quasi_rd/
lib.rs

1//! An implementation of the quasirandom _Rd_ sequence described [in this blog
2//! post][1] via a fast and accurate fixed-point representation correct for up
3//! to `2^64` samples; samples can be produced with one 128-bit multiplication
4//! per dimension and are guaranteed accurate to within one part per `2^64`.
5//!
6//! [1]: http://extremelearning.com.au/unreasonable-effectiveness-of-quasirandom-sequences/
7
8#![forbid(missing_docs, unsafe_code)]
9
10use num_bigint::BigInt;
11use num_rational::BigRational;
12use num_traits::{One, ToPrimitive};
13
14/// A d-dimensional quasirandom Rd sequence.
15///
16/// Successive samples are generated dimension by dimension, so every `d`
17/// outputs generated constitute one individual sample from the sequence.
18#[derive(Clone, Debug)]
19pub struct Sequence {
20    parameters: Box<[u128]>,
21    dimensionality: usize,
22    sample: u64,
23    dimension: usize,
24}
25
26impl Sequence {
27    /// Creates a new quasirandom Rd sequence.
28    pub fn new(dimensionality: usize) -> Self {
29        Self::new_with_offset(dimensionality, 0)
30    }
31
32    /// Creates a new sequence and specifies the starting sample offset.
33    pub fn new_with_offset(dimensionality: usize, sample: u64) -> Self {
34        let mut parameters = vec![0; dimensionality].into_boxed_slice();
35
36        generate_parameters(dimensionality, &mut parameters);
37
38        Self {
39            parameters,
40            dimensionality,
41            sample,
42            dimension: 0,
43        }
44    }
45
46    /// Seeks to the given sample offset.
47    pub fn seek(&mut self, sample: u64) {
48        self.sample = sample;
49        self.dimension = 0;
50    }
51
52    /// Generates the next sample dimension as a [0, 1) fixed-point value.
53    pub fn next_u64(&mut self) -> u64 {
54        (1u64 << 63).wrapping_add(self.next_raw())
55    }
56
57    /// Generates the next sample dimension as a [0, 1) fixed-point value.
58    pub fn next_u32(&mut self) -> u32 {
59        (1u32 << 31).wrapping_add(Self::shift_round(self.next_raw(), 32) as u32)
60    }
61
62    /// Generates the next sample dimension as a [0, 1) floating-point value.
63    pub fn next_f64(&mut self) -> f64 {
64        (0.5 + f64::from_bits(0x3FF0_0000_0000_0000 | Self::shift_round(self.next_raw(), 12)))
65            .fract()
66    }
67
68    /// Generates the next sample dimension as a [0, 1) floating-point value.
69    pub fn next_f32(&mut self) -> f32 {
70        (0.5 + f32::from_bits(0x3F80_0000 | Self::shift_round(self.next_raw(), 41) as u32)).fract()
71    }
72
73    fn next_raw(&mut self) -> u64 {
74        let output = self.parameters[self.dimension].wrapping_mul(self.sample as u128);
75
76        if self.dimension + 1 == self.dimensionality {
77            self.sample = self.sample.wrapping_add(1);
78            self.dimension = 0; // set to next sample
79        } else {
80            self.dimension += 1;
81        }
82
83        (output >> 64) as u64
84    }
85
86    fn shift_round(value: u64, n: u32) -> u64 {
87        (value + (1 << (n - 1))) >> n
88    }
89}
90/// Populates a buffer with all parameters for a given dimensionality.
91///
92/// If you intend to generate sequence samples yourself, the `i`th parameter in
93/// the buffer will equal `2^128 / phi^(i + 1)` rounded to the nearest integer.
94pub fn generate_parameters(dimensionality: usize, buffer: &mut [u128]) {
95    assert!(dimensionality > 0 && buffer.len() == dimensionality);
96    assert!(dimensionality <= 1_000_000, "max dimensionality 1M");
97
98    let (phi, compute_precision) = compute_phi(dimensionality);
99    let scale = BigInt::one() << 128; // fixed-point parameters
100
101    // Generate the parameters for all dimensions as successive powers of the
102    // reciprocal of `phi_d` using the appropriate precision for correctness.
