68 lines
2 KiB
Bash
68 lines
2 KiB
Bash
#!/usr/bin/env bash
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###############################################################################
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# This script performs the same task as "slower_e_demo.sh" but with a major
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# performance optimization. The speedup is especially noticeable on GNU
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# emulation layers for Windows such as Cygwin and minGW, where the overhead
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# of subshelling is quite significant.
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#
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# The speedup uses global storage space to simulate pass-and-return by
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# reference so that you can capture the side effects of a function call without
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# writing to stdout and wrapping the call in a subshell. How to use:
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#
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# Turn on "__shellmath_isOptimized" as shown below.
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# Then instead of invoking "mySum = $(_shellmath_add $x $y)",
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# call "_shellmath_add $x $y; _shellmath_getReturnValue mySum".
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###############################################################################
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source shellmath.sh
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# Setting the '-t' flag will cause the script to time the algorithm
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if [[ "$1" == '-t' ]]; then
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do_timing=${__shellmath_true}
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shift
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fi
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if [[ $# -ne 1 ]]; then
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echo "USAGE: ${BASH_SOURCE##*/} [-t] *N*"
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echo " Approximates 'e' using the N-th order Maclaurin polynomial"
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echo " (i.e. the Taylor polynomial centered at 0)."
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echo " Specify the '-t' flag to time the main algorithm."
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exit 0
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elif [[ ! "$1" =~ ^[0-9]+$ ]]; then
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echo "Illegal argument. Whole numbers only, please."
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exit 1
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fi
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__shellmath_isOptimized=${__shellmath_true}
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function run_algorithm()
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{
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# Initialize
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n=0; N=$1; zero_factorial=1
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# Initialize "e" to its zeroth-order term
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_shellmath_divide 1 $zero_factorial
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_shellmath_getReturnValue term
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e=$term
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# Compute successive terms T(n) := T(n-1)/n and accumulate into e
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for ((n=1; n<=N; n++)); do
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_shellmath_divide "$term" "$n"
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_shellmath_getReturnValue term
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_shellmath_add "$e" "$term"
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_shellmath_getReturnValue e
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done
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echo "e = $e"
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}
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if (( do_timing == __shellmath_true )); then
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time run_algorithm "$1"
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else
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run_algorithm "$1"
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fi
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exit 0
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