9407da0461
dxc lowers float min/max/clamp to dx.op FMin/FMax (36/35) and saturate to dx.op Saturate (7). DXIL.rst defines them: FMin(a, b) is a < b ? a : b, FMax(a, b) is a >= b ? a : b, a NaN operand returns the other, and Saturate is FMin(1, FMax(0, x)). C# used MathF.Min/Max, which pass NaN through and order signed zeros, so saturate(NaN) was NaN instead of 0. Every float overload now follows the spec, normalize uses the same max as its mirror, and the mirror's saturate spells Saturate's operand order (which maps -0 to +0, where clamp(x, 0, 1) keeps -0). Non-NaN results change only in the sign of a zero. design.md records the rules and that dxc marks float math fast, so GPU NaN results are not guaranteed. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
356 lines
16 KiB
HLSL
356 lines
16 KiB
HLSL
#ifndef CULTMATH_HLSL
|
|
#define CULTMATH_HLSL
|
|
|
|
// CultMath HLSL mirror.
|
|
//
|
|
// HLSL already owns the float2/float3/float4 type names and most primitive
|
|
// intrinsics. This include names the CultMath semantic surface explicitly so
|
|
// shader code, C# wrappers, and Rust/native parity fixtures can share the same
|
|
// small vocabulary without local helper drift.
|
|
|
|
static const float CULTMATH_PI = 3.14159265358979323846;
|
|
static const float CULTMATH_TAU = 6.28318530717958647692;
|
|
static const float CULTMATH_HALF_PI = 1.57079632679489661923;
|
|
static const float CULTMATH_NORMALIZE_EPSILON = 1.0e-20;
|
|
|
|
float cultmath_radians(float degrees_value) { return degrees_value * (CULTMATH_PI / 180.0); }
|
|
float cultmath_degrees(float radians_value) { return radians_value * (180.0 / CULTMATH_PI); }
|
|
|
|
float cultmath_frac(float value) { return value - floor(value); }
|
|
float2 cultmath_frac(float2 value) { return value - floor(value); }
|
|
float3 cultmath_frac(float3 value) { return value - floor(value); }
|
|
float4 cultmath_frac(float4 value) { return value - floor(value); }
|
|
|
|
float cultmath_clamp(float value, float minimum, float maximum) { return min(max(value, minimum), maximum); }
|
|
float2 cultmath_clamp(float2 value, float2 minimum, float2 maximum) { return min(max(value, minimum), maximum); }
|
|
float3 cultmath_clamp(float3 value, float3 minimum, float3 maximum) { return min(max(value, minimum), maximum); }
|
|
float4 cultmath_clamp(float4 value, float4 minimum, float4 maximum) { return min(max(value, minimum), maximum); }
|
|
|
|
// DXIL Saturate is FMin(1, FMax(0, x)); dxc lowers min/max to the same FMin/FMax, NaN rules included.
|
|
float cultmath_saturate(float value) { return min(1.0, max(0.0, value)); }
|
|
float2 cultmath_saturate(float2 value) { return min(float2(1.0, 1.0), max(float2(0.0, 0.0), value)); }
|
|
float3 cultmath_saturate(float3 value) { return min(float3(1.0, 1.0, 1.0), max(float3(0.0, 0.0, 0.0), value)); }
|
|
float4 cultmath_saturate(float4 value) { return min(float4(1.0, 1.0, 1.0, 1.0), max(float4(0.0, 0.0, 0.0, 0.0), value)); }