103
104    let mut power = phi.clone();
105
106    for parameter in buffer.iter_mut() {
107        *parameter = (power.recip() * &scale).round().numer().to_u128().unwrap();
108        power = (power * &phi * &compute_precision).round() / &compute_precision;
109    }
110}
111
112fn fixed_point_pow(mut x: BigRational, scale: &BigInt, mut n: usize) -> BigRational {
113    let mut result = BigRational::one();
114
115    while n > 0 {
116        if n & 1 != 0 {
117            result = ((result * &x) * scale).round() / scale;
118        }
119
120        x = ((&x * &x) * scale).round() / scale;
121
122        n >>= 1;
123    }
124
125    result
126}
127
128fn compute_phi(dimensionality: usize) -> (BigRational, BigInt) {
129    let mut xi = BigRational::one();
130
131    // TODO: required precision for the Newton-Raphson stage has not been fully
132    // analyzed yet; use 200-bit precision just to be sure, but it is too much.
133
134    let one = BigRational::one();
135    let precision = one.numer() << 200;
136    let n = BigInt::from(1 + dimensionality);
137
138    for _ in 0..12 {
139        let xi_n_minus_1 = fixed_point_pow(xi.clone(), &precision, dimensionality);
140
141        let derv = &xi_n_minus_1 * &n - &one;
142        let func = (xi_n_minus_1 - &one) * &xi - &one;
143
144        // Generate the next Newton-Raphson approximation then immediately round it
145        // to a multiple of `precision` to keep intermediate results under control.
146
147        xi = ((&xi - func / derv) * &precision).round() / &precision;
148    }
149
150    (xi, (one.numer() << 132) * (dimensionality + 1))
151}
152
153#[cfg(test)]
154mod tests {
155    use super::Sequence;
156
157    #[test]
158    fn test_2d_u64() {
159        let mut seq = Sequence::new(2);
160
161        assert_eq!(seq.next_u64(), 9223372036854775808);
162        assert_eq!(seq.next_u64(), 9223372036854775808);
163        assert_eq!(seq.next_u64(), 4701663079357100687);
164        assert_eq!(seq.next_u64(), 1288325974074489628);
165    }
166
167    #[test]
168    fn test_2d_f64() {
169        let mut seq = Sequence::new(2);
170
171        assert_eq!(seq.next_f64(), 0.5);
172        assert_eq!(seq.next_f64(), 0.5);
173        assert_eq!(seq.next_f64(), 0.25487766624669295);
174        assert_eq!(seq.next_f64(), 0.06984029099805333);
175    }
176
177    #[test]
178    fn test_offset() {
179        let mut seq1 = Sequence::new(1);
180        let mut seq2 = Sequence::new_with_offset(1, 100);
181
182        for _ in 0..100 {
183            seq1.next_u64();
184        }
185
186        assert_eq!(seq1.next_u64(), seq2.next_u64());
187        assert_eq!(seq1.next_u64(), seq2.next_u64());
188    }
189
190    // Reference tests against a SageMath computation of parameters for various
191    // dimensionalities carried out at 1024-bit precision with the mpf package.
192
193    #[test]
194    fn check_reference_parameters_1d() {
195        let seq = Sequence::new(1);
196
197        assert_eq!(seq.parameters[0], 0x9e3779b97f4a7c15f39cc0605cedc834);
198    }
199
200    #[test]
201    fn check_reference_parameters_2d() {
