204 lines
8.2 KiB
C++
204 lines
8.2 KiB
C++
/*
|
|
* Copyright 2016-present Facebook, Inc.
|
|
*
|
|
* Licensed under the Apache License, Version 2.0 (the "License");
|
|
* you may not use this file except in compliance with the License.
|
|
* You may obtain a copy of the License at
|
|
*
|
|
* http://www.apache.org/licenses/LICENSE-2.0
|
|
*
|
|
* Unless required by applicable law or agreed to in writing, software
|
|
* distributed under the License is distributed on an "AS IS" BASIS,
|
|
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
|
|
* See the License for the specific language governing permissions and
|
|
* limitations under the License.
|
|
*/
|
|
|
|
/**
|
|
* Some arithmetic functions that seem to pop up or get hand-rolled a lot.
|
|
* So far they are all focused on integer division.
|
|
*/
|
|
|
|
#pragma once
|
|
|
|
#include <stdint.h>
|
|
|
|
#include <limits>
|
|
#include <type_traits>
|
|
|
|
namespace folly {
|
|
|
|
namespace detail {
|
|
|
|
template <typename T>
|
|
inline constexpr T divFloorBranchless(T num, T denom) {
|
|
// floor != trunc when the answer isn't exact and truncation went the
|
|
// wrong way (truncation went toward positive infinity). That happens
|
|
// when the true answer is negative, which happens when num and denom
|
|
// have different signs. The following code compiles branch-free on
|
|
// many platforms.
|
|
return (num / denom) +
|
|
((num % denom) != 0 ? 1 : 0) *
|
|
(std::is_signed<T>::value && (num ^ denom) < 0 ? -1 : 0);
|
|
}
|
|
|
|
template <typename T>
|
|
inline constexpr T divFloorBranchful(T num, T denom) {
|
|
// First case handles negative result by preconditioning numerator.
|
|
// Preconditioning decreases the magnitude of the numerator, which is
|
|
// itself sign-dependent. Second case handles zero or positive rational
|
|
// result, where trunc and floor are the same.
|
|
return std::is_signed<T>::value && (num ^ denom) < 0 && num != 0
|
|
? (num + (num > 0 ? -1 : 1)) / denom - 1
|
|
: num / denom;
|
|
}
|
|
|
|
template <typename T>
|
|
inline constexpr T divCeilBranchless(T num, T denom) {
|
|
// ceil != trunc when the answer isn't exact (truncation occurred)
|
|
// and truncation went away from positive infinity. That happens when
|
|
// the true answer is positive, which happens when num and denom have
|
|
// the same sign.
|
|
return (num / denom) +
|
|
((num % denom) != 0 ? 1 : 0) *
|
|
(std::is_signed<T>::value && (num ^ denom) < 0 ? 0 : 1);
|
|
}
|
|
|
|
template <typename T>
|
|
inline constexpr T divCeilBranchful(T num, T denom) {
|
|
// First case handles negative or zero rational result, where trunc and ceil
|
|
// are the same.
|
|
// Second case handles positive result by preconditioning numerator.
|
|
// Preconditioning decreases the magnitude of the numerator, which is
|
|
// itself sign-dependent.
|
|
return (std::is_signed<T>::value && (num ^ denom) < 0) || num == 0
|
|
? num / denom
|
|
: (num + (num > 0 ? -1 : 1)) / denom + 1;
|
|
}
|
|
|
|
template <typename T>
|
|
inline constexpr T divRoundAwayBranchless(T num, T denom) {
|
|
// away != trunc whenever truncation actually occurred, which is when
|
|
// there is a non-zero remainder. If the unrounded result is negative
|
|
// then fixup moves it toward negative infinity. If the unrounded
|
|
// result is positive then adjustment makes it larger.
|
|
return (num / denom) +
|
|
((num % denom) != 0 ? 1 : 0) *
|
|
(std::is_signed<T>::value && (num ^ denom) < 0 ? -1 : 1);
|
|
}
|
|
|
|
template <typename T>
|
|
inline constexpr T divRoundAwayBranchful(T num, T denom) {
|
|
// First case of second ternary operator handles negative rational
|
|
// result, which is the same as divFloor. Second case of second ternary
|
|
// operator handles positive result, which is the same as divCeil.
|
|
// Zero case is separated for simplicity.
|
|
return num == 0 ? 0
|
|
: (num + (num > 0 ? -1 : 1)) / denom +
|
|
(std::is_signed<T>::value && (num ^ denom) < 0 ? -1 : 1);
|
|
}
|
|
|
|
template <typename N, typename D>
|
|
using IdivResultType = typename std::enable_if<
|
|
std::is_integral<N>::value && std::is_integral<D>::value &&
|
|
!std::is_same<N, bool>::value && !std::is_same<D, bool>::value,
|
|
decltype(N{1} / D{1})>::type;
|
|
} // namespace detail
|
|
|
|
#if defined(__arm__) && !FOLLY_AARCH64
|
|
constexpr auto kIntegerDivisionGivesRemainder = false;
|
|
#else
|
|
constexpr auto kIntegerDivisionGivesRemainder = true;
|
|
#endif
|
|
|
|
/**
|
|
* Returns num/denom, rounded toward negative infinity. Put another way,
|
|
* returns the largest integral value that is less than or equal to the
|
|
* exact (not rounded) fraction num/denom.
