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Merge pull request #639 from chiphogg/chiphogg/jacobi#509

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Add utilities to make Strong Lucas tests easier
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Mateusz Pusz
2024-11-15 15:57:09 +01:00
committed by GitHub
parent 1581fa59ad 26639dab34
commit c901b73ee5
2 changed files with 120 additions and 0 deletions
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test/static/prime_test.cpp
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@ -122,4 +122,47 @@ static_assert(miller_rabin_probable_prime(2u, 9'007'199'254'740'881u), "Large kn
static_assert(miller_rabin_probable_prime(2u, 18'446'744'073'709'551'557u), "Largest 64-bit prime");
// Jacobi symbols --- a building block for the Strong Lucas probable prime test, needed for Baillie-PSW.
static_assert(jacobi_symbol(1, 1u) == 1, "Jacobi symbol always 1 when 'numerator' is 1");
static_assert(jacobi_symbol(1, 3u) == 1, "Jacobi symbol always 1 when 'numerator' is 1");
static_assert(jacobi_symbol(1, 5u) == 1, "Jacobi symbol always 1 when 'numerator' is 1");
static_assert(jacobi_symbol(1, 987654321u) == 1, "Jacobi symbol always 1 when 'numerator' is 1");
static_assert(jacobi_symbol(3, 1u) == 1, "Jacobi symbol always 1 when 'denominator' is 1");
static_assert(jacobi_symbol(5, 1u) == 1, "Jacobi symbol always 1 when 'denominator' is 1");
static_assert(jacobi_symbol(-1234567890, 1u) == 1, "Jacobi symbol always 1 when 'denominator' is 1");
static_assert(jacobi_symbol(10, 5u) == 0, "Jacobi symbol always 0 when there's a common factor");
static_assert(jacobi_symbol(25, 15u) == 0, "Jacobi symbol always 0 when there's a common factor");
static_assert(jacobi_symbol(-24, 9u) == 0, "Jacobi symbol always 0 when there's a common factor");
static_assert(jacobi_symbol(14, 9u) == +jacobi_symbol(7, 9u),
"Divide numerator by 2: positive when (denom % 8) in {1, 7}");
static_assert(jacobi_symbol(14, 15u) == +jacobi_symbol(7, 15u),
"Divide numerator by 2: positive when (denom % 8) in {1, 7}");
static_assert(jacobi_symbol(14, 11u) == -jacobi_symbol(7, 11u),
"Divide numerator by 2: negative when (denom % 8) in {3, 5}");
static_assert(jacobi_symbol(14, 13u) == -jacobi_symbol(7, 13u),
"Divide numerator by 2: negative when (denom % 8) in {3, 5}");
static_assert(jacobi_symbol(19, 9u) == +jacobi_symbol(9, 19u), "Flip is identity when (n % 4) = 1");
static_assert(jacobi_symbol(17, 7u) == +jacobi_symbol(7, 17u), "Flip is identity when (a % 4) = 1");
static_assert(jacobi_symbol(19, 7u) == -jacobi_symbol(9, 7u), "Flip changes sign when (n % 4) = 3 and (a % 4) = 3");
static_assert(jacobi_symbol(1001, 9907u) == -1, "Example from Wikipedia page");
static_assert(jacobi_symbol(19, 45u) == 1, "Example from Wikipedia page");
static_assert(jacobi_symbol(8, 21u) == -1, "Example from Wikipedia page");
static_assert(jacobi_symbol(5, 21u) == 1, "Example from Wikipedia page");
// Tests for perfect square finder
static_assert(is_perfect_square(0u));
static_assert(is_perfect_square(1u));
static_assert(!is_perfect_square(2u));
static_assert(is_perfect_square(4u));
constexpr std::uint64_t BIG_SQUARE = [](auto x) { return x * x; }((std::uint64_t{1u} << 32) - 1u);
static_assert(!is_perfect_square(BIG_SQUARE - 1u));
static_assert(is_perfect_square(BIG_SQUARE));
static_assert(!is_perfect_square(BIG_SQUARE + 1u));
} // namespace