21 Sep
2024
21 Sep
'24
12:22 a.m.
Moved to Coff, because it's about programming style, not history.
Perhaps I'm missing something? Clever arithmetic
in the index
calculation aside, this is semantically different than using an actual
negative integer to index into an array? Moreover, if the intent is to
start the sequence with 0, why set `fib(0)` to 1? How is this
substantially different from the usual way of writing this:
I said the Fibonacci example was silly. Maybe you'll be more convinced by
the binomial-coefficient program below.
The array of interest is fib. base is simply scaffolding and doesn't appear
in the working code. You won't find the ith Fibonacci in base[i]; it's in
fib(i). But fib(-1) exists. What's important is that the C convention of
array indexes beginning at 0 has been circumvented.
I could be accused of subterfuge in depending on the semantics of static
storage to initialize fib(-1) to zero. Subterfuge or not, it's customary C
usage. The binomial-coefficient program relies on "out-of-bounds" zeros
abutting two sides of a triangle.
int base[N][N+2];
#define binom(n,i) base[n][(i)+1]
void fill() {
binom(0,0) = 1;
for(n=1; n<N; n++)
for(i=0; i<=n; i++)
binom(n,i) = binom(n-1,i) + binom(n,i-1);
}
I think the offset algorithm above looks better than the more typical one
below.
The two programs happen to have identical character counts.
int binom[N][N+1];
void fill() {
for(n=0; n<N; n++) {
binom[n][0] = 1;
for(i=1; i<n; i++)
binom[n][i] = binom[n-1][i] + binom[n][i-1];
binom[n][n] = 1;
}
}
Doug