introduction to dataflow computing - hpcfinance davies_max… · explaining control flow versus...

Craig Davies

Introduction to

Dataflow Computing

HPC Finance Conference, Tampere – May, 2013

2

Overview

• Maxeler Overview

• Dataflow Technology

• HPC Finance: Risk Management

• MAX-UP: Maxeler University Program

• Example Application: Credit Derivatives

Valuation & Risk

• Maxeler delivers dataflow solutions for Analytics including Risk, Trading infrastructure (low-latency), HPC for Scientific Computing

• Building the HPC compute fabric based on the application in a multi-disciplinary, data-centric approach

What we do

Hardware

We build 1U boxes, Workstations and the cards inside.

We build custom large memory systems to deal with Big Data

We integrate rack system with networking and storage.

Full stack of software for runtime, compile time, and monitoring

MaxJ - Java-based programming and MaxIDE development tools

Consulting

HPC System Performance Architecture

Algorithms and Numerical Optimization

Integration into business and technical processes

Software

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Dataflow Technology

Programmable Spectrum

5

Single-Core CPU Multi-Core Several-Cores FPGA

Intel, AMD GPU (NVIDIA, AMD) Tilera, XMOS etc...

Maxeler

Hybrid e.g. AMD Fusion, IBM Cell

Control-flow processors Dataflow processor

Increasing Parallelism (#cores)

Increasing Core Complexity

Many-Cores

GK110

Where silicon is used?

Intel 6-Core X5680 “Westmere”

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Where silicon is used?

Intel 6-Core X5680 “Westmere”

Dataflow Processor

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Computation

MaxelerOS

Computation (Dataflow cores)

DataFlow Engine (DFE) vs FPGA

ASIC

CPU DFE GPU

DRAM Ctrl

Cores

Cores

FPGA

PCIe DRAM Ctrl PCIe DRAM Ctrl PCIe

CPU Interconnect DFE Interconnect

Compiler

Technology

Compute Architecture

Run-time system

OpenCL MaxCompiler C Compiler

Operating System MaxelerOS Driver

ASIC

8

Traditional (CPU) Computing

Dataflow computes 30-200x faster, with

10-50x smaller physical footprint and

10-50x power efficiency

Multiscale Dataflow Computing

Only a small proportion of chip is actually

used for computation, time is wasted

talking to levels of cache.

Solution scalability – how it works…

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Maxeler Dataflow Engines (DFEs) computes in space not in time. In dataflow

computing the trick is in maximising data movement and bandwidth.

CPUs compute

in time

DFEs compute in

space

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Explaining Control Flow versus Data Flow

• Many specialized workers are more efficient (data flow)

• Experts are expensive and slow (control flow)

Analogy 1: The Ford Production Line

Maxeler Hardware Solutions

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CPUs plus DFEs Intel Xeon CPU cores and up to

6 DFEs with 288GB of RAM

DFEs shared over Infiniband Up to 8 DFEs with 384GB of RAM and dynamic allocation

of DFEs to CPU servers

Low latency connectivity Intel Xeon CPUs and 1-2 DFEs with up to six 10Gbit Ethernet

connections

MaxWorkstation Desktop development system

MaxCloud On-demand scalable accelerated compute resource, hosted in London

MPC-X1000

• 8 dataflow engines (192-384GB RAM)

• High-speed MaxRing

• Zero-copy RDMA between CPUs and DFEs over Infiniband

• Dynamic CPU/DFE balancing

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Accelerator Programming Models

DSL

DSL

DSL DSL

Possible applications

Leve

l of

Ab

stra

ctio

n

Flexible Compiler System: MaxCompiler

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Higher Level Libraries

Risk Library

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Programming with MaxCompiler Host

Application *.c, *.f90 ...

User Input

Compiler

Linker

Executable

Output

MAX File Sim or H/W

(.max)

MaxCompiler

Output

MyKernel.maxj MyManager.maxj

User Input MaxIDE

Rewrite only code to be accelerated

maxelerOS Library

SLiC Library

HPC Finance: Risk Management

Problem statement

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Problem

Provide consistent, real-time, valuation and risk

management across all major asset classes, that enables

measurement and control of risk, as well as optimal

capital use.

