[Question] About GLOBAL_FIELD_P

[a2468834]

Hello everyone~ 😀

These days, I have been studying about arithmetic in Circom, in order to implement UQ number with saturation arithmetic.
But some weird outcomes really bothered me.

(1) Why did the relational operator x > y fail?

var p_minus_one = 21888242871839275222246405745257275088548364400416034343698204186575808495616;
assert(p_minus_one > 0); // I got compiled error msg: error[T3001]: False assert reached

According to the docs, relational operators are based on a math function val(z).

In this case, p_minus_one would be val(p_minus_one) = 2188...5616, which is literally GLOBAL_FIELD_P minus integer one.
Hence, the condition p_minus_one > 0 should be hold and passed the assertion.

I believe that there must be something I have not understood, so I inaccurately think about how the above codes work.

(2) Is it available to access GLOBAL_FIELD_P in Circom language?
It doesn't a big problem.
I can do the some things like the above which just hard-coded numbers.
But I think there must be a more elegant way to achieve this task.

Thanks for anyone willing to reply me or give me the clues. 🙏❤

[a2468834]

I got the answer from iden3 telegram group, thanks everyone. 🙏

Circom defines the range of positives are [0, p/2] and the range of negatives are [(p/2)+1, (p-1)].
You could find more information at val(z) in the section "Relational operators" of this page.
Although there is no negative number in the formal finite field GF(p), Circom devs choose a slightly different definition for convenience.

[Update @11/23] Here are some useful constants

10944121435919637611123202872628637544274182200208017171849102093287904247808 // The most positive number
10944121435919637611123202872628637544274182200208017171849102093287904247809 // The most negative number
21888242871839275222246405745257275088548364400416034343698204186575808495616 // aka (-1) in int32