| <!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="Source of the Rust file `/root/.cargo/git/checkouts/rulinalg-309246e5a94bf5cf/1ed8b93/src/ulp.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>ulp.rs - source</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceSerif4-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../FiraSans-Regular.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../FiraSans-Medium.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceCodePro-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceSerif4-Bold.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceCodePro-Semibold.ttf.woff2"><link rel="stylesheet" href="../../normalize.css"><link rel="stylesheet" href="../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" href="../../ayu.css" disabled><link rel="stylesheet" href="../../dark.css" disabled><link rel="stylesheet" href="../../light.css" id="themeStyle"><script id="default-settings" ></script><script src="../../storage.js"></script><script defer src="../../source-script.js"></script><script defer src="../../source-files.js"></script><script defer src="../../main.js"></script><noscript><link rel="stylesheet" href="../../noscript.css"></noscript><link rel="alternate icon" type="image/png" href="../../favicon-16x16.png"><link rel="alternate icon" type="image/png" href="../../favicon-32x32.png"><link rel="icon" type="image/svg+xml" href="../../favicon.svg"></head><body class="rustdoc source"><!--[if lte IE 11]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><a class="sidebar-logo" href="../../rulinalg/index.html"><div class="logo-container"><img class="rust-logo" src="../../rust-logo.svg" alt="logo"></div></a></nav><main><div class="width-limiter"><nav class="sub"><a class="sub-logo-container" href="../../rulinalg/index.html"><img class="rust-logo" src="../../rust-logo.svg" alt="logo"></a><form class="search-form"><div class="search-container"><span></span><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"><div id="help-button" title="help" tabindex="-1"><a href="../../help.html">?</a></div><div id="settings-menu" tabindex="-1"><a href="../../settings.html" title="settings"><img width="22" height="22" alt="Change settings" src="../../wheel.svg"></a></div></div></form></nav><section id="main-content" class="content"><div class="example-wrap"><pre class="src-line-numbers"><span id="1">1</span> |
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| </pre><pre class="rust"><code><span class="doccomment">//! Tools for ULP-based comparison of floating point numbers. |
| </span><span class="kw">use </span>std::mem; |
| |
| <span class="doccomment">/// Represents the result of an ULP-based comparison between two floating point numbers. |
| </span><span class="attribute">#[derive(Debug, Copy, Clone, PartialEq)] |
| </span><span class="kw">pub enum </span>UlpComparisonResult |
| { |
| <span class="doccomment">/// Signifies an exact match between two floating point numbers. |
| </span>ExactMatch, |
| <span class="doccomment">/// The difference in ULP between two floating point numbers. |
| </span>Difference(u64), |
| <span class="doccomment">/// The two floating point numbers have different signs, |
| /// and cannot be compared in a meaningful way. |
| </span>IncompatibleSigns, |
| <span class="doccomment">/// One or both of the two floating point numbers is a NaN, |
| /// in which case the ULP comparison is not meaningful. |
| </span>Nan |
| } |
| |
| <span class="doccomment">/// Floating point types for which two instances can be compared for Unit in the Last Place (ULP) difference. |
| /// |
| /// Implementing this trait enables the usage of the `ulp` comparator in |
