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
use rand::Rng;
/// A trait containing methods that generate
/// floating point numbers out of pseudorandom `u64` integers in
/// several experimental ways.
pub trait NonCanonical {
/// Generates an `f64`. The maximum is 0.9999999999999999.
/// The minimum is 0.000030517578125, and therefore much closer
/// to zero than with the standard method. However, it comes at the cost of not
/// getting equidistributed values. The orders of magnitude are roughly
/// equidistributed.
/// # Example
/// ```
/// use rand_core::{RngCore, SeedableRng};
/// use rand_xoshiro::Xoshiro256PlusPlus;
/// use floaters::NonCanonical;
///
/// let mut rng = Xoshiro256PlusPlus::seed_from_u64(78787878);
/// (0..125).for_each(|_| { rng.next_u64(); } );
/// assert_eq!(0.0008912212147751437, rng.noncanonical_f64());
/// ```
fn noncanonical_f64(&mut self) -> f64;
/// Generate a signed `f64` roughly equidistributed in the range
/// `-1.0` - `1.0`.
/// The eleventh least significant bit of the PRNG's output
/// is used as sign bit.
/// # Example
/// ```
/// use rand_core::{RngCore, SeedableRng};
/// use rand_xoshiro::Xoshiro256PlusPlus;
/// use floaters::NonCanonical;
///
/// let mut rng = Xoshiro256PlusPlus::seed_from_u64(1234);
/// (0..10).for_each(|_| { rng.next_u64(); } );
/// assert_eq!(-0.8926449323284786, rng.signed_uniform());
/// ```
fn signed_uniform(&mut self) -> f64;
/// Generates an `f64` with a specified exponent. If `Sign` is the `Signed` variant,
/// you will also get signed numbers. The mantissa will always be pseudorandomly
/// generated.
/// Only the lowest 11 bits of the specified `u16` will be used as the exponent, due to
/// the specifications of the `f64` type.
/// # Example
/// ```
/// use rand_core::{RngCore, SeedableRng};
/// use rand_xoshiro::Xoshiro256StarStar;
/// use floaters::{NonCanonical, Sign};
///
/// let mut rng = Xoshiro256StarStar::seed_from_u64(7878);
/// (0..42).for_each(|_| { rng.next_u64(); } );
/// let exp = 0b100_0000_0001;
/// let sign = Sign::Signed;
/// assert_eq!(-4.569802780283289, rng.exp_f64(exp, sign));
/// ```
fn exp_f64(&mut self, exponent: u16, signed: Sign) -> f64;
/// Generate an `f64` by specifying parameters.
/// Reasonable values for `left_shift` are in the range
/// `53..=61`. The higher the value the closer the number gets
/// to zero. The `left_shift` parameter is automatically kept
/// within that range, i.e. it saturates at 53 and 61 in order to
/// prevent overflow errors and/or unexpected behaviour.
/// If `Sign` is the `Signed` variant, you will also get signed
/// numbers.
/// The numbers closest to zero in the given example are
/// 0.0078125 and -0.0078125. The numbers farthest from zero
/// are 0.9999999999999999 and -0.9999999999999999.
/// The numbers are not evenly distributed.
///
/// # Example
/// ```
/// use rand_core::{RngCore, SeedableRng};
/// use rand_xoshiro::Xoshiro256StarStar;
/// use floaters::{NonCanonical, Sign};
///
/// let mut rng = Xoshiro256StarStar::seed_from_u64(42);
/// (0..7878).for_each(|_| { rng.next_u64(); } );
/// assert_eq!(-0.05579455843802982, rng.with_params_f64(55, Sign::Signed));
/// ```
fn with_params_f64(&mut self, left_shift: i8, signed: Sign) -> f64;
/// Generates an `f32` tuple. Values are not evenly distributed, but get
/// close to zero. The minimum is 0.0078125, the maximum is 0.99999994.
///
/// The first element of the tuple is generated from the
/// lowest 32 bits, and the second element is generated using the
/// highest 32 bits of the underlying `u64`.
/// Keep in mind that the lowest bits might be of low linear complexity,
/// depending on the chosen (P)RNG.
