Namespace for MRG32k3a implementation details. More...

Classes
struct	Precalculated
	The transition matrices of the two MRG components (in matrix form), raised to all powers of 2 from 1 to 191. More...

Typedefs
typedef double	Matrix[3][3]
	Type for 3x3 matrix of doubles.

Functions
void	MatMatModM (const Matrix A, const Matrix B, Matrix C, double m)
	Compute the matrix C = A*B MOD m.

void	MatPowModM (const double A[3][3], double B[3][3], double m, int32_t n)
	Compute the matrix B = (A^n Mod m); works even if A = B.

void	MatTwoPowModM (const Matrix src, Matrix dst, double m, int32_t e)
	Compute the matrix B = (A^(2^e) Mod m); works also if A = B.

void	MatVecModM (const Matrix A, const double s[3], double v[3], double m)
	Compute the vector v = A*s MOD m.

double	MultModM (double a, double s, double c, double m)
	Return (a*s + c) MOD m; a, s, c and m must be < 2^35.

Precalculated	PowerOfTwoConstants ()
	Compute the transition matrices of the two MRG components raised to all powers of 2 from 1 to 191.

void	PowerOfTwoMatrix (int n, Matrix a1p, Matrix a2p)
	Get the transition matrices raised to a power of 2.

Variables
const double	a12 = 1403580.0
	First component multiplier of n - 2 value.

const double	a13n = 810728.0
	First component multiplier of n - 3 value.

const Matrix	A1p0
	First component transition matrix.

const double	a21 = 527612.0
	Second component multiplier of n - 1 value.

const double	a23n = 1370589.0
	Second component multiplier of n - 3 value.

const Matrix	A2p0
	Second component transition matrix.

const double	m1 = 4294967087.0
	First component modulus, 2³² - 209.

const double	m2 = 4294944443.0
	Second component modulus, 2³² - 22853.

const double	norm = 1.0 / (m1 + 1.0)
	Normalization to obtain randoms on [0,1).

const double	two17 = 131072.0
	Decomposition factor for computing a*s in less than 53 bits, 2¹⁷

const double	two53 = 9007199254740992.0
	IEEE-754 floating point precision, 2⁵³

Detailed Description

Namespace for MRG32k3a implementation details.

Typedef Documentation

◆ Matrix

typedef double MRG32k3a::Matrix[3][3]

Type for 3x3 matrix of doubles.

Definition at line 46 of file rng-stream.cc.

Function Documentation

◆ MatMatModM()

void MRG32k3a::MatMatModM	(	const Matrix	A,
		const Matrix	B,
		Matrix	C,
		double	m )

Compute the matrix C = A*B MOD m.

Assume that -m < s[i] < m. Note: works also if A = C or B = C or A = B = C.

Parameters

[in]	A	First matrix argument.
[in]	B	Second matrix argument.
[out]	C	Result matrix.
[in]	m	Modulus.

Definition at line 172 of file rng-stream.cc.

References MatVecModM().

Referenced by MatPowModM(), and MatTwoPowModM().

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◆ MatPowModM()

void MRG32k3a::MatPowModM	(	const double	A[3][3],
		double	B[3][3],
		double	m,
		int32_t	n )

Compute the matrix B = (A^n Mod m); works even if A = B.

Parameters

[in]	A	Matrix input argument.
[out]	B	Matrix output.
[in]	m	Modulus.
[in]	n	Exponent.

Definition at line 241 of file rng-stream.cc.

References MatMatModM().

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◆ MatTwoPowModM()

void MRG32k3a::MatTwoPowModM	(	const Matrix	src,
		Matrix	dst,
		double	m,
		int32_t	e )

Compute the matrix B = (A^(2^e) Mod m); works also if A = B.

Parameters

[in]	src	Matrix input argument `A`.
[out]	dst	Matrix output `B`.
[in]	m	Modulus.
[in]	e	The exponent.

Definition at line 211 of file rng-stream.cc.

References MatMatModM().

Referenced by PowerOfTwoConstants().

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◆ MatVecModM()

void MRG32k3a::MatVecModM	(	const Matrix	A,
		const double	s[3],
		double	v[3],
		double	m )

Compute the vector v = A*s MOD m.

Assume that -m < s[i] < m. Works also when v = s.

Parameters

[in]	A	Matrix argument, 3x3.
[in]	s	Three component input vector.
[out]	v	Three component output vector.
[in]	m	Modulus.

Definition at line 143 of file rng-stream.cc.

References MultModM().

Referenced by ns3::RngStream::AdvanceNthBy(), and MatMatModM().

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◆ MultModM()

double MRG32k3a::MultModM	(	double	a,
		double	s,
		double	c,
		double	m )

Return (a*s + c) MOD m; a, s, c and m must be < 2^35.

This computes the result exactly, without exceeding the 53 bit precision of doubles.

Parameters

[in]	a	First multiplicative argument.
[in]	s	Second multiplicative argument.
[in]	c	Additive argument.
[in]	m	Modulus.

Returns: (a*s +c) MOD m

Definition at line 103 of file rng-stream.cc.

References two17, and two53.

Referenced by MatVecModM().

