yagi 0.1.3

Batteries-included DSP library
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397

use crate::error::{Error, Result};

const MAX_FACTORS: usize = 40;

/// Determine if number is prime (slow, simple method)
///
/// # Arguments
///
/// * `n` - Number to check for primality
///
/// # Returns
///
/// `true` if prime, `false` otherwise
pub fn is_prime(n: u32) -> bool {
    // check base cases (0, 1, 2, 3, divisible by 2, divisible by 3)
    if n <= 1 {
        return false;
    } else if n <= 3 {
        return true;
    } else if n % 2 == 0 {
        return false; // divisible by 2
    } else if n % 3 == 0 {
        return false; // divisible by 3
    }

    let mut r = 5;
    while r * r <= n {
        if n % r == 0 || n % (r + 2) == 0 {
            return false;
        }
        r += 6;
    }
    true
}

/// Compute number's prime factors
///
/// # Arguments
///
/// * `n` - Number to factor
/// * `factors` - Output slice of factors [size: MAX_FACTORS x 1]
///
/// # Returns
///
/// A tuple containing:
/// - The number of factors found
pub fn factor(n: u32, factors: &mut Vec<u32>) -> Result<usize> {
    let mut num = n;
    let mut num_factors = 0;

    while num > 1 && num_factors < MAX_FACTORS {
        for k in 2..=num {
            if num % k == 0 {
                // k factors n; append to list
                factors.push(k);
                num_factors += 1;
                num /= k;
                break;
            }
        }
    }

    if num > 1 && num_factors == MAX_FACTORS {
        return Err(Error::NoConvergence("could not factor number in MAX_FACTORS numbers".to_string()));
    }

    factors.shrink_to_fit();
    Ok(num_factors)
}

/// Compute number's unique prime factors
///
/// # Arguments
///
/// * `n` - Number to factor
/// * `factors` - Output slice of factors [size: MAX_FACTORS x 1]
///
/// # Returns
/// 
/// A tuple containing:
/// - The number of unique factors found
pub fn unique_factor(n: u32, factors: &mut Vec<u32>) -> Result<usize> {
    let mut num = n;
    let mut num_factors = 0;

    while num > 1 && num_factors < MAX_FACTORS {
        for k in 2..=num {
            if num % k == 0 {
                // k factors n; append to list
                if num_factors == 0 || factors[num_factors - 1] != k {
                    factors.push(k);
                    num_factors += 1;
                }

                num /= k;

                break;
            }
        }
    }

    if num > 1 && num_factors == MAX_FACTORS {
        return Err(Error::NoConvergence("could not factor number in MAX_FACTORS numbers".to_string()));
    }

    Ok(num_factors)
}

/// Compute greatest common divisor between two integers p and q
///
/// # Arguments
///
/// * `p` - First integer
/// * `q` - Second integer
///
/// # Returns
///
/// Greatest common divisor
pub fn gcd(mut p: u32, mut q: u32) -> Result<u32> {
    // check base cases
    if p == 0 || q == 0 {
        return Err(Error::Value("input cannot be zero".to_string()));
    } else if p == 1 || q == 1 {
        return Ok(1);
    } else if p == q {
        return Ok(p);
    } else if p < q {
        return gcd(q, p);
    }

    // dumb, slow method
    let mut gcd = 1;
    let mut r = 2; // root
    while r <= q {
        while p % r == 0 && q % r == 0 {
            p /= r;
            q /= r;
            gcd *= r;
        }
        r += if r == 2 { 1 } else { 2 };
    }
    
    Ok(gcd)
}

/// Compute c = base^exp (mod n)
///
/// # Arguments
///
/// * `base` - Base
/// * `exp` - Exponent
/// * `n` - Modulus
///
/// # Returns
///
/// Result of modular exponentiation
pub fn modpow(base: u32, exp: u32, n: u32) -> u32 {
    let mut c = 1;
    for _ in 0..exp {
        c = (c * base) % n;
    }
    c
}

/// Find smallest primitive root of n
///
/// # Arguments
///
/// * `n` - Number to find primitive root for
///
/// # Returns
///
/// Smallest primitive root
pub fn primitive_root(_n: u32) -> u32 {
    unimplemented!()
}

/// Find smallest primitive root of n (assuming n is prime)
///
/// # Arguments
///
/// * `n` - Prime number to find primitive root for
///
/// # Returns
///
/// Smallest primitive root
pub fn primitive_root_prime(n: u32) -> Result<u32> {
    // find unique factors of n-1
    let mut unique_factors = Vec::with_capacity(MAX_FACTORS);
    let num_unique_factors = unique_factor(n - 1, &mut unique_factors).unwrap();

    // search for minimum integer for which
    //   g^( (n-1)/m ) != 1 (mod n)
    // for all unique roots 'm'
    for g in 2..n {
        let mut is_root = true;
        for &factor in &unique_factors[0..num_unique_factors] {
            let e = (n - 1) / factor;
            if modpow(g, e, n) == 1 {
                // not a root
                is_root = false;
                break;
            }
        }

        if is_root {
            return Ok(g);
        }
    }

    // This should never happen for prime n
    Err(Error::Value("No primitive root found for prime".to_string()))
}