202        let seq = Sequence::new(2);
203
204        assert_eq!(seq.parameters[0], 0xc13fa9a902a6328f434ff71b2d97724b);
205        assert_eq!(seq.parameters[1], 0x91e10da5c79e7b1cd438a0a8e6c9c0fc);
206    }
207
208    #[test]
209    fn check_reference_parameters_3d() {
210        let seq = Sequence::new(3);
211
212        assert_eq!(seq.parameters[0], 0xd1b54a32d192ed039fdcaa7d6e9dfe0f);
213        assert_eq!(seq.parameters[1], 0xabc98388fb8fac028c2245930757dd50);
214        assert_eq!(seq.parameters[2], 0x8cb92ba72f3d8dd732e5bf2dbe798195);
215    }
216
217    #[test]
218    fn check_reference_parameters_5d() {
219        let seq = Sequence::new(5);
220
221        assert_eq!(seq.parameters[0], 0xe19b01aa9d42c6333587690489ecb903);
222        assert_eq!(seq.parameters[1], 0xc6d1d6c8ed0c9631c8f17386e81d96a8);
223        assert_eq!(seq.parameters[2], 0xaf36d01ef7518dbbd36071fc91bf9f6e);
224        assert_eq!(seq.parameters[3], 0x9a69443f36f710e68a65d16792971bec);
225        assert_eq!(seq.parameters[4], 0x881403b9339bd42dfd680e7ae5211382);
226    }
227
228    #[test]
229    fn check_reference_parameters_50d() {
230        #[rustfmt::skip]
231        const REFERENCE: &[u128] = &[
232            0xfc8296a209364b84342308d1429bd922, 0xf9115b2c5756892c42754a2f380e0ce3, 0xf5ac231dc3dba58bb2d705886af43014, 0xf252c4897e427e1bfa398ad678c89f07, 
233            0xef051615065ccebe1e8a792351b5c0e2, 0xebc2eef62db2c107dce7f0bb56c69963, 0xe88c26f11fda7c6a57bd604ac36c610e, 0xe560965671ad6c33e18c6ddd2acce765, 
234            0xe240160137434536124e925a36d1cdca, 0xdf2a7f55209b28790f5ed35fa68778a3, 0xdc1fac3c9cdb92e0d146cbcc4b4c0acd, 0xd91f772704121b053a1a920a62c4b881, 
235            0xd629bb06c75c4ebde6dd4aaab058fb4a, 0xd33e534fa763510aad9bac8821f42a43, 0xd05d1bf4f114271581e79affc3cec797, 0xcd85f167c07ef00dc63a740d68845005, 
236            0xcab8b09549c78f9399687452a6fe60c3, 0xc7f536e528129d571db5b0aca48c07ad, 0xc53b6237b259b677a87245a274a9da8d, 0xc28b10e456129614cdd8652a970a4d17, 
237            0xbfe421b7f794a26ad95bfe8ba115147f, 0xbd4673f35828e2c0ee8ba75c57e88792, 0xbab1e74981b0986435cd7920ec073d59, 0xb8265bde37cef9ec7a78c7c15b3aae16, 
238            0xb5a3b2446e82d416d11850ffea6aa29e, 0xb329cb7cc61d16a5856baf9954985cf4, 0xb0b888f40c8195eced015efcd3cedf28, 0xae4fcc81c39f8b05fea6613dc848d5c8, 
239            0xabef7866ad0f9d0cdef1fc6e46600114, 0xa9976f4b5ac57d5e0a68bbb9581fa0d6, 0xa747943ec4c35f7376bf574006e06096, 0xa4ffcab4e3bdd2d6f4a757ef78ddc740, 
240            0xa2bff685509ec29b45b21b31a7af10ae, 0xa087fbe9e8d699f4af40ddec8f5ed96b, 0x9e57bf7d776ac8df3aeb50b7e6ceb82e, 0x9c2f263a62b11e472ae3675a1a187f18, 
241            0x9a0e15795ea7a6e240494d6a74f9ceb5, 0x97f472f023d8f8d912e86968c659e183, 0x95e224b02abd0c89a4894e1253573542, 0x93d711256b86fa124361ef4b8c7be216, 
242            0x91d31f15225029f8633eb85dcd76ab01, 0x8fd6359c9791bd24f67a5a349e408c8b, 0x8de03c2fecdd25999842c468b8fb3ed7, 0x8bf11a98edc51db219709c807eede0ea, 
243            0x8a08b8f5e4e85f7f3fd9a52c8b3f2739, 0x8826ffb8750fb0cc44302fcbb9039b9b, 0x864bd7a476510ab34a2752a191b2decf, 0x847729ced729d5481f1426f2513c3ac9, 
