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Improve axis regular precision #387

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b2ac83c
refactored regular
ryanelandt Jun 15, 2023
4d9393e
added test for vakokako #336 example
ryanelandt Jun 15, 2023
e9b1a5e
update serialization xml files
ryanelandt Jun 15, 2023
ab28542
fixed assert issue with -0.0 and +0.0
ryanelandt Jun 16, 2023
fb35257
made lines at most 80 characters long
ryanelandt Jun 16, 2023
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12 changes: 9 additions & 3 deletions examples/getting_started_listing_01.cpp
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Expand Up @@ -72,18 +72,24 @@ int main() {
Edges can be accessed with methods `lower()` and `upper()`.
*/

// IEEE 754 has a positive and a negative zero, which are equal, but have
// different signs. This lambda function converts negative zero to positive
// zero for the purposes of string formatting.
auto fn_negative_zero_to_zero = [](double x) { return (x == 0) ? 0.0 : x; };

std::ostringstream os;
for (auto&& x : indexed(h, coverage::all)) {
os << boost::format("bin %2i [%4.1f, %4.1f): %i\n")
% x.index() % x.bin().lower() % x.bin().upper() % *x;
% x.index() % fn_negative_zero_to_zero(x.bin().lower())
% fn_negative_zero_to_zero(x.bin().upper()) % *x;
}

std::cout << os.str() << std::flush;

assert(os.str() == "bin -1 [-inf, -1.0): 1\n"
"bin 0 [-1.0, -0.5): 1\n"
"bin 1 [-0.5, -0.0): 1\n"
"bin 2 [-0.0, 0.5): 2\n"
"bin 1 [-0.5, 0.0): 1\n"
"bin 2 [ 0.0, 0.5): 2\n"
"bin 3 [ 0.5, 1.0): 0\n"
"bin 4 [ 1.0, 1.5): 1\n"
"bin 5 [ 1.5, 2.0): 1\n"
Expand Down
120 changes: 71 additions & 49 deletions include/boost/histogram/axis/regular.hpp
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Expand Up @@ -83,18 +83,19 @@ struct id {
void serialize(Archive&, unsigned /* version */) {}
};

/// Log transform for equidistant bins in log-space.
/// Log transform for equidistant bins in log-space. Note, the base does not matter
/// because of the change of base formula which says: log_b(x) = log_a(x) / log_a(b).
struct log {
/// Returns log(x) of external value x.
template <class T>
static T forward(T x) {
return std::log(x);
return std::log2(x);
}

/// Returns exp(x) for internal value x.
template <class T>
static T inverse(T x) {
return std::exp(x);
return std::pow(2, x);
}

template <class Archive>
Expand Down Expand Up @@ -221,8 +222,13 @@ class regular : public iterator_mixin<regular<Value, Transform, MetaData, Option
: transform_type(std::move(trans))
, metadata_base(std::move(meta))
, size_(static_cast<index_type>(n))
, min_(this->forward(detail::get_scale(start)))
, delta_(this->forward(detail::get_scale(stop)) - min_) {
, min_(this->forward(detail::get_scale(start))) {
{
const auto delta = this->forward(detail::get_scale(stop)) - min_;
b0_ = static_cast<internal_value_type>(delta / size());
b0_inv_ = static_cast<internal_value_type>(size() / delta);
}

// static_asserts were moved here from class scope to satisfy deduction in gcc>=11
static_assert(std::is_nothrow_move_constructible<transform_type>::value,
"transform must be no-throw move constructible");
Expand All @@ -233,11 +239,10 @@ class regular : public iterator_mixin<regular<Value, Transform, MetaData, Option
static_assert(!(options.test(option::circular) && options.test(option::growth)),
"circular and growth options are mutually exclusive");
if (size() <= 0) BOOST_THROW_EXCEPTION(std::invalid_argument("bins > 0 required"));
if (!std::isfinite(min_) || !std::isfinite(delta_))
if (b0_ == 0) BOOST_THROW_EXCEPTION(std::invalid_argument("range of axis is zero"));
if (!std::isfinite(min_) || !std::isfinite(b0_) || !std::isfinite(b0_inv_))
BOOST_THROW_EXCEPTION(
std::invalid_argument("forward transform of start or stop invalid"));
if (delta_ == 0)
BOOST_THROW_EXCEPTION(std::invalid_argument("range of axis is zero"));
}

