Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

More precise error estimate for elementary functions #3973

Merged
merged 2 commits into from
Apr 10, 2024
Merged

More precise error estimate for elementary functions #3973

Changes from all commits
Commits
Show all changes
2 commits
Select commit Hold shift + click to select a range
59b9706
More precise error estimate.
pleroy Apr 9, 2024
672f7af
Lint.
pleroy Apr 9, 2024
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
59 changes: 42 additions & 17 deletions functions/std_accuracy_test.cpp
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -1,13 +1,17 @@
#include <algorithm>
#include <cmath>
#include <limits>
#include <random>

#include "functions/multiprecision.hpp"
#include "glog/logging.h"
#include "gmock/gmock.h"
#include "gtest/gtest.h"
#include "numerics/ulp_distance.hpp"
#include "quantities/numbers.hpp"
#include "quantities/si.hpp"
#include "testing_utilities/almost_equals.hpp"
#include "testing_utilities/approximate_quantity.hpp"
#include "testing_utilities/is_near.hpp"

namespace principia {
namespace functions {
Expand All @@ -16,10 +20,35 @@ namespace _multiprecision {
using ::testing::AnyOf;
using ::testing::Eq;
using namespace boost::multiprecision;
using namespace principia::numerics::_ulp_distance;
using namespace principia::quantities::_si;
using namespace principia::testing_utilities::_almost_equals;
using namespace principia::testing_utilities::_approximate_quantity;
using namespace principia::testing_utilities::_is_near;

class StdAccuracyTest : public ::testing::Test {};
class StdAccuracyTest : public ::testing::Test {
protected:
static double ULPDistance(cpp_bin_float_50 const& actual,
cpp_bin_float_50 const& expected) {
std::int64_t actual_exponent;
std::int64_t expected_exponent;
auto actual_mantissa = frexp(actual, &actual_exponent);
auto expected_mantissa = frexp(expected, &expected_exponent);
if (actual_exponent == expected_exponent) {
} else if (actual_exponent == expected_exponent + 1) {
--actual_exponent;
actual_mantissa *= 2.0;
} else if (actual_exponent == expected_exponent - 1) {
++actual_exponent;
actual_mantissa /= 2.0;
} else {
LOG(FATAL) << actual_exponent << " " << actual_mantissa << " "
<< expected_exponent << " " << expected_mantissa;
}
return 2.0 *
std::abs(static_cast<double>(actual_mantissa - expected_mantissa)) /
std::numeric_limits<double>::epsilon();
}
};

#if !_DEBUG

Expand All @@ -28,30 +57,26 @@ TEST_F(StdAccuracyTest, SinCos) {
{
std::mt19937_64 random(42);
std::uniform_real_distribution<> angle_distribution(0, π / 4);
std::int64_t max_sin_ulp_distance = 0;
std::int64_t max_cos_ulp_distance = 0;
double max_sin_ulp_distance = 0;
double max_cos_ulp_distance = 0;
for (int i = 0; i < 1e5; ++i) {
double const α = angle_distribution(random);
max_sin_ulp_distance =
std::max(max_sin_ulp_distance,
ULPDistance(std::sin(α), static_cast<double>(Sin(α))));
std::max(max_sin_ulp_distance, ULPDistance(std::sin(α), Sin(α)));
max_cos_ulp_distance =
std::max(max_cos_ulp_distance,
ULPDistance(std::cos(α), static_cast<double>(Cos(α))));
std::max(max_cos_ulp_distance, ULPDistance(std::cos(α), Cos(α)));
}
EXPECT_EQ(1, max_sin_ulp_distance);
EXPECT_EQ(1, max_cos_ulp_distance);
EXPECT_THAT(max_sin_ulp_distance, IsNear(0.727_(1)));
EXPECT_THAT(max_cos_ulp_distance, IsNear(0.834_(1)));
}

// Hardest argument reduction, [Mul+10] table 11.1.
{
double const x = 0x16ac5b262ca1ffp797;
EXPECT_EQ(
0,
ULPDistance(std::sin(x), static_cast<double>(Sin(x))));
EXPECT_THAT(ULPDistance(std::cos(x), static_cast<double>(Cos(x))),
AnyOf(Eq(0), // Windows, macOS.
Eq(8))); // Linux.
EXPECT_THAT(ULPDistance(std::sin(x), Sin(x)), IsNear(9.89e-22_(1)));
Copy link
Member

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

Note: this is consistent with the result given by floating_point.wl:

In[1]:= << \
"C:\\Users\\robin\\Projects\\mockingbirdnest\\Principia\\mathematica\\\
floating_point.wl"

In[2]:= SetFloatingPointFormat[binary64]

In[3]:= SetRoundingMode[NearestTiesToEven]

In[4]:= x = 16^^16ac5b262ca1ff*2^797;

In[5]:= Block[{$MaxExtraPrecision = 300}, CorrectlyRound[Sin[x]]]

Out[5]= 1

In[6]:= Block[{$MaxExtraPrecision = 300}, 
 N[UlpDistance[Sin[16^^16ac5b262ca1ff*2^797], 1], 10]]

Out[6]= 9.894194191*10^-22

EXPECT_THAT(ULPDistance(std::cos(x), Cos(x)),
AnyOf(IsNear(0.0454_(1)), // Windows, macOS.
Eq(8))); // Linux.
}
}

Expand Down