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Fix ulp distance calculation for numbers with different signs
This is a simplification of the fix proposed in #2152, with the critical function split out so that it can be tested directly, without having to go through the ULP matcher. Closes #2152
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| Original file line number | Diff line number | Diff line change |
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| // Copyright Catch2 Authors | ||
| // Distributed under the Boost Software License, Version 1.0. | ||
| // (See accompanying file LICENSE_1_0.txt or copy at | ||
| // https://www.boost.org/LICENSE_1_0.txt) | ||
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| // SPDX-License-Identifier: BSL-1.0 | ||
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| #include <catch2/internal/catch_floating_point_helpers.hpp> | ||
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| #include <cstring> | ||
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| namespace Catch { | ||
| namespace Detail { | ||
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| uint32_t convertToBits(float f) { | ||
| static_assert(sizeof(float) == sizeof(uint32_t), "Important ULP matcher assumption violated"); | ||
| uint32_t i; | ||
| std::memcpy(&i, &f, sizeof(f)); | ||
| return i; | ||
| } | ||
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| uint64_t convertToBits(double d) { | ||
| static_assert(sizeof(double) == sizeof(uint64_t), "Important ULP matcher assumption violated"); | ||
| uint64_t i; | ||
| std::memcpy(&i, &d, sizeof(d)); | ||
| return i; | ||
| } | ||
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| } // end namespace Detail | ||
| } // end namespace Catch | ||
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| // Copyright Catch2 Authors | ||
| // Distributed under the Boost Software License, Version 1.0. | ||
| // (See accompanying file LICENSE_1_0.txt or copy at | ||
| // https://www.boost.org/LICENSE_1_0.txt) | ||
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| // SPDX-License-Identifier: BSL-1.0 | ||
| #ifndef CATCH_FLOATING_POINT_HELPERS_HPP_INCLUDED | ||
| #define CATCH_FLOATING_POINT_HELPERS_HPP_INCLUDED | ||
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| #include <catch2/internal/catch_polyfills.hpp> | ||
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| #include <cmath> | ||
| #include <cstdint> | ||
| #include <utility> | ||
| #include <limits> | ||
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| namespace Catch { | ||
| namespace Detail { | ||
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| uint32_t convertToBits(float f); | ||
| uint64_t convertToBits(double d); | ||
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| } // end namespace Detail | ||
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| /** | ||
| * Calculates the ULP distance between two floating point numbers | ||
| * | ||
| * The ULP distance of two floating point numbers is the count of | ||
| * valid floating point numbers representable between them. | ||
| * | ||
| * There are some exceptions between how this function counts the | ||
| * distance, and the interpretation of the standard as implemented. | ||
| * by e.g. `nextafter`. For this function it always holds that: | ||
| * * `(x == y) => ulpDistance(x, y) == 0` (so `ulpDistance(-0, 0) == 0`) | ||
| * * `ulpDistance(maxFinite, INF) == 1` | ||
| * * `ulpDistance(x, -x) == 2 * ulpDistance(x, 0)` | ||
| * | ||
| * \pre `!isnan( lhs )` | ||
| * \pre `!isnan( rhs )` | ||
| * \pre floating point numbers are represented in IEEE-754 format | ||
| */ | ||
| template <typename FP> | ||
| uint64_t ulpDistance( FP lhs, FP rhs ) { | ||
| assert( std::numeric_limits<FP>::is_iec559 && | ||
| "ulpDistance assumes IEEE-754 format for floating point types" ); | ||
| assert( !Catch::isnan( lhs ) && | ||
| "Distance between NaN and number is not meaningful" ); | ||
| assert( !Catch::isnan( rhs ) && | ||
| "Distance between NaN and number is not meaningful" ); | ||
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| // We want X == Y to imply 0 ULP distance even if X and Y aren't | ||
| // bit-equal (-0 and 0), or X - Y != 0 (same sign infinities). | ||
| if ( lhs == rhs ) { return 0; } | ||
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| // We need a properly typed positive zero for type inference. | ||
| static constexpr FP positive_zero{}; | ||
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| // We want to ensure that +/- 0 is always represented as positive zero | ||
| if ( lhs == positive_zero ) { lhs = positive_zero; } | ||
| if ( rhs == positive_zero ) { rhs = positive_zero; } | ||
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| // If arguments have different signs, we can handle them by summing | ||
| // how far are they from 0 each. | ||
| if ( std::signbit( lhs ) != std::signbit( rhs ) ) { | ||
| return ulpDistance( std::abs( lhs ), positive_zero ) + | ||
| ulpDistance( std::abs( rhs ), positive_zero ); | ||
| } | ||
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| // When both lhs and rhs are of the same sign, we can just | ||
| // read the numbers bitwise as integers, and then subtract them | ||
| // (assuming IEEE). | ||
| uint64_t lc = Detail::convertToBits( lhs ); | ||
| uint64_t rc = Detail::convertToBits( rhs ); | ||
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| // The ulp distance between two numbers is symmetric, so to avoid | ||
| // dealing with overflows we want the bigger converted number on the lhs | ||
| if ( lc < rc ) { | ||
| std::swap( lc, rc ); | ||
| } | ||
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| return lc - rc; | ||
| } | ||
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| } // end namespace Catch | ||
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| #endif // CATCH_FLOATING_POINT_HELPERS_HPP_INCLUDED |
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