Tune linear->sRGB constants to round-trip all bytes.

src/core/SkSRGB.h

Index: src/core/SkSRGB.h
diff --git a/src/core/SkSRGB.h b/src/core/SkSRGB.h
index d567a962d84a598ab24fd60994085761bfb6f5a9..98a9b6c930f1a76696c272ce266f17622a932cc7 100644
--- a/src/core/SkSRGB.h
+++ b/src/core/SkSRGB.h
@@ -14,37 +14,32 @@
  *
  *  Current best practices:
  *      - for sRGB -> linear, lookup R,G,B in sk_linear_from_srgb;
- *      - for linear -> sRGB, call sk_linear_to_srgb() for R,G,B, and round;
+ *      - for linear -> sRGB, call sk_linear_to_srgb() for R,G,B;
  *      - the alpha channel is linear in both formats, needing at most *(1/255.0f) or *255.0f.
  *
- *  sk_linear_to_srgb()'s output requires rounding; it does not round for you.
- *
- *  Given inputs in [0,1], sk_linear_to_srgb() will not underflow 0 but may overflow 255.
- *  The overflow is small enough to be handled by rounding.
- *  (But if you don't trust the inputs are in [0,1], you'd better clamp both sides immediately.)
- *
  *  sk_linear_to_srgb() will run a little faster than usual when compiled with SSE4.1+.
  */
 
 extern const float sk_linear_from_srgb[256];
 
-static inline Sk4f sk_linear_to_srgb(const Sk4f& x) {
+static inline Sk4i sk_linear_to_srgb(const Sk4f& x) {
     // Approximation of the sRGB gamma curve (within 1 when scaled to 8-bit pixels).
-    // For 0.00000f <= x <  0.00349f,    12.92 * x
-    // For 0.00349f <= x <= 1.00000f,    0.679*(x.^0.5) + 0.423*x.^(0.25) - 0.101
-    // Note that 0.00349 was selected because it is a point where both functions produce the
-    // same pixel value when rounded.
+    // Tuned by brute force to minimize the number of bytes that fail to round trip, here 0.
+    //
+    // TODO: It was easy enough to find these constants that we should probably further tune

[msarett, 2016/07/20 13:37:18]

I've got something like this...  Minimizes the absolute error to 0.49 (which
means it should roundtrip if the hardware error doesn't mess us up).
int -> float -> round(int +/- 0.49) = int

I'm still refining things, but you might try:
0.702406539530268*sqrt + 0.393127893958605*ftrt -0.093617117847240
With the exact sRGB lower half and interval.

+    // to find one that round trips all bytes correctly while minimizing some overall error.
+
     auto rsqrt = x.rsqrt(),
          sqrt  = rsqrt.invert(),
          ftrt  = rsqrt.rsqrt();
 
-    auto lo = (12.92f * 255.0f) * x;
+    auto lo = (12.9232f * 255.0f) * x;
 
-    auto hi = (-0.101115084998961f * 255.0f) +
-              (+0.678513029959381f * 255.0f) * sqrt +
-              (+0.422602055039580f * 255.0f) * ftrt;
+    auto hi = (-0.0958f * 255.0f)
+            + (+0.6946f * 255.0f) * sqrt
+            + (+0.4047f * 255.0f) * ftrt;
 
-    return (x < 0.00349f).thenElse(lo, hi);
+    return SkNx_cast<int>( (x < 0.005f).thenElse(lo, hi) );
 }
 
 #endif//SkSRGB_DEFINED