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float: correctly handle double comparisons

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This commit is contained in:
Danny Robson 2015-02-03 15:54:55 +11:00
parent 2ae1c5e465
commit 9a6c4572fa
2 changed files with 62 additions and 23 deletions
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26
float.cpp
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@ -101,7 +101,7 @@ ieee_float<E, S>::almost_equal (floating_t a,
} }
// Based on the cynus `AlmostEqualUlps` // Based on the cynus `AlmostEqual2sComplement`
template <unsigned int E, unsigned int S> template <unsigned int E, unsigned int S>
bool bool
ieee_float<E, S>::almost_equal (floating_t _a, ieee_float<E, S>::almost_equal (floating_t _a,
@ -115,29 +115,39 @@ ieee_float<E, S>::almost_equal (floating_t _a,
union { union {
floating_t f; floating_t f;
sint_t s; sint_t s;
uint_t u;
} a, b; } a, b;
a.f = _a; a.f = _a;
b.f = _b; b.f = _b;
// Special case the NaNs early so simplify diffs
if (std::isnan (a.f) || std::isnan (b.f)) if (std::isnan (a.f) || std::isnan (b.f))
return false; return false;
// Early out, as identity comparisons are reasonably common
if (a.s == b.s) if (a.s == b.s)
return true; return true;
// Order as twos complement to avoid negative zero/zero comparison issues // Re-base negative floats to be continuous against +ve/-ve 0
if (a.s < 0) static const union {
a.s = (1L << (TOTAL_BITS - 1)) - a.s; floating_t f;
if (b.s < 0) sint_t s;
b.s = (1L << (TOTAL_BITS - 1)) - b.s; } NEG_ZERO { -floating_t {0} };
uint_t diff = std::abs (a.s - b.s); 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; return diff <= ulps;
} }
//-----------------------------------------------------------------------------
template class ieee_float< 5, 10>; // ieee_half template class ieee_float< 5, 10>; // ieee_half
template class ieee_float< 8, 23>; // ieee_single; template class ieee_float< 8, 23>; // ieee_single;
template class ieee_float<11, 52>; // ieee_double; template class ieee_float<11, 52>; // ieee_double;

59
test/maths.cpp
View File

@ -8,28 +8,57 @@
using std::sqrt; using std::sqrt;
using std::numeric_limits; using std::numeric_limits;
int
main (int, char **) {
std::cerr.precision (15);
std::cout.precision (15);
CHECK (!almost_equal (-2.0, 0.0)); void
CHECK (!almost_equal (-2.f, 0.f)); test_comparisons (void)
CHECK ( almost_equal ( 0.0, 0.0)); {
//CHECK_HARD ( almost_equal ( 0.0, numeric_limits<double>::min ())); // Check pos/neg zeroes
CHECK ( almost_equal (numeric_limits<double>::infinity (), CHECK (almost_equal ( 0.f, 0.f));
numeric_limits<double>::infinity ())); CHECK (almost_equal ( 0.f, -0.f));
CHECK (!almost_equal (numeric_limits<double>::infinity (), 0.0)); CHECK (almost_equal (-0.f, 0.f));
CHECK (!almost_equal (numeric_limits<double>::quiet_NaN (), CHECK (almost_equal (-0.f, -0.f));
numeric_limits<double>::quiet_NaN ()));
CHECK (almost_equal (0.f, -0.f)); CHECK (almost_equal ( 0., 0.));
CHECK (almost_equal (0., -0.)); CHECK (almost_equal ( 0., -0.));
CHECK (almost_equal (-0., 0.));
CHECK (almost_equal (-0., -0.));
// Check zero comparison with values near the expected cutoff
CHECK ( almost_zero (1e-45f)); CHECK ( almost_zero (1e-45f));
CHECK (!almost_zero (1e-40f)); CHECK (!almost_zero (1e-40f));
CHECK (!exactly_zero (1e-45f)); CHECK (!exactly_zero (1e-45f));
// Compare values a little away from zero
CHECK (!almost_equal (-2.0, 0.0));
CHECK (!almost_equal (-2.f, 0.f));
// Compare values at the maximum extreme
CHECK (!almost_equal (-std::numeric_limits<float>::max (), 0.f));
CHECK (!almost_equal (-std::numeric_limits<float>::max (),
std::numeric_limits<float>::max ()));
// Compare infinity values
CHECK ( almost_equal (numeric_limits<double>::infinity (),
numeric_limits<double>::infinity ()));
CHECK (!almost_equal (numeric_limits<double>::infinity (), 0.0));
// Compare NaNs
CHECK (!almost_equal (0., numeric_limits<double>::quiet_NaN ()));
CHECK (!almost_equal (numeric_limits<double>::quiet_NaN (), 0.));
CHECK (!almost_equal (numeric_limits<double>::quiet_NaN (),
numeric_limits<double>::quiet_NaN ()));
}
int
main (int, char **) {
// Max out the precision in case we trigger debug output
std::cerr.precision (std::numeric_limits<double>::digits10);
std::cout.precision (std::numeric_limits<double>::digits10);
test_comparisons ();
CHECK_EQ (min (-2, 0, 2), -2); CHECK_EQ (min (-2, 0, 2), -2);
CHECK_EQ (max (-2, 0, 2), 2); CHECK_EQ (max (-2, 0, 2), 2);