Description
1. (40) In this problem, you will utilize the IEEE 754 format and evaluate the
performance implications of using floats versus doubles in a computation.
a.) Compute f(x) = sin (x) using a Taylor series expansion. To refresh your memory:
sin(x) = ∑ (“#)!
(%&’#)!
)
* � %&’#
sin(x) = � − !!
“! + !”
$! − !#
%! + !$
&! . . . .
You select the number of terms you want to compute (but at least 10 terms).
Compute sin(x) for 4 different values, though be careful not to use too large a value.
Generate two versions of your code, first defining x and sin(x) to use floats (SP),
and second, defining them as doubles (DP). Discuss any differences you find in
your results for f(x). You should provide an in-depth discussion on the results you
get and the reasons for any differences.
b.) Explore the benefits of compiling on the Discovery cluster with floating point
vector extensions (e.g., AVX). Use the single-precision code from part (a). First run
on a node on Discovery that does not support AVX-512. Then run on a node that
supports AVX-512 and report on the performance benefits. Additional information
is provided on AVX support on Discovery.
c.) Continuing with part (b), generate an assembly listing (using the -S flag) and
identify 2 different AVX instructions that the compiler generated, explaining their
operation.
d.) Provide both IEEE 754 single and double precision representations for the
following numbers: 2.1, 6300, and -1.044.
2. (30) In this problem, you will modify the matmul.c program provided, optimizing the
execution of the matrix multiplication with first a dense matrix, and second with a
sparse matrix. You are welcome to use pthreads, OpenMP or any of the optimizations
that were presented in class to accelerate this code. There will be prizes awarded for
the fastest dense and the fastest sparse implementations.
3. (30) In this problem, you will utilize the OpenBLAS library available on Discovery. To
use OpenBLAS, you will need to issue load openblas/0.3.6. Using the malmul.c
program, replace the math with a call to appropriate gemm library function. Compare
the speed of your solution for problem 2 with the gemm method you used.
(15 points for MS and 25 points for Undergraduate/Plus-One) (Extra quiz credit for everyone)
Find a published paper from an ACM or IEEE conference that discusses a novel sparse
matrix format that was not covered in class. Discuss why the proposed format is
superior to the CSR or CSC format. Make sure cite your sources.
* Written answers to the questions should be included in your homework 3 write-up in pdf
format. You should include your C/C++ programs and the README file in the zip file
submitted.