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Upon completion of this module, you will be able to:

Performance Features

Using the Library

MKL Addresses:Solvers (BLAS, LAPACKEigenvector/eigenvalue solvers (BLAS, LAPACK)Some quantum chemistry needs (dgemm)PDEs, signal processing, seismic, solid-state physics (FFTs)Geneal scientific, financial [vector transcendental functions (VML) and vector random number generators (VSL)

Software Construction

Geometric Transformation

Don’t use Intel® Math Kernel (Intel® MKL) on …

Don’t use Intel® MKL on “small” counts.Don’t call vector math functions on small n.

§ But you could use Intel® Performance Primitives

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BLAS (Basic Linear Algebra SubroutinesLevel 1 BLAS – vector-vector operations

15 function types48 functions

Level 2 BLAS – matrix-vector operations26 function types66 functions

Level 3 BLAS – matrix-matrix operations9 function types30 functions

Extended BLAS – level 1 BLAS for sparse vectors8 function types24 functions

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LAPACK (linear algebra packageSolvers and eigensolvers. Many hundreds of routines totalThere are more than 1000 total user callable and support routinesDiscrete Fourier Transformations (DFT)Mixed radix, multi-dimensional transformsMulti threadedVML (Vector Math Library)Set of vectorized transcendental functionsMost of libm functions, but fasterVSL (Vector Statistics Library)Set of vectorized ran

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BLAS and LAPACK* are both FortranLegacy of high performance computation

VSL and VML have Fortran and C interfacesDFTs have Fortran 95 and C interfacescblas intercate. It is more convenient for a C/C++ programmer to call BLAS

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Support 32-bit and 64-bit Intel Processors

Large set of examples and testsExtensive documentation

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The goal of all optimization is maximum speed.Resource limited optimization – exhaust one or more resource of system:

CPU: Register use, FP unitsCache: Keep data in cache as long as possible; deal with cache interleaving.TLBs: Maximally use data on each pageMemory bandwidth: Minimally access memoryComputer: Use all the processors available using threadingSystem: Use all the nodes available (cluster software)

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Most of Intel MKL could be threaded but:Limited resource is memory bandwidthThreading level 1 and level 2 BLAS are mostly ineffective (O(n) )

There are numerous opportunities for threading:Level 3 BLAS (O(n3) )LAPACK* (O(n3) )FFTs (O(n log(n) )VML, VSL? Depends on processor and function

All threading is via OpenMP*All Intel MKL is designed and compiled for thread safety

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Scenario 1: ifort, BLAS, IA-32 processor:ifort myprog.f mkl_c.lib

Scenario 2: CVF, LAPACK, IA-32 processor:f77 myprog.f mkl_s.lib

Scenario 3: Statically link a C program with DLL linked at runtime:link myprog.obj mkl_c_dll.libNote: Optimal binary code will execute at run time based on processor.

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Most important LAPACK optimizations:Threading – effectively uses multiple CPUsRecursive factorization

Reduces scalar time (Amdahl’s law: t=tscalar + tparallel/pExtends blocking further into the code

No runtime library support required

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One dimensional, two-dimensional, three-dimensionalMultithreadedMixed radixUser – specified scaling, transform signTransforms on imbedded matricesMultiple one-dimensional transforms on single cellStridesC and F90 interfaces

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Basically a three-step processCreate a descriptor

Status = DftiCreate Descriptor (MDH,…)Commit the descriptor (instantiates it)

Status = DftiCommit Descriptor (MDH)Perform the transform

Status = DftiComputeForard (MDH, X)Optionally free the descriptor

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Vector Math Library: Vectorized transcendental functions – like libm but better (faster)Interface: Have both Fortran and C interfacesMultiple accuracies

High accuracy (<1ulp)Lower accuracy, faster (<4 ulps)

Special value handling √(-a), sin(0), and so onError handling – can not duplicate libm here

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It is important for financial codes (Monte Carlo simulations)Exponentials, logarithms

Other scientific codes depend on transcendental functionsError functions can be big time sinks in come codes

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Set of random number generators (RNGs)Numerous non-uniform distributionsVML used extensively for transformationsParallel computation support – some functionsUser can supply own BRNG or transformationsFive basic RNGs (BRNGs) – bits, integer, FP

◦ MCG31, R250, MRG32, MCG59, WH

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Gaussian (two methods)ExponentialLaplaceWeibullCauchyRayleighLognormalGumbel

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Basically a 3-step ProcessCreate a stream pointer. VSLStreamStatePtr stream;Create a stream.vslNewStream(&stream,VSL_BRNG_MC_G31, seed );Generate a set of RNGs.vsRngUniform( 0, &stream, size, out, start, end );Delete a stream (optional).vslDeleteStream(&stream);

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Compare the performance of C source code (RAND function) and VSL.Exercise control of the threading capabilities in MKL/VSL.

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Intel® Math Kernel Library is a broad scientific/engineering math library.It is optimized for Intel® processors.It is threaded for effective use on SMP machines.