K&R answer book exercise 1.21

Question

Here is the question:

Write the program entab that replaces strings of blanks by the minimum number of tabs and blanks to achieve the same spacing. Use th

Answer 1

It does not have a name or something like that.
In detail:

First of all, how much pos has to be increased depends on pos%TABINC,
ie. TABINC is 8, so if pos is a multiple from 8, add 8,
if pos%8 is 1 (like 9, 17...) then add 7,
if pos%8 is 2 (10, 18...) add 6 and so on.

Full list:
pos%8 -> number to add
0 -> 8
1 -> 7
2 -> 6
3 -> 5
4 -> 4
5 -> 3
6 -> 2
7 -> 1

That would be 8 - pos%8 or, more general TABINC - pos%TABINC

Important: A negative number modulo something in C is mathematically not correct
In C, for a,b >= 0: (-a)%b == -(a%b)

What is added in the code is (TABINC - (pos - 1) % TABINC) - 1
With some basic math and the fact above, this is
(TABINC - (pos - 1) % TABINC) - 1
= TABINC - ((pos - 1) % TABINC)) - 1
= TABINC - ((pos % TABINC) - 1) - 1
= TABINC + 1 - (pos % TABINC) - 1
= TABINC - (pos % TABINC)
which is the same as my short formula above, only more complex for no reason.