floating point calculations in awk

Question

I am surprised with behaviour of awk while performing floating point calculations. It lead me to wrong calculation on table data.

Answer 1

The following section from the manual should help you understand the issue you're observing:

15.1.1.2 Floating Point Numbers Are Not Abstract Numbers

Unlike numbers in the abstract sense (such as what you studied in high school or college arithmetic), numbers stored in computers are limited in certain ways. They cannot represent an infinite number of digits, nor can they always represent things exactly. In particular, floating-point numbers cannot always represent values exactly. Here is an example:

 $ awk '{ printf("%010d\n", $1 * 100) }'
 515.79
 -| 0000051579
 515.80
 -| 0000051579
 515.81
 -| 0000051580
 515.82
 -| 0000051582
 Ctrl-d

This shows that some values can be represented exactly, whereas others are only approximated. This is not a “bug” in awk, but simply an artifact of how computers represent numbers.

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A highly recommended reading:

What every computer scientist should know about floating-point arithmetic