# Benchmark of MCAmericanEngineMultiKernel¶

## Overview¶

This is a benchmark of MC (Monte-Carlo) European Engine using the Xilinx Vitis environment to compare with QuantLib. It supports software and hardware emulation as well as running the hardware accelerator on the Alveo U250.

This example resides in L2/benchmarks/MCAmericanEngineMultiKernel directory. The tutorial provides a step-by-step guide that covers commands for build and runging kernel.

## Executable Usage¶

• Work Directory(Step 1)

The steps for library download and environment setup can be found in Vitis Quantitative_Finance Library. For getting the design,

cd L2/benchmarks/MCEuropeanEngine

• Build kernel(Step 2)

Run the following make command to build your XCLBIN and host binary targeting a specific device. Please be noticed that this process will take a long time, maybe couple of hours.

source /opt/xilinx/Vitis/2021.1/settings64.sh
source /opt/xilinx/xrt/setenv.sh
export DEVICE=/opt/xilinx/platforms/xilinx_u250_xdma_201830_2/xilinx_u250_xdma_201830_2.xpfm
export TARGET=hw
make run

• Run kernel(Step 3)

To get the benchmark results, please run the following command.

./build_dir.hw.xilinx_u250_xdma_201830_2/host.exe -xclbin build_dir.hw.xilinx_u250_xdma_201830_2/MCAE_k.xclbin -cal 4096 -s 100 -p 2


Input Arguments:

Usage: test.exe    -[-xclbin -cal -s -p]
-xclbin     MCEuropeanEngine binary;
-cal        to config the value calibSamples, default value is 4096;
-s          to config the value timeSteps, default value is 100;
-p          to config the valude requiredSamples, default value is 24576/cu_number, the cu_number is 2;

• Example output(Step 4)
----------------------MC(American) Engine-----------------
data_size is 409600
Found Platform
Platform Name: Xilinx
Found Device=xilinx_u250_xdma_201830_2
INFO: Importing MCAE_k.xclbin
kernel has been created
kernel start------
kernel end------
Execution time 8333us
output = 3.97936
PASSED!!! the output is confidential!


## Profiling¶

The application scenario in this case is:

 Option Type put strike 40 underlying 36 risk-free rate 6% volatility 20% dividend yield 0 maturity 1 year tolerance 0.02 workload 100 steps, 24576 paths

The performance comparison of the MCAmericanEngine is shown in the table below, where timesteps is 100, requiredSamples is 24576, calibSamples is 4096, and FPGA frequency is 300MHz. Baseline is Quantlib, a Widely Used C++ Open Source Library, running on CPU with 1 thread. The CPU is Intel(R) Xeon(R) CPU E5-2667 v3 @3.200GHz, 8 cores per procssor and 2 threads per core. Our cold run has 197X and warm run has 590X compared to baseline.

Table 19 Timing_Performance
Platform Execution time
cold run warm run
Baseline 1156.5ms 1156.5ms
Runtime on U250 5.87ms 1.96ms
Accelaration Ratio 197X 590X

Note

What is cold run and warm run?

• Cold run means to run the application on board 1 time.
• Warm run means to run the application multiple times on board. And for pipeline mode, the application is always running multiple times.

The resource utilization and performance of MCAmericanEngine on U250 FPGA card is listed in the following tables (using viviado 2021.1).

 Engine APIs LUT FF BRAM URAM DSP 3-kernel MCAmericanEnginePreSamples (k0: UN=2) 120756 185169 43 0 416 MCAmericanEngineCalibrate (k1: UN=(2, 2)) 181793 267405 68 0 462 MCAmericanEnginePricing (k2_0: UN=4; k2_1: UN=4) 251370 368839 71 0 911

Table 20 gives the resource utilization report of four American option APIs. Note that the resource statistics are under specific UN (Unroll Number) configurations. These UN configurations are the templated parameters of the corresponding API.

The complete Vitis demos of MCAmericanEngineMultiKernel is executed with a U250 card on Nimbix. The performance is listed in Table 21. In this table, kernel execution time and end-to-end execution time (E2E) are calculated.

 Engine Kernel Configuration Frequency Total Execution Time (ms) Execution Time - pipeline (ms) kernel E2E E2E pipeline 3-kernel MCAmericanEnginePreSamples k0: UN=2 260MHz 5.33 5.45 1.96 1.23 MCAmericanEngineCalibrate k1: Un=2 1.35 MCAmericanEnginePricing k2_0: UN=4, k2_1: UN=4 1.56

Due to place and route on FPGA, the kernel runs at 260MHz finally. Because the last kernel takes the longest time while execution, it is duplicated. The total execution time of k2_0 and k2_1 is 1.56ms. The end-to-end execution time in pipeline mode is 1.96ms, which is only slightly bigger than the execution time of Pricing kernels.

Hint

Why instance two kernels of MCAmericanEnginePricing with UN=4 instead of using one pricing kernel with UN=8?

For one pricing kernel with UN=4, the resource it used is around 74% of one SLR. When UN=8, two SLRs are required to fit 1 kernel. This means that cross SLR for single kernel has to be processed. This may decrease the overall frequency dramatically. In real applications, we are always trying to avoid cross SLR place & routing. Using two exactly the same pricing kernel with UN=4, each kernel can be successfully placed on one SLR. The cross SLR logic can be avoided. Therefore, two pricing kernels with UN=4 are employed in the end.