How to eliminate Perl rounding errors

Question

Consider the following program:

$x=12345678901.234567000;
$y=($x-int($x))*1000000000;
printf("%f:%f\n",$x,$y);

Here's what is prints:

12345678901.234568:234567642.211914

I was expecting:

12345678901.234567:234567000

This appears to be some sort of rounding issue in Perl.
How could I change it to get 234567000 instead?
Did I do something wrong?

Answer 1

Homework (Googlework?) for you: How are floating point numbers represented by computers?

You can only have a limited number of precise digits, everything beyond that is just the noise from base conversion (binary to decimal). That is also why the last digit of your $x appears to be 8.

$x - (int($x) is 0.23456linenoise, which is also a floating point number. Multiplied by 1000000000, it gives another floating point number, with more random digits pulled from the incommensurability of the bases.

Answer 2

Perl does not do arbitrary precision arithmetic for its built-in floating point types. So your initial variable $x is an approximation. You can see this by doing:

$ perl -e 'printf "%.10f", 12345678901.234567000'
12345678901.2345676422

Answer 3

Make "use bignum;" the first line of your program.

Other answers explain what to expect when using floating point arithmetic -- that some digits towards the end are not really part of the answer. This is to make the computations do-able in a reasonable amount of time and space. If you are willing to use unbounded time and space to work with numbers, then you can use arbitrary-precision numbers and math, which is what "use bignum" enables. It's slower and uses more memory, but it works like math you learned in elementary school.

In general, it's best to learn more about how floating point math works before converting your program to arbitrary-precision math. It's only needed in very strange situations.

Answer 4

This is a frequently-asked question.

Why am I getting long decimals (eg, 19.9499999999999) instead of the numbers I should be getting (eg, 19.95)?

Internally, your computer represents floating-point numbers in binary. Digital (as in powers of two) computers cannot store all numbers exactly. Some real numbers lose precision in the process. This is a problem with how computers store numbers and affects all computer languages, not just Perl.

perlnumber shows the gory details of number representations and conversions. To limit the number of decimal places in your numbers, you can use the printf or sprintf function. See the Floating Point Arithmetic for more details.

printf "%.2f", 10/3;
my $number = sprintf "%.2f", 10/3;

Answer 5

The whole issue of floating point precision has been answered, but you're still seeing the problem despite bignum. Why? The culprit is printf. bignum is a shallow pragma. It only affects how numbers are represented in variables and math operations. Even though bignum makes Perl do the math right, printf is still implemented in C. %f takes your precise number and turns it right back into an imprecise floating point number.

Print your numbers with just print and they should do fine. You'll have to format them manually.

The other thing you can do is to recompile Perl with -Duse64bitint -Duselongdouble which will force Perl to internally use 64 bit integers and long double floating point numbers. This will give you a lot more accuracy, more consistently and almost no performance cost (bignum is a bit of a performance hog for math intensive code). Its not 100% accurate like bignum, but it will affect things like printf. However, recompiling Perl this way makes it binary incompatible, so you're going to have to recompile all your extensions. If you do this, I suggest installing a fresh Perl in a different location (/usr/local/perl/64bit or something) rather than trying to manage parallel Perl installs sharing the same library.