Learning new things!
Using multiplicative group of size 16 to demonstrate the concept of coset.
suppose we have a trace \([1,2,3,4]\) , and we want to prove \(f(x)+1=f(gx)\)
\(g\) is the group generator for cyclic group of size 4, the same size of the trace.
Canonical coset:
odd coset setup
CirclePointIndex is just a wrapper of usize, which represent actually the order of the coset generator.
when creating a new coset, we need a generator and shiftoffset, the shiftoffset mostly be the generator of the subgroup of one log size bigger
so here, CirclePointIndex::subgroup_gen is …
Files structure:
In the context of programming, a prelude is generally a set of common imports or definitions that a module or program can use directly without needing to specify them every time. It acts like a convenience layer, making certain functions, traits, or types available by default.…
Trace table looks like this:
| a_wire | a_val | b_wire | b_val | c_wire | c_val | multiplicity |
| 0 | 1 | 1 | 1 | 2 | 2 | 2 |
| 1 | 1 | 2 | 2 | 3 | 3 | 2 |
| 2 | 2 | 3 | 3 | 4 | 5 | 1 |
| 3 |
following the first post
got two tasks:
let’s talk about generate trace first.
in stwo, the trace is in this format as showed in last post
ColumnVec<CircleEvaluation<SimdBackend, BaseField, BitReversedOrder>>how powdr …
in Powdr, the proving function of Plonky3 is in function prove_with_key, in stark.rs
you can see the inputs for prove_with_key function has “air”, this is what used to define constraints, powdr gives “&circuit” to it, and it is a powdrcircuit, probably powdrcircuit applies the trait of AIR
so at this …
it is about this example in stwo
two parameters:
FIB_SEQUENCE_LENGTH specifies the rounds of fibo sequence
LOG_N_INSTANCES as stwo use SIMD, data parallel data struct, this number specify how many instances of fibo sequences are proved at the same time. The data are packed in LOG_N_LANES chunks, which is 16 …
following note1
packed31 is a vector of length 16
try to understand how the trace is generated
the bottom lines actually transfer the M31 values into circleDomain
from start:
N is log N instances
this code is to initialise the witness columns, later use to store the witness.
this code …
backend trait in powdr
how plonky3 implemented? this is in mod.rs
in mod.rs the backend trait is implemented for plonky3prover, in the prove function, it calls prove in stark.rs, where plonky3prover is implemented
so this prove function in stark.rs should be simliarly implemented in prover.rs …