substrate_fixed/
consts.rs

1// Copyright © 2018–2019 Trevor Spiteri
2
3// This library is free software: you can redistribute it and/or
4// modify it under the terms of either
5//
6//   * the Apache License, Version 2.0 or
7//   * the MIT License
8//
9// at your option.
10//
11// You should have recieved copies of the Apache License and the MIT
12// License along with the library. If not, see
13// <https://www.apache.org/licenses/LICENSE-2.0> and
14// <https://opensource.org/licenses/MIT>.
15
16/*!
17This module contains constants.
18
19The constants have the maximum precision possible for a fixed-point
20number, and are rounded down at that precision.
21
22# Examples
23
24```rust
25use substrate_fixed::{consts, types::I4F28};
26let tau = I4F28::from_num(consts::TAU);
27println!("τ = 2π with eight binary places is {:.8b}", tau);
28assert_eq!(format!("{:.8b}", tau), "110.01001000");
29println!("τ = 2π with six decimal places is {:.8}", tau);
30assert_eq!(format!("{:.8}", tau), "6.28318531");
31```
32*/
33
34use crate::types::{U0F128, U1F127, U2F126, U3F125};
35
36/// τ = 6.28318…
37// TAU = 6.283185307179586476925286766559005768394...
38pub const TAU: U3F125 = U3F125::from_bits(0xC90F_DAA2_2168_C234_C4C6_628B_80DC_1CD1);
39
40/// τ/2 = 3.14159…
41// FRAC_TAU_2 = 3.141592653589793238462643383279502884197...
42pub const FRAC_TAU_2: U2F126 = U2F126::from_bits(0xC90F_DAA2_2168_C234_C4C6_628B_80DC_1CD1);
43
44/// τ/3 = 2.09439…
45// FRAC_TAU_3 = 2.094395102393195492308428922186335256131...
46pub const FRAC_TAU_3: U2F126 = U2F126::from_bits(0x860A_91C1_6B9B_2C23_2DD9_9707_AB3D_688B);
47
48/// τ/4 = 1.57079…
49// FRAC_TAU_4 = 1.570796326794896619231321691639751442098...
50pub const FRAC_TAU_4: U1F127 = U1F127::from_bits(0xC90F_DAA2_2168_C234_C4C6_628B_80DC_1CD1);
51
52/// τ/6 = 1.04719…
53// FRAC_TAU_6 = 1.047197551196597746154214461093167628065...
54pub const FRAC_TAU_6: U1F127 = U1F127::from_bits(0x860A_91C1_6B9B_2C23_2DD9_9707_AB3D_688B);
55
56/// τ/8 = 0.785398…
57// FRAC_TAU_8 = 0.7853981633974483096156608458198757210492...
58pub const FRAC_TAU_8: U0F128 = U0F128::from_bits(0xC90F_DAA2_2168_C234_C4C6_628B_80DC_1CD1);
59
60/// τ/12 = 0.523598…
61// FRAC_TAU_12 = 0.5235987755982988730771072305465838140328...
62pub const FRAC_TAU_12: U0F128 = U0F128::from_bits(0x860A_91C1_6B9B_2C23_2DD9_9707_AB3D_688B);
63
64/// 1/τ = 0.159154…
65// FRAC_1_TAU = 0.1591549430918953357688837633725143620344...
66pub const FRAC_1_TAU: U0F128 = U0F128::from_bits(0x28BE_60DB_9391_054A_7F09_D5F4_7D4D_3770);
67
68/// 2/τ = 0.318309…
69// FRAC_2_TAU = 0.3183098861837906715377675267450287240689...
70pub const FRAC_2_TAU: U0F128 = U0F128::from_bits(0x517C_C1B7_2722_0A94_FE13_ABE8_FA9A_6EE0);
71
72/// 4/τ = 0.636619…
73// FRAC_4_TAU = 0.6366197723675813430755350534900574481378...
74pub const FRAC_4_TAU: U0F128 = U0F128::from_bits(0xA2F9_836E_4E44_1529_FC27_57D1_F534_DDC0);
75
76/// π = 3.14159…
77// PI = 3.141592653589793238462643383279502884197...
