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/* -*- Mode: C++; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 2 -*-
* vim: set ts=8 sts=2 et sw=2 tw=80:
* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
#ifndef builtin_temporal_TemporalRoundingMode_h
#define builtin_temporal_TemporalRoundingMode_h
#include "mozilla/Assertions.h"
#include <cmath>
#include <stdint.h>
#include "builtin/temporal/Int128.h"
namespace js::temporal {
// Overview of integer rounding modes is available at
enum class TemporalRoundingMode {
// 1. Directed rounding to an integer.
// Round toward positive infinity.
Ceil,
// Round toward negative infinity.
Floor,
// Round toward infinity or round away from zero.
Expand,
// Round toward zero or round away from infinity.
Trunc,
// 2. Rounding to the nearest integer.
// Round half toward positive infinity.
HalfCeil,
// Round half toward negative infinity.
HalfFloor,
// Round half toward infinity or round half away from zero.
HalfExpand,
// Round half toward zero or round half away from infinity.
HalfTrunc,
// Round half to even.
HalfEven,
};
/**
* NegateTemporalRoundingMode ( roundingMode )
*/
constexpr auto NegateTemporalRoundingMode(TemporalRoundingMode roundingMode) {
// Steps 1-5.
switch (roundingMode) {
case TemporalRoundingMode::Ceil:
return TemporalRoundingMode::Floor;
case TemporalRoundingMode::Floor:
return TemporalRoundingMode::Ceil;
case TemporalRoundingMode::HalfCeil:
return TemporalRoundingMode::HalfFloor;
case TemporalRoundingMode::HalfFloor:
return TemporalRoundingMode::HalfCeil;
case TemporalRoundingMode::Expand:
case TemporalRoundingMode::Trunc:
case TemporalRoundingMode::HalfExpand:
case TemporalRoundingMode::HalfTrunc:
case TemporalRoundingMode::HalfEven:
return roundingMode;
}
MOZ_CRASH("invalid rounding mode");
}
/**
* Adjust the rounding mode to round negative values in the same direction as
* positive values.
*/
constexpr auto ToPositiveRoundingMode(TemporalRoundingMode roundingMode) {
switch (roundingMode) {
case TemporalRoundingMode::Ceil:
case TemporalRoundingMode::Floor:
case TemporalRoundingMode::HalfCeil:
case TemporalRoundingMode::HalfFloor:
case TemporalRoundingMode::HalfEven:
// (Half-)Ceil/Floor round toward the same infinity for negative and
// positive values, so the rounding mode doesn't need to be adjusted. The
// same applies for half-even rounding.
return roundingMode;
case TemporalRoundingMode::Expand:
// Expand rounds positive values toward +infinity, but negative values
// toward -infinity. Adjust the rounding mode to Ceil to round negative
// values in the same direction as positive values.
return TemporalRoundingMode::Ceil;
case TemporalRoundingMode::Trunc:
// Truncation rounds positive values down toward zero, but negative values
// up toward zero. Adjust the rounding mode to Floor to round negative
// values in the same direction as positive values.
return TemporalRoundingMode::Floor;
case TemporalRoundingMode::HalfExpand:
// Adjust the rounding mode to Half-Ceil, similar to the Expand case.
return TemporalRoundingMode::HalfCeil;
case TemporalRoundingMode::HalfTrunc:
// Adjust the rounding mode to Half-Floor, similar to the Trunc case.
return TemporalRoundingMode::HalfFloor;
}
MOZ_CRASH("unexpected rounding mode");
}
// Temporal performs division on "mathematical values" [1] with implies using
// infinite precision. This rules out using IEE-754 floating point types like
// `double`. It also means we can't implement the algorithms from the
// specification verbatim, but instead have to translate them into equivalent
// operations.
//
// Throughout the following division functions, the divisor is required to be
// positive. This allows to simplify the implementation, because it ensures
// non-zero quotient and remainder values have the same sign as the dividend.
//
/**
* Compute ceiling division ⌈dividend / divisor⌉. The divisor must be a positive
* number.
