forked from mpusz/mp-units
624 lines
20 KiB
C++
624 lines
20 KiB
C++
// The MIT License (MIT)
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//
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// Copyright (c) 2018 Mateusz Pusz
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//
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// Permission is hereby granted, free of charge, to any person obtaining a copy
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// of this software and associated documentation files (the "Software"), to deal
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// in the Software without restriction, including without limitation the rights
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// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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// copies of the Software, and to permit persons to whom the Software is
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// furnished to do so, subject to the following conditions:
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//
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// The above copyright notice and this permission notice shall be included in all
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// copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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// SOFTWARE.
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#include <catch2/catch.hpp>
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#include <units/magnitude.h>
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#include <units/ratio.h>
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#include <type_traits>
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using namespace units;
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using namespace units::detail;
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template<>
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inline constexpr std::optional<std::intmax_t> units::known_first_factor<9223372036854775783> = 9223372036854775783;
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namespace {
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// A set of non-standard bases for testing purposes.
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struct noninteger_base {
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static constexpr long double value = 1.234L;
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};
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struct noncanonical_two_base {
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static constexpr long double value = 2.0L;
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};
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struct other_noncanonical_two_base {
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static constexpr long double value = 2.0L;
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};
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struct invalid_zero_base {
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static constexpr long double value = 0.0L;
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};
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struct invalid_negative_base {
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static constexpr long double value = -1.234L;
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};
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template<ratio Power>
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constexpr auto pi_to_the()
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{
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return magnitude<base_power<pi_base>{Power}>{};
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}
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template<typename T, typename U>
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void check_same_type_and_value(T actual, U expected)
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{
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CHECK(std::is_same_v<T, U>);
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CHECK(actual == expected);
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}
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template<ratio R>
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void check_ratio_round_trip_is_identity()
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{
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constexpr Magnitude auto m = mag<R>();
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constexpr ratio round_trip = ratio{
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get_value<std::intmax_t>(numerator(m)),
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get_value<std::intmax_t>(denominator(m)),
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};
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CHECK(round_trip == R);
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}
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TEST_CASE("base_power")
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{
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SECTION("base rep deducible for integral base")
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{
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CHECK(base_power{2} == base_power<std::intmax_t>{2, ratio{1}});
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CHECK(base_power{2, 3} == base_power<std::intmax_t>{2, ratio{3}});
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CHECK(base_power{2, ratio{3, 4}} == base_power<std::intmax_t>{2, ratio{3, 4}});
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}
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SECTION("get_base retrieves base for integral base")
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{
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CHECK(base_power{2}.get_base() == 2);
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CHECK(base_power{3, 5}.get_base() == 3);
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CHECK(base_power{5, ratio{1, 3}}.get_base() == 5);
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}
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SECTION("get_base retrieves member value for non-integer base")
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{
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CHECK(base_power<noninteger_base>{}.get_base() == 1.234L);
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CHECK(base_power<noninteger_base>{2}.get_base() == 1.234L);
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CHECK(base_power<noninteger_base>{ratio{5, 8}}.get_base() == 1.234L);
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}
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SECTION("same-base values not equal if types are different")
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{
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const auto a = base_power<noncanonical_two_base>{};
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const auto b = base_power{2};
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const auto c = base_power<other_noncanonical_two_base>{};
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REQUIRE(a.get_base() == b.get_base());
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CHECK(a != b);
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REQUIRE(a.get_base() == c.get_base());
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CHECK(a != c);
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}
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SECTION("same-type values not equal if bases are different")
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{
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CHECK(base_power{2} != base_power{3});
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CHECK(base_power{2, ratio{5, 4}} != base_power{3, ratio{5, 4}});
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}
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SECTION("same-type, same-base values not equal if powers are different")
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{