78pub const PI: U2F126 = U2F126::from_bits(0xC90F_DAA2_2168_C234_C4C6_628B_80DC_1CD1);
79
80/// π/2 = 1.57079…
81// FRAC_PI_2 = 1.570796326794896619231321691639751442098...
82pub const FRAC_PI_2: U1F127 = U1F127::from_bits(0xC90F_DAA2_2168_C234_C4C6_628B_80DC_1CD1);
83
84/// π/3 = 1.04719…
85// FRAC_PI_3 = 1.047197551196597746154214461093167628065...
86pub const FRAC_PI_3: U1F127 = U1F127::from_bits(0x860A_91C1_6B9B_2C23_2DD9_9707_AB3D_688B);
87
88/// π/4 = 0.785398…
89// FRAC_PI_4 = 0.7853981633974483096156608458198757210492...
90pub const FRAC_PI_4: U0F128 = U0F128::from_bits(0xC90F_DAA2_2168_C234_C4C6_628B_80DC_1CD1);
91
92/// π/6 = 0.523598…
93// FRAC_PI_6 = 0.5235987755982988730771072305465838140328...
94pub const FRAC_PI_6: U0F128 = U0F128::from_bits(0x860A_91C1_6B9B_2C23_2DD9_9707_AB3D_688B);
95
96/// π/8 = 0.392699…
97// FRAC_PI_8 = 0.3926990816987241548078304229099378605246...
98pub const FRAC_PI_8: U0F128 = U0F128::from_bits(0x6487_ED51_10B4_611A_6263_3145_C06E_0E68);
99
100/// 1/π = 0.318309…
101// FRAC_1_PI = 0.3183098861837906715377675267450287240689...
102pub const FRAC_1_PI: U0F128 = U0F128::from_bits(0x517C_C1B7_2722_0A94_FE13_ABE8_FA9A_6EE0);
103
104/// 2/π = 0.636619…
105// FRAC_2_PI = 0.6366197723675813430755350534900574481378...
106pub const FRAC_2_PI: U0F128 = U0F128::from_bits(0xA2F9_836E_4E44_1529_FC27_57D1_F534_DDC0);
107
108/// 2/√π = 1.12837…
109// FRAC_2_SQRT_PI = 1.128379167095512573896158903121545171688...
110pub const FRAC_2_SQRT_PI: U1F127 = U1F127::from_bits(0x906E_BA82_14DB_688D_71D4_8A7F_6BFE_C344);
111
112/// √2 = 1.41421…
113// SQRT_2 = 1.414213562373095048801688724209698078569...
114pub const SQRT_2: U1F127 = U1F127::from_bits(0xB504_F333_F9DE_6484_597D_89B3_754A_BE9F);
115
116/// 1/√2 = 0.707106…
117// FRAC_1_SQRT_2 = 0.7071067811865475244008443621048490392848...
118pub const FRAC_1_SQRT_2: U0F128 = U0F128::from_bits(0xB504_F333_F9DE_6484_597D_89B3_754A_BE9F);
119
120/// e = 2.71828…
121// E = 2.718281828459045235360287471352662497757...
122pub const E: U2F126 = U2F126::from_bits(0xADF8_5458_A2BB_4A9A_AFDC_5620_273D_3CF1);
123
124/// log<sub>2</sub> 10 = 3.32192…
125// LOG2_10 = 3.321928094887362347870319429489390175864...
126pub const LOG2_10: U2F126 = U2F126::from_bits(0xD49A_784B_CD1B_8AFE_492B_F6FF_4DAF_DB4C);
127
128/// log<sub>2</sub> e = 1.44269…
129// LOG2_E = 1.442695040888963407359924681001892137426...
130pub const LOG2_E: U1F127 = U1F127::from_bits(0xB8AA_3B29_5C17_F0BB_BE87_FED0_691D_3E88);
131
132/// log<sub>10</sub> 2 = 0.301029…
133// LOG10_2 = 0.3010299956639811952137388947244930267681...
134pub const LOG10_2: U0F128 = U0F128::from_bits(0x4D10_4D42_7DE7_FBCC_47C4_ACD6_05BE_48BC);
135
136/// log<sub>10</sub> e = 0.434294…
137// LOG10_E = 0.4342944819032518276511289189166050822943...