///
/// # Example
/// ```
/// use rand_core::{RngCore, SeedableRng};
/// use rand_xoshiro::Xoshiro256StarStar;
/// use floaters::NonCanonical;
///
/// let mut rng = Xoshiro256StarStar::seed_from_u64(43214321);
/// (0..987).for_each(|_| { rng.next_u64(); } );
/// assert_eq!( (0.009435893, 0.24692793),
/// rng.noncanonical_tuple_f32() );
/// ```
fn noncanonical_tuple_f32(&mut self) -> (f32, f32);
/// Generates a signed `f32` tuple. The `.0` element of
/// the tuple might be of low linear complexity, depending
/// on the chosen (P)RNG.
fn signed_tuple_f32(&mut self) -> (f32, f32);
/// Generates an `f32` tuple with specified parameters.
/// Values are likely not evenly distributed.
/// The `left_shift` parameter saturates at 21 and 29.
/// Creates signed values if `Sign` is the `Signed` variant.
/// The `.0` element of the tuple might be of low linear
/// complexity, depending on the chosen (P)RNG.
///
/// # Example
/// ```
/// use rand_core::{RngCore, SeedableRng};
/// use rand_xoshiro::Xoshiro256PlusPlus;
/// use floaters::{NonCanonical, Sign};
///
/// let mut rng = Xoshiro256PlusPlus::seed_from_u64(42);
/// (0..1234).for_each(|_| { rng.next_u64(); } );
/// let tuple_f32 = rng.with_params_tuple_f32(26, Sign::Signed);
///
/// assert_eq!( (-0.0095176855, 0.24847426), tuple_f32 );
/// ```
fn with_params_tuple_f32(&mut self, left_shift: i8, signed: Sign) -> (f32, f32);
/// Generates an `f32` tuple with a specified exponent.
/// Creates signed values if `Sign` is the `Signed` variant.
/// The `.0` element of the tuple might be of low linear
/// complexity, depending on the chosen (P)RNG.
///
/// # Example
/// ```
/// use rand_core::{RngCore, SeedableRng};
/// use rand_xoshiro::Xoshiro256PlusPlus;
/// use floaters::{NonCanonical, Sign};
///
/// let mut rng = Xoshiro256PlusPlus::seed_from_u64(42);
/// (0..1234).for_each(|_| { rng.next_u64(); } );
/// let tuple_f32 = rng.exp_f32(0b1000_0001u8, Sign::Signed);
///
/// assert_eq!((-4.873055f32, 7.951176f32), tuple_f32);
/// ```
fn exp_f32(&mut self, exp: u8, signed: Sign) -> (f32, f32);
/// Generates an `f64` out of 64 pseudorandom bits including
/// negative zero, infinity, negative infinity and Nan.
///
/// # Example
/// ```
/// use rand_core::{RngCore, SeedableRng};
/// use rand_xoshiro::Xoshiro512StarStar;
/// use floaters::NonCanonical;
///
/// let mut rng = Xoshiro512StarStar::seed_from_u64(1234);
/// (0..123).for_each(|_| { rng.next_u64(); } );
/// let wild_f64 = rng.wild_f64();
///
/// assert_eq!(2.640929385653772e-105, wild_f64);
/// ```
fn wild_f64(&mut self) -> f64;
/// Generates an `f32` tuple out of 64 pseudorandom bits including
/// negative zero, infinity, negative infinity and Nan.
/// Keep in mind that the lower bits of the underlying `u64`
/// might be of low linear complexity, so you might prefer the
/// second element of the tuple.
