symplex 0.3.0

Exact symbolic mathematics for Rust: calculus, summation, solving, linear algebra, transforms, compile-time dimensional analysis, and Rust/C code generation
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

//! Tests for numerical evaluation of special functions (Wave β).
//!
//! Covers: Gamma, LogGamma, Digamma, erf, erfc, Beta.

use symplex::prelude::*;
#[test]
fn evalf_gamma_at_5() {
    let ctx = Context::new();
    // Gamma(5) = 4! = 24
    let result = ctx.int(5).gamma().eval_f64().unwrap();
    assert!(
        (result - 24.0).abs() < 1e-10,
        "Gamma(5) should be 24, got {result}"
    );
}

#[test]
fn evalf_gamma_at_half() {
    let ctx = Context::new();
    // Gamma(0.5) = sqrt(pi) ≈ 1.7724538509
    let half = ctx.rational(1, 2);
    let result = half.gamma().eval_f64().unwrap();
    assert!(
        (result - std::f64::consts::PI.sqrt()).abs() < 1e-10,
        "Gamma(1/2) should be sqrt(pi), got {result}"
    );
}

#[test]
fn evalf_gamma_at_1() {
    let ctx = Context::new();
    // Gamma(1) = 0! = 1
    let result = ctx.int(1).gamma().eval_f64().unwrap();
    assert!(
        (result - 1.0).abs() < 1e-10,
        "Gamma(1) should be 1, got {result}"
    );
}

#[test]
fn evalf_gamma_at_3_5() {
    let ctx = Context::new();
    // Gamma(3.5) = 2.5 * 1.5 * 0.5 * sqrt(pi) ≈ 3.32335097
    let val = ctx.rational(7, 2);
    let result = val.gamma().eval_f64().unwrap();
    let expected = 2.5 * 1.5 * 0.5 * std::f64::consts::PI.sqrt();
    assert!(
        (result - expected).abs() < 1e-8,
        "Gamma(3.5) should be {expected}, got {result}"
    );
}

#[test]
fn evalf_gamma_at_negative_half() {
    let ctx = Context::new();
    // Gamma(-0.5) = -2*sqrt(pi) ≈ -3.5449077018
    let val = ctx.rational(-1, 2);
    let result = val.gamma().eval_f64().unwrap();
    let expected = -2.0 * std::f64::consts::PI.sqrt();
    assert!(
        (result - expected).abs() < 1e-8,
        "Gamma(-0.5) should be {expected}, got {result}"
    );
}

#[test]
fn evalf_erf_at_zero() {
    let ctx = Context::new();
    // erf(0) = 0
    let result = ctx.int(0).erf().eval_f64().unwrap();
    assert!(result.abs() < 1e-15, "erf(0) should be 0, got {result}");
}

#[test]
fn evalf_erf_at_one() {
    let ctx = Context::new();
    // erf(1) ≈ 0.8427007929
    let result = ctx.int(1).erf().eval_f64().unwrap();
    assert!(
        (result - 0.8427007929497148).abs() < 1e-10,
        "erf(1) should be ~0.8427, got {result}"
    );
}

#[test]
fn evalf_erf_at_large() {
    let ctx = Context::new();
    // erf(5) ≈ 1.0 (very close)
    let result = ctx.int(5).erf().eval_f64().unwrap();
    assert!(
        (result - 1.0).abs() < 1e-10,
        "erf(5) should be ~1.0, got {result}"
    );
}

#[test]
fn evalf_erf_negative_symmetry() {
    let ctx = Context::new();
    // erf is odd: erf(-x) = -erf(x)
    let pos = ctx.rational(3, 4).erf().eval_f64().unwrap();
    let neg = ctx.rational(-3, 4).erf().eval_f64().unwrap();
    assert!(
        (pos + neg).abs() < 1e-12,
        "erf(-x) should be -erf(x): erf(0.75)={pos}, erf(-0.75)={neg}"
    );
}

#[test]
fn evalf_erfc_at_zero() {
    let ctx = Context::new();
    // erfc(0) = 1 - erf(0) = 1
    let result = ctx.int(0).erfc().eval_f64().unwrap();
    assert!(
        (result - 1.0).abs() < 1e-12,
        "erfc(0) should be 1, got {result}"
    );
}

#[test]
fn evalf_erfc_plus_erf_is_one() {
    let ctx = Context::new();
    // erf(x) + erfc(x) = 1
    let x = ctx.rational(7, 5);
    let erf_val = x.erf().eval_f64().unwrap();
    let erfc_val = x.erfc().eval_f64().unwrap();
    assert!(
        (erf_val + erfc_val - 1.0).abs() < 1e-12,
        "erf(x) + erfc(x) should be 1: {erf_val} + {erfc_val}"
    );
}

#[test]
fn evalf_beta_2_3() {
    let ctx = Context::new();
    // Beta(2, 3) = Gamma(2)*Gamma(3)/Gamma(5) = 1*2/24 = 1/12
    let result = ctx.int(2).beta(&ctx.int(3)).eval_f64().unwrap();
    assert!(
        (result - 1.0 / 12.0).abs() < 1e-10,
        "Beta(2,3) should be 1/12, got {result}"
    );
}

#[test]
fn evalf_beta_symmetry() {
    let ctx = Context::new();
    // Beta(a,b) = Beta(b,a)
    let ab = ctx
        .rational(3, 2)
        .beta(&ctx.rational(5, 2))
        .eval_f64()
        .unwrap();
    let ba = ctx
        .rational(5, 2)
        .beta(&ctx.rational(3, 2))
        .eval_f64()
        .unwrap();
    assert!(
        (ab - ba).abs() < 1e-10,
        "Beta(3/2,5/2)={ab} should equal Beta(5/2,3/2)={ba}"
    );
}

#[test]
fn evalf_beta_half_half() {
    let ctx = Context::new();
    // Beta(1/2, 1/2) = Gamma(1/2)^2 / Gamma(1) = pi / 1 = pi
    let result = ctx
        .rational(1, 2)
        .beta(&ctx.rational(1, 2))
        .eval_f64()
        .unwrap();
    assert!(
        (result - std::f64::consts::PI).abs() < 1e-8,
        "Beta(1/2,1/2) should be pi, got {result}"
    );
}

#[test]
fn evalf_log_gamma_at_5() {
    let ctx = Context::new();
    // LogGamma(5) = ln(Gamma(5)) = ln(24) ≈ 3.17805383
    let result = ctx.int(5).log_gamma().eval_f64().unwrap();
    let expected = 24.0_f64.ln();
    assert!(
        (result - expected).abs() < 1e-10,
        "LogGamma(5) should be ln(24)={expected}, got {result}"
    );
}

#[test]
fn evalf_digamma_at_1() {
    let ctx = Context::new();
    // psi(1) = -gamma (Euler-Mascheroni) ≈ -0.5772156649
    let result = ctx.int(1).digamma().eval_f64().unwrap();
    let euler_mascheroni = 0.5772156649015329;
    assert!(
        (result + euler_mascheroni).abs() < 1e-10,
        "psi(1) should be -{euler_mascheroni}, got {result}"
    );
}

#[test]
fn evalf_digamma_at_2() {
    let ctx = Context::new();
    // psi(2) = psi(1) + 1/1 = 1 - gamma ≈ 0.42278433
    let result = ctx.int(2).digamma().eval_f64().unwrap();
    let expected = 1.0 - 0.5772156649015329;
    assert!(
        (result - expected).abs() < 1e-10,
        "psi(2) should be {expected}, got {result}"
    );
}