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3f3b5b23 KS |
1 | use std::f32::{self, consts}; |
2 | use std::ops::{Not, Neg, Add, AddAssign, Sub, SubAssign, Mul, MulAssign}; | |
3 | use std::fmt; | |
4 | ||
5 | #[derive(Debug,Clone,Copy,PartialEq)] | |
6 | pub struct FFTComplex { | |
7 | pub re: f32, | |
8 | pub im: f32, | |
9 | } | |
10 | ||
11 | impl FFTComplex { | |
12 | pub fn exp(val: f32) -> Self { | |
13 | FFTComplex { re: val.cos(), im: val.sin() } | |
14 | } | |
15 | pub fn rotate(self) -> Self { | |
16 | FFTComplex { re: -self.im, im: self.re } | |
17 | } | |
18 | pub fn scale(self, scale: f32) -> Self { | |
19 | FFTComplex { re: self.re * scale, im: self.im * scale } | |
20 | } | |
21 | } | |
22 | ||
23 | impl Neg for FFTComplex { | |
24 | type Output = FFTComplex; | |
25 | fn neg(self) -> Self::Output { | |
26 | FFTComplex { re: -self.re, im: -self.im } | |
27 | } | |
28 | } | |
29 | ||
30 | impl Not for FFTComplex { | |
31 | type Output = FFTComplex; | |
32 | fn not(self) -> Self::Output { | |
33 | FFTComplex { re: self.re, im: -self.im } | |
34 | } | |
35 | } | |
36 | ||
37 | impl Add for FFTComplex { | |
38 | type Output = FFTComplex; | |
39 | fn add(self, other: Self) -> Self::Output { | |
40 | FFTComplex { re: self.re + other.re, im: self.im + other.im } | |
41 | } | |
42 | } | |
43 | ||
44 | impl AddAssign for FFTComplex { | |
45 | fn add_assign(&mut self, other: Self) { | |
46 | self.re += other.re; | |
47 | self.im += other.im; | |
48 | } | |
49 | } | |
50 | ||
51 | impl Sub for FFTComplex { | |
52 | type Output = FFTComplex; | |
53 | fn sub(self, other: Self) -> Self::Output { | |
54 | FFTComplex { re: self.re - other.re, im: self.im - other.im } | |
55 | } | |
56 | } | |
57 | ||
58 | impl SubAssign for FFTComplex { | |
59 | fn sub_assign(&mut self, other: Self) { | |
60 | self.re -= other.re; | |
61 | self.im -= other.im; | |
62 | } | |
63 | } | |
64 | ||
65 | impl Mul for FFTComplex { | |
66 | type Output = FFTComplex; | |
67 | fn mul(self, other: Self) -> Self::Output { | |
68 | FFTComplex { re: self.re * other.re - self.im * other.im, | |
69 | im: self.im * other.re + self.re * other.im } | |
70 | } | |
71 | } | |
72 | ||
73 | impl MulAssign for FFTComplex { | |
74 | fn mul_assign(&mut self, other: Self) { | |
75 | let re = self.re * other.re - self.im * other.im; | |
76 | let im = self.im * other.re + self.re * other.im; | |
77 | self.re = re; | |
78 | self.im = im; | |
79 | } | |
80 | } | |
81 | ||
82 | impl fmt::Display for FFTComplex { | |
83 | fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { | |
84 | write!(f, "({}, {})", self.re, self.im) | |
85 | } | |
86 | } | |
87 | ||
88 | pub const FFTC_ZERO: FFTComplex = FFTComplex { re: 0.0, im: 0.0 }; | |
89 | ||
90 | #[derive(Debug,Clone,Copy,PartialEq)] | |
91 | pub enum FFTMode { | |
92 | Matrix, | |
93 | CooleyTukey, | |
94 | SplitRadix, | |
95 | } | |
96 | ||
97 | pub struct FFT { | |
98 | table: Vec<FFTComplex>, | |
99 | perms: Vec<usize>, | |
100 | swaps: Vec<usize>, | |
101 | bits: u32, | |
102 | mode: FFTMode, | |
103 | } | |
104 | ||
105 | impl FFT { | |
106 | fn do_fft_inplace_ct(&mut self, data: &mut [FFTComplex], bits: u32, forward: bool) { | |
107 | if bits == 0 { return; } | |
108 | if bits == 1 { | |
