Repo created

libs/base/math.cpp

@@ -0,0 +1,46 @@
+#include "math.hpp"
+
+#include <boost/integer.hpp>
+
+#include <cstring>
+#include <limits>
+
+template <typename Float>
+bool AlmostEqualULPs(Float x, Float y, uint32_t maxULPs)
+{
+  static_assert(std::is_floating_point<Float>::value, "");
+  static_assert(std::numeric_limits<Float>::is_iec559, "");
+
+  // Make sure maxUlps is non-negative and small enough that the
+  // default NaN won't compare as equal to anything.
+  ASSERT_LESS(maxULPs, 4 * 1024 * 1024, ());
+
+  int constexpr bits = CHAR_BIT * sizeof(Float);
+  typedef typename boost::int_t<bits>::exact IntType;
+  typedef typename boost::uint_t<bits>::exact UIntType;
+
+  // Same as *reinterpret_cast<IntType const *>(&x), but without warnings.
+  IntType xInt, yInt;
+  static_assert(sizeof(xInt) == sizeof(x), "bit_cast impossible");
+  std::memcpy(&xInt, &x, sizeof(x));
+  std::memcpy(&yInt, &y, sizeof(y));
+
+  // Make xInt and yInt lexicographically ordered as a twos-complement int.
+  IntType const highestBit = IntType(1) << (bits - 1);
+  if (xInt < 0)
+    xInt = highestBit - xInt;
+  if (yInt < 0)
+    yInt = highestBit - yInt;
+
+  // Calculate diff with special case to avoid IntType overflow.
+  UIntType diff;
+  if ((xInt >= 0) == (yInt >= 0))
+    diff = math::Abs(xInt - yInt);
+  else
+    diff = UIntType(math::Abs(xInt)) + UIntType(math::Abs(yInt));
+
+  return diff <= maxULPs;
+}
+
+template bool AlmostEqualULPs<float>(float x, float y, uint32_t maxULPs);
+template bool AlmostEqualULPs<double>(double x, double y, uint32_t maxULPs);