1use std::arch::x86_64::{
  2    __m128d, __m256d, _mm_load_pd, _mm256_add_pd, _mm256_fmadd_pd, _mm256_fmsub_pd, _mm256_loadu_pd, _mm256_mul_pd,
  3    _mm256_permute2f128_pd, _mm256_set_m128d, _mm256_storeu_pd, _mm256_sub_pd, _mm256_unpackhi_pd, _mm256_unpacklo_pd,
  4};
  5
  6use crate::reim::{as_arr, as_arr_mut};
  7
  8#[target_feature(enable = "avx2,fma")]
  9pub(crate) fn fft_avx2_fma(m: usize, omg: &[f64], data: &mut [f64]) {
 10    if m < 16 {
 11        use poulpy_hal::reference::fft64::reim::fft_ref;
 12
 13        fft_ref(m, omg, data);
 14        return;
 15    }
 16
 17    assert!(data.len() == 2 * m);
 18    let (re, im) = data.split_at_mut(m);
 19
 20    if m == 16 {
 21        fft16_avx2_fma(
 22            as_arr_mut::<16, f64>(re),
 23            as_arr_mut::<16, f64>(im),
 24            as_arr::<16, f64>(omg),
 25        )
 26    } else if m <= 2048 {
 27        fft_bfs_16_avx2_fma(m, re, im, omg, 0);
 28    } else {
 29        fft_rec_16_avx2_fma(m, re, im, omg, 0);
 30    }
 31}
 32
 33unsafe extern "sysv64" {
 34    unsafe fn fft16_avx2_fma_asm(re: *mut f64, im: *mut f64, omg: *const f64);
 35}
 36
 37#[target_feature(enable = "avx2,fma")]
 38fn fft16_avx2_fma(re: &mut [f64; 16], im: &mut [f64; 16], omg: &[f64; 16]) {
 39    unsafe {
 40        fft16_avx2_fma_asm(re.as_mut_ptr(), im.as_mut_ptr(), omg.as_ptr());
 41    }
 42}
 43
 44#[target_feature(enable = "avx2,fma")]
 45fn fft_rec_16_avx2_fma(m: usize, re: &mut [f64], im: &mut [f64], omg: &[f64], mut pos: usize) -> usize {
 46    if m <= 2048 {
 47        return fft_bfs_16_avx2_fma(m, re, im, omg, pos);
 48    };
 49
 50    let h: usize = m >> 1;
 51    twiddle_fft_avx2_fma(h, re, im, *as_arr::<2, f64>(&omg[pos..]));
 52    pos += 2;
 53    pos = fft_rec_16_avx2_fma(h, re, im, omg, pos);
 54    pos = fft_rec_16_avx2_fma(h, &mut re[h..], &mut im[h..], omg, pos);
 55    pos
 56}
 57
 58#[target_feature(enable = "avx2,fma")]
 59fn fft_bfs_16_avx2_fma(m: usize, re: &mut [f64], im: &mut [f64], omg: &[f64], mut pos: usize) -> usize {
 60    let log_m: usize = (usize::BITS - (m - 1).leading_zeros()) as usize;
 61    let mut mm: usize = m;
 62
 63    if !log_m.is_multiple_of(2) {
 64        let h: usize = mm >> 1;
 65        twiddle_fft_avx2_fma(h, re, im, *as_arr::<2, f64>(&omg[pos..]));
 66        pos += 2;
 67        mm = h
 68    }
 69
 70    while mm > 16 {
 71        let h: usize = mm >> 2;
 72        for off in (0..m).step_by(mm) {
 73            bitwiddle_fft_avx2_fma(
 74                h,
 75                &mut re[off..],
 76                &mut im[off..],
 77                as_arr::<4, f64>(&omg[pos..]),
 78            );
 79
 80            pos += 4;
 81        }
 82        mm = h
 83    }
 84
 85    for off in (0..m).step_by(16) {
 86        fft16_avx2_fma(
 87            as_arr_mut::<16, f64>(&mut re[off..]),
 88            as_arr_mut::<16, f64>(&mut im[off..]),
 89            as_arr::<16, f64>(&omg[pos..]),
 90        );
 91
 92        pos += 16;
 93    }
 94
 95    pos
 96}
 97
 98#[target_feature(enable = "avx2,fma")]
 99fn twiddle_fft_avx2_fma(h: usize, re: &mut [f64], im: &mut [f64], omg: [f64; 2]) {
100    unsafe {
101        let omx: __m128d = _mm_load_pd(omg.as_ptr());
102        let omra: __m256d = _mm256_set_m128d(omx, omx);
103        let omi: __m256d = _mm256_unpackhi_pd(omra, omra);