*/
constexpr int64_t CeilDiv(int64_t dividend, int64_t divisor) {
MOZ_ASSERT(divisor > 0, "negative divisor not supported");
// NB: Division and modulo operation are fused into a single machine code
// instruction by the compiler.
int64_t quotient = dividend / divisor;
int64_t remainder = dividend % divisor;
// Ceiling division rounds the quotient toward positive infinity. When the
// quotient is negative, this is equivalent to rounding toward zero. See [1].
//
// int64_t division truncates, so rounding toward zero for negative quotients
// is already covered. When there is a non-zero positive remainder, the
// quotient is positive and we have to increment it by one to implement
// rounding toward positive infinity.
//
// [1]
if (remainder > 0) {
quotient += 1;
}
return quotient;
}
/**
* Compute floor division ⌊dividend / divisor⌋. The divisor must be a positive
* number.
*/
constexpr int64_t FloorDiv(int64_t dividend, int64_t divisor) {
MOZ_ASSERT(divisor > 0, "negative divisor not supported");
// NB: Division and modulo operation are fused into a single machine code
// instruction by the compiler.
int64_t quotient = dividend / divisor;
int64_t remainder = dividend % divisor;
// Floor division rounds the quotient toward negative infinity. When the
// quotient is positive, this is equivalent to rounding toward zero. See [1].
//
// int64_t division truncates, so rounding toward zero for positive quotients
// is already covered. When there is a non-zero negative remainder, the
// quotient is negative and we have to decrement it by one to implement
// rounding toward negative infinity.
//
// [1]
if (remainder < 0) {
quotient -= 1;
}
return quotient;
}
/**
* Compute "round toward infinity" division `dividend / divisor`. The divisor
* must be a positive number.
*/
constexpr int64_t ExpandDiv(int64_t dividend, int64_t divisor) {
MOZ_ASSERT(divisor > 0, "negative divisor not supported");
// NB: Division and modulo operation are fused into a single machine code
// instruction by the compiler.
int64_t quotient = dividend / divisor;
int64_t remainder = dividend % divisor;
// "Round toward infinity" division rounds positive quotients toward positive
// infinity and negative quotients toward negative infinity. See [1].
//
// When there is a non-zero positive remainder, the quotient is positive and
// we have to increment it by one to implement rounding toward positive
// infinity. When there is a non-zero negative remainder, the quotient is
// negative and we have to decrement it by one to implement rounding toward
// negative infinity.
//
// [1]
if (remainder > 0) {
quotient += 1;
}
if (remainder < 0) {
quotient -= 1;
}
return quotient;
}
/**
* Compute truncating division `dividend / divisor`. The divisor must be a
* positive number.
*/
constexpr int64_t TruncDiv(int64_t dividend, int64_t divisor) {
MOZ_ASSERT(divisor > 0, "negative divisor not supported");
// Truncating division rounds both positive and negative quotients toward
// zero, cf. [1].
//
// int64_t division truncates, so rounding toward zero implicitly happens.
//
// [1]
return dividend / divisor;
}
/**
* Compute "round half toward positive infinity" division `dividend / divisor`.
* The divisor must be a positive number.
*/
inline int64_t HalfCeilDiv(int64_t dividend, int64_t divisor) {
MOZ_ASSERT(divisor > 0, "negative divisor not supported");
// NB: Division and modulo operation are fused into a single machine code
// instruction by the compiler.
int64_t quotient = dividend / divisor;
int64_t remainder = dividend % divisor;
// "Round half toward positive infinity" division rounds the quotient toward
// positive infinity when the fractional part of the remainder is ≥0.5. When
// the quotient is negative, this is equivalent to rounding toward zero
// instead of toward positive infinity. See [1].
//
// When the remainder is a non-zero positive value, the quotient is positive,
// too. When additionally the fractional part of the remainder is ≥0.5, we
// have to increment the quotient by one to implement rounding toward positive
// infinity.
//
// int64_t division truncates, so we implicitly round toward zero for negative
// quotients. When the absolute value of the fractional part of the remainder
// is >0.5, we should instead have rounded toward negative infinity, so we
// need to decrement the quotient by one.
