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//
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//
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// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
// Authors: wan@google.com (Zhanyong Wan), eefacm@gmail.com (Sean Mcafee)
//
// The Google C++ Testing Framework (Google Test)
//
// This header file declares functions and macros used internally by
// Google Test.  They are subject to change without notice.

#pragma once

#include <limits>

// This template class serves as a compile-time function from size to
// type.  It maps a size in bytes to a primitive type with that
// size. e.g.
//
//   TypeWithSize<4>::UInt
//
// is typedef-ed to be unsigned int (unsigned integer made up of 4
// bytes).
//
// Such functionality should belong to STL, but I cannot find it
// there.
//
// Google Test uses this class in the implementation of floating-point
// comparison.
//
// For now it only handles UInt (unsigned int) as that's all Google Test
// needs.  Other types can be easily added in the future if need
// arises.
template <size_t size>
class TypeWithSize {
public:
	// This prevents the user from using TypeWithSize<N> with incorrect
	// values of N.
	typedef void UInt;
};

// The specialization for size 4.
template <>
class TypeWithSize<4> {
public:
	// unsigned int has size 4 in both gcc and MSVC.
	//
	// As base/basictypes.h doesn't compile on Windows, we cannot use
	// uint32, uint64, and etc here.
	typedef int Int;
	typedef unsigned int UInt;
};

// The specialization for size 8.
template <>
class TypeWithSize<8> {
public:
#if _MSC_VER
	typedef __int64 Int;
	typedef unsigned __int64 UInt;
#else
	typedef long long Int;  // NOLINT
	typedef unsigned long long UInt;  // NOLINT
#endif  // _MSC_VER
};

// This template class represents an IEEE floating-point number
// (either single-precision or double-precision, depending on the
// template parameters).
//
// The purpose of this class is to do more sophisticated number
// comparison.  (Due to round-off error, etc, it's very unlikely that
// two floating-points will be equal exactly.  Hence a naive
// comparison by the == operation often doesn't work.)
//
// Format of IEEE floating-point:
//
//   The most-significant bit being the leftmost, an IEEE
//   floating-point looks like
//
//     sign_bit exponent_bits fraction_bits
//
//   Here, sign_bit is a single bit that designates the sign of the
//   number.
//
//   For float, there are 8 exponent bits and 23 fraction bits.
//
//   For double, there are 11 exponent bits and 52 fraction bits.
//
//   More details can be found at
//   http://en.wikipedia.org/wiki/IEEE_floating-point_standard.
//
// Template parameter:
//
//   RawType: the raw floating-point type (either float or double)
template <typename RawType>
class FloatingPoint {
public:
	// Defines the unsigned integer type that has the same size as the
	// floating point number.
	typedef typename TypeWithSize<sizeof(RawType)>::UInt Bits;

	// Constants.

	// # of bits in a number.
	static const size_t kBitCount = 8 * sizeof(RawType);

	// # of fraction bits in a number.
	static const size_t kFractionBitCount =
		std::numeric_limits<RawType>::digits - 1;

	// # of exponent bits in a number.
	static const size_t kExponentBitCount = kBitCount - 1 - kFractionBitCount;

	// The mask for the sign bit.
	static const Bits kSignBitMask = static_cast<Bits>(1) << (kBitCount - 1);

	// The mask for the fraction bits.
	static const Bits kFractionBitMask =
		~static_cast<Bits>(0) >> (kExponentBitCount + 1);

	// The mask for the exponent bits.
	static const Bits kExponentBitMask = ~(kSignBitMask | kFractionBitMask);

	// How many ULP's (Units in the Last Place) we want to tolerate when
	// comparing two numbers.  The larger the value, the more error we
	// allow.  A 0 value means that two numbers must be exactly the same
	// to be considered equal.
	//
	// The maximum error of a single floating-point operation is 0.5
	// units in the last place.  On Intel CPU's, all floating-point
	// calculations are done with 80-bit precision, while double has 64
	// bits.  Therefore, 4 should be enough for ordinary use.
	//
	// See the following article for more details on ULP:
	// http://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/
	static const size_t kMaxUlps = 4;

