336 lines
13 KiB
C++
336 lines
13 KiB
C++
/*
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* Copyright 2017 The WebRTC Project Authors. All rights reserved.
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*
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* Use of this source code is governed by a BSD-style license
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* that can be found in the LICENSE file in the root of the source
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* tree. An additional intellectual property rights grant can be found
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* in the file PATENTS. All contributing project authors may
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* be found in the AUTHORS file in the root of the source tree.
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*/
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// Minimum and maximum
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// ===================
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//
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// rtc::SafeMin(x, y)
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// rtc::SafeMax(x, y)
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//
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// (These are both constexpr.)
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//
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// Accept two arguments of either any two integral or any two floating-point
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// types, and return the smaller and larger value, respectively, with no
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// truncation or wrap-around. If only one of the input types is statically
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// guaranteed to be able to represent the result, the return type is that type;
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// if either one would do, the result type is the smaller type. (One of these
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// two cases always applies.)
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//
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// * The case with one floating-point and one integral type is not allowed,
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// because the floating-point type will have greater range, but may not
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// have sufficient precision to represent the integer value exactly.)
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//
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// Clamp (a.k.a. constrain to a given interval)
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// ============================================
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//
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// rtc::SafeClamp(x, a, b)
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//
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// Accepts three arguments of any mix of integral types or any mix of
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// floating-point types, and returns the value in the closed interval [a, b]
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// that is closest to x (that is, if x < a it returns a; if x > b it returns b;
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// and if a <= x <= b it returns x). As for SafeMin() and SafeMax(), there is
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// no truncation or wrap-around. The result type
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//
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// 1. is statically guaranteed to be able to represent the result;
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//
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// 2. is no larger than the largest of the three argument types; and
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//
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// 3. has the same signedness as the type of the first argument, if this is
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// possible without violating the First or Second Law.
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//
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// There is always at least one type that meets criteria 1 and 2. If more than
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// one type meets these criteria equally well, the result type is one of the
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// types that is smallest. Note that unlike SafeMin() and SafeMax(),
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// SafeClamp() will sometimes pick a return type that isn't the type of any of
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// its arguments.
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//
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// * In this context, a type A is smaller than a type B if it has a smaller
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// range; that is, if A::max() - A::min() < B::max() - B::min(). For
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// example, int8_t < int16_t == uint16_t < int32_t, and all integral types
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// are smaller than all floating-point types.)
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//
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// * As for SafeMin and SafeMax, mixing integer and floating-point arguments
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// is not allowed, because floating-point types have greater range than
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// integer types, but do not have sufficient precision to represent the
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// values of most integer types exactly.
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//
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// Requesting a specific return type
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// =================================
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//
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// All three functions allow callers to explicitly specify the return type as a
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// template parameter, overriding the default return type. E.g.
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//
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// rtc::SafeMin<int>(x, y) // returns an int
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//
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// If the requested type is statically guaranteed to be able to represent the
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// result, then everything's fine, and the return type is as requested. But if
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// the requested type is too small, a static_assert is triggered.
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#ifndef RTC_BASE_NUMERICS_SAFE_MINMAX_H_
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#define RTC_BASE_NUMERICS_SAFE_MINMAX_H_
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#include <limits>
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#include <type_traits>
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#include "rtc_base/checks.h"
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#include "rtc_base/numerics/safe_compare.h"
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#include "rtc_base/type_traits.h"
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namespace rtc {
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namespace safe_minmax_impl {
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// Make the range of a type available via something other than a constexpr
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// function, to work around MSVC limitations. See
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// https://blogs.msdn.microsoft.com/vcblog/2015/12/02/partial-support-for-expression-sfinae-in-vs-2015-update-1/
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template <typename T>
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struct Limits {
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static constexpr T lowest = std::numeric_limits<T>::lowest();
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static constexpr T max = std::numeric_limits<T>::max();
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};
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template <typename T, bool is_enum = std::is_enum<T>::value>
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struct UnderlyingType;
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template <typename T>
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struct UnderlyingType<T, false> {
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using type = T;
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};
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template <typename T>
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struct UnderlyingType<T, true> {
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using type = typename std::underlying_type<T>::type;
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};
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// Given two types T1 and T2, find types that can hold the smallest (in
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// ::min_t) and the largest (in ::max_t) of the two values.
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template <typename T1,
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typename T2,
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bool int1 = IsIntlike<T1>::value,
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bool int2 = IsIntlike<T2>::value>
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struct MType {
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static_assert(int1 == int2,
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"You may not mix integral and floating-point arguments");
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};
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// Specialization for when neither type is integral (and therefore presumably
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// floating-point).