//
// [1]
if (remainder > 0 && uint64_t(std::abs(remainder)) * 2 >= uint64_t(divisor)) {
quotient += 1;
}
if (remainder < 0 && uint64_t(std::abs(remainder)) * 2 > uint64_t(divisor)) {
quotient -= 1;
}
return quotient;
}
/**
* Compute "round half toward negative infinity" division `dividend / divisor`.
* The divisor must be a positive number.
*/
inline int64_t HalfFloorDiv(int64_t dividend, int64_t divisor) {
MOZ_ASSERT(divisor > 0, "negative divisor not supported");
// NB: Division and modulo operation are fused into a single machine code
// instruction by the compiler.
int64_t quotient = dividend / divisor;
int64_t remainder = dividend % divisor;
// "Round half toward negative infinity" division rounds the quotient toward
// negative infinity when the fractional part of the remainder is ≥0.5. When
// the quotient is positive, this is equivalent to rounding toward zero
// instead of toward negative infinity. See [1].
//
// When the remainder is a non-zero negative value, the quotient is negative,
// too. When additionally the fractional part of the remainder is ≥0.5, we
// have to decrement the quotient by one to implement rounding toward negative
// infinity.
//
// int64_t division truncates, so we implicitly round toward zero for positive
// quotients. When the absolute value of the fractional part of the remainder
// is >0.5, we should instead have rounded toward positive infinity, so we
// need to increment the quotient by one.
//
// [1]
if (remainder < 0 && uint64_t(std::abs(remainder)) * 2 >= uint64_t(divisor)) {
quotient -= 1;
}
if (remainder > 0 && uint64_t(std::abs(remainder)) * 2 > uint64_t(divisor)) {
quotient += 1;
}
return quotient;
}
/**
* Compute "round half toward infinity" division `dividend / divisor`. The
* divisor must be a positive number.
*/
inline int64_t HalfExpandDiv(int64_t dividend, int64_t divisor) {
MOZ_ASSERT(divisor > 0, "negative divisor not supported");
// NB: Division and modulo operation are fused into a single machine code
// instruction by the compiler.
int64_t quotient = dividend / divisor;
int64_t remainder = dividend % divisor;
// "Round half toward infinity" division rounds positive quotients whose
// remainder has a fractional part ≥0.5 toward positive infinity. And negative
// quotients whose remainder has a fractional part ≥0.5 toward negative
// infinity. See [1].
//
// int64_t division truncates, which means it rounds toward zero, so we have
// to increment resp. decrement the quotient when the fractional part of the
// remainder is ≥0.5 to round toward ±infinity.
//
// [1]
if (uint64_t(std::abs(remainder)) * 2 >= uint64_t(divisor)) {
quotient += (dividend > 0) ? 1 : -1;
}
return quotient;
}
/**
* Compute "round half toward zero" division `dividend / divisor`. The divisor
* must be a positive number.
*/
inline int64_t HalfTruncDiv(int64_t dividend, int64_t divisor) {
MOZ_ASSERT(divisor > 0, "negative divisor not supported");
// NB: Division and modulo operation are fused into a single machine code
// instruction by the compiler.
int64_t quotient = dividend / divisor;
int64_t remainder = dividend % divisor;
// "Round half toward zero" division rounds both positive and negative
// quotients whose remainder has a fractional part ≤0.5 toward zero. See [1].
//
// int64_t division truncates, so we implicitly round toward zero. When the
// fractional part of the remainder is >0.5, we should instead have rounded
// toward ±infinity, so we need to increment resp. decrement the quotient by
// one.
//
// [1]
if (uint64_t(std::abs(remainder)) * 2 > uint64_t(divisor)) {
quotient += (dividend > 0) ? 1 : -1;
}
return quotient;
}
/**
* Compute "round half to even" division `dividend / divisor`. The divisor must
* be a positive number.
