Approximate sqrt(2)/2 with ints to avoid floats

src/MouseWrapper.cpp

@@ -112,24 +112,19 @@ uint8_t MouseWrapper_::acceleration(uint8_t cycles) {
   return i;
 }
 
-static int8_t roundAwayFromZero(float value) {
-  if (value < 0.0f) {
-    return static_cast<int8_t>(value - 0.5f);
-  }
-
-  return static_cast<int8_t>(value + 0.5f);
-}
-
 void MouseWrapper_::move(int8_t x, int8_t y) {
   int16_t moveX = 0;
   int16_t moveY = 0;
   static int8_t remainderX = 0;
   static int8_t remainderY = 0;
-  static const float HALF_SQRT_2 = 0.7071f;
 
   if (x != 0 && y != 0) {
-    x = roundAwayFromZero(HALF_SQRT_2 * x);
-    y = roundAwayFromZero(HALF_SQRT_2 * y);
+    // 99 / 140 closely approximates sqrt(2) / 2.
+    int8_t adjusted_x = x * 99 / 140;
+    int8_t adjusted_y = y * 99 / 140;
+
+    x = (adjusted_x == 0 ? x : adjusted_x);
+    y = (adjusted_y == 0 ? y : adjusted_y);
   }
 
   if (x != 0) {