244            0x82a8df9c818260d6618630c73dfe6938, 0x80e0e2c1438cf67b2cdfbf859f814657, 
245        ];
246
247        for (index, &parameter) in Sequence::new(50).parameters.iter().enumerate() {
248            assert_eq!(parameter, REFERENCE[index]);
249        }
250    }
251
252    #[test]
253    fn check_reference_parameters_272d() {
254        #[rustfmt::skip]
255        const REFERENCE: &[u128] = &[
256            0xff5982a853359d81dce8b2829f9f1426,0xfeb37197717e0e3fffc59b976d75c340,0xfe0dcc86efedfdb91101d10b247fb334,0xfd6893309165e6574aa5a50ac9094741,
257            0xfcc3c54e467448dc1860be901dd1f44f,0xfc1f629a2d37f72a5cee22d95c81e981,0xfb7b6ace91427262c3f71e9fe0a74cc1,0xfad7dda5eb7a5c458fcb46c2167978dc,
258            0xfa34badae1fdfbcd5a6fbd1d6b551052,0xf99202284805d4f649ae8adc44083f61,0xf8efb3491dc753a53df038f6ea7b340c,0xf84dcdf8905789a28bc5dd878776f06c,
259            0xf7ac51f1f98dff9bd8209c48e6bcfbfa,0xf70b3ef0dfe79920b7451d940742b95e,0xf66a94b0f6698b8db695c4dd301a0875,0xf5ca52ee1c8467d9815579780ba9a4ff,
260            0xf52a79645df73737d886a5b28d749f87,0xf48b07cff2b2aa861e06ac85533c13db,0xf3ebfded3ebc5c753afd8090c3e49d00,0xf34d5b78d2122664b1ab43412c866081,
261            0xf2af202f688d87e2b28ae4201b4ea40f,0xf2114bcde9c720c514a8a1ea9c4598d0,0xf173de1168fa3dcf18ee1454f9fd32bc,0xf0d6d6b724e877d7e80309cd41df2f6e,
262            0xf03a357c87bd6565c23b0b63e2c264f5,0xef9dfa1f26f25eb1e0dac598fad67ad7,0xef02245cc33254090fceea76d421c4d7,0xee66b3f3483db67d0eb7636e0093d204,
263            0xedcba8a0ccce72dacfeddb22b4d0af28,0xed310223927bfed9b3edcc107a671d7e,0xec96c03a059f7877e73e5be201e8cb60,0xebfce2a2bd37d77810b35fdd8b3cb1cd,
264            0xeb63691c7ace30f4858af817ace685a6,0xeaca53662a5a0cfc40984080c02a9444,0xea31a13ee225ce2de151ab954777a1c4,0xe9995265e2b32b44ff3ab5bd9089f8da,
265            0xe901669a969fba8e25bcc578ca82b2bc,0xe869dd9c92898f35d41a3e85dd4fbdb4,0xe7d2b72b94f3e866e4b910907d9a91a5,0xe73bf307862bf22cc68f5fb121834992,
266            0xe6a590f0782d980dfb05517e6aaf2faa,0xe60f90a6a688695352228fb8087835b5,0xe579f1ea76448ef0665cb4e5a45cf1a5,0xe4e4b47c75c7d301e0d59acdabc21143,
267            0xe44fd81d5cbab9d6164d69933c2045c9,0xe3bb5c8e0bedac74947c53c18993e2cd,0xe327418f8d3e34993ef322b52cba8ab4,0xe29386e3137c4a17a2081ad6301797b4,
268            0xe2002c49fa4fb19b29b75313bf52e15d,0xe16d3185c61d6cb8f1ba622d419e26f1,0xe0da965823ed3b47eb7341aba15c54c2,0xe0485a82e94f2df41d997d1dbafff667,
269            0xdfb67dc814414a01c8e7374f8abeb729,0xdf24ffe9cb153e35444d41e5d5d1a7d9,0xde93e0aa5c5628d46a7a791ed657cab5,0xde031fcc3eae6eb679c2d088fbe42146,
270            0xdd72bd1210cda3574eae015e386a0f85,0xdce2b83e994e81e2e8ac9aedabd5f43d,0xdc531114c69cf72e2fa45425ebd086b0,0xdbc3c757aedc3c91f831edf4bf4ab3f2,
271            0xdb34daca8fcd039d4ba7bbd910d60faf,0xdaa64b30ceb3b293fff405ba3f1e690d,0xda18184df83eb1aeb2b9eee3fe4a746f,0xd98a41e5c06cc911420264ece5aef925,
272            0xd8fcc7bc02738f6ce400d152ca512744,0xd86fa994c0a5e9430678e4bc71d4a06d,0xd7e2e734245a98be255fd6134ff4ea25,0xd756805e7dd2de15cf5bdd0744dbfc48,
