1 //! FFT and RDFT implementation.
2 use std::f32::{self, consts};
3 use std::ops::{Not, Neg, Add, AddAssign, Sub, SubAssign, Mul, MulAssign};
8 #[derive(Debug,Clone,Copy,PartialEq)]
9 pub struct FFTComplex {
10 /// Real part of the numner.
12 /// Complex part of the number.
17 /// Calculates `exp(i * val)`.
18 pub fn exp(val: f32) -> Self {
19 FFTComplex { re: val.cos(), im: val.sin() }
21 /// Returns `-Im + i * Re`.
22 pub fn rotate(self) -> Self {
23 FFTComplex { re: -self.im, im: self.re }
25 /// Multiplies complex number by scalar.
26 pub fn scale(self, scale: f32) -> Self {
27 FFTComplex { re: self.re * scale, im: self.im * scale }
31 impl Neg for FFTComplex {
32 type Output = FFTComplex;
33 fn neg(self) -> Self::Output {
34 FFTComplex { re: -self.re, im: -self.im }
38 impl Not for FFTComplex {
39 type Output = FFTComplex;
40 fn not(self) -> Self::Output {
41 FFTComplex { re: self.re, im: -self.im }
45 impl Add for FFTComplex {
46 type Output = FFTComplex;
47 fn add(self, other: Self) -> Self::Output {
48 FFTComplex { re: self.re + other.re, im: self.im + other.im }
52 impl AddAssign for FFTComplex {
53 fn add_assign(&mut self, other: Self) {
59 impl Sub for FFTComplex {
60 type Output = FFTComplex;
61 fn sub(self, other: Self) -> Self::Output {
62 FFTComplex { re: self.re - other.re, im: self.im - other.im }
66 impl SubAssign for FFTComplex {
67 fn sub_assign(&mut self, other: Self) {
73 impl Mul for FFTComplex {
74 type Output = FFTComplex;
75 fn mul(self, other: Self) -> Self::Output {
76 FFTComplex { re: self.re * other.re - self.im * other.im,
77 im: self.im * other.re + self.re * other.im }
81 impl MulAssign for FFTComplex {
82 fn mul_assign(&mut self, other: Self) {
83 let re = self.re * other.re - self.im * other.im;
84 let im = self.im * other.re + self.re * other.im;
90 impl fmt::Display for FFTComplex {
91 fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
92 write!(f, "({}, {})", self.re, self.im)
96 /// Complex number with zero value.
97 pub const FFTC_ZERO: FFTComplex = FFTComplex { re: 0.0, im: 0.0 };
99 /// Calculates forward or inverse FFT in the straightforward way.
100 pub fn generic_fft(data: &mut [FFTComplex], forward: bool) {
101 let mut tmp = Vec::with_capacity(data.len());
102 tmp.resize(data.len(), FFTC_ZERO);
103 let base = if forward { -consts::PI * 2.0 / (data.len() as f32) }
104 else { consts::PI * 2.0 / (data.len() as f32) };
105 for k in 0..data.len() {
106 let mut sum = FFTC_ZERO;
107 for n in 0..data.len() {
108 let w = FFTComplex::exp(base * ((n * k) as f32));
113 for k in 0..data.len() {
119 table: Vec<FFTComplex>,
120 tmp: Vec<FFTComplex>,
121 twiddle: Vec<FFTComplex>,
129 const FFT3_CONST: f32 = 0.86602540378443864677;
