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mp-units/test/static/unit_magnitude_test.cpp

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// The MIT License (MIT)
//
// Copyright (c) 2018 Mateusz Pusz
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in all
// copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
// SOFTWARE.
#ifdef MP_UNITS_MODULES
import mp_units;
#else
#include <units/bits/ratio.h>
#include <units/bits/unit_magnitude.h>
#include <type_traits>
#endif
using namespace units;
using namespace units::detail;
namespace {
// A set of non-standard bases for testing purposes.
// struct noninteger_base {
// static constexpr long double value = 1.234L;
// };
// struct noncanonical_two_base {
// static constexpr long double value = 2.0L;
// };
// struct other_noncanonical_two_base {
// static constexpr long double value = 2.0L;
// };
// struct invalid_zero_base {
// static constexpr long double value = 0.0L;
// };
// struct invalid_negative_base {
// static constexpr long double value = -1.234L;
// };
// template<typename T, typename U>
// void check_same_type_and_value(T actual, U expected)
// {
// CHECK(std::is_same_v<T, U>);
// CHECK(actual == expected);
// }
// template<ratio R>
// void check_ratio_round_trip_is_identity()
// {
// constexpr UnitMagnitude auto m = mag<R>();
// constexpr ratio round_trip = ratio{
// get_value<std::intmax_t>(numerator(m)),
// get_value<std::intmax_t>(denominator(m)),
// };
// CHECK(round_trip == R);
// }
inline constexpr struct mag_2_ : unit_magnitude<2> {
} mag_2;
// inline constexpr struct mag_2_other : unit_magnitude<2> {
// } mag_2_other;
// inline constexpr struct mag_3 : unit_magnitude<2> {
// } mag_3;
// concepts verification
static_assert(UnitMagnitude<decltype(mag<2>)>);
static_assert(UnitMagnitude<mag_2_>);
// is_named_magnitude
static_assert(!is_named_magnitude<decltype(mag<2>)>);
static_assert(is_named_magnitude<mag_2_>);
// power_v
template<template<auto, int, int...> typename P>
concept invalid_power_v = requires {
requires !requires { typename P<123, 0>; };
requires !requires { typename P<123, 0, 2>; };
requires !requires { typename P<123, 1, 0>; };
requires !requires { typename P<123, 0, 0>; };
requires !requires { typename P<123, 1>; };
requires !requires { typename P<123, 1, 1>; };
requires !requires { typename P<123, 5, 5>; };
};
static_assert(invalid_power_v<power_v>);
// get_base
// get_base retrieves value for integral base
static_assert(get_base(2) == 2);
static_assert(get_base(power_v<3, 5>{}) == 3);
static_assert(get_base(power_v<5, 1, 3>{}) == 5);
// get_base retrieves value for integral base
static_assert(get_base(2) == 2);
static_assert(get_base(power_v<3, 5>{}) == 3);
static_assert(get_base(power_v<5, 1, 3>{}) == 5);
// get_base retrieves named magnitude for named base
static_assert(std::is_same_v<decltype(get_base(mag_2)), mag_2_>);
static_assert(std::is_same_v<decltype(get_base(power_v<mag_2, 2>{})), mag_2_>);
static_assert(std::is_same_v<decltype(get_base(power_v<mag_2, 5, 8>{})), mag_2_>);
// equality
// static_assert(mag_2 == mag_2);
// static_assert(mag_2 != mag_3);
// static_assert(mag_2 != mag_2_other);
// {
// const auto a = base_power<noncanonical_two_base>{};
// const auto b = base_power{2};
// const auto c = base_power<other_noncanonical_two_base>{};
// REQUIRE(a.get_base() == b.get_base());
// CHECK(a != b);
// REQUIRE(a.get_base() == c.get_base());
// CHECK(a != c);
// }
// SECTION("same-type values not equal if bases are different")
// {
// CHECK(base_power{2} != base_power{3});
// CHECK(base_power{2, ratio{5, 4}} != base_power{3, ratio{5, 4}});