273            0xd6ca74d84421287315c88a05250f792e,0xd63ec466150fd74aace5e830b4522320,0xd5b36eccb5080c2207d313833c7fc34e,0xd52873d10ef88cb4c2eb20beaae39967,
274            0xd49dd338343cb56fb60ce165d7e6b355,0xd4138cc75c837c370f43364f18cc4abe,0xd389a043e5b6836cdd2c4a9e59e41a58,0xd3000d7353e13d2d776239edb887882f,
275            0xd276d41b51181eb73a075212f702e94e,0xd1edf401ad5fe3f31073562f5a5c02f3,0xd1656cec5e94e31351d5e876ce9a3f57,0xd0dd3ea18052703e79748d40f1a35e2c,
276            0xd05568e753da513b4af897675bf2a8fb,0xcfcdeb843ffc4113fa0abe92c4df2ba6,0xcf46c63ed0fd83a5f33f26c530eafa7d,0xcebff8ddb8808913eb1540090fabf664,
277            0xce398327cd6ca10fde8b20910a5520bb,0xcdb364e40bd5bdf2b77bd59d651a26c8,0xcd2d9dd994e447974db3a30382737755,0xcca82dcfaebcfdee84544911bb45b56f,
278            0xcc23148dc468eb4249ce2f92ec9d86a8,0xcb9e51db65bd661d4759c5bd8db224af,0xcb19e580474422cd137e84b3bb29f7c8,0xca95cf4442235474c1d2cfb475a5c1df,
279            0xca120eef5405dda5b0b96d08938f8a91,0xc98ea4499f0390747c7687dc00282940,0xc90b8f1b69897e000587186068fcfdf1,0xc888cf2d1e4255607eb2379233c08cd5,
280            0xc80664474bfed1f47dd4498a75d94d8e,0xc7844e32a59e390210e80f35d3603c13,0xc7028cb801f6e6a1df519953fe10890c,0xc6811fa05bbee9ea65eac58f9320dcef,
281            0xc60006b4d174b05162c8660a13979a6f,0xc57f41bea547c0398c2276a19e285ec2,0xc4fed0873d0182a2b438d43a1c449db5,0xc47eb2d821ee1bf28278cc2c26a07e89,
282            0xc3fee87b00c553cbf08e8f61a2a6f53d,0xc37f7139a9938bebc0702051dfccd245,0xc3004cde0fa2c60026cdb7b1e312998e,0xc2817b324963b871ebaddbfcef3ecd13,
283            0xc202fc009056f215495186a6c6bf878a,0xc184cf1340f60cb8d7ceb184758be352,0xc106f434da9cee88da1d8a6fbb5008b7,0xc0896b2fff731a3d479e5508c7fc4ceb,
284            0xc00c33cf74550e08f363b56c80bb48bb,0xbf8f4dde20bdb14038cebd63cfb0bca0,0xbf12b9270eafd0ad9b47a2a1b93a6ff3,0xbe9675756a9fa98acd1782bf7f9665ab,
285            0xbe1a8294835c8314979d0b6bb319dc8f,0xbd9ee04fc9fa56b025474554a365eaa9,0xbd238e72d1bb869833ef215880ca68cb,0xbca88cc94ffaa308bc51c4142aa2ae4b,
286            0xbc2ddb1f1c143ddfa192e6a202250d83,0xbbb379402f50cca901cffed7481cd7f1,0xbb3966f8a4ce990dc6ea402a04b39423,0xbabfa414b96bbf9b1cc6eb3aff5dbb25,
287            0xba463060cbb03cd9785acf5cf7180b0c,0xb9cd0ba95bb808a9e0e759f07eb4cc5e,0xb95435bb0b1d3fe032dd159d56d72c67,0xb8dbae629ce25c1119e111e7e3d283b5,
288            0xb863756cf55c798a857854ead210c0dd,0xb7eb8aa71a1dab6d61de37a7d6c91b37,0xb773edde31df5ddf648863faca6cdd8a,0xb6fc9edf846cc64bc1d51c4a83f18f90,
289            0xb6859d787a8d61a9a75683239eb7b0c6,0xb60ee9769def80bf5c1fc681c903f511,0xb59882a79912e258ee676231d2c7fcef,0xb52268d937335b695bbc20ed43fb19cf,
290            0xb4ac9bd964338d0d26f11f19f47be0be,0xb4371b762c87a86554c7d6f581343eda,0xb3c1e77dbd204041ce3e2ee476434db6,0xb34cffbe635528922d41a21ce7fcc4ac,
291            0xb2d864068cd06393fe5fec6fa9e0eeaf,0xb2641424c7791cb587e126046b2342db,0xb1f00fe7c15eb1242c86f5ec2f66276b,0xb17c571e48a3c5fd85f874f1b82c7d3a,
292            0xb108e9974b696c1a58aa877dbe0cc362,0xb095c721d7ba516a88d8e030f49b223a,0xb022ef8d1b75ffd93de48771cdc4972c,0xafb062a8643c29b06729b1083e4c4ca8,
