A Discrete-Event Network Simulator
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MRG32k3a Namespace Reference

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 57 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]AFirst matrix argument.
[in]BSecond matrix argument.
[out]CResult matrix.
[in]mModulus.

Definition at line 183 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]AMatrix input argument.
[out]BMatrix output.
[in]mModulus.
[in]nExponent.

Definition at line 252 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]srcMatrix input argument A.
[out]dstMatrix output B.
[in]mModulus.
[in]eThe exponent.

Definition at line 222 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]AMatrix argument, 3x3.
[in]sThree component input vector.
[out]vThree component output vector.
[in]mModulus.

Definition at line 154 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]aFirst multiplicative argument.
[in]sSecond multiplicative argument.
[in]cAdditive argument.
[in]mModulus.
Returns
(a*s +c) MOD m

Definition at line 114 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 300 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]nThe power of 2.
[out]a1pThe first transition matrix power.
[out]a2pThe second transition matrix power.

Definition at line 318 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 69 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 72 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 87 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 75 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 78 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 94 of file rng-stream.cc.

Referenced by PowerOfTwoConstants().

◆ m1

◆ m2

◆ norm

◆ two17

const double MRG32k3a::two17 = 131072.0

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

Definition at line 81 of file rng-stream.cc.

Referenced by MultModM().

◆ two53

const double MRG32k3a::two53 = 9007199254740992.0

IEEE-754 floating point precision, 253

Definition at line 84 of file rng-stream.cc.

Referenced by MultModM().