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Overview of Streaming Project

- Main PIs:
- Pat Hanrahan, [email protected]
- Bill Dally, [email protected]
- Objectives:
- Cost/Performance: 100:1 compared to clusters.
- Programmable: applicable to large class of scientific applications.
- Porting and developing new code made easier: stream language, support of legacy codes.

Eric Darve - Stanford Streaming Supercomputer

Performance/Cost

Cost estimate – about $1K/node

Preliminary numbers, parts cost only, no I/O included.

Expect 2x to 4x to account for margin and I/O

Eric Darve - Stanford Streaming Supercomputer

News Center

News Releases | Publications | Resources | Multimedia Gallery

News Release Archive | Awards

FOR IMMEDIATE RELEASE

October 21, 2002

Sandia National Laboratories and Cray Inc. finalize $90 million contract for new supercomputer

Collaboration on Red Storm System under Department of Energy’s Advanced Simulation and Computing Program (ASCI)

ALBUQUERQUE, N.M. and SEATTLE, Wash. — The Department of Energy’s Sandia National Laboratories and Cray Inc. (Nasdaq NM: CRAY) today announced that they have finalized a multiyear contract, valued at approximately $90 million, under which Cray will collaborate with Sandia to develop and deliver a new massively parallel processing (MPP) supercomputer called Red Storm. In

June 2002, Sandia reported that Cray had been selected for the award, subject to successful contract negotiations.

Performance/Cost Comparisons

- Earth Simulator (today)
- Peak 40TFLOPS, ~$450M
- 0.09MFLOPS/$
- Sustained 0.03MFLOPS/$
- Red Storm (2004)
- Peak 40TFLOPS, ~$90M
- 0.44MFLOPS/$
- SSS (proposed 2006)
- Peak 40TFLOPS, < $1M
- 128MFLOPS/$
- Sustained 30MFLOPS/$ (single node)
- Numbers are sketchy today, but even if we are off by 2x, improvement over status quo is large

Eric Darve - Stanford Streaming Supercomputer

How did we achieve that?

Eric Darve - Stanford Streaming Supercomputer

VLSI Makes Computation Plentiful

VLSI: very large-scale integration. This is the current level of computer microchip miniaturization (refers to microchips containing in the hundreds of thousands of transistors.)

- Abundant, inexpensive arithmetic
- Can put 100s of 64-bit ALUs on a chip
- 20pJ per FP operation
- (Relatively) high off-chip bandwidth
- 1Tb/s demonstrated, 2nJ per word off chip
- Memory is inexpensive $100/Gbyte

nVidia GeForce4

~120 Gflops/sec

~1.2 Tops/sec

Velio VC3003

1Tb/s I/O BW

Eric Darve - Stanford Streaming Supercomputer

Current Architecture: few ALUs / chip = expensive and limited performance.

Objective for SSS architecture:

Keep hundreds of ALUs/chip busy.

Difficulty:

Locality of data: we need to match 20Tb/s ALU bandwidth to ~100Gb/s chip bandwidth.

Latency tolerance:to cover 500 cycle remote memory access time.

Chip

64-bit ALU

(to scale)

But VLSI imposes some constraintsArchitecture of Pentium 4

Arithmetic is cheap, global bandwidth is expensive

Local << global on-chip << off-chip << global system

Eric Darve - Stanford Streaming Supercomputer

The Stream Model exposes parallelism and locality in applications

- Streams of records passing through kernels
- Parallelism
- Across stream elements
- Across kernels
- Locality
- Within kernels
- Producer-consumer locality between kernels