130 const FFT5_CONST1: FFTComplex = FFTComplex { re: 0.80901699437494742410, im: 0.58778525229247312915 };
131 const FFT5_CONST2: FFTComplex = FFTComplex { re: 0.30901699437494742411, im: 0.95105651629515357211 };
133 fn twiddle5(a: FFTComplex, b: FFTComplex, c: FFTComplex) -> (FFTComplex, FFTComplex) {
134 let re = a.re * c.re;
135 let im = a.im * c.re;
136 let diffre = b.im * c.im;
137 let diffim = b.re * c.im;
139 (FFTComplex { re: re - diffre, im: im + diffim }, FFTComplex { re: re + diffre, im: im - diffim })
143 fn new_data(size: usize, forward: bool) -> FFTData {
144 let mut table: Vec<FFTComplex> = Vec::with_capacity(size * size);
145 table.resize(size * size, FFTC_ZERO);
146 let base = consts::PI * 2.0 / (size as f32);
150 table[n * size + k] = FFTComplex::exp(-base * ((n * k) as f32));
156 table[n * size + k] = FFTComplex::exp( base * ((n * k) as f32));
160 let mut tmp = Vec::with_capacity(size);
161 tmp.resize(size, FFTC_ZERO);
162 FFTData { table, tmp, twiddle: Vec::new(), size, step: 0, div: 0 }
164 fn fft(tbl: &mut FFTData, size: usize, data: &mut [FFTComplex], step: usize) {
166 let s0 = data[step * 0];
167 let s1 = data[step * 1];
168 let s2 = data[step * 2];
170 data[step * 0] += t0;
171 let t1 = s0 - t0.scale(0.5);
172 let t2 = (s2 - s1).rotate().scale(FFT3_CONST);
173 data[step * 1] = t1 + t2;
174 data[step * 2] = t1 - t2;
178 let s0 = data[step * 0];
179 let s1 = data[step * 1];
180 let s2 = data[step * 2];
181 let s3 = data[step * 3];
182 let s4 = data[step * 4];
188 let (t4, t5) = twiddle5(t0, t1, FFT5_CONST2);
189 let (t6, t7) = twiddle5(t2, t3, FFT5_CONST1);
190 let (t8, t9) = twiddle5(t0, t1, FFT5_CONST1);
191 let (ta, tb) = twiddle5(t2, t3, FFT5_CONST2);
193 data[step * 0] = s0 + t0 + t2;
194 data[step * 1] = s0 + t5 - t6;
195 data[step * 2] = s0 - t8 + ta;
196 data[step * 3] = s0 - t9 + tb;
197 data[step * 4] = s0 + t4 - t7;
200 for k in 0..tbl.size {
201 tbl.tmp[k] = FFTC_ZERO;
202 for n in 0..tbl.size {
203 tbl.tmp[k] += data[n * step] * tbl.table[k * tbl.size + n];
206 for n in 0..tbl.size {
207 data[n * step] = tbl.tmp[n];
210 fn ifft(tbl: &mut FFTData, size: usize, data: &mut [FFTComplex], step: usize) {
212 let s0 = data[step * 0];
213 let s1 = data[step * 1];
214 let s2 = data[step * 2];
216 data[step * 0] += t0;
217 let t1 = s0 - t0.scale(0.5);
218 let t2 = (s2 - s1).rotate().scale(FFT3_CONST);
219 data[step * 1] = t1 - t2;
220 data[step * 2] = t1 + t2;
224 let s0 = data[step * 0];
225 let s1 = data[step * 1];
226 let s2 = data[step * 2];
227 let s3 = data[step * 3];
228 let s4 = data[step * 4];
234 let (t4, t5) = twiddle5(t0, t1, FFT5_CONST2);
235 let (t6, t7) = twiddle5(t2, t3, FFT5_CONST1);
236 let (t8, t9) = twiddle5(t0, t1, FFT5_CONST1);
237 let (ta, tb) = twiddle5(t2, t3, FFT5_CONST2);
