rtc_base/numerics/safe_minmax.h

/*
 *  Copyright 2017 The WebRTC Project Authors. All rights reserved.
 *
 *  Use of this source code is governed by a BSD-style license
 *  that can be found in the LICENSE file in the root of the source
 *  tree. An additional intellectual property rights grant can be found
 *  in the file PATENTS.  All contributing project authors may
 *  be found in the AUTHORS file in the root of the source tree.
 */

// Minimum and maximum
// ===================
//
//   webrtc::SafeMin(x, y)
//   webrtc::SafeMax(x, y)
//
// (These are both constexpr.)
//
// Accept two arguments of either any two integral or any two floating-point
// types, and return the smaller and larger value, respectively, with no
// truncation or wrap-around. If only one of the input types is statically
// guaranteed to be able to represent the result, the return type is that type;
// if either one would do, the result type is the smaller type. (One of these
// two cases always applies.)
//
//   * The case with one floating-point and one integral type is not allowed,
//     because the floating-point type will have greater range, but may not
//     have sufficient precision to represent the integer value exactly.)
//
// Clamp (a.k.a. constrain to a given interval)
// ============================================
//
//   webrtc::SafeClamp(x, a, b)
//
// Accepts three arguments of any mix of integral types or any mix of
// floating-point types, and returns the value in the closed interval [a, b]
// that is closest to x (that is, if x < a it returns a; if x > b it returns b;
// and if a <= x <= b it returns x). As for SafeMin() and SafeMax(), there is
// no truncation or wrap-around. The result type
//
//   1. is statically guaranteed to be able to represent the result;
//
//   2. is no larger than the largest of the three argument types; and
//
//   3. has the same signedness as the type of the first argument, if this is
//      possible without violating the First or Second Law.
//
// There is always at least one type that meets criteria 1 and 2. If more than
// one type meets these criteria equally well, the result type is one of the
// types that is smallest. Note that unlike SafeMin() and SafeMax(),
// SafeClamp() will sometimes pick a return type that isn't the type of any of
// its arguments.
//
//   * In this context, a type A is smaller than a type B if it has a smaller
//     range; that is, if A::max() - A::min() < B::max() - B::min(). For
//     example, int8_t < int16_t == uint16_t < int32_t, and all integral types
//     are smaller than all floating-point types.)
//
//   * As for SafeMin and SafeMax, mixing integer and floating-point arguments
//     is not allowed, because floating-point types have greater range than
//     integer types, but do not have sufficient precision to represent the
//     values of most integer types exactly.
//
// Requesting a specific return type
// =================================
//
// All three functions allow callers to explicitly specify the return type as a
// template parameter, overriding the default return type. E.g.
//
//   webrtc::SafeMin<int>(x, y)  // returns an int
//
// If the requested type is statically guaranteed to be able to represent the
// result, then everything's fine, and the return type is as requested. But if
// the requested type is too small, a static_assert is triggered.

#ifndef RTC_BASE_NUMERICS_SAFE_MINMAX_H_
#define RTC_BASE_NUMERICS_SAFE_MINMAX_H_

#include <cstdint>
#include <limits>
#include <type_traits>

#include "rtc_base/checks.h"
#include "rtc_base/numerics/safe_compare.h"
#include "rtc_base/type_traits.h"

namespace webrtc {

namespace safe_minmax_impl {

// Make the range of a type available via something other than a constexpr
// function, to work around MSVC limitations. See
// https://blogs.msdn.microsoft.com/vcblog/2015/12/02/partial-support-for-expression-sfinae-in-vs-2015-update-1/
template <typename T>
struct Limits {
  static constexpr T lowest = std::numeric_limits<T>::lowest();
  static constexpr T max = std::numeric_limits<T>::max();
};

template <typename T, bool is_enum = std::is_enum<T>::value>
struct UnderlyingType;

template <typename T>
struct UnderlyingType<T, false> {
  using type = T;
};

template <typename T>
struct UnderlyingType<T, true> {
  using type = typename std::underlying_type<T>::type;
};

// Given two types T1 and T2, find types that can hold the smallest (in
// ::min_t) and the largest (in ::max_t) of the two values.
template <typename T1,
          typename T2,
          bool int1 = IsIntlike<T1>::value,
          bool int2 = IsIntlike<T2>::value>
struct MType {
  static_assert(int1 == int2,
                "You may not mix integral and floating-point arguments");
};

