juce_MathsFunctions_test.cpp

/*
  ==============================================================================
 
   This file is part of the JUCE library.
   Copyright (c) 2022 - Raw Material Software Limited
 
   JUCE is an open source library subject to commercial or open-source
   licensing.
 
   The code included in this file is provided under the terms of the ISC license
   http://www.isc.org/downloads/software-support-policy/isc-license. Permission
   To use, copy, modify, and/or distribute this software for any purpose with or
   without fee is hereby granted provided that the above copyright notice and
   this permission notice appear in all copies.
 
   JUCE IS PROVIDED "AS IS" WITHOUT ANY WARRANTY, AND ALL WARRANTIES, WHETHER
   EXPRESSED OR IMPLIED, INCLUDING MERCHANTABILITY AND FITNESS FOR PURPOSE, ARE
   DISCLAIMED.
 
  ==============================================================================
*/
 
namespace juce
{
 
//==============================================================================
template <typename T>
String getTemplatedMathsFunctionUnitTestName (const String& functionName)
{
    const auto getTypeName = []() -> String
    {
        if constexpr (std::is_same_v<int, T>)
            return "int";
 
        if constexpr (std::is_same_v<float, T>)
            return "float";
 
        if constexpr (std::is_same_v<double, T>)
            return "double";
 
        if constexpr (std::is_same_v<long double, T>)
            return "long double";
    };
 
    return functionName + "<" + getTypeName() + ">";
}
 
template <typename T>
class ApproximatelyEqualTests final : public UnitTest
{
public:
    ApproximatelyEqualTests()
        : UnitTest { getTemplatedMathsFunctionUnitTestName<T> ("approximatelyEqual"), UnitTestCategories::maths }
    {}
 
    void runTest() final
    {
        using limits = std::numeric_limits<T>;
 
        constexpr auto zero = T{};
        constexpr auto one = T (1);
        constexpr auto min = limits::min();
        constexpr auto max = limits::max();
        constexpr auto epsilon = limits::epsilon();
        constexpr auto oneThird = one / (T) 3;
 
        beginTest ("Equal values are always equal");
        {
            expect (approximatelyEqual (zero, zero));
            expect (approximatelyEqual (zero, -zero));
            expect (approximatelyEqual (-zero, -zero));
 
            expect (approximatelyEqual (min, min));
            expect (approximatelyEqual (-min, -min));
 
            expect (approximatelyEqual (one, one));
            expect (approximatelyEqual (-one, -one));
 
            expect (approximatelyEqual (max, max));
            expect (approximatelyEqual (-max, -max));
 
            const Tolerance<T> zeroTolerance{};
 
            expect (approximatelyEqual (zero, zero, zeroTolerance));
            expect (approximatelyEqual (zero, -zero, zeroTolerance));
            expect (approximatelyEqual (-zero, -zero, zeroTolerance));
 
            expect (approximatelyEqual (min, min, zeroTolerance));
            expect (approximatelyEqual (-min, -min, zeroTolerance));
 
            expect (approximatelyEqual (one, one, zeroTolerance));
            expect (approximatelyEqual (-one, -one, zeroTolerance));
 
            expect (approximatelyEqual (max, max, zeroTolerance));
            expect (approximatelyEqual (-max, -max, zeroTolerance));
        }
 
        beginTest ("Comparing subnormal values to zero, returns true");
        {
            expect (! exactlyEqual     (zero, nextFloatUp (zero)));
            expect (approximatelyEqual (zero, nextFloatUp (zero)));
 
            expect (! exactlyEqual     (zero, nextFloatDown (zero)));
            expect (approximatelyEqual (zero, nextFloatDown (zero)));
 
            expect (! exactlyEqual     (zero, nextFloatDown (min)));
            expect (approximatelyEqual (zero, nextFloatDown (min)));
 
            expect (! exactlyEqual     (zero, nextFloatUp (-min)));
            expect (approximatelyEqual (zero, nextFloatUp (-min)));
        }
 
        beginTest ("Comparing the minimum normal value to zero, returns true");
        {
            expect (approximatelyEqual (zero, min));
            expect (approximatelyEqual (zero, -min));
        }
 
        beginTest ("Comparing normal values greater than the minimum to zero, returns true");
        {
            expect (! approximatelyEqual (zero, one));
            expect (! approximatelyEqual (zero, epsilon));
            expect (! approximatelyEqual (zero, nextFloatUp (min)));
            expect (! approximatelyEqual (zero, nextFloatDown (-min)));
        }
 