239 data[step * 0] = s0 + t0 + t2;
240 data[step * 1] = s0 + t4 - t7;
241 data[step * 2] = s0 - t9 + tb;
242 data[step * 3] = s0 - t8 + ta;
243 data[step * 4] = s0 + t5 - t6;
246 Self::fft(tbl, size, data, step);
250 struct FFTSplitRadix {}
253 fn new_data(bits: u8, _forward: bool) -> FFTData {
254 let size = 1 << bits;
255 let mut table = Vec::with_capacity(size);
256 for _ in 0..4 { table.push(FFTC_ZERO); }
258 let qsize = (1 << (b - 2)) as usize;
259 let base = -consts::PI / ((qsize * 2) as f32);
261 table.push(FFTComplex::exp(base * ((k * 1) as f32)));
262 table.push(FFTComplex::exp(base * ((k * 3) as f32)));
265 FFTData { table, tmp: Vec::new(), twiddle: Vec::new(), size, step: 0, div: 0 }
267 fn fft(fftdata: &mut FFTData, bits: u8, data: &mut [FFTComplex]) {
268 if bits == 0 { return; }
270 let sum01 = data[0] + data[1];
271 let dif01 = data[0] - data[1];
277 let sum01 = data[0] + data[2];
278 let dif01 = data[0] - data[2];
279 let sum23 = data[1] + data[3];
280 let dif23 = data[1] - data[3];
281 data[0] = sum01 + sum23;
282 data[1] = dif01 - dif23.rotate();
283 data[2] = sum01 - sum23;
284 data[3] = dif01 + dif23.rotate();
287 let qsize = (1 << (bits - 2)) as usize;
288 let hsize = (1 << (bits - 1)) as usize;
289 let q3size = qsize + hsize;
291 Self::fft(fftdata, bits - 1, &mut data[0 ..hsize]);
292 Self::fft(fftdata, bits - 2, &mut data[hsize ..q3size]);
293 Self::fft(fftdata, bits - 2, &mut data[q3size..]);
296 let t3 = data[0 + hsize] + data[0 + q3size];
297 let t4 = (data[0 + hsize] - data[0 + q3size]).rotate();
299 let e2 = data[0 + qsize];
301 data[0 + qsize] = e2 - t4;
302 data[0 + hsize] = e1 - t3;
303 data[0 + q3size] = e2 + t4;
306 let t1 = fftdata.table[off + k * 2 + 0] * data[k + hsize];
307 let t2 = fftdata.table[off + k * 2 + 1] * data[k + q3size];
309 let t4 = (t1 - t2).rotate();
311 let e2 = data[k + qsize];
313 data[k + qsize] = e2 - t4;
314 data[k + hsize] = e1 - t3;
315 data[k + qsize * 3] = e2 + t4;
318 fn ifft(fftdata: &mut FFTData, bits: u8, data: &mut [FFTComplex]) {
319 if bits == 0 { return; }
321 let sum01 = data[0] + data[1];
322 let dif01 = data[0] - data[1];
328 let sum01 = data[0] + data[2];
329 let dif01 = data[0] - data[2];
330 let sum23 = data[1] + data[3];
331 let dif23 = data[1] - data[3];
332 data[0] = sum01 + sum23;
333 data[1] = dif01 + dif23.rotate();
334 data[2] = sum01 - sum23;
335 data[3] = dif01 - dif23.rotate();
338 let qsize = (1 << (bits - 2)) as usize;
339 let hsize = (1 << (bits - 1)) as usize;
340 let q3size = qsize + hsize;
342 Self::ifft(fftdata, bits - 1, &mut data[0 ..hsize]);
343 Self::ifft(fftdata, bits - 2, &mut data[hsize ..q3size]);
344 Self::ifft(fftdata, bits - 2, &mut data[q3size..]);