|
|
|
|
float cultmath_lerp(float start, float end, float amount) { return start + (end - start) * amount; }
|
|
float2 cultmath_lerp(float2 start, float2 end, float2 amount) { return start + (end - start) * amount; }
|
|
float3 cultmath_lerp(float3 start, float3 end, float3 amount) { return start + (end - start) * amount; }
|
|
float4 cultmath_lerp(float4 start, float4 end, float4 amount) { return start + (end - start) * amount; }
|
|
|
|
float cultmath_step(float edge, float value) { return value < edge ? 0.0 : 1.0; }
|
|
float2 cultmath_step(float2 edge, float2 value) { return float2(cultmath_step(edge.x, value.x), cultmath_step(edge.y, value.y)); }
|
|
float3 cultmath_step(float3 edge, float3 value) { return float3(cultmath_step(edge.x, value.x), cultmath_step(edge.y, value.y), cultmath_step(edge.z, value.z)); }
|
|
float4 cultmath_step(float4 edge, float4 value) { return float4(cultmath_step(edge.x, value.x), cultmath_step(edge.y, value.y), cultmath_step(edge.z, value.z), cultmath_step(edge.w, value.w)); }
|
|
|
|
float cultmath_smoothstep(float minimum, float maximum, float value)
|
|
{
|
|
float t = cultmath_saturate((value - minimum) / (maximum - minimum));
|
|
return t * t * (3.0 - 2.0 * t);
|
|
}
|
|
|
|
float2 cultmath_smoothstep(float2 minimum, float2 maximum, float2 value)
|
|
{
|
|
float2 t = cultmath_saturate((value - minimum) / (maximum - minimum));
|
|
return t * t * (float2(3.0, 3.0) - float2(2.0, 2.0) * t);
|
|
}
|
|
|
|
float3 cultmath_smoothstep(float3 minimum, float3 maximum, float3 value)
|
|
{
|
|
float3 t = cultmath_saturate((value - minimum) / (maximum - minimum));
|
|
return t * t * (float3(3.0, 3.0, 3.0) - float3(2.0, 2.0, 2.0) * t);
|
|
}
|
|
|
|
float4 cultmath_smoothstep(float4 minimum, float4 maximum, float4 value)
|
|
{
|
|
float4 t = cultmath_saturate((value - minimum) / (maximum - minimum));
|
|
return t * t * (float4(3.0, 3.0, 3.0, 3.0) - float4(2.0, 2.0, 2.0, 2.0) * t);
|
|
}
|
|
|
|
float cultmath_smoothstep01(float value) { return cultmath_smoothstep(0.0, 1.0, value); }
|
|
|
|
float cultmath_smootherstep(float value)
|
|
{
|
|
value = cultmath_saturate(value);
|
|
return value * value * value * (value * (value * 6.0 - 15.0) + 10.0);
|
|
}
|
|
|
|
float2 cultmath_snoise_mod289(float2 value) { return value - floor(value * (1.0 / 289.0)) * 289.0; }
|
|
float3 cultmath_snoise_mod289(float3 value) { return value - floor(value * (1.0 / 289.0)) * 289.0; }
|
|
float4 cultmath_snoise_mod289(float4 value) { return value - floor(value * (1.0 / 289.0)) * 289.0; }
|
|
float3 cultmath_snoise_permute(float3 value) { return cultmath_snoise_mod289(((value * 34.0) + 1.0) * value); }
|
|
float4 cultmath_snoise_permute(float4 value) { return cultmath_snoise_mod289(((value * 34.0) + 1.0) * value); }
|
|
|
|
// Ashima Arts / Ian McEwan 3D simplex noise (MIT), same float32 evaluation
|
|
// order as the C# math.snoise(float3) mirror.
