Exercise set 4

1. Let’s assume you have a stack-architecture CPU, with the following instructions:

   LOAD [address]	Loads from memory into the register stack.
   LOAD imm	Loads an immediate onto the register stack.
   STORE [address]	Pops the stack top into memory.
   COPY	Pushes a new copy of the value at the top of the stack.
   SWAP	Swaps the top two values on the stack.
   ADD	Pops the top two values from the stack, then pushes their sum.
   SUB	Pops the top two values from the stack, then pushes their difference. The first value popped is the subtrahend and the second value is the minuend (difference=minuend−subtrahend).
   MUL	Pops the top two values from the stack, then pushes their product.
   DIV	Pops the top two values from the stack, then pushes their quotient. The first value popped is the divisor and the second value is the dividend (quotient=dividend÷divisor).

   If you need to implement a complex math library for this architecture, how would you implement the following? (Assume that you can load from a, b, c, and d by name, and that you’re storing the real and imaginary components to x and y, respectively.)
1. Complex addition: (a+bi)+(c+di)=(a+c)+(b+d)i
2. Complex multiplication: (a+bi)(c+di)=(ac−bd)+(bc+ad)i
3. Complex division:

   a+bi	=	(ac+bd)+(bc−ad)i
   c+di		c²+d²

2. Implement these three fragments for an Intel 80387-class FPU. (If you’re feeling specific, assume that each component is double-precision.) Remember, you have FLD, FST/FSTP, FADD/FADDP, FSUB/FSUBP, FSUBR/FSUBRP, FMUL/FMULP, and FDIV/FDIVP at your disposal. (You’ve got plenty of other stuff too, but this is all you should need.)