109 | let sum01 = data[0] + data[1]; | |
110 | let dif01 = data[0] - data[1]; | |
111 | data[0] = sum01; | |
112 | data[1] = dif01; | |
113 | return; | |
114 | } | |
115 | if bits == 2 { | |
116 | let sum01 = data[0] + data[1]; | |
117 | let dif01 = data[0] - data[1]; | |
118 | let sum23 = data[2] + data[3]; | |
119 | let dif23 = data[2] - data[3]; | |
120 | if forward { | |
121 | data[0] = sum01 + sum23; | |
122 | data[1] = dif01 - dif23.rotate(); | |
123 | data[2] = sum01 - sum23; | |
124 | data[3] = dif01 + dif23.rotate(); | |
125 | } else { | |
126 | data[0] = sum01 + sum23; | |
127 | data[1] = dif01 + dif23.rotate(); | |
128 | data[2] = sum01 - sum23; | |
129 | data[3] = dif01 - dif23.rotate(); | |
130 | } | |
131 | return; | |
132 | } | |
133 | ||
134 | let hsize = (1 << (bits - 1)) as usize; | |
135 | self.do_fft_inplace_ct(&mut data[0..hsize], bits - 1, forward); | |
136 | self.do_fft_inplace_ct(&mut data[hsize..], bits - 1, forward); | |
137 | let offs = hsize; | |
138 | { | |
139 | let e = data[0]; | |
140 | let o = data[hsize]; | |
141 | data[0] = e + o; | |
142 | data[hsize] = e - o; | |
143 | } | |
144 | if forward { | |
145 | for k in 1..hsize { | |
146 | let e = data[k]; | |
147 | let o = data[k + hsize] * self.table[offs + k]; | |
148 | data[k] = e + o; | |
149 | data[k + hsize] = e - o; | |
150 | } | |
151 | } else { | |
152 | for k in 1..hsize { | |
153 | let e = data[k]; | |
154 | let o = data[k + hsize] * !self.table[offs + k]; | |
155 | data[k] = e + o; | |
156 | data[k + hsize] = e - o; | |
157 | } | |
158 | } | |
159 | } | |
160 | ||
161 | fn do_fft_inplace_splitradix(&mut self, data: &mut [FFTComplex], bits: u32, forward: bool) { | |
162 | if bits == 0 { return; } | |
163 | if bits == 1 { | |
164 | let sum01 = data[0] + data[1]; | |
165 | let dif01 = data[0] - data[1]; | |
166 | data[0] = sum01; | |
167 | data[1] = dif01; | |
168 | return; | |
169 | } | |
170 | if bits == 2 { | |
171 | let sum01 = data[0] + data[2]; | |
172 | let dif01 = data[0] - data[2]; | |
173 | let sum23 = data[1] + data[3]; | |
174 | let dif23 = data[1] - data[3]; | |
175 | if forward { | |
176 | data[0] = sum01 + sum23; | |
177 | data[1] = dif01 - dif23.rotate(); | |
178 | data[2] = sum01 - sum23; | |
179 | data[3] = dif01 + dif23.rotate(); | |
180 | } else { | |
181 | data[0] = sum01 + sum23; | |
182 | data[1] = dif01 + dif23.rotate(); | |
183 | data[2] = sum01 - sum23; | |
184 | data[3] = dif01 - dif23.rotate(); | |
185 | } | |
186 | return; | |
187 | } | |
188 | let qsize = (1 << (bits - 2)) as usize; | |
189 | let hsize = (1 << (bits - 1)) as usize; | |
190 | let q3size = qsize + hsize; | |
191 | ||
192 | self.do_fft_inplace_splitradix(&mut data[0 ..hsize], bits - 1, forward); | |
193 | self.do_fft_inplace_splitradix(&mut data[hsize ..q3size], bits - 2, forward); | |
194 | self.do_fft_inplace_splitradix(&mut data[q3size..], bits - 2, forward); | |
195 | let off = hsize; | |
196 | if forward { | |
197 | { | |
198 | let t3 = data[0 + hsize] + data[0 + q3size]; | |
199 | let t4 = (data[0 + hsize] - data[0 + q3size]).rotate(); | |
200 | let e1 = data[0]; | |
201 | let e2 = data[0 + qsize]; | |
202 | data[0] = e1 + t3; | |
203 | data[0 + qsize] = e2 - t4; | |
204 | data[0 + hsize] = e1 - t3; | |
205 | data[0 + q3size] = e2 + t4; | |
