Is < faster than <=?

Question

Is if( a < 901 ) faster than if( a <= 900 ).

Not exactly as in this simple example, but there are slight performance changes on loop

Answer 1

Historically (we're talking the 1980s and early 1990s), there were some architectures in which this was true. The root issue is that integer comparison is inherently implemented via integer subtractions. This gives rise to the following cases.

Comparison     Subtraction
----------     -----------
A < B      --> A - B < 0
A = B      --> A - B = 0
A > B      --> A - B > 0

Now, when A < B the subtraction has to borrow a high-bit for the subtraction to be correct, just like you carry and borrow when adding and subtracting by hand. This "borrowed" bit was usually referred to as the carry bit and would be testable by a branch instruction. A second bit called the zero bit would be set if the subtraction were identically zero which implied equality.

There were usually at least two conditional branch instructions, one to branch on the carry bit and one on the zero bit.

Now, to get at the heart of the matter, let's expand the previous table to include the carry and zero bit results.

Comparison     Subtraction  Carry Bit  Zero Bit
----------     -----------  ---------  --------
A < B      --> A - B < 0    0          0
A = B      --> A - B = 0    1          1
A > B      --> A - B > 0    1          0

So, implementing a branch for A < B can be done in one instruction, because the carry bit is clear only in this case, , that is,

;; Implementation of "if (A < B) goto address;"
cmp  A, B          ;; compare A to B
bcz  address       ;; Branch if Carry is Zero to the new address

But, if we want to do a less-than-or-equal comparison, we need to do an additional check of the zero flag to catch the case of equality.

;; Implementation of "if (A <= B) goto address;"
cmp A, B           ;; compare A to B
bcz address        ;; branch if A < B
bzs address        ;; also, Branch if the Zero bit is Set

So, on some machines, using a "less than" comparison might save one machine instruction. This was relevant in the era of sub-megahertz processor speed and 1:1 CPU-to-memory speed ratios, but it is almost totally irrelevant today.