Prime Numbers

546 Appendix BOOK PSEUDOCODE
Functions and return/report values
Typically a customized function in our pseudocode is cast in the form
func(x) {
...;
...;
return y;
}
and the idea is the same as in most any modern language: One calls func(x)
in the same way one would call a trigonometric function or a square root,
with the attained value y. Similarly, a procedure (as opposed to a function)
has the same syntax, with no returned value, although certain variables are
usually set within a procedure. Also, a return statement is an exit statement,
e.g., a sequence
if(x = y) return x 3 ;
return x 4 ;
does not need an “else” structure for the x 4 case, because we always assume
the current function/procedure exits immediately on any demand by the if()
statement here. Likewise, a return statement, when executed, immediately
causes exit from within any while() or for() loop.
Finally, we use report statements in the following way. Instead of returning
a value from a function/procedure, a report statement simply relays the
value—as in printing it, or reporting it to another program—on the fly, as
it were. Thus the following function exemplifies the use of report/return (the
function assumes a subroutine that evaluates the number-of-divisors function
d(n)):
mycustomπ(x) { //Report (and count!) all primes not exceeding x.
c =0; //This c will be the primes count.
for(2 ≤ n ≤ x) {
if(d(n) ==2) {
c = c +1;
report n; //As in “print” n, but keep looping.
}
}
return c;
}
Primes will be reported in ascending order, with the return value of function
mycustomπ(x) being the classical π(x).