Question

C++

Suppose we are given the task of generating code to multiply integer variable x by various different constant factors K. To be efficient, we want to use only the operations +, -, and <<. For the following values of K, write C expressions to perform the multiplication using at most three operations per expression.

A. K = 17: B. K =− 7: C. K = 60: D. K =− 112:

Must obey bit integer coding rules:

• Assumptions
  • Integers are represented in two's-complement form.
  • Right shifts of signed data are performed arithmetically.
  • Data type int is w bits long. For some of the problems, you will be given a specific value for w, but otherwise your code should work as long as w is a multiple of 8. You can use the expression sizeof(int) << 3 to compute w.

• Forbidden
  • Conditionals (if or ?:), loops, switch statements, function calls, and macro invocations.
  • Division, modulus, and multiplication.
  • Relative comparison operators (<, >, <=, and >=).
  • Casting, either explicit or implicit.

• Allowed operations
  • All bit-level and logic operations.
  • Left and right shifts, but only with shift amounts between 0 and w − 1.
  • Addition and subtraction.
  • Equality (==) and inequality (!=) tests. (Some of the problems do not allow these.)
  • Integer constants INT_MIN and INT_MAX.

Answer 1

(A)K=17
K = 16 + 1
X*K = X*(16) + X
X*K = (X << 4) + X

C expression
X = (X << 4) + X

(B)K=-7
K = 1 - 8
X*K = X - X*8
X*K = X - (X<<3)

C expression
X = X - (X << 3)

(C) K=60
K = 64 - 4
X*K = X*64 - X*4
X*K = (X << 6) - (X << 2)
C expression
X = (X << 6) - (X << 2)

(D) K=-112
K = 16 - 128
X*K = X*16 - X*128
X*K = (X << 4) - (X << 7)
C expression
X = (X << 4) - (X << 7)