From 125902a87257f41f0051cc3ea283c732f0db2f66 Mon Sep 17 00:00:00 2001
From: Will Bainbridge <http://cfd.direct>
Date: Wed, 5 Jun 2024 12:29:00 +0100
Subject: [PATCH] randomGenerator: Global flag

A random generator can now be constructed with a global flag. If the
flag is false then the provided seed will be randomised across the
different processes. If the flag is true then the synchronicity of the
generators state will be checked when performing certain operations in
debug mode.
---
 applications/test/parallel/Test-parallel.C    |   2 +-
 applications/test/syncTools/Test-syncTools.C  |   2 +-
 .../randomGenerator/randomGenerator.C         |  69 ++++-
 .../randomGenerator/randomGenerator.H         | 128 ++++++++--
 .../randomGenerator/randomGeneratorI.H        | 237 +++++++++++++-----
 .../clouds/Templates/DSMCCloud/DSMCCloud.C    |   4 +-
 .../patchIntersection/star/starTemplates.C    |   3 +-
 .../decompositionMethods/random/random.C      |   2 +-
 .../boundaryRandom/boundaryRandom.C           |   2 +-
 .../sampledSet/circleRandom/circleRandom.C    |   2 +-
 .../sampledSet/sphereRandom/sphereRandom.C    |   2 +-
 src/waves/waveModels/irregular/irregular.C    |   2 +-
 12 files changed, 363 insertions(+), 92 deletions(-)

diff --git a/applications/test/parallel/Test-parallel.C b/applications/test/parallel/Test-parallel.C
index f679fefc13..09449c2435 100644
--- a/applications/test/parallel/Test-parallel.C
+++ b/applications/test/parallel/Test-parallel.C
@@ -56,7 +56,7 @@ int main(int argc, char *argv[])
 
     if (true)
     {
-        randomGenerator rndGen(43544*Pstream::myProcNo());
+        randomGenerator rndGen(43544);
 
         // Generate random data.
         List<Tuple2<label, List<scalar>>> complexData(100);
diff --git a/applications/test/syncTools/Test-syncTools.C b/applications/test/syncTools/Test-syncTools.C
index f7051cd29f..df898a803b 100644
--- a/applications/test/syncTools/Test-syncTools.C
+++ b/applications/test/syncTools/Test-syncTools.C
@@ -593,7 +593,7 @@ int main(int argc, char *argv[])
     #include "createPolyMesh.H"
 
 
-    randomGenerator rndGen(5341*(Pstream::myProcNo()+1));
+    randomGenerator rndGen(5341);
 
 
     // Face sync
diff --git a/src/OpenFOAM/primitives/randomGenerator/randomGenerator.C b/src/OpenFOAM/primitives/randomGenerator/randomGenerator.C
index e37d8f9c08..608bd0bb31 100644
--- a/src/OpenFOAM/primitives/randomGenerator/randomGenerator.C
+++ b/src/OpenFOAM/primitives/randomGenerator/randomGenerator.C
@@ -28,17 +28,75 @@ License
 
 // * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
 
-Foam::randomGenerator::randomGenerator(Istream& is)
+Foam::randomGenerator::randomGenerator(Istream& is, const bool global)
 :
+    global_(global),
     x_(pTraits<uint64_t>(is))
+{
+    checkSync();
+}
+
+
+Foam::randomGenerator::randomGenerator
+(
+    const word& name,
+    const dictionary& dict,
+    randomGenerator&& defaultRndGen
+)
+:
+    global_(defaultRndGen.global_),
+    x_
+    (
+        dict.found(name)
+      ? dict.lookup<uint64_t>(name)
+      : dict.found(name + "Seed")
+      ? seed(dict.lookup<label>(name + "Seed")).x(global_)
+      : defaultRndGen.x_
+    )
 {}
 