347 let t3 = data[0 + hsize] + data[0 + q3size];
348 let t4 = (data[0 + hsize] - data[0 + q3size]).rotate();
350 let e2 = data[0 + qsize];
352 data[0 + qsize] = e2 + t4;
353 data[0 + hsize] = e1 - t3;
354 data[0 + q3size] = e2 - t4;
357 let t1 = !fftdata.table[off + k * 2 + 0] * data[k + hsize];
358 let t2 = !fftdata.table[off + k * 2 + 1] * data[k + q3size];
360 let t4 = (t1 - t2).rotate();
362 let e2 = data[k + qsize];
364 data[k + qsize] = e2 + t4;
365 data[k + hsize] = e1 - t3;
366 data[k + qsize * 3] = e2 - t4;
373 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 ];
374 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 ];
377 fn new_data(size: usize, _forward: bool) -> FFTData {
378 FFTData { table: Vec::new(), tmp: Vec::new(), twiddle: Vec::new(), size, step: 0, div: 0 }
380 fn fft3(dst: &mut [FFTComplex], src: &[FFTComplex], step: usize, n: usize) {
386 let t1 = s0 - t0.scale(0.5);
387 let t2 = (s2 - s1).rotate().scale(FFT3_CONST);
389 dst[FFT15_OUTSWAP[n * 4 + 0] * step] = s0 + t0;
390 dst[FFT15_OUTSWAP[n * 4 + 1] * step] = t1 + t2;
391 dst[FFT15_OUTSWAP[n * 4 + 2] * step] = t1 - t2;
393 fn ifft3(dst: &mut [FFTComplex], src: &[FFTComplex], step: usize, n: usize) {
399 let t1 = s0 - t0.scale(0.5);
400 let t2 = (s2 - s1).rotate().scale(FFT3_CONST);
402 dst[FFT15_OUTSWAP[n * 4 + 0] * step] = s0 + t0;
403 dst[FFT15_OUTSWAP[n * 4 + 1] * step] = t1 - t2;
404 dst[FFT15_OUTSWAP[n * 4 + 2] * step] = t1 + t2;
406 fn fft5(dst: &mut [FFTComplex], src: &[FFTComplex], step: usize, n: usize) {
407 let s0 = src[FFT15_INSWAP[n + 0 * 4] * step];
408 let s1 = src[FFT15_INSWAP[n + 1 * 4] * step];
409 let s2 = src[FFT15_INSWAP[n + 2 * 4] * step];
410 let s3 = src[FFT15_INSWAP[n + 3 * 4] * step];
411 let s4 = src[FFT15_INSWAP[n + 4 * 4] * step];
417 let (t4, t5) = twiddle5(t0, t1, FFT5_CONST2);
418 let (t6, t7) = twiddle5(t2, t3, FFT5_CONST1);
419 let (t8, t9) = twiddle5(t0, t1, FFT5_CONST1);
420 let (ta, tb) = twiddle5(t2, t3, FFT5_CONST2);
422 dst[0 * 3] = s0 + t0 + t2;
423 dst[1 * 3] = s0 + t5 - t6;
424 dst[2 * 3] = s0 - t8 + ta;
425 dst[3 * 3] = s0 - t9 + tb;
426 dst[4 * 3] = s0 + t4 - t7;
428 fn ifft5(dst: &mut [FFTComplex], src: &[FFTComplex], step: usize, n: usize) {
429 let s0 = src[FFT15_INSWAP[n + 0 * 4] * step];
430 let s1 = src[FFT15_INSWAP[n + 1 * 4] * step];
431 let s2 = src[FFT15_INSWAP[n + 2 * 4] * step];
432 let s3 = src[FFT15_INSWAP[n + 3 * 4] * step];
433 let s4 = src[FFT15_INSWAP[n + 4 * 4] * step];
439 let (t4, t5) = twiddle5(t0, t1, FFT5_CONST2);
440 let (t6, t7) = twiddle5(t2, t3, FFT5_CONST1);
441 let (t8, t9) = twiddle5(t0, t1, FFT5_CONST1);
442 let (ta, tb) = twiddle5(t2, t3, FFT5_CONST2);
444 dst[0 * 3] = s0 + t0 + t2;
445 dst[1 * 3] = s0 + t4 - t7;
446 dst[2 * 3] = s0 - t9 + tb;
