stats.h

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/* *****************************************************************************
 * kblib is a general utility library for C++14 and C++17, intended to provide
 * performant high-level abstractions and more expressive ways to do simple
 * things.
 *
 * Copyright (c) 2021 killerbee
 *
 * This program is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program.  If not, see <https://www.gnu.org/licenses/>.
 * ****************************************************************************/
 
#ifndef KBLIB_STATS_H
#define KBLIB_STATS_H
 
#include <array>
#include <cassert>
#include <cinttypes>
#include <cstdlib>
#include <limits>
#include <numeric>
 
#include "fakestd.h"
#include "logic.h"
#include "tdecl.h"
 
namespace KBLIB_NS {
 
template <typename T, typename U>
KBLIB_NODISCARD constexpr auto div(T num, U den) noexcept
    -> decltype(std::div(num, den)) {
   decltype(std::div(num, den)) ret{};
   ret.quot = num / den;
   ret.rem = num % den;
   return ret;
}
 
template <typename T>
struct trivial_pair {
   T first;
   T second;
};
 
#if 0 and KBLIB_USE_CXX17
 
template <typename T, std::size_t N>
using trivial_array = std::array<T, N>;
 
#else
 
template <typename T, std::size_t N>
struct trivial_array {
   T arr[N];
   KBLIB_NODISCARD constexpr auto operator[](std::size_t n) -> T& {
      return arr[n];
   }
   KBLIB_NODISCARD constexpr auto operator[](std::size_t n) const -> const T& {
      return arr[n];
   }
   KBLIB_NODISCARD constexpr auto size() const -> std::size_t { return N; }
   KBLIB_NODISCARD constexpr auto begin() & noexcept -> T* { return arr; }
   KBLIB_NODISCARD constexpr auto begin() const& noexcept -> const T* {
      return arr;
   }
   KBLIB_NODISCARD constexpr auto end() & noexcept -> T* { return arr + N; }
   KBLIB_NODISCARD constexpr auto end() const& noexcept -> const T* {
      return arr + N;
   }
 
   KBLIB_NODISCARD constexpr friend auto operator==(
       const trivial_array& a, const trivial_array& b) noexcept -> bool {
      return equal(a.begin(), a.end(), b.begin());
   }
   KBLIB_NODISCARD constexpr friend auto operator!=(
       const trivial_array& a, const trivial_array& b) noexcept -> bool {
      return not (a == b);
   }
};
 
#endif
 
template <typename U>
KBLIB_NODISCARD constexpr auto calc_fib_size() noexcept -> std::size_t {
   static_assert(std::is_unsigned<U>::value, "U must be unsigned");
   std::size_t n{};
   trivial_pair<U> state{0, 1};
   U& a = state.first;
   U& b = state.second;
   while (b >= a) {
      state = {b, static_cast<U>(a + b)};
      ++n;
   }
   return n;
}
 
template <typename U, std::size_t N = calc_fib_size<U>() + 1>
KBLIB_NODISCARD constexpr auto make_fib_arr() noexcept -> trivial_array<U, N> {
   static_assert(
       implies<(N > calc_fib_size<U>()), std::is_unsigned<U>::value>::value,
       "signed U with large N would trigger signed overflow");
   // Initialize the first two elements of the array
   trivial_array<U, N> ret{{0, 1}};
   // A loop initializes the rest
   for (std::size_t i = 2; i < N; ++i) {
      ret[i] = ret[i - 1] + ret[i - 2];
   }
   return ret;
}
 
template <typename U = std::uintmax_t>
KBLIB_NODISCARD constexpr auto fibonacci(int n) noexcept -> U {
   constexpr auto arr = make_fib_arr<U>();
   assert(n >= 0 and static_cast<std::size_t>(n) < arr.size());
   return arr[to_unsigned(n)];
}
 
inline namespace nums {
   constexpr struct max_t {
      template <typename T,
                std::enable_if_t<std::numeric_limits<T>::is_specialized,
                                 void>* = nullptr>
      constexpr /* implicit*/ operator T() const
          noexcept(noexcept(std::numeric_limits<T>::max())) {
         return std::numeric_limits<T>::max();
      }
      template <typename T>
      KBLIB_NODISCARD constexpr static auto of() noexcept(
          noexcept(std::numeric_limits<T>::max())) {
         return std::numeric_limits<T>::max();
      }
 
      template <typename L, typename R>
      KBLIB_NODISCARD constexpr auto operator()(L&& lhs, R&& rhs) const noexcept
          -> decltype(auto) {
         return std::less<>{}(lhs, rhs) ? std::forward<R>(rhs)
                                        : std::forward<L>(lhs);
      }
 
