From ec5ca60a60fc18d4e4bb38587e3837852c6ca650 Mon Sep 17 00:00:00 2001 From: student-t Date: Mon, 13 Apr 2015 11:09:53 +1000 Subject: [PATCH] Added Google's support for floating comparison. Refer to http://stackoverflow.com/questions/17333/most-effective-way-for-float-and-double-comparison. --- include/catch.hpp | 4 + include/internal/catch_float.hpp | 263 +++++++++++++++++++++++++++++++ 2 files changed, 267 insertions(+) create mode 100644 include/internal/catch_float.hpp diff --git a/include/catch.hpp b/include/catch.hpp index 9f82c72d..4b49a97a 100644 --- a/include/catch.hpp +++ b/include/catch.hpp @@ -24,6 +24,7 @@ #include "internal/catch_notimplemented_exception.h" #include "internal/catch_context.h" +#include "internal/catch_float.hpp" #include "internal/catch_test_registry.hpp" #include "internal/catch_capture.hpp" #include "internal/catch_section.h" @@ -129,6 +130,9 @@ #define REQUIRE( expr ) INTERNAL_CATCH_TEST( expr, Catch::ResultDisposition::Normal, "REQUIRE" ) #define REQUIRE_FALSE( expr ) INTERNAL_CATCH_TEST( expr, Catch::ResultDisposition::Normal | Catch::ResultDisposition::FalseTest, "REQUIRE_FALSE" ) +#define REQUIRE_FLOAT(x, y) FloatingPoint(x).AlmostEquals(FloatingPoint(y)) +#define REQUIRE_DOUBLE(x, y) FloatingPoint(x).AlmostEquals(FloatingPoint(y)) + #define REQUIRE_THROWS( expr ) INTERNAL_CATCH_THROWS( expr, Catch::ResultDisposition::Normal, "REQUIRE_THROWS" ) #define REQUIRE_THROWS_AS( expr, exceptionType ) INTERNAL_CATCH_THROWS_AS( expr, exceptionType, Catch::ResultDisposition::Normal, "REQUIRE_THROWS_AS" ) #define REQUIRE_NOTHROW( expr ) INTERNAL_CATCH_NO_THROW( expr, Catch::ResultDisposition::Normal, "REQUIRE_NOTHROW" ) diff --git a/include/internal/catch_float.hpp b/include/internal/catch_float.hpp new file mode 100644 index 00000000..97fd6ee1 --- /dev/null +++ b/include/internal/catch_float.hpp @@ -0,0 +1,263 @@ +#include + +// 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: wan@google.com (Zhanyong Wan), eefacm@gmail.com (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 +class TypeWithSize { + public: + // This prevents the user from using TypeWithSize 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 +class FloatingPoint { + public: + // Defines the unsigned integer type that has the same size as the + // floating point number. + typedef typename TypeWithSize::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::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(1) << (kBitCount - 1); + + // The mask for the fraction bits. + static const Bits kFractionBitMask = + ~static_cast(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_; +}; \ No newline at end of file