        beginTest ("Values with large ranges can be compared");
        {
            expect (! approximatelyEqual (zero, max));
            expect (  approximatelyEqual (zero, max, absoluteTolerance (max)));
            expect (  approximatelyEqual (zero, max, relativeTolerance (one)));
            expect (! approximatelyEqual (-one, max));
            expect (! approximatelyEqual (-max, max));
        }
 
        beginTest ("Larger values have a boundary that is a factor of the epsilon");
        {
            for (auto exponent = 0; exponent < 127; ++exponent)
            {
                const auto value = std::pow ((T) 2, (T) exponent);
                const auto boundaryValue = value * (one + epsilon);
 
                expect (juce_isfinite (value));
                expect (juce_isfinite (boundaryValue));
 
                expect (  approximatelyEqual (value, boundaryValue));
                expect (! approximatelyEqual (value, nextFloatUp (boundaryValue)));
 
                expect (  approximatelyEqual (-value, -boundaryValue));
                expect (! approximatelyEqual (-value, nextFloatDown (-boundaryValue)));
            }
        }
 
        beginTest ("Tolerances scale with the values being compared");
        {
 
            expect (approximatelyEqual ((T) 100'000'000'000'000.01,
                                        (T) 100'000'000'000'000.011));
 
            expect (! approximatelyEqual ((T) 100.01,
                                          (T) 100.011));
 
            expect (! approximatelyEqual ((T) 123'000, (T) 121'000, relativeTolerance ((T) 1e-2)));
            expect (  approximatelyEqual ((T) 123'000, (T) 122'000, relativeTolerance ((T) 1e-2)));
            expect (  approximatelyEqual ((T) 123'000, (T) 123'000, relativeTolerance ((T) 1e-2)));
            expect (  approximatelyEqual ((T) 123'000, (T) 124'000, relativeTolerance ((T) 1e-2)));
            expect (! approximatelyEqual ((T) 123'000, (T) 125'000, relativeTolerance ((T) 1e-2)));
 
            expect (! approximatelyEqual ((T) 123, (T) 121, relativeTolerance ((T) 1e-2)));
            expect (  approximatelyEqual ((T) 123, (T) 122, relativeTolerance ((T) 1e-2)));
            expect (  approximatelyEqual ((T) 123, (T) 123, relativeTolerance ((T) 1e-2)));
            expect (  approximatelyEqual ((T) 123, (T) 124, relativeTolerance ((T) 1e-2)));
            expect (! approximatelyEqual ((T) 123, (T) 125, relativeTolerance ((T) 1e-2)));
 
            expect (! approximatelyEqual ((T) 12.3, (T) 12.1, relativeTolerance ((T) 1e-2)));
            expect (  approximatelyEqual ((T) 12.3, (T) 12.2, relativeTolerance ((T) 1e-2)));
            expect (  approximatelyEqual ((T) 12.3, (T) 12.3, relativeTolerance ((T) 1e-2)));
            expect (  approximatelyEqual ((T) 12.3, (T) 12.4, relativeTolerance ((T) 1e-2)));
            expect (! approximatelyEqual ((T) 12.3, (T) 12.5, relativeTolerance ((T) 1e-2)));
 
            expect (! approximatelyEqual ((T) 1.23, (T) 1.21, relativeTolerance ((T) 1e-2)));
            expect (  approximatelyEqual ((T) 1.23, (T) 1.22, relativeTolerance ((T) 1e-2)));
            expect (  approximatelyEqual ((T) 1.23, (T) 1.23, relativeTolerance ((T) 1e-2)));
            expect (  approximatelyEqual ((T) 1.23, (T) 1.24, relativeTolerance ((T) 1e-2)));
            expect (! approximatelyEqual ((T) 1.23, (T) 1.25, relativeTolerance ((T) 1e-2)));
 
            expect (! approximatelyEqual ((T) 0.123, (T) 0.121, relativeTolerance ((T) 1e-2)));
            expect (  approximatelyEqual ((T) 0.123, (T) 0.122, relativeTolerance ((T) 1e-2)));
            expect (  approximatelyEqual ((T) 0.123, (T) 0.123, relativeTolerance ((T) 1e-2)));
            expect (  approximatelyEqual ((T) 0.123, (T) 0.124, relativeTolerance ((T) 1e-2)));
            expect (! approximatelyEqual ((T) 0.123, (T) 0.125, relativeTolerance ((T) 1e-2)));
 