Constraints

• Time to deliver completed client solution.

• Integration with pre-existing client technology stack.

• Increasing complexity of regulatory requirements.

• Scalability of solution in time, space and performance.

• Reliability and support.

• Deliver previously infeasible results.

• Total cost of solution.

Solution architecture

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Consistent, real-time, valuation and risk management

calculations across all major asset classes

Maxeler’s dataflow

accelerated finance library

provides ultra high speed

computation of PV and risk

Client provides trade,

market and static data

in own format

Finance appliance

covers 10 asset classes

Risk summarizations in

hardware avoid use of

complex databases

Basic finance • Dates

• Cashflows

• Products

• European, Bermudan &

American options

• Utilities

• Maths and Stats

Risk management • Scenario engine generator

• Monte Carlo VaR

• VaR & CVaR

• Expected Shortfall

• EVT

• CVA/DVA

• Basel II/III and MiFID II

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Risk management functionality

Risk management reporting • First and second order risks – deltas,

gammas and cross-partial risks

• Consistent risk sensitivities over all asset

classes

• Client driven, flexible, risk summarizations

Sp

ot M

ark

et

Ra

nd

om

B

um

ps

His

tori

ca

l

Historical Markets

Bump Scenarios

Monte Carlo

Market Scenarios

Bootstrap

Market Curves

Pricing Engine

Price Scenarios

Risk Analysis

Results Aggregation

Market Instruments

Cashflow Generator

Trade Portfolio

Cashflow Generator

Maxeler Finance Appliance

functionality and information flow

Risk management architecture

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Client input data

Clie

nt

inp

ut

dat

a

Client generated risk management data is passed to client risk database for analysis

• Maxeler’s finance appliance accepts client input data and generates required risk management data at any and all requested levels of aggregation.

• Scenario analysis can be either permutative, combinatorial, ad- hoc or Monte Carlo.

• The finance appliance is fully scalable to client requirements.

Maxeler’s finance library provides accelerated analytics for valuation and risk management across all major asset classes