*/
inline int64_t HalfEvenDiv(int64_t dividend, int64_t divisor) {
MOZ_ASSERT(divisor > 0, "negative divisor not supported");
// NB: Division and modulo operation are fused into a single machine code
// instruction by the compiler.
int64_t quotient = dividend / divisor;
int64_t remainder = dividend % divisor;
// "Round half to even" division rounds both positive and negative quotients
// to the nearest even integer. See [1].
//
// int64_t division truncates, so we implicitly round toward zero. When the
// fractional part of the remainder is 0.5 and the quotient is odd or when the
// fractional part of the remainder is >0.5, we should instead have rounded
// toward ±infinity, so we need to increment resp. decrement the quotient by
// one.
//
// [1]
if ((quotient & 1) == 1 &&
uint64_t(std::abs(remainder)) * 2 == uint64_t(divisor)) {
quotient += (dividend > 0) ? 1 : -1;
}
if (uint64_t(std::abs(remainder)) * 2 > uint64_t(divisor)) {
quotient += (dividend > 0) ? 1 : -1;
}
return quotient;
}
/**
* Perform `dividend / divisor` and round the result according to the given
* rounding mode.
*/
inline int64_t Divide(int64_t dividend, int64_t divisor,
TemporalRoundingMode roundingMode) {
switch (roundingMode) {
case TemporalRoundingMode::Ceil:
return CeilDiv(dividend, divisor);
case TemporalRoundingMode::Floor:
return FloorDiv(dividend, divisor);
case TemporalRoundingMode::Expand:
return ExpandDiv(dividend, divisor);
case TemporalRoundingMode::Trunc:
return TruncDiv(dividend, divisor);
case TemporalRoundingMode::HalfCeil:
return HalfCeilDiv(dividend, divisor);
case TemporalRoundingMode::HalfFloor:
return HalfFloorDiv(dividend, divisor);
case TemporalRoundingMode::HalfExpand:
return HalfExpandDiv(dividend, divisor);
case TemporalRoundingMode::HalfTrunc:
return HalfTruncDiv(dividend, divisor);
case TemporalRoundingMode::HalfEven:
return HalfEvenDiv(dividend, divisor);
}
MOZ_CRASH("invalid rounding mode");
}
/**
* Compute ceiling division ⌈dividend / divisor⌉. The divisor must be a positive
* number.
*/
constexpr Int128 CeilDiv(const Int128& dividend, const Int128& divisor) {
MOZ_ASSERT(divisor > Int128{0}, "negative divisor not supported");
auto [quotient, remainder] = dividend.divrem(divisor);
// Ceiling division rounds the quotient toward positive infinity. When the
// quotient is negative, this is equivalent to rounding toward zero. See [1].
//
// Int128 division truncates, so rounding toward zero for negative quotients
// is already covered. When there is a non-zero positive remainder, the
// quotient is positive and we have to increment it by one to implement
// rounding toward positive infinity.
//
// [1]
if (remainder > Int128{0}) {
quotient += Int128{1};
}
return quotient;
}
/**
* Compute floor division ⌊dividend / divisor⌋. The divisor must be a positive
* number.
*/
constexpr Int128 FloorDiv(const Int128& dividend, const Int128& divisor) {
MOZ_ASSERT(divisor > Int128{0}, "negative divisor not supported");
auto [quotient, remainder] = dividend.divrem(divisor);
// Floor division rounds the quotient toward negative infinity. When the
// quotient is positive, this is equivalent to rounding toward zero. See [1].
//
// Int128 division truncates, so rounding toward zero for positive quotients
// is already covered. When there is a non-zero negative remainder, the
// quotient is negative and we have to decrement it by one to implement
// rounding toward negative infinity.
//
// [1]
if (remainder < Int128{0}) {
quotient -= Int128{1};
}
return quotient;
}
/**
* Compute "round toward infinity" division `dividend / divisor`. The divisor
* must be a positive number.
*/
constexpr Int128 ExpandDiv(const Int128& dividend, const Int128& divisor) {
MOZ_ASSERT(divisor > Int128{0}, "negative divisor not supported");
auto [quotient, remainder] = dividend.divrem(divisor);
// "Round toward infinity" division rounds positive quotients toward positive
// infinity and negative quotients toward negative infinity. See [1].