// }
// SECTION("same-type, same-base values not equal if powers are different")
// {
// CHECK(base_power{2} != base_power{2, 2});
// CHECK(base_power<pi_base>{} != base_power<pi_base>{ratio{1, 3}});
// }
// SECTION("product with inverse equals identity")
// {
// auto check_product_with_inverse_is_identity = [](auto x) { CHECK(x * pow<-1>(x) == mag<1>()); };
// check_product_with_inverse_is_identity(mag<3>());
// check_product_with_inverse_is_identity(mag_ratio<4, 17>());
// check_product_with_inverse_is_identity(pi_to_the<ratio{-22, 7}>());
// }
// SECTION("pow() multiplies exponent")
// {
// CHECK(pow(base_power{2}, 0) == base_power{2, 0});
// CHECK(pow(base_power{2, 3}, ratio{-1, 2}) == base_power{2, ratio{-3, 2}});
// CHECK(pow(base_power<pi_base>{ratio{3, 2}}, ratio{1, 3}) == base_power<pi_base>{ratio{1, 2}});
// }
// TEST_CASE("make_ratio performs prime factorization correctly")
// {
// SECTION("Performs prime factorization when denominator is 1")
// {
// CHECK(mag<1>() == unit_magnitude<>{});
// CHECK(mag<2>() == unit_magnitude<base_power{2}>{});
// CHECK(mag<3>() == unit_magnitude<base_power{3}>{});
// CHECK(mag<4>() == unit_magnitude<base_power{2, 2}>{});
// CHECK(mag<792>() == unit_magnitude<base_power{2, 3}, base_power{3, 2}, base_power{11}>{});
// }
// SECTION("Supports fractions") { CHECK(mag_ratio<5, 8>() == unit_magnitude<base_power{2, -3}, base_power{5}>{}); }
// SECTION("Can handle prime factor which would be large enough to overflow int")
// {
// // This was taken from a case which failed when we used `int` for our base to store prime numbers.
// // The failure was due to a prime factor which is larger than 2^31.
// mag_ratio<16'605'390'666'050, 10'000'000'000'000>();
// }
// TEST_CASE("unit_magnitude converts to numerical value")
// {
// SECTION("Positive integer powers of integer bases give integer values")
// {
// constexpr auto mag_412 = mag<412>();
// check_same_type_and_value(get_value<int>(mag_412), 412);
// check_same_type_and_value(get_value<std::size_t>(mag_412), std::size_t{412});
// check_same_type_and_value(get_value<float>(mag_412), 412.0f);
// check_same_type_and_value(get_value<double>(mag_412), 412.0);
// }
// SECTION("Negative integer powers of integer bases compute correct values")
// {
// constexpr auto mag_0p125 = mag_ratio<1, 8>();
// check_same_type_and_value(get_value<float>(mag_0p125), 0.125f);
// check_same_type_and_value(get_value<double>(mag_0p125), 0.125);
// }
// SECTION("pi to the 1 supplies correct values")
// {
// check_same_type_and_value(get_value<float>(mag<π>), std::numbers::pi_v<float>);
// check_same_type_and_value(get_value<double>(mag<π>), std::numbers::pi_v<double>);
// check_same_type_and_value(get_value<long double>(mag<π>), std::numbers::pi_v<long double>);
// }
// SECTION("pi to arbitrary power performs computations in most accurate type at compile time")
// {
// if constexpr (sizeof(float) < sizeof(long double)) {
// constexpr auto pi_cubed = pi_to_the<3>();
// auto cube = [](auto x) { return x * x * x; };
// constexpr auto via_float = cube(std::numbers::pi_v<float>);
// constexpr auto via_long_double = static_cast<float>(cube(std::numbers::pi_v<long double>));
// constexpr auto pi_cubed_value = get_value<float>(pi_cubed);
// REQUIRE(pi_cubed_value != via_float);
// CHECK(pi_cubed_value == via_long_double);
// }
// }
// SECTION("Impossible requests are prevented at compile time")
// {
// // Naturally, we cannot actually write a test to verify a compiler error. But any of these can
// // be uncommented if desired to verify that it breaks the build.