|
|
float cultmath_snoise(float3 value)
|
|
{
|
|
float2 c = float2(1.0 / 6.0, 1.0 / 3.0);
|
|
float3 i = floor(value + dot(value, c.yyy));
|
|
float3 x0 = value - i + dot(i, c.xxx);
|
|
float3 g = step(x0.yzx, x0.xyz);
|
|
float3 l = 1.0 - g;
|
|
float3 i1 = min(g.xyz, l.zxy);
|
|
float3 i2 = max(g.xyz, l.zxy);
|
|
float3 x1 = x0 - i1 + c.xxx;
|
|
float3 x2 = x0 - i2 + c.yyy;
|
|
float3 x3 = x0 - 0.5;
|
|
|
|
i = cultmath_snoise_mod289(i);
|
|
float4 p = cultmath_snoise_permute(cultmath_snoise_permute(cultmath_snoise_permute(
|
|
i.z + float4(0.0, i1.z, i2.z, 1.0)) + i.y + float4(0.0, i1.y, i2.y, 1.0)) + i.x + float4(0.0, i1.x, i2.x, 1.0));
|
|
|
|
const float n_ = 0.142857142857;
|
|
float3 ns = float3(2.0 * n_, 0.5 * n_ - 1.0, n_);
|
|
float4 j = p - 49.0 * floor(p * ns.z * ns.z);
|
|
float4 x_ = floor(j * ns.z);
|
|
float4 y_ = floor(j - 7.0 * x_);
|
|
float4 x = x_ * ns.x + ns.yyyy;
|
|
float4 y = y_ * ns.x + ns.yyyy;
|
|
float4 h = 1.0 - abs(x) - abs(y);
|
|
|
|
float4 b0 = float4(x.xy, y.xy);
|
|
float4 b1 = float4(x.zw, y.zw);
|
|
float4 s0 = floor(b0) * 2.0 + 1.0;
|
|
float4 s1 = floor(b1) * 2.0 + 1.0;
|
|
float4 sh = -step(h, 0.0);
|
|
float4 a0 = b0.xzyw + s0.xzyw * sh.xxyy;
|
|
float4 a1 = b1.xzyw + s1.xzyw * sh.zzww;
|
|
|
|
float3 p0 = float3(a0.xy, h.x);
|
|
float3 p1 = float3(a0.zw, h.y);
|
|
float3 p2 = float3(a1.xy, h.z);
|
|
float3 p3 = float3(a1.zw, h.w);
|
|
float4 norm = 1.79284291400159 - 0.85373472095314 * float4(dot(p0, p0), dot(p1, p1), dot(p2, p2), dot(p3, p3));
|
|
p0 *= norm.x;
|
|
p1 *= norm.y;
|
|
p2 *= norm.z;
|
|
p3 *= norm.w;
|
|
|
|
float4 m = max(0.6 - float4(dot(x0, x0), dot(x1, x1), dot(x2, x2), dot(x3, x3)), 0.0);
|
|
m = m * m;
|
|
return 42.0 * dot(m * m, float4(dot(p0, x0), dot(p1, x1), dot(p2, x2), dot(p3, x3)));
|
|
}
|
|
|
|
float cultmath_snoise(float2 value)
|
|
{
|
|
float4 c = float4(
|
|
0.211324865405187,
|
|
0.366025403784439,
|
|
-0.577350269189626,
|
|
0.024390243902439);
|
|
float2 i = floor(value + dot(value, c.yy));
|
|
float2 x0 = value - i + dot(i, c.xx);
|
|
float2 i1 = x0.x > x0.y ? float2(1.0, 0.0) : float2(0.0, 1.0);
|
|
float4 x12 = float4(x0.x + c.x - i1.x, x0.y + c.x - i1.y, x0.x + c.z, x0.y + c.z);
|
|
|
|
i = cultmath_snoise_mod289(i);
|
|
float3 p = cultmath_snoise_permute(
|
|
cultmath_snoise_permute(i.y + float3(0.0, i1.y, 1.0)) + i.x + float3(0.0, i1.x, 1.0));
|
|
float3 m = max(0.5 - float3(dot(x0, x0), dot(x12.xy, x12.xy), dot(x12.zw, x12.zw)), 0.0);
|
|
m *= m;
|
|
m *= m;
|
|
|
|
float3 x = 2.0 * frac(p * c.w) - 1.0;
|
|
float3 h = abs(x) - 0.5;
|
|
float3 ox = floor(x + 0.5);
|
|
float3 a0 = x - ox;
|
|
m *= 1.79284291400159 - 0.85373472095314 * (a0 * a0 + h * h);
|
|
|
|
float3 g = float3(
|
|
a0.x * x0.x + h.x * x0.y,
|
|
a0.y * x12.x + h.y * x12.y,
|
|
a0.z * x12.z + h.z * x12.w);
|
|
return 130.0 * dot(m, g);
|
|
}
|
|
|
|
float cultmath_lengthsq(float2 value) { return dot(value, value); }
|
|
float cultmath_lengthsq(float3 value) { return dot(value, value); }