206 | } | |
207 | for k in 1..qsize { | |
208 | let t1 = self.table[off + k * 2 + 0] * data[k + hsize]; | |
209 | let t2 = self.table[off + k * 2 + 1] * data[k + q3size]; | |
210 | let t3 = t1 + t2; | |
211 | let t4 = (t1 - t2).rotate(); | |
212 | let e1 = data[k]; | |
213 | let e2 = data[k + qsize]; | |
214 | data[k] = e1 + t3; | |
215 | data[k + qsize] = e2 - t4; | |
216 | data[k + hsize] = e1 - t3; | |
217 | data[k + qsize * 3] = e2 + t4; | |
218 | } | |
219 | } else { | |
220 | { | |
221 | let t3 = data[0 + hsize] + data[0 + q3size]; | |
222 | let t4 = (data[0 + hsize] - data[0 + q3size]).rotate(); | |
223 | let e1 = data[0]; | |
224 | let e2 = data[0 + qsize]; | |
225 | data[0] = e1 + t3; | |
226 | data[0 + qsize] = e2 + t4; | |
227 | data[0 + hsize] = e1 - t3; | |
228 | data[0 + q3size] = e2 - t4; | |
229 | } | |
230 | for k in 1..qsize { | |
231 | let t1 = !self.table[off + k * 2 + 0] * data[k + hsize]; | |
232 | let t2 = !self.table[off + k * 2 + 1] * data[k + q3size]; | |
233 | let t3 = t1 + t2; | |
234 | let t4 = (t1 - t2).rotate(); | |
235 | let e1 = data[k]; | |
236 | let e2 = data[k + qsize]; | |
237 | data[k] = e1 + t3; | |
238 | data[k + qsize] = e2 + t4; | |
239 | data[k + hsize] = e1 - t3; | |
240 | data[k + qsize * 3] = e2 - t4; | |
241 | } | |
242 | } | |
243 | } | |
244 | ||
245 | pub fn do_fft(&mut self, src: &[FFTComplex], dst: &mut [FFTComplex], forward: bool) { | |
246 | match self.mode { | |
247 | FFTMode::Matrix => { | |
248 | let base = if forward { -consts::PI * 2.0 / (src.len() as f32) } | |
249 | else { consts::PI * 2.0 / (src.len() as f32) }; | |
250 | for k in 0..src.len() { | |
251 | let mut sum = FFTC_ZERO; | |
252 | for n in 0..src.len() { | |
253 | let w = FFTComplex::exp(base * ((n * k) as f32)); | |
254 | sum += src[n] * w; | |
255 | } | |
256 | dst[k] = sum; | |
257 | } | |
258 | }, | |
259 | FFTMode::CooleyTukey => { | |
260 | let bits = self.bits; | |
261 | for k in 0..src.len() { dst[k] = src[self.perms[k]]; } | |
262 | self.do_fft_inplace_ct(dst, bits, forward); | |
263 | }, | |
264 | FFTMode::SplitRadix => { | |
265 | let bits = self.bits; | |
266 | for k in 0..src.len() { dst[k] = src[self.perms[k]]; } | |
267 | self.do_fft_inplace_splitradix(dst, bits, forward); | |
268 | }, | |
269 | }; | |
270 | } | |
271 | ||
272 | pub fn do_fft_inplace(&mut self, data: &mut [FFTComplex], forward: bool) { | |
273 | for idx in 0..self.swaps.len() { | |
274 | let nidx = self.swaps[idx]; | |
275 | if idx != nidx { | |
276 | let t = data[nidx]; | |
277 | data[nidx] = data[idx]; | |
278 | data[idx] = t; | |
279 | } | |
280 | } | |
281 | match self.mode { | |
282 | FFTMode::Matrix => { | |
283 | let size = (1 << self.bits) as usize; | |
284 | let base = if forward { -consts::PI * 2.0 / (size as f32) } | |
285 | else { consts::PI * 2.0 / (size as f32) }; | |
286 | let mut res: Vec<FFTComplex> = Vec::with_capacity(size); | |
287 | for k in 0..size { | |
288 | let mut sum = FFTC_ZERO; | |
289 | for n in 0..size { | |
290 | let w = FFTComplex::exp(base * ((n * k) as f32)); | |
291 | sum += data[n] * w; | |
292 | } | |
293 | res.push(sum); | |
294 | } | |
295 | for k in 0..size { | |
296 | data[k] = res[k]; | |
297 | } | |
298 | }, | |
299 | FFTMode::CooleyTukey => { | |