      KBLIB_NODISCARD constexpr inline friend auto operator==(max_t, max_t)
          -> std::true_type {
         return {};
      }
      KBLIB_NODISCARD constexpr inline friend auto operator!=(max_t, max_t)
          -> std::false_type {
         return {};
      }
      KBLIB_NODISCARD constexpr inline friend auto operator<(max_t, max_t)
          -> std::false_type {
         return {};
      }
      KBLIB_NODISCARD constexpr inline friend auto operator>(max_t, max_t)
          -> std::false_type {
         return {};
      }
      KBLIB_NODISCARD constexpr inline friend auto operator<=(max_t, max_t)
          -> std::true_type {
         return {};
      }
      KBLIB_NODISCARD constexpr inline friend auto operator>=(max_t, max_t)
          -> std::true_type {
         return {};
      }
 
      template <typename T>
      KBLIB_NODISCARD constexpr friend auto operator==(T t, max_t) -> bool {
         return t == of<T>();
      }
      template <typename T>
      KBLIB_NODISCARD constexpr friend auto operator==(max_t, T t) -> bool {
         return t == of<T>();
      }
      template <typename T>
      KBLIB_NODISCARD constexpr friend auto operator!=(T t, max_t) -> bool {
         return t != of<T>();
      }
      template <typename T>
      KBLIB_NODISCARD constexpr friend auto operator!=(max_t, T t) -> bool {
         return t != of<T>();
      }
 
      template <typename T>
      KBLIB_NODISCARD constexpr friend auto operator<(T t, max_t) -> bool {
         return t < of<T>();
      }
      template <typename T>
      KBLIB_NODISCARD constexpr friend auto operator<(max_t, T t) -> bool {
         return of<T>() < t;
      }
      template <typename T>
      KBLIB_NODISCARD constexpr friend auto operator>(T t, max_t) -> bool {
         return t > of<T>();
      }
      template <typename T>
      KBLIB_NODISCARD constexpr friend auto operator>(max_t, T t) -> bool {
         return of<T>() > t;
      }
 
      template <typename T>
      KBLIB_NODISCARD constexpr friend auto operator<=(T t, max_t) -> bool {
         return t <= of<T>();
      }
      template <typename T>
      KBLIB_NODISCARD constexpr friend auto operator<=(max_t, T t) -> bool {
         return of<T>() <= t;
      }
      template <typename T>
      KBLIB_NODISCARD constexpr friend auto operator>=(T t, max_t) -> bool {
         return t >= of<T>();
      }
      template <typename T>
      KBLIB_NODISCARD constexpr friend auto operator>=(max_t, T t) -> bool {
         return of<T>() >= t;
      }
 
   } max; 
   constexpr struct min_t {
      template <typename T, enable_if_t<std::numeric_limits<T>::is_specialized,
                                        void>* = nullptr>
      constexpr /* implicit*/ operator T() const
          noexcept(noexcept(std::numeric_limits<T>::min())) {
         return std::numeric_limits<T>::min();
      }
      template <typename T>
      KBLIB_NODISCARD constexpr static auto of() noexcept(
          noexcept(std::numeric_limits<T>::min())) {
         return std::numeric_limits<T>::min();
      }
 
      template <typename L, typename R>
      KBLIB_NODISCARD constexpr auto operator()(L&& lhs, R&& rhs) const noexcept
          -> decltype(auto) {
         return std::less<>{}(lhs, rhs) ? std::forward<R>(lhs)
                                        : std::forward<L>(rhs);
      }
 
      template <typename T>
      KBLIB_NODISCARD constexpr friend auto operator==(T t, min_t) -> bool {
         return t == of<T>();
      }
      template <typename T>
      KBLIB_NODISCARD constexpr friend auto operator==(min_t, T t) -> bool {
         return t == of<T>();
      }
      template <typename T>
      KBLIB_NODISCARD constexpr friend auto operator!=(T t, min_t) -> bool {
         return t != of<T>();
      }
      template <typename T>
      KBLIB_NODISCARD constexpr friend auto operator!=(min_t, T t) -> bool {
         return t != of<T>();
      }
 
      template <typename T>
      KBLIB_NODISCARD constexpr friend auto operator<(T t, min_t) -> bool {
         return t < of<T>();
      }
      template <typename T>
      KBLIB_NODISCARD constexpr friend auto operator<(min_t, T t) -> bool {
         return of<T>() < t;
      }
      template <typename T>
      KBLIB_NODISCARD constexpr friend auto operator>(T t, min_t) -> bool {
         return t > of<T>();
      }
      template <typename T>
      KBLIB_NODISCARD constexpr friend auto operator>(min_t, T t) -> bool {
         return of<T>() > t;
      }
 
      template <typename T>
      KBLIB_NODISCARD constexpr friend auto operator<=(T t, min_t) -> bool {
         return t <= of<T>();
      }
      template <typename T>
      KBLIB_NODISCARD constexpr friend auto operator<=(min_t, T t) -> bool {
         return of<T>() <= t;
      }
      template <typename T>
      KBLIB_NODISCARD constexpr friend auto operator>=(T t, min_t) -> bool {
         return t >= of<T>();
      }
      template <typename T>
      KBLIB_NODISCARD constexpr friend auto operator>=(min_t, T t) -> bool {
         return of<T>() >= t;
      }
 
