Pastebin: gnu bc little sum for a bernoulli trial

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Post date

2022-11-27 20:26

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Unlimited

 # we want the following:
 # #  \sum_{i=0}^{N} \left ( 1-\frac{1}{64^{5}} \right )^i \cdot \frac{1}{64^{5}}
 # see http://pier4r.wikidot.com/pierworks:articles:obscurity-could-be-secure
 
 # excel breaks, online calculators break too somehow (it would be nice to just use sum)
 # therefore employing at first bc + bash, other possibilities are awk or other more equipped languages.
 
 # echo "scale=32; (1 - 1 / 64^5)^0 * ( 1 / 64^5) " | bc
 # .00000000093132257461547851562500
 
 
 # update 2022-11-27
 # Bash is ok, awk could be better in some cases. Surely both could be heavily extended by bc
 # but bc on its own is quite powerful in theory, if one writes libraries for it.
 # https://www.gnu.org/software/bc/manual/html_mono/bc.html
 # http://phodd.net/gnu-bc/
 # so let's go full bc
 
 # usage as of 2022-11-27:
 # bc -l -q sum_probabilities_base_64.bc , then press enter and get the result (or use the quit command)
 # time bc sum_probabilities_base_64.bc for the timings.
 
 define formula (exponent) {
   return (1 - 1 / 64^5)^exponent * ( 1 / 64^5)
 }
 
 scale=32
 "attempts? (+1):" ; attempts = read()
 sum=0
 for (i = 0; i <= attempts; i++ ){
     sum += formula(i)
 }
 "sum:"; sum #leave sum as output
 quit