rustfft 4.1.0

use std::sync::Arc;

use num_complex::Complex;
use num_traits::Zero;
use strength_reduce::StrengthReducedUsize;

use crate::common::{verify_length, verify_length_divisible, FFTnum};

use crate::math_utils;
use crate::twiddles;
use crate::{IsInverse, Length, FFT};

/// Implementation of Rader's Algorithm
///
/// This algorithm computes a prime-sized FFT in O(nlogn) time. It does this by converting this size n FFT into a
/// size (n - 1) FFT, which is guaranteed to be composite.
///
/// The worst case for this algorithm is when (n - 1) is 2 * prime, resulting in a
/// [Cunningham Chain](https://en.wikipedia.org/wiki/Cunningham_chain)
///
/// ~~~
/// // Computes a forward FFT of size 1201 (prime number), using Rader's Algorithm
/// use rustfft::algorithm::RadersAlgorithm;
/// use rustfft::{FFT, FFTplanner};
/// use rustfft::num_complex::Complex;
/// use rustfft::num_traits::Zero;
///
/// let mut input:  Vec<Complex<f32>> = vec![Zero::zero(); 1201];
/// let mut output: Vec<Complex<f32>> = vec![Zero::zero(); 1201];
///
/// // plan a FFT of size n - 1 = 1200
/// let mut planner = FFTplanner::new(false);
/// let inner_fft = planner.plan_fft(1200);
///
/// let fft = RadersAlgorithm::new(1201, inner_fft);
/// fft.process(&mut input, &mut output);
/// ~~~
///
/// Rader's Algorithm is relatively expensive compared to other FFT algorithms. Benchmarking shows that it is up to
/// an order of magnitude slower than similar composite sizes. In the example size above of 1201, benchmarking shows
/// that it takes 2.5x more time to compute than a FFT of size 1200.

pub struct RadersAlgorithm<T> {
    inner_fft: Arc<dyn FFT<T>>,
    inner_fft_data: Box<[Complex<T>]>,

    primitive_root: usize,
    primitive_root_inverse: usize,

    len: StrengthReducedUsize,
}

impl<T: FFTnum> RadersAlgorithm<T> {
    /// Creates a FFT instance which will process inputs/outputs of size `len`. `inner_fft.len()` must be `len - 1`
    ///
    /// Note that this constructor is quite expensive to run; This algorithm must run a FFT of size n - 1 within the
    /// constructor. This further underlines the fact that Rader's Algorithm is more expensive to run than other
    /// FFT algorithms
    ///
    /// Note also that if `len` is not prime, this algorithm may silently produce garbage output
    pub fn new(len: usize, inner_fft: Arc<dyn FFT<T>>) -> Self {
        assert_eq!(
            len - 1,
            inner_fft.len(),
            "For raders algorithm, inner_fft.len() must be self.len() - 1. Expected {}, got {}",
            len - 1,
            inner_fft.len()
        );

        let inner_fft_len = len - 1;
        let reduced_len = StrengthReducedUsize::new(len);

        // compute the primitive root and its inverse for this size
        let primitive_root = math_utils::primitive_root(len as u64).unwrap() as usize;
        let primitive_root_inverse =
            math_utils::multiplicative_inverse(primitive_root as usize, len);

        // precompute the coefficients to use inside the process method
        let unity_scale = T::from_f64(1f64 / inner_fft_len as f64).unwrap();
        let mut inner_fft_input = vec![Complex::zero(); inner_fft_len];
        let mut twiddle_input = 1;
        for input_cell in &mut inner_fft_input {
            let twiddle = twiddles::single_twiddle(twiddle_input, len, inner_fft.is_inverse());
            *input_cell = twiddle * unity_scale;

            twiddle_input = (twiddle_input * primitive_root_inverse) % reduced_len;
        }

        //precompute a FFT of our reordered twiddle factors
        let mut inner_fft_output = vec![Zero::zero(); inner_fft_len];
        inner_fft.process(&mut inner_fft_input, &mut inner_fft_output);

        Self {
            inner_fft,
            inner_fft_data: inner_fft_output.into_boxed_slice(),

            primitive_root,
            primitive_root_inverse,

            len: reduced_len,
        }
    }

    fn perform_fft(&self, input: &mut [Complex<T>], output: &mut [Complex<T>]) {
        // The first output element is just the sum of all the input elements
        output[0] = input.iter().sum();
        let first_input_val = input[0];

        // we're now done with the first input and output
        let (_, output) = output.split_first_mut().unwrap();
        let (_, input) = input.split_first_mut().unwrap();

        // copy the input into the output, reordering as we go
        let mut input_index = 1;
        for output_element in output.iter_mut() {
            input_index = (input_index * self.primitive_root) % self.len;
            *output_element = input[input_index - 1];
        }

        // perform the first of two inner FFTs
        self.inner_fft.process(output, input);

        // multiply the inner result with our cached setup data
        // also conjugate every entry. this sets us up to do an inverse FFT
        // (because an inverse FFT is equivalent to a normal FFT where you conjugate both the inputs and outputs)
        for ((&input_cell, output_cell), &multiple) in input
            .iter()
            .zip(output.iter_mut())
            .zip(self.inner_fft_data.iter())
        {
            *output_cell = (input_cell * multiple).conj();
        }

        // execute the second FFT
        self.inner_fft.process(output, input);

        // copy the final values into the output, reordering as we go
        let mut output_index = 1;
        for input_element in input {
            output_index = (output_index * self.primitive_root_inverse) % self.len;
            output[output_index - 1] = input_element.conj() + first_input_val;
        }
    }
}

impl<T: FFTnum> FFT<T> for RadersAlgorithm<T> {
    fn process(&self, input: &mut [Complex<T>], output: &mut [Complex<T>]) {
        verify_length(input, output, self.len());

        self.perform_fft(input, output);
    }
    fn process_multi(&self, input: &mut [Complex<T>], output: &mut [Complex<T>]) {
        verify_length_divisible(input, output, self.len());

        for (in_chunk, out_chunk) in input
            .chunks_exact_mut(self.len())
            .zip(output.chunks_exact_mut(self.len()))
        {
            self.perform_fft(in_chunk, out_chunk);
        }
    }
}
impl<T> Length for RadersAlgorithm<T> {
    #[inline(always)]
    fn len(&self) -> usize {
        self.len.get()
    }
}
impl<T> IsInverse for RadersAlgorithm<T> {
    #[inline(always)]
    fn is_inverse(&self) -> bool {
        self.inner_fft.is_inverse()
    }
}

#[cfg(test)]
mod unit_tests {
    use super::*;
    use crate::algorithm::DFT;
    use crate::test_utils::check_fft_algorithm;
    use std::sync::Arc;

    #[test]
    fn test_raders() {
        for &len in &[3, 5, 7, 11, 13] {
            test_raders_with_length(len, false);
            test_raders_with_length(len, true);
        }
    }

    fn test_raders_with_length(len: usize, inverse: bool) {
        let inner_fft = Arc::new(DFT::new(len - 1, inverse));
        let fft = RadersAlgorithm::new(len, inner_fft);

        check_fft_algorithm(&fft, len, inverse);
    }
}