 
+Foam::randomGenerator::randomGenerator
+(
+    const word& name,
+    const dictionary& dict,
+    const seed defaultS,
+    const bool global
+)
+:
+    randomGenerator(name, dict, randomGenerator(defaultS, global))
+{}
+
+
+// * * * * * * * * * * * * * * Member Operators  * * * * * * * * * * * * * * //
+
+void Foam::randomGenerator::operator=(const randomGenerator& rndGen)
+{
+    if (global_ != rndGen.global_)
+    {
+        FatalErrorInFunction
+            << "Attempted assignment of a " << (global_ ? "" : "non-")
+            << "global random generator to a " << (rndGen.global_ ? "" : "non-")
+            << "global random generator"
+            << exit(FatalError);
+    }
+    x_ = rndGen.x_;
+    checkSync();
+}
+
+
+void Foam::randomGenerator::operator=(randomGenerator&& rndGen)
+{
+    *this = static_cast<const randomGenerator&>(rndGen);
+}
+
+
 // * * * * * * * * * * * * * * Friend Operators * * * * * * * * * * * * * * //
 
 Foam::Istream& Foam::operator>>(Istream& is, randomGenerator& rndGen)
 {
     is >> rndGen.x_;
+    rndGen.checkSync();
     is.check("operator>>(Istream& is, randomGenerator& rndGen)");
     return is;
 }
@@ -46,10 +104,19 @@ Foam::Istream& Foam::operator>>(Istream& is, randomGenerator& rndGen)
 
 Foam::Ostream& Foam::operator<<(Ostream& os, const randomGenerator& rndGen)
 {
+    rndGen.checkSync();
     os << rndGen.x_;
     os.check("operator<<(Ostream& os, const randomGenerator& rndGen)");
     return os;
 }
 
 
+// * * * * * * * * * * * * * * * Global Functions  * * * * * * * * * * * * * //
+
+void Foam::writeEntry(Ostream& os, const randomGenerator& rndGen)
+{
+    os << rndGen;
+}
+
+
 // ************************************************************************* //
diff --git a/src/OpenFOAM/primitives/randomGenerator/randomGenerator.H b/src/OpenFOAM/primitives/randomGenerator/randomGenerator.H
index f2305eced7..370b9d6ce0 100644
--- a/src/OpenFOAM/primitives/randomGenerator/randomGenerator.H
+++ b/src/OpenFOAM/primitives/randomGenerator/randomGenerator.H
@@ -67,6 +67,43 @@ Ostream& operator<<(Ostream&, const randomGenerator&);
 
 class randomGenerator
 {
+public:
+
+    // Public Classes
+
+        //- Seed class
+        class seed
+        {
+            // Private Data
+
+                //- The seed value
+                const uint64_t s_;
+
+
+            // Private Member Functions
+
+                //- Return the initial integer
+                inline uint64_t x(const bool global) const;
+
+
+        public:
+
+            //- Allow randomGenerator to access the seed value
+            friend class randomGenerator;
+
+
+            // Constructors
+
+                //- Construct from a label
+                inline seed(const label s);
+
+                //- Construct from a word
+                inline seed(const word& s);
+        };
+
+
+private:
+
     // Private Static Data
 
         //- The parameters of the linear congruential iteration
@@ -75,42 +112,78 @@ class randomGenerator
 
     // Private Data
 
+        //- Is this generator global?
+        const bool global_;
+
         //- The stored integer
         uint64_t x_;
 
 
     // Private Member Functions
 
+        //- Check the state is synchronised
+        void checkSync() const;
+
         //- Advance the state and return an integer sample
         inline uint64_t sample();
 
 
-protected:
+        // Scalars
 
-    // Protected Constructors
+            //- Return a scalar uniformly distributed between zero and one.
+            //  Don't check synchronisation.
+            inline scalar scalar01NoCheckSync();
 
-        //- Construct from a 64-bit unsigned integer seed
-        inline randomGenerator(const pTraits<uint64_t> s);
+            //- Return a scalar uniformly distributed between zero and one.
+            //  Don't check synchronisation.
+            inline scalar scalarABNoCheckSync(const scalar a, const scalar b);
 
 
-    // Protected Member Functions
+        // Other Types
 
-        //- Access the stored integer
-        uint64_t x() const;
+            //- Return a type with components uniformly distributed between
+            //  zero and one. Don't check synchronisation.
+            template<class Type>
+            inline Type sample01NoCheckSync();
+
+            //- Return a type with components uniformly distributed between two
+            //  limits. Don't check synchronisation.
+            template<class Type>
+            inline Type sampleABNoCheckSync(const Type& a, const Type& b);
 
 
 public:
 
