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
|
// Copyright 2011 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
// This file implements operations on ideal constants.
package types
import (
"big"
"go/token"
"strconv"
)
// TODO(gri) Consider changing the API so Const is an interface
// and operations on consts don't have to type switch.
// A Const implements an ideal constant Value.
// The zero value z for a Const is not a valid constant value.
type Const struct {
// representation of constant values:
// ideal bool -> bool
// ideal int -> *big.Int
// ideal float -> *big.Rat
// ideal complex -> cmplx
// ideal string -> string
val interface{}
}
// Representation of complex values.
type cmplx struct {
re, im *big.Rat
}
func assert(cond bool) {
if !cond {
panic("go/types internal error: assertion failed")
}
}
// MakeConst makes an ideal constant from a literal
// token and the corresponding literal string.
func MakeConst(tok token.Token, lit string) Const {
switch tok {
case token.INT:
var x big.Int
_, ok := x.SetString(lit, 0)
assert(ok)
return Const{&x}
case token.FLOAT:
var y big.Rat
_, ok := y.SetString(lit)
assert(ok)
return Const{&y}
case token.IMAG:
assert(lit[len(lit)-1] == 'i')
var im big.Rat
_, ok := im.SetString(lit[0 : len(lit)-1])
assert(ok)
return Const{cmplx{big.NewRat(0, 1), &im}}
case token.CHAR:
assert(lit[0] == '\'' && lit[len(lit)-1] == '\'')
code, _, _, err := strconv.UnquoteChar(lit[1:len(lit)-1], '\'')
assert(err == nil)
return Const{big.NewInt(int64(code))}
case token.STRING:
s, err := strconv.Unquote(lit)
assert(err == nil)
return Const{s}
}
panic("unreachable")
}
// MakeZero returns the zero constant for the given type.
func MakeZero(typ *Type) Const {
// TODO(gri) fix this
return Const{0}
}
// Match attempts to match the internal constant representations of x and y.
// If the attempt is successful, the result is the values of x and y,
// if necessary converted to have the same internal representation; otherwise
// the results are invalid.
func (x Const) Match(y Const) (u, v Const) {
switch a := x.val.(type) {
case bool:
if _, ok := y.val.(bool); ok {
u, v = x, y
}
case *big.Int:
switch y.val.(type) {
case *big.Int:
u, v = x, y
case *big.Rat:
var z big.Rat
z.SetInt(a)
u, v = Const{&z}, y
case cmplx:
var z big.Rat
z.SetInt(a)
u, v = Const{cmplx{&z, big.NewRat(0, 1)}}, y
}
case *big.Rat:
switch y.val.(type) {
case *big.Int:
v, u = y.Match(x)
case *big.Rat:
u, v = x, y
case cmplx:
u, v = Const{cmplx{a, big.NewRat(0, 0)}}, y
}
case cmplx:
switch y.val.(type) {
case *big.Int, *big.Rat:
v, u = y.Match(x)
case cmplx:
u, v = x, y
}
case string:
if _, ok := y.val.(string); ok {
u, v = x, y
}
default:
panic("unreachable")
}
return
}
// Convert attempts to convert the constant x to a given type.
// If the attempt is successful, the result is the new constant;
// otherwise the result is invalid.