//
// When there is a non-zero positive remainder, the quotient is positive and
// we have to increment it by one to implement rounding toward positive
// infinity. When there is a non-zero negative remainder, the quotient is
// negative and we have to decrement it by one to implement rounding toward
// negative infinity.
//
// [1]
if (remainder > Int128{0}) {
quotient += Int128{1};
}
if (remainder < Int128{0}) {
quotient -= Int128{1};
}
return quotient;
}
/**
* Compute truncating division `dividend / divisor`. The divisor must be a
* positive number.
*/
constexpr Int128 TruncDiv(const Int128& dividend, const Int128& divisor) {
MOZ_ASSERT(divisor > Int128{0}, "negative divisor not supported");
// Truncating division rounds both positive and negative quotients toward
// zero, cf. [1].
//
// Int128 division truncates, so rounding toward zero implicitly happens.
//
// [1]
return dividend / divisor;
}
/**
* Compute "round half toward positive infinity" division `dividend / divisor`.
* The divisor must be a positive number.
*/
inline Int128 HalfCeilDiv(const Int128& dividend, const Int128& divisor) {
MOZ_ASSERT(divisor > Int128{0}, "negative divisor not supported");
auto [quotient, remainder] = dividend.divrem(divisor);
// "Round half toward positive infinity" division rounds the quotient toward
// positive infinity when the fractional part of the remainder is ≥0.5. When
// the quotient is negative, this is equivalent to rounding toward zero
// instead of toward positive infinity. See [1].
//
// When the remainder is a non-zero positive value, the quotient is positive,
// too. When additionally the fractional part of the remainder is ≥0.5, we
// have to increment the quotient by one to implement rounding toward positive
// infinity.
//
// Int128 division truncates, so we implicitly round toward zero for negative
// quotients. When the absolute value of the fractional part of the remainder
// is >0.5, we should instead have rounded toward negative infinity, so we
// need to decrement the quotient by one.
//
// [1]
if (remainder > Int128{0} &&
Uint128(remainder.abs()) * Uint128{2} >= static_cast<Uint128>(divisor)) {
quotient += Int128{1};
}
if (remainder < Int128{0} &&
Uint128(remainder.abs()) * Uint128{2} > static_cast<Uint128>(divisor)) {
quotient -= Int128{1};
}
return quotient;
}
/**
* Compute "round half toward negative infinity" division `dividend / divisor`.
* The divisor must be a positive number.
*/
inline Int128 HalfFloorDiv(const Int128& dividend, const Int128& divisor) {
MOZ_ASSERT(divisor > Int128{0}, "negative divisor not supported");
auto [quotient, remainder] = dividend.divrem(divisor);
// "Round half toward negative infinity" division rounds the quotient toward
// negative infinity when the fractional part of the remainder is ≥0.5. When
// the quotient is positive, this is equivalent to rounding toward zero
// instead of toward negative infinity. See [1].
//
// When the remainder is a non-zero negative value, the quotient is negative,
// too. When additionally the fractional part of the remainder is ≥0.5, we
// have to decrement the quotient by one to implement rounding toward negative
// infinity.
//
// Int128 division truncates, so we implicitly round toward zero for positive
// quotients. When the absolute value of the fractional part of the remainder
// is >0.5, we should instead have rounded toward positive infinity, so we
// need to increment the quotient by one.
//
// [1]
if (remainder < Int128{0} &&
Uint128(remainder.abs()) * Uint128{2} >= static_cast<Uint128>(divisor)) {
quotient -= Int128{1};
}
if (remainder > Int128{0} &&
Uint128(remainder.abs()) * Uint128{2} > static_cast<Uint128>(divisor)) {
quotient += Int128{1};
}
return quotient;
}
/**
* Compute "round half toward infinity" division `dividend / divisor`. The
* divisor must be a positive number.