     // Constructors
 
-        //- Construct from a label seed
-        inline randomGenerator(const label s);
+        //- Construct from a seed
+        inline randomGenerator(const seed s, const bool global = false);
 
-        //- Construct from a word seed
-        inline randomGenerator(const word& s);
+        //- Copy construct
+        inline randomGenerator(const randomGenerator&);
+
+        //- Move construct
+        inline randomGenerator(randomGenerator&&);
 
         //- Construct from a stream
-        randomGenerator(Istream& is);
+        randomGenerator(Istream& is, const bool global = false);
+
+        //- Construct from a dictionary
+        randomGenerator
+        (
+            const word& name,
+            const dictionary& dict,
+            randomGenerator&& defaultRndGen
+        );
+
+        //- Construct from a dictionary
+        randomGenerator
+        (
+            const word& name,
+            const dictionary& dict,
+            const seed defaultS,
+            const bool global = false
+        );
 
 
     //- Destructor
@@ -171,6 +244,18 @@ public:
         template<class Container>
         inline void permute(Container& l);
 
+        //- Create a randomly seeded generator
+        inline randomGenerator generator();
+
+
+    // Member Operators
+
+        //- Copy-assignment
+        void operator=(const randomGenerator&);
+
+        //- Move-assignment
+        void operator=(randomGenerator&&);
+
 
     // IOstream Operators
 
@@ -183,16 +268,27 @@ public:
 
 
 template<>
-inline scalar randomGenerator::sample01();
+inline scalar randomGenerator::sample01NoCheckSync();
 
 template<>
-inline label randomGenerator::sample01();
+inline label randomGenerator::sample01NoCheckSync();
 
 template<>
-inline scalar randomGenerator::sampleAB(const scalar& a, const scalar& b);
+inline scalar randomGenerator::sampleABNoCheckSync
+(
+    const scalar& a,
+    const scalar& b
+);
 
 template<>
-inline label randomGenerator::sampleAB(const label& a, const label& b);
+inline label randomGenerator::sampleABNoCheckSync
+(
+    const label& a,
+    const label& b
+);
+
+
+void writeEntry(Ostream& os, const randomGenerator& rndGen);
 
 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
diff --git a/src/OpenFOAM/primitives/randomGenerator/randomGeneratorI.H b/src/OpenFOAM/primitives/randomGenerator/randomGeneratorI.H
index fab9fdf353..f809733b0e 100644
--- a/src/OpenFOAM/primitives/randomGenerator/randomGeneratorI.H
+++ b/src/OpenFOAM/primitives/randomGenerator/randomGeneratorI.H
@@ -28,6 +28,31 @@ License
 
 // * * * * * * * * * * * * * Private Member Functions  * * * * * * * * * * * //
 
+inline uint64_t Foam::randomGenerator::seed::x(const bool global) const
+{
+    const uint64_t localS =
+        global ? s_ : s_ + (UINT64_MAX/Pstream::nProcs())*Pstream::myProcNo();
+
+    return (localS << 16) + 0x330E;
+}
+
+
+inline void Foam::randomGenerator::checkSync() const
+{
+    if (global_)
+    {
+        uint64_t xMaster = x_;
+        Pstream::scatter(xMaster);
+        if (xMaster != x_)
+        {
+            FatalErrorInFunction
+                << "Global random number generator is not synchronised"
+                << exit(FatalError);
+        }
+    }
+}
+
+
 inline uint64_t Foam::randomGenerator::sample()
 {
     x_ = (A*x_ + C) % M;
@@ -35,33 +60,116 @@ inline uint64_t Foam::randomGenerator::sample()
 }
 
