|Perl: the Markov chain saw|
Why am I getting long decimals (eg, 19.9499999999999) instead of the numbers I should be getting (eg, 19.95)?by faq_monk (Initiate)
|on Oct 08, 1999 at 00:20 UTC||Need Help??|
Current Perl documentation can be found at perldoc.perl.org.
Here is our local, out-dated (pre-5.6) version:
The infinite set that a mathematician thinks of as the real numbers can only be approximate on a computer, since the computer only has a finite number of bits to store an infinite number of, um, numbers.
Internally, your computer represents floating-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 the 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 displayed in either the format you specify with
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.
To get rid of the superfluous digits, just use a format (eg, printf("%.2f", 19.95)) to get the required precision. See Floating-point Arithmetic.