Sprout/sprout/random/detail/const_mod.hpp

/*=============================================================================
  Copyright (c) 2011-2017 Bolero MURAKAMI
  https://github.com/bolero-MURAKAMI/Sprout

  Distributed under the Boost Software License, Version 1.0. (See accompanying
  file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
=============================================================================*/
#ifndef SPROUT_RANDOM_DETAIL_CONST_MOD_HPP
#define SPROUT_RANDOM_DETAIL_CONST_MOD_HPP

#include <type_traits>
#include <sprout/config.hpp>
#include <sprout/limits.hpp>
#include <sprout/assert.hpp>
#ifdef SPROUT_WORKAROUND_NOT_TERMINATE_RECURSIVE_CONSTEXPR_FUNCTION_TEMPLATE
#	include <sprout/workaround/recursive_function_template.hpp>
#endif

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 supress_warnings = m == 0;
				SPROUT_STATIC_CONSTEXPR IntType modulus = m + supress_warnings;
			private:
				static_assert(supress_warnings == 0, "supress_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 + supress_warnings);
				}
				static SPROUT_CONSTEXPR IntType mult_schrage_1(IntType a, IntType value, IntType q, IntType r) {
					return SPROUT_ASSERT(r < q),
						sub(a * (value % q), r * (value / 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) <= sprout::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)) // ???
						: (SPROUT_ASSERT_MSG(0, "Sorry, not implemented."), IntType())
						;
				}
				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((sprout::numeric_limits<IntType>::max)()) + 1 : unsigned_type(m);
				}
#ifdef SPROUT_WORKAROUND_NOT_TERMINATE_RECURSIVE_CONSTEXPR_FUNCTION_TEMPLATE
				template<int D, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
				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<D + 1>(c, l1, l2, n, p);
				}
				template<int D, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
				static SPROUT_CONSTEXPR IntType invert_euclidian_3(IntType, IntType, IntType, IntType, IntType) {
					return sprout::throw_recursive_function_template_instantiation_exeeded();
				}
				template<int D, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
				static SPROUT_CONSTEXPR IntType invert_euclidian_2(IntType c, IntType l1, IntType l2, IntType n, IntType p) {
					return p == 0 ? l2 : invert_euclidian_3<D + 1>(c, l1, l2 + (n / p) * l1, n - (n / p) * p, p);
				}
				template<int D, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
				static SPROUT_CONSTEXPR IntType invert_euclidian_2(IntType, IntType, IntType, IntType, IntType) {
					return sprout::throw_recursive_function_template_instantiation_exeeded();
				}
				template<int D, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
				static SPROUT_CONSTEXPR IntType invert_euclidian_1(IntType c, IntType l1, IntType l2, IntType n, IntType p) {
					return invert_euclidian_2<D + 1>(c, l1 + (p / n) * l2, l2, n, p - (p / n) * n);
				}
				template<int D, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
				static SPROUT_CONSTEXPR IntType invert_euclidian_1(IntType, IntType, IntType, IntType, IntType) {
					return sprout::throw_recursive_function_template_instantiation_exeeded();
				}
				template<int D = 16, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
				static SPROUT_CONSTEXPR IntType invert_euclidian(IntType c) {
					return SPROUT_ASSERT(c > 0),
						c == 1 ? 1 : invert_euclidian_1<D + 1>(c, 0, 1, c, m)
						;
				}
				template<int D = 16, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
				static SPROUT_CONSTEXPR IntType invert_euclidian(IntType) {
					return sprout::throw_recursive_function_template_instantiation_exeeded();
				}
				template<int D, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
				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<D + 1>(c, l1 + (p / n) * l2, l2, n, p - (p / n) * n);
				}
				template<int D, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
				static SPROUT_CONSTEXPR IntType invert_euclidian0_3(IntType, IntType, IntType, IntType, IntType) {
					return sprout::throw_recursive_function_template_instantiation_exeeded();
				}
				template<int D, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
				static SPROUT_CONSTEXPR IntType invert_euclidian0_2(IntType c, IntType l1, IntType l2, IntType n, IntType p) {
					return p == 0 ? l2 : invert_euclidian0_3<D + 1>(c, l1, l2 + (n / p) * l1, n - (n / p) * p, p);
				}
				template<int D, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
				static SPROUT_CONSTEXPR IntType invert_euclidian0_2(IntType, IntType, IntType, IntType, IntType) {
					return sprout::throw_recursive_function_template_instantiation_exeeded();
				}
				template<int D, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
				static SPROUT_CONSTEXPR IntType invert_euclidian0_1(IntType c, IntType l1, IntType l2, IntType n) {
					return SPROUT_ASSERT_MSG(sprout::numeric_limits<IntType>::max() % n != n - 1, "c must be relatively prime to m."),
						invert_euclidian0_2<D + 1>(
							c, l1 + (sprout::numeric_limits<IntType>::max() / n) * l2, l2, n,
							sprout::numeric_limits<IntType>::max() - (sprout::numeric_limits<IntType>::max() / n) * n + 1
							)
						;
				}
				template<int D, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
				static SPROUT_CONSTEXPR IntType invert_euclidian0_1(IntType, IntType, IntType, IntType) {
					return sprout::throw_recursive_function_template_instantiation_exeeded();
				}
				template<int D = 16, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_CONTINUE(D)>
				static SPROUT_CONSTEXPR IntType invert_euclidian0(IntType c) {
					return SPROUT_ASSERT(c > 0),
						c == 1 ? 1 : invert_euclidian0_1<D + 1>(c, 0, 1, c)
						;
				}
				template<int D = 16, SPROUT_RECURSIVE_FUNCTION_TEMPLATE_BREAK(D)>
				static SPROUT_CONSTEXPR IntType invert_euclidian0(IntType) {
					return sprout::throw_recursive_function_template_instantiation_exeeded();
				}
#else
				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 SPROUT_ASSERT(c > 0),
						c == 1 ? 1 : invert_euclidian_1(c, 0, 1, c, m)
						;
				}
				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) {
					return SPROUT_ASSERT_MSG(sprout::numeric_limits<IntType>::max() % n != n - 1, "c must be relatively prime to m."),
						invert_euclidian0_2(
							c, l1 + (sprout::numeric_limits<IntType>::max() / n) * l2, l2, n,
							sprout::numeric_limits<IntType>::max() - (sprout::numeric_limits<IntType>::max() / n) * n + 1
							)
						;
				}
				static SPROUT_CONSTEXPR IntType invert_euclidian0(IntType c) {
					return SPROUT_ASSERT(c > 0),
						c == 1 ? 1 : invert_euclidian0_1(c, 0, 1, c)
						;
				}
#endif
			public:
				static SPROUT_CONSTEXPR IntType apply(IntType x) {
					return ((unsigned_m() - 1) & unsigned_m()) == 0
						? (unsigned_type(x)) & (unsigned_m() - 1)
						: x % (m + supress_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 <= sprout::numeric_limits<IntType>::max() / a ? mult_small(a, x)
						: sprout::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 <= (sprout::numeric_limits<IntType>::max() - c) / a ? (a * x + c) % (m + supress_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() SPROUT_DELETED_FUNCTION_DECL
			};
		}	// namespace detail
	}	// namespace random
}	// namespace sprout

#endif	// #ifndef SPROUT_RANDOM_DETAIL_CONST_MOD_HPP