Functions and class for high precision Q64.64 fixed point arithmetic. More...

Files
file	cairo-wideint-private.h
	`cairo_x` function declarations, which provide the fallback high precision arithmetic implementation.

file	cairo-wideint.c
	Implementation of the cairo_x functions which implement high precision arithmetic.

file	int64x64-128.cc
	Implementation of the ns3::int64x64_t type using a native int128_t type.

file	int64x64-128.h
	Declaration of the ns3::int64x64_t type using a native int128_t type.

file	int64x64-cairo.cc
	Implementation of the ns3::int64x64_t type using the Cairo implementation.

file	int64x64-cairo.h
	Declaration of the ns3::int64x64_t type using the Cairo implementation.

file	int64x64-double.h
	Declaration and implementation of the ns3::int64x64_t type using the double type.

file	int64x64.cc
	Implementation of the streaming input and output operators for the ns3::int64x64_t type.

file	int64x64.h
	Declaration of the ns3::int64x64_t type and associated operators.

Classes
class	ns3::int64x64_t
	High precision numerical type, implementing Q64.64 fixed precision. More...

Macros
#define	HEXHILOW(hi, lo)
	Print the high and low words of an int64x64 in hex, for debugging. More...

Functions
int64x64_t	ns3::Abs (const int64x64_t &value)
	Absolute value. More...

int64x64_t	ns3::Max (const int64x64_t &a, const int64x64_t &b)
	Maximum. More...

int64x64_t	ns3::Min (const int64x64_t &a, const int64x64_t &b)
	Minimum. More...

int64x64_t	ns3::operator! (const int64x64_t &lhs)
	Logical not operator. More...

bool	ns3::operator!= (const int64x64_t &lhs, const int64x64_t &rhs)
	Inequality operator. More...

int64x64_t	ns3::operator* (const int64x64_t &lhs, const int64x64_t &rhs)
	Multiplication operator. More...

int64x64_t &	ns3::operator*= (int64x64_t &lhs, const int64x64_t &rhs)
	Compound multiplication operator. More...

int64x64_t	ns3::operator+ (const int64x64_t &lhs, const int64x64_t &rhs)
	Addition operator. More...

int64x64_t	ns3::operator+ (const int64x64_t &lhs)
	Unary plus operator. More...

int64x64_t &	ns3::operator+= (int64x64_t &lhs, const int64x64_t &rhs)
	Compound addition operator. More...

int64x64_t	ns3::operator- (const int64x64_t &lhs, const int64x64_t &rhs)
	Subtraction operator. More...

int64x64_t	ns3::operator- (const int64x64_t &lhs)
	Unary negation operator (change sign operator). More...

int64x64_t &	ns3::operator-= (int64x64_t &lhs, const int64x64_t &rhs)
	Compound subtraction operator. More...

int64x64_t	ns3::operator/ (const int64x64_t &lhs, const int64x64_t &rhs)
	Division operator. More...

int64x64_t &	ns3::operator/= (int64x64_t &lhs, const int64x64_t &rhs)
	Compound division operator. More...

bool	ns3::operator< (const int64x64_t &lhs, const int64x64_t &rhs)
	Less than operator. More...

std::ostream &	ns3::operator<< (std::ostream &os, const int64x64_t &value)
	Output streamer for int64x64_t. More...

bool	ns3::operator<= (const int64x64_t &lhs, const int64x64_t &rhs)
	Less or equal operator. More...

bool	ns3::operator== (const int64x64_t &lhs, const int64x64_t &rhs)
	Equality operator. More...

bool	ns3::operator> (const int64x64_t &lhs, const int64x64_t &rhs)
	Greater operator. More...

bool	ns3::operator>= (const int64x64_t &lhs, const int64x64_t &rhs)
	Greater or equal operator. More...

std::istream &	ns3::operator>> (std::istream &is, int64x64_t &value)
	Input streamer for int64x64_t. More...

static bool	ns3::output_sign (const int128_t sa, const int128_t sb, uint128_t &ua, uint128_t &ub)
	Compute the sign of the result of multiplying or dividing Q64.64 fixed precision operands. More...

static bool	ns3::output_sign (const cairo_int128_t sa, const cairo_int128_t sb, cairo_uint128_t &ua, cairo_uint128_t &ub)
	Compute the sign of the result of multiplying or dividing Q64.64 fixed precision operands. More...

static uint64_t	ns3::ReadHiDigits (std::string str)
	Read the integer portion of a number from a string containing just the integral digits (no decimal point or fractional part). More...

static uint64_t	ns3::ReadLoDigits (std::string str)
	Read the fractional part of a number from a string containing just the decimal digits of the fractional part (no integral part or decimal point). More...