/** Construct n bins over real range [start, stop).
Expand Down Expand Up @@ -306,52 +311,32 @@ class regular : public iterator_mixin<regular<Value, Transform, MetaData, Option

/// Return index for value argument.
index_type index(value_type x) const noexcept {
// Runs in hot loop, please measure impact of changes
auto z = (this->forward(x / unit_type{}) - min_) / delta_;
if (options_type::test(option::circular)) {
if (std::isfinite(z)) {
z -= std::floor(z);
return static_cast<index_type>(z * size());
}
} else {
if (z < 1) {
if (z >= 0)
return static_cast<index_type>(z * size());
else
return -1;
}
// upper edge of last bin is inclusive if overflow bin is not present
if (!options_type::test(option::overflow) && z == 1) return size() - 1;
}
return size(); // also returned if x is NaN
return index_impl(options_type::test(axis::option::circular),
static_cast<double>(x / unit_type{}));
}

/// Returns index and shift (if axis has grown) for the passed argument.
std::pair<index_type, index_type> update(value_type x) noexcept {
assert(options_type::test(option::growth));
const auto z = (this->forward(x / unit_type{}) - min_) / delta_;
if (z < 1) { // don't use i here!
if (z >= 0) {
const auto i = static_cast<axis::index_type>(z * size());
auto y = (this->forward(x / unit_type{}) - min_) * b0_inv_;
if (y < size()) {
if (0 <= y) {
const auto i = static_cast<axis::index_type>(y);
return {i, 0};
}
if (z != -std::numeric_limits<internal_value_type>::infinity()) {
const auto stop = min_ + delta_;
const auto i = static_cast<axis::index_type>(std::floor(z * size()));
min_ += i * (delta_ / size());
delta_ = stop - min_;
if (y != -std::numeric_limits<internal_value_type>::infinity()) {
const auto i = static_cast<axis::index_type>(std::floor(y));
min_ += i * b0_;
size_ -= i;
return {0, -i};
}
// z is -infinity
return {-1, 0};
}
// z either beyond range, infinite, or NaN
if (z < std::numeric_limits<internal_value_type>::infinity()) {
const auto i = static_cast<axis::index_type>(z * size());
// y either beyond range, infinite, or NaN
if (y < std::numeric_limits<internal_value_type>::infinity()) {
const auto i = static_cast<axis::index_type>(y);
const auto n = i - size() + 1;
delta_ /= size();
delta_ *= size() + n;
size_ += n;
return {i, -n};
}
Expand All @@ -361,13 +346,13 @@ class regular : public iterator_mixin<regular<Value, Transform, MetaData, Option

/// Return value for fractional index argument.
value_type value(real_index_type i) const noexcept {
auto z = i / size();
if (!options_type::test(option::circular) && z < 0.0)
z = -std::numeric_limits<internal_value_type>::infinity() * delta_;
else if (options_type::test(option::circular) || z <= 1.0)
z = (1.0 - z) * min_ + z * (min_ + delta_);
real_index_type z;
if (!options_type::test(option::circular) && i < 0.0)
z = -std::numeric_limits<internal_value_type>::infinity() * b0_;
else if (options_type::test(option::circular) || i <= size())
z = min_ + i * b0_;
else {
z = std::numeric_limits<internal_value_type>::infinity() * delta_;
z = std::numeric_limits<internal_value_type>::infinity() * b0_;
}
return static_cast<value_type>(this->inverse(z) * unit_type());
}
Expand All @@ -386,7 +371,7 @@ class regular : public iterator_mixin<regular<Value, Transform, MetaData, Option
template <class V, class T, class M, class O>
bool operator==(const regular<V, T, M, O>& o) const noexcept {
return detail::relaxed_equal{}(transform(), o.transform()) && size() == o.size() &&
min_ == o.min_ && delta_ == o.delta_ &&
min_ == o.min_ && b0_ == o.b0_ && b0_inv_ == o.b0_inv_ &&
detail::relaxed_equal{}(this->metadata(), o.metadata());
}
template <class V, class T, class M, class O>
Expand All @@ -400,12 +385,49 @@ class regular : public iterator_mixin<regular<Value, Transform, MetaData, Option
ar& make_nvp("size", size_);
ar& make_nvp("meta", this->metadata());
ar& make_nvp("min", min_);
ar& make_nvp("delta", delta_);
ar& make_nvp("b0", b0_);
ar& make_nvp("b0_inv", b0_inv_);
}

