GNU BC: “modulo” % with scale other than 0

Question

If the scale is other than zero, calculations with %, such as 3%2 and 46%4, tend to output 0. How is the algorithm designed with the scale other than 0?

bc
scale=10
print 4%3   // output 0

Answer 1

The command manual says this about how BC calculates the modulo:

The result of the expression is the "remainder" and it is computed in the following way. To compute a%b, first a/b is computed to scale digits. That result is used to compute a - ( a/b ) * b to the scale of the maximum of scale+scale(b) and scale(a). If scale is set to zero and both expressions are integers this expression is the integer remainder function.

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EDIT: I looked at the source code for GNU BC and found that the mod operator extends the division operator. In other words, the modulo is calculated as a by-product of the division. It relies on integer division to calculate the modulo. When scale is set, however integer division does not take place.

Try this in BC:

bc
scale = 0
print 5/2

scale = 5
print 5/2

you should get:

2        << Integer Division
2.50000  << NOT integer division!

Now let's plug in these figures the way BC does. The manual says it uses a-(a/b)*b to calculate. Let's plug in our two results, the one resulting from integer division and the one with a scale other than 0.

a - ( a/b ) * b
5 - ( 2   ) * 2  = 1  << CORRECT!
5 - ( 2.5 ) * 2  = 0  << VERY WRONG!

Without integer division:

a - ( a/b ) * b == a - (  a  ) == 0

This is why scale must be set to 0 for the modulo to work properly.
The issue seems to arise out of the design of BC and how it handles numbers with a 'scale'. In order for the modulo to work correctly we need integer division.

There are other much more advanced tools that are free and open source for this purpose, and I recommend you use them.