Why do these produce different values?

mr.nick has asked for the wisdom of the Perl Monks concerning the following question:

Greetings from an old Monk, Can someone explain to me why the following code snippet produces the following?

-output-
46
45
[download]

-code snippet-
$foo= 44123.2000 / 959.2;
print "$foo\n";
print int($foo),"\n";
[download]

Thanks as this has been driving me crazy! (And I have this horrible feeling I'm doing something crazy-stupid :) (btw, perl 5.005_03 on Solaris)

mr.nick ...

Comment on Why do these produce different values? Select or Download Code

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Re: Why do these produce different values? by ikegami (Patriarch) on Jan 25, 2006 at 20:20 UTC
`perl -e "printf '%.20f', 44123.2 / 959.2; 45.99999999999999300000` [download] Numbers have 52 bits of precision. `print` round off a few of the least significant of the 52 bits. In this case, this causes `45.999999999999993` to display as `46`. `int`, on the other hand, truncates `45.999999999999993` to `45`. So why is the answer `45.999999999999993` and not `46`? That's because `44123.2` and/or `959.2` is a periodic number in binary, or one of the intermidiary numbers in the conversion from string to number is a periodic number in binary. Others and searches will provide more info on this.	[reply] [d/l] [select]
Re: Why do these produce different values? by Roy Johnson (Monsignor) on Jan 25, 2006 at 20:07 UTC
simple arithmetic creates rounding errors Caution: Contents may have been coded under pressure.	[reply]
Re: Why do these produce different values? by davido (Cardinal) on Jan 25, 2006 at 21:11 UTC
Observe the output of the following code: `printf "%2.15f", 44123.200/959.2;` [download] The output, due to rounding errors inherent in any system where base 10 floating point numbers are converted to base 2 for arithmetic work, and then converted back to base 10 for display, is "45.999999999999993". Unless you tell it to do otherwise (as I have done with printf, Perl, like most languages rounds that to 46 for display purposes (I can't remember the number of decimal digits Perl will display before rounding). But int does something entirely different from rounding; it simply drops everything after the decimal point. So 45.9999999999999993 gets truncated by int to 45, while printing 45.99999999999993 gets rounded up to 46. I first encountered this fact of life back in my first high school Computer Science course in 1983 or so, taught on Apple II+ computers with some sort of Apple floating point BASIC. But it existed long before 1983, and will continue to exist as long as we use a finite number of base-2 digits to internally represent (and perform operations on) floating point base-10 numbers. Dave	[reply] [d/l]
Re: Why do these produce different values? by Aristotle (Chancellor) on Jan 25, 2006 at 20:34 UTC
See Floating-Point Basics, which explains the issues about doing math on computers in detail. Makeshifts last the longest.	[reply]
Re: Why do these produce different values? by GrandFather (Saint) on Jan 26, 2006 at 03:19 UTC
Others have answered the basic question well. The fundemental issue is that finite resolution binary fractions can not exactly represent decimal fractions so you always get rounding or truncation issues when using decimal fractions. DWIM is Perl's answer to Gödel	[reply]