138pub const LOG10_E: U0F128 = U0F128::from_bits(0x6F2D_EC54_9B94_38CA_9AAD_D557_D699_EE19);
139
140/// ln 2 = 0.693147…
141// LN_2 = 0.6931471805599453094172321214581765680755...
142pub const LN_2: U0F128 = U0F128::from_bits(0xB172_17F7_D1CF_79AB_C9E3_B398_03F2_F6AF);
143
144/// ln 10 = 2.30258…
145// LN_10 = 2.302585092994045684017991454684364207601...
146pub const LN_10: U2F126 = U2F126::from_bits(0x935D_8DDD_AAA8_AC16_EA56_D62B_82D3_0A28);
147
148#[cfg(test)]
149#[allow(clippy::cognitive_complexity, clippy::float_cmp)]
150mod tests {
151    use crate::{
152        consts::*,
153        traits::{Fixed, FromFixed},
154    };
155    use core::{convert::TryFrom, f32, f64};
156
157    #[cfg(feature = "f16")]
158    #[test]
159    fn cmp_f16() {
160        use half::{self, f16};
161        assert_eq!(f16::from_fixed(TAU), f16::from_f32(f32::consts::PI * 2.0));
162        assert_eq!(f16::from_fixed(FRAC_TAU_2), f16::PI);
163        assert_eq!(
164            f16::from_fixed(FRAC_TAU_3),
165            f16::from_f32(f32::consts::FRAC_PI_3 * 2.0)
166        );
167        assert_eq!(f16::from_fixed(FRAC_TAU_4), f16::FRAC_PI_2);
168        assert_eq!(f16::from_fixed(FRAC_TAU_6), f16::FRAC_PI_3);
169        assert_eq!(f16::from_fixed(FRAC_TAU_8), f16::FRAC_PI_4);
170        assert_eq!(f16::from_fixed(FRAC_TAU_12), f16::FRAC_PI_6);
171        assert_eq!(
172            f16::from_fixed(FRAC_1_TAU),
173            f16::from_f32(f32::consts::FRAC_1_PI * 0.5)
174        );
175        assert_eq!(f16::from_fixed(FRAC_2_TAU), f16::FRAC_1_PI);
176        assert_eq!(f16::from_fixed(FRAC_4_TAU), f16::FRAC_2_PI);
177        assert_eq!(f16::from_fixed(PI), f16::PI);
178        assert_eq!(f16::from_fixed(FRAC_PI_2), f16::FRAC_PI_2);
179        assert_eq!(f16::from_fixed(FRAC_PI_3), f16::FRAC_PI_3);
180        assert_eq!(f16::from_fixed(FRAC_PI_4), f16::FRAC_PI_4);
181        assert_eq!(f16::from_fixed(FRAC_PI_6), f16::FRAC_PI_6);
182        assert_eq!(f16::from_fixed(FRAC_PI_8), f16::FRAC_PI_8);
183        assert_eq!(f16::from_fixed(FRAC_1_PI), f16::FRAC_1_PI);
184        assert_eq!(f16::from_fixed(FRAC_2_PI), f16::FRAC_2_PI);
185        assert_eq!(f16::from_fixed(FRAC_2_SQRT_PI), f16::FRAC_2_SQRT_PI);
186        assert_eq!(f16::from_fixed(SQRT_2), f16::SQRT_2);
187        assert_eq!(f16::from_fixed(FRAC_1_SQRT_2), f16::FRAC_1_SQRT_2);
188        assert_eq!(f16::from_fixed(E), f16::E);
189        // assert_eq!(f16::from_fixed(LOG2_10), f16::LOG2_10);
190        assert_eq!(f16::from_fixed(LOG2_E), f16::LOG2_E);
191        // assert_eq!(f16::from_fixed(LOG10_2), f16::LOG10_2);
192        assert_eq!(f16::from_fixed(LOG10_E), f16::LOG10_E);
193        assert_eq!(f16::from_fixed(LN_2), f16::LN_2);
194        assert_eq!(f16::from_fixed(LN_10), f16::LN_10);
195    }
196
197    #[cfg(feature = "f16")]
198    #[test]
199    fn cmp_bf16() {
200        use half::{self, bf16};
201        assert_eq!(bf16::from_fixed(TAU), bf16::from_f32(f32::consts::PI * 2.0));
