tang 0.2.0

Math library for physical reality — geometry, spatial algebra, tensor, training, GPU compute, and 3D gaussian splatting
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

//! Compile expression graphs to optimized Rust closures.

use std::collections::HashSet;

use super::graph::ExprGraph;
use super::node::{ExprId, Node};

/// Compiled single-output expression closure.
pub type CompiledExpr = Box<dyn Fn(&[f64]) -> f64>;

/// Compiled multi-output expression closure.
pub type CompiledMany = Box<dyn Fn(&[f64], &mut [f64])>;

impl ExprGraph {
    /// Compile a single expression to a closure `&[f64] -> f64`.
    ///
    /// Shared subexpressions (from interning) are computed once.
    /// Dead nodes (not reachable from output) are skipped.
    pub fn compile(&self, expr: ExprId) -> CompiledExpr {
        let live = self.live_set(&[expr]);
        let nodes = self.collect_eval_order(&live, expr.0 as usize + 1);
        let out_idx = expr.0 as usize;

        Box::new(move |inputs: &[f64]| {
            let mut vals = vec![0.0f64; out_idx + 1];
            for &(i, ref node) in &nodes {
                vals[i] = eval_node(node, &vals, inputs);
            }
            vals[out_idx]
        })
    }

    /// Compile multiple output expressions to a single closure.
    ///
    /// Writes results into the output slice.
    pub fn compile_many(&self, exprs: &[ExprId]) -> CompiledMany {
        if exprs.is_empty() {
            return Box::new(|_, _| {});
        }

        let live = self.live_set(exprs);
        let max_id = exprs.iter().map(|e| e.0).max().unwrap() as usize;
        let nodes = self.collect_eval_order(&live, max_id + 1);
        let out_indices: Vec<usize> = exprs.iter().map(|e| e.0 as usize).collect();

        Box::new(move |inputs: &[f64], outputs: &mut [f64]| {
            let mut vals = vec![0.0f64; max_id + 1];
            for &(i, ref node) in &nodes {
                vals[i] = eval_node(node, &vals, inputs);
            }
            for (k, &idx) in out_indices.iter().enumerate() {
                outputs[k] = vals[idx];
            }
        })
    }

    /// Find all node indices reachable from the given outputs.
    pub fn live_set(&self, outputs: &[ExprId]) -> HashSet<usize> {
        let mut live = HashSet::new();
        let mut stack: Vec<usize> = outputs.iter().map(|e| e.0 as usize).collect();
        while let Some(i) = stack.pop() {
            if !live.insert(i) {
                continue;
            }
            match self.node(ExprId(i as u32)) {
                Node::Var(_) | Node::Lit(_) => {}
                Node::Add(a, b) | Node::Mul(a, b) | Node::Atan2(a, b) => {
                    stack.push(a.0 as usize);
                    stack.push(b.0 as usize);
                }
                Node::Neg(a)
                | Node::Recip(a)
                | Node::Sqrt(a)
                | Node::Sin(a)
                | Node::Exp2(a)
                | Node::Log2(a) => {
                    stack.push(a.0 as usize);
                }
                Node::Select(c, a, b) => {
                    stack.push(c.0 as usize);
                    stack.push(a.0 as usize);
                    stack.push(b.0 as usize);
                }
            }
        }
        live
    }

    /// Collect (index, node) pairs in topological order, only for live nodes.
    fn collect_eval_order(&self, live: &HashSet<usize>, count: usize) -> Vec<(usize, Node)> {
        (0..count)
            .filter(|i| live.contains(i))
            .map(|i| (i, self.node(ExprId(i as u32))))
            .collect()
    }
}

#[inline]
fn eval_node(node: &Node, vals: &[f64], inputs: &[f64]) -> f64 {
    match *node {
        Node::Var(idx) => inputs[idx as usize],
        Node::Lit(bits) => f64::from_bits(bits),
        Node::Add(a, b) => vals[a.0 as usize] + vals[b.0 as usize],
        Node::Mul(a, b) => vals[a.0 as usize] * vals[b.0 as usize],
        Node::Neg(a) => -vals[a.0 as usize],
        Node::Recip(a) => 1.0 / vals[a.0 as usize],
        Node::Sqrt(a) => vals[a.0 as usize].sqrt(),
        Node::Sin(a) => vals[a.0 as usize].sin(),
        Node::Atan2(y, x) => vals[y.0 as usize].atan2(vals[x.0 as usize]),
        Node::Exp2(a) => vals[a.0 as usize].exp2(),
        Node::Log2(a) => vals[a.0 as usize].log2(),
        Node::Select(c, a, b) => {
            if vals[c.0 as usize] > 0.0 {
                vals[a.0 as usize]
            } else {
                vals[b.0 as usize]
            }
        }
    }
}

#[cfg(test)]
mod tests {
    use super::graph::ExprGraph;

    #[test]
    fn compile_add_lits() {
        let mut g = ExprGraph::new();
        let a = g.lit(3.0);
        let b = g.lit(4.0);
        let sum = g.add(a, b);
        let f = g.compile(sum);
        assert!((f(&[]) - 7.0).abs() < 1e-10);
    }

    #[test]
    fn compile_with_vars() {
        let mut g = ExprGraph::new();
        let x = g.var(0);
        let y = g.var(1);
        let sum = g.add(x, y);
        let prod = g.mul(sum, x);
        let f = g.compile(prod);
        // (3 + 4) * 3 = 21
        assert!((f(&[3.0, 4.0]) - 21.0).abs() < 1e-10);
    }

    #[test]
    fn compile_sin() {
        let mut g = ExprGraph::new();
        let x = g.var(0);
        let s = g.sin(x);
        let f = g.compile(s);
        assert!((f(&[std::f64::consts::FRAC_PI_2]) - 1.0).abs() < 1e-10);
    }

    #[test]
    fn compile_many_outputs() {
        let mut g = ExprGraph::new();
        let x = g.var(0);
        let y = g.var(1);
        let sum = g.add(x, y);
        let prod = g.mul(x, y);
        let f = g.compile_many(&[sum, prod]);
        let mut out = [0.0; 2];
        f(&[3.0, 4.0], &mut out);
        assert!((out[0] - 7.0).abs() < 1e-10);
        assert!((out[1] - 12.0).abs() < 1e-10);
    }

    #[test]
    fn compile_dead_code_elimination() {
        let mut g = ExprGraph::new();
        let x = g.var(0);
        let _dead = g.sin(x); // not used in output
        let result = g.mul(x, x);
        let f = g.compile(result);
        assert!((f(&[5.0]) - 25.0).abs() < 1e-10);
    }

    #[test]
    fn compile_matches_eval() {
        let mut g = ExprGraph::new();
        let x = g.var(0);
        let y = g.var(1);
        let xx = g.mul(x, x);
        let yy = g.mul(y, y);
        let sum = g.add(xx, yy);
        let dist = g.sqrt(sum);

        let inputs = [3.0, 4.0];
        let eval_result: f64 = g.eval(dist, &inputs);
        let f = g.compile(dist);
        let compile_result = f(&inputs);
        assert!((eval_result - compile_result).abs() < 1e-10);
        assert!((compile_result - 5.0).abs() < 1e-10);
    }
}