// Specialization for when neither type is integral (and therefore presumably
// floating-point).
template <typename T1, typename T2>
struct MType<T1, T2, false, false> {
  using min_t = typename std::common_type<T1, T2>::type;
  static_assert(std::is_same<min_t, T1>::value ||
                    std::is_same<min_t, T2>::value,
                "");

  using max_t = typename std::common_type<T1, T2>::type;
  static_assert(std::is_same<max_t, T1>::value ||
                    std::is_same<max_t, T2>::value,
                "");
};

// Specialization for when both types are integral.
template <typename T1, typename T2>
struct MType<T1, T2, true, true> {
  // The type with the lowest minimum value. In case of a tie, the type with
  // the lowest maximum value. In case that too is a tie, the types have the
  // same range, and we arbitrarily pick T1.
  using min_t = typename std::conditional<
      SafeLt(Limits<T1>::lowest, Limits<T2>::lowest),
      T1,
      typename std::conditional<
          SafeGt(Limits<T1>::lowest, Limits<T2>::lowest),
          T2,
          typename std::conditional<SafeLe(Limits<T1>::max, Limits<T2>::max),
                                    T1,
                                    T2>::type>::type>::type;
  static_assert(std::is_same<min_t, T1>::value ||
                    std::is_same<min_t, T2>::value,
                "");

  // The type with the highest maximum value. In case of a tie, the types have
  // the same range (because in C++, integer types with the same maximum also
  // have the same minimum).
  static_assert(SafeNe(Limits<T1>::max, Limits<T2>::max) ||
                    SafeEq(Limits<T1>::lowest, Limits<T2>::lowest),
                "integer types with the same max should have the same min");
  using max_t = typename std::
      conditional<SafeGe(Limits<T1>::max, Limits<T2>::max), T1, T2>::type;
  static_assert(std::is_same<max_t, T1>::value ||
                    std::is_same<max_t, T2>::value,
                "");
};

// A dummy type that we pass around at compile time but never actually use.
// Declared but not defined.
struct DefaultType;

// ::type is A, except we fall back to B if A is DefaultType. We static_assert
// that the chosen type can hold all values that B can hold.
template <typename A, typename B>
struct TypeOr {
  using type = typename std::
      conditional<std::is_same<A, DefaultType>::value, B, A>::type;
  static_assert(SafeLe(Limits<type>::lowest, Limits<B>::lowest) &&
                    SafeGe(Limits<type>::max, Limits<B>::max),
                "The specified type isn't large enough");
  static_assert(IsIntlike<type>::value == IsIntlike<B>::value &&
                    std::is_floating_point<type>::value ==
                        std::is_floating_point<type>::value,
                "float<->int conversions not allowed");
};

}  // namespace safe_minmax_impl

template <
    typename R = safe_minmax_impl::DefaultType,
    typename T1 = safe_minmax_impl::DefaultType,
    typename T2 = safe_minmax_impl::DefaultType,
    typename R2 = typename safe_minmax_impl::TypeOr<
        R,
        typename safe_minmax_impl::MType<
            typename safe_minmax_impl::UnderlyingType<T1>::type,
            typename safe_minmax_impl::UnderlyingType<T2>::type>::min_t>::type>
constexpr R2 SafeMin(T1 a, T2 b) {
  static_assert(IsIntlike<T1>::value || std::is_floating_point<T1>::value,
                "The first argument must be integral or floating-point");
  static_assert(IsIntlike<T2>::value || std::is_floating_point<T2>::value,
                "The second argument must be integral or floating-point");
  return SafeLt(a, b) ? static_cast<R2>(a) : static_cast<R2>(b);
}

template <
    typename R = safe_minmax_impl::DefaultType,
    typename T1 = safe_minmax_impl::DefaultType,
    typename T2 = safe_minmax_impl::DefaultType,
    typename R2 = typename safe_minmax_impl::TypeOr<
        R,
        typename safe_minmax_impl::MType<
            typename safe_minmax_impl::UnderlyingType<T1>::type,
            typename safe_minmax_impl::UnderlyingType<T2>::type>::max_t>::type>
constexpr R2 SafeMax(T1 a, T2 b) {
  static_assert(IsIntlike<T1>::value || std::is_floating_point<T1>::value,
                "The first argument must be integral or floating-point");
  static_assert(IsIntlike<T2>::value || std::is_floating_point<T2>::value,
                "The second argument must be integral or floating-point");
  return SafeGt(a, b) ? static_cast<R2>(a) : static_cast<R2>(b);
}

namespace safe_minmax_impl {

// Given three types T, L, and H, let ::type be a suitable return value for
// SafeClamp(T, L, H). See the docs at the top of this file for details.
template <typename T,
          typename L,
          typename H,
          bool int1 = IsIntlike<T>::value,
          bool int2 = IsIntlike<L>::value,
          bool int3 = IsIntlike<H>::value>
struct ClampType {
  static_assert(int1 == int2 && int1 == int3,
                "You may not mix integral and floating-point arguments");
};