///
/// # Example
/// ```
/// use rand_core::{RngCore, SeedableRng};
/// use rand_xoshiro::Xoshiro512StarStar;
/// use floaters::NonCanonical;
///
/// let mut rng = Xoshiro512StarStar::seed_from_u64(123);
/// (0..123).for_each(|_| { rng.next_u64(); } );
/// let wild_f32 = rng.wild_tuple_f32();
///
/// assert_eq!((-6.6361835e20, -1.9641858), wild_f32);
/// ```
fn wild_tuple_f32(&mut self) -> (f32, f32);
}
impl<T: Rng> NonCanonical for T {
fn noncanonical_f64(&mut self) -> f64 {
let mut x = self.next_u64();
x |= u64::MAX << (56 + 2) >> 2;
x &= !(3u64 << 62 | 1u64 << 52);
f64::from_bits(x)
}
fn exp_f64(&mut self, exponent: u16, signed: Sign) -> f64 {
let mut x = self.next_u64();
let exp = (exponent << 5 >> 5) as u64;
if signed == Sign::Signed
{ x &= !(2047u64 << 52); } else { x &= !(4095u64 << 52); }
x |= exp << 52;
f64::from_bits(x)
}
fn signed_uniform(&mut self) -> f64 {
let x = self.next_u64();
let sign_bit = x >> 10 << 63;
let output = (x >> 11) as f64 * 1.110223e-16;
f64::from_bits(output.to_bits() | sign_bit)
}
fn with_params_f64(&mut self, left_shift: i8, signed: Sign) -> f64 {
let left_shift_sat = if left_shift < 53 { 53 }
else if left_shift > 61 { 61 }
else { left_shift };
let mut x = self.next_u64();
let sign_mask = if signed == Sign::Signed { 1u64 } else { 3u64 };
let ls = left_shift_sat as usize;
x |= u64::MAX << (ls + 2) >> 2;
x &= !(sign_mask << 62 | 1u64 << 52);
f64::from_bits(x)
}
fn noncanonical_tuple_f32(&mut self) -> (f32, f32) {
let x = self.next_u64();
let (mut le, mut be) = u32_from_u64(x);
( f32_from_u32(&mut le, 26, Sign::Unsigned),
f32_from_u32(&mut be, 26, Sign::Unsigned) )
}
fn signed_tuple_f32(&mut self) -> (f32, f32) {
let x = self.next_u64();
let (le, be) = u32_from_u64(x);
( f32_with_sign(le), f32_with_sign(be) )
}
fn exp_f32(&mut self, exp: u8, signed: Sign) -> (f32, f32) {
let x = self.next_u64();
let (mut le, mut be) = u32_from_u64(x);
( specified_exp_f32(&mut le, exp, signed),
specified_exp_f32(&mut be, exp, signed) )
}
fn with_params_tuple_f32(&mut self, left_shift: i8, signed: Sign) -> (f32, f32) {
let left_shift_sat = if left_shift < 21 { 21 }
else if left_shift > 29 { 29 }
else { left_shift };
let x = self.next_u64();
let (mut le, mut be) = u32_from_u64(x);
( f32_from_u32(&mut le, left_shift_sat, signed),
f32_from_u32(&mut be, left_shift_sat, signed) )
}
fn wild_f64(&mut self) -> f64 {
let x = self.next_u64();
f64::from_bits(x)
}
fn wild_tuple_f32(&mut self) -> (f32, f32) {
let x = self.next_u64();
let (le, be) = u32_from_u64(x);
( f32::from_bits(le),
f32::from_bits(be) )
}
}
/// Return either signed or unsigned values.
#[derive(PartialEq, Copy, Clone)]
pub enum Sign {
Signed,
Unsigned
}
// f32 helper functions
fn u32_from_u64(bits: u64) -> (u32, u32) {
( (bits << 32 >> 32) as u32,
(bits >> 32) as u32 )
}
// reasonable values for left_shift: 26, 21..=29
fn f32_from_u32(bits: &mut u32, left_shift: i8, signed: Sign) -> f32 {
let sign_mask = if signed == Sign::Signed { 1u32 } else { 3u32 };
*bits |= u32::MAX << (left_shift + 2) >> 2;
*bits &= !(sign_mask << 30 | 1u32 << 23);
f32::from_bits(*bits)
}
fn f32_with_sign(bits: u32) -> f32 {
let sign_bit = bits >> 8 << 31;
let output = (bits >> 9) as f32 * 1.192093e-07;
f32::from_bits(output.to_bits() | sign_bit)
}
fn specified_exp_f32(bits: &mut u32, exponent: u8, signed: Sign) -> f32 {
if signed == Sign::Signed
{ *bits &= !(255u32 << 23); }
else
{ *bits &= !(511u32 << 23); }
*bits |= (exponent as u32) << 23;
f32::from_bits(*bits)
}