| /// [assert_matrix_eq!](../macro.assert_matrix_eq!.html) for the given type. |
| /// |
| /// The definition here leverages the fact that for two adjacent floating point numbers, |
| /// their integer representations are also adjacent. |
| /// |
| /// A somewhat accessible (but not exhaustive) guide on the topic is available in the popular article |
| /// [Comparing Floating Point Numbers, 2012 Edition] |
| /// (https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/). |
| /// |
| /// Implementations for `f32` and `f64` are already available, and so users should not normally |
| /// need to implement this. In the case when a custom implementation is necessary, |
| /// please see the possible return values for [UlpComparisonResult](ulp/enum.UlpComparisonResult.html). |
| /// Otherwise, we can recommend to read the source code of the included `f32` and `f64` implementations. |
| </span><span class="kw">pub trait </span>Ulp { |
| <span class="doccomment">/// Returns the difference between two floating point numbers, measured in ULP. |
| </span><span class="kw">fn </span>ulp_diff(a: <span class="kw-2">&</span><span class="self">Self</span>, b: <span class="kw-2">&</span><span class="self">Self</span>) -> UlpComparisonResult; |
| } |
| |
| <span class="macro">macro_rules! </span>impl_float_ulp { |
| (<span class="macro-nonterminal">$ftype</span>:ty, <span class="macro-nonterminal">$itype</span>:ty) => { |
| <span class="kw">impl </span>Ulp <span class="kw">for </span><span class="macro-nonterminal">$ftype </span>{ |
| <span class="kw">fn </span>ulp_diff(a: <span class="kw-2">&</span><span class="self">Self</span>, b: <span class="kw-2">&</span><span class="self">Self</span>) -> UlpComparisonResult { |
| <span class="kw">if </span>a == b { |
| UlpComparisonResult::ExactMatch |
| } <span class="kw">else if </span>a.is_nan() || b.is_nan() { |
| <span class="comment">// ULP comparison does not make much sense for NaN |
| </span>UlpComparisonResult::Nan |
| } <span class="kw">else if </span>a.is_sign_positive() != b.is_sign_positive() { |
| <span class="comment">// ULP is not meaningful when the signs of the two numbers differ |
| </span>UlpComparisonResult::IncompatibleSigns |
| } <span class="kw">else </span>{ |
| <span class="comment">// Otherwise, we compute the ULP diff as the difference of the signed integer representations |
| </span><span class="kw">let </span>a_int = <span class="kw">unsafe </span>{ mem::transmute::<<span class="macro-nonterminal">$ftype</span>, <span class="macro-nonterminal">$itype</span>>(a.to_owned()) }; |
| <span class="kw">let </span>b_int = <span class="kw">unsafe </span>{ mem::transmute::<<span class="macro-nonterminal">$ftype</span>, <span class="macro-nonterminal">$itype</span>>(b.to_owned()) }; |
| UlpComparisonResult::Difference((b_int - a_int).abs() <span class="kw">as </span>u64) |
| } |
| } |
| } |
| } |
| } |
| |
| <span class="macro">impl_float_ulp!</span>(f32, i32); |
| <span class="macro">impl_float_ulp!</span>(f64, i64); |
| |
| <span class="attribute">#[cfg(test)] |
| </span><span class="kw">mod </span>tests { |
| <span class="kw">use </span><span class="kw">super</span>::Ulp; |
| <span class="kw">use </span><span class="kw">super</span>::UlpComparisonResult; |
| <span class="kw">use </span>std::mem; |
| <span class="kw">use </span>std::{f32, f64}; |
| <span class="kw">use </span>quickcheck::TestResult; |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>plus_minus_zero_is_exact_match_f32() { |
| <span class="macro">assert!</span>(f32::ulp_diff(<span class="kw-2">&</span><span class="number">0.0</span>, <span class="kw-2">&</span><span class="number">0.0</span>) == UlpComparisonResult::ExactMatch); |
