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Using FPGAs to Supplement Ray-Tracing Computations on the Cray XD-1PowerPoint Presentation

Using FPGAs to Supplement Ray-Tracing Computations on the Cray XD-1

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Using FPGAs to Supplement Ray-Tracing Computations on the Cray XD-1

Charles B. Cameron

United States Naval Academy

Department of Electrical Engineering

United States Naval Academy

105 Maryland Avenue, Stop 14B

Annapolis, Maryland 21402-5025

- Research supported by:
- NASA Goddard Space Flight Center (Code 586)
- NRL Applied Optics Branch (Code 5630)
- DoD High Performance Computing Modernization Program at NRL (Code 5593)
- United States Naval Academy
- Xilinx, Inc.

Topics Cray XD-1

- Ray tracing
- Conventional parallel processing
- Modulo scheduling
- Coordination of sequential and parallel processing
- Expected Performance

Ray tracing Cray XD-1

- MODIS
- Moderate-resolution Imaging Spectroradiometer

- The Intersection Problem
- Finding the Perpendicular
- Refraction
- Reflection

MODIS Optical System Cray XD-1 (Moderate-resolution Imaging Spectroradiometer)

MODIS Optical System Cray XD-1

- 485 pinholes
- 400 rays per pinhole
- 241 ´ 121 rays reflected from the diffuser
- 5.66 ´ 109 rays

Ray Directed to a Surface Cray XD-1

- MODIS
- Moderate-resolution Imaging Spectroradiometer

- The Intersection Problem
- Finding the Perpendicular
- Refraction
- Reflection
- Coordinate Transformation

Calculate the Intercept Point Cray XD-1

- MODIS
- Moderate-resolution Imaging Spectroradiometer

- The Intersection Problem
- Finding the Perpendicular
- Refraction
- Reflection
- Coordinate Transformation

Find the Normal Cray XD-1

- MODIS
- Moderate-resolution Imaging Spectroradiometer

- The Intersection Problem
- Finding the Perpendicular
- Refraction
- Reflection
- Coordinate Transformation

Find the Refracted Ray Cray XD-1

- MODIS
- Moderate-resolution Imaging Spectroradiometer

- The Intersection Problem
- Finding the Perpendicular
- Refraction
- Reflection
- Coordinate Transformation

Find the Reflected Ray Cray XD-1

- MODIS
- Moderate-resolution Imaging Spectroradiometer

- The Intersection Problem
- Finding the Perpendicular
- Refraction
- Reflection
- Coordinate Transformation

Coordinate Transformation Cray XD-1

- MODIS
- Moderate-resolution Imaging Spectroradiometer

- The Intersection Problem
- Finding the Perpendicular
- Refraction
- Reflection
- Coordinate Transformation
(Hard to visualize this!)

Topics Cray XD-1

- Ray tracing
- Conventional parallel processing
- Modulo scheduling
- Coordination of sequential and parallel processing
- Expected Performance

Parallelism Cray XD-1

Performance Cray XD-1 (5.66 ´ 109 rays)

*

99.998 %

5,857 %

* Rate based on a linear regression of results obtained using a varying numbers of processors.

Performance Cray XD-1 (5.66 ´ 109 rays)

Efficiency Cray XD-1

Topics Cray XD-1

- Ray tracing
- Conventional parallel processing
- Modulo scheduling
- Coordination of sequential and parallel processing
- Expected Performance

Operations Required as a Function of Surface, Aperture, and Interaction Types

Not too many of these

Lots of these

Modulo Scheduling: Interaction TypesOne Multiplier

Modulo Scheduling: Interaction TypesOne Multiplier

Modulo Scheduling: Interaction TypesOne Multiplier

Modulo Scheduling: Interaction TypesOne Multiplier

Modulo Scheduling: Interaction TypesOne Multiplier

Modulo Scheduling: Interaction TypesOne Multiplier

Modulo Scheduling: Interaction TypesOne Multiplier

Modulo Scheduling: Interaction TypesOne Multiplier

Equal to the Data-Flow Limit

Modulo Scheduling: Interaction TypesFilling the Pipeline

One collective computation

Modulo Scheduling: Interaction TypesFilling the Pipeline

Modulo Scheduling: Interaction TypesFilling the Pipeline

Multipliers are 100 % utilized

No schedule conflicts

Modulo Scheduling: Interaction TypesTwo Multipliers

Two multipliers with two multiplications each

Modulo Scheduling: Interaction TypesTwo Multipliers

One adder with two additions

Two cycles

Maximum efficiency

Modulo Scheduling: Interaction TypesTwo Multipliers

Modulo Scheduling: Interaction TypesTwo Multipliers

Modulo Scheduling: Interaction TypesTwo Multipliers

Less than the Data-Flow Limit

Modulo Scheduling: Interaction TypesTwo Multipliers

Less than the Data-Flow Limit, but double the throughput.

Topics Interaction Types

- Ray tracing
- Conventional parallel processing
- Modulo scheduling
- Coordination of sequential and parallel processing
- Expected Performance

Cray XD-1 Interaction Types

- MPI (Message Passing Interface)
- Master node
- Reads file
- Distributes file
- Collates results

One Node of the Cray XD-1 Interaction Types

- Open MP (Multi Processing)
- 144 of 220 nodes have a Xilinx Virtex II Pro FPGA
- Opteron processors
- Sequential program
- Depth first

- FPGA
- Pipelined hardware
- Breadth first

Topics Interaction Types

- Ray tracing
- Conventional parallel processing
- Modulo scheduling
- Coordination of sequential and parallel processing
- Expected Performance

Performance Interaction Types

Performance Interaction Types

Performance Interaction Types

Performance Interaction Types

Summary Interaction Types

- Modulo scheduling produces 100 % efficiency of critical resources.
- Sequential processors get a boost from supplemental FPGA processing.
- Deep pipelines are efficient only if filled much of the time.
- FPGAs beat ASICs only if they can take advantage of special problem knowledge.
- Opteron uses 55 W.
- Virtex II Pro FPGA uses 4 W to 45 W.

Equations Interaction Types

- Intersection of a Ray with a Plane
- Intersection of a Ray with a Sphere
- Intersection of a Ray with a Conicoid
- Finding the Perpendicular
- Interaction of a Ray with an Optical Surface
- Coordinate Transformations

Intersection of a Ray with a Plane Interaction Types

Point in the plane

Initial direction

Final point

Initial point

Normal to the plane

List of equations

Intersection of a Ray with a Sphere Interaction Types

Initial direction

Final point

Initial point

List of equations

Intersection of a Ray with a Conicoid Interaction Types

Final point

Initial point

Initial direction

List of equations

Finding the Perpendicular Interaction Types

Unit Vector Normal to a Sphere

Unit Vector Normal to a Conicoid

List of equations

Interaction of a Ray with an Optical Surface Interaction Types

Refraction

Reflection

Initial index of refraction

Final index of refraction

Normal to the plane

Initial direction

Final direction

List of equations

Coordinate Transformations Interaction Types

Position in Frame of Reference k

Positionin Frame of Reference k+1

Rotation and Translation

Rotation

Direction in Frame of Reference k+1

Rotation Matrix

Direction in Frame of Reference k

Translation Vector

List of equations

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