            expect (! approximatelyEqual ((T) 0.000123, (T) 0.000121, relativeTolerance ((T) 1e-2)));
            expect (  approximatelyEqual ((T) 0.000123, (T) 0.000122, relativeTolerance ((T) 1e-2)));
            expect (  approximatelyEqual ((T) 0.000123, (T) 0.000123, relativeTolerance ((T) 1e-2)));
            expect (  approximatelyEqual ((T) 0.000123, (T) 0.000124, relativeTolerance ((T) 1e-2)));
            expect (! approximatelyEqual ((T) 0.000123, (T) 0.000125, relativeTolerance ((T) 1e-2)));
        }
 
        beginTest ("The square of the square root of 2 is approximately 2");
        {
            constexpr auto two = (T) 2;
            const auto sqrtOfTwo = std::sqrt (two);
 
            expect (approximatelyEqual (sqrtOfTwo * sqrtOfTwo, two));
            expect (approximatelyEqual (-sqrtOfTwo * sqrtOfTwo, -two));
            expect (approximatelyEqual (two / sqrtOfTwo, sqrtOfTwo));
        }
 
        if constexpr (limits::has_quiet_NaN)
        {
            beginTest ("Values are never equal to NaN");
            {
                const auto nan = limits::quiet_NaN();
 
                expect (! approximatelyEqual (nan, nan));
 
                const auto expectNotEqualTo = [&] (auto value)
                {
                    expect (! approximatelyEqual (value, nan));
                    expect (! approximatelyEqual (nan, value));
                };
 
                expectNotEqualTo (zero);
                expectNotEqualTo (-zero);
                expectNotEqualTo (min);
                expectNotEqualTo (-min);
                expectNotEqualTo (one);
                expectNotEqualTo (-one);
                expectNotEqualTo (max);
                expectNotEqualTo (-max);
            }
        }
 
        if constexpr (limits::has_infinity)
        {
            beginTest ("Only infinity is equal to infinity");
            {
                const auto inf = limits::infinity();
                expect (approximatelyEqual (inf, inf));
                expect (approximatelyEqual (-inf, -inf));
                expect (! approximatelyEqual (inf, -inf));
                expect (! approximatelyEqual (-inf, inf));
 
                const auto expectNotEqualTo = [&] (auto value)
                {
                    expect (! approximatelyEqual (value, inf));
                    expect (! approximatelyEqual (value, -inf));
                    expect (! approximatelyEqual (inf, value));
                    expect (! approximatelyEqual (-inf, value));
                };
 
                expectNotEqualTo (zero);
                expectNotEqualTo (-zero);
                expectNotEqualTo (min);
                expectNotEqualTo (-min);
                expectNotEqualTo (one);
                expectNotEqualTo (-one);
                expectNotEqualTo (max);
                expectNotEqualTo (-max);
            }
        }
 
        beginTest ("Can set an absolute tolerance");
        {
            constexpr std::array<T, 7> negativePowersOfTwo
            {
                (T) 0.5 /* 2^-1 */,
                (T) 0.25 /* 2^-2 */,
                (T) 0.125 /* 2^-3 */,
                (T) 0.0625 /* 2^-4 */,
                (T) 0.03125 /* 2^-5 */,
                (T) 0.015625 /* 2^-6 */,
                (T) 0.0078125 /* 2^-7 */
            };
 
            const auto testTolerance = [&] (auto tolerance)
            {
                const auto t = Tolerance<T>{}.withAbsolute ((T) tolerance);
 
                const auto testValue= [&] (auto value)
                {
                    const auto boundary = value + tolerance;
 
                    expect (approximatelyEqual (value, boundary, t));
                    expect (! approximatelyEqual (value, nextFloatUp (boundary), t));
 
                    expect (approximatelyEqual (-value, -boundary, t));
                    expect (! approximatelyEqual (-value, nextFloatDown (-boundary), t));
                };
 
                testValue (zero);
                testValue (min);
                testValue (epsilon);
                testValue (one);
 
                for (const auto value : negativePowersOfTwo)
                    testValue (value);
            };
 
            for (const auto toleranceValue : negativePowersOfTwo)
                testTolerance (toleranceValue);
        }
 
        beginTest ("Can set a relative tolerance");
        {
            expect (! approximatelyEqual (oneThird, (T) 0.34,  relativeTolerance ((T) 1e-2)));
            expect (  approximatelyEqual (oneThird, (T) 0.334, relativeTolerance ((T) 1e-2)));
 
