NB. Models of Division Algorithms discussed in Section 3.5 of
NB. Computer Organization &  Design by Patterson and Hennessy

NB. Binary To Decimal

btd =: monad define
  digits =. # y.
   if. 1 = 1 take y.
    do. ((digits copy 2) base x: y. ) - 2^ x: digits
    else. (digits copy 2) base x: y.
   end.
)

NB. Non-circuit based 32-bit ALU

alu_32 =: monad define 
NB. a and b are each 32-bit summands
NB. the result is a 32-bit sum
NB. sub = 0 for addition
NB. sub = 1 for subtraction
('a' ; 'b' ; 'sub') =. y.
if. sub
  do. (32#2) rep (base x: a) - base x: b
  else. (32#2) rep (base x: a) + base x: b
end.
)

NB. Some alu_32 tests.

a =: (31#1),0
b=: (30#0), 1 0
alu_32 a;b;0
alu_32 a;b;1
c=:32#1
alu_32 b;c;1

NB. Note that decimal args may be used with alu_32
alu_32 3 4 0


NB. Model of Divider Hardware, Page 271 of CO&D (2ed).

NB. Assume 32-bit Quotient (maintained in right half
NB. of remainder register), Divisor and Dividend and64-bit
NB. Remainder
NB. div3 uses alu_32.

div3 =: monad define 
('dividend' ; 'divisor') =. y.
remainder=: (32#0) , dividend
count=. 32
remainder =: (1 drop remainder) , 0
while. 0 not_equal count
      do. remainder =: (alu_32 (32 take remainder) ; divisor ; 1) , 32 drop remainder
      if. control =. first remainder
        do. remainder =: (alu_32 (32 take remainder) ; divisor ; 0) , 32 drop remainder
            remainder =: (1 drop remainder) , 0
        else. remainder =: (1 drop remainder) , 1
        end.
      count =. <: count
  end.
remainder =: (0 , _1 drop 32 take remainder) , 32 drop remainder
)

NB. a test quotient of 3%2
div3 ((30#0), 1 1) ; (30#0) , 1 0

NB. a test quotient of 7%2
div3 ((29#0), 1 1 1) ; (30#0) , 1 0

NB. a test quotient of _6%2
div3 ((29#0),1 1 0) ; (30#0) , 1 0

NB. A Tracing Model of Divider Hardware, Page 271 of CO&D (2ed).

NB. Assume 32-bit Quotient (maintained in right half
NB. of remainder register), Divisor and Dividend and64-bit
NB. Remainder
NB. div3 uses alu_32.

traced_div3 =: monad define 
('dividend' ; 'divisor') =. y.
display'rem-init';remainder=: (32#0) , dividend
count=. 32
display'rem-init-shift';remainder =: (1 drop remainder) , 0
while. 0 not_equal count
      do. display'rem-sub';remainder =: (alu_32 (32 take remainder) ; divisor ; 1) , 32 drop remainder
      if. control =. first remainder
        do. display'less';remainder =: (alu_32 (32 take remainder) ; divisor ; 0) , 32 drop remainder
            display'less-shift';remainder =: (1 drop remainder) , 0
        else. display'more-shift';remainder =: (1 drop remainder) , 1
        end.
      count =. <: count
  end.
remainder =: (0 , _1 drop 32 take remainder) , 32 drop remainder
)

NB. a test quotient of 3%2
traced_div3 ((30#0), 1 1) ; (30#0) , 1 0

NB. a test quotient of 7%2
traced_div3 ((29#0), 1 1 1) ; (30#0) , 1 0

NB. a test quotient of _6%2
traced_div3 ((29#0),1 1 0) ; (30#0) , 1 0