Random Number MersenneTwister

LinearCongruence

UniformContinuous

UniformDiscrete

UnivariateGaussian

MultivariateGaussian

UnivariateLognormal

MultivariateLognormal

Poisson

Exponential

Gamma

ChiSquare

NonCentralChiSquare

UniformPerturbation

LatinHypercube

InverseCummulativeMethod

AcceptanceRejectionMethod

GaussianWallace

Stochastic Process

UnivariateGaussianProcess

MultivariateGaussianProcess

UnivariateLognormalProcess

MultivariateLognormalProcess

SquareRootProcess

HestonProcess

PoissonProcess

CompoundPoissonProcess

AffineJumpProcess

CEVProcess

GenericEulerStepper

GenericPredictorCorrectorStepper

GenericTerminalDistributionStepper

Finance library coverage - details

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Pricing and Risk CDSPricer

CDSRisk

CDSIndexPricer

CDSIndexRisk

SwapPricer

SwapRisk

OISPricer

OISRisk

BondPricer

BondRisk

EurodollarOptionPricer

EuroDollarOptionRisk

Pricing and Risk continued…

TNoteOptionPricer

TNoteOptionRisk

FXOption

FXOptionRisk

FXBarrierOption

FXBarrierOptionRisk

FuturesConvexityPricer

EuropeanFuturesOptionPricer

EuropeanFuturesOptionRisk

AmericanFuturesOptionPricer

AmericanFuturesOptionRisk

AsianFuturesOptionPricer

AsianFuturesOptionRisk

Finance library coverage - details

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Distribution

NormalCummulative

NormalDensity

InverseNormalCummulative

PoissonDensity

PoissonCummulative

GaussianCopulaCummulative

NonCentralChiSquareCummulative

Distribution continued…

ExponentialDensity

ExponentialCummulative

GammaDensity

GammaCummulative

Financial Support Functions

ExponentialInterpolation

PWLinearSimpleSpotInterpolation

PWLinearForwardInterpolation

PWConstantForwardInterpolation

ConvexMonotoneInterpolation

CDSHazardCurveBootstrap

CDSHazardToUpfront

OISRateCurveBootstrap

Swap1CurveBootstrap

Swap2CurveBootstrap

GenericObjectiveBootstrap

Discount

RiskyDiscount

BusinessDayLogic

DateLogic

HolidayLogic

Models

BlackScholes

AmericanOptionBAW

HullWhiteTree

StaticCashflow

MultiStateMonteCarlo

1DExplicitFiniteDifference

2DExplicitFiniteDifference

3DExplicitFiniteDifference

1DImplicitFiniteDifference

2DImplicitFiniteDifference

3DImplicitFiniteDifference

FourierTimeStepping

Finance library coverage - details

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Math Library

CholeskyDecomposition

SchurDecomposition

GaussianElimination

SOR

AMG

ForwardBackwardSubstitution

LUDecomposition

QRDecomposition

SVDecomposition

SteepestDecent

ThomasAlgorithm

FactorAnalysis

CubicSplineInterpolation

ConjugateGradient

BisectionSolver

SecantSolver

BrentSolver

NewtonRaphsonSolver

1DFFT, 2DFFT & 3DFFT

JacobiSolver

Math Library continued…

GaussSeidelSolver

GeneralFunctionApproximation

InverseMatrix

MatrixMultiply

NumericalQuadrature

1DConvolution

2DConvolution

3DConvolution

WaveletTransforms

LeastSquareRegression

HermitePolynomial

LaguerrePolynomial

LegendrePolynomial

BinarySearch

BackwardsEulerODESolver

LeapfrogODESolver

RungeKuttaODESOlver

ImplicitRungeKuttaNystromODESolver

ExplicitRungeKuttaNystromODESolver

Finance library coverage - details

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Function Library

abs

ceil

cos

sin

tan

cosh

sinh

tanh

arcsin

arccos

arctan

erf

erfc

divMod

exp

floor

log

log2

Function Library

max

min

modulo

pow2

scalb

sin

sqrt

Risk Analysis

BumpMarket

PerturbMarket

LogDistHistorical

ExpWgtLogDistHistorical

VaRFromSample

ExpectedShortfallFromSample

ComponentVaR

SystemicVaR

VaRBucketAggregation

Finance library coverage - details

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MAX-UP:

Maxeler University Program

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Maxeler University Program Members

There are over 89 affiliated academic members across disciplines, here is a sample!

• Access to the fastest HPC computing technology

• Academic pricing on Maxeler dataflow computing hardware

• Free access to Maxeler software

• Free access to Maxeler educational material

• Guest lectures

• Internships for undergraduates and postgraduates

• Support for research proposals or joint project proposals

• An online forum for exchanging experience, expertise and ideas

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MAX-UP Program Benefits

http://www.maxeler.com/solutions/universities/

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Maxeler University Program

http://www.maxeler.com/joinmaxup/

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How To Enroll

Example Accelerated

Applications

Credit Derivatives Valuation & Risk

• Compute value of complex financial derivatives (CDOs)

• Typically run overnight, but beneficial to compute in real-time

• Many independent jobs

• Speedup: 220-270x

• Power consumption per node drops from 250W to 235W/node

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O. Mencer and S. Weston, 2010

Application Analysis

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DFE Convolution Architecture

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• Calculation of current value and credit spread risk for population of 2,925 bespoke tranches.

• Speedup from 1 MAX2:

– 219 – 270x compared to 1 core

– ~30x compared to 8-core node

• Power consumption drops from 250W/node to 235W/node with acceleration

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Credit Derivatives Results

• Dataflow engines provide massive parallelism at low clock frequencies

• Many applications are amenable to dataflow processing, and can achieve high acceleration

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Summary & Conclusions