numeric calculation with shell or awk

1) For processing two variables with one number given to each variable

Shell language is usually not used for complex scientific calculation. But sometimes we may will use it to do some simple calculations with text files. What can we do ?

set  a = 1.25E-02
set b = 3.289E-02

There are two ways to calculate numerically with these two variables in the shell language: either use the echo + bc, or the awk.
For example, when we do the addition:
1) echo "$a+$b" | /usr/bin/bc 
2) echo "$a $b" | awk '{print $1+$2}'

For comparisons:
1) echo "$a > 0 &  $b > 0" | /usr/bin/bc
2) echo "$a  $b" | awk '{if ($1 > 0 & $2 > 0) print 1; else print 0}'
3) echo "$a" | awk '{if ($1 > 1 || $1 < -1) print 1; else print 0}'

If we have to do some complicated computation with shell,  the AWK is more accurate than the echo + bc, esp when the data is the the scientific format (eg., 1.236778E-02).


2) For processing the data from different files
---- if want to substract two columns of data which are from two files file1 and file2 respectively:
cat file1   | awk '{column1=$which_column_in_file1; getline <"file2"; print column1 - $which_column_in_file2}'