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# shanemhansen/euler.sh

Last active Aug 29, 2015
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 #!/bin/bash # this is a fun little script to compute euler's number using bash. # It attempts to produce n digits of e when invoked as: ./euler.sh n # There's a well known taylor series for approximating e: # e = sum from 1 to infinity of 1/n! # unfortunately bash doesn't support fractions, just integers. # so we basically fake a rational number data structure, storing the numerator # and denominator as integers. At that point we have to deal with the fact # that bash integers are finite precision, so large numerator and large denominators # overflow very fast. We constantly have to reduce the fraction to shrink the numerator # and denominator. I use euclid's method for finding the gcd because it's extremely efficient. # this script gives you about 9 digits max. function numerator() { local __resultvar=\$1 local fraction=\$2 if [[ \$fraction =~ (.*)/.* ]] ; then eval \$__resultvar="'\${BASH_REMATCH[1]}'" fi } function denominator() { local __resultvar=\$1 local fraction=\$2 if [[ \$fraction =~ .*/(.*) ]] ; then eval \$__resultvar="'\${BASH_REMATCH[1]}'" fi } function multiply() { local __resultvar=\$1 local fraction1=\$2 local fraction2=\$3 local n local d numerator a \$fraction1 denominator b \$fraction1 numerator c \$fraction2 denominator d \$fraction2 let "n=a*c" let "d=b*d" eval \$__resultvar="\$n/\$d" } function sum() { local __resultvar=\$1 local fraction1=\$2 local fraction2=\$3 #a/b+c/d is #(ad+bc)/bd numerator a \$fraction1 denominator b \$fraction1 numerator c \$fraction2 denominator d \$fraction2 let "sum_n=a*d+b*c" let "sum_d=b*d" eval \$__resultvar="\$sum_n/\$sum_d" } function to_dec { local __resultvar=\$1 local r local accum numerator n \$2 denominator d \$2 let r=n/d let n=n-r*d let n=n*10 let precision=0 accum="\${r}." while [[ \$precision -lt 12 ]];do let r=n/d let n=n-r*d accum="\${accum}\${r}" let n=n*10 let precision=precision+1 done eval \$__resultvar="\$accum" } common_prefix() { local n=0 while [[ "\${1:n:1}" == "\${2:n:1}" ]]; do ((n++)) done echo \$n } function euler() { local accum=1/1 local term=1/1 local numer local denom local result local new_result for n in \$(seq 1 13);do multiply term \$term 1/\$n sum accum \$accum \$term #reduce numerator numer \$accum denominator denom \$accum gcd common \$numer \$denom let numer=numer/common let denom=denom/common accum=\$numer/\$denom to_dec new_result \$accum if [[ \$(common_prefix \$new_result \$result) -ge \$((\$1+2)) ]]; then echo \$result return fi result=\$new_result done echo "Couldn't get that many digits. Sorry" } function gcd() { local __resultvar=\$1 local tmp local num1=\$2 local num2=\$3 while [[ \$num1 -gt 0 ]];do let "tmp=num1" let "num1=num2%num1" let "num2=tmp" done eval \$__resultvar="\$num2" } euler \$1
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