Examine more carefully on the bound for UInt `addmany` implementation

[weikengchen]

The current implementation of addmany has a number of bounds:

https://github.com/arkworks-rs/r1cs-std/blob/master/src/bits/uint.rs#L184

// Make some arbitrary bounds for ourselves to avoid overflows
// in the scalar field
assert!(F::Params::MODULUS_BITS >= 2 * $size);

assert!($size * operands.len() <= F::Params::MODULUS_BITS as usize);

However, these bounds seem to be too strict. This part of the code is supposed for additions. And the bounds here seem for multiplication.

[Pratyush]

Hmm so it should $size + operands.len()?

[weikengchen]

or $size + log2(operands.len() + 1)?

[Pratyush]

why the + 1?