// // get_value<int8_t>(mag<412>());
// // Would work for pow<62>:
// // get_value<int64_t>(pow<63>(mag<2>()));
// // Would work for pow<63>:
// // get_value<uint64_t>(pow<64>(mag<2>()));
// get_value<double>(pow<308>(mag<10>())); // Compiles, correctly.
// // get_value<double>(pow<309>(mag<10>()));
// // get_value<double>(pow<3099>(mag<10>()));
// // get_value<double>(pow<3099999>(mag<10>()));
// auto sqrt_2 = pow<ratio{1, 2}>(mag<2>());
// CHECK(!is_integral(sqrt_2));
// // get_value<int>(sqrt_2);
// }
// }
// TEST_CASE("Equality works for magnitudes")
// {
// SECTION("Equivalent ratios are equal")
// {
// CHECK(mag<1>() == mag<1>());
// CHECK(mag<3>() == mag<3>());
// CHECK(mag_ratio<3, 4>() == mag_ratio<9, 12>());
// }
// SECTION("Different ratios are unequal")
// {
// CHECK(mag<3>() != mag<5>());
// CHECK(mag<3>() != mag_ratio<3, 2>());
// }
// SECTION("Supports constexpr")
// {
// constexpr auto eq = (mag_ratio<4, 5>() == mag_ratio<4, 3>());
// CHECK(!eq);
// }
// }
// TEST_CASE("Multiplication works for magnitudes")
// {
// SECTION("Reciprocals reduce to null unit_magnitude") { CHECK(mag_ratio<3, 4>() * mag_ratio<4, 3>() == mag<1>()); }
// SECTION("Products work as expected") { CHECK(mag_ratio<4, 5>() * mag_ratio<4, 3>() == mag_ratio<16, 15>()); }
// SECTION("Products handle pi correctly")
// {
// CHECK(pi_to_the<1>() * mag_ratio<2, 3>() * pi_to_the<ratio{-1, 2}>() ==
// unit_magnitude<base_power{2}, base_power{3, -1}, base_power<pi_base>{ratio{1, 2}}>{});
// }
// SECTION("Supports constexpr")
// {
// constexpr auto p = mag_ratio<4, 5>() * mag_ratio<4, 3>();
// CHECK(p == mag_ratio<16, 15>());
// }
// }
// TEST_CASE("Common Magnitude")
// {
// SECTION("Identity for identical magnitudes")
// {
// CHECK(common_magnitude(mag<1>(), mag<1>()) == mag<1>());
// CHECK(common_magnitude(mag<15>(), mag<15>()) == mag<15>());
// CHECK(common_magnitude(pi_to_the<ratio{3, 4}>(), pi_to_the<ratio{3, 4}>()) == pi_to_the<ratio{3, 4}>());
// }
// SECTION("Greatest Common Factor for integers")
// {
// CHECK(common_magnitude(mag<24>(), mag<36>()) == mag<12>());
// CHECK(common_magnitude(mag<24>(), mag<37>()) == mag<1>());
// }
// SECTION("Handles fractions")
// {
// CHECK(common_magnitude(mag_ratio<3, 8>(), mag_ratio<5, 6>()) == mag_ratio<1, 24>());
// }
// }
// TEST_CASE("Division works for magnitudes")
// {
// SECTION("Dividing anything by itself reduces to null unit_magnitude")
// {
// CHECK(mag_ratio<3, 4>() / mag_ratio<3, 4>() == mag<1>());
// CHECK(mag<15>() / mag<15>() == mag<1>());
// }
// SECTION("Quotients work as expected") { CHECK(mag_ratio<4, 5>() / mag_ratio<4, 3>() == mag_ratio<3, 5>()); }
