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Constants for some fixed square root math.

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This commit is contained in:
Jens True
2024-02-15 10:12:45 +00:00
parent 5bebd9310d
commit f372d9a028
2 changed files with 16 additions and 14 deletions
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28
src/Numerics/GaussianDistribution.php
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@ -12,6 +12,13 @@ namespace DNW\Skills\Numerics;
*/
class GaussianDistribution implements \Stringable
{
//sqrt(2*pi)
//from https://www.wolframalpha.com/input?i=sqrt%282*pi%29
const M_SQRT_2_PI = 2.5066282746310005024157652848110452530069867406099383166299235763;
//log(sqrt(2*pi))
//From https://www.wolframalpha.com/input?i=log%28sqrt%282*pi%29%29
const M_LOG_SQRT_2_PI = 0.9189385332046727417803297364056176398613974736377834128171515404;
// precision and precisionMean are used because they make multiplying and dividing simpler
// (the the accompanying math paper for more details)
private float $precision;
@ -62,7 +69,7 @@ class GaussianDistribution implements \Stringable
public function getNormalizationConstant(): float
{
// Great derivation of this is at http://www.astro.psu.edu/~mce/A451_2/A451/downloads/notes0.pdf
return 1.0 / (sqrt(2 * M_PI) * $this->standardDeviation);
return 1.0 / (self::M_SQRT_2_PI * $this->standardDeviation);
}
public static function fromPrecisionMean(float $precisionMean, float $precision): self
@ -115,9 +122,7 @@ class GaussianDistribution implements \Stringable
$varianceSum = $left->variance + $right->variance;
$meanDifference = $left->mean - $right->mean;
$logSqrt2Pi = log(sqrt(2 * M_PI));
return -$logSqrt2Pi - (log($varianceSum) / 2.0) - (BasicMath::square($meanDifference) / (2.0 * $varianceSum));
return -self::M_LOG_SQRT_2_PI - (log($varianceSum) / 2.0) - (BasicMath::square($meanDifference) / (2.0 * $varianceSum));
}
public static function divide(GaussianDistribution $numerator, GaussianDistribution $denominator): self
@ -137,9 +142,7 @@ class GaussianDistribution implements \Stringable
$varianceDifference = $denominator->variance - $numerator->variance;
$meanDifference = $numerator->mean - $denominator->mean;
$logSqrt2Pi = log(sqrt(2 * M_PI));
return log($denominator->variance) + $logSqrt2Pi - log($varianceDifference) / 2.0 +
return log($denominator->variance) + self::M_LOG_SQRT_2_PI - log($varianceDifference) / 2.0 +
BasicMath::square($meanDifference) / (2 * $varianceDifference);
}
@ -150,7 +153,7 @@ class GaussianDistribution implements \Stringable
// P(x) = ------------------- * e
// stdDev * sqrt(2*pi)
$multiplier = 1.0 / ($standardDeviation * sqrt(2 * M_PI));
$multiplier = 1.0 / ($standardDeviation * self::M_SQRT_2_PI);
$expPart = exp((-1.0 * BasicMath::square($x - $mean)) / (2 * BasicMath::square($standardDeviation)));
return $multiplier * $expPart;
@ -158,8 +161,7 @@ class GaussianDistribution implements \Stringable
public static function cumulativeTo(float $x, float $mean = 0.0, float $standardDeviation = 1.0): float
{
$invsqrt2 = -0.707106781186547524400844362104;
$result = GaussianDistribution::errorFunctionCumulativeTo($invsqrt2 * $x);
$result = GaussianDistribution::errorFunctionCumulativeTo(-M_SQRT1_2 * $x);
return 0.5 * $result;
}
@ -231,11 +233,11 @@ class GaussianDistribution implements \Stringable
$pp = ($p < 1.0) ? $p : 2 - $p;
$t = sqrt(-2 * log($pp / 2.0)); // Initial guess
$x = -0.70711 * ((2.30753 + $t * 0.27061) / (1.0 + $t * (0.99229 + $t * 0.04481)) - $t);
$x = -M_SQRT1_2 * ((2.30753 + $t * 0.27061) / (1.0 + $t * (0.99229 + $t * 0.04481)) - $t);
for ($j = 0; $j < 2; $j++) {
$err = GaussianDistribution::errorFunctionCumulativeTo($x) - $pp;
$x += $err / (1.12837916709551257 * exp(-BasicMath::square($x)) - $x * $err); // Halley
$x += $err / (M_2_SQRTPI * exp(-BasicMath::square($x)) - $x * $err); // Halley
}
return ($p < 1.0) ? $x : -$x;
@ -244,7 +246,7 @@ class GaussianDistribution implements \Stringable
public static function inverseCumulativeTo(float $x, float $mean = 0.0, float $standardDeviation = 1.0): float
{
// From numerical recipes, page 320
return $mean - sqrt(2) * $standardDeviation * GaussianDistribution::inverseErrorFunctionCumulativeTo(2 * $x);
return $mean - M_SQRT2 * $standardDeviation * GaussianDistribution::inverseErrorFunctionCumulativeTo(2 * $x);
}
public function __toString(): string

2
src/TrueSkill/DrawMargin.php
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@ -18,6 +18,6 @@ final class DrawMargin
//
// margin = inversecdf((draw probability + 1)/2) * sqrt(n1+n2) * beta
// n1 and n2 are the number of players on each team
return GaussianDistribution::inverseCumulativeTo(.5 * ($drawProbability + 1), 0, 1) * sqrt(1 + 1) * $beta;
return GaussianDistribution::inverseCumulativeTo(.5 * ($drawProbability + 1), 0, 1) * M_SQRT2 * $beta;
}
}