Parallelism

• Introduction
  • Approaches to Parallelism
• Magma Kernel Distributed Parallelism
  • Introduction
  • POSIX Threads
    • SetNthreads(n): RngIntElt
    • GetNthreads() → RngIntElt
    • magma -t N
• GPUs
  • SetGPU(b): BoolElt
  • GetGPU() → 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: Linear Algebra Threaded
    • Example: Linear Algebra GPU
    • Example: Linear Algebra Dual GPU
    • Example: representations
• Gröbner Bases
  • Example: minrank
  • Example: randsys
  • Example: hfe
• Polynomial System Solving
  • Variety(I): RngMPol → [ ModTupFldElt ]
  • VarietySize(I): RngMPol → RngIntElt
• Polynomial Rings
  • SetParallelFFT(b): BoolElt
  • Example: Polynomial Multiplication
• Distributed Computation for Internal Algorithms
  • Automatic Worker Startup
    • StartWorkers(H, T): MonStgElt, RngIntElt
    • SetWorkerPort(P): RngIntElt
    • Example: Start Workers
  • Manual Worker Startup
    • Example: Set Worker Port
• Integer Factorisation
  • Example: Integer Factorisation
• 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: Vector Enum
    • A Single Shortest Vector
      • ShortVector(L, B): Lat, RngIntElt → LatElt
      • ShortVector(L, A, B): Lat, RngIntElt, RngIntElt → LatElt
      • ShortestVector(L): Lat → LatElt
      • Example: Short Vector1
    • 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: Close Vector1
      • Example: Close Vector2
    • 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: Close Vector
    • Intrinsics that Use Enumeration
      • Example: Lattice Minimum1
      • Example: Lattice Minimum2
      • Example: Kissing Number
    • Theta Series
      • Example: Theta Ex
      • Example: Theta Ex 2
      • Example: Lat 72
• Linear Codes
  • Minimum Weight
    • Example: QR Code Minimum
    • Example: BKLC256Minimum
  • Weight Distribution
    • Example: Code Weight Distribution
• User-Implemented Distributed Parallelism
  • Introduction
  • The Manager/Worker Model
  • Basic Usage
    • DistributedManager(socket, items : parameters): IO, SeqEnum
    • DistributedManager(socket, items : parameters): IO, List
    • DistributedManager(socket, items : parameters): IO, Process
    • DistributedWorker({host, port, }{work_function}): MonStgElt, RngIntElt, UserProgram
  • Basic Example
    • Example: Basic Worker
  • Verbose Output
    • SetVerbose("ManagerWorker", v): MonStgElt, RngIntElt
    • SetVerbose("ManagerWorkerTime", v): MonStgElt, RngIntElt
    • Example: Verbose
  • Alternative Results Handling
    • Example: List Results
    • Example: Variation One
    • Example: Variation Two
  • Task Groups
  • Task Group Management
    • Example: Advanced
    • Example: Advanced Variation One
  • Monitoring and Respawning Workers
    • MonitoredDistributedWorker({host, }{port, work_function}): MonStgElt, RngIntElt, UserProgram
    • Example: Advanced Variation Two
  • 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: Mw Trans
  • A Note on Security
• Timing
  • Example: Time1