39 lines
1.4 KiB
C#
39 lines
1.4 KiB
C#
using PeterO.Numbers;
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namespace PerfectNumbers.Core;
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public static class AlphaCalculations
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{
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public static ERational ComputeAlphaP(EInteger p, int k)
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{
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int exponent = checked(4 * k + 1);
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EInteger y = PowerCache.Get(p, exponent);
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// TODO: Reuse pooled numerator/denominator buffers here so the alphaP computation stops allocating
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// intermediate EInteger instances every invocation.
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return ERational.Create(y * p - 1, y * (p - 1));
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}
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public static ERational ComputeAlphaFactor(EInteger q, int a2)
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{
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EInteger num = PowerCache.Get(q, a2 + 1) - EInteger.One;
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EInteger den = PowerCache.Get(q, a2) * (q - EInteger.One);
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// TODO: Reuse pooled ERational builders here so repeated factor computations pull precomputed
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// numerator/denominator tuples instead of re-executing PowerCache chains each time, matching the
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// fastest alpha benchmarks.
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return ERational.Create(num, den);
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}
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public static ERational ComputeAlphaM(ReadOnlySpan<EInteger> primes, int maxR, int a2)
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{
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ERational result = ERational.One;
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for (int i = 0; i < maxR; i++)
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{
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// TODO: Replace the repeated Multiply calls with a span-based aggregator that batches factors,
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// avoiding transient ERational instances when maxR grows large.
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result = result.Multiply(ComputeAlphaFactor(primes[i], a2));
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}
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return result;
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}
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}
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