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
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
//! Abstracts over Elemental expressions.
use std::{
fmt::{
Display,
Result,
Formatter,
},
collections::HashMap,
};
use crate::{
standard::get_std_function,
Matrix,
};
use crate::error::*;
/// Defines the expression types that are available in Elemental.
#[derive(Clone, Debug)]
pub enum Expression {
Assignment {
identifier: String,
value: Box<Expression>,
},
Identifier (String),
Int (i64),
Float (f64),
Matrix {
rows: usize,
cols: usize,
values: Vec<Expression>,
},
BinOp {
left: Box<Expression>,
op: String,
right: Box<Expression>,
},
Call {
name: String,
args: Vec<Expression>,
},
Nil,
}
/// Implementing `std::fmt::Display` allows us to print expressions
/// using the default formatter.
impl Display for Expression {
/// Display each `Expression`.
fn fmt(&self, f: &mut Formatter<'_>) -> Result {
match self {
Expression::Assignment {
identifier: _,
value: v,
} => {
write!(f, "{}", v)
},
Expression::Identifier (s) => {
write!(f, "{}", s)
},
Expression::Int (i) => {
write!(f, "{}", i)
},
Expression::Float (float) => {
write!(f, "{:.8}", float)
},
Expression::Matrix {
rows: r,
cols: c,
values: v,
} => {
let mut result = String::new();
for i in 0..*r {
result.push('[');
for j in 0..*c {
let index = i*c + j;
result.push_str(
&format!(
"{:^10}",
format!("{}", v[index as usize])
)
);
// Write a tab if we're not at the end yet
if j != c - 1 {
result.push(' ');
}
}
result.push(']');
result.push('\n');
}
write!(f, "{}", result)
}
Expression::BinOp {
left: l,
op: o,
right: r,
} => {
write!(f, "{} {} {}", l, o, r)
},
Expression::Call {
name: _,
args: _,
} => {
unreachable!()
}
Expression::Nil => {
write!(f, "")
},
}
}
}
impl Expression {
/// Simplify this expression, given a reference to a list of variables.
pub fn simplify(&self, variables: &mut HashMap<String, Expression>) -> Self {
match self {
// Look up the variable and plug in
Expression::Identifier (s) => {
let expr = match variables.get(s) {
Some(e) => (*e).to_owned(),
None => {
throw(UndeclaredVariable (s.to_string()));
return Expression::Nil;
},
};
// Simplify
expr.simplify(variables)
},
// Insert the assigned variable into the list of variables
Expression::Assignment {
identifier: ref i,
value: ref v,
} => {
// Simplify the value of assignment
let simplified = (**v).simplify(variables);
// Register the variable
variables.insert(i.to_owned(), simplified.to_owned());
// Return the simplified value
simplified.to_owned()
}
// Simplify the left and right and return
Expression::BinOp {
left: l,
op: o,
right: r,
} => {
// Simplify the left-hand and right-hand sides
let left = l.simplify(variables);
let right = r.simplify(variables);
if let Expression::Int (l) = left {
if let Expression::Int (r) = right {
// Evaluate this as a float, then try to cast it to an `Int`
let f = binop(l as f64, r as f64, &o);
if f.fract() == 0.0 {
Expression::Int (f as i64)
} else {
Expression::Float (f)
}
} else if let Expression::Float (r) = right {
let left_float = l as f64;
Expression::Float (binop(left_float, r, &o))
} else if let Expression::Matrix {
rows: r,
cols: c,
values: v,
} = right {
let mut values = Vec::new();
for val in v {
values.push(Expression::BinOp {
left: Box::new(left.to_owned()),
op: "*".to_string(),
right: Box::new(val),
}.simplify(variables));
}
Expression::Matrix {
rows: r,
cols: c,
values,
}
} else {
throw(InvalidOperands);
return Expression::Nil;
}
} else if let Expression::Float (l) = left {
if let Expression::Int (r) = right {
let right_float = r as f64;
Expression::Float (binop(l, right_float, &o))