 
-// * * * * * * * * * * * * * Protected Constructors  * * * * * * * * * * * * //
-
-inline Foam::randomGenerator::randomGenerator(const pTraits<uint64_t> s)
-:
-    x_((s << 16) + 0x330E)
-{}
-
-
-// * * * * * * * * * * * * Protected Member Functions  * * * * * * * * * * * //
-
-inline uint64_t Foam::randomGenerator::x() const
+inline Foam::scalar Foam::randomGenerator::scalar01NoCheckSync()
 {
-    return x_;
+    return scalar(sample())/(M >> 17);
+}
+
+
+inline Foam::scalar Foam::randomGenerator::scalarABNoCheckSync
+(
+    const scalar a,
+    const scalar b
+)
+{
+    return a + scalar01NoCheckSync()*(b - a);
+}
+
+
+template<class Type>
+inline Type Foam::randomGenerator::sample01NoCheckSync()
+{
+    Type value;
+    for (direction i = 0; i < pTraits<Type>::nComponents; ++ i)
+    {
+        value.component(i) = scalar01NoCheckSync();
+    }
+    return value;
+}
+
+
+template<>
+inline Foam::scalar Foam::randomGenerator::sample01NoCheckSync()
+{
+    return scalar01NoCheckSync();
+}
+
+
+template<>
+inline Foam::label Foam::randomGenerator::sample01NoCheckSync()
+{
+    return sample() % 2;
+}
+
+
+template<class Type>
+inline Type Foam::randomGenerator::sampleABNoCheckSync
+(
+    const Type& a,
+    const Type& b
+)
+{
+    return a + cmptMultiply(sample01NoCheckSync<Type>(), b - a);
+}
+
+
+template<>
+inline Foam::scalar Foam::randomGenerator::sampleABNoCheckSync
+(
+    const scalar& a,
+    const scalar& b
+)
+{
+    return scalarABNoCheckSync(a, b);
+}
+
+
+template<>
+inline Foam::label Foam::randomGenerator::sampleABNoCheckSync
+(
+    const label& a,
+    const label& b
+)
+{
+    return a + sample() % (b - a);
 }
 
 
 // * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
 
-inline Foam::randomGenerator::randomGenerator(const label s)
+inline Foam::randomGenerator::seed::seed(const label s)
 :
-    randomGenerator(pTraits<uint64_t>(s))
+    s_(s)
 {}
 
 
-inline Foam::randomGenerator::randomGenerator(const word& s)
+inline Foam::randomGenerator::seed::seed(const word& s)
 :
-    randomGenerator(pTraits<uint64_t>(Hash<word>()(s)))
+    s_(Hash<word>()(s))
+{}
+
+
+inline Foam::randomGenerator::randomGenerator(const seed s, const bool global)
+:
+    global_(global),
+    x_(s.x(global))
+{
+    checkSync();
+}
+
+
+inline Foam::randomGenerator::randomGenerator(const randomGenerator& rndGen)
+:
+    global_(rndGen.global_),
+    x_(rndGen.x_)
+{
+    checkSync();
+}
+
+
+inline Foam::randomGenerator::randomGenerator(randomGenerator&& rndGen)
+:
+    randomGenerator(static_cast<const randomGenerator&>(rndGen))
 {}
 
 
@@ -75,7 +183,11 @@ inline Foam::randomGenerator::~randomGenerator()
 
 inline Foam::scalar Foam::randomGenerator::scalar01()
 {
-    return scalar(sample())/(M >> 17);
+    #ifdef FULLDEBUG
+    checkSync();
+    #endif
+
+    return scalar01NoCheckSync();
 }
 
 
@@ -84,10 +196,14 @@ inline Foam::tmp<Foam::scalarField> Foam::randomGenerator::scalar01
     const label n
 )
 {
+    #ifdef FULLDEBUG
+    checkSync();
+    #endif
+
     tmp<scalarField> tValues(new scalarField(n));
     for (label i = 0; i < n; ++ i)
     {
-        tValues.ref()[i] = scalar01();
+        tValues.ref()[i] = scalar01NoCheckSync();
     }
     return tValues;
 }
@@ -99,7 +215,11 @@ inline Foam::scalar Foam::randomGenerator::scalarAB
     const scalar b
 )
 {
-    return a + scalar01()*(b - a);
+    #ifdef FULLDEBUG
+    checkSync();
+    #endif
+
+    return scalarABNoCheckSync(a, b);
 }
 
 
@@ -110,10 +230,14 @@ inline Foam::tmp<Foam::scalarField> Foam::randomGenerator::scalarAB
     const scalar b
 )
 {
+    #ifdef FULLDEBUG
+    checkSync();
+    #endif
+
     tmp<scalarField> tValues(new scalarField(n));
     for (label i = 0; i < n; ++ i)
     {
-        tValues.ref()[i] = scalarAB(a, b);
+        tValues.ref()[i] = scalarABNoCheckSync(a, b);
     }
     return tValues;
 }
@@ -122,26 +246,11 @@ inline Foam::tmp<Foam::scalarField> Foam::randomGenerator::scalarAB
 template<class Type>
 inline Type Foam::randomGenerator::sample01()
 {
-    Type value;
-    for (direction i = 0; i < pTraits<Type>::nComponents; ++ i)
-    {
-        value.component(i) = scalar01();
-    }
-    return value;
-}
+    #ifdef FULLDEBUG
+    checkSync();
+    #endif
 