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CHECK(base_power{2} != base_power{2, 2});
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CHECK(base_power<pi_base>{} != base_power<pi_base>{ratio{1, 3}});
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}
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SECTION("product with inverse equals identity")
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{
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auto check_product_with_inverse_is_identity = [](auto x) { CHECK(x * pow<-1>(x) == mag<1>()); };
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check_product_with_inverse_is_identity(mag<3>());
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check_product_with_inverse_is_identity(mag<ratio{4, 17}>());
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check_product_with_inverse_is_identity(pi_to_the<ratio{-22, 7}>());
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}
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SECTION("pow() multiplies exponent")
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{
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CHECK(pow(base_power{2}, 0) == base_power{2, 0});
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CHECK(pow(base_power{2, 3}, ratio{-1, 2}) == base_power{2, ratio{-3, 2}});
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CHECK(pow(base_power<pi_base>{ratio{3, 2}}, ratio{1, 3}) == base_power<pi_base>{ratio{1, 2}});
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}
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}
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TEST_CASE("make_ratio performs prime factorization correctly")
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{
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SECTION("Performs prime factorization when denominator is 1")
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{
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CHECK(mag<1>() == magnitude<>{});
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CHECK(mag<2>() == magnitude<base_power{2}>{});
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CHECK(mag<3>() == magnitude<base_power{3}>{});
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CHECK(mag<4>() == magnitude<base_power{2, 2}>{});
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CHECK(mag<792>() == magnitude<base_power{2, 3}, base_power{3, 2}, base_power{11}>{});
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}
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SECTION("Supports fractions") { CHECK(mag<ratio{5, 8}>() == magnitude<base_power{2, -3}, base_power{5}>{}); }
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SECTION("Can handle prime factor which would be large enough to overflow int")
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{
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// This was taken from a case which failed when we used `int` for our base to store prime numbers.
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// The failure was due to a prime factor which is larger than 2^31.
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mag<ratio(16'605'390'666'050, 10'000'000'000'000)>();
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}
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SECTION("Can bypass computing primes by providing known_first_factor<N>")
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{
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// Sometimes, even wheel factorization isn't enough to handle the compilers' limits on constexpr steps and/or
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// iterations. To work around these cases, we can explicitly provide the correct answer directly to the compiler.
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//
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// In this case, we test that we can represent the largest prime that fits in a signed 64-bit int. The reason this
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// test can pass is that we have provided the answer, by specializing the `known_first_factor` variable template
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// above in this file.
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mag<9'223'372'036'854'775'783>();
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}
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}
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TEST_CASE("magnitude converts to numerical value")
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{
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SECTION("Positive integer powers of integer bases give integer values")
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{
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constexpr auto mag_412 = mag<412>();
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check_same_type_and_value(get_value<int>(mag_412), 412);
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check_same_type_and_value(get_value<std::size_t>(mag_412), std::size_t{412});
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check_same_type_and_value(get_value<float>(mag_412), 412.0f);
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check_same_type_and_value(get_value<double>(mag_412), 412.0);
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}
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SECTION("Negative integer powers of integer bases compute correct values")
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{
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constexpr auto mag_0p125 = mag<ratio{1, 8}>();
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check_same_type_and_value(get_value<float>(mag_0p125), 0.125f);
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check_same_type_and_value(get_value<double>(mag_0p125), 0.125);
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}
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SECTION("pi to the 1 supplies correct values")
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{
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constexpr auto pi = pi_to_the<1>();
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check_same_type_and_value(get_value<float>(pi), std::numbers::pi_v<float>);
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check_same_type_and_value(get_value<double>(pi), std::numbers::pi_v<double>);
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check_same_type_and_value(get_value<long double>(pi), std::numbers::pi_v<long double>);
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}
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SECTION("pi to arbitrary power performs computations in most accurate type at compile time")
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{
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if constexpr (sizeof(float) < sizeof(long double)) {
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constexpr auto pi_cubed = pi_to_the<3>();
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auto cube = [](auto x) { return x * x * x; };
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constexpr auto via_float = cube(std::numbers::pi_v<float>);
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constexpr auto via_long_double = static_cast<float>(cube(std::numbers::pi_v<long double>));
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constexpr auto pi_cubed_value = get_value<float>(pi_cubed);
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REQUIRE(pi_cubed_value != via_float);
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CHECK(pi_cubed_value == via_long_double);
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}
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}
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SECTION("Impossible requests are prevented at compile time")
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{
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// Naturally, we cannot actually write a test to verify a compiler error. But any of these can
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// be uncommented if desired to verify that it breaks the build.