Eric Darve - Stanford Streaming Supercomputer

Streams match scientific computation to constraints of VLSI

Stream Cache

Local Registers

Memory

Stream Reg File

Grid of

K1

5

5

Cells

Cells

50 Ops

7

Indices

K2

6

Table

Table

Results 1

100 Ops

8

0.5

8

Results 2

K3

3

3

70 Ops

Results 2

8

K4

8

Results 3

80 Ops

Indices

5

300 Ops

Grid of

4

Results 4

900W

Cells

9.5Words

12Words

58Words

Stream program matches application to Bandwidth Hierarchy 32:4:1

Eric Darve - Stanford Streaming Supercomputer

Scientific programs stream well

StreamFEM results show L:S:M ratios of 206:13:1 to 50:3:1

Eric Darve - Stanford Streaming Supercomputer

BW Hierarchy of SSS

Eric Darve - Stanford Streaming Supercomputer

Stream processor = Vector processor + Local registers

- Like a vector processor, stream processors
- Amortize instruction overhead over records of a stream
- Hide latency by loading (storing) streams of records
- Can exploit producer consumer locality at the SRF (VRF) level
- Stream processors add local registers and microcoded kernels
- >90% of all references from local registers
- Increases effective bandwidth and capacity of SRF (VRF) by 10x
- Enables 10x number of ALUs
- Enables SRF to capture working set

Eric Darve - Stanford Streaming Supercomputer

Brook: streaming language

- C with streaming
- Make data parallelism explicit
- Declare communication pattern
- Streams
- View of records in memory
- Operated on in parallel
- Accessing stream values not is permitted outside of kernels

Kernel

Eric Darve - Stanford Streaming Supercomputer

KernelBrook Kernels

- Kernels
- Functions which operate only on streams
- Stream arguments are read-only or write-only
- Reduction variables (associative operations only)
- Restricted communication between records
- No state or “static” variables
- No global memory access

Eric Darve - Stanford Streaming Supercomputer

Brook Example: Molecular Dynamics

struct Vector { float x, y, z ;} ;

typedef stream struct Vector Vectors ;

kernel void UpdatePosition (

Vectors sPos,

Vectors sVel,

const float timestep,

out Vectors sNewPos )

{

sNewPos.x = sPos.x + timestep * sVel.x;

sNewPos.y = sPos.y + timestep * sVel.y;

sNewPos.z = sPos.z + timestep * sVel.z;

}

Eric Darve - Stanford Streaming Supercomputer

struct Vector { float x, y, z ;} ;

typedef stream struct Vector Vectors ;

void main () {

struct Vector Pos[MAX] = {…} ;

struct Vector Vel[MAX] = {…} ;

Vectors sPos, sVel, sNewPos ;

streamLoad (sPos, Pos, MAX) ;

streamLoad (sVel, Vel, MAX) ;

UpdatePosition (sPos, sVel, 0.2f, sNewPos) ;

streamStore (sNewPos, Pos) ;

}

Eric Darve - Stanford Streaming Supercomputer

StreamMD: motivation

- Application: study the folding of human proteins.
- Molecular Dynamics: computer simulation of the dynamics of macro molecules.
- Why this application?
- Expect high arithmetic intensity.
- Requires variable length neighborlists.
- Molecular Dynamics can be used in engine simulation to model spray, e.g. droplet formation and breakup, drag, deformation of droplet.
- Test case chosen for initial evaluation: box of water molecules.

DNA molecule

Human immunodeficiency virus (HIV)

Eric Darve - Stanford Streaming Supercomputer

Numerical Algorithm

- Interaction between atoms is modeled by the potential energy associated to each configuration. Includes:
- Chemical bond potentials.
- Electrostatic interactions.
- Van der Waals interactions.
- Newton’s second law of motion used to compute the trajectory of all atoms:
- Velocity Verlet time integrator (leap-frog):

Eric Darve - Stanford Streaming Supercomputer

High-Level Implementation in Brook

- Cutoff is used to compute non-bonded forces: two particles do not interact if they are at a distance larger than cutoff radius.
- Gridding technique is used to accelerate search of all atoms within cutoff radius.
- Stream of variable length is associated to each cell of the grid: contains all the water molecules inside the cell.
- High level Brook functionality are used:
- streamGatherOP: used to construct the list of all water molecules inside a cell.
- streamScatterOP: used to reduce the partial forces computed for each molecule.