-
-template<>
-inline Foam::scalar Foam::randomGenerator::sample01()
-{
-    return scalar01();
-}
-
-
-template<>
-inline Foam::label Foam::randomGenerator::sample01()
-{
-    return sample() % 2;
+    return sample01NoCheckSync<Type>();
 }
 
 
@@ -151,10 +260,14 @@ inline Foam::tmp<Foam::Field<Type>> Foam::randomGenerator::sample01
     const label n
 )
 {
+    #ifdef FULLDEBUG
+    checkSync();
+    #endif
+
     tmp<Field<Type>> tValues(new Field<Type>(n));
     for (label i = 0; i < n; ++ i)
     {
-        tValues.ref()[i] = sample01<Type>();
+        tValues.ref()[i] = sample01NoCheckSync<Type>();
     }
     return tValues;
 }
@@ -163,29 +276,11 @@ inline Foam::tmp<Foam::Field<Type>> Foam::randomGenerator::sample01
 template<class Type>
 inline Type Foam::randomGenerator::sampleAB(const Type& a, const Type& b)
 {
-    return a + cmptMultiply(sample01<Type>(), b - a);
-}
+    #ifdef FULLDEBUG
+    checkSync();
+    #endif
 
-
-template<>
-inline Foam::scalar Foam::randomGenerator::sampleAB
-(
-    const scalar& a,
-    const scalar& b
-)
-{
-    return scalarAB(a, b);
-}
-
-
-template<>
-inline Foam::label Foam::randomGenerator::sampleAB
-(
-    const label& a,
-    const label& b
-)
-{
-    return a + sample() % (b - a);
+    return sampleABNoCheckSync(a, b);
 }
 
 
@@ -197,10 +292,14 @@ inline Foam::tmp<Foam::Field<Type>> Foam::randomGenerator::sampleAB
     const Type& b
 )
 {
+    #ifdef FULLDEBUG
+    checkSync();
+    #endif
+
     tmp<Field<Type>> tValues(new Field<Type>(n));
     for (label i = 0; i < n; ++ i)
     {
-        tValues.ref()[i] = sampleAB(a, b);
+        tValues.ref()[i] = sampleABNoCheckSync(a, b);
     }
     return tValues;
 }
@@ -209,11 +308,21 @@ inline Foam::tmp<Foam::Field<Type>> Foam::randomGenerator::sampleAB
 template<class Container>
 inline void Foam::randomGenerator::permute(Container& l)
 {
+    #ifdef FULLDEBUG
+    checkSync();
+    #endif
+
     for (label i = 0; i < l.size(); ++ i)
     {
-        Swap(l[i], l[sampleAB<label>(i, l.size())]);
+        Swap(l[i], l[sampleABNoCheckSync<label>(i, l.size())]);
     }
 }
 
 
+inline Foam::randomGenerator Foam::randomGenerator::generator()
+{
+    return randomGenerator(sample(), global_);
+}
+
+
 // ************************************************************************* //
diff --git a/src/lagrangian/DSMC/clouds/Templates/DSMCCloud/DSMCCloud.C b/src/lagrangian/DSMC/clouds/Templates/DSMCCloud/DSMCCloud.C
index b2a842321e..db61f055c0 100644
--- a/src/lagrangian/DSMC/clouds/Templates/DSMCCloud/DSMCCloud.C
+++ b/src/lagrangian/DSMC/clouds/Templates/DSMCCloud/DSMCCloud.C
@@ -650,7 +650,7 @@ Foam::DSMCCloud<ParcelType>::DSMCCloud
         mesh_
     ),
     constProps_(),
-    rndGen_(label(149382906) + 7183*Pstream::myProcNo()),
+    rndGen_(label(149382906)),
     boundaryT_
     (
         volScalarField
@@ -904,7 +904,7 @@ Foam::DSMCCloud<ParcelType>::DSMCCloud
         )
     ),
     constProps_(),
-    rndGen_(label(971501) + 1526*Pstream::myProcNo()),
+    rndGen_(label(971501)),
     boundaryT_
     (
         volScalarField
diff --git a/src/meshTools/patchIntersection/star/starTemplates.C b/src/meshTools/patchIntersection/star/starTemplates.C
index b89cacf0f8..8c43050fa9 100644
--- a/src/meshTools/patchIntersection/star/starTemplates.C
+++ b/src/meshTools/patchIntersection/star/starTemplates.C
@@ -23,8 +23,7 @@ License
 