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◆ PowerOfTwoConstants()

Precalculated MRG32k3a::PowerOfTwoConstants ( )

Compute the transition matrices of the two MRG components raised to all powers of 2 from 1 to 191.

Returns: The precalculated powers of the transition matrices.

Definition at line 289 of file rng-stream.cc.

References MRG32k3a::Precalculated::a1, A1p0, MRG32k3a::Precalculated::a2, A2p0, m1, m2, and MatTwoPowModM().

Referenced by PowerOfTwoMatrix().

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◆ PowerOfTwoMatrix()

void MRG32k3a::PowerOfTwoMatrix	(	int	n,
		Matrix	a1p,
		Matrix	a2p )

Get the transition matrices raised to a power of 2.

Parameters

[in]	n	The power of 2.
[out]	a1p	The first transition matrix power.
[out]	a2p	The second transition matrix power.

Definition at line 307 of file rng-stream.cc.

References MRG32k3a::Precalculated::a1, MRG32k3a::Precalculated::a2, and PowerOfTwoConstants().

Referenced by ns3::RngStream::AdvanceNthBy().

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Variable Documentation

◆ a12

const double MRG32k3a::a12 = 1403580.0

First component multiplier of n - 2 value.

Definition at line 58 of file rng-stream.cc.

Referenced by ns3::RngStream::RandU01().

◆ a13n

const double MRG32k3a::a13n = 810728.0

First component multiplier of n - 3 value.

Definition at line 61 of file rng-stream.cc.

Referenced by ns3::RngStream::RandU01().

◆ A1p0

const Matrix MRG32k3a::A1p0

Initial value:

= {
  {       0.0,        1.0,       0.0 },
  {       0.0,        0.0,       1.0 },
  { -810728.0,  1403580.0,       0.0 }
}

First component transition matrix.

Definition at line 76 of file rng-stream.cc.

Referenced by PowerOfTwoConstants().

◆ a21

const double MRG32k3a::a21 = 527612.0

Second component multiplier of n - 1 value.

Definition at line 64 of file rng-stream.cc.

Referenced by ns3::RngStream::RandU01().

◆ a23n

const double MRG32k3a::a23n = 1370589.0

Second component multiplier of n - 3 value.

Definition at line 67 of file rng-stream.cc.

Referenced by ns3::RngStream::RandU01().

◆ A2p0

const Matrix MRG32k3a::A2p0

Initial value:

= {
  {        0.0,        1.0,       0.0 },
  {        0.0,        0.0,       1.0 },
  { -1370589.0,        0.0,  527612.0 }
}

Second component transition matrix.

Definition at line 83 of file rng-stream.cc.

Referenced by PowerOfTwoConstants().

◆ m1

const double MRG32k3a::m1 = 4294967087.0

First component modulus, 2³² - 209.

Definition at line 49 of file rng-stream.cc.

Referenced by PbbTestSuite::PbbTestSuite(), ns3::RngStream::RngStream(), ns3::RngStream::AdvanceNthBy(), UanTest::DoPhyTests(), ns3::tests::ComplexMatrixArrayTestCase::DoRun(), ns3::tests::MatrixArrayTestCase< T >::DoRun(), PowerOfTwoConstants(), and ns3::RngStream::RandU01().

◆ m2

const double MRG32k3a::m2 = 4294944443.0

Second component modulus, 2³² - 22853.

Definition at line 52 of file rng-stream.cc.

Referenced by PbbTestSuite::PbbTestSuite(), ns3::RngStream::RngStream(), ns3::RngStream::AdvanceNthBy(), ns3::tests::ComplexMatrixArrayTestCase::DoRun(), ns3::tests::MatrixArrayTestCase< T >::DoRun(), PowerOfTwoConstants(), and ns3::RngStream::RandU01().

◆ norm

const double MRG32k3a::norm = 1.0 / (m1 + 1.0)

Normalization to obtain randoms on [0,1).

Definition at line 55 of file rng-stream.cc.

Referenced by ns3::TwoRaySpectrumPropagationLossModel::CalcBeamformingGain(), ns3::PhasedArrayModel::GetBeamformingVector(), ns3::TwoRaySpectrumPropagationLossModel::GetFtrFastFading(), ns3::PhasedArrayModel::norm(), and ns3::RngStream::RandU01().

◆ two17

const double MRG32k3a::two17 = 131072.0

Decomposition factor for computing a*s in less than 53 bits, 2¹⁷

Definition at line 70 of file rng-stream.cc.

Referenced by MultModM().

◆ two53

const double MRG32k3a::two53 = 9007199254740992.0

IEEE-754 floating point precision, 2⁵³

Definition at line 73 of file rng-stream.cc.

Referenced by MultModM().

Classes

Typedefs

Functions

Variables

Detailed Description

Typedef Documentation

◆ Matrix

Function Documentation

◆ MatMatModM()

◆ MatPowModM()

◆ MatTwoPowModM()

◆ MatVecModM()

◆ MultModM()

◆ PowerOfTwoConstants()

◆ PowerOfTwoMatrix()

Variable Documentation

◆ a12

◆ a13n

◆ A1p0

◆ a21

◆ a23n

◆ A2p0

◆ m1

◆ m2

◆ norm

◆ two17

◆ two53