|
|
float cultmath_lengthsq(float4 value) { return dot(value, value); }
|
|
|
|
float cultmath_distance(float2 left, float2 right) { return length(left - right); }
|
|
float cultmath_distance(float3 left, float3 right) { return length(left - right); }
|
|
float cultmath_distance(float4 left, float4 right) { return length(left - right); }
|
|
|
|
float2 cultmath_normalize(float2 value) { return value / max(length(value), CULTMATH_NORMALIZE_EPSILON); }
|
|
float3 cultmath_normalize(float3 value) { return value / max(length(value), CULTMATH_NORMALIZE_EPSILON); }
|
|
float4 cultmath_normalize(float4 value) { return value / max(length(value), CULTMATH_NORMALIZE_EPSILON); }
|
|
|
|
float2 cultmath_reflect(float2 incident, float2 normal_value)
|
|
{
|
|
return incident - 2.0 * dot(normal_value, incident) * normal_value;
|
|
}
|
|
|
|
float3 cultmath_reflect(float3 incident, float3 normal_value)
|
|
{
|
|
return incident - 2.0 * dot(normal_value, incident) * normal_value;
|
|
}
|
|
|
|
float2 cultmath_rotate(float2 value, float radians_value)
|
|
{
|
|
float s = sin(radians_value);
|
|
float c = cos(radians_value);
|
|
return float2(value.x * c - value.y * s, value.x * s + value.y * c);
|
|
}
|
|
|
|
float2 cultmath_rotate_degrees(float2 value, float degrees_value)
|
|
{
|
|
return cultmath_rotate(value, cultmath_radians(degrees_value));
|
|
}
|
|
|
|
float cultmath_csum(float2 value) { return value.x + value.y; }
|
|
float cultmath_csum(float3 value) { return value.x + value.y + value.z; }
|
|
float cultmath_csum(float4 value) { return value.x + value.y + value.z + value.w; }
|
|
|
|
float cultmath_decay(float source, float lambda_value, float dt) { return source * exp(-lambda_value * dt); }
|
|
float2 cultmath_decay(float2 source, float lambda_value, float dt) { return source * exp(-lambda_value * dt); }
|
|
float3 cultmath_decay(float3 source, float lambda_value, float dt) { return source * exp(-lambda_value * dt); }
|
|
float4 cultmath_decay(float4 source, float lambda_value, float dt) { return source * exp(-lambda_value * dt); }
|
|
|
|
float cultmath_damp(float start, float end, float lambda_value, float dt)
|
|
{
|
|
return cultmath_lerp(start, end, 1.0 - exp(-lambda_value * dt));
|
|
}
|
|
|
|
float2 cultmath_damp(float2 start, float2 end, float lambda_value, float dt)
|
|
{
|
|
return cultmath_lerp(start, end, 1.0 - exp(-lambda_value * dt));
|
|
}
|
|
|
|
float3 cultmath_damp(float3 start, float3 end, float lambda_value, float dt)
|
|
{
|
|
return cultmath_lerp(start, end, 1.0 - exp(-lambda_value * dt));
|
|
}
|
|
|
|
float4 cultmath_damp(float4 start, float4 end, float lambda_value, float dt)
|
|
{
|
|
return cultmath_lerp(start, end, 1.0 - exp(-lambda_value * dt));
|
|
}
|
|
|
|
float cultmath_catmullrom(float p0, float p1, float p2, float p3, float t)
|
|
{
|
|
float t2 = t * t;
|
|
float t3 = t2 * t;
|
|
return 0.5 * ((2.0 * p1) + (p2 - p0) * t + (2.0 * p0 - 5.0 * p1 + 4.0 * p2 - p3) * t2 + (-p0 + 3.0 * p1 - 3.0 * p2 + p3) * t3);