447 dst[3 * 3] = s0 - t8 + ta;
448 dst[4 * 3] = s0 + t5 - t6;
450 fn fft(_fftdata: &mut FFTData, data: &mut [FFTComplex], step: usize) {
451 let mut tmp = [FFTC_ZERO; 15];
453 Self::fft5(&mut tmp[n..], data, step, n);
456 Self::fft3(data, &tmp[n * 3..][..3], step, n);
459 fn ifft(_fftdata: &mut FFTData, data: &mut [FFTComplex], step: usize) {
460 let mut tmp = [FFTC_ZERO; 15];
462 Self::ifft5(&mut tmp[n..], data, step, n);
465 Self::ifft3(data, &tmp[n * 3..][..3], step, n);
478 fn permute(&self, perms: &mut [usize]) {
480 FFTMode::Generic(_) => {},
481 FFTMode::SplitRadix(bits) => {
482 let div = perms.len() >> bits;
483 gen_sr_perms(perms, 1 << bits);
485 for i in 0..(1 << bits) {
489 for j in 0..(1 << bits) {
490 perms[(i << bits) + j] = perms[j] + i;
495 FFTMode::Prime15 => {},
498 fn do_fft(&self, fftdata: &mut FFTData, data: &mut [FFTComplex]) {
500 FFTMode::Generic(size) => FFTGeneric::fft(fftdata, size, data, 1),
501 FFTMode::SplitRadix(bits) => FFTSplitRadix::fft(fftdata, bits, data),
502 FFTMode::Prime15 => FFT15::fft(fftdata, data, 1),
505 fn do_fft2(&self, fftdata: &mut FFTData, data: &mut [FFTComplex], step: usize) {
507 FFTMode::Generic(size) => FFTGeneric::fft(fftdata, size, data, step),
508 FFTMode::SplitRadix(_) => unreachable!(),
509 FFTMode::Prime15 => FFT15::fft(fftdata, data, step),
512 fn do_ifft(&self, fftdata: &mut FFTData, data: &mut [FFTComplex]) {
514 FFTMode::Generic(size) => FFTGeneric::ifft(fftdata, size, data, 1),
515 FFTMode::SplitRadix(bits) => FFTSplitRadix::ifft(fftdata, bits, data),
516 FFTMode::Prime15 => FFT15::ifft(fftdata, data, 1),
519 fn do_ifft2(&self, fftdata: &mut FFTData, data: &mut [FFTComplex], step: usize) {
521 FFTMode::Generic(size) => FFTGeneric::ifft(fftdata, size, data, step),
522 FFTMode::SplitRadix(_) => unreachable!(),
523 FFTMode::Prime15 => FFT15::ifft(fftdata, data, step),
526 fn get_size(&self) -> usize {
528 FFTMode::Generic(size) => size,
529 FFTMode::SplitRadix(bits) => 1 << bits,
530 FFTMode::Prime15 => 15,
535 /// FFT working context.
539 ffts: Vec<(FFTMode, FFTData)>,
543 /// Calculates Fourier transform.
544 pub fn do_fft(&mut self, src: &[FFTComplex], dst: &mut [FFTComplex]) {
545 for k in 0..src.len() { dst[k] = src[self.perms[k]]; }
546 self.do_fft_core(dst);
548 /// Calculates inverse Fourier transform.
549 pub fn do_ifft(&mut self, src: &[FFTComplex], dst: &mut [FFTComplex]) {
550 for k in 0..src.len() { dst[k] = src[self.perms[k]]; }
551 self.do_ifft_core(dst);
553 /// Performs inplace FFT.
554 pub fn do_fft_inplace(&mut self, data: &mut [FFTComplex]) {
555 for idx in 0..self.swaps.len() {
556 let nidx = self.swaps[idx];
558 data.swap(nidx, idx);
561 self.do_fft_core(data);
563 /// Performs inplace inverse FFT.