            expect (! approximatelyEqual (oneThird, (T) 0.334,  relativeTolerance ((T) 1e-3)));
            expect (  approximatelyEqual (oneThird, (T) 0.3334, relativeTolerance ((T) 1e-3)));
 
            expect (! approximatelyEqual (oneThird, (T) 0.3334,  relativeTolerance ((T) 1e-4)));
            expect (  approximatelyEqual (oneThird, (T) 0.33334, relativeTolerance ((T) 1e-4)));
 
            expect (! approximatelyEqual (oneThird, (T) 0.33334,  relativeTolerance ((T) 1e-5)));
            expect (  approximatelyEqual (oneThird, (T) 0.333334, relativeTolerance ((T) 1e-5)));
 
            expect (! approximatelyEqual (oneThird, (T) 0.333334,  relativeTolerance ((T) 1e-6)));
            expect (  approximatelyEqual (oneThird, (T) 0.3333334, relativeTolerance ((T) 1e-6)));
 
            expect (! approximatelyEqual (oneThird, (T) 0.3333334,  relativeTolerance ((T) 1e-7)));
            expect (  approximatelyEqual (oneThird, (T) 0.33333334, relativeTolerance ((T) 1e-7)));
 
            expect (  approximatelyEqual ((T) 1e6, (T) 1e6 + (T) 1, relativeTolerance ((T) 1e-6)));
            expect (! approximatelyEqual ((T) 1e6, (T) 1e6 + (T) 1, relativeTolerance ((T) 1e-7)));
 
            expect (  approximatelyEqual ((T) -1e-6, (T) -1.0000009e-6, relativeTolerance ((T) 1e-6)));
            expect (! approximatelyEqual ((T) -1e-6, (T) -1.0000009e-6, relativeTolerance ((T) 1e-7)));
 
            const auto a = (T) 1.234567;
            const auto b = (T) 1.234568;
 
            for (auto exponent = 0; exponent < 39; ++exponent)
            {
                const auto m = std::pow ((T) 10, (T) exponent);
                expect (  approximatelyEqual (a * m, b * m, relativeTolerance ((T) 1e-6)));
                expect (! approximatelyEqual (a * m, b * m, relativeTolerance ((T) 1e-7)));
            }
        }
 
        beginTest ("A relative tolerance is always scaled by the maximum value");
        {
            expect (  approximatelyEqual ((T) 9, (T) 10, absoluteTolerance ((T) 10.0 * (T) 0.1)));
            expect (! approximatelyEqual ((T) 9, (T) 10, absoluteTolerance ((T)  9.0 * (T) 0.1)));
 
            expect (approximatelyEqual ((T)  9, (T) 10, relativeTolerance ((T) 0.1)));
            expect (approximatelyEqual ((T) 10, (T)  9, relativeTolerance ((T) 0.1)));
        }
 
        beginTest ("Documentation examples");
        {
            constexpr auto pi = MathConstants<T>::pi;
 
            expect (! approximatelyEqual (zero, std::sin (pi)));
            expect (  approximatelyEqual (zero, std::sin (pi), absoluteTolerance (std::sin (pi))));
 
            expect (  approximatelyEqual ((T) 100, (T) 95, relativeTolerance ((T) 0.05)));
            expect (! approximatelyEqual ((T) 100, (T) 94, relativeTolerance ((T) 0.05)));
        }
    }
};
 
template<>
class ApproximatelyEqualTests<int> final : public UnitTest
{
public:
    ApproximatelyEqualTests()
        : UnitTest { getTemplatedMathsFunctionUnitTestName<int> ("approximatelyEqual"), UnitTestCategories::maths }
    {}
 
    void runTest() final
    {
        beginTest ("Identical integers are always equal");
        {
            expect (approximatelyEqual ( 0,  0));
            expect (approximatelyEqual (-0, -0));
 
            expect (approximatelyEqual ( 1,  1));
            expect (approximatelyEqual (-1, -1));
 
            using limits = std::numeric_limits<int>;
            constexpr auto min = limits::min();
            constexpr auto max = limits::max();
 
            expect (approximatelyEqual (min, min));
            expect (approximatelyEqual (max, max));
        }
 
        beginTest ("Non-identical integers are never equal");
        {
            expect (! approximatelyEqual ( 0,  1));
            expect (! approximatelyEqual ( 0, -1));
 
            expect (! approximatelyEqual ( 1,  2));
            expect (! approximatelyEqual (-1, -2));
 