293            0xaf3e20431f580372db17da6d447d8a54,0xaecc282cd9abab244f0ca51bee1389f1,0xae5a7a353f9b9cf66c23a261c8e989a2,0xade9162c1cfa35524adb544f2e45da01,
294            0xad77fbe15cf34035a51a03e5438e335e,0xad072b2509f795db13c3b9dedcfa2e9d,0xac96a3c74da8c4a4b2b5a7d8178308f1,0xac26659870c4c8408b9aa58a600389d7,
295            0xabb67068db11cdfe2da813b2096e0eab,0xab46c409134a064cddea7e60517ab523,0xaad76049bf078359d15dbd57fc9306bd,0xaa6844fba2b024c5e79d14f93680e344,
296            0xa9f971efa161906a6284ff8f4b10e3a7,0xa98ae6f6bcdd38241ca9cfe2ad120db5,0xa91ca3e215746c9cc60c4d1cb7a1da50,0xa8aea882e9f47d09b3f7bfa82b56e84b,
297            0xa840f4aa9792e3d7d673a91fa6856040,0xa7d3882a99d9803c6b2e90dec07f3d20,0xa76662d48a92dca20b3eedbe026096ed,0xa6f9847a21b681e9b68b463730c0359c,
298            0xa68ceced35555777851b24f63299936b,0xa6209bffb9861002abff7b01d41385cc,0xa5b49183c051a32088ea7c7ba87ed3e3,0xa548cd4b799fd3826cf4f3c2e018fd81,
299            0xa4dd4f293323c1dde47172d4ffc7806a,0xa47216ef58488c773f0cb6618a04d6a7,0xa4072470721dfb4620d5fb71d35f938d,0xa39c777f274538abea21fa09f9d18a13,
300            0xa3320fee3bdd96b3c98faf07524238b2,0xa2c7ed90917160d450c71ffe2ee9938a,0xa25e103926e2ba2a69d7cf35bfe40ef6,0xa1f477bb185888259066ae5ca1b13cd9,
301            0xa18b23e99f2b699d37220669a1bf9085,0xa122149811d2ba474735048f105b0406,0xa0b94999e3d1a287acb4696ee5a23c32,0xa050c2c2a5a43390e83a3b14dd593e38,
302            0x9fe87fe604ac8fcda31f55d9d9c045a2,0x9f8080d7cb201f8b48f74e704493e22d,0x9f18c56bdff4d1ddae254a2942e95334,0x9eb14d7646ce69b3d08f443a70d40191,
303            0x9e4a18cb1febd715c4a0a99e19efe321,0x9de3273ea8149c83e5f54b45b373e82b,0x9d7c78a53886406f682a61ef7dbb41dd,0x9d160cd346e1cac46974c232fca62326,
304            0x9cafe39d65194e7dadb96c71530efaca,0x9c49fcd8415d7f3a2e005d71feeb398a,0x9be45858a60b52ccad30ebbc1153fee2,0x9b7ef5f37999aebd881b155877164412,
305            0x9b19d57dbe8721b6fbe1ebc2838db311,0x9ab4f6cc9347a8d422e8ca8691ed0b98,0x9a5059b5323280caed6f3a8fb49120b7,0x99ebfe0cf17002e9600e529025b98b10,
306            0x9987e3a942e78dde674e0e663460baf5,0x99240a5fb42d7a4694897e010b6337e6,0x98c07205ee711af51d55d234df2bf7ae,0x985d1a71b66ac8f17b9a35425411bf4a,
307            0x97fa0378ec49fb22117d07ad7aa48fe5,0x97972cf18ba3699c393e8a785d3990e7,0x973496b1ab5f3c922e0938053a85beb1,0x96d2408f7da746d73fad0ee53dfc8276,
308            0x96702a614fd54bf2c824dfc0853dbf18,0x960e53fd8a6151ba5eab4b68e3b5f767,0x95acbd3ab0cffd6bc9088a1e195cea53,0x954b65ef61a0fc3f30a25322bbf1a91c,
309            0x94ea4df2563d776a25b44e0e2eca71ee,0x9489751a62e6938bfff15fd9a7ac0131,0x9428db3e76a3fb7c30a4e68b0326c740,0x93c880359b3276731f3e91a5563cae3a,
310            0x936863d6f4f289862e03fd38ad7fc3bc,0x930885f9c2d7246f89708b92dea2f65a,0x92a8e6755e54599a6996303bffeb6e33,0x924985213b4e216c7198f819f560a877,
311            0x91ea61d4e80728c4de231856302a36fa,0x918b7c680d0faaaa387031f48a1791d8,0x912cd4b26d34551f484c44f61644cd06,0x90ce6a8be56d3918041d8569810556b0,
312            0x90703dcc6cccc58742c7e8ed8ed09158,0x90124e4c146ecd7df7edd5e9881696fa,0x8fb49be307679954c7c2e119add951e9,0x8f5726698ab302d8c453fc00ababb43d,
