g_math 0.4.2

Multi-domain fixed-point arithmetic with geometric extension: Lie groups, manifolds, ODE solvers, tensors, fiber bundles — zero-float, 0 ULP transcendentals
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

//! Validation tests for DomainMatrix — multi-domain matrix operations.
//!
//! Tests:
//! 1. Pure binary matrices (baseline)
//! 2. Pure decimal matrices (financial-grade 0-ULP)
//! 3. Mixed-domain operations (cross-domain via rational)
//! 4. Symbolic matrices (exact rational arithmetic)

use g_math::canonical::{gmath, evaluate, DomainMatrix, StackValue};
use g_math::fixed_point::{FixedPoint, FixedMatrix};
use g_math::fixed_point::universal::ugod::DomainType;

fn fp(s: &str) -> FixedPoint {
    if s.starts_with('-') { -FixedPoint::from_str(&s[1..]) }
    else { FixedPoint::from_str(s) }
}

fn sv_to_fp(sv: &StackValue) -> FixedPoint {
    match sv.as_binary_storage() {
        Some(raw) => FixedPoint::from_raw(raw),
        None => {
            // Non-binary domain — convert via formatted string
            let s = format!("{}", sv);
            fp(&s)
        }
    }
}

fn tight() -> FixedPoint {
    #[cfg(table_format = "q16_16")]
    { fp("0.01") }
    #[cfg(table_format = "q32_32")]
    { fp("0.0001") }
    #[cfg(not(any(table_format = "q16_16", table_format = "q32_32")))]
    { fp("0.000000001") }
}

fn assert_fp(got: FixedPoint, exp: FixedPoint, tol: FixedPoint, name: &str) {
    let d = (got - exp).abs();
    assert!(d < tol, "{}: got {}, expected {}, diff={}", name, got, exp, d);
}

// ============================================================================
// Binary domain (baseline)
// ============================================================================

#[test]
fn test_binary_domain_matrix_identity() {
    let id = DomainMatrix::identity_binary(3);
    assert_eq!(id.rows(), 3);
    assert_eq!(id.cols(), 3);
    assert!(id.is_uniform_domain());
    assert_eq!(id.dominant_domain(), Some(DomainType::Binary));
}

#[test]
fn test_binary_domain_matrix_from_strings() {
    let m = DomainMatrix::from_strings(2, 2, &["1", "2", "3", "4"]).unwrap();
    assert_eq!(m.rows(), 2);
    assert_eq!(m.cols(), 2);
}

#[test]
fn test_binary_domain_matrix_add() {
    let a = DomainMatrix::from_strings(2, 2, &["1", "2", "3", "4"]).unwrap();
    let b = DomainMatrix::from_strings(2, 2, &["10", "20", "30", "40"]).unwrap();
    let c = a.add(&b).unwrap();
    // [1+10, 2+20; 3+30, 4+40] = [11, 22; 33, 44]
    assert_fp(sv_to_fp(c.get(0, 0)), fp("11"), tight(), "binary_add[0,0]");
    assert_fp(sv_to_fp(c.get(0, 1)), fp("22"), tight(), "binary_add[0,1]");
    assert_fp(sv_to_fp(c.get(1, 0)), fp("33"), tight(), "binary_add[1,0]");
    assert_fp(sv_to_fp(c.get(1, 1)), fp("44"), tight(), "binary_add[1,1]");
}

#[test]
fn test_binary_domain_matrix_matmul() {
    // [[1, 2], [3, 4]] * [[5, 6], [7, 8]] = [[19, 22], [43, 50]]
    let a = DomainMatrix::from_strings(2, 2, &["1", "2", "3", "4"]).unwrap();
    let b = DomainMatrix::from_strings(2, 2, &["5", "6", "7", "8"]).unwrap();
    let c = a.mat_mul(&b).unwrap();
    assert_fp(sv_to_fp(c.get(0, 0)), fp("19"), tight(), "matmul[0,0]");
    assert_fp(sv_to_fp(c.get(0, 1)), fp("22"), tight(), "matmul[0,1]");
    assert_fp(sv_to_fp(c.get(1, 0)), fp("43"), tight(), "matmul[1,0]");
    assert_fp(sv_to_fp(c.get(1, 1)), fp("50"), tight(), "matmul[1,1]");
}