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// get_value<int8_t>(mag<412>());
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// Would work for pow<62>:
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// get_value<int64_t>(pow<63>(mag<2>()));
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// Would work for pow<63>:
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// get_value<uint64_t>(pow<64>(mag<2>()));
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get_value<double>(pow<308>(mag<10>())); // Compiles, correctly.
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// get_value<double>(pow<309>(mag<10>()));
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// get_value<double>(pow<3099>(mag<10>()));
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// get_value<double>(pow<3099999>(mag<10>()));
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auto sqrt_2 = pow<ratio{1, 2}>(mag<2>());
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CHECK(!is_integral(sqrt_2));
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// get_value<int>(sqrt_2);
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}
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}
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TEST_CASE("Equality works for magnitudes")
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{
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SECTION("Equivalent ratios are equal")
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{
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CHECK(mag<1>() == mag<1>());
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CHECK(mag<3>() == mag<3>());
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CHECK(mag<ratio{3, 4}>() == mag<ratio{9, 12}>());
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}
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SECTION("Different ratios are unequal")
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{
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CHECK(mag<3>() != mag<5>());
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CHECK(mag<3>() != mag<ratio{3, 2}>());
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}
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SECTION("Supports constexpr")
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{
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constexpr auto eq = (mag<ratio{4, 5}>() == mag<ratio{4, 3}>());
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CHECK(!eq);
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}
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}
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TEST_CASE("Multiplication works for magnitudes")
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{
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SECTION("Reciprocals reduce to null magnitude") { CHECK(mag<ratio{3, 4}>() * mag<ratio{4, 3}>() == mag<1>()); }
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SECTION("Products work as expected") { CHECK(mag<ratio{4, 5}>() * mag<ratio{4, 3}>() == mag<ratio{16, 15}>()); }
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SECTION("Products handle pi correctly")
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{
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CHECK(pi_to_the<1>() * mag<ratio{2, 3}>() * pi_to_the<ratio{-1, 2}>() ==
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magnitude<base_power{2}, base_power{3, -1}, base_power<pi_base>{ratio{1, 2}}>{});
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}
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SECTION("Supports constexpr")
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{
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constexpr auto p = mag<ratio{4, 5}>() * mag<ratio{4, 3}>();
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CHECK(p == mag<ratio{16, 15}>());
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}
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}
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TEST_CASE("Common Magnitude")
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{
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SECTION("Identity for identical magnitudes")
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{
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CHECK(common_magnitude(mag<1>(), mag<1>()) == mag<1>());
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CHECK(common_magnitude(mag<15>(), mag<15>()) == mag<15>());
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CHECK(common_magnitude(pi_to_the<ratio{3, 4}>(), pi_to_the<ratio{3, 4}>()) == pi_to_the<ratio{3, 4}>());
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}
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SECTION("Greatest Common Factor for integers")
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{
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CHECK(common_magnitude(mag<24>(), mag<36>()) == mag<12>());
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CHECK(common_magnitude(mag<24>(), mag<37>()) == mag<1>());
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}
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SECTION("Handles fractions")
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{
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CHECK(common_magnitude(mag<ratio{3, 8}>(), mag<ratio{5, 6}>()) == mag<ratio{1, 24}>());
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}
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}
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TEST_CASE("Division works for magnitudes")
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{
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SECTION("Dividing anything by itself reduces to null magnitude")
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{
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CHECK(mag<ratio{3, 4}>() / mag<ratio{3, 4}>() == mag<1>());
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CHECK(mag<15>() / mag<15>() == mag<1>());
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}
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SECTION("Quotients work as expected") { CHECK(mag<ratio{4, 5}>() / mag<ratio{4, 3}>() == mag<ratio{3, 5}>()); }
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SECTION("Supports constexpr")