// SECTION("Supports constexpr")
// {
// constexpr auto q = mag_ratio<4, 5>() / mag_ratio<4, 3>();
// CHECK(q == mag_ratio<3, 5>());
// }
// }
// TEST_CASE("Can raise Magnitudes to rational powers")
// {
// SECTION("Anything to the 0 is 1")
// {
// CHECK(pow<0>(mag<1>()) == mag<1>());
// CHECK(pow<0>(mag<123>()) == mag<1>());
// CHECK(pow<0>(mag_ratio<3, 4>()) == mag<1>());
// CHECK(pow<0>(pi_to_the<ratio{-1, 2}>()) == mag<1>());
// }
// SECTION("Anything to the 1 is itself")
// {
// CHECK(pow<1>(mag<1>()) == mag<1>());
// CHECK(pow<1>(mag<123>()) == mag<123>());
// CHECK(pow<1>(mag_ratio<3, 4>()) == mag_ratio<3, 4>());
// CHECK(pow<1>(pi_to_the<ratio{-1, 2}>()) == pi_to_the<ratio{-1, 2}>());
// }
// SECTION("Can raise to arbitrary rational power")
// {
// CHECK(pow<ratio{-8, 3}>(pi_to_the<ratio{-1, 2}>()) == pi_to_the<ratio{4, 3}>());
// }
// }
// TEST_CASE("can distinguish integral, rational, and irrational magnitudes")
// {
// SECTION("Integer magnitudes are integral and rational")
// {
// auto check_rational_and_integral = [](UnitMagnitude auto m) {
// CHECK(is_integral(m));
// CHECK(is_rational(m));
// };
// check_rational_and_integral(unit_magnitude<>{});
// check_rational_and_integral(mag<1>());
// check_rational_and_integral(mag<3>());
// check_rational_and_integral(mag<8>());
// check_rational_and_integral(mag<412>());
// check_rational_and_integral(mag_ratio<1, 1>());
// }
// SECTION("Fractional magnitudes are rational, but not integral")
// {
// auto check_rational_but_not_integral = [](UnitMagnitude auto m) {
// CHECK(!is_integral(m));
// CHECK(is_rational(m));
// };
// check_rational_but_not_integral(mag_ratio<1, 2>());
// check_rational_but_not_integral(mag_ratio<5, 8>());
// }
// }
// TEST_CASE("Constructing ratio from rational unit_magnitude")
// {
// SECTION("Round trip is identity")
// {
// // Note that not every Magnitude can be represented as a ratio. However, if we _start_ with a
// // ratio, we must guarantee to recover the same ratio in a round trip.
// check_ratio_round_trip_is_identity<1>();
// check_ratio_round_trip_is_identity<9>();
// check_ratio_round_trip_is_identity<ratio{5, 8}>();
// }
// SECTION("Rational magnitude converts to ratio")
// {
// constexpr ratio r = as_ratio(mag_ratio<22, 7>());
// CHECK(r == ratio{22, 7});
// }
// SECTION("Irrational magnitude does not convert to ratio")
// {
// // The following code should not compile.
// // as_ratio(pow<ratio{1, 2}>(mag<2>()));
// // The following code should not compile.
// // as_ratio(mag<180>() / pi_to_the<1>());
// }
// }
// ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
// // Detail function tests below.