// ============================================================================
// Decimal domain — financial-grade
// ============================================================================

#[test]
fn test_decimal_domain_matrix_creation() {
    let m = DomainMatrix::from_strings(2, 2, &["0.10", "0.20", "0.30", "0.40"]).unwrap();
    assert_eq!(m.rows(), 2);
    assert!(m.is_uniform_domain());
    assert_eq!(m.dominant_domain(), Some(DomainType::Decimal));
}

#[test]
fn test_decimal_domain_matrix_add() {
    // Decimal addition should be exact (0 ULP)
    let a = DomainMatrix::from_strings(2, 2, &["0.10", "0.20", "0.30", "0.40"]).unwrap();
    let b = DomainMatrix::from_strings(2, 2, &["0.01", "0.02", "0.03", "0.04"]).unwrap();
    let c = a.add(&b).unwrap();
    // 0.10 + 0.01 = 0.11 (exact in decimal domain)
    let r = c.to_fixed_matrix().unwrap();
    assert_fp(r.get(0, 0), fp("0.11"), tight(), "decimal_add[0,0]");
    assert_fp(r.get(1, 1), fp("0.44"), tight(), "decimal_add[1,1]");
}

#[test]
fn test_decimal_domain_matrix_sub() {
    let a = DomainMatrix::from_strings(2, 2, &["0.50", "0.60", "0.70", "0.80"]).unwrap();
    let b = DomainMatrix::from_strings(2, 2, &["0.10", "0.20", "0.30", "0.40"]).unwrap();
    let c = a.sub(&b).unwrap();
    let r = c.to_fixed_matrix().unwrap();
    assert_fp(r.get(0, 0), fp("0.40"), tight(), "decimal_sub[0,0]");
    assert_fp(r.get(1, 1), fp("0.40"), tight(), "decimal_sub[1,1]");
}

#[test]
fn test_decimal_identity_matmul() {
    // Decimal identity * decimal matrix = same matrix
    let id = DomainMatrix::from_strings(2, 2, &["1.00", "0.00", "0.00", "1.00"]).unwrap();
    let v = DomainMatrix::from_strings(2, 1, &["0.10", "0.20"]).unwrap();
    let result = id.mat_mul(&v).unwrap();
    let r = result.to_fixed_matrix().unwrap();
    assert_fp(r.get(0, 0), fp("0.10"), tight(), "decimal_id_mul[0]");
    assert_fp(r.get(1, 0), fp("0.20"), tight(), "decimal_id_mul[1]");
}

// ============================================================================
// Cross-domain operations (mixed decimal + binary)
// ============================================================================

#[test]
fn test_cross_domain_add() {
    // Binary + Decimal — should route through rational and produce correct result
    let a = DomainMatrix::from_strings(2, 2, &["1", "2", "3", "4"]).unwrap();
    let b = DomainMatrix::from_strings(2, 2, &["0.50", "0.50", "0.50", "0.50"]).unwrap();
    let c = a.add(&b).unwrap();
    let r = c.to_fixed_matrix().unwrap();
    assert_fp(r.get(0, 0), fp("1.5"), tight(), "cross_add[0,0]");
    assert_fp(r.get(1, 1), fp("4.5"), tight(), "cross_add[1,1]");
}

