BPMemory: Handle fog configuration where both A and C are infinity/NaN

The console appears to behave against standard IEEE754 specification
here, in particular around how NaNs are handled. NaNs appear to have no
effect on the result, and are treated the same as positive or negative
infinity, based on the sign bit.

However, when the result would be NaN (inf - inf, or (-inf) - (-inf)),
this results in a completely fogged color, or unfogged color
respectively. We handle this by returning a constant zero for the A
varaible, and positive or negative infinity for C depending on the sign
bits of the A and C registers. This ensures that no NaN value is passed
to the GPU in the first place, and that the result of the fog
calculation cannot be NaN.

Source/Core/VideoBackends/Software/Tev.cpp

@@ -751,14 +751,14 @@ void Tev::Draw()
       // ze = A/(B - (Zs >> B_SHF))
       const s32 denom = bpmem.fog.b_magnitude - (Position[2] >> bpmem.fog.b_shift);
       // in addition downscale magnitude and zs to 0.24 bits
-      ze = (bpmem.fog.a.GetA() * 16777215.0f) / (float)denom;
+      ze = (bpmem.fog.GetA() * 16777215.0f) / static_cast<float>(denom);
     }
     else
     {
       // orthographic
       // ze = a*Zs
       // in addition downscale zs to 0.24 bits
-      ze = bpmem.fog.a.GetA() * ((float)Position[2] / 16777215.0f);
+      ze = bpmem.fog.GetA() * (static_cast<float>(Position[2]) / 16777215.0f);
     }
 
     if (bpmem.fogRange.Base.Enabled)
@@ -796,7 +796,7 @@ void Tev::Draw()
                        // GXInitFogAdjTable): 1/cos = c/b = sqrt(a^2+b^2)/b
     }
 
-    ze -= bpmem.fog.c_proj_fsel.GetC();
+    ze -= bpmem.fog.GetC();
 
     // clamp 0 to 1
     float fog = (ze < 0.0f) ? 0.0f : ((ze > 1.0f) ? 1.0f : ze);

Source/Core/VideoCommon/BPMemory.cpp

@@ -23,21 +23,55 @@ bool BlendMode::UseLogicOp() const
   return true;
 }
 
-float FogParam0::GetA() const
+bool FogParams::IsNaNCase() const
 {
+  // Check for the case where both a and c are infinity or NaN.
+  // On hardware, this results in the following colors:
+  //
+  // -------------------------------------------------------
+  // |   A   |   C   |  Result  |   A   |   C   |  Result  |
+  // -------------------------------------------------------
+  // |  inf  |  inf  |  Fogged  |  inf  |  nan  |  Fogged  |
+  // |  inf  | -inf  | Unfogged |  inf  | -nan  | Unfogged |
+  // | -inf  |  inf  | Unfogged | -inf  |  nan  | Unfogged |
+  // | -inf  | -inf  | Unfogged | -inf  | -nan  | Unfogged |
+  // -------------------------------------------------------
+  // |  nan  |  inf  |  Fogged  |  nan  |  nan  |  Fogged  |
+  // |  nan  | -inf  | Unfogged |  nan  | -nan  | Unfogged |
+  // | -nan  |  inf  | Unfogged | -nan  |  nan  | Unfogged |
+  // | -nan  | -inf  | Unfogged | -nan  | -nan  | Unfogged |
+  // -------------------------------------------------------
+  //
+  // We replicate this by returning A=0, and C=inf for the inf/inf case, otherwise -inf.
+  // This ensures we do not pass a NaN to the GPU, and -inf/inf clamp to 0/1 respectively.
+  return a.exp == 255 && c_proj_fsel.c_exp == 255;
+}
+
+float FogParams::GetA() const
+{
+  if (IsNaNCase())
+    return 0.0f;
+
   // scale mantissa from 11 to 23 bits
-  const u32 integral = (static_cast<u32>(sign) << 31) | (static_cast<u32>(exponent) << 23) |
-                       (static_cast<u32>(mantissa) << 12);
+  const u32 integral = (static_cast<u32>(a.sign) << 31) | (static_cast<u32>(a.exp) << 23) |
+                       (static_cast<u32>(a.mant) << 12);
 
   float real;
   std::memcpy(&real, &integral, sizeof(u32));
   return real;
 }
 
-float FogParam3::GetC() const
+float FogParams::GetC() const
 {
+  if (IsNaNCase())
+  {
+    constexpr float inf = std::numeric_limits<float>::infinity();
+    return !a.sign && !c_proj_fsel.c_sign ? -inf : inf;
+  }
+
   // scale mantissa from 11 to 23 bits
-  const u32 integral = (c_sign.Value() << 31) | (c_exp.Value() << 23) | (c_mant.Value() << 12);
+  const u32 integral = (c_proj_fsel.c_sign.Value() << 31) | (c_proj_fsel.c_exp.Value() << 23) |
+                       (c_proj_fsel.c_mant.Value() << 12);
 
   float real;
   std::memcpy(&real, &integral, sizeof(u32));

Source/Core/VideoCommon/BPMemory.h

@@ -654,14 +654,9 @@ union BlendMode
 
 union FogParam0
 {
-  struct
-  {
-    u32 mantissa : 11;
-    u32 exponent : 8;
-    u32 sign : 1;
-  };
-
-  float GetA() const;
+  BitField<0, 11, u32> mant;
+  BitField<11, 8, u32> exp;
+  BitField<19, 1, u32> sign;
 
   u32 hex;
 };
@@ -675,9 +670,6 @@ union FogParam3
   BitField<21, 3, u32> fsel;  // 0 - off, 2 - linear, 4 - exp, 5 - exp2, 6 -
                               // backward exp, 7 - backward exp2
 
-  // amount to subtract from eyespacez after range adjustment
-  float GetC() const;
-
   u32 hex;
 };
 
@@ -721,6 +713,13 @@ struct FogParams
   };
 
   FogColor color;  // 0:b 8:g 16:r - nice!
+
+  // Special case where a and c are infinite and the sign matches, resulting in a result of NaN.
+  bool IsNaNCase() const;
+  float GetA() const;
+
+  // amount to subtract from eyespacez after range adjustment
+  float GetC() const;
 };
 
 union ZMode

Source/Core/VideoCommon/PixelShaderManager.cpp

@@ -409,9 +409,9 @@ void PixelShaderManager::SetFogParamChanged()
 {
   if (!g_ActiveConfig.bDisableFog)
   {
-    constants.fogf[1][0] = bpmem.fog.a.GetA();
+    constants.fogf[1][0] = bpmem.fog.GetA();
     constants.fogi[1] = bpmem.fog.b_magnitude;
-    constants.fogf[1][2] = bpmem.fog.c_proj_fsel.GetC();
+    constants.fogf[1][2] = bpmem.fog.GetC();
     constants.fogi[3] = bpmem.fog.b_shift;
     constants.fogParam3 = bpmem.fog.c_proj_fsel.hex;
   }