1  // Copyright (c) 2019-2025 Alpha-Delta Network Inc.
 2  // This file is part of the alphavm library.
 3  
 4  // Licensed under the Apache License, Version 2.0 (the "License");
 5  // you may not use this file except in compliance with the License.
 6  // You may obtain a copy of the License at:
 7  
 8  // http://www.apache.org/licenses/LICENSE-2.0
 9  
10  // Unless required by applicable law or agreed to in writing, software
11  // distributed under the License is distributed on an "AS IS" BASIS,
12  // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
13  // See the License for the specific language governing permissions and
14  // limitations under the License.
15  
16  use alphavm_utilities::biginteger::BigInteger;
17  
18  /// A trait that defines parameters for a field that can be used for FFTs.
19  pub trait FftParameters: 'static + Send + Sync + Sized {
20      type BigInteger: BigInteger;
21  
22      /// Let `N` be the size of the multiplicative group defined by the field.
23      /// Then `TWO_ADICITY` is the two-adicity of `N`, i.e. the integer `s`
24      /// such that `N = 2^s * t` for some odd integer `t`.
25      /// 2^s * t = MODULUS - 1 with t odd. This is the two-adicity of the prime.
26      const TWO_ADICITY: u32;
27  
28      /// 2^s root of unity, defined as `GENERATOR^t`.
29      const TWO_ADIC_ROOT_OF_UNITY: Self::BigInteger;
30  
31      /// An integer `b` such that there exists a multiplicative subgroup
32      /// of size `b^k` for some integer `k`.
33      const SMALL_SUBGROUP_BASE: Option<u32> = None;
34  
35      /// The integer `k` such that there exists a multiplicative subgroup
36      /// of size `Self::SMALL_SUBGROUP_BASE^k`.
37      const SMALL_SUBGROUP_BASE_ADICITY: Option<u32> = None;
38  
39      /// GENERATOR^((MODULUS-1) / (2^s *
40      /// SMALL_SUBGROUP_BASE^SMALL_SUBGROUP_BASE_ADICITY)) Used for mixed-radix FFT.
41      const LARGE_SUBGROUP_ROOT_OF_UNITY: Option<Self::BigInteger> = None;
42  
43      /// `TWO_ADIC_ROOT_OF_UNITY^2^i` for `i := 0..TWO_ADICITY-1`
44      const POWERS_OF_ROOTS_OF_UNITY: &'static [Self::BigInteger];
45  }