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template <typename T1, typename T2>
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struct MType<T1, T2, false, false> {
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using min_t = typename std::common_type<T1, T2>::type;
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static_assert(std::is_same<min_t, T1>::value ||
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std::is_same<min_t, T2>::value,
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"");
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using max_t = typename std::common_type<T1, T2>::type;
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static_assert(std::is_same<max_t, T1>::value ||
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std::is_same<max_t, T2>::value,
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"");
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};
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// Specialization for when both types are integral.
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template <typename T1, typename T2>
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struct MType<T1, T2, true, true> {
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// The type with the lowest minimum value. In case of a tie, the type with
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// the lowest maximum value. In case that too is a tie, the types have the
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// same range, and we arbitrarily pick T1.
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using min_t = typename std::conditional<
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SafeLt(Limits<T1>::lowest, Limits<T2>::lowest),
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T1,
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typename std::conditional<
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SafeGt(Limits<T1>::lowest, Limits<T2>::lowest),
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T2,
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typename std::conditional<SafeLe(Limits<T1>::max, Limits<T2>::max),
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T1,
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T2>::type>::type>::type;
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static_assert(std::is_same<min_t, T1>::value ||
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std::is_same<min_t, T2>::value,
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"");
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// The type with the highest maximum value. In case of a tie, the types have
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// the same range (because in C++, integer types with the same maximum also
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// have the same minimum).
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static_assert(SafeNe(Limits<T1>::max, Limits<T2>::max) ||
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SafeEq(Limits<T1>::lowest, Limits<T2>::lowest),
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"integer types with the same max should have the same min");
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using max_t = typename std::
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conditional<SafeGe(Limits<T1>::max, Limits<T2>::max), T1, T2>::type;
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static_assert(std::is_same<max_t, T1>::value ||
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std::is_same<max_t, T2>::value,
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"");
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};
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// A dummy type that we pass around at compile time but never actually use.
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// Declared but not defined.
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struct DefaultType;
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// ::type is A, except we fall back to B if A is DefaultType. We static_assert
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// that the chosen type can hold all values that B can hold.
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template <typename A, typename B>
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struct TypeOr {
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using type = typename std::
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conditional<std::is_same<A, DefaultType>::value, B, A>::type;
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static_assert(SafeLe(Limits<type>::lowest, Limits<B>::lowest) &&
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SafeGe(Limits<type>::max, Limits<B>::max),
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"The specified type isn't large enough");
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static_assert(IsIntlike<type>::value == IsIntlike<B>::value &&
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std::is_floating_point<type>::value ==
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std::is_floating_point<type>::value,
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"float<->int conversions not allowed");
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};
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} // namespace safe_minmax_impl
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template <
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typename R = safe_minmax_impl::DefaultType,
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typename T1 = safe_minmax_impl::DefaultType,
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typename T2 = safe_minmax_impl::DefaultType,
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typename R2 = typename safe_minmax_impl::TypeOr<
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R,
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typename safe_minmax_impl::MType<
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typename safe_minmax_impl::UnderlyingType<T1>::type,
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typename safe_minmax_impl::UnderlyingType<T2>::type>::min_t>::type>
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constexpr R2 SafeMin(T1 a, T2 b) {
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static_assert(IsIntlike<T1>::value || std::is_floating_point<T1>::value,
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"The first argument must be integral or floating-point");
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static_assert(IsIntlike<T2>::value || std::is_floating_point<T2>::value,
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"The second argument must be integral or floating-point");
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return SafeLt(a, b) ? static_cast<R2>(a) : static_cast<R2>(b);
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}
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template <
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typename R = safe_minmax_impl::DefaultType,
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typename T1 = safe_minmax_impl::DefaultType,
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typename T2 = safe_minmax_impl::DefaultType,
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typename R2 = typename safe_minmax_impl::TypeOr<
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R,
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typename safe_minmax_impl::MType<
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typename safe_minmax_impl::UnderlyingType<T1>::type,
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typename safe_minmax_impl::UnderlyingType<T2>::type>::max_t>::type>
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constexpr R2 SafeMax(T1 a, T2 b) {
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static_assert(IsIntlike<T1>::value || std::is_floating_point<T1>::value,
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"The first argument must be integral or floating-point");
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static_assert(IsIntlike<T2>::value || std::is_floating_point<T2>::value,
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"The second argument must be integral or floating-point");
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return SafeGt(a, b) ? static_cast<R2>(a) : static_cast<R2>(b);
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}
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namespace safe_minmax_impl {
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// Given three types T, L, and H, let ::type be a suitable return value for
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// SafeClamp(T, L, H). See the docs at the top of this file for details.