|
|
}
|
|
|
|
float2 cultmath_catmullrom(float2 p0, float2 p1, float2 p2, float2 p3, float t)
|
|
{
|
|
float t2 = t * t;
|
|
float t3 = t2 * t;
|
|
return 0.5 * ((2.0 * p1) + (p2 - p0) * t + (2.0 * p0 - 5.0 * p1 + 4.0 * p2 - p3) * t2 + (-p0 + 3.0 * p1 - 3.0 * p2 + p3) * t3);
|
|
}
|
|
|
|
float3 cultmath_catmullrom(float3 p0, float3 p1, float3 p2, float3 p3, float t)
|
|
{
|
|
float t2 = t * t;
|
|
float t3 = t2 * t;
|
|
return 0.5 * ((2.0 * p1) + (p2 - p0) * t + (2.0 * p0 - 5.0 * p1 + 4.0 * p2 - p3) * t2 + (-p0 + 3.0 * p1 - 3.0 * p2 + p3) * t3);
|
|
}
|
|
|
|
float4 cultmath_catmullrom(float4 p0, float4 p1, float4 p2, float4 p3, float t)
|
|
{
|
|
float t2 = t * t;
|
|
float t3 = t2 * t;
|
|
return 0.5 * ((2.0 * p1) + (p2 - p0) * t + (2.0 * p0 - 5.0 * p1 + 4.0 * p2 - p3) * t2 + (-p0 + 3.0 * p1 - 3.0 * p2 + p3) * t3);
|
|
}
|
|
|
|
float cultmath_quadratic_bezier(float p0, float p1, float p2, float t)
|
|
{
|
|
t = cultmath_saturate(t);
|
|
float inv = 1.0 - t;
|
|
return inv * inv * p0 + 2.0 * inv * t * p1 + t * t * p2;
|
|
}
|
|
|
|
float3 cultmath_quadratic_bezier(float3 p0, float3 p1, float3 p2, float t)
|
|
{
|
|
t = cultmath_saturate(t);
|
|
float inv = 1.0 - t;
|
|
return inv * inv * p0 + 2.0 * inv * t * p1 + t * t * p2;
|
|
}
|
|
|
|
float cultmath_cubic_bezier(float p0, float p1, float p2, float p3, float t)
|
|
{
|
|
t = cultmath_saturate(t);
|
|
float inv = 1.0 - t;
|
|
return inv * inv * inv * p0 + 3.0 * inv * inv * t * p1 + 3.0 * inv * t * t * p2 + t * t * t * p3;
|
|
}
|
|
|
|
float3 cultmath_cubic_bezier(float3 p0, float3 p1, float3 p2, float3 p3, float t)
|
|
{
|
|
t = cultmath_saturate(t);
|
|
float inv = 1.0 - t;
|
|
return inv * inv * inv * p0 + 3.0 * inv * inv * t * p1 + 3.0 * inv * t * t * p2 + t * t * t * p3;
|
|
}
|
|
|
|
float cultmath_hash(float value) { return cultmath_frac(sin(value) * 43758.5453); }
|
|
float cultmath_hash(float2 value) { return cultmath_hash(dot(value, float2(127.1, 311.7))); }
|
|
float cultmath_hash(float3 value) { return cultmath_hash(dot(value, float3(127.1, 311.7, 74.7))); }
|
|
|
|
float cultmath_value_noise(float2 position)
|
|
{
|
|
float2 cell = floor(position);
|
|
float2 local = cultmath_frac(position);
|
|
float2 u = local * local * (float2(3.0, 3.0) - float2(2.0, 2.0) * local);
|
|
|
|
float a = cultmath_hash(cell);
|
|
float b = cultmath_hash(cell + float2(1.0, 0.0));
|
|
float c = cultmath_hash(cell + float2(0.0, 1.0));
|
|
float d = cultmath_hash(cell + float2(1.0, 1.0));
|
|
|
|
return cultmath_lerp(cultmath_lerp(a, b, u.x), cultmath_lerp(c, d, u.x), u.y);
|
|
}
|
|
|
|
float cultmath_value_noise_bicubic(float2 position)
|
|
{
|
|
float2 cell = floor(position);
|
|
float2 local = cultmath_frac(position);
|
|
|
|
float y0 = cultmath_catmullrom(cultmath_hash(cell + float2(-1.0, -1.0)), cultmath_hash(cell + float2(0.0, -1.0)), cultmath_hash(cell + float2(1.0, -1.0)), cultmath_hash(cell + float2(2.0, -1.0)), local.x);
|
|