564 pub fn do_ifft_inplace(&mut self, data: &mut [FFTComplex]) {
565 for idx in 0..self.swaps.len() {
566 let nidx = self.swaps[idx];
568 data.swap(nidx, idx);
571 self.do_ifft_core(data);
573 fn do_fft_core(&mut self, data: &mut [FFTComplex]) {
574 for el in self.ffts.iter_mut() {
575 let (mode, ref mut fftdata) = el;
576 let bsize = mode.get_size();
577 let div = fftdata.div;
578 let step = fftdata.step;
580 mode.do_fft(fftdata, data);
582 mode.do_fft(fftdata, &mut data[i * bsize..]);
585 mode.do_fft2(fftdata, data, div);
586 let mut toff = bsize;
589 data[i + j * div] *= fftdata.twiddle[toff + j];
591 mode.do_fft2(fftdata, &mut data[i..], div);
597 fn do_ifft_core(&mut self, data: &mut [FFTComplex]) {
598 for el in self.ffts.iter_mut() {
599 let (mode, ref mut fftdata) = el;
600 let bsize = mode.get_size();
601 let div = fftdata.div;
602 let step = fftdata.step;
604 mode.do_ifft(fftdata, data);
606 mode.do_ifft(fftdata, &mut data[i * bsize..]);
609 mode.do_ifft2(fftdata, data, div);
610 let mut toff = bsize;
613 data[i + j * div] *= fftdata.twiddle[toff + j];
615 mode.do_ifft2(fftdata, &mut data[i..], div);
623 /// [`FFT`] context creator.
625 /// [`FFT`]: ./struct.FFT.html
626 pub struct FFTBuilder {
629 /*fn reverse_bits(inval: u32) -> u32 {
630 const REV_TAB: [u8; 16] = [
631 0b0000, 0b1000, 0b0100, 0b1100, 0b0010, 0b1010, 0b0110, 0b1110,
632 0b0001, 0b1001, 0b0101, 0b1101, 0b0011, 0b1011, 0b0111, 0b1111,
638 ret = (ret << 4) | (REV_TAB[(val & 0xF) as usize] as u32);
644 fn swp_idx(idx: usize, bits: u32) -> usize {
645 let s = reverse_bits(idx as u32) as usize;
649 fn gen_sr_perms(swaps: &mut [usize], size: usize) {
650 if size <= 4 { return; }
651 let mut evec: Vec<usize> = Vec::with_capacity(size / 2);
652 let mut ovec1: Vec<usize> = Vec::with_capacity(size / 4);
653 let mut ovec2: Vec<usize> = Vec::with_capacity(size / 4);
655 evec.push (swaps[k * 4 + 0]);
656 ovec1.push(swaps[k * 4 + 1]);
657 evec.push (swaps[k * 4 + 2]);
658 ovec2.push(swaps[k * 4 + 3]);
660 for k in 0..size/2 { swaps[k] = evec[k]; }
661 for k in 0..size/4 { swaps[k + size/2] = ovec1[k]; }
662 for k in 0..size/4 { swaps[k + 3*size/4] = ovec2[k]; }
663 gen_sr_perms(&mut swaps[0..size/2], size/2);
664 gen_sr_perms(&mut swaps[size/2..3*size/4], size/4);
665 gen_sr_perms(&mut swaps[3*size/4..], size/4);
668 fn gen_swaps_for_perm(swaps: &mut Vec<usize>, perms: &[usize]) {
669 let mut idx_arr: Vec<usize> = Vec::with_capacity(perms.len());
670 for i in 0..perms.len() { idx_arr.push(i); }
671 let mut run_size = 0;
673 for idx in 0..perms.len() {
674 if perms[idx] == idx_arr[idx] {
675 if run_size == 0 { run_pos = idx; }
678 for i in 0..run_size {
679 swaps.push(run_pos + i);
682 let mut spos = idx + 1;
683 while idx_arr[spos] != perms[idx] { spos += 1; }
684 idx_arr[spos] = idx_arr[idx];
685 idx_arr[idx] = perms[idx];
692 fn generate_twiddle(data: &mut FFTData, size: usize, cur_size: usize, forward: bool) {
693 if size == cur_size { return; }
694 data.twiddle = Vec::with_capacity(size);
695 let div = size / cur_size;
696 let base = if forward { -2.0 * consts::PI / (size as f32) } else { 2.0 * consts::PI / (size as f32) };
698 for k in 0..cur_size {
699 data.twiddle.push(FFTComplex::exp(base * ((k * n) as f32)));
703 /// Constructs a new `FFT` context.
