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#!/usr/bin/env bash
###############################################################################
# This script illustrates the use of the shellmath APIs to perform
# decimal calculations. Here we approximate the mathematical constant 'e'
# using its Maclaurin polynomials (i.e. its Taylor polynomials centered at 0).
###############################################################################
source shellmath.sh
# Setting the '-t' flag will cause the script to time the algorithm
if [[ "$1" == '-t' ]]; then
do_timing=${__shellmath_true}
shift
fi
if [[ $# -ne 1 ]]; then
echo "USAGE: ${BASH_SOURCE##*/} [-t] *N*"
echo " Approximates 'e' using the N-th order Maclaurin polynomial"
echo " (i.e. the Taylor polynomial centered at 0)."
echo " Specify the '-t' flag to time the main algorithm."
exit 0
elif [[ ! "$1" =~ ^[0-9]+$ ]]; then
echo "Illegal argument. Whole numbers only, please."
exit 1
fi
function run_algorithm()
{
# Initialize
n=0; N=$1; zero_factorial=1
# Initialize e to the zeroth-order term
term=$(_shellmath_divide 1 $zero_factorial)
e=$term
# Compute successive terms T(n) := T(n-1)/n and accumulate into e
for ((n=1; n<=N; n++)); do
term=$(_shellmath_divide "$term" "$n")
e=$(_shellmath_add "$e" "$term")
done
echo "e = $e"
}
if (( do_timing == __shellmath_true )); then
time run_algorithm "$1"
else
run_algorithm "$1"
fi
exit 0
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