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Polynomial evaluation

Started by GWS, December 03, 2019, 04:59:16 PM

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Hi folks,

Here's an old computing method by IBM (Engineering Analysis for Computers - 1961).

This computes the value of a polynomial using only multiply and add operations ..

' Polynomial evaluation


def x,y:float

' To compute the value of a polynomial

' f(x) = ax^5 + bx^4 + cx^3 + dx^2 + ex + f
' simplify to

' f(x) = (((((a)x + b)x + c)x + d)x +e)x + f
' ie. by repeating the steps (multiply and add) ..

' Example:
print "Polynomial evaluation":print:print STRING$(25, "_" )

setprecision 10

x = 2.55

' direct evaluation ..
y = 2.1 * x^5 + 0.4 * x^4 + 32 * x^3 + 12.5 * x^2 + 0.34 * x + 100

print "Direct method using exponentiation and add"
print y

' alternatively ..
y = (((((2.1)*x + 0.4)*x + 32)*x + 12.5)*x + 0.34)*x + 100

print "Alternative method using only multiply and add"
print y

print "Press any key to exit .."

do:until inkey$<>""

Best wishes, :)

Tomorrow may be too late ..


Thanks Graham,

We had a similar example when I first learnt to code in 1962 or 1963. I beleive the languag was called RPG.
The computer occupied most of the basement of a large office building, and when we had done the coding on paper sheets, the papers where then sent to some busy ladies, that punched the cards we fed the large IBC computer with.
Those were the days....
Support Amateur Radio  -  Have a ham  for dinner!


Hi Egil,

Yes it was an interesting time - we were very lucky to have experienced it.

All the best, :)

Tomorrow may be too late ..


when I was going to nite school after I got out of the AF I remember having to take a semester of RPG and of COBOL. We had to punch our own cards and submit them. Then wait for them to be run on the same main frame that handle all the university business.
Larry McCaughn :)
Author of IWB+, Custom Button Designer library, Custom Chart Designer library, Snippet Manager, IWGrid control library, LM_Image control library


Hi Larry,

A stack of punched cards had to be carried with care - if you dropped them, your program statements could be shuffled.  ;D

Best wishes, :)

Tomorrow may be too late ..


Just FYI, I work on an iSeries (AS/400) machine, where I program in RPG and COBOL.  Both languages are still alive and running.  RPG was Report Program Generator, but now it is used like we used to use COBOL/CICS.  It has green screen entry screens, to enter data into and respond back from and will do batch report processing and file manipulation.  It also allows access to DB2 to use SQL.

When all else fails, get a bigger hammer.