42 lines
1.3 KiB
D
42 lines
1.3 KiB
D
import std.stdio, std.random, std.math, std.algorithm, std.range, std.format;
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real analytical(in int n) pure nothrow @safe /*@nogc*/ {
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enum aux = (int k) => reduce!q{a * b}(1.0L, iota(n - k + 1, n + 1));
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return iota(1, n + 1)
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.map!(k => (aux(k) * k ^^ 2) / (real(n) ^^ (k + 1)))
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.sum;
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}
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size_t loopLength(size_t maxN)(in int size, ref Xorshift rng) {
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__gshared static bool[maxN + 1] seen;
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seen[0 .. size + 1] = false;
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int current = 1;
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size_t steps = 0;
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while (!seen[current]) {
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seen[current] = true;
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current = uniform(1, size + 1, rng);
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steps++;
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}
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return steps;
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}
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void main() {
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enum maxN = 40;
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enum nTrials = 300_000;
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auto rng = Xorshift(unpredictableSeed);
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writeln(" n average analytical (error)");
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writeln("=== ========= ============ ==========");
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foreach (immutable n; 1 .. maxN + 1) {
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long total = 0;
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foreach (immutable _; 0 .. nTrials)
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total += loopLength!maxN(n, rng);
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immutable average = total / real(nTrials);
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immutable an = n.analytical;
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immutable percentError = abs(an - average) / an * 100;
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immutable errorS = format("%2.4f", percentError);
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writefln("%3d %9.5f %12.5f (%7s%%)",
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n, average, an, errorS);
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}
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}
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