awk: negative exponential is not correctly interpreted

user_5355800 0
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I have this table:

a   0
b   0
c   1.6149e-315
d   5.2587e-265
e   8.2045e-227
f   8.2045e-227

If I type

$awk '($2<1){print}' my_file.txt

it returns

a   0
b   0
d   5.2587e-265
e   8.2045e-227
f   8.2045e-227

but it considers the value in the third row, 1.6149e-315, to be larger than 1:

$awk '($2>1){print}' my_file.txt 
c   1.6149e-315

Which is the reason for this behaviour? Is a negative exponential <1e-300 too small so it removes the "e-" part? It looks so, since

$awk '($2>1.6149){print}' my_file.txt 
c   1.6149e-315

but if I run

$ awk '($2>1.615){print}' my_file.txt

nothing is output.

How can I overcome this problem?

exponential if-statement awk shell unix
2 Answers

Run your awk like this:

awk '($2+0) < 1' file

This will output:

a   0
b   0
c   1.6149e-315
d   5.2587e-265
e   8.2045e-227
f   8.2045e-227

$2+0 converts $2 into a numeric value.

btw on GNU Awk 5.0.1, I get correct output even without this trick.

user_5482250

Reproduced the OP's issue with GNU Awk 4.2.1.

First of all, $NF+0 seems not to solve this issue, as we can see in this example:

> cat file
a   0
b   0
c   1.6149e-315
d   5.2587e-265
e   8.2045e-227
f   8.2045e-227

> awk '$2+0>0' file
d   5.2587e-265
e   8.2045e-227
f   8.2045e-227

The third number of the sample input is not printed again, while it should be greater than zero.

And here we see only zeros for the third number.

awk '{printf "%.320f\n",$2+0}' file

The above are indicating that e^-315 is not being represented in an expected way.

It seems like you have exceeded the limit which is -308 for double-precision floating point. Around e^-308 is the minimum positive non zero value to be represented.

https://www.gnu.org/software/gawk/manual/gawk.html#Computer-Arithmetic

Furthermore, if your gnu awk is compiled with MPFR support, you can have multiple precision numbers, using the -M option, which seems the only way to represent a positive number less that 10^-308

https://www.gnu.org/software/gawk/manual/html_node/MPFR-features.html

One last argument, a simple test:

> cat file
a   1.1e-312
b   1.1e-311
c   1.1e-310
d   1.1e-309
e   1.1e-308
f   1.1e-307
g   1.1e-306
h   1.1e-305
> awk '$2+0>0' file
f   1.1e-307
g   1.1e-306
h   1.1e-305

exponents less than -308 are not treated as expected.

> awk '{print($2+0)}' file
0
0
0
0
0
1.1e-307
1.1e-306
1.1e-305

and this is the proof, that $NF+0 forces to zero and not to the expontential number, any numbers beyond ^-308 cannot be represented because of that limit, which exists for awk instances with double-precision and no support for multi-precision.

user_75896360
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