| <span class="macro">assert!</span>(f32::ulp_diff(<span class="kw-2">&</span>-<span class="number">0.0</span>, <span class="kw-2">&</span>-<span class="number">0.0</span>) == UlpComparisonResult::ExactMatch); |
| <span class="macro">assert!</span>(f32::ulp_diff(<span class="kw-2">&</span><span class="number">0.0</span>, <span class="kw-2">&</span>-<span class="number">0.0</span>) == UlpComparisonResult::ExactMatch); |
| <span class="macro">assert!</span>(f32::ulp_diff(<span class="kw-2">&</span>-<span class="number">0.0</span>, <span class="kw-2">&</span><span class="number">0.0</span>) == UlpComparisonResult::ExactMatch); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>plus_minus_zero_is_exact_match_f64() { |
| <span class="macro">assert!</span>(f64::ulp_diff(<span class="kw-2">&</span><span class="number">0.0</span>, <span class="kw-2">&</span><span class="number">0.0</span>) == UlpComparisonResult::ExactMatch); |
| <span class="macro">assert!</span>(f64::ulp_diff(<span class="kw-2">&</span>-<span class="number">0.0</span>, <span class="kw-2">&</span>-<span class="number">0.0</span>) == UlpComparisonResult::ExactMatch); |
| <span class="macro">assert!</span>(f64::ulp_diff(<span class="kw-2">&</span><span class="number">0.0</span>, <span class="kw-2">&</span>-<span class="number">0.0</span>) == UlpComparisonResult::ExactMatch); |
| <span class="macro">assert!</span>(f64::ulp_diff(<span class="kw-2">&</span>-<span class="number">0.0</span>, <span class="kw-2">&</span><span class="number">0.0</span>) == UlpComparisonResult::ExactMatch); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>f32_double_nan() { |
| <span class="macro">assert!</span>(f32::ulp_diff(<span class="kw-2">&</span>f32::NAN, <span class="kw-2">&</span>f32::NAN) == UlpComparisonResult::Nan); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>f64_double_nan() { |
| <span class="macro">assert!</span>(f64::ulp_diff(<span class="kw-2">&</span>f64::NAN, <span class="kw-2">&</span>f64::NAN) == UlpComparisonResult::Nan); |
| } |
| |
| <span class="macro">quickcheck! </span>{ |
| <span class="kw">fn </span>property_exact_match_for_finite_f32_self_comparison(x: f32) -> TestResult { |
| <span class="kw">if </span>x.is_finite() { |
| TestResult::from_bool(f32::ulp_diff(<span class="kw-2">&</span>x, <span class="kw-2">&</span>x) == UlpComparisonResult::ExactMatch) |
| } <span class="kw">else </span>{ |
| TestResult::discard() |
| } |
| } |
| } |
| |
| <span class="macro">quickcheck! </span>{ |
| <span class="kw">fn </span>property_exact_match_for_finite_f64_self_comparison(x: f64) -> TestResult { |
| <span class="kw">if </span>x.is_finite() { |
| TestResult::from_bool(f64::ulp_diff(<span class="kw-2">&</span>x, <span class="kw-2">&</span>x) == UlpComparisonResult::ExactMatch) |
| } <span class="kw">else </span>{ |
| TestResult::discard() |
| } |
| } |
| } |
| |
| <span class="macro">quickcheck! </span>{ |
| <span class="kw">fn </span>property_recovers_ulp_diff_when_f32_constructed_from_i32(a: i32, b: i32) -> TestResult { |
| <span class="kw">if </span>a == b { |
| <span class="comment">// Ignore self-comparisons, as it makes the below test have more complicated logic, |
| // and moreover we test self-comparisons in another property. |
| </span><span class="kw">return </span>TestResult::discard(); |
| } |
| |
| <span class="kw">let </span>x = <span class="kw">unsafe </span>{ mem::transmute::<i32, f32>(a) }; |
| <span class="kw">let </span>y = <span class="kw">unsafe </span>{ mem::transmute::<i32, f32>(b) }; |
| |