func (x Const) Convert(typ *Type) Const {
// TODO(gri) implement this
switch x := x.val.(type) {
case bool:
case *big.Int:
case *big.Rat:
case cmplx:
case string:
}
return x
}
func (x Const) String() string {
switch x := x.val.(type) {
case bool:
if x {
return "true"
}
return "false"
case *big.Int:
return x.String()
case *big.Rat:
return x.FloatString(10) // 10 digits of precision after decimal point seems fine
case cmplx:
// TODO(gri) don't print 0 components
return x.re.FloatString(10) + " + " + x.im.FloatString(10) + "i"
case string:
return x
}
panic("unreachable")
}
func (x Const) UnaryOp(op token.Token) Const {
panic("unimplemented")
}
func (x Const) BinaryOp(op token.Token, y Const) Const {
var z interface{}
switch x := x.val.(type) {
case bool:
z = binaryBoolOp(x, op, y.val.(bool))
case *big.Int:
z = binaryIntOp(x, op, y.val.(*big.Int))
case *big.Rat:
z = binaryFloatOp(x, op, y.val.(*big.Rat))
case cmplx:
z = binaryCmplxOp(x, op, y.val.(cmplx))
case string:
z = binaryStringOp(x, op, y.val.(string))
default:
panic("unreachable")
}
return Const{z}
}
func binaryBoolOp(x bool, op token.Token, y bool) interface{} {
switch op {
case token.EQL:
return x == y
case token.NEQ:
return x != y
}
panic("unreachable")
}
func binaryIntOp(x *big.Int, op token.Token, y *big.Int) interface{} {
var z big.Int
switch op {
case token.ADD:
return z.Add(x, y)
case token.SUB:
return z.Sub(x, y)
case token.MUL:
return z.Mul(x, y)
case token.QUO:
return z.Quo(x, y)
case token.REM:
return z.Rem(x, y)
case token.AND:
return z.And(x, y)
case token.OR:
return z.Or(x, y)
case token.XOR:
return z.Xor(x, y)
case token.AND_NOT:
return z.AndNot(x, y)
case token.SHL:
panic("unimplemented")
case token.SHR:
panic("unimplemented")
case token.EQL:
return x.Cmp(y) == 0
case token.NEQ:
return x.Cmp(y) != 0
case token.LSS:
return x.Cmp(y) < 0
case token.LEQ:
return x.Cmp(y) <= 0
case token.GTR:
return x.Cmp(y) > 0
case token.GEQ:
return x.Cmp(y) >= 0
}
panic("unreachable")
}
func binaryFloatOp(x *big.Rat, op token.Token, y *big.Rat) interface{} {
var z big.Rat
switch op {
case token.ADD:
return z.Add(x, y)
case token.SUB:
return z.Sub(x, y)
case token.MUL:
return z.Mul(x, y)
case token.QUO:
return z.Quo(x, y)
case token.EQL:
return x.Cmp(y) == 0
case token.NEQ:
return x.Cmp(y) != 0
case token.LSS:
return x.Cmp(y) < 0
case token.LEQ:
return x.Cmp(y) <= 0
case token.GTR:
return x.Cmp(y) > 0
case token.GEQ:
return x.Cmp(y) >= 0
}
panic("unreachable")
}
func binaryCmplxOp(x cmplx, op token.Token, y cmplx) interface{} {
a, b := x.re, x.im
c, d := y.re, y.im
switch op {
case token.ADD:
// (a+c) + i(b+d)
var re, im big.Rat
re.Add(a, c)
im.Add(b, d)
return cmplx{&re, &im}
case token.SUB:
// (a-c) + i(b-d)
var re, im big.Rat
re.Sub(a, c)
im.Sub(b, d)
return cmplx{&re, &im}
case token.MUL:
// (ac-bd) + i(bc+ad)
var ac, bd, bc, ad big.Rat
ac.Mul(a, c)
bd.Mul(b, d)
bc.Mul(b, c)
ad.Mul(a, d)
var re, im big.Rat
re.Sub(&ac, &bd)
im.Add(&bc, &ad)
return cmplx{&re, &im}
case token.QUO:
// (ac+bd)/s + i(bc-ad)/s, with s = cc + dd
var ac, bd, bc, ad, s big.Rat
ac.Mul(a, c)
bd.Mul(b, d)
bc.Mul(b, c)
ad.Mul(a, d)
s.Add(c.Mul(c, c), d.Mul(d, d))
var re, im big.Rat
re.Add(&ac, &bd)
re.Quo(&re, &s)
im.Sub(&bc, &ad)
im.Quo(&im, &s)
return cmplx{&re, &im}
case token.EQL:
return a.Cmp(c) == 0 && b.Cmp(d) == 0
case token.NEQ:
return a.Cmp(c) != 0 || b.Cmp(d) != 0
}
panic("unreachable")
}
func binaryStringOp(x string, op token.Token, y string) interface{} {
switch op {
case token.ADD:
return x + y
case token.EQL:
return x == y
case token.NEQ:
return x != y
case token.LSS:
return x < y
case token.LEQ:
return x <= y
case token.GTR:
return x > y
case token.GEQ:
return x >= y
}
panic("unreachable")
}
|