How to resolve the algorithm Averages/Root mean square step by step in the ALGOL 68 programming language

Published on 12 May 2024 09:40 PM
#Algol 68

How to resolve the algorithm Averages/Root mean square step by step in the ALGOL 68 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 ALGOL 68 programming language

Source code in the algol programming language

# Define the rms PROCedure & ABS OPerators for LONG... REAL #
MODE RMSFIELD = #LONG...# REAL;
PROC (RMSFIELD)RMSFIELD rms field sqrt = #long...# sqrt;
INT rms field width = #long...# real width;

PROC crude rms = ([]RMSFIELD v)RMSFIELD: (
  RMSFIELD sum := 0;
  FOR i FROM LWB v TO UPB v DO sum +:= v[i]**2 OD;
  rms field sqrt(sum / (UPB v - LWB v + 1))
);
 
PROC rms = ([]RMSFIELD v)RMSFIELD: (
# round off error accumulated at standard precision #
  RMSFIELD sum := 0, round off error:= 0;
  FOR i FROM LWB v TO UPB v DO 
    RMSFIELD org = sum, prod = v[i]**2;
    sum +:= prod;
    round off error +:= sum - org - prod
  OD;
  rms field sqrt((sum - round off error)/(UPB v - LWB v + 1))
);

main: (
  []RMSFIELD one to ten = (1,2,3,4,5,6,7,8,9,10);

  print(("crude rms(one to ten): ", crude rms(one to ten), new line));
  print(("rms(one to ten): ",       rms(one to ten), new line))
)

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