path ops near exact

src/pathops/SkPathOpsTypes.cpp

 /*
  * Copyright 2012 Google Inc.
  *
  * Use of this source code is governed by a BSD-style license that can be
  * found in the LICENSE file.
  */
 #include "SkFloatBits.h"
 #include "SkPathOpsTypes.h"
 
 
 
 // from http://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/
 // FIXME: move to SkFloatBits.h
 static bool equal_ulps(float A, float B, int epsilon) {
     SkFloatIntUnion floatIntA, floatIntB;
     floatIntA.fFloat = A;
     floatIntB.fFloat = B;
     // Different signs means they do not match.
-    if ((floatIntA.fSignBitInt < 0) != (floatIntB.fSignBitInt < 0))
-    {
+    if ((floatIntA.fSignBitInt < 0) != (floatIntB.fSignBitInt < 0)) {
         // Check for equality to make sure +0 == -0
         return A == B;
     }
     // Find the difference in ULPs.
     int ulpsDiff = abs(floatIntA.fSignBitInt - floatIntB.fSignBitInt);
     return ulpsDiff <= epsilon;
 }
 
+static bool less_ulps(float A, float B, int epsilon) {
+    SkFloatIntUnion floatIntA, floatIntB;
+    floatIntA.fFloat = A;
+    floatIntB.fFloat = B;
+    // Check different signs with float epsilon since we only care if they're both close to 0.
+    if ((floatIntA.fSignBitInt < 0) != (floatIntB.fSignBitInt < 0)) {
+        return A <= B + FLT_EPSILON * epsilon;
+    }
+    // Find the difference in ULPs.
+    return floatIntA.fSignBitInt <= floatIntB.fSignBitInt + epsilon;
+}
+
 bool AlmostEqualUlps(float A, float B) {
     const int UlpsEpsilon = 16;
     return equal_ulps(A, B, UlpsEpsilon);
 }
 
 bool RoughlyEqualUlps(float A, float B) {
     const int UlpsEpsilon = 256;
     return equal_ulps(A, B, UlpsEpsilon);
 }
 
+bool AlmostBetweenUlps(float a, float b, float c) {
+    const int UlpsEpsilon = 1;
+    return a <= c ? less_ulps(a, b, UlpsEpsilon) && less_ulps(b, c, UlpsEpsilon)
+        : less_ulps(b, a, UlpsEpsilon) && less_ulps(c, b, UlpsEpsilon);
+}
+
 // cube root approximation using bit hack for 64-bit float
 // adapted from Kahan's cbrt
 static double cbrt_5d(double d) {
     const unsigned int B1 = 715094163;
     double t = 0.0;
     unsigned int* pt = (unsigned int*) &t;
     unsigned int* px = (unsigned int*) &d;
     pt[1] = px[1] / 3 + B1;
     return t;
 }
@@ skipping 16 matching lines @@
 double SkDCubeRoot(double x) {
     if (approximately_zero_cubed(x)) {
         return 0;
     }
     double result = halley_cbrt3d(fabs(x));
     if (x < 0) {
         result = -result;
     }
     return result;
 }