300 | let bits = self.bits; | |
301 | self.do_fft_inplace_ct(data, bits, forward); | |
302 | }, | |
303 | FFTMode::SplitRadix => { | |
304 | let bits = self.bits; | |
305 | self.do_fft_inplace_splitradix(data, bits, forward); | |
306 | }, | |
307 | }; | |
308 | } | |
309 | } | |
310 | ||
311 | pub struct FFTBuilder { | |
312 | } | |
313 | ||
314 | fn reverse_bits(inval: u32) -> u32 { | |
315 | const REV_TAB: [u8; 16] = [ | |
316 | 0b0000, 0b1000, 0b0100, 0b1100, 0b0010, 0b1010, 0b0110, 0b1110, | |
317 | 0b0001, 0b1001, 0b0101, 0b1101, 0b0011, 0b1011, 0b0111, 0b1111, | |
318 | ]; | |
319 | ||
320 | let mut ret = 0; | |
321 | let mut val = inval; | |
322 | for _ in 0..8 { | |
323 | ret = (ret << 4) | (REV_TAB[(val & 0xF) as usize] as u32); | |
324 | val = val >> 4; | |
325 | } | |
326 | ret | |
327 | } | |
328 | ||
329 | fn swp_idx(idx: usize, bits: u32) -> usize { | |
330 | let s = reverse_bits(idx as u32) as usize; | |
331 | s >> (32 - bits) | |
332 | } | |
333 | ||
334 | fn gen_sr_perms(swaps: &mut [usize], size: usize) { | |
335 | if size <= 4 { return; } | |
336 | let mut evec: Vec<usize> = Vec::with_capacity(size / 2); | |
337 | let mut ovec1: Vec<usize> = Vec::with_capacity(size / 4); | |
338 | let mut ovec2: Vec<usize> = Vec::with_capacity(size / 4); | |
339 | for k in 0..size/4 { | |
340 | evec.push (swaps[k * 4 + 0]); | |
341 | ovec1.push(swaps[k * 4 + 1]); | |
342 | evec.push (swaps[k * 4 + 2]); | |
343 | ovec2.push(swaps[k * 4 + 3]); | |
344 | } | |
345 | for k in 0..size/2 { swaps[k] = evec[k]; } | |
346 | for k in 0..size/4 { swaps[k + size/2] = ovec1[k]; } | |
347 | for k in 0..size/4 { swaps[k + 3*size/4] = ovec2[k]; } | |
348 | gen_sr_perms(&mut swaps[0..size/2], size/2); | |
349 | gen_sr_perms(&mut swaps[size/2..3*size/4], size/4); | |
350 | gen_sr_perms(&mut swaps[3*size/4..], size/4); | |
351 | } | |
352 | ||
353 | fn gen_swaps_for_perm(swaps: &mut Vec<usize>, perms: &Vec<usize>) { | |
354 | let mut idx_arr: Vec<usize> = Vec::with_capacity(perms.len()); | |
355 | for i in 0..perms.len() { idx_arr.push(i); } | |
356 | let mut run_size = 0; | |
357 | let mut run_pos = 0; | |
358 | for idx in 0..perms.len() { | |
359 | if perms[idx] == idx_arr[idx] { | |
360 | if run_size == 0 { run_pos = idx; } | |
361 | run_size += 1; | |
362 | } else { | |
363 | for i in 0..run_size { | |
364 | swaps.push(run_pos + i); | |
365 | } | |
366 | run_size = 0; | |
367 | let mut spos = idx + 1; | |
368 | while idx_arr[spos] != perms[idx] { spos += 1; } | |
369 | idx_arr[spos] = idx_arr[idx]; | |
370 | idx_arr[idx] = perms[idx]; | |
371 | swaps.push(spos); | |
372 | } | |
373 | } | |
374 | } | |
375 | ||
376 | impl FFTBuilder { | |
377 | pub fn new_fft(mode: FFTMode, size: usize) -> FFT { | |
378 | let mut swaps: Vec<usize>; | |
379 | let mut perms: Vec<usize>; | |
380 | let mut table: Vec<FFTComplex>; | |
381 | let bits = 31 - (size as u32).leading_zeros(); | |
382 | match mode { | |
383 | FFTMode::Matrix => { | |
384 | swaps = Vec::new(); | |
385 | perms = Vec::new(); | |
386 | table = Vec::new(); | |
387 | }, | |
388 | FFTMode::CooleyTukey => { | |
389 | perms = Vec::with_capacity(size); | |
390 | for i in 0..size { | |
391 | perms.push(swp_idx(i, bits)); | |
392 | } | |
393 | swaps = Vec::with_capacity(size); | |