313            0x8ef9edb7fd239c742ad3e1568efb4e8c,0x8e9cf1a6d751e34bfc22eda4fe753e0b,0x8e40320eab8b7c4b506eebe0da72f907,0x8de3aec825c27c154a69b1f36b581a59,
314            0x8d8767ac0b7cb9d69334b9bfd75d95fc,0x8d2b5c933bc32cef4cbc323a89ff2276,0x8ccf8d56af11556e6cd55394015908c3,0x8c73f9cf7744af57780a133a50fca2cc,
315            0x8c18a1d6bf8c30ab978faa7e892bafdb,0x8bbd8545cc57d22f0a75beedc441fc72,0x8b62a3f5fb4822e3f6a95fd84e9082b8,0x8b07fdc0c31de633a2f17b02591142a4,
316            0x8aad927fb3a9bcbf2791e4fdd5ca88f8,0x8a53620c75bbd7d0a7c69a202585ef8a,0x89f96c40cb13b7662aca755289fe16e7,0x899fb0f68e4ff2cf2f9b440b073935a9,
317            0x89463007b2de0bd61b28dc746db10a40,0x88ece94e44ea4c6ea515ae165b1bfb42,0x8893dca4694faee26ba5300e8a95a760,0x883b09e45d87d074dbe79408043ffb67,
318            0x87e270e8779aee779fa244759b125a88,0x878a118b260fedc8c6e1f10d6e209e78,0x8731eba6efdc6cb3e78d47fb5896fe3a,0x86d9ff167454df2f71b6f697afde7ca6,
319            0x86824bb46b1cb56f7bd22b847903be49,0x862ad15ba4168cc74e4e97c23dcf5888,0x85d38fe707546ad2fa7fd672891f334b,0x857c8731950802e24d10357345bfa1b3,
320            0x8525b7166573059e7098159d03738f19,0x84cf1f70a8d77ae39949820e8f79567d,0x8478c01ba76825c816f33469321238f2,0x842298f2c138f2ca2eef0207e89a09cd,
321            0x83cca9d16e2f701e23dda5e591584d32,0x8376f2933df35015d55d05e5787eb22e,0x83217313d7def59b662e725921f9f065,0x82cc2b2efaf00ab85b87f5be6feb17a0,
322            0x82771ac07db82122ac8e9a9a1990eef1,0x822241a44e4d5cc93d3797d2544787d1,0x81cd9fb6723b2859440b9ad1f56c06af,0x817934d30672f3b61e81ebd161b3c46c,
323            0x812500d63f3cfc5d1be0edb35ae6f88c,0x80d1039c68291faecac681ba03700df8,0x807d3d01e3ffb71759ad21bcf18d17d3,0x8029ace32cb27e0f9ef2134372e1305a,
324        ];
325
326        for (index, &parameter) in Sequence::new(272).parameters.iter().enumerate() {
327            assert_eq!(parameter, REFERENCE[index]);
328        }
329    }
330
331    #[test]
332    #[ignore]
333    fn check_reference_parameters_40000d() {
334        let seq = Sequence::new(40000);
335
336        assert_eq!(seq.parameters[0], 0xfffedd47769e0240104c06f7343b7241);
337        assert_eq!(seq.parameters[9], 0xfff4a504aa45d10d26450725c843317c);
338        assert_eq!(seq.parameters[99], 0xff8e88d67f9a0aafcb869a6de63d35eb);
339        assert_eq!(seq.parameters[18930], 0xb867948c981e001579b7c46882c694b9);
340        assert_eq!(seq.parameters[37919], 0x84b2e6946df6ad7c7c968dae86083dd4);
341        assert_eq!(seq.parameters[39998], 0x8000da0b87eca68f3ee760b18f991c7d);
342        assert_eq!(seq.parameters[39999], 0x800048ae4b9d6a67de0a620ebab103c6);
343    }
344
345    #[test]
346    #[ignore]
347    fn check_reference_parameters_1000000d() {
348        let seq = Sequence::new(1000000);
349
350        assert_eq!(seq.parameters[0], 0xfffff45ef542aa0acd04b35a993aa9a8);
351        assert_eq!(seq.parameters[10], 0xffff8014a6eb3b2225d711ecd213d01c);
352        assert_eq!(seq.parameters[100], 0xfffb69812ef796cc3756e4b28aeced9f);
353        assert_eq!(seq.parameters[1000], 0xffd28b55902c3b44798d606fa56be3fa);
