How to resolve the algorithm Averages/Root mean square step by step in the Quackery programming language

Published on 12 May 2024 09:40 PM
#Quackery

How to resolve the algorithm Averages/Root mean square step by step in the Quackery programming language

Table of Contents

Problem Statement

Compute the   Root mean square   of the numbers 1..10.

The   root mean square   is also known by its initials RMS (or rms), and as the quadratic mean. The RMS is calculated as the mean of the squares of the numbers, square-rooted:

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Averages/Root mean square step by step in the Quackery programming language

Source code in the quackery programming language

[ $ "bigrat.qky" loadfile ] now!

[ [] swap
  witheach
    [ unpack 2dup v*
      join nested join ] ] is squareall (   [ --> [   )

[ dup size n->v rot
  0 n->v rot
  witheach
    [ unpack v+ ]
  2swap v/ ]               is arithmean (   [ --> n/d )
 
[ dip
  [ squareall arithmean ]
  vsqrt drop ]             is rms       ( [ n --> n/d )
 
say "The RMS of the integers 1 to 10, to 80 decimal places with rounding." cr
say "(Checked on Wolfram Alpha. The final digit is correctly rounded up.)" cr cr
 
' [ [ 1 1 ] [ 2 1 ] [ 3 1 ] [ 4 1 ] [  5 1 ] 
    [ 6 1 ] [ 7 1 ] [ 8 1 ] [ 9 1 ] [ 10 1 ] ]
 
( ^^^ the integers 1 to 10 represented as a nest of nested rational numbers )
 
80 rms 
80 point$ echo$

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