private:
// axis not circular
index_type index_impl(std::false_type, double x) const noexcept {
auto y = (this->forward(x) - min_) * b0_inv_;
if (y < size()) {
if (0 <= y)
return static_cast<index_type>(y);
else
return -1;
}
// upper edge of last bin is inclusive if overflow bin is not present
if (!options_type::test(option::overflow) && y == size()) return size() - 1;
return size(); // also returned if x is NaN
}

// value_type is integer, axis circular
index_type index_impl(std::true_type, double x) const noexcept {
auto lambda_circ = [&](auto x) -> index_type {
auto delta = size() * b0_;
// Need to wrap in input space x, not output space y in case of a non-identify
// transform.
x -= std::floor((x - min_) / delta) * delta;
x += min_;
auto y = (this->forward(x) - min_) * b0_inv_;
return static_cast<index_type>(y);
};

return detail::static_if<std::is_floating_point<value_type>>(
[&](auto x) {
if (std::isfinite(x))
return lambda_circ(x);
else
return size();
},
lambda_circ, x);
}

index_type size_{0};
internal_value_type min_{0}, delta_{1};
internal_value_type min_{0}, b0_{0}, b0_inv_{0};

template <class V, class T, class M, class O>
friend class regular;
Expand Down
38 changes: 38 additions & 0 deletions test/axis_regular_test.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -301,5 +301,43 @@ int main() {
BOOST_TEST_EQ(b.value(2), 5);
}

// Test based on the example https://godbolt.org/z/oaPo6n17h
// from @vakokako in #336
{
auto fn_test_precision = [](int N, double x0, double xN, auto fn_axis) {
const auto a = fn_axis(N, x0, xN);
BOOST_TEST(a.size() == N);

// // Calculate bin spacing b0
const double b0 = (xN - x0) / N;

// Check to see if the index and value calculations are exact
for (int y = 0; y < a.size(); ++y) {
const double x = x0 + y * b0;
BOOST_TEST_EQ(y, a.index(x));
BOOST_TEST_EQ((double)(x), a.value(y));
}
};

auto fn_test_regular = [](int N, double x0, double xN) {
return boost::histogram::axis::regular<double>(N, x0, xN);
};

// The original example
fn_test_precision(27000, 0, 27000, fn_test_regular);

// Bin spacings and starting points that take few floating point bits to represent
const std::vector<double> v_spacing = {0.125, 0.375, 0.5, 0.75, 1, 1.625, 3, 7.25};
const std::vector<double> v_x0 = {-1000.25, -2.5, -0.5, 0, 0.5, 2.5, 1000.25};

for (const int n : {1, 16, 27000, 350017, 1234567}) {
for (const double spacing : v_spacing) {
for (const double x0 : v_x0) {
fn_test_precision(n, x0, x0 + n * spacing, fn_test_regular);
}
}
}
}

return boost::report_errors();
}
5 changes: 3 additions & 2 deletions test/axis_variant_serialization_test.xml
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Original file line number Diff line number Diff line change
Expand Up @@ -8,7 +8,7 @@