float y1 = cultmath_catmullrom(cultmath_hash(cell + float2(-1.0, 0.0)), cultmath_hash(cell + float2(0.0, 0.0)), cultmath_hash(cell + float2(1.0, 0.0)), cultmath_hash(cell + float2(2.0, 0.0)), local.x);
|
|
float y2 = cultmath_catmullrom(cultmath_hash(cell + float2(-1.0, 1.0)), cultmath_hash(cell + float2(0.0, 1.0)), cultmath_hash(cell + float2(1.0, 1.0)), cultmath_hash(cell + float2(2.0, 1.0)), local.x);
|
|
float y3 = cultmath_catmullrom(cultmath_hash(cell + float2(-1.0, 2.0)), cultmath_hash(cell + float2(0.0, 2.0)), cultmath_hash(cell + float2(1.0, 2.0)), cultmath_hash(cell + float2(2.0, 2.0)), local.x);
|
|
|
|
return cultmath_catmullrom(y0, y1, y2, y3, local.y);
|
|
}
|
|
|
|
float cultmath_value_noise_texture(Texture2D<float> noise_texture, SamplerState noise_sampler, float2 uv, float scale)
|
|
{
|
|
return noise_texture.SampleLevel(noise_sampler, uv * scale, 0.0).r;
|
|
}
|
|
|
|
float cultmath_value_noise_texture_bicubic(Texture2D<float> noise_texture, SamplerState noise_sampler, float2 uv, float scale, float2 texel_size)
|
|
{
|
|
float2 position = uv * scale;
|
|
float2 cell = floor(position);
|
|
float2 local = cultmath_frac(position);
|
|
float2 base_uv = cell / scale;
|
|
|
|
float row0 = cultmath_catmullrom(
|
|
noise_texture.SampleLevel(noise_sampler, base_uv + texel_size * float2(-1.0, -1.0), 0.0).r,
|
|
noise_texture.SampleLevel(noise_sampler, base_uv + texel_size * float2(0.0, -1.0), 0.0).r,
|
|
noise_texture.SampleLevel(noise_sampler, base_uv + texel_size * float2(1.0, -1.0), 0.0).r,
|
|
noise_texture.SampleLevel(noise_sampler, base_uv + texel_size * float2(2.0, -1.0), 0.0).r,
|
|
local.x);
|
|
float row1 = cultmath_catmullrom(
|
|
noise_texture.SampleLevel(noise_sampler, base_uv + texel_size * float2(-1.0, 0.0), 0.0).r,
|
|
noise_texture.SampleLevel(noise_sampler, base_uv + texel_size * float2(0.0, 0.0), 0.0).r,
|
|
noise_texture.SampleLevel(noise_sampler, base_uv + texel_size * float2(1.0, 0.0), 0.0).r,
|
|
noise_texture.SampleLevel(noise_sampler, base_uv + texel_size * float2(2.0, 0.0), 0.0).r,
|
|
local.x);
|
|
float row2 = cultmath_catmullrom(
|
|
noise_texture.SampleLevel(noise_sampler, base_uv + texel_size * float2(-1.0, 1.0), 0.0).r,
|
|
noise_texture.SampleLevel(noise_sampler, base_uv + texel_size * float2(0.0, 1.0), 0.0).r,
|
|
noise_texture.SampleLevel(noise_sampler, base_uv + texel_size * float2(1.0, 1.0), 0.0).r,
|
|
noise_texture.SampleLevel(noise_sampler, base_uv + texel_size * float2(2.0, 1.0), 0.0).r,
|
|
local.x);
|
|
float row3 = cultmath_catmullrom(
|
|
noise_texture.SampleLevel(noise_sampler, base_uv + texel_size * float2(-1.0, 2.0), 0.0).r,
|
|
noise_texture.SampleLevel(noise_sampler, base_uv + texel_size * float2(0.0, 2.0), 0.0).r,
|
|
noise_texture.SampleLevel(noise_sampler, base_uv + texel_size * float2(1.0, 2.0), 0.0).r,
|
|
noise_texture.SampleLevel(noise_sampler, base_uv + texel_size * float2(2.0, 2.0), 0.0).r,
|
|
local.x);
|
|
|
|
return cultmath_catmullrom(row0, row1, row2, row3, local.y);
|
|
}
|
|
|
|
#endif
|