      KBLIB_NODISCARD constexpr inline friend auto operator==(min_t, min_t)
          -> std::true_type {
         return {};
      }
      KBLIB_NODISCARD constexpr inline friend auto operator!=(min_t, min_t)
          -> std::false_type {
         return {};
      }
      KBLIB_NODISCARD constexpr inline friend auto operator<(min_t, min_t)
          -> std::false_type {
         return {};
      }
      KBLIB_NODISCARD constexpr inline friend auto operator>(min_t, min_t)
          -> std::false_type {
         return {};
      }
      KBLIB_NODISCARD constexpr inline friend auto operator<=(min_t, min_t)
          -> std::true_type {
         return {};
      }
      KBLIB_NODISCARD constexpr inline friend auto operator>=(min_t, min_t)
          -> std::true_type {
         return {};
      }
 
      KBLIB_NODISCARD constexpr inline friend auto operator==(max_t, min_t)
          -> std::false_type {
         return {};
      }
      KBLIB_NODISCARD constexpr inline friend auto operator==(min_t, max_t)
          -> std::false_type {
         return {};
      }
      KBLIB_NODISCARD constexpr inline friend auto operator!=(max_t, min_t)
          -> std::true_type {
         return {};
      }
      KBLIB_NODISCARD constexpr inline friend auto operator!=(min_t, max_t)
          -> std::true_type {
         return {};
      }
      KBLIB_NODISCARD constexpr inline friend auto operator<(max_t, min_t)
          -> std::false_type {
         return {};
      }
      KBLIB_NODISCARD constexpr inline friend auto operator<(min_t, max_t)
          -> std::true_type {
         return {};
      }
      KBLIB_NODISCARD constexpr inline friend auto operator>(max_t, min_t)
          -> std::true_type {
         return {};
      }
      KBLIB_NODISCARD constexpr inline friend auto operator>(min_t, max_t)
          -> std::false_type {
         return {};
      }
      KBLIB_NODISCARD constexpr inline friend auto operator<=(max_t, min_t)
          -> std::false_type {
         return {};
      }
      KBLIB_NODISCARD constexpr inline friend auto operator<=(min_t, max_t)
          -> std::true_type {
         return {};
      }
      KBLIB_NODISCARD constexpr inline friend auto operator>=(max_t, min_t)
          -> std::true_type {
         return {};
      }
      KBLIB_NODISCARD constexpr inline friend auto operator>=(min_t, max_t)
          -> std::false_type {
         return {};
      }
 
   } min; 
} // namespace nums
 
template <typename T = double>
KBLIB_NODISCARD constexpr auto pi() -> T {
   return 3.1415926535897932384626433832795028841971693993751l;
}
template <typename T = double>
KBLIB_NODISCARD constexpr auto tau() -> T {
   return 2 * pi<T>;
}
template <typename T = double>
KBLIB_NODISCARD constexpr auto e() -> T {
   return 2.7182818284590452353602874713526624977572470937000l;
}
template <typename T = double>
KBLIB_NODISCARD constexpr auto root_2() -> T {
   return 1.4142135623730950488016887242096980785696718753769l;
}
template <typename T = double>
KBLIB_NODISCARD constexpr auto phi() -> T {
   return 1.6180339887498948482045868343656381177203091798058l;
}
 
// saturating to_unsigned
template <typename A, typename F>
KBLIB_NODISCARD constexpr auto saturating_cast(F x) noexcept
    -> enable_if_t<std::is_integral<A>::value and std::is_integral<F>::value
                       and std::is_unsigned<A>::value,
                   A> {
   if (x < 0) {
      return 0;
   } else if (to_unsigned(x) > A(max)) {
      return max;
   } else {
      return static_cast<A>(x);
   }
}
 
// saturating to_signed(signed)
template <typename A, typename F>
KBLIB_NODISCARD constexpr auto saturating_cast(F x) noexcept
    -> enable_if_t<std::is_integral<A>::value and std::is_integral<F>::value
                       and std::is_signed<A>::value
                       and std::is_signed<F>::value,
                   A> {
   if (x < A(min)) {
      return min;
   } else if (to_unsigned(x) > A(max)) {
      return max;
   } else {
      return x;
   }
}
// saturating to_signed(unsigned)
template <typename A, typename F>
KBLIB_NODISCARD constexpr auto saturating_cast(F x) noexcept
    -> enable_if_t<std::is_integral<A>::value and std::is_integral<F>::value
                       and std::is_signed<A>::value
                       and std::is_unsigned<F>::value,
                   A> {
   if (x > to_unsigned(A(max))) {
      return max;
   } else {
      return x;
   }
}
 
 
template <typename T, typename F>
KBLIB_NODISCARD constexpr auto quantize_step(F low, F delta, F val) noexcept
    -> T {
   static_assert(std::is_unsigned<T>::value, "Destination must be unsigned.");
   return static_cast<T>((val - low) * static_cast<T>(max) * delta);
}
 
template <typename T, typename F>
KBLIB_NODISCARD constexpr auto quantize_range(F low, F high, F val) noexcept
    -> T {
   static_assert(std::is_unsigned<T>::value, "Destination must be unsigned.");
   auto delta = (high - low) / static_cast<T>(max);
   return static_cast<T>((val - low) * static_cast<T>(max) * delta);
}
 
} // namespace KBLIB_NS
 
#endif // KBLIB_STATS_H