Detailed Description

Functions and class for high precision Q64.64 fixed point arithmetic.

A Q64.64 fixed precision number consists of:

Bits	Function
1	Sign bit
63	Integer portion
64	Fractional portion

The high word consists of the sign bit and integer value; the low word is the fractional part, unscaled.

All standard arithmetic operations are supported:

Category	Operators
Computation	`+`, `+=`, `-`, `-=`, ``, `=`, `/`, `/=`
Comparison	`==`, `!=`, `<`, `<=`, `>`, `>=`
Unary	`+`, `-`, `!`

Macro Definition Documentation

◆ HEXHILOW

#define HEXHILOW	(	hi,
		lo
	)

Value:

std::hex << std::setfill ('0') << std::right << " (0x"                \
           << std::setw (16) << hi << " "                               \
           << std::setw (16) << lo                                      \
           << std::dec << std::setfill (' ') << std::left << ")"

Print the high and low words of an int64x64 in hex, for debugging.

Parameters

[in]	hi	The high (integer) word.
[in]	lo	The low (fractional) work.

Definition at line 49 of file int64x64.cc.

Referenced by ns3::operator<<().

Function Documentation

◆ Abs()

int64x64_t ns3::Abs ( const int64x64_t & value )

inline

Absolute value.

Parameters

[in] value The value to operate on.

Returns: The absolute value of value.

Definition at line 184 of file int64x64.h.

Referenced by ns3::int64x64::test::Int64x64InputOutputTestCase::Check(), ns3::int64x64::test::Int64x64DoubleTestCase::Check(), ns3::int64x64::test::Int64x64InvertTestCase::CheckCase(), ns3::RttMeanDeviation::FloatingPointUpdate(), and ns3::DelayJitterEstimation::RecordRx().

◆ Max()

int64x64_t ns3::Max	(	const int64x64_t &	a,
		const int64x64_t &	b
	)

inline

Maximum.

Parameters

[in]	a	The first value.
[in]	b	The second value.

Returns: The larger of the arguments.

Definition at line 209 of file int64x64.h.

Referenced by ns3::int64x64::test::Int64x64HiLoTestCase::Check(), ns3::int64x64::test::Int64x64InputTestCase::Check(), ns3::TcpSocketBase::DoPeerClose(), ns3::AarfWifiManager::DoReportDataFailed(), ns3::AarfcdWifiManager::DoReportDataFailed(), ns3::TcpSocketBase::EstimateRtt(), ns3::WifiPhyStateHelper::GetDelayUntilIdle(), ns3::WifiPhyStateHelper::LogPreviousIdleAndCcaBusyStates(), ns3::ChannelAccessManager::MostRecent(), ns3::TcpSocketBase::NewAck(), ns3::MinstrelHtWifiManager::PrintTable(), ns3::TcpSocketSmallAcks::SendEmptyPacket(), ns3::TcpSocketBase::SendEmptyPacket(), ns3::WifiPhyStateHelper::SwitchToChannelSwitching(), ns3::WifiPhyStateHelper::SwitchToOff(), ns3::WifiPhyStateHelper::SwitchToRx(), ns3::WifiPhyStateHelper::SwitchToSleep(), and ns3::WifiPhyStateHelper::SwitchToTx().

◆ Min()

int64x64_t ns3::Min	(	const int64x64_t &	a,
		const int64x64_t &	b
	)

inline

Minimum.

Parameters

[in]	a	The first value.
[in]	b	The second value.

Returns: The smaller of the arguments.

Definition at line 197 of file int64x64.h.

Referenced by ns3::RemoteChannelBundle::AddChannel(), ns3::NullMessageSimulatorImpl::CalculateGuaranteeTime(), ns3::MinstrelHtWifiManager::CalculateRetransmits(), ns3::int64x64::test::Int64x64HiLoTestCase::Check(), ns3::int64x64::test::Int64x64InputTestCase::Check(), ns3::ConstantRateWifiManager::DoGetDataTxVector(), ns3::AarfWifiManager::DoReportDataFailed(), ns3::AarfcdWifiManager::DoReportDataFailed(), ns3::RemoteChannelBundleManager::GetSafeTime(), ns3::NullMessageSimulatorImpl::NullMessageEventHandler(), and ns3::TcpSocketBase::ReTxTimeout().

