I found that the Google C++ Testing Framework contains a nice cross-platform template-based implementation of AlmostEqual2sComplement which works on both doubles and floats. Given that it is released under the BSD license, using it in your own code should be no problem, as long as you retain the license. I extracted the below code from http://code.google.com/p/googletest/source/browse/trunk/include/gtest/internal/gtest-internal.h and added the license on top.

Be sure to #define GTEST_OS_WINDOWS to some value (or to change the code where it's used to something that fits your codebase - it's BSD licensed after all).

Usage example:

```
double left = // something
double right = // something
const FloatingPoint<double> lhs(left), rhs(right);
if (lhs.AlmostEquals(rhs)) {
//they're equal!
}
```

Here's the code:

```
// Copyright 2005, Google Inc.
// All rights reserved.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
//
// * Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
// * Redistributions in binary form must reproduce the above
// copyright notice, this list of conditions and the following disclaimer
// in the documentation and/or other materials provided with the
// distribution.
// * Neither the name of Google Inc. nor the names of its
// contributors may be used to endorse or promote products derived from
// this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
// Authors: [email protected] (Zhanyong Wan), [email protected] (Sean Mcafee)
//
// The Google C++ Testing Framework (Google Test)
// 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 GTEST_OS_WINDOWS
typedef __int64 Int;
typedef unsigned __int64 UInt;
#else
typedef long long Int; // NOLINT
typedef unsigned long long UInt; // NOLINT
#endif // GTEST_OS_WINDOWS
};
// 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://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm.
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);
}
// 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_;
};
```