;; lisp compiler input
;; `integer` maps to 64 bit integer / uint64_t / i64

(compile-function
 'factorial 'integer '((x . integer))
 '((entry (goto-if (= integer x 0) zero else))
   (zero  (return integer 1))
   (else  (return integer (* integer x (call integer factorial (integer - integer x 1)))))))

;; LLVM output

define i64 @factorial(i64 %x) {
;; if X = 0, factorial(X) = 1
;; if X > 0, factorial(X) = x * factorial(X-1)
ENTRY:
  %ENTRY0_1 = icmp eq i64 %x, 0  ;; compare X to 0
  br i1 %ENTRY0_1, label %ZERO, label %ELSE ;; if X is zero, go to ZERO, else ELSE
ZERO:
  ret i64 1 ;; return 1
ELSE:
  %ELSE0_1 = sub i64 %x, 1 ;; take 1 from X
  %ELSE0_2 = call i64 @factorial(i64 %ELSE0_1) ;; call factorial with the decremented X
  %ELSE0_3 = mul i64 %x, %ELSE0_2 ;; multiply it by X
  ret i64 %ELSE0_3 ;; return X * factorial(x-1)
}
* ^D

$ cat testfact.c
#include <stdint.h>
#include <stdio.h>

extern uint64_t factorial(uint64_t x);

int main() {
  uint64_t x = 10;
  printf("%llu! = %llu", x, factorial(x));
  return (int)x;
}

$ clang -c fact.ll -o fact.o
$ clang fact.o testfact.c -o fact

$ ./fact
10! = 3628800