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// Copyright Catch2 Authors
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE.txt or copy at
// https://www.boost.org/LICENSE_1_0.txt)
// SPDX-License-Identifier: BSL-1.0
#ifndef CATCH_FLOATING_POINT_HELPERS_HPP_INCLUDED
#define CATCH_FLOATING_POINT_HELPERS_HPP_INCLUDED
#include <catch2/internal/catch_polyfills.hpp>
#include <cassert>
#include <cmath>
#include <cstdint>
#include <utility>
#include <limits>
namespace Catch {
namespace Detail {
uint32_t convertToBits(float f);
uint64_t convertToBits(double d);
// Used when we know we want == comparison of two doubles
// to centralize warning suppression
bool directCompare( float lhs, float rhs );
bool directCompare( double lhs, double rhs );
} // end namespace Detail
#if defined( __GNUC__ ) || defined( __clang__ )
# pragma GCC diagnostic push
// We do a bunch of direct compensations of floating point numbers,
// because we know what we are doing and actually do want the direct
// comparison behaviour.
# pragma GCC diagnostic ignored "-Wfloat-equal"
#endif
/**
* 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" );
// 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; }
// We need a properly typed positive zero for type inference.
static constexpr FP positive_zero{};
// 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; }
// 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 );
}
// 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 );
// 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 );
}
return lc - rc;
}
#if defined( __GNUC__ ) || defined( __clang__ )
# pragma GCC diagnostic pop
#endif
} // end namespace Catch
#endif // CATCH_FLOATING_POINT_HELPERS_HPP_INCLUDED
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