            using limits = std::numeric_limits<int>;
            constexpr auto min = limits::min();
            constexpr auto max = limits::max();
 
            expect (! approximatelyEqual (min, min + 1));
            expect (! approximatelyEqual (max, max - 1));
        }
 
        beginTest ("Zero is equal regardless of the sign");
        {
            expect (approximatelyEqual ( 0, -0));
            expect (approximatelyEqual (-0,  0));
        }
    }
};
 
template <typename T>
class IsFiniteTests final : public UnitTest
{
public:
    IsFiniteTests()
        : UnitTest { getTemplatedMathsFunctionUnitTestName<T> ("juce_isfinite"), UnitTestCategories::maths }
    {}
 
    void runTest() final
    {
        using limits = std::numeric_limits<T>;
 
        constexpr auto zero = T{};
        constexpr auto one = (T) 1;
        constexpr auto max = limits::max();
        constexpr auto inf = limits::infinity();
        constexpr auto nan = limits::quiet_NaN();
 
        beginTest ("Zero is finite");
        {
            expect (juce_isfinite (zero));
            expect (juce_isfinite (-zero));
        }
 
        beginTest ("Subnormals are finite");
        {
            expect (juce_isfinite (nextFloatUp (zero)));
            expect (juce_isfinite (nextFloatDown (zero)));
        }
 
        beginTest ("One is finite");
        {
            expect (juce_isfinite (one));
            expect (juce_isfinite (-one));
        }
 
        beginTest ("Max is finite");
        {
            expect (juce_isfinite (max));
            expect (juce_isfinite (-max));
        }
 
        beginTest ("Infinity is not finite");
        {
            expect (! juce_isfinite (inf));
            expect (! juce_isfinite (-inf));
        }
 
        beginTest ("NaN is not finite");
        {
            expect (! juce_isfinite (nan));
            expect (! juce_isfinite (-nan));
            expect (! juce_isfinite (std::sqrt ((T) -1)));
            expect (! juce_isfinite (inf * zero));
        }
    }
};
 
template <typename T>
class NextFloatTests final : public UnitTest
{
public:
    NextFloatTests()
        : UnitTest { getTemplatedMathsFunctionUnitTestName<T> ("nextFloat"), UnitTestCategories::maths }
    {}
 
    void runTest() final
    {
        using limits = std::numeric_limits<T>;
 
        constexpr auto zero = T{};
        constexpr auto one = T (1);
        constexpr auto min = limits::min();
        constexpr auto epsilon = limits::epsilon();
 
        beginTest ("nextFloat from zero is subnormal");
        {
            expect (juce_isfinite (nextFloatUp (zero)));
            expect (! exactlyEqual (zero, nextFloatUp (zero)));
            expect (! std::isnormal (nextFloatUp (zero)));
 
            expect (juce_isfinite (nextFloatDown (zero)));
            expect (! exactlyEqual (zero, nextFloatDown (zero)));
            expect (! std::isnormal (nextFloatDown (zero)));
        }
 
        beginTest ("nextFloat from min, towards zero, is subnormal");
        {
            expect (std::isnormal (min));
            expect (std::isnormal (-min));
            expect (! std::isnormal (nextFloatDown (min)));
            expect (! std::isnormal (nextFloatUp (-min)));
        }
 
        beginTest ("nextFloat from one matches epsilon");
        {
            expect (! exactlyEqual (one,           nextFloatUp (one)));
            expect (  exactlyEqual (one + epsilon, nextFloatUp (one)));
 
            expect (! exactlyEqual (-one,           nextFloatDown (-one)));
            expect (  exactlyEqual (-one - epsilon, nextFloatDown (-one)));
        }
    }
};
 
template <typename Type>
struct MathsFloatingPointFunctionsTests
{
    IsFiniteTests<Type> isFiniteTests;
    NextFloatTests<Type> nextFloatTests;
    ApproximatelyEqualTests<Type> approximatelyEqualTests;
};
 
template<>
struct MathsFloatingPointFunctionsTests<int>
{
    ApproximatelyEqualTests<int> approximatelyEqualTests;
};
 
struct MathsFunctionsTests
{
    MathsFloatingPointFunctionsTests<int> intFunctionTests;
    MathsFloatingPointFunctionsTests<float> floatFunctionTests;
    MathsFloatingPointFunctionsTests<double> doubleFunctionTests;
    MathsFloatingPointFunctionsTests<long double> longDoubleFunctionTests;
};
 
static MathsFunctionsTests mathsFunctionsTests;
 
} // namespace juce