Gate2017 cs Q55

0. Consider the expression (a-1) * ((( b + c ) / 3 ) + d) Let X be the minimum number of registers required by an optimal code generation (without any register spill) algorithm for a load/store architecture in which
(i) only loads and store instructions can have memory operands and
(ii) arithmetic instructions can have only register or immediate operands.
The value of X is _____.

Note – Numerical Type question

Answer
Comment
Array

Option : A
Explanation :

The given expression is (a-1) * ((( b + c ) / 3 ) + d)
The optimal generated code is:
Load R₁, b R₁ ⟵ b
Load R₂, c R₂ ⟵ c
ADD R₁, R₂ R₁ ⟵ R₁ + R₂
Div R₁, 3 R₁ ⟵ R₁/3
Load R₂, d R₂ ⟵ d
Add R₁, R₂ R₁ ⟵ R₁ + R₂
Load R₂, a R₂ ⟵ a
Sub R₂, 1 R₂ ⟵ R₂ - 1
Mul R₂, R₁ R2 ⟵ R₂ * R₁
Hence minimum 2 registers required.

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