202        assert_eq!(bf16::from_fixed(FRAC_TAU_2), bf16::PI);
203        assert_eq!(
204            bf16::from_fixed(FRAC_TAU_3),
205            bf16::from_f32(f32::consts::FRAC_PI_3 * 2.0)
206        );
207        assert_eq!(bf16::from_fixed(FRAC_TAU_4), bf16::FRAC_PI_2);
208        assert_eq!(bf16::from_fixed(FRAC_TAU_6), bf16::FRAC_PI_3);
209        assert_eq!(bf16::from_fixed(FRAC_TAU_8), bf16::FRAC_PI_4);
210        assert_eq!(bf16::from_fixed(FRAC_TAU_12), bf16::FRAC_PI_6);
211        assert_eq!(
212            bf16::from_fixed(FRAC_1_TAU),
213            bf16::from_f32(f32::consts::FRAC_1_PI * 0.5)
214        );
215        assert_eq!(bf16::from_fixed(FRAC_2_TAU), bf16::FRAC_1_PI);
216        assert_eq!(bf16::from_fixed(FRAC_4_TAU), bf16::FRAC_2_PI);
217        assert_eq!(bf16::from_fixed(PI), bf16::PI);
218        assert_eq!(bf16::from_fixed(FRAC_PI_2), bf16::FRAC_PI_2);
219        assert_eq!(bf16::from_fixed(FRAC_PI_3), bf16::FRAC_PI_3);
220        assert_eq!(bf16::from_fixed(FRAC_PI_4), bf16::FRAC_PI_4);
221        assert_eq!(bf16::from_fixed(FRAC_PI_6), bf16::FRAC_PI_6);
222        assert_eq!(bf16::from_fixed(FRAC_PI_8), bf16::FRAC_PI_8);
223        assert_eq!(bf16::from_fixed(FRAC_1_PI), bf16::FRAC_1_PI);
224        assert_eq!(bf16::from_fixed(FRAC_2_PI), bf16::FRAC_2_PI);
225        assert_eq!(bf16::from_fixed(FRAC_2_SQRT_PI), bf16::FRAC_2_SQRT_PI);
226        assert_eq!(bf16::from_fixed(SQRT_2), bf16::SQRT_2);
227        assert_eq!(bf16::from_fixed(FRAC_1_SQRT_2), bf16::FRAC_1_SQRT_2);
228        assert_eq!(bf16::from_fixed(E), bf16::E);
229        // assert_eq!(bf16::from_fixed(LOG2_10), bf16::LOG2_10);
230        assert_eq!(bf16::from_fixed(LOG2_E), bf16::LOG2_E);
231        // assert_eq!(bf16::from_fixed(LOG10_2), bf16::LOG10_2);
232        assert_eq!(bf16::from_fixed(LOG10_E), bf16::LOG10_E);
233        assert_eq!(bf16::from_fixed(LN_2), bf16::LN_2);
234        assert_eq!(bf16::from_fixed(LN_10), bf16::LN_10);
235    }
236
237    #[test]
238    fn cmp_f32() {
239        assert_eq!(f32::from_fixed(TAU), f32::consts::PI * 2.0);
240        assert_eq!(f32::from_fixed(FRAC_TAU_2), f32::consts::PI);
241        assert_eq!(f32::from_fixed(FRAC_TAU_3), f32::consts::FRAC_PI_3 * 2.0);
242        assert_eq!(f32::from_fixed(FRAC_TAU_4), f32::consts::FRAC_PI_2);
243        assert_eq!(f32::from_fixed(FRAC_TAU_6), f32::consts::FRAC_PI_3);
244        assert_eq!(f32::from_fixed(FRAC_TAU_8), f32::consts::FRAC_PI_4);
245        assert_eq!(f32::from_fixed(FRAC_TAU_12), f32::consts::FRAC_PI_6);
246        assert_eq!(f32::from_fixed(FRAC_1_TAU), f32::consts::FRAC_1_PI * 0.5);
247        assert_eq!(f32::from_fixed(FRAC_2_TAU), f32::consts::FRAC_1_PI);
248        assert_eq!(f32::from_fixed(FRAC_4_TAU), f32::consts::FRAC_2_PI);
249        assert_eq!(f32::from_fixed(PI), f32::consts::PI);
250        assert_eq!(f32::from_fixed(FRAC_PI_2), f32::consts::FRAC_PI_2);
251        assert_eq!(f32::from_fixed(FRAC_PI_3), f32::consts::FRAC_PI_3);