354        assert_eq!(seq.parameters[10000], 0xfe3b43d01c0595637b7b2c71a4aa6378);
355        assert_eq!(seq.parameters[100000], 0xeedb35b9f1f390caa3abbde7ee8ec634);
356        assert_eq!(seq.parameters[162834], 0xe4ad372d72d7b768c9241bf29896218f);
357        assert_eq!(seq.parameters[528192], 0xb18428c86a7ad3d9a5f8a74daad3ea02);
358        assert_eq!(seq.parameters[819383], 0x9112341a999df0647adf6bf344803ed5);
359        assert_eq!(seq.parameters[999994], 0x80001ffae238e372bf5e3efe7339c557);
360        assert_eq!(seq.parameters[999998], 0x800008b8c8845531179837fa8ad9c164);
361        assert_eq!(seq.parameters[999999], 0x800002e842c03d050808f7952847fac9);
362    }
363
364    #[test]
365    fn check_sequence_samples_5d() {
366        let mut seq = Sequence::new(5);
367
368        assert_eq!(seq.next_raw(), 0x0);
369        assert_eq!(seq.next_raw(), 0x0);
370        assert_eq!(seq.next_raw(), 0x0);
371        assert_eq!(seq.next_raw(), 0x0);
372        assert_eq!(seq.next_raw(), 0x0);
373
374        seq.seek(1_000);
375
376        assert_eq!(seq.next_raw(), 0x457e82764cd63809);
377        assert_eq!(seq.next_raw(), 0xa3af00ddf92ab278);
378        assert_eq!(seq.next_raw(), 0x6e1cf8f61691a5b1);
379        assert_eq!(seq.next_raw(), 0x2b3296eeb51a048c);
380        assert_eq!(seq.next_raw(), 0x8e2e8b7198b4d3a5);
381
382        seq.seek(1_000_000);
383
384        assert_eq!(seq.next_raw(), 0x762d9e1c24cae389);
385        assert_eq!(seq.next_raw(), 0x639b63154ec92866);
386        assert_eq!(seq.next_raw(), 0x212c814828ef3e1a);
387        assert_eq!(seq.next_raw(), 0xbd9d94736da1c548);
388        assert_eq!(seq.next_raw(), 0x65d0b3bc825abfed);
389
390        seq.seek(1_000_000_000);
391
392        assert_eq!(seq.next_raw(), 0xa2319defb888d0e6);
393        assert_eq!(seq.next_raw(), 0x16fb0b3bc1c5cf6e);
394        assert_eq!(seq.next_raw(), 0x95d901dfe68a9713);
395        assert_eq!(seq.next_raw(), 0xaf8be2e43feaa1b7);
396        assert_eq!(seq.next_raw(), 0xb73e185d327db5e3);
397
398        seq.seek(1_000_000_000_000);
399
400        assert_eq!(seq.next_raw(), 0x91d0f068d67002b3);
401        assert_eq!(seq.next_raw(), 0xc4a3e16cecb2461c);
402        assert_eq!(seq.next_raw(), 0x57af529c8d5e25a8);
403        assert_eq!(seq.next_raw(), 0xba6e4b99ac87b38c);
404        assert_eq!(seq.next_raw(), 0xca8f2c0d3b0e7f45);
405
406        seq.seek(1_000_000_000_000_000);
407
408        assert_eq!(seq.next_raw(), 0x982b1985a58a8ebf);
409        assert_eq!(seq.next_raw(), 0x2028917c9861dfd1);
410        assert_eq!(seq.next_raw(), 0x84dab38837c31b23);
411        assert_eq!(seq.next_raw(), 0x3ed75049f2155e95);
412        assert_eq!(seq.next_raw(), 0x3f4413aeb0a12689);
413
414        seq.seek(1_000_000_000_000_000_000);
415
416        assert_eq!(seq.next_raw(), 0x685bb20ea53d9b28);
417        assert_eq!(seq.next_raw(), 0x9e784eb33e524b91);
418        assert_eq!(seq.next_raw(), 0xf64d4c19d2220204);
419        assert_eq!(seq.next_raw(), 0x7911a0d9a37979a6);
420        assert_eq!(seq.next_raw(), 0x21ece261f57e87da);
421    }
422}
quasi_rd/lib.rs

quasi_rd/
lib.rs
