p3-dft 0.4.3

use alloc::vec::Vec;

use p3_field::{Field, PrimeCharacteristicRing, TwoAdicField};
use p3_matrix::Matrix;
use p3_matrix::dense::{RowMajorMatrix, RowMajorMatrixViewMut};
use p3_matrix::util::reverse_matrix_index_bits;
use p3_maybe_rayon::prelude::*;
use p3_util::{flatten_to_base, log2_strict_usize, reverse_slice_index_bits};
use tracing::instrument;

use crate::TwoAdicSubgroupDft;
use crate::butterflies::{Butterfly, DifButterfly, DitButterfly, TwiddleFreeButterfly};
use crate::util::divide_by_height;

/// The Bowers G FFT algorithm.
/// See: "Improved Twiddle Access for Fast Fourier Transforms"
#[derive(Default, Clone)]
pub struct Radix2Bowers;

impl<F: TwoAdicField> TwoAdicSubgroupDft<F> for Radix2Bowers {
    type Evaluations = RowMajorMatrix<F>;

    fn dft_batch(&self, mut mat: RowMajorMatrix<F>) -> RowMajorMatrix<F> {
        reverse_matrix_index_bits(&mut mat);
        bowers_g(&mut mat.as_view_mut());
        mat
    }

    /// Compute the inverse DFT of each column in `mat`.
    fn idft_batch(&self, mut mat: RowMajorMatrix<F>) -> RowMajorMatrix<F> {
        bowers_g_t(&mut mat.as_view_mut());
        divide_by_height(&mut mat);
        reverse_matrix_index_bits(&mut mat);
        mat
    }

    fn lde_batch(&self, mut mat: RowMajorMatrix<F>, added_bits: usize) -> RowMajorMatrix<F> {
        bowers_g_t(&mut mat.as_view_mut());
        divide_by_height(&mut mat);
        mat = mat.bit_reversed_zero_pad(added_bits);
        bowers_g(&mut mat.as_view_mut());
        mat
    }

    #[instrument(skip_all, fields(dims = %mat.dimensions(), added_bits))]
    fn coset_lde_batch(
        &self,
        mut mat: RowMajorMatrix<F>,
        added_bits: usize,
        shift: F,
    ) -> RowMajorMatrix<F> {
        let h = mat.height();
        let log_h = log2_strict_usize(h);
        // It's cheaper to use div_2exp_u64 as this usually avoids an inversion.
        // It's also cheaper to work in the PrimeSubfield whenever possible.
        let h_inv_subfield = F::PrimeSubfield::ONE.div_2exp_u64(log_h as u64);
        let h_inv = F::from_prime_subfield(h_inv_subfield);

        bowers_g_t(&mut mat.as_view_mut());

        // Rescale coefficients in two ways:
        // - divide by height (since we're doing an inverse DFT)
        // - multiply by powers of the coset shift (see default coset LDE impl for an explanation)
        let mut weights = shift.shifted_powers(h_inv).collect_n(h);
        // reverse_bits because mat is encoded in bit-reversed order
        reverse_slice_index_bits(&mut weights);

        mat.par_rows_mut()
            .zip(weights.into_par_iter())
            .for_each(|(row, weight)| row.iter_mut().for_each(|elem| *elem *= weight));

        mat = mat.bit_reversed_zero_pad(added_bits);

        bowers_g(&mut mat.as_view_mut());

        mat
    }
}

/// Executes the Bowers G network. This is like a DFT, except it assumes the input is in
/// bit-reversed order.
fn bowers_g<F: TwoAdicField>(mat: &mut RowMajorMatrixViewMut<'_, F>) {
    let h = mat.height();
    let log_h = log2_strict_usize(h);

    let root = F::two_adic_generator(log_h);
    let mut twiddles = root.powers().collect_n(h / 2);
    reverse_slice_index_bits(&mut twiddles);
    // SAFETY: DifButterfly is `repr(transparent)`
    let twiddles: Vec<DifButterfly<F>> = unsafe { flatten_to_base(twiddles) };

    for log_half_block_size in 0..log_h {
        butterfly_layer(mat, 1 << log_half_block_size, &twiddles);
    }
}

/// Executes the Bowers G^T network. This is like an inverse DFT, except we skip rescaling by
/// 1/height, and the output is bit-reversed.
fn bowers_g_t<F: TwoAdicField>(mat: &mut RowMajorMatrixViewMut<'_, F>) {
    let h = mat.height();
    let log_h = log2_strict_usize(h);

    let root_inv = F::two_adic_generator(log_h).inverse();
    let mut twiddles = root_inv.powers().collect_n(h / 2);
    reverse_slice_index_bits(&mut twiddles);
    // SAFETY: DitButterfly is `repr(transparent)`
    let twiddles: Vec<DitButterfly<F>> = unsafe { flatten_to_base(twiddles) };

    for log_half_block_size in (0..log_h).rev() {
        butterfly_layer(mat, 1 << log_half_block_size, &twiddles);
    }
}

fn butterfly_layer<F: Field, B: Butterfly<F>>(
    mat: &mut RowMajorMatrixViewMut<'_, F>,
    half_block_size: usize,
    twiddles: &[B],
) {
    mat.par_row_chunks_exact_mut(2 * half_block_size)
        .enumerate()
        .for_each(|(block, mut chunks)| {
            let (mut hi_chunks, mut lo_chunks) = chunks.split_rows_mut(half_block_size);
            hi_chunks
                .par_rows_mut()
                .zip(lo_chunks.par_rows_mut())
                .for_each(|(hi_chunk, lo_chunk)| {
                    if block == 0 {
                        TwiddleFreeButterfly.apply_to_rows(hi_chunk, lo_chunk);
                    } else {
                        twiddles[block].apply_to_rows(hi_chunk, lo_chunk);
                    }
                });
        });
}