Compute Sine using Taylor Series

April 6, 2023 · View on GitHub

Overview

This project stresses the use of floating point instructions to create a program that computes the sine of an angle given to you in degrees on the command line.

Taylor Series

The sine of an angle given in radians can be found using the Taylor Series:

sin x = x - x^3/3! + x^5/5! - x^7/7! ...

Notice each term flips from addition to subtraction.

Notice each term is based on the odd integers starting at 1. While the "1" case might look different, it is the same as all the others since 1 is just 1 to the first power divided by 1 factorial.

Command line

You are to accept two arguments on the command line. getopt is not being used here to concentrate on the floating point math. Both arguments are therefore required.

The angle in degrees whose sine you wish to calculate. Take this to be a double.
The number of terms to evaluate. The number of terms must lie between 1 and 10 inclusive. Note the value of 10 as an upper bound in new. It was 8.

C version

To assist your efforts, here is a version of this project written in C. This has been updated to print nice debugging output which is not part of the project.

This C version also demonstrates a different way of calculating the toggle. This version flips the sign of the toggle by multiplying by -1. The previous version used odd and even values of the term.

Sample executions

pk_taylor_series > gcc main.S -o a
pk_taylor_series > ./a 0 10
The sine of 0.00 degrees is 0.00000000.
pk_taylor_series > ./a 30 10
The sine of 30.00 degrees is 0.50000000.
pk_taylor_series > ./a 45 10
The sine of 45.00 degrees is 0.70710678.
pk_taylor_series > ./a 90 10
The sine of 90.00 degrees is 1.00000000.
pk_taylor_series > ./a 180 10
The sine of 180.00 degrees is -0.00000000.
pk_taylor_series > ./a 360 10
The sine of 360.00 degrees is -0.00104818.
pk_taylor_series > ./a 360 100
Number of terms is out of range.
pk_taylor_series > ./a 360 -1
Number of terms is out of range.
pk_taylor_series >

Floating point instructions I used

These are the floating point instructions I used in my implementation.

fmov
scvtf
fmul
fdiv
fadd

How I broke up the program

I have functions named:

main
HandleOptions
Factorial
IntegerPower - x to the nth power
ComputeSine - The main calculation
PrintAnswer
ConvertTheta - Wrap D2R
D2R - Degrees to radians