This problem set is designed to familiarize you with computer programming, shell scripting, and simple visualization. You will also learn about benchmarking and optimization.

*HINT*: If you plan to use C for this assignment, and you're new to the language or need a refresher, be sure to read the*Intro to C*document first. It provides information on, for example, using internal clocks to measure code performance. You should also read the other introductory documents on Unix (especially scripting) and visualization.

- Write a program to time the CPU expense of various mathematical
operations, as listed in the table below. Do each operation
times, where
is supplied by the user. Your program
should output the final value obtained after cumulative
iterations of each operation, and the CPU time required to complete
them. For the moment, do not make use of compiler optimizations.
Operand Type Starting Value Operation integer 0 add 5 integer 0 subtract 5 integer 1 multiply by 1 integer 1 divide by 1 double-precision 0.0 add 5.0 double-precision 0.0 subtract 5.0 double-precision 1.0 multiply by 1.000001 double-precision 1.0 divide by 1.000001 double-precision 1.1 take square root ( `sqrt(x)`)double-precision 1.1 raise to the 0.5 power ( `pow(x,0.5)`)- Write a shell script to construct a table of execution times
for double-precision addition and multiplication as a function of
for = , , , ,
, , and . Do the
square-root and raise-to-the-power functions give much different
execution times? Comment.
- Plot the data in the table, execution time as a function of
, using any plotting package you like. The axes should use a
logarithmic scale. Estimate the number of floating-point
additions and multiplications (MFLOPs) your code carried out on
average per second.
- Redo one or more plots in question after
recompiling your code with optimizations turned on (e.g., try the
``
`-O2`'' compiler flag) and plot the results. Is there a difference? Also try a different compiler if possible, with and without optimizations (e.g., if you used`gcc`, try`icc`next.^{1}) Comment on the results and suggest why differences exist.

- Write a shell script to construct a table of execution times
for double-precision addition and multiplication as a function of
for = , , , ,
, , and . Do the
square-root and raise-to-the-power functions give much different
execution times? Comment.
- How long did it take you to finish this problem set?

__CHECKLIST__

Your submitted assignment should contain at least the following:

- Source file for benchmark code.
- Scripts for generating runtimes as a function of and plot the results.
- Document providing written answers to questions in PDF format.
- Plots showing runtimes and optionally MFLOPs as a function of ; these can be included in the written document. Feel free to include multiple plots on a page.
- A Makefile and/or README file written in plain text describing all the files being submitted, how to run the source code, and how to run the script. Optionally include information on how to generate the plots from the script output, but this is not required.