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bolero-MURAKAMI 2011-09-29 00:51:12 +09:00
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commit 77c3faa42e
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sprout/random/detail/const_mod.hpp Normal file
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#ifndef SPROUT_RANDOM_CONST_MOD_HPP
#define SPROUT_RANDOM_CONST_MOD_HPP
#include <type_traits>
#include <limits>
#include <sprout/config.hpp>
namespace sprout {
namespace random {
namespace detail {
template<typename IntType, IntType m>
class const_mod {
private:
typedef typename std::make_unsigned<IntType>::type unsigned_type;
private:
SPROUT_STATIC_CONSTEXPR IntType suppress_warnings = m == 0;
SPROUT_STATIC_CONSTEXPR IntType modulus = m + suppress_warnings;
private:
static_assert(suppress_warnings == 0, "suppress_warnings == 0");
static_assert(modulus == m, "modulus == m");
private:
static SPROUT_CONSTEXPR IntType pow_1(IntType a, std::uintmax_t exponent, IntType result = 1) {
return exponent != 0
? pow_1(mult(a, a), exponent / 2, exponent % 2 == 1 ? mult(result, a) : result)
: result
;
}
static SPROUT_CONSTEXPR IntType mult_small(IntType a, IntType x) {
return a * x % (m + suppress_warnings);
}
static SPROUT_CONSTEXPR IntType mult_schrage_1(IntType a, IntType value, IntType q, IntType r) {
return r < q
? sub(a * (value % q), r * (value / q))
: throw "assert(r < q)"
;
}
static SPROUT_CONSTEXPR IntType mult_schrage(IntType a, IntType value) {
return mult_schrage_1(a, value, m / a, m % a);
}
static SPROUT_CONSTEXPR IntType mult_general(IntType a, IntType b) {
return std::uintmax_t(modulus) <= std::numeric_limits<std::uintmax_t>::max() / modulus
? static_cast<IntType>(std::uintmax_t(a) * b % modulus)
: /*static_cast<IntType>(sprout::random::detail::mulmod(a, b, modulus))*/throw "Sorry, not implemented."
;
}
static SPROUT_CONSTEXPR IntType sub(IntType a, IntType b) {
return a < b ? m - (b - a) : a - b;
}
static SPROUT_CONSTEXPR unsigned_type unsigned_m() {
return m == 0 ? unsigned_type((std::numeric_limits<IntType>::max)()) + 1 : unsigned_type(m);
}
static SPROUT_CONSTEXPR IntType invert_euclidian_3(IntType c, IntType l1, IntType l2, IntType n, IntType p) {
return n == 0 ? m - l1 : invert_euclidian_1(c, l1, l2, n, p);
}
static SPROUT_CONSTEXPR IntType invert_euclidian_2(IntType c, IntType l1, IntType l2, IntType n, IntType p) {
return p == 0 ? l2 : invert_euclidian_3(c, l1, l2 + (n / p) * l1, n - (n / p) * p, p);
}
static SPROUT_CONSTEXPR IntType invert_euclidian_1(IntType c, IntType l1, IntType l2, IntType n, IntType p) {
return invert_euclidian_2(c, l1 + (p / n) * l2, l2, n, p - (p / n) * n);
}
static SPROUT_CONSTEXPR IntType invert_euclidian(IntType c) {
return c > 0
? c == 1 ? 1 : invert_euclidian_1(c, 0, 1, c, m)
: throw "assert(c > 0)"
;
}
static SPROUT_CONSTEXPR IntType invert_euclidian0_3(IntType c, IntType l1, IntType l2, IntType n, IntType p) {
return n == 0 ? m - l1 : invert_euclidian0_2(c, l1 + (p / n) * l2, l2, n, p - (p / n) * n);
}
static SPROUT_CONSTEXPR IntType invert_euclidian0_2(IntType c, IntType l1, IntType l2, IntType n, IntType p) {
return p == 0 ? l2 : invert_euclidian0_3(c, l1, l2 + (n / p) * l1, n - (n / p) * p, p);
}
static SPROUT_CONSTEXPR IntType invert_euclidian0_1(IntType c, IntType l1, IntType l2, IntType n, IntType p) {
return std::numeric_limits<IntType>::max() % n != n - 1
? invert_euclidian0_2(c, l1 + (std::numeric_limits<IntType>::max() / n) * l2, l2, n, std::numeric_limits<IntType>::max() - (std::numeric_limits<IntType>::max() / n) * n + 1)
: throw "assert(std::numeric_limits<IntType>::max() % n != n - 1)"
;
}
static SPROUT_CONSTEXPR IntType invert_euclidian0(IntType c) {
return c > 0
? c == 1 ? 1 : invert_euclidian0_1(c, 0, 1, c, m)
: throw "assert(c > 0)"
;
}
public:
static SPROUT_CONSTEXPR IntType apply(IntType x) {
return ((unsigned_m() - 1) & unsigned_m()) == 0
? (unsigned_type(x)) & (unsigned_m() - 1)
: x % (m + suppress_warnings)
;
}
static SPROUT_CONSTEXPR IntType add(IntType x, IntType c) {
return ((unsigned_m() - 1) & unsigned_m()) == 0 ? (unsigned_type(x) + unsigned_type(c)) & (unsigned_m() - 1)
: c == 0 ? x
: x < m - c ? x + c
: x - (m - c)
;
}
static SPROUT_CONSTEXPR IntType mult(IntType a, IntType x) {
return ((unsigned_m() - 1) & unsigned_m()) == 0 ? unsigned_type(a) * unsigned_type(x) & (unsigned_m() - 1)
: a == 0 ? 0
: a == 1 ? x
: m <= std::numeric_limits<IntType>::max() / a ? mult_small(a, x)
: std::numeric_limits<IntType>::is_signed && (m % a < m / a) ? mult_schrage(a, x)
: mult_general(a, x)
;
}
static SPROUT_CONSTEXPR IntType mult_add(IntType a, IntType x, IntType c) {
return ((unsigned_m() - 1) & unsigned_m()) == 0 ? (unsigned_type(a) * unsigned_type(x) + unsigned_type(c)) & (unsigned_m() - 1)
: a == 0 ? c
: m <= (std::numeric_limits<IntType>::max() - c) / a ? (a * x + c) % (m + suppress_warnings)
: add(mult(a, x), c)
;
}
static SPROUT_CONSTEXPR IntType pow(IntType a, std::uintmax_t exponent) {
return pow_1(a, exponent);
}
static SPROUT_CONSTEXPR IntType invert(IntType x) {
return x == 0 ? 0
: m == 0 ? invert_euclidian0(x)
: invert_euclidian(x)
;
}
private:
const_mod() = delete;
};
} // namespace detail
} // namespace random
} // namespace sprout
#endif // #ifndef SPROUT_RANDOM_CONST_MOD_HPP