*/
inline Int128 HalfExpandDiv(const Int128& dividend, const Int128& divisor) {
MOZ_ASSERT(divisor > Int128{0}, "negative divisor not supported");
auto [quotient, remainder] = dividend.divrem(divisor);
// "Round half toward infinity" division rounds positive quotients whose
// remainder has a fractional part ≥0.5 toward positive infinity. And negative
// quotients whose remainder has a fractional part ≥0.5 toward negative
// infinity. See [1].
//
// Int128 division truncates, which means it rounds toward zero, so we have
// to increment resp. decrement the quotient when the fractional part of the
// remainder is ≥0.5 to round toward ±infinity.
//
// [1]
if (Uint128(remainder.abs()) * Uint128{2} >= static_cast<Uint128>(divisor)) {
quotient += (dividend > Int128{0}) ? Int128{1} : Int128{-1};
}
return quotient;
}
/**
* Compute "round half toward zero" division `dividend / divisor`. The divisor
* must be a positive number.
*/
inline Int128 HalfTruncDiv(const Int128& dividend, const Int128& divisor) {
MOZ_ASSERT(divisor > Int128{0}, "negative divisor not supported");
auto [quotient, remainder] = dividend.divrem(divisor);
// "Round half toward zero" division rounds both positive and negative
// quotients whose remainder has a fractional part ≤0.5 toward zero. See [1].
//
// Int128 division truncates, so we implicitly round toward zero. When the
// fractional part of the remainder is >0.5, we should instead have rounded
// toward ±infinity, so we need to increment resp. decrement the quotient by
// one.
//
// [1]
if (Uint128(remainder.abs()) * Uint128{2} > static_cast<Uint128>(divisor)) {
quotient += (dividend > Int128{0}) ? Int128{1} : Int128{-1};
}
return quotient;
}
/**
* Compute "round half to even" division `dividend / divisor`. The divisor must
* be a positive number.
*/
inline Int128 HalfEvenDiv(const Int128& dividend, const Int128& divisor) {
MOZ_ASSERT(divisor > Int128{0}, "negative divisor not supported");
auto [quotient, remainder] = dividend.divrem(divisor);
// "Round half to even" division rounds both positive and negative quotients
// to the nearest even integer. See [1].
//
// Int128 division truncates, so we implicitly round toward zero. When the
// fractional part of the remainder is 0.5 and the quotient is odd or when the
// fractional part of the remainder is >0.5, we should instead have rounded
// toward ±infinity, so we need to increment resp. decrement the quotient by
// one.
//
// [1]
if ((quotient & Int128{1}) == Int128{1} &&
Uint128(remainder.abs()) * Uint128{2} == static_cast<Uint128>(divisor)) {
quotient += (dividend > Int128{0}) ? Int128{1} : Int128{-1};
}
if (Uint128(remainder.abs()) * Uint128{2} > static_cast<Uint128>(divisor)) {
quotient += (dividend > Int128{0}) ? Int128{1} : Int128{-1};
}
return quotient;
}
/**
* Perform `dividend / divisor` and round the result according to the given
* rounding mode.
*/
inline Int128 Divide(const Int128& dividend, const Int128& divisor,
TemporalRoundingMode roundingMode) {
switch (roundingMode) {
case TemporalRoundingMode::Ceil:
return CeilDiv(dividend, divisor);
case TemporalRoundingMode::Floor:
return FloorDiv(dividend, divisor);
case TemporalRoundingMode::Expand:
return ExpandDiv(dividend, divisor);
case TemporalRoundingMode::Trunc:
return TruncDiv(dividend, divisor);
case TemporalRoundingMode::HalfCeil:
return HalfCeilDiv(dividend, divisor);
case TemporalRoundingMode::HalfFloor:
return HalfFloorDiv(dividend, divisor);
case TemporalRoundingMode::HalfExpand:
return HalfExpandDiv(dividend, divisor);
case TemporalRoundingMode::HalfTrunc:
return HalfTruncDiv(dividend, divisor);
case TemporalRoundingMode::HalfEven:
return HalfEvenDiv(dividend, divisor);
}
MOZ_CRASH("invalid rounding mode");
}
} /* namespace js::temporal */
#endif /* builtin_temporal_TemporalRoundingMode_h */