#[test]
fn test_cross_domain_matmul() {
    // Binary matrix * Decimal matrix
    let a = DomainMatrix::from_strings(2, 2, &["2", "0", "0", "3"]).unwrap();
    let b = DomainMatrix::from_strings(2, 2, &["0.10", "0.20", "0.30", "0.40"]).unwrap();
    let c = a.mat_mul(&b).unwrap();
    let r = c.to_fixed_matrix().unwrap();
    // [[2,0],[0,3]] * [[0.1,0.2],[0.3,0.4]] = [[0.2,0.4],[0.9,1.2]]
    assert_fp(r.get(0, 0), fp("0.2"), tight(), "cross_mul[0,0]");
    assert_fp(r.get(0, 1), fp("0.4"), tight(), "cross_mul[0,1]");
    assert_fp(r.get(1, 0), fp("0.9"), tight(), "cross_mul[1,0]");
    assert_fp(r.get(1, 1), fp("1.2"), tight(), "cross_mul[1,1]");
}

// ============================================================================
// Symbolic domain (exact rational)
// ============================================================================

#[test]
fn test_symbolic_domain_matrix() {
    // Rational entries: 1/3, 2/3 — exact symbolic representation
    let m = DomainMatrix::from_strings(2, 2, &["1/3", "2/3", "1/6", "5/6"]).unwrap();
    assert_eq!(m.rows(), 2);
    assert!(m.is_uniform_domain());
    assert_eq!(m.dominant_domain(), Some(DomainType::Symbolic));
}

#[test]
fn test_symbolic_domain_add() {
    // 1/3 + 1/6 = 1/2 (exact)
    let a = DomainMatrix::from_strings(1, 1, &["1/3"]).unwrap();
    let b = DomainMatrix::from_strings(1, 1, &["1/6"]).unwrap();
    let c = a.add(&b).unwrap();
    let r = c.to_fixed_matrix().unwrap();
    assert_fp(r.get(0, 0), fp("0.5"), tight(), "symbolic_1/3+1/6=1/2");
}

// ============================================================================
// Utility operations
// ============================================================================

#[test]
fn test_domain_matrix_transpose() {
    let m = DomainMatrix::from_strings(2, 3, &["1", "2", "3", "4", "5", "6"]).unwrap();
    let mt = m.transpose();
    assert_eq!(mt.rows(), 3);
    assert_eq!(mt.cols(), 2);
}

#[test]
fn test_domain_matrix_neg() {
    let m = DomainMatrix::from_strings(2, 2, &["1", "2", "3", "4"]).unwrap();
    let neg = m.neg().unwrap();
    let r = neg.to_fixed_matrix().unwrap();
    assert_fp(r.get(0, 0), fp("-1"), tight(), "neg[0,0]");
    assert_fp(r.get(1, 1), fp("-4"), tight(), "neg[1,1]");
}

#[test]
fn test_domain_matrix_scalar_mul() {
    let m = DomainMatrix::from_strings(2, 2, &["1", "2", "3", "4"]).unwrap();
    let s = evaluate(&gmath("3")).unwrap();
    let scaled = m.scalar_mul(&s).unwrap();
    let r = scaled.to_fixed_matrix().unwrap();
    assert_fp(r.get(0, 0), fp("3"), tight(), "scalar_mul[0,0]");
    assert_fp(r.get(1, 1), fp("12"), tight(), "scalar_mul[1,1]");
}

#[test]
fn test_domain_matrix_trace() {
    let m = DomainMatrix::from_strings(3, 3, &[
        "1", "0", "0",
        "0", "2", "0",
        "0", "0", "3",
    ]).unwrap();
    let tr = m.trace().unwrap();
    assert_fp(sv_to_fp(&tr), fp("6"), tight(), "trace");
}

#[test]
fn test_domain_matrix_to_from_fixed() {
    let fm = FixedMatrix::from_fn(2, 2, |r, c| fp(&format!("{}", (r * 2 + c + 1))));
    let dm = DomainMatrix::from_fixed_matrix(&fm);
    let roundtrip = dm.to_fixed_matrix().unwrap();
    for r in 0..2 {
        for c in 0..2 {
            assert_fp(roundtrip.get(r, c), fm.get(r, c), tight(), &format!("roundtrip[{r},{c}]"));
        }
    }
}