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{
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constexpr auto q = mag<ratio{4, 5}>() / mag<ratio{4, 3}>();
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CHECK(q == mag<ratio{3, 5}>());
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}
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}
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TEST_CASE("Can raise Magnitudes to rational powers")
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{
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SECTION("Anything to the 0 is 1")
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{
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CHECK(pow<0>(mag<1>()) == mag<1>());
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CHECK(pow<0>(mag<123>()) == mag<1>());
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CHECK(pow<0>(mag<ratio{3, 4}>()) == mag<1>());
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CHECK(pow<0>(pi_to_the<ratio{-1, 2}>()) == mag<1>());
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}
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SECTION("Anything to the 1 is itself")
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{
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CHECK(pow<1>(mag<1>()) == mag<1>());
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CHECK(pow<1>(mag<123>()) == mag<123>());
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CHECK(pow<1>(mag<ratio{3, 4}>()) == mag<ratio{3, 4}>());
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CHECK(pow<1>(pi_to_the<ratio{-1, 2}>()) == pi_to_the<ratio{-1, 2}>());
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}
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SECTION("Can raise to arbitrary rational power")
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{
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CHECK(pow<ratio{-8, 3}>(pi_to_the<ratio{-1, 2}>()) == pi_to_the<ratio{4, 3}>());
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}
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}
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TEST_CASE("can distinguish integral, rational, and irrational magnitudes")
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{
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SECTION("Integer magnitudes are integral and rational")
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{
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auto check_rational_and_integral = [](Magnitude auto m) {
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CHECK(is_integral(m));
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CHECK(is_rational(m));
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};
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check_rational_and_integral(magnitude<>{});
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check_rational_and_integral(mag<1>());
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check_rational_and_integral(mag<3>());
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check_rational_and_integral(mag<8>());
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check_rational_and_integral(mag<412>());
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check_rational_and_integral(mag<ratio{1, 1}>());
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}
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SECTION("Fractional magnitudes are rational, but not integral")
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{
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auto check_rational_but_not_integral = [](Magnitude auto m) {
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CHECK(!is_integral(m));
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CHECK(is_rational(m));
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};
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check_rational_but_not_integral(mag<ratio{1, 2}>());
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check_rational_but_not_integral(mag<ratio{5, 8}>());
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}
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}
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TEST_CASE("Constructing ratio from rational magnitude")
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{
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SECTION("Round trip is identity")
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{
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// Note that not every Magnitude can be represented as a ratio. However, if we _start_ with a
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// ratio, we must guarantee to recover the same ratio in a round trip.
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check_ratio_round_trip_is_identity<1>();
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check_ratio_round_trip_is_identity<9>();
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check_ratio_round_trip_is_identity<ratio{5, 8}>();
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}
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SECTION("Rational magnitude converts to ratio")
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{
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constexpr ratio r = as_ratio(mag<ratio{22, 7}>());
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CHECK(r == ratio{22, 7});
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}
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SECTION("Irrational magnitude does not convert to ratio")
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{
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// The following code should not compile.
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// as_ratio(pow<ratio{1, 2}>(mag<2>()));
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// The following code should not compile.
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// as_ratio(mag<180>() / pi_to_the<1>());
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}
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}
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////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
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// Detail function tests below.