◆ operator!()

int64x64_t ns3::operator! ( const int64x64_t & lhs )

inline

Logical not operator.

Definition at line 426 of file int64x64-128.h.

References ns3::int64x64_t::_v.

◆ operator!=()

bool ns3::operator!=	(	const int64x64_t &	lhs,
		const int64x64_t &	rhs
	)

inline

Inequality operator.

Definition at line 129 of file int64x64.h.

◆ operator*()

int64x64_t ns3::operator*	(	const int64x64_t &	lhs,
		const int64x64_t &	rhs
	)

inline

Multiplication operator.

Definition at line 108 of file int64x64.h.

◆ operator*=()

int64x64_t & ns3::operator*=	(	int64x64_t &	lhs,
		const int64x64_t &	rhs
	)

inline

Compound multiplication operator.

Definition at line 391 of file int64x64-128.h.

References ns3::int64x64_t::Mul().

◆ operator+() [1/2]

int64x64_t ns3::operator+	(	const int64x64_t &	lhs,
		const int64x64_t &	rhs
	)

inline

Addition operator.

Definition at line 86 of file int64x64.h.

◆ operator+() [2/2]

int64x64_t ns3::operator+ ( const int64x64_t & lhs )

inline

Unary plus operator.

Definition at line 410 of file int64x64-128.h.

◆ operator+=()

int64x64_t & ns3::operator+=	(	int64x64_t &	lhs,
		const int64x64_t &	rhs
	)

inline

Compound addition operator.

Definition at line 373 of file int64x64-128.h.

References ns3::int64x64_t::_v.

◆ operator-() [1/2]

int64x64_t ns3::operator-	(	const int64x64_t &	lhs,
		const int64x64_t &	rhs
	)

inline

Subtraction operator.

Definition at line 97 of file int64x64.h.

◆ operator-() [2/2]

int64x64_t ns3::operator- ( const int64x64_t & lhs )

inline

Unary negation operator (change sign operator).

Unary negation operator (change sign operator)

Definition at line 418 of file int64x64-128.h.

References ns3::int64x64_t::_v.

◆ operator-=()

int64x64_t & ns3::operator-=	(	int64x64_t &	lhs,
		const int64x64_t &	rhs
	)

inline

Compound subtraction operator.

Definition at line 382 of file int64x64-128.h.

References ns3::int64x64_t::_v.

◆ operator/()

int64x64_t ns3::operator/	(	const int64x64_t &	lhs,
		const int64x64_t &	rhs
	)

inline

Division operator.

Definition at line 119 of file int64x64.h.

◆ operator/=()

int64x64_t & ns3::operator/=	(	int64x64_t &	lhs,
		const int64x64_t &	rhs
	)

inline

Compound division operator.

Definition at line 400 of file int64x64-128.h.

References ns3::int64x64_t::Div().

◆ operator<()

bool ns3::operator<	(	const int64x64_t &	lhs,
		const int64x64_t &	rhs
	)

inline

Less than operator.

Definition at line 356 of file int64x64-128.h.

References ns3::int64x64_t::_v.

◆ operator<<()

std::ostream & ns3::operator<<	(	std::ostream &	os,
		const int64x64_t &	value
	)

Output streamer for int64x64_t.

Internal:: This algorithm is exact to the precision requested, up to the full 64 decimal digits required to exactly represent a 64-bit fraction.

Proper rounding turns out to be surprisingly hard. In y.xxxx5|6, where the | marks follows the last output digit, rounding the 5|6 to 6| is straightforward. However, rounding y.xxx99|6 should result in y.xx100|. Notice the effect of rounding percolates to higher digits. We accumulate the output digits in a string, then carry out the rounding in the string directly.

Values are printed with the following format flags (independent of the stream flags):

showpos
left

The stream width is ignored. If floatfield is set, precision decimal places are printed. If floatfield is not set, all digits of the fractional part are printed, up to the representation limit of 20 digits; trailing zeros are omitted.

Parameters

[in,out]	os	The output stream.
[in]	value	The numerical value to print.

Returns: The stream.

Definition at line 69 of file int64x64.cc.

References ns3::int64x64_t::GetHigh(), ns3::int64x64_t::GetLow(), HEXHILOW, NS_ASSERT_MSG(), and NS_LOG_LOGIC().