252        assert_eq!(f32::from_fixed(FRAC_PI_4), f32::consts::FRAC_PI_4);
253        assert_eq!(f32::from_fixed(FRAC_PI_6), f32::consts::FRAC_PI_6);
254        assert_eq!(f32::from_fixed(FRAC_PI_8), f32::consts::FRAC_PI_8);
255        assert_eq!(f32::from_fixed(FRAC_1_PI), f32::consts::FRAC_1_PI);
256        assert_eq!(f32::from_fixed(FRAC_2_PI), f32::consts::FRAC_2_PI);
257        assert_eq!(f32::from_fixed(FRAC_2_SQRT_PI), f32::consts::FRAC_2_SQRT_PI);
258        assert_eq!(f32::from_fixed(SQRT_2), f32::consts::SQRT_2);
259        assert_eq!(f32::from_fixed(FRAC_1_SQRT_2), f32::consts::FRAC_1_SQRT_2);
260        assert_eq!(f32::from_fixed(E), f32::consts::E);
261        // assert_eq!(f32::from_fixed(LOG2_10), f32::consts::LOG2_10);
262        assert_eq!(f32::from_fixed(LOG2_E), f32::consts::LOG2_E);
263        // assert_eq!(f32::from_fixed(LOG10_2), f32::consts::LOG10_2);
264        assert_eq!(f32::from_fixed(LOG10_E), f32::consts::LOG10_E);
265        assert_eq!(f32::from_fixed(LN_2), f32::consts::LN_2);
266        assert_eq!(f32::from_fixed(LN_10), f32::consts::LN_10);
267    }
268
269    #[test]
270    fn cmp_f64() {
271        assert_eq!(f64::from_fixed(TAU), f64::consts::PI * 2.0);
272        assert_eq!(f64::from_fixed(FRAC_TAU_2), f64::consts::PI);
273        assert_eq!(f64::from_fixed(FRAC_TAU_3), f64::consts::FRAC_PI_3 * 2.0);
274        assert_eq!(f64::from_fixed(FRAC_TAU_4), f64::consts::FRAC_PI_2);
275        assert_eq!(f64::from_fixed(FRAC_TAU_6), f64::consts::FRAC_PI_3);
276        assert_eq!(f64::from_fixed(FRAC_TAU_8), f64::consts::FRAC_PI_4);
277        assert_eq!(f64::from_fixed(FRAC_TAU_12), f64::consts::FRAC_PI_6);
278        assert_eq!(f64::from_fixed(FRAC_1_TAU), f64::consts::FRAC_1_PI * 0.5);
279        assert_eq!(f64::from_fixed(FRAC_2_TAU), f64::consts::FRAC_1_PI);
280        assert_eq!(f64::from_fixed(FRAC_4_TAU), f64::consts::FRAC_2_PI);
281        assert_eq!(f64::from_fixed(PI), f64::consts::PI);
282        assert_eq!(f64::from_fixed(FRAC_PI_2), f64::consts::FRAC_PI_2);
283        assert_eq!(f64::from_fixed(FRAC_PI_3), f64::consts::FRAC_PI_3);
284        assert_eq!(f64::from_fixed(FRAC_PI_4), f64::consts::FRAC_PI_4);
285        assert_eq!(f64::from_fixed(FRAC_PI_6), f64::consts::FRAC_PI_6);
286        assert_eq!(f64::from_fixed(FRAC_PI_8), f64::consts::FRAC_PI_8);
287        assert_eq!(f64::from_fixed(FRAC_1_PI), f64::consts::FRAC_1_PI);
288        assert_eq!(f64::from_fixed(FRAC_2_PI), f64::consts::FRAC_2_PI);
289        assert_eq!(f64::from_fixed(FRAC_2_SQRT_PI), f64::consts::FRAC_2_SQRT_PI);
290        assert_eq!(f64::from_fixed(SQRT_2), f64::consts::SQRT_2);
291        assert_eq!(f64::from_fixed(FRAC_1_SQRT_2), f64::consts::FRAC_1_SQRT_2);
292        assert_eq!(f64::from_fixed(E), f64::consts::E);
293        // assert_eq!(f64::from_fixed(LOG2_10), f64::consts::LOG2_10);
294        assert_eq!(f64::from_fixed(LOG2_E), f64::consts::LOG2_E);
