Merge branch 'master' into chiphogg/prime-wheel
This commit is contained in:
Chip Hogg committed
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@@ -65,25 +65,29 @@ void check_same_type_and_value(T actual, U expected)
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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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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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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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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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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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@@ -95,17 +99,20 @@ TEST_CASE("base_power")
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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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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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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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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) == as_magnitude<1>()); };
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check_product_with_inverse_is_identity(as_magnitude<3>());
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@@ -113,7 +120,8 @@ TEST_CASE("base_power")
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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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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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@@ -122,7 +130,8 @@ TEST_CASE("base_power")
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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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SECTION("Performs prime factorization when denominator is 1")
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{
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CHECK(as_magnitude<1>() == magnitude<>{});
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CHECK(as_magnitude<2>() == magnitude<base_power{2}>{});
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CHECK(as_magnitude<3>() == magnitude<base_power{3}>{});
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@@ -131,17 +140,17 @@ TEST_CASE("make_ratio performs prime factorization correctly")
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CHECK(as_magnitude<792>() == magnitude<base_power{2, 3}, base_power{3, 2}, base_power{11}>{});
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}
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SECTION ("Supports fractions") {
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CHECK(as_magnitude<ratio{5, 8}>() == magnitude<base_power{2, -3}, base_power{5}>{});
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}
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SECTION("Supports fractions") { CHECK(as_magnitude<ratio{5, 8}>() == magnitude<base_power{2, -3}, base_power{5}>{}); }
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SECTION ("Supports nonzero exp") {
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SECTION("Supports nonzero exp")
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{
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constexpr ratio r{3, 1, 2};
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REQUIRE(r.exp == 2);
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CHECK(as_magnitude<r>() == as_magnitude<300>());
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}
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SECTION ("Can handle prime factor which would be large enough to overflow int") {
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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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as_magnitude<ratio(16'605'390'666'050, 10'000'000'000'000)>();
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@@ -168,7 +177,8 @@ TEST_CASE("make_ratio performs prime factorization correctly")
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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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SECTION("Positive integer powers of integer bases give integer values")
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{
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constexpr auto mag_412 = as_magnitude<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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@@ -176,20 +186,23 @@ TEST_CASE("magnitude converts to numerical value")
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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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SECTION("Negative integer powers of integer bases compute correct values")
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{
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constexpr auto mag_0p125 = as_magnitude<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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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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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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@@ -203,7 +216,8 @@ TEST_CASE("magnitude converts to numerical value")
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}
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}
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SECTION ("Impossible requests are prevented at compile time") {
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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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@@ -228,18 +242,21 @@ TEST_CASE("magnitude converts to numerical value")
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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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SECTION("Equivalent ratios are equal")
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{
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CHECK(as_magnitude<1>() == as_magnitude<1>());
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CHECK(as_magnitude<3>() == as_magnitude<3>());
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CHECK(as_magnitude<ratio{3, 4}>() == as_magnitude<ratio{9, 12}>());
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}
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SECTION ("Different ratios are unequal") {
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SECTION("Different ratios are unequal")
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{
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CHECK(as_magnitude<3>() != as_magnitude<5>());
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CHECK(as_magnitude<3>() != as_magnitude<ratio{3, 2}>());
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}
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SECTION ("Supports constexpr") {
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SECTION("Supports constexpr")
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{
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constexpr auto eq = (as_magnitude<ratio{4, 5}>() == as_magnitude<ratio{4, 3}>());
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CHECK(!eq);
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}
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@@ -247,20 +264,24 @@ TEST_CASE("Equality works for magnitudes")
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TEST_CASE("Multiplication works for magnitudes")
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{
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SECTION ("Reciprocals reduce to null magnitude") {
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SECTION("Reciprocals reduce to null magnitude")
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{
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CHECK(as_magnitude<ratio{3, 4}>() * as_magnitude<ratio{4, 3}>() == as_magnitude<1>());
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}
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SECTION ("Products work as expected") {
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SECTION("Products work as expected")
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{
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CHECK(as_magnitude<ratio{4, 5}>() * as_magnitude<ratio{4, 3}>() == as_magnitude<ratio{16, 15}>());
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}
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SECTION ("Products handle pi correctly") {
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SECTION("Products handle pi correctly")
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{
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CHECK(pi_to_the<1>() * as_magnitude<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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SECTION("Supports constexpr")
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{
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constexpr auto p = as_magnitude<ratio{4, 5}>() * as_magnitude<ratio{4, 3}>();
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CHECK(p == as_magnitude<ratio{16, 15}>());
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}
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@@ -268,16 +289,19 @@ TEST_CASE("Multiplication works for magnitudes")
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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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SECTION("Dividing anything by itself reduces to null magnitude")
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{
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CHECK(as_magnitude<ratio{3, 4}>() / as_magnitude<ratio{3, 4}>() == as_magnitude<1>());
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CHECK(as_magnitude<15>() / as_magnitude<15>() == as_magnitude<1>());
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}
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SECTION ("Quotients work as expected") {
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SECTION("Quotients work as expected")
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{
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CHECK(as_magnitude<ratio{4, 5}>() / as_magnitude<ratio{4, 3}>() == as_magnitude<ratio{3, 5}>());
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}
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SECTION ("Supports constexpr") {