/// Euler's totient function
///
/// # Arguments
///
/// * `n` - Number to compute totient for
///
/// # Returns
///
/// Euler's totient
pub fn totient(x: u32) -> u32 {
    let mut t = x;
    let mut n = x;
    let mut p = 0;
    loop {
        for k in 2..=n {
            if n % k == 0 {
                n /= k;

                if p != k {
                    // factor is unique
                    t *= k - 1;
                    t /= k;
                }
                p = k;
                break;
            }
        }

        if n < 2 {
            break;
        }
    }

    t
}

#[cfg(test)]
mod tests {
    use super::*;
    use test_macro::autotest_annotate;

    #[test]
    #[autotest_annotate(autotest_prime_small)]
    fn test_prime_small() {
        for (n, &expected_is_prime) in IS_PRIME_ARRAY.iter().enumerate() {
            assert_eq!(is_prime(n as u32), expected_is_prime != 0);
        }
    }

    #[test]
    #[autotest_annotate(autotest_factors)]
    fn test_factors() {
        const FACTORS_280: [u32; 5] = [2, 2, 2, 5, 7];
        const FACTORS_280_UNIQUE: [u32; 3] = [2, 5, 7];

        let mut factors = Vec::with_capacity(MAX_FACTORS);
        let num_factors = factor(280, &mut factors).unwrap();
        assert_eq!(num_factors, 5);
        assert_eq!(factors, FACTORS_280);

        let mut factors = Vec::with_capacity(MAX_FACTORS);
        let num_unique_factors = unique_factor(280, &mut factors).unwrap();
        assert_eq!(num_unique_factors, 3);
        assert_eq!(factors, FACTORS_280_UNIQUE);
    }

    #[test]
    #[autotest_annotate(autotest_totient)]
    fn test_totient() {
        assert_eq!(totient(9), 6);
        assert_eq!(totient(20), 8);
        assert_eq!(totient(100), 40);
        assert_eq!(totient(1200), 320);
        assert_eq!(totient(1201), 1200);
    }

    fn testbench_gcd(gcd_expected: u32, p: u32, q: u32) {
        let p = p * gcd_expected;
        let q = q * gcd_expected;
        let gcd_test = gcd(p, q).unwrap();
        
        assert_eq!(gcd_test, gcd_expected, "gcd({}, {}) = {} (expected {})", p, q, gcd_test, gcd_expected);
    }

    #[test]
    #[autotest_annotate(autotest_gcd_one)]
    fn test_gcd_one() {
        testbench_gcd(1, 2, 3);
        testbench_gcd(1, 2, 5);
        testbench_gcd(1, 2, 7);
        testbench_gcd(1, 7, 2);
        testbench_gcd(1, 17, 19);
        testbench_gcd(1, 23, 31);
        testbench_gcd(1, 2*2*2*2*2, 3*5*7*19);
    }

    #[test]
    #[autotest_annotate(autotest_gcd_edge_cases)]
    fn test_gcd_edge_cases() {
        testbench_gcd(1, 1, 1);
        testbench_gcd(1, 1, 2);
        testbench_gcd(1, 1, 2400);
        testbench_gcd(12345, 1, 1);    // P==Q
        testbench_gcd((1<<17)-1, 1, 1);    // P==Q
    }

    #[test]
    #[autotest_annotate(autotest_gcd_base)]
    fn test_gcd_base() {
        testbench_gcd(2*2*3*5*7, 2*3, 17);
        testbench_gcd(2*2*3*5*7, 2*3, 17*17);
        testbench_gcd(2*2*3*5*7, 2*3, 17*17*17);
        testbench_gcd(11, 3, 1);
        testbench_gcd(3, 127, 131);
        testbench_gcd(131, 127, 3);
        testbench_gcd(127, 131, 3);
    }

    #[test]
    fn test_modpow() {
        assert_eq!(modpow(2, 3, 5), 3);
        assert_eq!(modpow(3, 4, 7), 4);
    }

    #[test]
    fn test_primitive_root_prime() {
        assert_eq!(primitive_root_prime(5).unwrap(), 2);
        assert_eq!(primitive_root_prime(7).unwrap(), 3);
    }

    const IS_PRIME_ARRAY: [u8; 2500] = [
        0,0,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,1,0,0,
		0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,
		0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,1,
		0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,1,0,1,
		0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,
		0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
		0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,1,
		0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,
		0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,
		0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,1,
		0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,
		0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,
		0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,1,0,0,
		0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,
		0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,
		0,1,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,
		0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
		0,0,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
		0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,0,0,
		0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,
		0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,
		0,1,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,1,0,0,
		0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
		0,1,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,
		0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,
		0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,0,
		0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
		0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,
		0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,
		0,1,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,
		0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,
		0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,
		0,1,0,0,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
		0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,
		0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,
		0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,
		0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,
		0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
		0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,
		0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,1,0,1,
		0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
		0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,1,
		0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,0,
		0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
		0,0,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,
		0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,1,0,0,
		0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,0,
		0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,
		0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,0,0,
		0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
    ];
}