using awk and printf not rounding correctly [duplicate]

Question

I have an issue where I'm using printf to round a float to the proper number of decimal points. I'm getting inconsistent results as shown below.

echo 104.45   |  awk '{printf "%.1f\n",$1}'
104.5                               <-- seem to be correct behaviour

echo 104.445  |  awk '{printf "%.2f\n",$1}'
104.44       (should be 104.45)     <-- seems to be INCORRECT behaviour

echo 104.4445 |  awk '{printf "%.3f\n",$1}'
104.445                             <-- seems to be correct behaviour

I've seen examples where float number in calculations may cause problems, but did not expect this with formatting.

Answer 1

The number 104.4445 cannot be represented exactly as a binary number. In other words, your computer doesn't know such a number.

# echo 104.4445 | awk '{printf "%.20f\n",$1}'
104.44450000000000500222

# echo 104.445 | awk '{printf "%.20f\n",$1}'
104.44499999999999317879

That's why the former is rounded to 104.445, while the latter is rounded to 104.44 .

The sjsam's answer is relevant only to numbers which can be represented exactly as a binary number, i. e. m/2**n , where m and n are integers and not too big. Changing ROUNDINGMODE to "A" has absolutely no effect on printing 104.45, 104.445, or 104.4445 :

# echo 104.4445  |  awk -v ROUNDMODE="A" '{printf "%.3f\n",$1}'
104.445
# echo 104.4445 | awk '{printf "%.3f\n",$1}'
104.445
# echo 104.445 | awk -v ROUNDMODE="A" '{printf "%.2f\n",$1}'
104.44
# echo 104.445 | awk '{printf "%.2f\n",$1}'
104.44

Answer 2

I tried something analogous in Python and got similar results to you:

>>> round(104.445, 2)
104.44
>>> round(104.4445, 3)
104.445

This seems to be run-of-the-mill wonky floating point wonkiness, especially considering that the floating-point representation of 104.445 is less than the actual mathematical value of 104.445:

>>> 104.445 - 104.44
0.0049999999999954525
>>> 104.445 - 104.44 + 104.44
104.445