704 pub fn new_fft(size: usize, forward: bool) -> FFT {
705 let mut ffts: Vec<(FFTMode, FFTData)> = Vec::with_capacity(1);
706 let mut perms: Vec<usize> = Vec::with_capacity(size);
707 let mut swaps: Vec<usize> = Vec::with_capacity(size);
708 let mut rem_size = size;
709 if rem_size.trailing_zeros() > 0 {
710 let bits = rem_size.trailing_zeros() as u8;
711 let mut data = FFTSplitRadix::new_data(bits, forward);
712 Self::generate_twiddle(&mut data, size, 1 << bits, forward);
714 data.div = rem_size >> bits;
715 ffts.push((FFTMode::SplitRadix(bits), data));
718 if (rem_size % 15) == 0 {
719 let mut data = FFT15::new_data(size, forward);
720 Self::generate_twiddle(&mut data, size, 15, forward);
721 data.step = size / rem_size;
722 data.div = size / rem_size;
723 ffts.push((FFTMode::Prime15, data));
727 let mut data = FFTGeneric::new_data(rem_size, forward);
728 Self::generate_twiddle(&mut data, size, rem_size, forward);
729 data.step = size / rem_size;
730 data.div = size / rem_size;
731 ffts.push((FFTMode::Generic(rem_size), data));
737 for (mode, _) in ffts.iter().rev() {
738 mode.permute(&mut perms);
740 gen_swaps_for_perm(&mut swaps, perms.as_slice());
742 FFT { perms, swaps, ffts }
746 /// RDFT working context.
748 table: Vec<FFTComplex>,
755 fn crossadd(a: FFTComplex, b: FFTComplex) -> FFTComplex {
756 FFTComplex { re: a.re + b.re, im: a.im - b.im }
761 pub fn do_rdft(&mut self, src: &[FFTComplex], dst: &mut [FFTComplex]) {
762 dst.copy_from_slice(src);
763 self.do_rdft_inplace(dst);
765 /// Calculates inplace RDFT.
766 pub fn do_rdft_inplace(&mut self, buf: &mut [FFTComplex]) {
768 for n in 0..self.size/2 {
769 let in0 = buf[n + 1];
770 let in1 = buf[self.size - n - 1];
772 let t0 = crossadd(in0, in1);
773 let t1 = FFTComplex { re: in1.im + in0.im, im: in1.re - in0.re };
774 let tab = self.table[n];
775 let t2 = FFTComplex { re: t1.im * tab.im + t1.re * tab.re, im: t1.im * tab.re - t1.re * tab.im };
777 buf[n + 1] = FFTComplex { re: t0.im - t2.im, im: t0.re - t2.re }; // (t0 - t2).conj().rotate()
778 buf[self.size - n - 1] = (t0 + t2).rotate();
786 self.fft.do_fft_inplace(buf);
788 self.fft.do_ifft_inplace(buf);
791 for n in 0..self.size/2 {
792 let in0 = buf[n + 1];
793 let in1 = buf[self.size - n - 1];
795 let t0 = crossadd(in0, in1).scale(0.5);
796 let t1 = FFTComplex { re: in0.im + in1.im, im: in0.re - in1.re };
797 let t2 = t1 * self.table[n];
799 buf[n + 1] = crossadd(t0, t2);
800 buf[self.size - n - 1] = FFTComplex { re: t0.re - t2.re, im: -(t0.im + t2.im) };
807 for n in 0..self.size {
808 buf[n] = FFTComplex{ re: buf[n].im, im: buf[n].re };
814 /// [`RDFT`] context creator.
