Erroneous Arithmetic
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#601 Erroneous Arithmetic
I noticed different results for a roseettacode task
https://rosettacode.org/wiki/Feigenbaum_constant_calculation
when running it with Regina and ooRexx
I found where the computations start to run differently
My test program:
Parse Version v; Say v
Numeric Digits 30
a=1.39699477705242943014290570625
Say 'a ='||a
x=0;
y=0
do 16
y=1-2xy
x=a-xx
end /2*i/
a=a-x/y
Say 'x ='||x
Say 'y ='||y
Say 'x/y='||(x/y)
Say 'a ='||a
K:>rexx fct
REXX-ooRexx_5.1.0(MT)_64-bit 6.05 7 Feb 2023
a =1.39699477705242943014290570625
x =0.00029308138955703591412484758
y =5.95900277121112209566741518314
x/y=0.0000491829590972768327194163898515
a =1.39694559409333215331018628986
K:>regina fct
REXX-Regina_3.9.6(MT) 5.00 29 Apr 2024
a =1.39699477705242943014290570625
x =0.00029308138955703591412484765
y =5.95900277121112209566741519523
x/y=0.0000491829590972768327194164014987
a =1.39694559409333215331018628985
The difference grows with the number of iterations and ends up as
20 12 4.66920160910168137440902081266 115.921000 ooRexx
20 12 4.66920160910169069039564432665 337.176000 Regina
?
true value= 4.66920160910299067185320382047
ooRexx is apparently quite a bit faster in this case
Hi Walter, I ran your program with 30 digits and 2 iterations giving
REXX-Regina_3.9.6(MT) 5.00 29 Apr 2024
a =1.39699477705242943014290570625
x =-0.55459963005933757900129440937
y =-1.79398955410485886028581141250
x/y=0.309143176887707328204272488685
a =1.08785160016472210193863321757
REXX-ooRexx_5.0.0(MT)_64-bit 6.05 23 Dec 2022
a =1.39699477705242943014290570625
x =-0.55459963005933757900129440936
y =-1.79398955410485886028581141250
x/y=0.309143176887707328204272488679
a =1.08785160016472210193863321757
Using 40 digits and 2 iterations I got
x =-0.554599630059337579001294409364602341965
for both Regina and ooRexx, showing that x should end in '0936'.
Apparently the last digit(s) may differ between Regina (wrong) and ooRexx (better). And your program 'magnifies' the difference by each iteration. Even ooRexx drifts away from the true values while taking more iterations.
This shows the pitfalls of numerical calculations. Always beware of precision loss, take enough digits in your programs.
This ain't the problem-
Regina and ooRexx (and other Rexxes) should give the same results!
Okay! In this case then, Regina doesn't always correctly round the numbers to the digits setting.
Such as
say 10/6 gives correct 1.66666667 with the default 9 digits (meaning internally at least 1 extra digit was taken into account).
But that is correct
Say 10/6
Numeric Digits 10
Say 10/6
K:>rexx 106
1.66666667
1.666666667
K:>regina 106
1.66666667
1.666666667
Using the original Rosettacode program and 'trace results' I succeeded in creating a small example.
Consider following code snippet:
numeric digits 9
x = 1.38154750
say x*x
Regina produces
1.90867350
and ooRexx
1.90867349
On a 12-digit calculator I get
1.90867349476
Both the ooRexx manual and the Standard state that results should be rounded to the number of numeric digits. So Regina is in error here!