104        let omr: __m256d = _mm256_unpacklo_pd(omra, omra);
105        let mut r0: *mut f64 = re.as_mut_ptr();
106        let mut r1: *mut f64 = re.as_mut_ptr().add(h);
107        let mut i0: *mut f64 = im.as_mut_ptr();
108        let mut i1: *mut f64 = im.as_mut_ptr().add(h);
109
110        for _ in (0..h).step_by(4) {
111            let mut ur0: __m256d = _mm256_loadu_pd(r0);
112            let mut ur1: __m256d = _mm256_loadu_pd(r1);
113            let mut ui0: __m256d = _mm256_loadu_pd(i0);
114            let mut ui1: __m256d = _mm256_loadu_pd(i1);
115            let mut tra: __m256d = _mm256_mul_pd(omi, ui1);
116            let mut tia: __m256d = _mm256_mul_pd(omi, ur1);
117
118            tra = _mm256_fmsub_pd(omr, ur1, tra);
119            tia = _mm256_fmadd_pd(omr, ui1, tia);
120            ur1 = _mm256_sub_pd(ur0, tra);
121            ui1 = _mm256_sub_pd(ui0, tia);
122            ur0 = _mm256_add_pd(ur0, tra);
123            ui0 = _mm256_add_pd(ui0, tia);
124
125            _mm256_storeu_pd(r0, ur0);
126            _mm256_storeu_pd(r1, ur1);
127            _mm256_storeu_pd(i0, ui0);
128            _mm256_storeu_pd(i1, ui1);
129
130            r0 = r0.add(4);
131            r1 = r1.add(4);
132            i0 = i0.add(4);
133            i1 = i1.add(4);
134        }
135    }
136}
137
138#[target_feature(enable = "avx2,fma")]
139fn bitwiddle_fft_avx2_fma(h: usize, re: &mut [f64], im: &mut [f64], omg: &[f64; 4]) {
140    unsafe {
141        let mut r0: *mut f64 = re.as_mut_ptr();
142        let mut r1: *mut f64 = re.as_mut_ptr().add(h);
143        let mut r2: *mut f64 = re.as_mut_ptr().add(2 * h);
144        let mut r3: *mut f64 = re.as_mut_ptr().add(3 * h);
145        let mut i0: *mut f64 = im.as_mut_ptr();
146        let mut i1: *mut f64 = im.as_mut_ptr().add(h);
147        let mut i2: *mut f64 = im.as_mut_ptr().add(2 * h);
148        let mut i3: *mut f64 = im.as_mut_ptr().add(3 * h);
149        let om0: __m256d = _mm256_loadu_pd(omg.as_ptr());
150        let omb: __m256d = _mm256_permute2f128_pd(om0, om0, 0x11);
151        let oma: __m256d = _mm256_permute2f128_pd(om0, om0, 0x00);
152        let omai: __m256d = _mm256_unpackhi_pd(oma, oma);
153        let omar: __m256d = _mm256_unpacklo_pd(oma, oma);
154        let ombi: __m256d = _mm256_unpackhi_pd(omb, omb);
155        let ombr: __m256d = _mm256_unpacklo_pd(omb, omb);
156        for _ in (0..h).step_by(4) {
157            let mut ur0: __m256d = _mm256_loadu_pd(r0);
158            let mut ur1: __m256d = _mm256_loadu_pd(r1);
159            let mut ur2: __m256d = _mm256_loadu_pd(r2);
160            let mut ur3: __m256d = _mm256_loadu_pd(r3);
161            let mut ui0: __m256d = _mm256_loadu_pd(i0);
162            let mut ui1: __m256d = _mm256_loadu_pd(i1);
163            let mut ui2: __m256d = _mm256_loadu_pd(i2);
164            let mut ui3: __m256d = _mm256_loadu_pd(i3);
165
166            let mut tra: __m256d = _mm256_mul_pd(omai, ui2);
167            let mut trb: __m256d = _mm256_mul_pd(omai, ui3);
168            let mut tia: __m256d = _mm256_mul_pd(omai, ur2);
169            let mut tib: __m256d = _mm256_mul_pd(omai, ur3);
170            tra = _mm256_fmsub_pd(omar, ur2, tra);
171            trb = _mm256_fmsub_pd(omar, ur3, trb);
172            tia = _mm256_fmadd_pd(omar, ui2, tia);
173            tib = _mm256_fmadd_pd(omar, ui3, tib);
174            ur2 = _mm256_sub_pd(ur0, tra);
175            ur3 = _mm256_sub_pd(ur1, trb);
176            ui2 = _mm256_sub_pd(ui0, tia);
177            ui3 = _mm256_sub_pd(ui1, tib);
178            ur0 = _mm256_add_pd(ur0, tra);
179            ur1 = _mm256_add_pd(ur1, trb);
180            ui0 = _mm256_add_pd(ui0, tia);
181            ui1 = _mm256_add_pd(ui1, tib);
182
183            tra = _mm256_mul_pd(ombi, ui1);
184            trb = _mm256_mul_pd(ombr, ui3);
185            tia = _mm256_mul_pd(ombi, ur1);
186            tib = _mm256_mul_pd(ombr, ur3);
187            tra = _mm256_fmsub_pd(ombr, ur1, tra);
188            trb = _mm256_fmadd_pd(ombi, ur3, trb);
189            tia = _mm256_fmadd_pd(ombr, ui1, tia);
190            tib = _mm256_fmsub_pd(ombi, ui3, tib);
191            ur1 = _mm256_sub_pd(ur0, tra);
192            ur3 = _mm256_add_pd(ur2, trb);
193            ui1 = _mm256_sub_pd(ui0, tia);
194            ui3 = _mm256_add_pd(ui2, tib);
195            ur0 = _mm256_add_pd(ur0, tra);
196            ur2 = _mm256_sub_pd(ur2, trb);
197            ui0 = _mm256_add_pd(ui0, tia);
198            ui2 = _mm256_sub_pd(ui2, tib);
199
200            _mm256_storeu_pd(r0, ur0);
201            _mm256_storeu_pd(r1, ur1);
202            _mm256_storeu_pd(r2, ur2);
203            _mm256_storeu_pd(r3, ur3);
204            _mm256_storeu_pd(i0, ui0);
205            _mm256_storeu_pd(i1, ui1);
206            _mm256_storeu_pd(i2, ui2);
207            _mm256_storeu_pd(i3, ui3);
208
209            r0 = r0.add(4);
210            r1 = r1.add(4);
211            r2 = r2.add(4);
212            r3 = r3.add(4);
213            i0 = i0.add(4);
214            i1 = i1.add(4);
215            i2 = i2.add(4);
216            i3 = i3.add(4);
217        }
218    }
219}
220
221#[test]
222fn test_fft_avx2_fma() {
223    use super::*;
224
225    #[target_feature(enable = "avx2,fma")]
226    fn internal(log_m: usize) {
227        use poulpy_hal::reference::fft64::reim::ReimFFTRef;
228
229        let m = 1 << log_m;
230
231        let table: ReimFFTTable<f64> = ReimFFTTable::<f64>::new(m);
232
233        let mut values_0: Vec<f64> = vec![0f64; m << 1];
234        let scale: f64 = 1.0f64 / m as f64;
235        values_0
236            .iter_mut()
237            .enumerate()
238            .for_each(|(i, x)| *x = (i + 1) as f64 * scale);
239
240        let mut values_1: Vec<f64> = vec![0f64; m << 1];
241        values_1
242            .iter_mut()
243            .zip(values_0.iter())
244            .for_each(|(y, x)| *y = *x);
245
246        ReimFFTAvx::reim_dft_execute(&table, &mut values_0);
247        ReimFFTRef::reim_dft_execute(&table, &mut values_1);
248
249        let max_diff: f64 = 1.0 / ((1u64 << (53 - log_m - 1)) as f64);
250
251        for i in 0..m * 2 {
252            let diff: f64 = (values_0[i] - values_1[i]).abs();
253            assert!(
254                diff <= max_diff,
255                "{} -> {}-{} = {}",
256                i,
257                values_0[i],
258                values_1[i],
259                diff
260            )
261        }
262    }
263
264    if std::is_x86_feature_detected!("avx2") {
265        for log_m in 0..16 {
266            unsafe { internal(log_m) }
267        }
268    } else {
269        eprintln!("skipping: CPU lacks avx2");
270    }
271}