More fact()

#  int fact( int n )
#  {
#    if ( n<=1)
#      return 1;
#    else
#      return n*fact(n-1);
#  }
         .text
         .globl  fact
fact:
                                  # prolog        
         . . . . . .
                                  # body of subroutine
         move    $s1,$a0          # save argument in $s1
         li      $t1,1            # get a 1
         bgt     $s1,$t1,recurse  # if ( n<=1)
         li      $v0,1            #   return 1
         b       epilog  

recurse:                          # else
                                  #   return n*fact(n-1);
         sub     $a0,$s1,1        #     argument0 = n-1
                       
                                  # subroutine call
                                  #   1. No T registers to push
                                  #   2. Argument is in $a0 
         jal     fact             #   3. Jump and link to subroutine

         mul     $___,$___,$___   # n*fact(n-1)

epilog:                           # epilog
                                  #   1. Return value is already in $v0        
         . . . . . .
         jr      $ra              #

The alternate branch of the if statement has the job of calculating n*fact(n-1). It does this by first calculating the argument n-1.

Then it calls the subroutine fact() in the normal way. It does not hurt for fact() to call fact() because each activation has its own data on the stack.

On return from the (inner) call to fact(), register $v0 has the returned value, and register $s1 has the argument n. Now the return value from the current activation must be placed in $v0 to be returned to the caller.