	// Constructs a FloatingPoint from a raw floating-point number.
	//
	// On an Intel CPU, passing a non-normalized NAN (Not a Number)
	// around may change its bits, although the new value is guaranteed
	// to be also a NAN.  Therefore, don't expect this constructor to
	// preserve the bits in x when x is a NAN.
	explicit FloatingPoint(const RawType& x) { u_.value_ = x; }

	// Static methods

	// Reinterprets a bit pattern as a floating-point number.
	//
	// This function is needed to test the AlmostEquals() method.
	static RawType ReinterpretBits(const Bits bits) {
		FloatingPoint fp(0);
		fp.u_.bits_ = bits;
		return fp.u_.value_;
	}

	// Returns the floating-point number that represent positive infinity.
	static RawType Infinity() {
		return ReinterpretBits(kExponentBitMask);
	}

	// Returns the maximum representable finite floating-point number.
	static RawType Max();

	// Non-static methods

	// Returns the bits that represents this number.
	const Bits &bits() const { return u_.bits_; }

	// Returns the exponent bits of this number.
	Bits exponent_bits() const { return kExponentBitMask & u_.bits_; }

	// Returns the fraction bits of this number.
	Bits fraction_bits() const { return kFractionBitMask & u_.bits_; }

	// Returns the sign bit of this number.
	Bits sign_bit() const { return kSignBitMask & u_.bits_; }

	// Returns true iff this is NAN (not a number).
	bool is_nan() const {
		// It's a NAN if the exponent bits are all ones and the fraction
		// bits are not entirely zeros.
		return (exponent_bits() == kExponentBitMask) && (fraction_bits() != 0);
	}

	// Returns true iff this number is at most kMaxUlps ULP's away from
	// rhs.  In particular, this function:
	//
	//   - returns false if either number is (or both are) NAN.
	//   - treats really large numbers as almost equal to infinity.
	//   - thinks +0.0 and -0.0 are 0 DLP's apart.
	bool AlmostEquals(const FloatingPoint& rhs) const {
		// The IEEE standard says that any comparison operation involving
		// a NAN must return false.
		if (is_nan() || rhs.is_nan()) return false;

		return DistanceBetweenSignAndMagnitudeNumbers(u_.bits_, rhs.u_.bits_)
			<= kMaxUlps;
	}

private:
	// The data type used to store the actual floating-point number.
	union FloatingPointUnion {
		RawType value_;  // The raw floating-point number.
		Bits bits_;      // The bits that represent the number.
	};

	// Converts an integer from the sign-and-magnitude representation to
	// the biased representation.  More precisely, let N be 2 to the
	// power of (kBitCount - 1), an integer x is represented by the
	// unsigned number x + N.
	//
	// For instance,
	//
	//   -N + 1 (the most negative number representable using
	//          sign-and-magnitude) is represented by 1;
	//   0      is represented by N; and
	//   N - 1  (the biggest number representable using
	//          sign-and-magnitude) is represented by 2N - 1.
	//
	// Read http://en.wikipedia.org/wiki/Signed_number_representations
	// for more details on signed number representations.
	static Bits SignAndMagnitudeToBiased(const Bits &sam) {
		if (kSignBitMask & sam) {
			// sam represents a negative number.
			return ~sam + 1;
		}
		else {
			// sam represents a positive number.
			return kSignBitMask | sam;
		}
	}

	// Given two numbers in the sign-and-magnitude representation,
	// returns the distance between them as an unsigned number.
	static Bits DistanceBetweenSignAndMagnitudeNumbers(const Bits &sam1,
		const Bits &sam2) {
		const Bits biased1 = SignAndMagnitudeToBiased(sam1);
		const Bits biased2 = SignAndMagnitudeToBiased(sam2);
		return (biased1 >= biased2) ? (biased1 - biased2) : (biased2 - biased1);
	}

	FloatingPointUnion u_;
};

#include <cfloat>
// We cannot use std::numeric_limits<T>::max() as it clashes with the max()
// macro defined by <windows.h>.
template <>
inline float FloatingPoint<float>::Max() { return FLT_MAX; }
template <>
inline double FloatingPoint<double>::Max() { return DBL_MAX; }

template <typename T>
bool AlmostEquals(T first, T second)
{
	FloatingPoint<T> firstAsFloatingPoint(first);
	FloatingPoint<T> secondAsFloatingPoint(second);

	return firstAsFloatingPoint.AlmostEquals(secondAsFloatingPoint);
}