Add a post about tail-recursive even/odd

content/posts/tail_recursive_even_odd/note.md

@@ -0,0 +1,73 @@
+X-Date: 2024-01-29T21:00:00Z
+X-Note-Id: c7df8c86-62cb-4032-98d8-6555645af220
+Subject: Tail-recursive even/odd
+X-Slug: tail_recursive_even_odd
+
+Tail calls are a way to save on call stack space. If a function call happens as a last thing a function performs, then
+it is possible for a language implementation to optimize the call by getting rid of all temporary values on the stack
+before the call is made.
+
+Consider this implementation of `even` and `odd` functions in Python:
+
+```
+def even(x):
+    if x == 0:
+        return True
+    return odd(x-1)
+
+def odd(x):
+    if x == 0:
+        return false
+    return even(x-1)
+```
+
+Here, the recursive calls are in the "tail" position, and thus in theory it is possible to just discard the caller's
+stack and proceed with evaluating the callee without making a regular function call. In Python there are no tail calls,
+but it's not hard to implement in a virtual machine.
+
+So, this is what I did in my virtual machine. Here's the same example written in the VM assembly:
+
+```
+;; Pick a reasonably big number
+;; to demonstrate that we don't
+;; use stack much
+(const val 1000000)
+(const one 1)
+(const zero 0)
+
+(sr 3)
+(setjump r0 even)
+(mov r1 val)
+(call r0 1)
+
+(aeq r0 one)
+(retnil)
+
+;; Even implementation
+(label even)
+(sr 3)
+(jeq r0 zero even-end)
+
+(setjump r1 odd)
+(sub r2 r0 one)
+(tailcall r1 1)
+
+(label even-end)
+(ret one)
+
+;; Odd implementation
+(label odd)
+(sr 3)
+(jeq r0 zero odd-end)
+
+(setjump r1 even)
+(sub r2 r0 one)
+(tailcall r1 1)
+
+(label odd-end)
+(ret zero)
+```
+
+
+In places where we want to make a tail call, instead of using `call`, you need to use `tailcall`. But otherwise
+the way you write such calls would be the same.