816 /// [`RDFT`]: ./struct.FFT.html
817 pub struct RDFTBuilder {
821 /// Constructs a new `RDFT` context.
822 pub fn new_rdft(size: usize, forward: bool, forward_fft: bool) -> RDFT {
823 let mut table: Vec<FFTComplex> = Vec::with_capacity(size / 4);
824 let (base, scale) = if forward { (consts::PI / (size as f32), 0.5) } else { (-consts::PI / (size as f32), 1.0) };
826 table.push(FFTComplex::exp(base * ((i + 1) as f32)).scale(scale));
828 let fft = FFTBuilder::new_fft(size, forward_fft);
829 RDFT { table, fft, size, fwd: forward, fwd_fft: forward_fft }
838 fn test_fft(size: usize) {
839 println!("testing FFT {}", size);
840 let mut fin: Vec<FFTComplex> = Vec::with_capacity(size);
841 let mut fout1: Vec<FFTComplex> = Vec::with_capacity(size);
842 let mut fout2: Vec<FFTComplex> = Vec::with_capacity(size);
843 fin.resize(size, FFTC_ZERO);
844 fout1.resize(size, FFTC_ZERO);
845 fout2.resize(size, FFTC_ZERO);
846 let mut fft = FFTBuilder::new_fft(size, true);
847 let mut seed: u32 = 42;
848 for i in 0..fin.len() {
849 seed = seed.wrapping_mul(1664525).wrapping_add(1013904223);
850 let val = (seed >> 16) as i16;
851 fin[i].re = (val as f32) / 256.0;
852 seed = seed.wrapping_mul(1664525).wrapping_add(1013904223);
853 let val = (seed >> 16) as i16;
854 fin[i].im = (val as f32) / 256.0;
856 fft.do_fft(&fin, &mut fout1);
857 fout2.copy_from_slice(&fin);
858 generic_fft(&mut fout2, true);
860 for i in 0..fin.len() {
861 assert!((fout1[i].re - fout2[i].re).abs() < 1.0);
862 assert!((fout1[i].im - fout2[i].im).abs() < 1.0);
864 let mut ifft = FFTBuilder::new_fft(size, false);
865 ifft.do_ifft_inplace(&mut fout1);
866 generic_fft(&mut fout2, false);
868 let sc = 1.0 / (size as f32);
869 for i in 0..fin.len() {
870 assert!((fin[i].re - fout1[i].re * sc).abs() < 1.0);
871 assert!((fin[i].im - fout1[i].im * sc).abs() < 1.0);
872 assert!((fout1[i].re - fout2[i].re).abs() * sc < 1.0);
873 assert!((fout1[i].im - fout2[i].im).abs() * sc < 1.0);
890 let mut fin: [FFTComplex; 128] = [FFTC_ZERO; 128];
891 let mut fout1: [FFTComplex; 128] = [FFTC_ZERO; 128];
892 let mut rdft = RDFTBuilder::new_rdft(fin.len(), true, true);
893 let mut seed: u32 = 42;
894 for i in 0..fin.len() {
895 seed = seed.wrapping_mul(1664525).wrapping_add(1013904223);
896 let val = (seed >> 16) as i16;
897 fin[i].re = (val as f32) / 256.0;
898 seed = seed.wrapping_mul(1664525).wrapping_add(1013904223);
899 let val = (seed >> 16) as i16;
900 fin[i].im = (val as f32) / 256.0;
902 rdft.do_rdft(&fin, &mut fout1);
903 let mut irdft = RDFTBuilder::new_rdft(fin.len(), false, true);
904 irdft.do_rdft_inplace(&mut fout1);
906 for i in 0..fin.len() {
907 let tst = fout1[i].scale(0.5/(fout1.len() as f32));
908 assert!((tst.re - fin[i].re).abs() < 1.0);
909 assert!((tst.im - fin[i].im).abs() < 1.0);