Memory

f+g (g)

n++

GatherOP

ScatterOP

SRF

n

f

Eric Darve - Stanford Streaming Supercomputer

FDIV

FADD

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DEC_CHK_UCR

280

SPWRITE

LOOP

DEC_UCR

32

SPWRITE

IADD

PASS

PASS

NSELECT

DATA_OUT

NSELECT

DATA_OUT

340

StreamMD Results120

FSUB

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FLT

FABS

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FLT

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SELECT

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- Preliminary schedule obtained using the Imagine architecture:
- High arithmetic intensity: all ALUs are kept busy. Gflops expected to be very high.
- SRF bandwidth is sufficient. About 1 word for 30 instructions.
- Results helped guide architectural decisions for SSS.

FSUB

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SPWRITE

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T

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Imagine

SSS

Eric Darve - Stanford Streaming Supercomputer

Observations

- Arithmetic intensity is sufficient. Bandwidth is not going to be the limiting factor in these applications. Computation can be naturally organized in a streaming fashion.
- The interaction between the application developers and the language development group has helped insured that Brook can be used to code real scientific applications.
- Architecture has been refined in the process of evaluating these applications.
- Implementation is much easier than MPI. Brook hides all the parallelization complexity from the user. The code is very clean and easy to understand. The streaming versions of these applications are in the range of 1000-5000 lines of code.

Eric Darve - Stanford Streaming Supercomputer

A GPU is a stream processor

- The GPU on a Graphics Card is streaming processor.
- n VIDIA recently announced that their latest graphics card, the NV30, will be programmable and capable of delivering 51 Gflops peak performance (1.6 Gflops for Pentium 4).

Can we use this computing power for scientific application?

Eric Darve - Stanford Streaming Supercomputer

Cg: Assembly or High-level?

Assembly

…

DP3 R0, c[11].xyzx, c[11].xyzx;

RSQ R0, R0.x;

MUL R0, R0.x, c[11].xyzx;

MOV R1, c[3];

MUL R1, R1.x, c[0].xyzx;

DP3 R2, R1.xyzx, R1.xyzx;

RSQ R2, R2.x;

MUL R1, R2.x, R1.xyzx;

ADD R2, R0.xyzx, R1.xyzx;

DP3 R3, R2.xyzx, R2.xyzx;

RSQ R3, R3.x;

MUL R2, R3.x, R2.xyzx;

DP3 R2, R1.xyzx, R2.xyzx;

MAX R2, c[3].z, R2.x;

MOV R2.z, c[3].y;

MOV R2.w, c[3].y;

LIT R2, R2;

...

or

PhongShader

Cg

COLOR cPlastic = Ca + Cd * dot(Nf, L)

+ Cs * pow(max(0, dot(Nf, H)), phongExp);

Eric Darve - Stanford Streaming Supercomputer

Cg uses separate vertex and fragment programs

VertexProcessor

FragmentProcessor

FramebufferOperations

Assembly &Rasterization

Application

Framebuffer

Textures

Program

Program

Eric Darve - Stanford Streaming Supercomputer

Characteristics of NV30 & Cg

- Characteristics of GPU:
- optimized for 4-vector arithmetic
- Cg has vector data types and operationse.g. float2, float3, float4
- Cg also has matrix data typese.g. float3x3, float3x4, float4x4
- Some Math:
- Sin/cos/etc.
- Normalize
- Dot product:dot(v1,v2);
- Matrix multiply:
- matrix-vector: mul(M, v); // returns a vector
- vector-matrix: mul(v, M); // returns a vector
- matrix-matrix: mul(M, N); // returns a matrix

Eric Darve - Stanford Streaming Supercomputer

Example: MD

Innermost loop in C: computation of LJ and Coulomb interactions.

