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### Simple math gone wrong

by sdyates (Scribe)
 on Sep 04, 2003 at 12:19 UTC Need Help??
sdyates has asked for the wisdom of the Perl Monks concerning the following question:

I try something simple like:

print 1062676995.614963 - 1062676995.594934;

And I get: 0.0200290679931641!!! Why

I should get: 0.020029 - why do I get data going back multiple decimal places? I have never seen this before. Should I be using certain command to do math. I tried going to 2 decimal places and still have the problem.

I got the variables from Time::HiRes but I dont see how this is the problem. Please help Monks, sdyates

Replies are listed 'Best First'.
Re: Simple math gone wrong
by tachyon (Chancellor) on Sep 04, 2003 at 12:24 UTC

It all comes back to how the computer actually stores and processes numbers. Floating point numbers are by nature inexact. If you need exact you need to use integer math and then correct for decimal places. See Bug? 1+1 != 2, Filthy Floats or the IEEE stuff here including What Every Computer Scientist Should Know about Floating-Point Arithmetic

If you don't really care to much just use printf/sprintf

```printf '%.6f', 1062676995.614963 - 1062676995.594934
__DATA__
0.020029

cheers

tachyon

s&&rsenoyhcatreve&&&s&n.+t&"\$'\$`\$\"\$\&"&ee&&y&srve&&d&&print

Re: Simple math gone wrong
by Abigail-II (Bishop) on Sep 04, 2003 at 12:26 UTC
```\$ perldoc -q decimal
Found in /opt/perl/lib/5.8.0/pod/perlfaq4.pod
Why am I getting long decimals (eg, 19.9499999999999)
instead of the numbers I should be getting (eg, 19.95)?

The infinite set that a mathematician thinks of as
the real numbers can only be approximated on a
computer, since the computer only has a finite
number of bits to store an infinite number of, um,
numbers.

point numbers in binary.  Floating-point numbers
read in from a file or appearing as literals in
your program are converted from their decimal
floating-point representation (eg, 19.95) to an
internal binary representation.

However, 19.95 can't be precisely represented as a
binary floating-point number, just like 1/3 can't
be exactly represented as a decimal floating-point
number.  The computer's binary representation of
19.95, therefore, isn't exactly 19.95.
When a floating-point number gets printed, the
binary floating-point representation is converted
back to decimal.  These decimal numbers are dis-
played in either the format you specify with
printf(), or the current output format for num-
bers.  (See "\$#" in perlvar if you use print.  \$#
has a different default value in Perl5 than it did
in Perl4.  Changing \$# yourself is deprecated.)

This affects all computer languages that represent
decimal floating-point numbers in binary, not just
Perl.  Perl provides arbitrary-precision decimal
numbers with the Math::BigFloat module (part of
the standard Perl distribution), but mathematical
operations are consequently slower.

If precision is important, such as when dealing
with money, it's good to work with integers and
then divide at the last possible moment.  For
example, work in pennies (1995) instead of dollars
and cents (19.95) and divide by 100 at the end.

To get rid of the superfluous digits, just use a
format (eg, "printf("%.2f", 19.95)") to get the
required precision.  See "Floating-point Arith-
metic" in perlop.

Abigail

Re: Simple math gone wrong
by gjb (Vicar) on Sep 04, 2003 at 12:25 UTC

It's due to the internal representation of numbers. Have a look at this (brilliant) node, it does a much better job at explaining the issue than I have the patience for ;-)

Hope this helps, -gjb-

Re: Simple math gone wrong
by Taulmarill (Deacon) on Sep 04, 2003 at 12:34 UTC
maybe you want to use one of the Math Modules (look for them at CPAN).

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