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

src/core/SkSRGB.h

 /*
  * Copyright 2016 Google Inc.
  *
  * Use of this source code is governed by a BSD-style license that can be
  * found in the LICENSE file.
  */
 
 #ifndef SkSRGB_DEFINED
 #define SkSRGB_DEFINED
 
 #include "SkNx.h"
 
 /** Components for building our canonical sRGB -> linear and linear -> sRGB transformations.
  *
  *  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 (of 256), and then to minimize the number of points halfway between bytes
+    // (in linear space) that fail to hit the right byte, here 131 (of 255), and to
+    // minimize the number of monotonicity regressions over the range [0,1], here 0.
+
     auto rsqrt = x.rsqrt(),
          sqrt  = rsqrt.invert(),
          ftrt  = rsqrt.rsqrt();
 
-    auto lo = (12.92f * 255.0f) * x;
+    auto lo = (13.0471f * 255.0f) * x;
 
-    auto hi = (-0.101115084998961f * 255.0f) +
-              (+0.678513029959381f * 255.0f) * sqrt +
-              (+0.422602055039580f * 255.0f) * ftrt;
+    auto hi = (-0.0974983f * 255.0f)
+            + (+0.687999f  * 255.0f) * sqrt
+            + (+0.412999f  * 255.0f) * ftrt;
 
-    return (x < 0.00349f).thenElse(lo, hi);
+    return SkNx_cast<int>( (x < 0.0048f).thenElse(lo, hi) );
 }
 
 #endif//SkSRGB_DEFINED