Software: Store offset in Slope

This is needed since we need a separate offset for zfreeze to work correctly.  It also makes the code a bit less jank.

Source/Core/VideoBackends/Software/Rasterizer.cpp

@@ -20,16 +20,82 @@ namespace Rasterizer
 {
 static constexpr int BLOCK_SIZE = 2;
 
+struct SlopeContext
+{
+  SlopeContext(const OutputVertexData* v0, const OutputVertexData* v1, const OutputVertexData* v2,
+               s32 x0, s32 y0)
+      : x0(x0), y0(y0)
+  {
+    // adjust a little less than 0.5
+    const float adjust = 0.495f;
+
+    xOff = ((float)x0 - v0->screenPosition.x) + adjust;
+    yOff = ((float)y0 - v0->screenPosition.y) + adjust;
+
+    dx10 = v1->screenPosition.x - v0->screenPosition.x;
+    dx20 = v2->screenPosition.x - v0->screenPosition.x;
+    dy10 = v1->screenPosition.y - v0->screenPosition.y;
+    dy20 = v2->screenPosition.y - v0->screenPosition.y;
+  }
+  s32 x0;
+  s32 y0;
+  float xOff;
+  float yOff;
+  float dx10;
+  float dx20;
+  float dy10;
+  float dy20;
+};
+
+struct Slope
+{
+  Slope() = default;
+  Slope(float f0, float f1, float f2, const SlopeContext& ctx) : f0(f0)
+  {
+    float delta_20 = f2 - f0;
+    float delta_10 = f1 - f0;
+
+    //        x2 - x0    y1 - y0    x1 - x0    y2 - y0
+    float a = delta_20 * ctx.dy10 - delta_10 * ctx.dy20;
+    float b = ctx.dx20 * delta_10 - ctx.dx10 * delta_20;
+    float c = ctx.dx20 * ctx.dy10 - ctx.dx10 * ctx.dy20;
+
+    dfdx = a / c;
+    dfdy = b / c;
+
+    x0 = ctx.x0;
+    y0 = ctx.y0;
+    xOff = ctx.xOff;
+    yOff = ctx.yOff;
+  }
+
+  // These default values are used in the unlikely case that zfreeze is enabled when drawing the
+  // first primitive.
+  // TODO: This is just a guess!
+  float dfdx = 0.0f;
+  float dfdy = 0.0f;
+  float f0 = 1.0f;
+
+  // Both an s32 value and a float value are used to minimize rounding error
+  // TODO: is this really needed?
+  s32 x0 = 0;
+  s32 y0 = 0;
+  float xOff = 0.0f;
+  float yOff = 0.0f;
+
+  float GetValue(s32 x, s32 y) const
+  {
+    float dx = xOff + (float)(x - x0);
+    float dy = yOff + (float)(y - y0);
+    return f0 + (dfdx * dx) + (dfdy * dy);
+  }
+};
+
 static Slope ZSlope;
 static Slope WSlope;
 static Slope ColorSlopes[2][4];
 static Slope TexSlopes[8][3];
 
-static s32 vertex0X;
-static s32 vertex0Y;
-static float vertexOffsetX;
-static float vertexOffsetY;
-
 static Tev tev;
 static RasterBlock rasterBlock;
 
@@ -37,11 +103,9 @@ void Init()
 {
   tev.Init();
 
-  // Set initial z reference plane in the unlikely case that zfreeze is enabled when drawing the
+  // The other slopes are set each for each primitive drawn, but zfreeze means that the z slope
-  // first primitive.
+  // needs to be set to an (untested) default value.
-  // TODO: This is just a guess!
+  ZSlope = Slope();
-  ZSlope.dfdx = ZSlope.dfdy = 0.f;
-  ZSlope.f0 = 1.f;
 }
 
 // Returns approximation of log2(f) in s28.4
@@ -75,10 +139,7 @@ static void Draw(s32 x, s32 y, s32 xi, s32 yi)
 {
   INCSTAT(g_stats.this_frame.rasterized_pixels);
 
-  float dx = vertexOffsetX + (float)(x - vertex0X);
+  s32 z = (s32)std::clamp<float>(ZSlope.GetValue(x, y), 0.0f, 16777215.0f);
-  float dy = vertexOffsetY + (float)(y - vertex0Y);
-
-  s32 z = (s32)std::clamp<float>(ZSlope.GetValue(dx, dy), 0.0f, 16777215.0f);
 
   if (bpmem.UseEarlyDepthTest())
   {
@@ -104,7 +165,7 @@ static void Draw(s32 x, s32 y, s32 xi, s32 yi)
   {
     for (int comp = 0; comp < 4; comp++)
     {
-      u16 color = (u16)ColorSlopes[i][comp].GetValue(dx, dy);
+      u16 color = (u16)ColorSlopes[i][comp].GetValue(x, y);
 
       // clamp color value to 0
       u16 mask = ~(color >> 8);
@@ -136,31 +197,6 @@ static void Draw(s32 x, s32 y, s32 xi, s32 yi)
   tev.Draw();
 }
 