295        // assert_eq!(f64::from_fixed(LOG10_2), f64::consts::LOG10_2);
296        assert_eq!(f64::from_fixed(LOG10_E), f64::consts::LOG10_E);
297        assert_eq!(f64::from_fixed(LN_2), f64::consts::LN_2);
298        assert_eq!(f64::from_fixed(LN_10), f64::consts::LN_10);
299    }
300
301    fn compare_parse<F: Fixed>(f: F, s: &str)
302    where
303        F::Bits: TryFrom<u8>,
304    {
305        let sf = F::from_str(s).unwrap();
306        let f_plus = f + F::from_bits(F::Bits::try_from(1).ok().unwrap());
307        assert!(f <= sf && sf <= f_plus);
308    }
309
310    #[test]
311    fn cmp_parse() {
312        compare_parse(TAU, "6.283185307179586476925286766559005768394");
313        compare_parse(FRAC_TAU_2, "3.141592653589793238462643383279502884197");
314        compare_parse(FRAC_TAU_3, "2.094395102393195492308428922186335256131");
315        compare_parse(FRAC_TAU_4, "1.570796326794896619231321691639751442098");
316        compare_parse(FRAC_TAU_6, "1.047197551196597746154214461093167628065");
317        compare_parse(FRAC_TAU_8, "0.7853981633974483096156608458198757210492");
318        compare_parse(FRAC_TAU_12, "0.5235987755982988730771072305465838140328");
319        compare_parse(FRAC_1_TAU, "0.1591549430918953357688837633725143620344");
320        compare_parse(FRAC_2_TAU, "0.3183098861837906715377675267450287240689");
321        compare_parse(FRAC_4_TAU, "0.6366197723675813430755350534900574481378");
322        compare_parse(PI, "3.141592653589793238462643383279502884197");
323        compare_parse(FRAC_PI_2, "1.570796326794896619231321691639751442098");
324        compare_parse(FRAC_PI_3, "1.047197551196597746154214461093167628065");
325        compare_parse(FRAC_PI_4, "0.7853981633974483096156608458198757210492");
326        compare_parse(FRAC_PI_6, "0.5235987755982988730771072305465838140328");
327        compare_parse(FRAC_PI_8, "0.3926990816987241548078304229099378605246");
328        compare_parse(FRAC_1_PI, "0.3183098861837906715377675267450287240689");
329        compare_parse(FRAC_2_PI, "0.6366197723675813430755350534900574481378");
330        compare_parse(FRAC_2_SQRT_PI, "1.128379167095512573896158903121545171688");
331        compare_parse(SQRT_2, "1.414213562373095048801688724209698078569");
332        compare_parse(FRAC_1_SQRT_2, "0.7071067811865475244008443621048490392848");
333        compare_parse(E, "2.718281828459045235360287471352662497757");
334        compare_parse(LOG2_10, "3.321928094887362347870319429489390175864");
335        compare_parse(LOG2_E, "1.442695040888963407359924681001892137426");
336        compare_parse(LOG10_2, "0.3010299956639811952137388947244930267681");
337        compare_parse(LOG10_E, "0.4342944819032518276511289189166050822943");
338        compare_parse(LN_2, "0.6931471805599453094172321214581765680755");
339        compare_parse(LN_10, "2.302585092994045684017991454684364207601");
340    }
341}
substrate_fixed/consts.rs

substrate_fixed/
consts.rs
