[erlang-questions] Maths Problem -> 2452.45*100. = 245244.99999999997

[Richard A. O'Keefe]

On 27/11/2013, at 2:28 PM, Sanath Prasanna wrote:

> Hi all,
> when running following sample in ERL shell, I got wrong value. What is the reason for this?
> 
> 2452.45*100. = 245244.99999999997
> 
> It should be 245245.0 or 245245
> 

What do you mean "should"?
Some programming languages lie to you about the number they give you.
Ruby for one.
You have to probe a little deeper.

m% irb
>> 2452.45*100
=> 245245.0
>> 2452.45*100 - 245245.0
=> -2.91038304567337e-11

So Ruby _actually_ calculated the *same* answer as Erlang,
but showed you a different number.

SWI Prolog calculated the same number as Erlang.

m% swipl
?- X is 2452.45*100.
X = 245244.99999999997.

Gambit Scheme calculated the same number as Erlang.

m% gsi
Gambit v4.6.0
> (* 2452.45 100) 
245244.99999999997

R calculates the same number as Erlang, but like Ruby,
rounds the number before displaying it:

m% R
> x <- 2452.45 * 100
> x
[1] 245245
> x - 245245
[1] -2.910383e-11

Javascript calculates the same number as Erlang.

m% /Scratch/js-1.6.20070208/js
js> 2452.45*100
245244.99999999997

I think we're beginning to see a pattern.

m% cat >foo.c
#include <stdio.h>

int main(void) {
    printf("%.12f\n", 2452.45*100);
    return 0;
}
<EOF>
m% cc foo.c
m% a.out
245244.999999999971

It looks very much as though Erlang calculates exactly the
answer that it "should" calculate.

Remember, this is IEEE double-precision *binary* floating-
point arithmetic.  100 can be represented exactly in that
arithmetic, but 2452.45 *cannot*.  From a C program, when
you convert 2452.45 to an IEEE double, what you get is
2452.44999999999981810106.

There _is_ an IEEE standard for decimal floating point
arithmetic, and recent IBM z/Series and Power computers
offer high speed hardware support for it, and there _is_
at least a draft of a standard for decimal floating point
in C, which IBM's XLC supports, GCC supports (see
http://gcc.gnu.org/onlinedocs/gcc/Decimal-Float.html),
but clang doesn't.