-static void InitTriangle(float X1, float Y1, s32 xi, s32 yi)
-{
-  vertex0X = xi;
-  vertex0Y = yi;
-
-  // adjust a little less than 0.5
-  const float adjust = 0.495f;
-
-  vertexOffsetX = ((float)xi - X1) + adjust;
-  vertexOffsetY = ((float)yi - Y1) + adjust;
-}
-
-static void InitSlope(Slope* slope, float f1, float f2, float f3, float DX31, float DX12,
-                      float DY12, float DY31)
-{
-  float DF31 = f3 - f1;
-  float DF21 = f2 - f1;
-  float a = DF31 * -DY12 - DF21 * DY31;
-  float b = DX31 * DF21 + DX12 * DF31;
-  float c = -DX12 * DY31 - DX31 * -DY12;
-  slope->dfdx = -a / c;
-  slope->dfdy = -b / c;
-  slope->f0 = f1;
-}
-
 static inline void CalculateLOD(s32* lodp, bool* linear, u32 texmap, u32 texcoord)
 {
   auto texUnit = bpmem.tex.GetUnit(texmap);
@@ -220,22 +256,22 @@ static void BuildBlock(s32 blockX, s32 blockY)
     {
       RasterBlockPixel& pixel = rasterBlock.Pixel[xi][yi];
 
-      float dx = vertexOffsetX + (float)(xi + blockX - vertex0X);
+      s32 x = xi + blockX;
-      float dy = vertexOffsetY + (float)(yi + blockY - vertex0Y);
+      s32 y = yi + blockY;
 
-      float invW = 1.0f / WSlope.GetValue(dx, dy);
+      float invW = 1.0f / WSlope.GetValue(x, y);
       pixel.InvW = invW;
 
       // tex coords
       for (unsigned int i = 0; i < bpmem.genMode.numtexgens; i++)
       {
         float projection = invW;
-        float q = TexSlopes[i][2].GetValue(dx, dy) * invW;
+        float q = TexSlopes[i][2].GetValue(x, y) * invW;
         if (q != 0.0f)
           projection = invW / q;
 
-        pixel.Uv[i][0] = TexSlopes[i][0].GetValue(dx, dy) * projection;
+        pixel.Uv[i][0] = TexSlopes[i][0].GetValue(x, y) * projection;
-        pixel.Uv[i][1] = TexSlopes[i][1].GetValue(dx, dy) * projection;
+        pixel.Uv[i][1] = TexSlopes[i][1].GetValue(x, y) * projection;
       }
     }
   }
@@ -335,18 +371,11 @@ void DrawTriangleFrontFace(const OutputVertexData* v0, const OutputVertexData* v
     return;
 
   // Set up slopes
-  float fltx1 = v0->screenPosition.x;
+  const SlopeContext ctx(v0, v1, v2, (X1 + 0xF) >> 4, (Y1 + 0xF) >> 4);
-  float flty1 = v0->screenPosition.y;
-  float fltdx31 = v2->screenPosition.x - fltx1;
-  float fltdx12 = fltx1 - v1->screenPosition.x;
-  float fltdy12 = flty1 - v1->screenPosition.y;
-  float fltdy31 = v2->screenPosition.y - flty1;
-
-  InitTriangle(fltx1, flty1, (X1 + 0xF) >> 4, (Y1 + 0xF) >> 4);
 
   float w[3] = {1.0f / v0->projectedPosition.w, 1.0f / v1->projectedPosition.w,
                 1.0f / v2->projectedPosition.w};
-  InitSlope(&WSlope, w[0], w[1], w[2], fltdx31, fltdx12, fltdy12, fltdy31);
+  WSlope = Slope(w[0], w[1], w[2], ctx);
 
   // TODO: The zfreeze emulation is not quite correct, yet!
   // Many things might prevent us from reaching this line (culling, clipping, scissoring).
@@ -355,21 +384,21 @@ void DrawTriangleFrontFace(const OutputVertexData* v0, const OutputVertexData* v
   // We're currently sloppy at this since we abort early if any of the culling/clipping/scissoring
   // tests fail.
   if (!bpmem.genMode.zfreeze)
-    InitSlope(&ZSlope, v0->screenPosition[2], v1->screenPosition[2], v2->screenPosition[2], fltdx31,
+    ZSlope = Slope(v0->screenPosition.z, v1->screenPosition.z, v2->screenPosition.z, ctx);
-              fltdx12, fltdy12, fltdy31);
 
   for (unsigned int i = 0; i < bpmem.genMode.numcolchans; i++)
   {
     for (int comp = 0; comp < 4; comp++)
-      InitSlope(&ColorSlopes[i][comp], v0->color[i][comp], v1->color[i][comp], v2->color[i][comp],
+      ColorSlopes[i][comp] = Slope(v0->color[i][comp], v1->color[i][comp], v2->color[i][comp], ctx);
-                fltdx31, fltdx12, fltdy12, fltdy31);
   }
 
   for (unsigned int i = 0; i < bpmem.genMode.numtexgens; i++)
   {
     for (int comp = 0; comp < 3; comp++)
-      InitSlope(&TexSlopes[i][comp], v0->texCoords[i][comp] * w[0], v1->texCoords[i][comp] * w[1],
+    {
-                v2->texCoords[i][comp] * w[2], fltdx31, fltdx12, fltdy12, fltdy31);
+      TexSlopes[i][comp] = Slope(v0->texCoords[i][comp] * w[0], v1->texCoords[i][comp] * w[1],
+                                 v2->texCoords[i][comp] * w[2], ctx);
+    }
   }
 
   // Half-edge constants

Source/Core/VideoBackends/Software/Rasterizer.h

@@ -16,15 +16,6 @@ void DrawTriangleFrontFace(const OutputVertexData* v0, const OutputVertexData* v
 
 void SetTevReg(int reg, int comp, s16 color);
 
-struct Slope
-{
-  float dfdx;
-  float dfdy;
-  float f0;
-
-  float GetValue(float dx, float dy) const { return f0 + (dfdx * dx) + (dfdy * dy); }
-};
-
 struct RasterBlockPixel
 {
   float InvW;