# Rounding errors?

#1

:~\$ ruby -e “p ((0.29)*100).to_i”
28

Really?! I know that digital storage of floating point numbers can lead
to things like this, but this one seems a little extreme to me.

:~\$ ruby -v
ruby 1.8.7 (2008-08-11 patchlevel 72) [i486-linux]

Cheers,
Pete

#2

Pete H. removed_email_address@domain.invalid writes:

:~\$ ruby -e “p ((0.29)*100).to_i”
28

Really?! I know that digital storage of floating point numbers can lead
to things like this, but this one seems a little extreme to me.

You may try a true Lisp instead of a Matzacred Lisp:

\$ clisp -q -norc -x ‘(values (truncate (* 0.29 100)))’
29

#3

On Jun 5, 2009, at 10:07 PM, Pete H. wrote:

:~\$ ruby -e “p ((0.29)*100).to_i”
28

Really?! I know that digital storage of floating point numbers can
to things like this, but this one seems a little extreme to me.

sprintf “%0.30f”, 0.29
=> “0.289999999999999980015985556747”

sprintf “%0.30f”, 0.29*100
=> “28.999999999999996447286321199499”

sprintf “%0.30f”, (0.29*100).to_i
=> “28.000000000000000000000000000000”

If you want to really understand what is going on:
http://docs.sun.com/source/806-3568/ncg_goldberg.html

Gary W.

#4

Pascal J. Bourguignon wrote:

\$ clisp -q -norc -x ‘(values (truncate (* 0.29 100)))’
29

There’s nothing strange here, just IEEE floats, which don’t represent
every decimal float:

irb(main):001:0> (0.29)*100
=> 29.0
irb(main):002:0> ((0.29)*100).to_i
=> 28
irb(main):003:0> ((0.29)*100).round
=> 29
irb(main):004:0> ((0.29)*100).floor
=> 28
irb(main):006:0> “%20.18f” % ((0.29)*100)
=> “28.999999999999996447”
irb(main):007:0> “%20.18f” % 0.29
=> “0.289999999999999980”

#5

On Jun 5, 2009, at 7:15 PM, Pascal J. Bourguignon wrote:

\$ clisp -q -norc -x ‘(values (truncate (* 0.29 100)))’
29

Pascal B.

The result of the calculation is undefined in pretty much any
language. The loose definition of the expression is “return a value
100 times a value approximating 29 and truncated to an integer using
the algorithm of your choice.” So, you claim the only right answer
must be the one yielded by Lisp. However, the correct answer is: The
result of evaluating this expression is implementation-specific.

In C:

#include <stdio.h>

int main(void) {
double d = 0.29;
float f = 0.29;

printf(“double truncated to integer is: %i\n”, (int)(d * 100));
printf(“float truncated to integer is: %i\n”, (int)(f * 100));

return 0;
}

Would ANSI[1] C results be correct enough to be used as a gold
standard? Well, if so, the result of the program above is:

\$ ./foo
double truncated to integer is: 28
float truncated to integer is: 29

The moral of the story is not “use Lisp”. The moral is use floating
point numbers with great care. Oh, geez, I totally forgot, this is a
Ruby list, not a C list.

[1] gcc version 4.0.1 (Apple Inc. build 5488)

#6

On 06.06.2009 05:46, s.ross wrote:

The result of the calculation is undefined in pretty much any
language. The loose definition of the expression is “return a value
100 times a value approximating 29 and truncated to an integer using
the algorithm of your choice.” So, you claim the only right answer
must be the one yielded by Lisp.

Agreed. And, btw, with BigDecimal even Ruby comes up with more
“natural” results:

require ‘bigdecimal’
x = BigDecimal.new “0.29”
x *= 100
puts x
printf “%f %10.8f\n”, x, x

->

0.29E2
29.000000 29.00000000

However, the correct answer is: The
result of evaluating this expression is implementation-specific.

Actually, this is only half true: if the implementation is IEEE-754
standards conform then it must yield certain results - regardless of
implementation. I believe nowadays most if not all math libraries
conform to the standard so you should expect to see the same results
from all implementations. I would assume that differences are mostly
due to numeric data type (see your C example) and conversion for
printing (e.g. how many places are output by default).

The moral of the story is not “use Lisp”. The moral is use floating
point numbers with great care.

Exactly.

Kind regards

robert

#7