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TEST_CASE("int_power computes integer powers")
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{
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SECTION("handles floating point")
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{
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check_same_type_and_value(int_power(0.123L, 0), 1.0L);
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check_same_type_and_value(int_power(0.246f, 1), 0.246f);
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check_same_type_and_value(int_power(0.5f, 3), 0.125f);
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check_same_type_and_value(int_power(2.5, 4), 39.0625);
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CHECK(std::is_same_v<long double, decltype(compute_base_power<double>(base_power{10, 20}))>);
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}
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SECTION("handles integral")
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{
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check_same_type_and_value(int_power(8, 0), 1);
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check_same_type_and_value(int_power(9L, 1), 9L);
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check_same_type_and_value(int_power(2, 10), 1024);
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}
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}
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TEST_CASE("integer_part picks out integer part of single-basis magnitude")
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{
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SECTION("integer_part of non-integer base is identity magnitude")
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{
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CHECK(integer_part(pi_to_the<1>()) == magnitude<>{});
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CHECK(integer_part(pi_to_the<-8>()) == magnitude<>{});
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CHECK(integer_part(pi_to_the<ratio{3, 4}>()) == magnitude<>{});
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}
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SECTION("integer_part of integer base to negative power is identity magnitude")
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{
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CHECK(integer_part(magnitude<base_power{2, -8}>{}) == magnitude<>{});
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CHECK(integer_part(magnitude<base_power{11, -1}>{}) == magnitude<>{});
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}
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SECTION("integer_part of integer base to fractional power is identity magnitude")
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{
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CHECK(integer_part(magnitude<base_power{2, ratio{1, 2}}>{}) == magnitude<>{});
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}
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SECTION("integer_part of integer base to power at least one takes integer part")
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{
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CHECK(integer_part(magnitude<base_power{2, 1}>{}) == magnitude<base_power{2, 1}>{});
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CHECK(integer_part(magnitude<base_power{2, ratio{19, 10}}>{}) == magnitude<base_power{2, 1}>{});
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CHECK(integer_part(magnitude<base_power{11, ratio{97, 9}}>{}) == magnitude<base_power{11, 10}>{});
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}
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}
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TEST_CASE("Prime helper functions")
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{
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SECTION("multiplicity")
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{
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CHECK(multiplicity(2, 8) == 3);
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CHECK(multiplicity(2, 1024) == 10);
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CHECK(multiplicity(11, 6655) == 3);
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}
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SECTION("remove_power()")
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{
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CHECK(remove_power(17, 0, 5) == 5);
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CHECK(remove_power(2, 3, 24) == 3);
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CHECK(remove_power(11, 3, 6655) == 5);
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}
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}
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TEST_CASE("Prime factorization")
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{
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SECTION("1 factors into the null magnitude") { CHECK(prime_factorization_v<1> == magnitude<>{}); }
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|
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SECTION("Prime numbers factor into themselves")
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{
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CHECK(prime_factorization_v<2> == magnitude<base_power{2}>{});
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CHECK(prime_factorization_v<3> == magnitude<base_power{3}>{});
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CHECK(prime_factorization_v<5> == magnitude<base_power{5}>{});
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CHECK(prime_factorization_v<7> == magnitude<base_power{7}>{});
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CHECK(prime_factorization_v<11> == magnitude<base_power{11}>{});
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|
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CHECK(prime_factorization_v<41> == magnitude<base_power{41}>{});
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}
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|
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SECTION("Prime factorization finds factors and multiplicities")
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{
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CHECK(prime_factorization_v<792> == magnitude<base_power{2, 3}, base_power{3, 2}, base_power{11}>{});
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}
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}
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|
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TEST_CASE("is_prime detects primes")
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|
{
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|
SECTION("Non-positive numbers are not prime")
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|
{
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CHECK(!is_prime(-1328));
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|
CHECK(!is_prime(-1));
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|
CHECK(!is_prime(0));
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|
}
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|
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SECTION("1 is not prime") { CHECK(!is_prime(1)); }
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|
|
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SECTION("Discriminates between primes and non-primes")
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|
{
|
|
CHECK(is_prime(2));
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|
CHECK(is_prime(3));
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|
CHECK(!is_prime(4));
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|
CHECK(is_prime(5));
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|
CHECK(!is_prime(6));
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|
CHECK(is_prime(7));
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|
CHECK(!is_prime(8));
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|
CHECK(!is_prime(9));
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|
|
|
CHECK(is_prime(7919));
|
|
}
|
|
}
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|
|
|
TEST_CASE("is_valid_base_power")
|
|
{
|
|
SECTION("0 power is invalid")
|
|
{
|
|
REQUIRE(is_valid_base_power(base_power{2}));
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|
CHECK(!is_valid_base_power(base_power{2, 0}));
|
|
|
|
REQUIRE(is_valid_base_power(base_power{41}));
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|
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
|