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>When a C function is called, its parameters are on the stack.
>When it returns, the results are also on the stack. To separate them, the
>function returns (in C) the number of results it is returning (in

Why is it necessary for the C API to return the number of results it pushed
onto the stack?  Wouldn?t it would be simpler and less error-prone for Lua
to infer that information directly from the stack?

IE, why can?t your example:

static int math_sin (lua_State *L) {
  lua_pushnumber(L, sin(TORAD(luaL_check_number(L, 1))));
  return 1;  /* <<<< Tells Lua it is returning one result */

be written as:

static void math_sin (lua_State *L) {
  lua_pushnumber(L, sin(TORAD(luaL_check_number(L, 1))));

It should be trivial for Lua to track the number of results pushed by the
API, yes?