Introduction

      Approaches to Parallelism

 
Magma Kernel Distributed Parallelism

      Introduction

      POSIX Threads
            SetNthreads(n) : RngIntElt ->
            GetNthreads() : -> RngIntElt
            magma -t N

 
GPUs
      SetGPU(b) : BoolElt ->
      SetNGPUs(n) : RngIntElt ->
      GetNGPUs() : -> RngIntElt
      SetGPUDevices(S) : SeqEnum ->
      SetGPUDevice(k) : RngIntElt ->

 
Linear Algebra

      Multi-threaded Linear Algebra

      GPU-based Linear Algebra

      Hybrid Linear Algebra
            Example Par_LinearAlgebraThreaded (H5E1)
            Example Par_LinearAlgebraGPU (H5E2)
            Example Par_LinearAlgebraDualGPU (H5E3)
            Example Par_representations (H5E4)

 
Gröbner Bases
      Example Par_minrank (H5E5)
      Example Par_randsys (H5E6)
      Example Par_hfe (H5E7)

 
Polynomial System Solving
      Variety(I) : RngMPol -> [ ModTupFldElt ]
      VarietySize(I) : RngMPol -> RngIntElt

 
Polynomial Rings
      SetParallelFFT(b) : BoolElt ->
      Example Par_PolynomialMultiplication (H5E8)

 
Distributed Computation for Internal Algorithms

      Automatic Worker Startup
            StartWorkers(H, T) : MonStgElt, RngIntElt ->
            SetWorkerPort(P) : RngIntElt ->
            Example Par_StartWorkers (H5E9)

      Manual Worker Startup
            Example Par_SetWorkerPort (H5E10)

 
Integer Factorisation
      Example Par_integer-factorisation (H5E11)

 
Ideal Class Group of Algebraic Number Fields

 
Integral Lattices

      Lattice Vector Enumeration

            Introduction

            Enumeration of Short Vectors
                  ShortVectors(L, B) : Lat, RngIntElt -> SeqEnum
                  ShortVectors(L, A, B) : Lat, RngIntElt, RngIntElt -> LatElt
                  ShortestVectors(L) : Lat -> SeqEnum
                  Example Par_vector_enum (H5E12)

            A Single Shortest Vector
                  ShortVector(L, B) : Lat, RngIntElt -> LatElt
                  ShortVector(L, A, B) : Lat, RngIntElt, RngIntElt -> LatElt
                  ShortestVector(L) : Lat -> LatElt
                  Example Par_ShortVector1 (H5E13)

            Enumeration of Close Vectors
                  CloseVectors(L, w, B) : Lat, ModTupRngElt, RngElt -> SeqEnum
                  CloseVectors(L, w, A, B) : Lat, ModTupRngElt, RngElt, RngElt -> SeqEnum
                  ClosestVectors(L, w) : Lat, ModTupRngElt -> SeqEnum
                  Example Par_CloseVector1 (H5E14)
                  Example Par_CloseVector2 (H5E15)

            A Single Closest Vector
                  CloseVector(L, w, B) : Lat, ModTupRngElt, RngElt -> LatElt
                  CloseVector(L, w, A, B) : Lat, ModTupRngElt, RngElt, RngElt -> LatElt
                  ClosestVector(L, w) : Lat, ModTupRngElt -> LatElt
                  Example Par_CloseVector (H5E16)

            Intrinsics that Use Enumeration
                  Example Par_LatticeMinimum1 (H5E17)
                  Example Par_LatticeMinimum2 (H5E18)
                  Example Par_KissingNumber (H5E19)

            Theta Series
                  Example Par_theta_ex (H5E20)
                  Example Par_theta_ex_2 (H5E21)
                  Example Par_lat_72 (H5E22)

 
Linear Codes

      Minimum Weight
            Example Par_QRCodeMinimum (H5E23)
            Example Par_BKLC256Minimum (H5E24)

      Weight Distribution
            Example Par_CodeWeightDistribution (H5E25)

 
User-Implemented Distributed Parallelism

      Introduction

      The Manager/Worker Model

      Basic Usage
            DistributedManager(socket, items : parameters) : IO, SeqEnum ->
            DistributedWorker(host, port, work_function) : MonStgElt, RngIntElt, UserProgram ->

      Basic Example
            Example Par_BasicWorker (H5E26)

      Verbose Output
            SetVerbose("ManagerWorker", v) : MonStgElt, RngIntElt ->
            SetVerbose("ManagerWorkerTime", v) : MonStgElt, RngIntElt ->
            Example Par_Verbose (H5E27)

      Alternative Results Handling
            Example Par_ListResults (H5E28)
            Example Par_VariationOne (H5E29)
            Example Par_VariationTwo (H5E30)

      Task Groups

      Task Group Management
            Example Par_Advanced (H5E31)
            Example Par_AdvancedVariationOne (H5E32)

      Monitoring and Respawning Workers
            MonitoredDistributedWorker(host, port, work_function) : MonStgElt, RngIntElt, UserProgram ->
            Example Par_AdvancedVariationTwo (H5E33)

      Implementing Distributed Parallelism
            ExchangeVersions(I) : IO ->
            ReadObject(I) : IO -> Any
            WriteObject(I, x) : IO, Any ->
            AsyncReadObject(I) : IO ->
            AsyncWriteObject(I, x) : IO, Any ->
            WaitForIO(R : parameters) : SeqEnum -> SeqEnum
            WaitForIO(R, W : parameters) : SeqEnum, SeqEnum -> SeqEnum, SeqEnum
            Example Par_mw-trans (H5E34)

      A Note on Security

 
Timing
      Example Par_Time1 (H5E35)

 
Bibliography

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