for (k=nj0;k

jnr = jjnr[k]; //get index of next j atom (array LOAD)

j3 = 3*jnr; //calc j atom index in coord & force arrays

jx = pos[j3]; //load x,y,z coordinates for j atom

jy = pos[j3+1];

jz = pos[j3+2];

qq = iq*charge[jnr]; //load j charge and calc. product

dx = ix – jx; //calc vector distance i-j

dy = iy – jy;

dz = iz – jz;

rsq = dx*dx+dy*dy+dz*dz; //calc square distance i-j

rinv = 1.0/sqrt(rsq); //1/r

rinvsq = rinv*rinv; //1/(r*r)

vcoul = qq*rinv; //potential from this interaction

fscal = vcoul*rinvsq; //scalarforce/|dr|

vctot += vcoul; //add to temporary potential variable

fix += dx*fscal; //add to i atom temporary force variable

fiy += dy*fscal; //F=dr*scalarforce/|dr|

fiz += dz*fscal;

force[j3] -= dx*fscal; //subtract from j atom forces

force[j3+1]-= dy*fscal;

force[j3+2]-= dz*fscal;

}

Inner loop in Cg

/* Find the index and coordinates of j atom */

jnr = f4tex1D (jjnr, k);

/* Get the atom position */

j1 = f3tex1D(pos, jnr.x);

j2 = f3tex1D(pos, jnr.y);

j3 = f3tex1D(pos, jnr.z);

j4 = f3tex1D(pos, jnr.w);

We are fetching coordinates of atom: data is stored as texture

We compute four interactions at a time so that we can take advantage of high performance of vector arithmetic.

Eric Darve - Stanford Streaming Supercomputer

/* Get the vectorial distance, and r^2 */

d1 = i - j1;

d2 = i - j2;

d3 = i - j3;

d4 = i - j4;

rsq.x = dot(d1, d1);

rsq.y = dot(d2, d2);

rsq.z = dot(d3, d3);

rsq.w = dot(d4, d4);

/* Calculate 1/r */

rinv.x = rsqrt(rsq.x);

rinv.y = rsqrt(rsq.y);

rinv.z = rsqrt(rsq.z);

rinv.w = rsqrt(rsq.w);

Computing the square of distance

We use built-in dot product for float3 arithmetic

Built-in function: rsqrt

Highly efficient float4 arithmetic

/* Calculate Interactions */

rinvsq = rinv * rinv;

rinvsix = rinvsq * rinvsq * rinvsq;

vnb6 = rinvsix * temp_nbfp;

vnb12 = rinvsix * rinvsix * temp_nbfp;

vnbtot = vnb12 - vnb6;

qq = iqA * temp_charge;

vcoul = qq*rinv;

fs = (12f * vnb12 - 6f * vnb6 + vcoul) * rinvsq;

vctot = vcoul;

/* Calculate vectorial force and update local i atom force */

fi1 = d1 * fs.x;

fi2 = d2 * fs.y;

fi3 = d3 * fs.z;

fi4 = d4 * fs.w;

This is the force computation

Computing total force due to 4 interactions

ret_prev.fi_with_vtot.xyz += fi1 + fi2 + fi3 + fi4;

ret_prev.fi_with_vtot.w += dot(vnbtot, float4(1, 1, 1, 1))

+ dot(vctot, float4(1, 1, 1, 1));

Computing total potential energy for this particle

Return type is:

struct inner_ret { float4 fi_with_vtot; };

Contains x, y and z coordinates of force and total energy.

Conclusion

- 3 representative applications show high bandwidth ratios: streamMD, streamFlo, StreamFEM.
- Feasibility of streaming established for scientific applications: high arithmetic intensity, bandwidth hierarchy is sufficient.
- Available today: NVidia NV30 graphics card.
- Future work:
- StreamMD to GROMACS (Folding @ Home)
- StreamFEM and StreamFLO to 3D
- Multinode versions of all applications
- Sparse solvers for implicit time-stepping
- Adaptive meshing
- Numerics

Eric Darve - Stanford Streaming Supercomputer

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