MUL and DIV

1
MUL and DIV

• How to use the x86 CPUs multiplication and
  division instructions

2
A comment about addition

• When two register-values are added add al,
  bl their total can sometimes be too
  large to fit in the destination
  register Example 150 160 310
• Both numbers 150 and 160 can be expressed as
  8-bit binary values 150 as 10010110 (base
  2) 160 as 10100000 (base 2)
• But not their sum 310 is 100110110 (base 2)

3
The Carry-Flag

• The extra bit becomes the CF-bit (i.e., the
  Carry Flag) in the RFLAGS register
• Programs can branch if a carry
  occurs jc toobig
• Or branch elsewhere if no-carry
  occurs jnc sumok
• Special instruction exists to handle adding of
  large numbers ADC (Add-with-Carry)

4
A Big Number example

• .section .data
• x .short 150
• y .short 160
• .section .text
• mov x, al
• add y, al
• mov x1, ah
• adc y1, ah

5
worst-cases add vs multiply

• Adding two n-bit numbers never requires more than
  (n1)-bits for their total, so the carry-flag bit
  suffices for holding the result
• But multiplication is another story!
• Biggest 8-bit number is 255 ( 11111111)
• 255x255 65025 ( 1111111000000001)
• So this product requires 16-bits 0xFE01

6
MUL

• Using MUL to multiply two 64-bit operands
• Put the 64-bit multiplicand into RAX
• Put the 64-bit multiplier into a general
  register
• The CPU will produce a 128-bit product
• The product will be in the (RDXRAX)
  register-pair
• (You can also put the 64-bit multiplier in a
  memory-variable if you then use MULQ)

7
DIV

• If you put your 128-bit dividend into the
  RDXRAX register-pair, then you can put your
  64-bit divisor into a general-register
• The quotient will appear in RAX and the
  remainder will appear in RDX unless the
  quotient is too large to fit in register RAX
• (You can also put your 64-bit divisor in a
  memory variable if you then use DIVQ)