Add Stark101 tutorial's prime field

[erhant]

Add Stark101 Prime Field

Description

I have been implementing the Stark101 tutorial using LambdaWorks (see here), and I had implemented the field used within the tutorial.

The prime field order is 3 * 2^30 + 1, which is FFT-friendly, however I cant implement the IsFFTFriendly trait for this custom field because the custom field is constructed as shown below:

#[derive(Clone, Debug, Hash, Copy, Serialize, Deserialize)]
pub struct MontgomeryConfigStark101PrimeField;
impl IsModulus<U64> for MontgomeryConfigStark101PrimeField {
    const MODULUS: U64 = U64::from_hex_unchecked("c0000001");
}

pub type Stark101PrimeField = U64PrimeField<MontgomeryConfigStark101PrimeField>;

which means that Stark101PrimeField is an alias of the U64PrimeField which does not belong to my crate, therefore I cant implement IsFFTFriendly (which also does not belong to my crate) to it.

The solution is therefore to add the field directly to LambdaWorks itself, and use it.

Note

Although it is ok to use the non-FFT interpolation for the tutorial, which is used for interpolating over 1024 elements, I think its nice that we have the opportunity to use FFT as well. If not, one can complete the tutorial by implementing the field themselves.

Type of change

• New feature: Added Stark101 prime field

Checklist

• Linked to Github Issue
• Unit tests added
• This change requires new documentation.
  • Documentation has been added/updated.
• This change is an Optimization
  • Benchmarks added/run

[codecov-commenter]

Codecov Report

Attention: Patch coverage is 83.63636% with 9 lines in your changes missing coverage. Please review.

Project coverage is 73.23%. Comparing base (eb14150) to head (b22b619).

Files with missing lines	Patch %	Lines
...field/fields/fft_friendly/stark_101_prime_field.rs	83.63%	9 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #875      +/-   ##
==========================================
+ Coverage   73.22%   73.23%   +0.01%     
==========================================
  Files         154      155       +1     
  Lines       35165    35220      +55     
==========================================
+ Hits        25750    25795      +45     
- Misses       9415     9425      +10     

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