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* math: implement discrete and continuous distributions Implement a comprehensive set of continuous and discrete probability distributions with support for PDF, CDF, inverse CDF, random sampling, mean, and variance calculations. The following distributions are implemented: * Normal * Uniform * Exponential * Chi-Squared * F-Distribution * Student t * Binomial * Poisson * update releasenotes.md * Formatting --------- Co-authored-by: Christoffer Lerno <christoffer@aegik.com>
71 lines
1.6 KiB
Plaintext
71 lines
1.6 KiB
Plaintext
module std::math::nolibc @if(env::NO_LIBC || $feature(C3_MATH));
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// Constants
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const double SQRT_PI = 1.7724538509055160272981674833411451;
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const double LN_SQRT_2PI = 0.9189385332046727417803297364056176;
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<*
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Natural logarithm of the gamma function using the Lanczos approximation.
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@require x > 0.0 : "x must be positive."
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*>
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fn double lgamma(double x)
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{
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// Lanczos approximation coefficients (g = 7, n = 9)
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const double[*] LANCZOS_COEF = {
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0.99999999999980993,
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676.5203681218851,
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-1259.1392167224028,
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771.32342877765313,
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-176.61502916214059,
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12.507343278686905,
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-0.13857109526572012,
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9.9843695780195716e-6,
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1.5056327351493116e-7
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};
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const double LANCZOS_G = 7.0;
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// For small x, use the reflection formula.
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if (x < 0.5)
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{
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return math::ln(math::PI) - math::ln(math::sin(math::PI * x)) - lgamma(1.0 - x);
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}
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// Shift to use approximation around x >= 1.5
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x -= 1.0;
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double base = x + LANCZOS_G + 0.5;
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double sum = LANCZOS_COEF[0];
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for (int i = 1; i < 9; i++)
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{
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sum += LANCZOS_COEF[i] / (x + (double)i);
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}
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return LN_SQRT_2PI + math::ln(sum) + (x + 0.5) * math::ln(base) - base;
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}
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<*
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Gamma function.
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Valid for x > 0 and some negative non-integer values.
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*>
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fn double tgamma(double x)
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{
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// Handle special cases.
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if (x == 0.0) return double.inf;
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// Check for negative integers (poles).
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if (x < 0.0 && x == math::floor(x))
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{
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return double.nan;
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}
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// For positive values, use exp(lgamma(x)).
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if (x > 0.0)
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{
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return math::exp(lgamma(x));
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}
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// For negative non-integer values, use the reflection formula.
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return math::PI / (math::sin(math::PI * x) * tgamma(1.0 - x));
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}
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