 \*---------------------------------------------------------------------------*/
 
-#include "OFstream.H"
-
+#include "star.H"
 
 // * * * * * * * * * * * * * Private Member Functions  * * * * * * * * * * * //
 
diff --git a/src/parallel/decompose/decompositionMethods/random/random.C b/src/parallel/decompose/decompositionMethods/random/random.C
index 407aa9b718..ee3f9350b6 100644
--- a/src/parallel/decompose/decompositionMethods/random/random.C
+++ b/src/parallel/decompose/decompositionMethods/random/random.C
@@ -79,7 +79,7 @@ Foam::labelList Foam::decompositionMethods::random::decompose
 {
     checkWeights(points, pointWeights);
 
-    randomGenerator rndGen(seed_);
+    randomGenerator rndGen(seed_, true);
 
     // Simple random integer. No guarantees about balance.
     /*
diff --git a/src/sampling/sampledSet/boundaryRandom/boundaryRandom.C b/src/sampling/sampledSet/boundaryRandom/boundaryRandom.C
index 7bb245d9d0..597c77540e 100644
--- a/src/sampling/sampledSet/boundaryRandom/boundaryRandom.C
+++ b/src/sampling/sampledSet/boundaryRandom/boundaryRandom.C
@@ -118,7 +118,7 @@ void Foam::sampledSets::boundaryRandom::calcSamples
     }
 
     // Generate the samples
-    randomGenerator rndGen(261782);
+    randomGenerator rndGen(261782, true);
     const label proci = Pstream::myProcNo();
     for (label i = 0; i < nPoints_; ++ i)
     {
diff --git a/src/sampling/sampledSet/circleRandom/circleRandom.C b/src/sampling/sampledSet/circleRandom/circleRandom.C
index 2824132dc8..68b5f05aef 100644
--- a/src/sampling/sampledSet/circleRandom/circleRandom.C
+++ b/src/sampling/sampledSet/circleRandom/circleRandom.C
@@ -55,7 +55,7 @@ void Foam::sampledSets::circleRandom::calcSamples
     DynamicList<label>& samplingFaces
 ) const
 {
-    randomGenerator rndGen(261782);
+    randomGenerator rndGen(261782, true);
 
     const vector radial1 = normalised(perpendicular(normal_));
     const vector radial2 = normalised(normal_ ^ radial1);
diff --git a/src/sampling/sampledSet/sphereRandom/sphereRandom.C b/src/sampling/sampledSet/sphereRandom/sphereRandom.C
index 5b831cd7ec..976d3201a9 100644
--- a/src/sampling/sampledSet/sphereRandom/sphereRandom.C
+++ b/src/sampling/sampledSet/sphereRandom/sphereRandom.C
@@ -55,7 +55,7 @@ void Foam::sampledSets::sphereRandom::calcSamples
     DynamicList<label>& samplingFaces
 ) const
 {
-    randomGenerator rndGen(261782);
+    randomGenerator rndGen(261782, true);
 
     for (label i = 0; i < nPoints_; ++ i)
     {
diff --git a/src/waves/waveModels/irregular/irregular.C b/src/waves/waveModels/irregular/irregular.C
index cda67a87d9..cb4912b064 100644
--- a/src/waves/waveModels/irregular/irregular.C
+++ b/src/waves/waveModels/irregular/irregular.C
@@ -135,7 +135,7 @@ Foam::waveModels::irregular::irregular
     }
 
     // Set random phases
-    randomGenerator rndGen(0);
+    randomGenerator rndGen(0, true);
     forAll(phases_, i)
     {
         phases_[i] = rndGen.scalarAB(0, constant::mathematical::twoPi);