#459 unequal computed values

[Gerard Schildberger]

For the REXX program (using all versions of Regina from 3.2 --> 3.9.1):

           /*REXX*/  parse version v;  say 'REXX version:' v
           H=249
           numeric digits max(9,length((H**5)*4))
           say 'digits=' digits()
           x=H**5
           say 'value of x=' x
           y=H**5 + 0
           say 'value of y=' y

           if x==y  then say 'x and y are exactly equal.'
                    else say "x and y aren't exactly equal."

           if x =y  then say 'x and y are equal.'
                    else say "x and y aren't equal."

---

The output of the REXX program:

           REXX version: REXX-Regina_3.9.1(MT) 5.00 5 Apr 2015
           digits= 14
           value of x= 9.57186876E+11
           value of y= 957186876249
           x and y aren't exactly equal.
           x and y aren't equal.

---

I don't understand why Regina REXX is putting the value of X
in exponential notation (with 14 numeric digits), and why,
even after normalization (by adding zero), the value of Y
is so much different that X.

           ___________________________ Gerard Schildberger

[Paul Kislanko]

Y is not "much" different from x - the percent difference is a little over 2.6E-08.

The real bug is x being expressed in fewer than DIGITS() significant figures, and it's stored that way since x+0 evaluates to 957186876000.

Interestnig that

x = h**5

and

x = h**5+0

evaluate to different results. Something about being involved in a more complicated expression makes ** behave correctly!

And this shows that it is definitely in the '**' function:

say pi
3.1415926535897932384626433832795028841971693993751

numeric digits 20

say pi**2
9.86960440

say pi**2+0
9.8696044010893586188