|
|
*
|
|
* The matching remainder (num - divFloor(num, denom) * denom) can be
|
|
* negative only if denom is negative, unlike in truncating division.
|
|
* Note that for unsigned types this is the same as the normal integer
|
|
* division operator. divFloor is equivalent to python's integral division
|
|
* operator //.
|
|
*
|
|
* This function undergoes the same integer promotion rules as a
|
|
* built-in operator, except that we don't allow bool -> int promotion.
|
|
* This function is undefined if denom == 0. It is also undefined if the
|
|
* result type T is a signed type, num is std::numeric_limits<T>::min(),
|
|
* and denom is equal to -1 after conversion to the result type.
|
|
*/
|
|
template <typename N, typename D>
|
|
inline constexpr detail::IdivResultType<N, D> divFloor(N num, D denom) {
|
|
using R = decltype(num / denom);
|
|
return detail::IdivResultType<N, D>(
|
|
kIntegerDivisionGivesRemainder && std::is_signed<R>::value
|
|
? detail::divFloorBranchless<R>(num, denom)
|
|
: detail::divFloorBranchful<R>(num, denom));
|
|
}
|
|
|
|
/**
|
|
* Returns num/denom, rounded toward positive infinity. Put another way,
|
|
* returns the smallest integral value that is greater than or equal to
|
|
* the exact (not rounded) fraction num/denom.
|
|
*
|
|
* This function undergoes the same integer promotion rules as a
|
|
* built-in operator, except that we don't allow bool -> int promotion.
|
|
* This function is undefined if denom == 0. It is also undefined if the
|
|
* result type T is a signed type, num is std::numeric_limits<T>::min(),
|
|
* and denom is equal to -1 after conversion to the result type.
|
|
*/
|
|
template <typename N, typename D>
|
|
inline constexpr detail::IdivResultType<N, D> divCeil(N num, D denom) {
|
|
using R = decltype(num / denom);
|
|
return detail::IdivResultType<N, D>(
|
|
kIntegerDivisionGivesRemainder && std::is_signed<R>::value
|
|
? detail::divCeilBranchless<R>(num, denom)
|
|
: detail::divCeilBranchful<R>(num, denom));
|
|
}
|
|
|
|
/**
|
|
* Returns num/denom, rounded toward zero. If num and denom are non-zero
|
|
* and have different signs (so the unrounded fraction num/denom is
|
|
* negative), returns divCeil, otherwise returns divFloor. If T is an
|
|
* unsigned type then this is always equal to divFloor.
|
|
*
|
|
* Note that this is the same as the normal integer division operator,
|
|
* at least since C99 (before then the rounding for negative results was
|
|
* implementation defined). This function is here for completeness and
|
|
* as a place to hang this comment.
|
|
*
|
|
* This function undergoes the same integer promotion rules as a
|
|
* built-in operator, except that we don't allow bool -> int promotion.
|
|
* This function is undefined if denom == 0. It is also undefined if the
|
|
* result type T is a signed type, num is std::numeric_limits<T>::min(),
|
|
* and denom is equal to -1 after conversion to the result type.
|
|
*/
|
|
template <typename N, typename D>
|
|
inline constexpr detail::IdivResultType<N, D> divTrunc(N num, D denom) {
|
|
return detail::IdivResultType<N, D>(num / denom);
|
|
}
|
|
|
|
/**
|
|
* Returns num/denom, rounded away from zero. If num and denom are
|
|
* non-zero and have different signs (so the unrounded fraction num/denom
|
|
* is negative), returns divFloor, otherwise returns divCeil. If T is
|
|
* an unsigned type then this is always equal to divCeil.
|
|
*
|
|
* This function undergoes the same integer promotion rules as a
|
|
* built-in operator, except that we don't allow bool -> int promotion.
|
|
* This function is undefined if denom == 0. It is also undefined if the
|
|
* result type T is a signed type, num is std::numeric_limits<T>::min(),
|
|
* and denom is equal to -1 after conversion to the result type.
|
|
*/
|
|
template <typename N, typename D>
|
|
inline constexpr detail::IdivResultType<N, D> divRoundAway(N num, D denom) {
|
|
using R = decltype(num / denom);
|
|
return detail::IdivResultType<N, D>(
|
|
kIntegerDivisionGivesRemainder && std::is_signed<R>::value
|
|
? detail::divRoundAwayBranchless<R>(num, denom)
|
|
: detail::divRoundAwayBranchful<R>(num, denom));
|
|
}
|
|
|
|
} // namespace folly
|