed by the rounding algorithm - which yields incorrect results for big <code>n</code> (as does your matrix algorithm). For smaller <code>n</code>, your algorithm performs even worse than everything else: <pre><code>fib.round(100) = 354224848179263100000 [20ms] fib.loop(100) = 354224848179262000000 [248ms] fib.loop_cached(100) = 354224848179262000000 [6ms] fib.matrix(100) = 354224848179261900000 [1911ms] fib.matrix_optimised(100) = 354224848179261900000 [380ms] fib.matrix_cached(100) = 354224848179261900000 [12ms] </code></pre>
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