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template <typename T,
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typename L,
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typename H,
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bool int1 = IsIntlike<T>::value,
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bool int2 = IsIntlike<L>::value,
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bool int3 = IsIntlike<H>::value>
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struct ClampType {
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static_assert(int1 == int2 && int1 == int3,
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"You may not mix integral and floating-point arguments");
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};
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// Specialization for when all three types are floating-point.
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template <typename T, typename L, typename H>
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struct ClampType<T, L, H, false, false, false> {
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using type = typename std::common_type<T, L, H>::type;
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};
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// Specialization for when all three types are integral.
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template <typename T, typename L, typename H>
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struct ClampType<T, L, H, true, true, true> {
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private:
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// Range of the return value. The return type must be able to represent this
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// full range.
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static constexpr auto r_min =
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SafeMax(Limits<L>::lowest, SafeMin(Limits<H>::lowest, Limits<T>::lowest));
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static constexpr auto r_max =
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SafeMin(Limits<H>::max, SafeMax(Limits<L>::max, Limits<T>::max));
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// Is the given type an acceptable return type? (That is, can it represent
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// all possible return values, and is it no larger than the largest of the
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// input types?)
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template <typename A>
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struct AcceptableType {
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private:
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static constexpr bool not_too_large = sizeof(A) <= sizeof(L) ||
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sizeof(A) <= sizeof(H) ||
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sizeof(A) <= sizeof(T);
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static constexpr bool range_contained =
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SafeLe(Limits<A>::lowest, r_min) && SafeLe(r_max, Limits<A>::max);
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public:
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static constexpr bool value = not_too_large && range_contained;
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};
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using best_signed_type = typename std::conditional<
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AcceptableType<int8_t>::value,
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int8_t,
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typename std::conditional<
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AcceptableType<int16_t>::value,
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int16_t,
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typename std::conditional<AcceptableType<int32_t>::value,
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int32_t,
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int64_t>::type>::type>::type;
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using best_unsigned_type = typename std::conditional<
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AcceptableType<uint8_t>::value,
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uint8_t,
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typename std::conditional<
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AcceptableType<uint16_t>::value,
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uint16_t,
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typename std::conditional<AcceptableType<uint32_t>::value,
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uint32_t,
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uint64_t>::type>::type>::type;
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public:
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// Pick the best type, preferring the same signedness as T but falling back
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// to the other one if necessary.
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using type = typename std::conditional<
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std::is_signed<T>::value,
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typename std::conditional<AcceptableType<best_signed_type>::value,
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best_signed_type,
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best_unsigned_type>::type,
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typename std::conditional<AcceptableType<best_unsigned_type>::value,
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best_unsigned_type,
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best_signed_type>::type>::type;
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static_assert(AcceptableType<type>::value, "");
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};
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} // namespace safe_minmax_impl
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template <
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typename R = safe_minmax_impl::DefaultType,
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typename T = safe_minmax_impl::DefaultType,
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typename L = safe_minmax_impl::DefaultType,
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typename H = safe_minmax_impl::DefaultType,
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typename R2 = typename safe_minmax_impl::TypeOr<
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R,
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typename safe_minmax_impl::ClampType<
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typename safe_minmax_impl::UnderlyingType<T>::type,
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typename safe_minmax_impl::UnderlyingType<L>::type,
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typename safe_minmax_impl::UnderlyingType<H>::type>::type>::type>
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R2 SafeClamp(T x, L min, H max) {
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static_assert(IsIntlike<H>::value || std::is_floating_point<H>::value,
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"The first argument must be integral or floating-point");
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static_assert(IsIntlike<T>::value || std::is_floating_point<T>::value,
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"The second argument must be integral or floating-point");
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static_assert(IsIntlike<L>::value || std::is_floating_point<L>::value,
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"The third argument must be integral or floating-point");
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RTC_DCHECK_LE(min, max);
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return SafeLe(x, min)
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? static_cast<R2>(min)
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: SafeGe(x, max) ? static_cast<R2>(max) : static_cast<R2>(x);
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}
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} // namespace rtc
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#endif // RTC_BASE_NUMERICS_SAFE_MINMAX_H_
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