// Specialization for when all three types are floating-point.
template <typename T, typename L, typename H>
struct ClampType<T, L, H, false, false, false> {
  using type = typename std::common_type<T, L, H>::type;
};

// Specialization for when all three types are integral.
template <typename T, typename L, typename H>
struct ClampType<T, L, H, true, true, true> {
 private:
  // Range of the return value. The return type must be able to represent this
  // full range.
  static constexpr auto r_min =
      SafeMax(Limits<L>::lowest, SafeMin(Limits<H>::lowest, Limits<T>::lowest));
  static constexpr auto r_max =
      SafeMin(Limits<H>::max, SafeMax(Limits<L>::max, Limits<T>::max));

  // Is the given type an acceptable return type? (That is, can it represent
  // all possible return values, and is it no larger than the largest of the
  // input types?)
  template <typename A>
  struct AcceptableType {
   private:
    static constexpr bool not_too_large = sizeof(A) <= sizeof(L) ||
                                          sizeof(A) <= sizeof(H) ||
                                          sizeof(A) <= sizeof(T);
    static constexpr bool range_contained =
        SafeLe(Limits<A>::lowest, r_min) && SafeLe(r_max, Limits<A>::max);

   public:
    static constexpr bool value = not_too_large && range_contained;
  };

  using best_signed_type = typename std::conditional<
      AcceptableType<int8_t>::value,
      int8_t,
      typename std::conditional<
          AcceptableType<int16_t>::value,
          int16_t,
          typename std::conditional<AcceptableType<int32_t>::value,
                                    int32_t,
                                    int64_t>::type>::type>::type;

  using best_unsigned_type = typename std::conditional<
      AcceptableType<uint8_t>::value,
      uint8_t,
      typename std::conditional<
          AcceptableType<uint16_t>::value,
          uint16_t,
          typename std::conditional<AcceptableType<uint32_t>::value,
                                    uint32_t,
                                    uint64_t>::type>::type>::type;

 public:
  // Pick the best type, preferring the same signedness as T but falling back
  // to the other one if necessary.
  using type = typename std::conditional<
      std::is_signed<T>::value,
      typename std::conditional<AcceptableType<best_signed_type>::value,
                                best_signed_type,
                                best_unsigned_type>::type,
      typename std::conditional<AcceptableType<best_unsigned_type>::value,
                                best_unsigned_type,
                                best_signed_type>::type>::type;
  static_assert(AcceptableType<type>::value, "");
};

}  // namespace safe_minmax_impl

template <
    typename R = safe_minmax_impl::DefaultType,
    typename T = safe_minmax_impl::DefaultType,
    typename L = safe_minmax_impl::DefaultType,
    typename H = safe_minmax_impl::DefaultType,
    typename R2 = typename safe_minmax_impl::TypeOr<
        R,
        typename safe_minmax_impl::ClampType<
            typename safe_minmax_impl::UnderlyingType<T>::type,
            typename safe_minmax_impl::UnderlyingType<L>::type,
            typename safe_minmax_impl::UnderlyingType<H>::type>::type>::type>
R2 SafeClamp(T x, L min, H max) {
  static_assert(IsIntlike<H>::value || std::is_floating_point<H>::value,
                "The first argument must be integral or floating-point");
  static_assert(IsIntlike<T>::value || std::is_floating_point<T>::value,
                "The second argument must be integral or floating-point");
  static_assert(IsIntlike<L>::value || std::is_floating_point<L>::value,
                "The third argument must be integral or floating-point");
  RTC_DCHECK_LE(min, max);
  return SafeLe(x, min)   ? static_cast<R2>(min)
         : SafeGe(x, max) ? static_cast<R2>(max)
                          : static_cast<R2>(x);
}

}  //  namespace webrtc


#endif  // RTC_BASE_NUMERICS_SAFE_MINMAX_H_