CUDA

MPIR - Parallel Algorithms and CUDA

Present : Carl Witty, Bill Hart, Michael Abshoff, Glenn Tarbox Virtually Present : Jeff Gilchrist, Gonzalo Tornaria

You can chat in a Linux text console by installing "irssi" and running: "irssi -c irc.freenode.net" and then type "/join #sage-devel"

Parallel algorithms:

• Multimodular algorithms
• Scalar algorithms

• Peter Montgomery's remainder algorithm a mod b, precompute b1 = B mod b, b2 = B^{2 mod b, b3 = B}3 mod b, then write a = a0 + a1*B + a2*B^2 +..., then compute a0 + a1*b1 + a2*b2 +.... and do final reduction mod b. Multiplications can be done in parallel.

• Addition and subtraction can be parallelised using nails - non-unique representation of numbers
• Classical algorithm is embarrassingly parallel - bad if you have an n log n algorithm in that range

Glenn Tarbox (Owner of cuda1, AMD K10 with NVIDA CUDA card - expert on large scale parallelisation)

• What are the top level integration issues, e.g. by libraries using MPIR

Michael Abshoff (Sage release manager)

• Link into Sage via cython and link in CUDA

CUDA documentation:

• NVIDA website

CUDA issues:

• Memory bandwidth limits algorithms - matrices n**2 entries to get in and out, matrix multiplication O(n**2.7), but for integers n limbs to get in and out O(n log n log log n) operations to multiply

Other Options:

• AMD Math library AML provides BLAS interface uses GPU - but that's for linear algebra
• PTX NVIDIA GPU assembler code for inner loops

Gonzalo Tornaria (theta functions expert)

• Is there a way to encode integer multiplication in linear algebra? (A. Perhaps vectors - multimodular, but not matrices)
• Kernel

• Launch threads - issues based on hierarchy of memory - CPU registers-> memory per processor block-> main graphics memory-> system memory

• Can launch all the threads on all cpus in a couple of cycles
• How GPU would compare to carefuly programmed FPGA?
• E.g a Stratix IV can have around 1000 18x18 multipliers, but maybe that's not too much, and this is probably very expensive hardware

• http://www.altera.com/products/devices/stratix-fpgas/stratix-iv/stxiv-index.jsp

• Carl Witty does FPGA programming - says it is probably very expensive
• Accoding to the spec the stratix can have parallel high-bandwith communication
• Up to 48 8.5Gb/s tranceivers or 24 11.3 gbps tranceivers
• Deal with 533MHz DDR3 memory directly

Jeff Gilchrist

• What about ATI hardware - why not support OpenCL?
• Carl Witty says - Nobody ships OpenCL yet but in a year or two it should be common
• Intel has Larrabee and will ship some intel library, NVIDIA has CUDA and PTX, ATI has AML (basically BLAS) + low level interface - OpenCL is slated to be common
• OSX will ship with OpenCL

Bill Hart

• Cell port will happen as it is funded by EPSRC Grant - will be proof of principle code to apply for a port to Cell2Xi

Glenn Tarbox

• What is the focus for mathematicians? E.g. mathematica is reputedly going to have parallel CUDA or something similar