How to simplify logical operation in C - conditional-statements

Question

I have this following logic which needs simplifing to look clearer and consise:
if (x1 < y1)
return 1;
else if (x1 == y1)) {
if (x2 < y2)
return 1;
else if (x2 == y2) {
if (x3 < y3)
return 1;
} else
return 0;
}
} else
return 0;
In order to solve this above problem, I have applied logical expressions to further simplify these few lines of conditions:
if (x1 < y1 || (x1 == y1 && x2 < y2) || (x1 == y1 && x2 == y2 && x3 < y3))
return 1;
else
return 0;
I am not sure how to simplify further from here. Can anyone help me?
Update:
For further simplifying, I tried applying boolean algebra to this expression, but no luck! I have come up with this:
A + (A1 * B) + (A1 * B1 * C)
Where A denotes to x1 < y1 and A1 denotes to x1 == y2

Answer 1

IMO the cleanest way to do this sort of chained relation in C is with ?::
return x1 == y1 ? x2 == y2 ? x3 < y3 : x2 < y2 : x1 < y1;
As noted in the question comments, if you really care about performance, and the values have limited range, you can use bit twiddling to combine them into a single value for comparison. If the fields are all uint16_t (unsigned 16-bit values), for example, you can do:
uint64_t x = ((uint64_t)x1 << 32) + ((uint64_t)x2 << 16) + x3;
uint64_t y = ((uint64_t)y1 << 32) + ((uint64_t)y2 << 16) + y3;
return x < y;
but this is probably less clear and probably a premature optimization.