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SECTION("Supports constexpr")
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{
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constexpr auto q = as_magnitude<ratio{4, 5}>() / as_magnitude<ratio{4, 3}>();
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CHECK(q == as_magnitude<ratio{3, 5}>());
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}
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@@ -285,28 +309,32 @@ TEST_CASE("Division works for magnitudes")
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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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SECTION("Anything to the 0 is 1")
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{
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CHECK(pow<0>(as_magnitude<1>()) == as_magnitude<1>());
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CHECK(pow<0>(as_magnitude<123>()) == as_magnitude<1>());
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CHECK(pow<0>(as_magnitude<ratio{3, 4}>()) == as_magnitude<1>());
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CHECK(pow<0>(pi_to_the<ratio{-1, 2}>()) == as_magnitude<1>());
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}
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SECTION ("Anything to the 1 is itself") {
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SECTION("Anything to the 1 is itself")
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{
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CHECK(pow<1>(as_magnitude<1>()) == as_magnitude<1>());
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CHECK(pow<1>(as_magnitude<123>()) == as_magnitude<123>());
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CHECK(pow<1>(as_magnitude<ratio{3, 4}>()) == as_magnitude<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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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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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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@@ -319,7 +347,8 @@ TEST_CASE("can distinguish integral, rational, and irrational magnitudes")
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check_rational_and_integral(as_magnitude<ratio{1, 1}>());
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}
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SECTION ("Fractional magnitudes are rational, but not integral") {
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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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@@ -334,7 +363,8 @@ TEST_CASE("can distinguish integral, rational, and irrational magnitudes")
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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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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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@@ -343,7 +373,8 @@ TEST_CASE("int_power computes integer powers")
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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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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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@@ -352,13 +383,15 @@ TEST_CASE("int_power computes integer powers")
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TEST_CASE("Prime helper functions")
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{
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SECTION ("multiplicity") {
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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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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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@@ -367,11 +400,10 @@ TEST_CASE("Prime helper functions")
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TEST_CASE("Prime factorization")
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{
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SECTION ("1 factors into the null magnitude") {
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CHECK(prime_factorization_v<1> == magnitude<>{});
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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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SECTION ("Prime numbers factor into themselves") {
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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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@@ -381,24 +413,25 @@ TEST_CASE("Prime factorization")
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CHECK(prime_factorization_v<41> == magnitude<base_power{41}>{});
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}
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SECTION ("Prime factorization finds factors and multiplicities") {
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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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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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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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SECTION ("1 is not prime") {
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CHECK(!is_prime(1));
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}
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SECTION("1 is not prime") { CHECK(!is_prime(1)); }
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SECTION ("Discriminates between primes and non-primes") {
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SECTION("Discriminates between primes and non-primes")
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{
|
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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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@@ -414,7 +447,8 @@ TEST_CASE("is_prime detects primes")
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TEST_CASE("is_valid_base_power")
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{
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SECTION ("0 power is invalid") {
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SECTION("0 power is invalid")
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{
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REQUIRE(is_valid_base_power(base_power{2}));
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CHECK(!is_valid_base_power(base_power{2, 0}));
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@@ -425,7 +459,8 @@ TEST_CASE("is_valid_base_power")
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CHECK(!is_valid_base_power(base_power<pi_base>{0}));
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}
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SECTION ("non-prime integers are invalid") {
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SECTION("non-prime integers are invalid")
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{
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CHECK(!is_valid_base_power(base_power{-8}));
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CHECK(!is_valid_base_power(base_power{0}));
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CHECK(!is_valid_base_power(base_power{1}));
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@@ -436,7 +471,8 @@ TEST_CASE("is_valid_base_power")
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CHECK(!is_valid_base_power(base_power{4}));
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}
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||||
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SECTION ("non-positive floating point bases are invalid") {
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SECTION("non-positive floating point bases are invalid")
|
||||
{
|
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CHECK(!is_valid_base_power(base_power<invalid_zero_base>{}));
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CHECK(!is_valid_base_power(base_power<invalid_negative_base>{}));
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}
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@@ -448,18 +484,21 @@ TEST_CASE("pairwise_all evaluates all pairs")
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const auto all_pairs_return_false = pairwise_all{[](auto, auto) { return false; }};
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const auto all_increasing = pairwise_all{std::less{}};
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||||
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||||
SECTION ("always true for empty tuples") {
|
||||
SECTION("always true for empty tuples")
|
||||
{
|
||||
CHECK(all_pairs_return_true());
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CHECK(all_pairs_return_false());
|
||||
}
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||||
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||||
SECTION ("always true for single-element tuples") {
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||||
SECTION("always true for single-element tuples")
|
||||
{
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||||
CHECK(all_pairs_return_true(1));
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||||
CHECK(all_pairs_return_false(3.14));
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||||
CHECK(all_pairs_return_true('x'));
|
||||
}
|
||||
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||||
SECTION ("true for longer tuples iff true for all neighbouring pairs") {
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SECTION("true for longer tuples iff true for all neighbouring pairs")
|
||||
{
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CHECK(all_increasing(1, 1.5));
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CHECK(all_increasing(1, 1.5, 2));
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||||
|
||||
@@ -473,17 +512,17 @@ TEST_CASE("pairwise_all evaluates all pairs")
|
||||
|
||||
TEST_CASE("strictly_increasing")
|
||||
{
|
||||
SECTION ("Empty input is sorted") {
|
||||
CHECK(strictly_increasing());
|
||||
}
|
||||
SECTION("Empty input is sorted") { CHECK(strictly_increasing()); }
|
||||
|
||||
SECTION ("Single-element input is sorted") {
|
||||
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") {
|
||||
SECTION("Multi-value inputs compare correctly")
|
||||
{
|
||||
CHECK(strictly_increasing(3, 3.14));
|
||||
CHECK(!strictly_increasing(3, 3.0));
|
||||
CHECK(!strictly_increasing(4, 3.0));
|
||||
|
||||
Reference in new issue
Block a user