// TEST_CASE("int_power computes integer powers")
// {
// SECTION("handles floating point")
// {
// check_same_type_and_value(int_power(0.123L, 0), 1.0L);
// check_same_type_and_value(int_power(0.246f, 1), 0.246f);
// check_same_type_and_value(int_power(0.5f, 3), 0.125f);
// check_same_type_and_value(int_power(2.5, 4), 39.0625);
// CHECK(std::is_same_v<long double, decltype(compute_base_power<double>(base_power{10, 20}))>);
// }
// SECTION("handles integral")
// {
// check_same_type_and_value(int_power(8, 0), 1);
// check_same_type_and_value(int_power(9L, 1), 9L);
// check_same_type_and_value(int_power(2, 10), 1024);
// }
// }
// TEST_CASE("integer_part picks out integer part of single-basis magnitude")
// {
// SECTION("integer_part of non-integer base is identity magnitude")
// {
// CHECK(integer_part(pi_to_the<1>()) == unit_magnitude<>{});
// CHECK(integer_part(pi_to_the<-8>()) == unit_magnitude<>{});
// CHECK(integer_part(pi_to_the<ratio{3, 4}>()) == unit_magnitude<>{});
// }
// SECTION("integer_part of integer base to negative power is identity magnitude")
// {
// CHECK(integer_part(unit_magnitude<base_power{2, -8}>{}) == unit_magnitude<>{});
// CHECK(integer_part(unit_magnitude<base_power{11, -1}>{}) == unit_magnitude<>{});
// }
// SECTION("integer_part of integer base to fractional power is identity magnitude")
// {
// CHECK(integer_part(unit_magnitude<base_power{2, ratio{1, 2}}>{}) == unit_magnitude<>{});
// }
// SECTION("integer_part of integer base to power at least one takes integer part")
// {
// CHECK(integer_part(unit_magnitude<base_power{2, 1}>{}) == unit_magnitude<base_power{2, 1}>{});
// CHECK(integer_part(unit_magnitude<base_power{2, ratio{19, 10}}>{}) == unit_magnitude<base_power{2, 1}>{});
// CHECK(integer_part(unit_magnitude<base_power{11, ratio{97, 9}}>{}) == unit_magnitude<base_power{11, 10}>{});
// }
// }
// TEST_CASE("Prime helper functions")
// {
// SECTION("multiplicity")
// {
// CHECK(multiplicity(2, 8) == 3);
// CHECK(multiplicity(2, 1024) == 10);
// CHECK(multiplicity(11, 6655) == 3);
// }
// SECTION("remove_power()")
// {
// CHECK(remove_power(17, 0, 5) == 5);
// CHECK(remove_power(2, 3, 24) == 3);
// CHECK(remove_power(11, 3, 6655) == 5);
// }
// }
// TEST_CASE("Prime factorization")
// {
// SECTION("1 factors into the null unit_magnitude") { CHECK(prime_factorization_v<1> == unit_magnitude<>{}); }
// SECTION("Prime numbers factor into themselves")
// {
// CHECK(prime_factorization_v<2> == unit_magnitude<base_power{2}>{});
// CHECK(prime_factorization_v<3> == unit_magnitude<base_power{3}>{});
// CHECK(prime_factorization_v<5> == unit_magnitude<base_power{5}>{});
// CHECK(prime_factorization_v<7> == unit_magnitude<base_power{7}>{});
// CHECK(prime_factorization_v<11> == unit_magnitude<base_power{11}>{});
// CHECK(prime_factorization_v<41> == unit_magnitude<base_power{41}>{});
// }
// SECTION("Prime factorization finds factors and multiplicities")
// {
// CHECK(prime_factorization_v<792> == unit_magnitude<base_power{2, 3}, base_power{3, 2}, base_power{11}>{});
// }
// }
// TEST_CASE("is_prime detects primes")
// {
// SECTION("Non-positive numbers are not prime")
// {
// CHECK(!is_prime(-1328));
// CHECK(!is_prime(-1));
// CHECK(!is_prime(0));
// }
// SECTION("1 is not prime") { CHECK(!is_prime(1)); }
// SECTION("Discriminates between primes and non-primes")
// {
// CHECK(is_prime(2));
// CHECK(is_prime(3));
// CHECK(!is_prime(4));
// CHECK(is_prime(5));
// CHECK(!is_prime(6));
// CHECK(is_prime(7));
// CHECK(!is_prime(8));
// CHECK(!is_prime(9));