} else if let Expression::Float (r) = right {
Expression::Float (binop(l, r, &o))
} else {
throw(InvalidOperands);
return Expression::Nil;
}
} else if let Expression::Matrix {
rows: r,
cols: k1,
values: vl,
} = left {
if let Expression::Matrix {
rows: k2,
cols: c,
values: vr,
} = right {
if k1 != k2 {
throw(ImproperDimensions);
return Expression::Nil;
}
matrix_dot(vl, vr, r, c, k1)
} else {
throw(InvalidOperands);
return Expression::Nil;
}
} else {
throw(InvalidOperands);
return Expression::Nil;
}
},
// `Int is already in simplest form
Expression::Int (_) => self.to_owned(),
// `Float` can be reduced to `Int` if it has no fractional part
Expression::Float (f) => {
if f.fract() == 0.0 {
Expression::Int (*f as i64)
} else {
Expression::Float (*f)
}
},
// To simplify a `Matrix`, simplify each value
Expression::Matrix {
rows: r,
cols: c,
values: v,
} => {
let mut new = Vec::new();
for val in v {
new.push(val.simplify(variables));
}
if *r == 1 && *c == 1 {
v[0].simplify(variables).to_owned()
} else {
Expression::Matrix {
rows: *r,
cols: *c,
values: new,
}
}
},
// To simplify a call, look up the function in the standard library
// and pass the arguments necessary
//
// In Elemental, all functions act on matrices.
Expression::Call {
name: n,
args: a,
} => {
// Simplify each argument and convert them to "native" matrices.
let mut args = Vec::<Matrix>::new();
for arg in a {
let simplified = arg.simplify(variables);
if let Expression::Matrix {
rows: r,
cols: c,
values: v,
} = simplified {
// Convert each value in the matrix from `Expression` to `f64`.
let mut values: Vec<f64> = Vec::new();
for value in v {
if let Self::Int (i) = value {
values.push(i as f64);
} else if let Self::Float (f) = value {
values.push(f);
} else {
// A value in one of the matrices is not a numeric literal
throw(InvalidValue);
return Expression::Nil;
}
}
args.push(Matrix::new(r, c, values));
} else if let Expression::Int (i) = simplified {
// If one value is a number, convert it into a 1x1 matrix
args.push(Matrix::new(1, 1, vec![i as f64]));
} else if let Expression::Float (f) = simplified {
// If one value is a number, convert it into a 1x1 matrix
args.push(Matrix::new(1, 1, vec![f]));
} else {
// One of the arguments is not a matrix or a number
throw(InvalidOperands);
}
}
let stdfn = get_std_function(n.to_owned());
let output_matrix = stdfn.eval(args);
let values = output_matrix.copy_vals().iter().map(|x| Self::Float (*x)).collect::<Vec<Self>>();
Self::Matrix {
rows: output_matrix.rows(),
cols: output_matrix.cols(),
values,
}.simplify(variables)
},
// `Nil` is already in simplest form
Expression::Nil => self.to_owned(),
}
}
}
/// Executes the given binary operation on two floats.
pub fn binop(x: f64, y: f64, binop: &str) -> f64 {
match binop {
"+" => x + y,
"-" => x - y,
"*" => x * y,
"/" => {
if y == 0.0 {
throw(DividedByZero);
0.0
} else {
x / y
}
},
_ => {
throw(InvalidOperator);
0.0
},
}
}
/// Computes the dot product of two matrices.
pub fn matrix_dot(left: Vec<Expression>, right: Vec<Expression>, rows: usize, cols: usize, count: usize) -> Expression {
let mut values = Vec::new();
for i in 0..rows {
for j in 0..cols {
let mut cell = Expression::Int (0);
for k in 0..count {
// Add the addend to the cell
let addend = Expression::BinOp {
left: Box::new(left[i*count + k].to_owned()),
right: Box::new(right[k*cols + j].to_owned()),
op: "*".to_string(),
};
cell = Expression::BinOp {
left: Box::new(cell),
right: Box::new(addend),
op: "+".to_string(),
};
}
// Push the cell to the list of values
values.push(cell.simplify(&mut HashMap::new()));
}
}
Expression::Matrix {
rows,
cols,
values,
}
}