Last active
August 29, 2015 14:24
-
-
Save shanemhansen/cd8f4178d33740b3e835 to your computer and use it in GitHub Desktop.
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
#!/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 |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment