1 use std::f32::{self, consts};
2 use std::ops::{Not, Neg, Add, AddAssign, Sub, SubAssign, Mul, MulAssign};
6 #[derive(Debug,Clone,Copy,PartialEq)]
7 pub struct FFTComplex {
13 pub fn exp(val: f32) -> Self {
14 FFTComplex { re: val.cos(), im: val.sin() }
16 pub fn rotate(self) -> Self {
17 FFTComplex { re: -self.im, im: self.re }
19 pub fn scale(self, scale: f32) -> Self {
20 FFTComplex { re: self.re * scale, im: self.im * scale }
24 impl Neg for FFTComplex {
25 type Output = FFTComplex;
26 fn neg(self) -> Self::Output {
27 FFTComplex { re: -self.re, im: -self.im }
31 impl Not for FFTComplex {
32 type Output = FFTComplex;
33 fn not(self) -> Self::Output {
34 FFTComplex { re: self.re, im: -self.im }
38 impl Add for FFTComplex {
39 type Output = FFTComplex;
40 fn add(self, other: Self) -> Self::Output {
41 FFTComplex { re: self.re + other.re, im: self.im + other.im }
45 impl AddAssign for FFTComplex {
46 fn add_assign(&mut self, other: Self) {
52 impl Sub for FFTComplex {
53 type Output = FFTComplex;
54 fn sub(self, other: Self) -> Self::Output {
55 FFTComplex { re: self.re - other.re, im: self.im - other.im }
59 impl SubAssign for FFTComplex {
60 fn sub_assign(&mut self, other: Self) {
66 impl Mul for FFTComplex {
67 type Output = FFTComplex;
68 fn mul(self, other: Self) -> Self::Output {
69 FFTComplex { re: self.re * other.re - self.im * other.im,
70 im: self.im * other.re + self.re * other.im }
74 impl MulAssign for FFTComplex {
75 fn mul_assign(&mut self, other: Self) {
76 let re = self.re * other.re - self.im * other.im;
77 let im = self.im * other.re + self.re * other.im;
83 impl fmt::Display for FFTComplex {
84 fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
85 write!(f, "({}, {})", self.re, self.im)
89 pub const FFTC_ZERO: FFTComplex = FFTComplex { re: 0.0, im: 0.0 };
91 pub fn generic_fft(data: &mut [FFTComplex], forward: bool) {
92 let mut tmp = Vec::with_capacity(data.len());
93 tmp.resize(data.len(), FFTC_ZERO);
94 let base = if forward { -consts::PI * 2.0 / (data.len() as f32) }
95 else { consts::PI * 2.0 / (data.len() as f32) };
96 for k in 0..data.len() {
97 let mut sum = FFTC_ZERO;
98 for n in 0..data.len() {
99 let w = FFTComplex::exp(base * ((n * k) as f32));
104 for k in 0..data.len() {
110 table: Vec<FFTComplex>,
111 tmp: Vec<FFTComplex>,
112 twiddle: Vec<FFTComplex>,
120 const FFT3_CONST: f32 = 0.86602540378443864677;
121 const FFT5_CONST1: FFTComplex = FFTComplex { re: 0.80901699437494742410, im: 0.58778525229247312915 };
122 const FFT5_CONST2: FFTComplex = FFTComplex { re: 0.30901699437494742411, im: 0.95105651629515357211 };
124 fn twiddle5(a: FFTComplex, b: FFTComplex, c: FFTComplex) -> (FFTComplex, FFTComplex) {
125 let re = a.re * c.re;
126 let im = a.im * c.re;
127 let diffre = b.im * c.im;
128 let diffim = b.re * c.im;
130 (FFTComplex { re: re - diffre, im: im + diffim }, FFTComplex { re: re + diffre, im: im - diffim })
134 fn new_data(size: usize, forward: bool) -> FFTData {
135 let mut table: Vec<FFTComplex> = Vec::with_capacity(size * size);
136 table.resize(size * size, FFTC_ZERO);
137 let base = consts::PI * 2.0 / (size as f32);
141 table[n * size + k] = FFTComplex::exp(-base * ((n * k) as f32));
147 table[n * size + k] = FFTComplex::exp( base * ((n * k) as f32));
151 let mut tmp = Vec::with_capacity(size);
152 tmp.resize(size, FFTC_ZERO);
153 FFTData { table, tmp, twiddle: Vec::new(), size, step: 0, div: 0 }
155 fn fft(tbl: &mut FFTData, size: usize, data: &mut [FFTComplex], step: usize) {
157 let s0 = data[step * 0];
158 let s1 = data[step * 1];
159 let s2 = data[step * 2];
161 data[step * 0] += t0;
162 let t1 = s0 - t0.scale(0.5);
163 let t2 = (s2 - s1).rotate().scale(FFT3_CONST);
164 data[step * 1] = t1 + t2;
165 data[step * 2] = t1 - t2;
169 let s0 = data[step * 0];
170 let s1 = data[step * 1];
171 let s2 = data[step * 2];
172 let s3 = data[step * 3];
173 let s4 = data[step * 4];
179 let (t4, t5) = twiddle5(t0, t1, FFT5_CONST2);
180 let (t6, t7) = twiddle5(t2, t3, FFT5_CONST1);
181 let (t8, t9) = twiddle5(t0, t1, FFT5_CONST1);
182 let (ta, tb) = twiddle5(t2, t3, FFT5_CONST2);
184 data[step * 0] = s0 + t0 + t2;
185 data[step * 1] = s0 + t5 - t6;
186 data[step * 2] = s0 - t8 + ta;
187 data[step * 3] = s0 - t9 + tb;
188 data[step * 4] = s0 + t4 - t7;
191 for k in 0..tbl.size {
192 tbl.tmp[k] = FFTC_ZERO;
193 for n in 0..tbl.size {
194 tbl.tmp[k] += data[n * step] * tbl.table[k * tbl.size + n];
197 for n in 0..tbl.size {
198 data[n * step] = tbl.tmp[n];
201 fn ifft(tbl: &mut FFTData, size: usize, data: &mut [FFTComplex], step: usize) {
203 let s0 = data[step * 0];
204 let s1 = data[step * 1];
205 let s2 = data[step * 2];
207 data[step * 0] += t0;
208 let t1 = s0 - t0.scale(0.5);
209 let t2 = (s2 - s1).rotate().scale(FFT3_CONST);
210 data[step * 1] = t1 - t2;
211 data[step * 2] = t1 + t2;
215 let s0 = data[step * 0];
216 let s1 = data[step * 1];
217 let s2 = data[step * 2];
218 let s3 = data[step * 3];
219 let s4 = data[step * 4];
225 let (t4, t5) = twiddle5(t0, t1, FFT5_CONST2);
226 let (t6, t7) = twiddle5(t2, t3, FFT5_CONST1);
227 let (t8, t9) = twiddle5(t0, t1, FFT5_CONST1);
228 let (ta, tb) = twiddle5(t2, t3, FFT5_CONST2);
230 data[step * 0] = s0 + t0 + t2;
231 data[step * 1] = s0 + t4 - t7;
232 data[step * 2] = s0 - t9 + tb;
233 data[step * 3] = s0 - t8 + ta;
234 data[step * 4] = s0 + t5 - t6;
237 Self::fft(tbl, size, data, step);
241 struct FFTSplitRadix {}
244 fn new_data(bits: u8, _forward: bool) -> FFTData {
245 let size = 1 << bits;
246 let mut table = Vec::with_capacity(size);
247 for _ in 0..4 { table.push(FFTC_ZERO); }
248 for b in 3..(bits+1) {
249 let qsize = (1 << (b - 2)) as usize;
250 let base = -consts::PI / ((qsize * 2) as f32);
252 table.push(FFTComplex::exp(base * ((k * 1) as f32)));
253 table.push(FFTComplex::exp(base * ((k * 3) as f32)));
256 FFTData { table, tmp: Vec::new(), twiddle: Vec::new(), size, step: 0, div: 0 }
258 fn fft(fftdata: &mut FFTData, bits: u8, data: &mut [FFTComplex]) {
259 if bits == 0 { return; }
261 let sum01 = data[0] + data[1];
262 let dif01 = data[0] - data[1];
268 let sum01 = data[0] + data[2];
269 let dif01 = data[0] - data[2];
270 let sum23 = data[1] + data[3];
271 let dif23 = data[1] - data[3];
272 data[0] = sum01 + sum23;
273 data[1] = dif01 - dif23.rotate();
274 data[2] = sum01 - sum23;
275 data[3] = dif01 + dif23.rotate();
278 let qsize = (1 << (bits - 2)) as usize;
279 let hsize = (1 << (bits - 1)) as usize;
280 let q3size = qsize + hsize;
282 Self::fft(fftdata, bits - 1, &mut data[0 ..hsize]);
283 Self::fft(fftdata, bits - 2, &mut data[hsize ..q3size]);
284 Self::fft(fftdata, bits - 2, &mut data[q3size..]);
287 let t3 = data[0 + hsize] + data[0 + q3size];
288 let t4 = (data[0 + hsize] - data[0 + q3size]).rotate();
290 let e2 = data[0 + qsize];
292 data[0 + qsize] = e2 - t4;
293 data[0 + hsize] = e1 - t3;
294 data[0 + q3size] = e2 + t4;
297 let t1 = fftdata.table[off + k * 2 + 0] * data[k + hsize];
298 let t2 = fftdata.table[off + k * 2 + 1] * data[k + q3size];
300 let t4 = (t1 - t2).rotate();
302 let e2 = data[k + qsize];
304 data[k + qsize] = e2 - t4;
305 data[k + hsize] = e1 - t3;
306 data[k + qsize * 3] = e2 + t4;
309 fn ifft(fftdata: &mut FFTData, bits: u8, data: &mut [FFTComplex]) {
310 if bits == 0 { return; }
312 let sum01 = data[0] + data[1];
313 let dif01 = data[0] - data[1];
319 let sum01 = data[0] + data[2];
320 let dif01 = data[0] - data[2];
321 let sum23 = data[1] + data[3];
322 let dif23 = data[1] - data[3];
323 data[0] = sum01 + sum23;
324 data[1] = dif01 + dif23.rotate();
325 data[2] = sum01 - sum23;
326 data[3] = dif01 - dif23.rotate();
329 let qsize = (1 << (bits - 2)) as usize;
330 let hsize = (1 << (bits - 1)) as usize;
331 let q3size = qsize + hsize;
333 Self::ifft(fftdata, bits - 1, &mut data[0 ..hsize]);
334 Self::ifft(fftdata, bits - 2, &mut data[hsize ..q3size]);
335 Self::ifft(fftdata, bits - 2, &mut data[q3size..]);
338 let t3 = data[0 + hsize] + data[0 + q3size];
339 let t4 = (data[0 + hsize] - data[0 + q3size]).rotate();
341 let e2 = data[0 + qsize];
343 data[0 + qsize] = e2 + t4;
344 data[0 + hsize] = e1 - t3;
345 data[0 + q3size] = e2 - t4;
348 let t1 = !fftdata.table[off + k * 2 + 0] * data[k + hsize];
349 let t2 = !fftdata.table[off + k * 2 + 1] * data[k + q3size];
351 let t4 = (t1 - t2).rotate();
353 let e2 = data[k + qsize];
355 data[k + qsize] = e2 + t4;
356 data[k + hsize] = e1 - t3;
357 data[k + qsize * 3] = e2 - t4;
364 const FFT15_INSWAP: [usize; 20] = [ 0, 5, 10, 42, 3, 8, 13, 42, 6, 11, 1, 42, 9, 14, 4, 42, 12, 2, 7, 42 ];
365 const FFT15_OUTSWAP: [usize; 20] = [ 0, 10, 5, 42, 6, 1, 11, 42, 12, 7, 2, 42, 3, 13, 8, 42, 9, 4, 14, 42 ];
368 fn new_data(size: usize, _forward: bool) -> FFTData {
369 FFTData { table: Vec::new(), tmp: Vec::new(), twiddle: Vec::new(), size, step: 0, div: 0 }
371 fn fft3(dst: &mut [FFTComplex], src: &[FFTComplex], step: usize, n: usize) {
377 let t1 = s0 - t0.scale(0.5);
378 let t2 = (s2 - s1).rotate().scale(FFT3_CONST);
380 dst[FFT15_OUTSWAP[n * 4 + 0] * step] = s0 + t0;
381 dst[FFT15_OUTSWAP[n * 4 + 1] * step] = t1 + t2;
382 dst[FFT15_OUTSWAP[n * 4 + 2] * step] = t1 - t2;
384 fn ifft3(dst: &mut [FFTComplex], src: &[FFTComplex], step: usize, n: usize) {
390 let t1 = s0 - t0.scale(0.5);
391 let t2 = (s2 - s1).rotate().scale(FFT3_CONST);
393 dst[FFT15_OUTSWAP[n * 4 + 0] * step] = s0 + t0;
394 dst[FFT15_OUTSWAP[n * 4 + 1] * step] = t1 - t2;
395 dst[FFT15_OUTSWAP[n * 4 + 2] * step] = t1 + t2;
397 fn fft5(dst: &mut [FFTComplex], src: &[FFTComplex], step: usize, n: usize) {
398 let s0 = src[FFT15_INSWAP[n + 0 * 4] * step];
399 let s1 = src[FFT15_INSWAP[n + 1 * 4] * step];
400 let s2 = src[FFT15_INSWAP[n + 2 * 4] * step];
401 let s3 = src[FFT15_INSWAP[n + 3 * 4] * step];
402 let s4 = src[FFT15_INSWAP[n + 4 * 4] * step];
408 let (t4, t5) = twiddle5(t0, t1, FFT5_CONST2);
409 let (t6, t7) = twiddle5(t2, t3, FFT5_CONST1);
410 let (t8, t9) = twiddle5(t0, t1, FFT5_CONST1);
411 let (ta, tb) = twiddle5(t2, t3, FFT5_CONST2);
413 dst[0 * 3] = s0 + t0 + t2;
414 dst[1 * 3] = s0 + t5 - t6;
415 dst[2 * 3] = s0 - t8 + ta;
416 dst[3 * 3] = s0 - t9 + tb;
417 dst[4 * 3] = s0 + t4 - t7;
419 fn ifft5(dst: &mut [FFTComplex], src: &[FFTComplex], step: usize, n: usize) {
420 let s0 = src[FFT15_INSWAP[n + 0 * 4] * step];
421 let s1 = src[FFT15_INSWAP[n + 1 * 4] * step];
422 let s2 = src[FFT15_INSWAP[n + 2 * 4] * step];
423 let s3 = src[FFT15_INSWAP[n + 3 * 4] * step];
424 let s4 = src[FFT15_INSWAP[n + 4 * 4] * step];
430 let (t4, t5) = twiddle5(t0, t1, FFT5_CONST2);
431 let (t6, t7) = twiddle5(t2, t3, FFT5_CONST1);
432 let (t8, t9) = twiddle5(t0, t1, FFT5_CONST1);
433 let (ta, tb) = twiddle5(t2, t3, FFT5_CONST2);
435 dst[0 * 3] = s0 + t0 + t2;
436 dst[1 * 3] = s0 + t4 - t7;
437 dst[2 * 3] = s0 - t9 + tb;
438 dst[3 * 3] = s0 - t8 + ta;
439 dst[4 * 3] = s0 + t5 - t6;
441 fn fft(_fftdata: &mut FFTData, data: &mut [FFTComplex], step: usize) {
442 let mut tmp = [FFTC_ZERO; 15];
444 Self::fft5(&mut tmp[n..], data, step, n);
447 Self::fft3(data, &tmp[n * 3..][..3], step, n);
450 fn ifft(_fftdata: &mut FFTData, data: &mut [FFTComplex], step: usize) {
451 let mut tmp = [FFTC_ZERO; 15];
453 Self::ifft5(&mut tmp[n..], data, step, n);
456 Self::ifft3(data, &tmp[n * 3..][..3], step, n);
469 fn permute(&self, perms: &mut [usize]) {
471 FFTMode::Generic(_) => {},
472 FFTMode::SplitRadix(bits) => {
473 let div = perms.len() >> bits;
474 gen_sr_perms(perms, 1 << bits);
476 for i in 0..(1 << bits) {
480 for j in 0..(1 << bits) {
481 perms[(i << bits) + j] = perms[j] + i;
486 FFTMode::Prime15 => {},
489 fn do_fft(&self, fftdata: &mut FFTData, data: &mut [FFTComplex]) {
491 FFTMode::Generic(size) => FFTGeneric::fft(fftdata, size, data, 1),
492 FFTMode::SplitRadix(bits) => FFTSplitRadix::fft(fftdata, bits, data),
493 FFTMode::Prime15 => FFT15::fft(fftdata, data, 1),
496 fn do_fft2(&self, fftdata: &mut FFTData, data: &mut [FFTComplex], step: usize) {
498 FFTMode::Generic(size) => FFTGeneric::fft(fftdata, size, data, step),
499 FFTMode::SplitRadix(_) => unreachable!(),
500 FFTMode::Prime15 => FFT15::fft(fftdata, data, step),
503 fn do_ifft(&self, fftdata: &mut FFTData, data: &mut [FFTComplex]) {
505 FFTMode::Generic(size) => FFTGeneric::ifft(fftdata, size, data, 1),
506 FFTMode::SplitRadix(bits) => FFTSplitRadix::ifft(fftdata, bits, data),
507 FFTMode::Prime15 => FFT15::ifft(fftdata, data, 1),
510 fn do_ifft2(&self, fftdata: &mut FFTData, data: &mut [FFTComplex], step: usize) {
512 FFTMode::Generic(size) => FFTGeneric::ifft(fftdata, size, data, step),
513 FFTMode::SplitRadix(_) => unreachable!(),
514 FFTMode::Prime15 => FFT15::ifft(fftdata, data, step),
517 fn get_size(&self) -> usize {
519 FFTMode::Generic(size) => size,
520 FFTMode::SplitRadix(bits) => 1 << bits,
521 FFTMode::Prime15 => 15,
529 ffts: Vec<(FFTMode, FFTData)>,
533 pub fn do_fft(&mut self, src: &[FFTComplex], dst: &mut [FFTComplex]) {
534 for k in 0..src.len() { dst[k] = src[self.perms[k]]; }
535 self.do_fft_core(dst);
537 pub fn do_ifft(&mut self, src: &[FFTComplex], dst: &mut [FFTComplex]) {
538 for k in 0..src.len() { dst[k] = src[self.perms[k]]; }
539 self.do_ifft_core(dst);
541 pub fn do_fft_inplace(&mut self, data: &mut [FFTComplex]) {
542 for idx in 0..self.swaps.len() {
543 let nidx = self.swaps[idx];
546 data[nidx] = data[idx];
550 self.do_fft_core(data);
552 pub fn do_ifft_inplace(&mut self, data: &mut [FFTComplex]) {
553 for idx in 0..self.swaps.len() {
554 let nidx = self.swaps[idx];
557 data[nidx] = data[idx];
561 self.do_ifft_core(data);
563 fn do_fft_core(&mut self, data: &mut [FFTComplex]) {
564 for el in self.ffts.iter_mut() {
565 let (mode, ref mut fftdata) = el;
566 let bsize = mode.get_size();
567 let div = fftdata.div;
568 let step = fftdata.step;
570 mode.do_fft(fftdata, data);
572 mode.do_fft(fftdata, &mut data[i * bsize..]);
575 mode.do_fft2(fftdata, data, div);
576 let mut toff = bsize;
579 data[i + j * div] *= fftdata.twiddle[toff + j];
581 mode.do_fft2(fftdata, &mut data[i..], div);
587 fn do_ifft_core(&mut self, data: &mut [FFTComplex]) {
588 for el in self.ffts.iter_mut() {
589 let (mode, ref mut fftdata) = el;
590 let bsize = mode.get_size();
591 let div = fftdata.div;
592 let step = fftdata.step;
594 mode.do_ifft(fftdata, data);
596 mode.do_ifft(fftdata, &mut data[i * bsize..]);
599 mode.do_ifft2(fftdata, data, div);
600 let mut toff = bsize;
603 data[i + j * div] *= fftdata.twiddle[toff + j];
605 mode.do_ifft2(fftdata, &mut data[i..], div);
613 pub struct FFTBuilder {
616 /*fn reverse_bits(inval: u32) -> u32 {
617 const REV_TAB: [u8; 16] = [
618 0b0000, 0b1000, 0b0100, 0b1100, 0b0010, 0b1010, 0b0110, 0b1110,
619 0b0001, 0b1001, 0b0101, 0b1101, 0b0011, 0b1011, 0b0111, 0b1111,
625 ret = (ret << 4) | (REV_TAB[(val & 0xF) as usize] as u32);
631 fn swp_idx(idx: usize, bits: u32) -> usize {
632 let s = reverse_bits(idx as u32) as usize;
636 fn gen_sr_perms(swaps: &mut [usize], size: usize) {
637 if size <= 4 { return; }
638 let mut evec: Vec<usize> = Vec::with_capacity(size / 2);
639 let mut ovec1: Vec<usize> = Vec::with_capacity(size / 4);
640 let mut ovec2: Vec<usize> = Vec::with_capacity(size / 4);
642 evec.push (swaps[k * 4 + 0]);
643 ovec1.push(swaps[k * 4 + 1]);
644 evec.push (swaps[k * 4 + 2]);
645 ovec2.push(swaps[k * 4 + 3]);
647 for k in 0..size/2 { swaps[k] = evec[k]; }
648 for k in 0..size/4 { swaps[k + size/2] = ovec1[k]; }
649 for k in 0..size/4 { swaps[k + 3*size/4] = ovec2[k]; }
650 gen_sr_perms(&mut swaps[0..size/2], size/2);
651 gen_sr_perms(&mut swaps[size/2..3*size/4], size/4);
652 gen_sr_perms(&mut swaps[3*size/4..], size/4);
655 fn gen_swaps_for_perm(swaps: &mut Vec<usize>, perms: &Vec<usize>) {
656 let mut idx_arr: Vec<usize> = Vec::with_capacity(perms.len());
657 for i in 0..perms.len() { idx_arr.push(i); }
658 let mut run_size = 0;
660 for idx in 0..perms.len() {
661 if perms[idx] == idx_arr[idx] {
662 if run_size == 0 { run_pos = idx; }
665 for i in 0..run_size {
666 swaps.push(run_pos + i);
669 let mut spos = idx + 1;
670 while idx_arr[spos] != perms[idx] { spos += 1; }
671 idx_arr[spos] = idx_arr[idx];
672 idx_arr[idx] = perms[idx];
679 fn generate_twiddle(data: &mut FFTData, size: usize, cur_size: usize, forward: bool) {
680 if size == cur_size { return; }
681 data.twiddle = Vec::with_capacity(size);
682 let div = size / cur_size;
683 let base = if forward { -2.0 * consts::PI / (size as f32) } else { 2.0 * consts::PI / (size as f32) };
685 for k in 0..cur_size {
686 data.twiddle.push(FFTComplex::exp(base * ((k * n) as f32)));
690 pub fn new_fft(size: usize, forward: bool) -> FFT {
691 let mut ffts: Vec<(FFTMode, FFTData)> = Vec::with_capacity(1);
692 let mut perms: Vec<usize> = Vec::with_capacity(size);
693 let mut swaps: Vec<usize> = Vec::with_capacity(size);
694 let mut rem_size = size;
695 if rem_size.trailing_zeros() > 0 {
696 let bits = rem_size.trailing_zeros() as u8;
697 let mut data = FFTSplitRadix::new_data(bits, forward);
698 Self::generate_twiddle(&mut data, size, 1 << bits, forward);
700 data.div = rem_size >> bits;
701 ffts.push((FFTMode::SplitRadix(bits), data));
704 if (rem_size % 15) == 0 {
705 let mut data = FFT15::new_data(size, forward);
706 Self::generate_twiddle(&mut data, size, 15, forward);
707 data.step = size / rem_size;
708 data.div = size / rem_size;
709 ffts.push((FFTMode::Prime15, data));
713 let mut data = FFTGeneric::new_data(rem_size, forward);
714 Self::generate_twiddle(&mut data, size, rem_size, forward);
715 data.step = size / rem_size;
716 data.div = size / rem_size;
717 ffts.push((FFTMode::Generic(rem_size), data));
723 for (mode, _) in ffts.iter().rev() {
724 mode.permute(&mut perms);
726 gen_swaps_for_perm(&mut swaps, &perms);
728 FFT { perms, swaps, ffts }
733 table: Vec<FFTComplex>,
740 fn crossadd(a: &FFTComplex, b: &FFTComplex) -> FFTComplex {
741 FFTComplex { re: a.re + b.re, im: a.im - b.im }
745 pub fn do_rdft(&mut self, src: &[FFTComplex], dst: &mut [FFTComplex]) {
746 dst.copy_from_slice(src);
747 self.do_rdft_inplace(dst);
749 pub fn do_rdft_inplace(&mut self, buf: &mut [FFTComplex]) {
751 for n in 0..self.size/2 {
752 let in0 = buf[n + 1];
753 let in1 = buf[self.size - n - 1];
755 let t0 = crossadd(&in0, &in1);
756 let t1 = FFTComplex { re: in1.im + in0.im, im: in1.re - in0.re };
757 let tab = self.table[n];
758 let t2 = FFTComplex { re: t1.im * tab.im + t1.re * tab.re, im: t1.im * tab.re - t1.re * tab.im };
760 buf[n + 1] = FFTComplex { re: t0.im - t2.im, im: t0.re - t2.re }; // (t0 - t2).conj().rotate()
761 buf[self.size - n - 1] = (t0 + t2).rotate();
769 self.fft.do_fft_inplace(buf);
771 self.fft.do_ifft_inplace(buf);
774 for n in 0..self.size/2 {
775 let in0 = buf[n + 1];
776 let in1 = buf[self.size - n - 1];
778 let t0 = crossadd(&in0, &in1).scale(0.5);
779 let t1 = FFTComplex { re: in0.im + in1.im, im: in0.re - in1.re };
780 let t2 = t1 * self.table[n];
782 buf[n + 1] = crossadd(&t0, &t2);
783 buf[self.size - n - 1] = FFTComplex { re: t0.re - t2.re, im: -(t0.im + t2.im) };
790 for n in 0..self.size {
791 buf[n] = FFTComplex{ re: buf[n].im, im: buf[n].re };
797 pub struct RDFTBuilder {
801 pub fn new_rdft(size: usize, forward: bool, forward_fft: bool) -> RDFT {
802 let mut table: Vec<FFTComplex> = Vec::with_capacity(size / 4);
803 let (base, scale) = if forward { (consts::PI / (size as f32), 0.5) } else { (-consts::PI / (size as f32), 1.0) };
805 table.push(FFTComplex::exp(base * ((i + 1) as f32)).scale(scale));
807 let fft = FFTBuilder::new_fft(size, forward_fft);
808 RDFT { table, fft, size, fwd: forward, fwd_fft: forward_fft }
817 fn test_fft(size: usize) {
818 println!("testing FFT {}", size);
819 let mut fin: Vec<FFTComplex> = Vec::with_capacity(size);
820 let mut fout1: Vec<FFTComplex> = Vec::with_capacity(size);
821 let mut fout2: Vec<FFTComplex> = Vec::with_capacity(size);
822 fin.resize(size, FFTC_ZERO);
823 fout1.resize(size, FFTC_ZERO);
824 fout2.resize(size, FFTC_ZERO);
825 let mut fft = FFTBuilder::new_fft(size, true);
826 let mut seed: u32 = 42;
827 for i in 0..fin.len() {
828 seed = seed.wrapping_mul(1664525).wrapping_add(1013904223);
829 let val = (seed >> 16) as i16;
830 fin[i].re = (val as f32) / 256.0;
831 seed = seed.wrapping_mul(1664525).wrapping_add(1013904223);
832 let val = (seed >> 16) as i16;
833 fin[i].im = (val as f32) / 256.0;
835 fft.do_fft(&fin, &mut fout1);
836 fout2.copy_from_slice(&fin);
837 generic_fft(&mut fout2, true);
839 for i in 0..fin.len() {
840 assert!((fout1[i].re - fout2[i].re).abs() < 1.0);
841 assert!((fout1[i].im - fout2[i].im).abs() < 1.0);
843 let mut ifft = FFTBuilder::new_fft(size, false);
844 ifft.do_ifft_inplace(&mut fout1);
845 generic_fft(&mut fout2, false);
847 let sc = 1.0 / (size as f32);
848 for i in 0..fin.len() {
849 assert!((fin[i].re - fout1[i].re * sc).abs() < 1.0);
850 assert!((fin[i].im - fout1[i].im * sc).abs() < 1.0);
851 assert!((fout1[i].re - fout2[i].re).abs() * sc < 1.0);
852 assert!((fout1[i].im - fout2[i].im).abs() * sc < 1.0);
869 let mut fin: [FFTComplex; 128] = [FFTC_ZERO; 128];
870 let mut fout1: [FFTComplex; 128] = [FFTC_ZERO; 128];
871 let mut rdft = RDFTBuilder::new_rdft(fin.len(), true, true);
872 let mut seed: u32 = 42;
873 for i in 0..fin.len() {
874 seed = seed.wrapping_mul(1664525).wrapping_add(1013904223);
875 let val = (seed >> 16) as i16;
876 fin[i].re = (val as f32) / 256.0;
877 seed = seed.wrapping_mul(1664525).wrapping_add(1013904223);
878 let val = (seed >> 16) as i16;
879 fin[i].im = (val as f32) / 256.0;
881 rdft.do_rdft(&fin, &mut fout1);
882 let mut irdft = RDFTBuilder::new_rdft(fin.len(), false, true);
883 irdft.do_rdft_inplace(&mut fout1);
885 for i in 0..fin.len() {
886 let tst = fout1[i].scale(0.5/(fout1.len() as f32));
887 assert!((tst.re - fin[i].re).abs() < 1.0);
888 assert!((tst.im - fin[i].im).abs() < 1.0);