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// texture.slang
// This class encapsulates a differentiable texture object that uses
// hardware sampling for the primal version, but substitutes a reference
// interpolation implementation to generate backward pass.
//
// This specific implementation also makes the choice to use fast fixed point
// atomics to accumulate the derivative (suitable for this example, but maybe
// not in general)
//
struct DifferentiableTexture
{
RWStructuredBuffer<int> accumulateBuffer; // Per-mip-level accumulate buffer
Texture2D texture; // Hardware texture handle.
float minLOD;
[BackwardDerivative(bwd_LoadTexel)]
float4 LoadTexel(int3 location, constexpr int2 offset, uint dLayerW, uint dMipOffset)
{
return texture.Load(location, offset);
}
void bwd_LoadTexel(int3 location, constexpr int2 offset, uint dLayerW, uint dMipOffset, float4 val)
{
// Ignore alpha dimension for this example..
int4 uval = int4(int3(val.xyz * 65536), 1);
// We'll use fast fixed point atomics instead of floats.
InterlockedAdd(accumulateBuffer[dMipOffset + ((uint)location.y * dLayerW + (uint)location.x) * 4 + 0], uval.x);
InterlockedAdd(accumulateBuffer[dMipOffset + ((uint)location.y * dLayerW + (uint)location.x) * 4 + 1], uval.y);
InterlockedAdd(accumulateBuffer[dMipOffset + ((uint)location.y * dLayerW + (uint)location.x) * 4 + 2], uval.z);
InterlockedAdd(accumulateBuffer[dMipOffset + ((uint)location.y * dLayerW + (uint)location.x) * 4 + 3], uval.w);
}
// Software reference implementation of linear filtering.
[BackwardDifferentiable]
float4 sampleTexture_linear(uint lod, float2 uv, uint w, uint h)
{
w >>= lod;
h >>= lod;
uv = uv - no_diff(floor(uv));
float2 loc = uv * float2(w, h) - float2(0.5);
float x0 = no_diff(floor(loc.x));
float y0 = no_diff(floor(loc.y));
float fracX = loc.x - x0;
float fracY = loc.y - y0;
float x1 = x0 + 1;
float y1 = y0 + 1;
if (x0 < 0) x0 += w;
if (y0 < 0) y0 += h;
if (x1 >= w) x1 -= w;
if (y1 >= h) y1 -= h;
float weight0 = 1.0f - fracY;
float weight1 = fracY;
float weight00 = weight0 * (1.0f - fracX);
float weight01 = weight0 * fracX;
float weight10 = weight1 * (1.0f - fracX);
float weight11 = weight1 * fracX;
uint dLayerW = w >>= lod;
var offset = mipOffset[lod / 4][lod % 4];
return LoadTexel(int3(int(x0), int(y0), int(lod)), int2(0), dLayerW, offset) * weight00 +
LoadTexel(int3(int(x1), int(y0), int(lod)), int2(0), dLayerW, offset) * weight01 +
LoadTexel(int3(int(x0), int(y1), int(lod)), int2(0), dLayerW, offset) * weight10 +
LoadTexel(int3(int(x1), int(y1), int(lod)), int2(0), dLayerW, offset) * weight11;
}
// Software reference implementation of trilinear filtering.
[BackwardDifferentiable]
float4 sampleTexture_trilinear(uint w, uint h, uint levels, float2 uv, float2 dX, float2 dY)
{
dX = dX * float2(w, h);
dY = dY * float2(w, h);
// Isotropic filter.
float lengthX = length(dX);
float lengthY = length(dY);
float LOD = log2(max(lengthX, lengthY));
float maxLOD = levels - 1;
float clampedLOD = max(minLOD, (min(maxLOD, LOD)));
float lodFrac = clampedLOD - no_diff(floor(clampedLOD));
uint lod0 = (uint)floor(clampedLOD);
uint lod1 = min(levels - 1, lod0 + 1);
float weightLod0 = 1.0 - lodFrac;
float weightLod1 = lodFrac;
let v0 = sampleTexture_linear(lod0, uv, w, h) * weightLod0;
let v1 = sampleTexture_linear(lod1, uv, w, h) * weightLod1;
return v0 + v1;
}
// Note that there is no need to mark this [BackwardDifferentiable] since it has a substitute
// that is marked [BackwardDifferentiable]. The compiler automatically considers a call to
// sample() to be differentiable.
//
static float4 sample(DifferentiableTexture t, SamplerState s, float2 uv, float2 dX, float2 dY)
{
return t.texture.Sample(s, uv);
}
// Software reference implementation of DifferentiableTexture.sample (trilinear only in this example)
[PrimalSubstituteOf(DifferentiableTexture.sample)]
[BackwardDifferentiable]
static float4 sample_reference_impl(DifferentiableTexture t, SamplerState s, float2 uv, float2 dX, float2 dY)
{
uint w;
uint h;
uint levels;
t.texture.GetDimensions(0, w, h, levels);
return t.sampleTexture_trilinear(w, h, levels, uv, dX, dY);
}
}
cbuffer Uniforms
{
float4x4 modelViewProjection;
uint4 mipOffset[16];
Texture2D texRef;
SamplerState sampler;
DifferentiableTexture bwdTexture;
}
struct AssembledVertex
{
float3 position : POSITION;
};
struct Fragment
{
float4 color;
};
struct VertexStageOutput
{
float2 uv : UV;
float4 sv_position : SV_Position;
};
[BackwardDifferentiable]
float4 shadeFragment(float2 uv)
{
uv = uv * 2;
// Compute fragment differentials using shader intrinsics.
float2 dX = no_diff ddx_coarse(uv);
float2 dY = no_diff ddy_coarse(uv);
float3 color = DifferentiableTexture.sample(bwdTexture, sampler, uv, dX, dY).xyz;
return float4(color, 1.0);
}
[BackwardDifferentiable]
float3 loss(no_diff float2 uv, no_diff float4 screenPos)
{
float3 refColor = (no_diff texRef.Load(int3(int2(screenPos.xy), 0))).xyz;
float3 rs = shadeFragment(uv).xyz - refColor;
rs *= rs;
return rs;
}
[shader("vertex")]
VertexStageOutput vertexMain(
AssembledVertex assembledVertex)
{
VertexStageOutput output;
float3 position = assembledVertex.position;
output.uv = position.xy;
output.sv_position = mul(modelViewProjection, float4(position, 1.0));
return output;
}
float3 sqr(float3 v) { return v * v; }
[shader("fragment")]
float4 fragmentMain(
float2 uv : UV) : SV_Target
{
return shadeFragment(uv);
}
[shader("fragment")]
float4 diffFragmentMain(
float2 uv : UV,
float4 screenPos : SV_POSITION) : SV_Target
{
__bwd_diff(loss)(uv, screenPos, float3(1.0));
return float4(loss(uv, screenPos), 1.0);
}
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