libcruft-util/float.cpp
Danny Robson 7b083df977 maths: tighten up type requirements for almost_equal
almost_equal only operates on two reals, or two integers (and even then
only on the same signedness).
2015-11-13 17:18:10 +11:00

154 lines
4.0 KiB
C++

#include "float.hpp"
#include <cmath>
using namespace std;
/* Constructors */
template <unsigned int E, unsigned int S>
ieee_float<E, S>::ieee_float (void)
{ ; }
template <unsigned int E, unsigned int S>
ieee_float<E, S>::ieee_float (floating_t _floating):
m_floating (_floating)
{ ; }
template <unsigned int E, unsigned int S>
ieee_float<E, S>::ieee_float (const ieee_float &rhs):
m_bits (rhs.m_bits)
{ ; }
/* Classifiers */
template <unsigned int E, unsigned int S>
bool
ieee_float<E, S>::is_zero (void) const {
return m_components.exponent == 0 &&
m_components.significand == 0;
}
template <unsigned int E, unsigned int S>
bool
ieee_float<E, S>::is_subnormal (void) const {
return m_components.exponent == 0 &&
m_components.significand != 0;
}
template <unsigned int E, unsigned int S>
bool
ieee_float<E, S>::is_inifinity (void) const {
return m_components.exponent == (1 << EXPONENT_BITS) - 1 &&
m_components.significand == 0;
}
template <unsigned int E, unsigned int S>
bool
ieee_float<E, S>::is_nan (void) const {
return m_components.exponent == (1 << EXPONENT_BITS) - 1 &&
m_components.significand != 0;
}
template <unsigned int E, unsigned int S>
bool
ieee_float<E, S>::operator==(floating_t _floating) const {
// TODO: This method really shouldn't be generated if there's no
// representative native floating point type. But I'm sick of
// C++'s template bullshit for tonight.
CHECK (bits_type<TOTAL_BITS>::has_floating);
union {
floating_t _floating;
uint_t _uint;
} convertor;
convertor._floating = _floating;
return m_bits == convertor._uint;
}
#include <iostream>
//template <unsigned int E, unsigned int S>
//bool
//ieee_float<E, S>::almost_equal (floating_t a,
// floating_t b) {
// // Static cast to avoid integer casting warnings when using uint16_t for half
// static const floating_t epsilon = static_cast<floating_t> (0.001);
// const floating_t diff = static_cast<floating_t> (std::fabs (a - b));
//
// // * Use an exact equality first so that infinities are not indirectly compared. This would generate NaNs in the diff.
// // * Do not use gte or lte. This stops an infinite from making infinities on both sides of the inequality.
// return exactly_equal (a, b) ||
// diff < epsilon * std::fabs (a) ||
// diff < epsilon * std::fabs (b);
//}
template <unsigned int E, unsigned int S>
bool
ieee_float<E, S>::almost_equal (floating_t a,
floating_t b)
{
return almost_equal (a, b, 128u);
}
// Based on the cynus `AlmostEqual2sComplement`
template <unsigned int E, unsigned int S>
bool
ieee_float<E, S>::almost_equal (floating_t _a,
floating_t _b,
unsigned ulps)
{
// Ensure ULPs is small enough that the default NaNs won't compare as
// equal to anything else.
CHECK_LE (ulps, 4 * 1024 * 1024u);
union {
floating_t f;
sint_t s;
uint_t u;
} a, b;
a.f = _a;
b.f = _b;
// Special case the NaNs early so simplify diffs
if (std::isnan (a.f) || std::isnan (b.f))
return false;
// Early out, as identity comparisons are reasonably common
if (a.s == b.s)
return true;
// Re-base negative floats to be continuous against +ve/-ve 0
static const union {
floating_t f;
sint_t s;
} NEG_ZERO { -floating_t {0} };
if (a.s < 0)
a.s = NEG_ZERO.s - a.s;
if (b.s < 0)
b.s = NEG_ZERO.s - b.s;
// Calculate ULP difference, but don't use abs(a.s - b.s) as it may cause
// signed overflow
uint_t diff = a.u > b.u ? a.u - b.u : b.u - a.u;
return diff <= ulps;
}
//-----------------------------------------------------------------------------
template class ieee_float< 5, 10>; // ieee_half
template class ieee_float< 8, 23>; // ieee_single;
template class ieee_float<11, 52>; // ieee_double;