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#!/usr/bin/env bash
###############################################################################
# This script performs the same task as "slower_e_demo.sh" but with a major
# performance optimization. The speedup is especially noticeable on GNU
# emulation layers for Windows such as Cygwin and minGW, where the overhead
# of subshelling is quite significant.
#
# The speedup uses global storage space to simulate pass-and-return by
# reference so that you can capture the side effects of a function call without
# writing to stdout and wrapping the call in a subshell. How to use:
#
# Turn on "__shellmath_isOptimized" as shown below.
# Then instead of invoking "mySum = $(_shellmath_add $x $y)",
# call "_shellmath_add $x $y; _shellmath_getReturnValue mySum".
###############################################################################
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
__shellmath_isOptimized=${__shellmath_true}
function run_algorithm()
{
# Initialize
n=0; N=$1; zero_factorial=1
# Initialize "e" to its zeroth-order term
_shellmath_divide 1 $zero_factorial
_shellmath_getReturnValue term
e=$term
# Compute successive terms T(n) := T(n-1)/n and accumulate into e
for ((n=1; n<=N; n++)); do
_shellmath_divide "$term" "$n"
_shellmath_getReturnValue term
_shellmath_add "$e" "$term"
_shellmath_getReturnValue e
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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