◆ operator<=()

bool ns3::operator<=	(	const int64x64_t &	lhs,
		const int64x64_t &	rhs
	)

inline

Less or equal operator.

Definition at line 137 of file int64x64.h.

◆ operator==()

bool ns3::operator==	(	const int64x64_t &	lhs,
		const int64x64_t &	rhs
	)

inline

Equality operator.

Definition at line 348 of file int64x64-128.h.

References ns3::int64x64_t::_v.

◆ operator>()

bool ns3::operator>	(	const int64x64_t &	lhs,
		const int64x64_t &	rhs
	)

inline

Greater operator.

Definition at line 364 of file int64x64-128.h.

References ns3::int64x64_t::_v.

◆ operator>=()

bool ns3::operator>=	(	const int64x64_t &	lhs,
		const int64x64_t &	rhs
	)

inline

Greater or equal operator.

Definition at line 145 of file int64x64.h.

◆ operator>>()

std::istream & ns3::operator>>	(	std::istream &	is,
		int64x64_t &	value
	)

Input streamer for int64x64_t.

Parameters

[in,out]	is	The input stream.
[out]	value	The numerical value to set.

Returns: The stream.

Definition at line 221 of file int64x64.cc.

References ns3::ReadHiDigits(), and ns3::ReadLoDigits().

◆ output_sign() [1/2]

static bool ns3::output_sign	(	const int128_t	sa,
		const int128_t	sb,
		uint128_t &	ua,
		uint128_t &	ub
	)

inlinestatic

Compute the sign of the result of multiplying or dividing Q64.64 fixed precision operands.

Parameters

[in]	sa	The signed value of the first operand.
[in]	sb	The signed value of the second operand.
[out]	ua	The unsigned magnitude of the first operand.
[out]	ub	The unsigned magnitude of the second operand.

Returns: true if the result will be negative.

Definition at line 51 of file int64x64-128.cc.

Referenced by ns3::int64x64_t::Div(), and ns3::int64x64_t::Mul().

◆ output_sign() [2/2]

static bool ns3::output_sign	(	const cairo_int128_t	sa,
		const cairo_int128_t	sb,
		cairo_uint128_t &	ua,
		cairo_uint128_t &	ub
	)

inlinestatic

Compute the sign of the result of multiplying or dividing Q64.64 fixed precision operands.

Parameters

[in]	sa	The signed value of the first operand.
[in]	sb	The signed value of the second operand.
[out]	ua	The unsigned magnitude of the first operand.
[out]	ub	The unsigned magnitude of the second operand.

Returns: True if the result will be negative.

Definition at line 59 of file int64x64-cairo.cc.

References _cairo_int128_negative, _cairo_int128_to_uint128, and _cairo_uint128_negate().

◆ ReadHiDigits()

static uint64_t ns3::ReadHiDigits ( std::string str )

static

Read the integer portion of a number from a string containing just the integral digits (no decimal point or fractional part).

Parameters

[in] str The string representation of the integral part of a number, with no fractional part or decimal point.

Returns: The integer.

Definition at line 179 of file int64x64.cc.

Referenced by ns3::operator>>().

◆ ReadLoDigits()

static uint64_t ns3::ReadLoDigits ( std::string str )

static

Read the fractional part of a number from a string containing just the decimal digits of the fractional part (no integral part or decimal point).

Parameters

[in] str The string representation of the fractional part of a number, without integral part or decimal point.

Returns: The decimal portion of the input number.

Definition at line 202 of file int64x64.cc.

References ns3::int64x64_t::GetLow(), and NS_ASSERT_MSG().

Referenced by ns3::operator>>().

Files

Classes

Macros

Functions

Detailed Description

Macro Definition Documentation

◆ HEXHILOW

Function Documentation

◆ Abs()

◆ Max()

◆ Min()

◆ operator!()

◆ operator!=()

◆ operator*()

◆ operator*=()

◆ operator+() [1/2]

◆ operator+() [2/2]

◆ operator+=()

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator-=()

◆ operator/()

◆ operator/=()

◆ operator<()

◆ operator<<()

◆ operator<=()

◆ operator==()

◆ operator>()

◆ operator>=()

◆ operator>>()

◆ output_sign() [1/2]

◆ output_sign() [2/2]

◆ ReadHiDigits()

◆ ReadLoDigits()