| <span class="comment">// Discard the input if it's non-finite or has different signs |
| </span><span class="kw">if </span>x.is_finite() && y.is_finite() && x.signum() == y.signum() { |
| TestResult::from_bool(f32::ulp_diff(<span class="kw-2">&</span>x, <span class="kw-2">&</span>y) == UlpComparisonResult::Difference((b - a).abs() <span class="kw">as </span>u64)) |
| } <span class="kw">else </span>{ |
| TestResult::discard() |
| } |
| } |
| } |
| |
| <span class="macro">quickcheck! </span>{ |
| <span class="kw">fn </span>property_recovers_ulp_diff_when_f64_constructed_from_i64(a: i64, b: i64) -> TestResult { |
| <span class="kw">if </span>a == b { |
| <span class="comment">// Ignore self-comparisons, as it makes the below test have more complicated logic, |
| // and moreover we test self-comparisons in another property. |
| </span><span class="kw">return </span>TestResult::discard(); |
| } |
| |
| <span class="kw">let </span>x = <span class="kw">unsafe </span>{ mem::transmute::<i64, f64>(a) }; |
| <span class="kw">let </span>y = <span class="kw">unsafe </span>{ mem::transmute::<i64, f64>(b) }; |
| |
| <span class="comment">// Discard the input if it's non-finite or has different signs |
| </span><span class="kw">if </span>x.is_finite() && y.is_finite() && x.signum() == y.signum() { |
| TestResult::from_bool(f64::ulp_diff(<span class="kw-2">&</span>x, <span class="kw-2">&</span>y) == UlpComparisonResult::Difference((b - a).abs() <span class="kw">as </span>u64)) |
| } <span class="kw">else </span>{ |
| TestResult::discard() |
| } |
| } |
| } |
| |
| <span class="macro">quickcheck! </span>{ |
| <span class="kw">fn </span>property_f32_incompatible_signs_yield_corresponding_enum_value(x: f32, y: f32) -> TestResult { |
| <span class="kw">if </span>x.signum() == y.signum() { |
| TestResult::discard() |
| } <span class="kw">else if </span>x.is_nan() || y.is_nan() { |
| TestResult::discard() |
| } <span class="kw">else </span>{ |
| TestResult::from_bool(f32::ulp_diff(<span class="kw-2">&</span>x, <span class="kw-2">&</span>y) == UlpComparisonResult::IncompatibleSigns) |
| } |
| } |
| } |
| |
| <span class="macro">quickcheck! </span>{ |
| <span class="kw">fn </span>property_f64_incompatible_signs_yield_corresponding_enum_value(x: f64, y: f64) -> TestResult { |
| <span class="kw">if </span>x.signum() == y.signum() { |
| TestResult::discard() |
| } <span class="kw">else if </span>x.is_nan() || y.is_nan() { |
| TestResult::discard() |
| } <span class="kw">else </span>{ |
| TestResult::from_bool(f64::ulp_diff(<span class="kw-2">&</span>x, <span class="kw-2">&</span>y) == UlpComparisonResult::IncompatibleSigns) |
| } |
| } |
| } |
| |
| <span class="macro">quickcheck! </span>{ |
| <span class="kw">fn </span>property_f32_nan_gives_nan_enum_value(x: f32) -> bool { |
| f32::ulp_diff(<span class="kw-2">&</span>f32::NAN, <span class="kw-2">&</span>x) == UlpComparisonResult::Nan |
| && f32::ulp_diff(<span class="kw-2">&</span>x, <span class="kw-2">&</span>f32::NAN) == UlpComparisonResult::Nan |
| } |
| } |
| |
| <span class="macro">quickcheck! </span>{ |
| <span class="kw">fn </span>property_f64_nan_gives_nan_enum_value(x: f64) -> bool { |
| f64::ulp_diff(<span class="kw-2">&</span>f64::NAN, <span class="kw-2">&</span>x) == UlpComparisonResult::Nan |
| && f64::ulp_diff(<span class="kw-2">&</span>x, <span class="kw-2">&</span>f64::NAN) == UlpComparisonResult::Nan |
| } |
| } |
| } |
| </code></pre></div> |
| </section></div></main><div id="rustdoc-vars" data-root-path="../../" data-current-crate="rulinalg" data-themes="ayu,dark,light" data-resource-suffix="" data-rustdoc-version="1.66.0-nightly (5c8bff74b 2022-10-21)" ></div></body></html> |