// CHECK(is_prime(7919));
// }
// }
// TEST_CASE("is_valid_base_power")
// {
// SECTION("0 power is invalid")
// {
// REQUIRE(is_valid_base_power(base_power{2}));
// CHECK(!is_valid_base_power(base_power{2, 0}));
// REQUIRE(is_valid_base_power(base_power{41}));
// CHECK(!is_valid_base_power(base_power{41, 0}));
// REQUIRE(is_valid_base_power(base_power<pi_base>{}));
// CHECK(!is_valid_base_power(base_power<pi_base>{0}));
// }
// SECTION("non-prime integers are invalid")
// {
// CHECK(!is_valid_base_power(base_power{-8}));
// CHECK(!is_valid_base_power(base_power{0}));
// CHECK(!is_valid_base_power(base_power{1}));
// CHECK(is_valid_base_power(base_power{2}));
// CHECK(is_valid_base_power(base_power{3}));
// CHECK(!is_valid_base_power(base_power{4}));
// }
// SECTION("non-positive floating point bases are invalid")
// {
// CHECK(!is_valid_base_power(base_power<invalid_zero_base>{}));
// CHECK(!is_valid_base_power(base_power<invalid_negative_base>{}));
// }
// }
// TEST_CASE("pairwise_all evaluates all pairs")
// {
// const auto all_pairs_return_true = pairwise_all{[](auto, auto) { return true; }};
// const auto all_pairs_return_false = pairwise_all{[](auto, auto) { return false; }};
// const auto all_increasing = pairwise_all{std::less{}};
// SECTION("always true for empty tuples")
// {
// CHECK(all_pairs_return_true());
// CHECK(all_pairs_return_false());
// }
// SECTION("always true for single-element tuples")
// {
// CHECK(all_pairs_return_true(1));
// CHECK(all_pairs_return_false(3.14));
// CHECK(all_pairs_return_true('x'));
// }
// SECTION("true for longer tuples iff true for all neighbouring pairs")
// {
// CHECK(all_increasing(1, 1.5));
// CHECK(all_increasing(1, 1.5, 2));
// CHECK(!all_increasing(1, 2.0, 2));
// CHECK(!all_increasing(1, 2.5, 2));
// CHECK(all_pairs_return_true('c', 1, 8.9, 42u));
// CHECK(!all_pairs_return_false('c', 1, 8.9, 42u));
// }
// }
// TEST_CASE("strictly_increasing")
// {
// SECTION("Empty input is sorted") { CHECK(strictly_increasing()); }
// SECTION("Single-element input is sorted")
// {
// CHECK(strictly_increasing(3));
// CHECK(strictly_increasing(15.42));
// CHECK(strictly_increasing('c'));
// }
// SECTION("Multi-value inputs compare correctly")
// {
// CHECK(strictly_increasing(3, 3.14));
// CHECK(!strictly_increasing(3, 3.0));
// CHECK(!strictly_increasing(4, 3.0));
// }
// }
// TEST_CASE("extract_power_of_10")
// {
// SECTION("Picks out positive powers")
// {
// CHECK(extract_power_of_10(mag<10>()) == 1);
// CHECK(extract_power_of_10(mag<20>()) == 1);
// CHECK(extract_power_of_10(mag<40>()) == 1);
// CHECK(extract_power_of_10(mag<50>()) == 1);
// CHECK(extract_power_of_10(mag<100>()) == 2);
// }
// SECTION("Picks out negative powers")
// {
// constexpr auto ONE = mag<1>();
// CHECK(extract_power_of_10(ONE / mag<10>()) == -1);
// CHECK(extract_power_of_10(ONE / mag<20>()) == -1);
// CHECK(extract_power_of_10(ONE / mag<40>()) == -1);
// CHECK(extract_power_of_10(ONE / mag<50>()) == -1);
// CHECK(extract_power_of_10(ONE / mag<100>()) == -2);
// }
// SECTION("Zero if signs disagree") { CHECK(extract_power_of_10(mag<2>() / mag<5>()) == 0); }
// SECTION("Handles rational powers") { CHECK(extract_power_of_10(sqrt(mag<1000>())) == 1); }
// }
} // namespace
// mag<2> * Constant<2> * Constant<3> * Constant<2> * mag<3> * mag<2> * mag<2> * Constant<2> -> pow<Constant<2>, 3>,
// pow<mag<2>, 3>, Constant<3>, mag<3>
// mag_A * mag<2> * magA
// mag<2> * mag_A * magAA * magA -> the same value different name
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