394 | table = Vec::with_capacity(size); | |
395 | for _ in 0..4 { table.push(FFTC_ZERO); } | |
396 | for b in 3..(bits+1) { | |
397 | let hsize = (1 << (b - 1)) as usize; | |
398 | let base = -consts::PI / (hsize as f32); | |
399 | for k in 0..hsize { | |
400 | table.push(FFTComplex::exp(base * (k as f32))); | |
401 | } | |
402 | } | |
403 | }, | |
404 | FFTMode::SplitRadix => { | |
405 | perms = Vec::with_capacity(size); | |
406 | for i in 0..size { | |
407 | perms.push(i); | |
408 | } | |
409 | gen_sr_perms(perms.as_mut_slice(), 1 << bits); | |
410 | swaps = Vec::with_capacity(size); | |
411 | table = Vec::with_capacity(size); | |
412 | for _ in 0..4 { table.push(FFTC_ZERO); } | |
413 | for b in 3..(bits+1) { | |
414 | let qsize = (1 << (b - 2)) as usize; | |
415 | let base = -consts::PI / ((qsize * 2) as f32); | |
416 | for k in 0..qsize { | |
417 | table.push(FFTComplex::exp(base * ((k * 1) as f32))); | |
418 | table.push(FFTComplex::exp(base * ((k * 3) as f32))); | |
419 | } | |
420 | } | |
421 | }, | |
422 | }; | |
423 | gen_swaps_for_perm(&mut swaps, &perms); | |
424 | FFT { mode: mode, swaps: swaps, perms: perms, bits: bits, table: table } | |
425 | } | |
426 | } | |
427 | ||
428 | ||
429 | #[cfg(test)] | |
430 | mod test { | |
431 | use super::*; | |
432 | ||
433 | #[test] | |
434 | fn test_fft() { | |
435 | let mut fin: [FFTComplex; 128] = [FFTC_ZERO; 128]; | |
436 | let mut fout1: [FFTComplex; 128] = [FFTC_ZERO; 128]; | |
437 | let mut fout2: [FFTComplex; 128] = [FFTC_ZERO; 128]; | |
438 | let mut fout3: [FFTComplex; 128] = [FFTC_ZERO; 128]; | |
439 | let mut fft1 = FFTBuilder::new_fft(FFTMode::Matrix, fin.len()); | |
440 | let mut fft2 = FFTBuilder::new_fft(FFTMode::CooleyTukey, fin.len()); | |
441 | let mut fft3 = FFTBuilder::new_fft(FFTMode::SplitRadix, fin.len()); | |
442 | let mut seed: u32 = 42; | |
443 | for i in 0..fin.len() { | |
444 | seed = seed.wrapping_mul(1664525).wrapping_add(1013904223); | |
445 | let val = (seed >> 16) as i16; | |
446 | fin[i].re = (val as f32) / 256.0; | |
447 | seed = seed.wrapping_mul(1664525).wrapping_add(1013904223); | |
448 | let val = (seed >> 16) as i16; | |
449 | fin[i].im = (val as f32) / 256.0; | |
450 | } | |
451 | fft1.do_fft(&fin, &mut fout1, true); | |
452 | fft2.do_fft(&fin, &mut fout2, true); | |
453 | fft3.do_fft(&fin, &mut fout3, true); | |
454 | ||
455 | for i in 0..fin.len() { | |
456 | assert!((fout1[i].re - fout2[i].re).abs() < 1.0); | |
457 | assert!((fout1[i].im - fout2[i].im).abs() < 1.0); | |
458 | assert!((fout1[i].re - fout3[i].re).abs() < 1.0); | |
459 | assert!((fout1[i].im - fout3[i].im).abs() < 1.0); | |
460 | } | |
461 | fft1.do_fft_inplace(&mut fout1, false); | |
462 | fft2.do_fft_inplace(&mut fout2, false); | |
463 | fft3.do_fft_inplace(&mut fout3, false); | |
464 | ||
465 | let sc = 1.0 / (fin.len() as f32); | |
466 | for i in 0..fin.len() { | |
467 | assert!((fin[i].re - fout1[i].re * sc).abs() < 1.0); | |
468 | assert!((fin[i].im - fout1[i].im * sc).abs() < 1.0); | |
469 | assert!((fout1[i].re - fout2[i].re).abs() < 1.0); | |
470 | assert!((fout1[i].im - fout2[i].im).abs() < 1.0); | |
471 | assert!((fout1[i].re - fout3[i].re).abs() < 1.0); | |
472 | assert!((fout1[i].im - fout3[i].im).abs() < 1.0); | |
473 | } | |
474 | } | |
475 | } |