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Cut 12.0: add erf and erfinv to CultMath

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Fire control's Gaussian scatter needs erf for a cell's probability mass
and erfinv to draw the lateral offset, both called per shot. Abramowitz-
Stegun 7.1.26 for erf (stated max abs error 1.5e-7), Giles 2010 (GPU
Computing Gems) for erfinv. Neither is an HLSL intrinsic, so there is no
shader-parity obligation.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
This commit is contained in:
Meta Vens 2026-09-22 20:42:57 +02:00
commit 87b95aefa5
1 changed files with 55 additions and 0 deletions
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55
packages/cultmath/src/CultMath/math.cs
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@ -521,6 +521,61 @@ public static partial class math
a._m20 * b._m01 + a._m21 * b._m11 + a._m22 * b._m21,
a._m20 * b._m02 + a._m21 * b._m12 + a._m22 * b._m22);
// Abramowitz & Stegun 7.1.26, a single-precision rational/exponential fit with a stated
// max absolute error of 1.5e-7. erf is odd, so only x >= 0 is fit and the sign is restored.
public static float erf(float value)
{
const float p = 0.3275911f;
const float a1 = 0.254829592f;
const float a2 = -0.284496736f;
const float a3 = 1.421413741f;
const float a4 = -1.453152027f;
const float a5 = 1.061405429f;
var s = sign(value);
var x = abs(value);
var t = 1.0f / (1.0f + p * x);
var poly = ((((a5 * t + a4) * t + a3) * t + a2) * t + a1) * t;
var result = 1.0f - poly * exp(-x * x);
return s * result;
}
// Giles, "Approximating the erfinv function" (GPU Computing Gems, 2010): a single-precision
// minimax polynomial in two ranges of w = -ln((1-x)(1+x)), central and tail.
public static float erfinv(float value)
{
var w = -log((1.0f - value) * (1.0f + value));
float p;
if (w < 5.0f)
{
w -= 2.5f;
p = 2.81022636e-08f;
p = 3.43273939e-07f + p * w;
p = -3.5233877e-06f + p * w;
p = -4.39150654e-06f + p * w;
p = 0.00021858087f + p * w;
p = -0.00125372503f + p * w;
p = -0.00417768164f + p * w;
p = 0.246640727f + p * w;
p = 1.50140941f + p * w;
}
else
{
w = sqrt(w) - 3.0f;
p = -0.000200214257f;
p = 0.000100950558f + p * w;
p = 0.00134934322f + p * w;
p = -0.00367342844f + p * w;
p = 0.00573950773f + p * w;
p = -0.0076224613f + p * w;
p = 0.00943887047f + p * w;
p = 1.00167406f + p * w;
p = 2.83297682f + p * w;
}
return p * value;
}
// Ashima Arts / Ian McEwan 3D simplex noise (MIT), mirrored by cultmath_snoise(float3)
// in shaders/CultMath.hlsl with the same float32 evaluation order.
public static float snoise(float3 value)