<?xml version="1.0" encoding="UTF-8" standalone="yes" ?>
<!DOCTYPE boost_serialization>
<boost_serialization signature="serialization::archive" version="17">
<boost_serialization signature="serialization::archive" version="19">
<item class_id="0" tracking_level="0" version="0">
<variant class_id="1" tracking_level="0" version="0">
<which>1</which>
Expand All @@ -17,7 +17,8 @@
<size>1</size>
<meta></meta>
<min>0.00000000000000000e+00</min>
<delta>1.00000000000000000e+00</delta>
<b0>1.00000000000000000e+00</b0>
<b0_inv>1.00000000000000000e+00</b0_inv>
</value>
</variant>
</item>
Expand Down
31 changes: 18 additions & 13 deletions test/histogram_serialization_test_dynamic.xml
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Original file line number Diff line number Diff line change
Expand Up @@ -8,49 +8,52 @@

<?xml version="1.0" encoding="UTF-8" standalone="yes" ?>
<!DOCTYPE boost_serialization>
<boost_serialization signature="serialization::archive" version="17">
<boost_serialization signature="serialization::archive" version="19">
<item class_id="0" tracking_level="0" version="0">
<axes class_id="1" tracking_level="0" version="0">
<count>7</count>
<item_version>0</item_version>
<item class_id="2" tracking_level="0" version="0">
<variant class_id="3" tracking_level="1" version="0" object_id="_0">
<variant class_id="3" tracking_level="0" version="0">
<which>0</which>
<value class_id="4" tracking_level="0" version="0">
<transform class_id="5" tracking_level="0" version="0"></transform>
<size>1</size>
<meta>reg</meta>
<min>-1.00000000000000000e+00</min>
<delta>2.00000000000000000e+00</delta>
<b0>2.00000000000000000e+00</b0>
<b0_inv>5.00000000000000000e-01</b0_inv>
</value>
</variant>
</item>
<item>
<variant object_id="_1">
<variant>
<which>1</which>
<value class_id="6" tracking_level="0" version="0">
<transform></transform>
<size>1</size>
<meta>cir</meta>
<min>0.000000000e+00</min>
<delta>1.000000000e+00</delta>
<b0>1.000000000e+00</b0>
<b0_inv>1.000000000e+00</b0_inv>
</value>
</variant>
</item>
<item>
<variant object_id="_2">
<variant>
<which>2</which>
<value class_id="7" tracking_level="0" version="0">
<transform class_id="8" tracking_level="0" version="0"></transform>
<size>1</size>
<meta>reg-log</meta>
<min>0.00000000000000000e+00</min>
<delta>2.00000000000000000e+00</delta>
<b0>2.88539008177792677e+00</b0>
<b0_inv>3.46573590279972643e-01</b0_inv>
</value>
</variant>
</item>
<item>
<variant object_id="_3">
<variant>
<which>3</which>
<value class_id="9" tracking_level="0" version="0">
<transform class_id="10" tracking_level="0" version="0">
Expand All @@ -65,12 +68,13 @@
<item>3</item>
</meta>
<min>1.00000000000000000e+00</min>
<delta>9.00000000000000000e+00</delta>
<b0>9.00000000000000000e+00</b0>
<b0_inv>1.11111111111111105e-01</b0_inv>
</value>
</variant>
</item>
<item>
<variant object_id="_4">
<variant>
<which>4</which>
<value class_id="12" tracking_level="0" version="0">
<seq>
Expand All @@ -84,7 +88,7 @@
</variant>
</item>
<item>
<variant object_id="_5">
<variant>
<which>5</which>
<value class_id="14" tracking_level="0" version="0">
<seq>
Expand All @@ -98,7 +102,7 @@
</variant>
</item>
<item>
<variant object_id="_6">
<variant>
<which>6</which>
<value class_id="15" tracking_level="0" version="0">
<size>1</size>
Expand All @@ -111,7 +115,7 @@
<storage class_id="17" tracking_level="0" version="0">
<type>0</type>
<size>4</size>
<buffer>
<buffer class_id="18" tracking_level="0" version="0">
<item>0</item>
<item>0</item>
<item>1</item>
Expand All @@ -120,3 +124,4 @@
</storage>
</item>
</boost_serialization>

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