aboutsummaryrefslogtreecommitdiff
path: root/calc.y
blob: 202d4ca8d6708f6673cc0486bbe45eb8022c61c0 (plain)
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
// XXX http://play.golang.org/p/V_dX9jzYzD
%{

package main

import (
	"fmt"
	"math"
)

type Number float64

type Interval struct {
	lo Number
	hi Number
}

var nreg = make(map[rune]Number)
var ireg = make(map[rune]Interval)

%}

%union{
	dval Number
	vval Interval
	rval rune
	sval string
}

%token <rval> DREG VREG
%token <dval> NUMBER
%token <sval> STRING

%type <dval> dexp
%type <vval> vexp

%left '+' '-'
%left '*' '/'
%left UMINUS

%%

line
	: dexp			{ fmt.Println($1) }
	| vexp			{ fmt.Println($1) }
	| DREG '=' dexp		{ $3.Set($1) }
	| VREG '=' vexp		{ $3.Set($1) }
	| STRING		{ fmt.Println($1) }
	;

dexp
	: NUMBER
	| DREG			{ $$.Get($1) }
	| dexp '+' dexp		{ $$ = $1 + $3 }
	| dexp '-' dexp		{ $$ = $1 - $3 }
	| dexp '*' dexp		{ $$ = $1 * $3 }
	| dexp '/' dexp		{ $$ = $1 / $3 }
	| '-' dexp %prec UMINUS	{ $$ = -$2 }
	| '(' dexp ')'		{ $$ = $2 }
	| error			{ $$ = Number(math.NaN()) }
	;

vexp
	: '(' dexp ',' dexp ')'	{
		if $2 > $4 {
			$$ = Interval{$4, $2}
		} else {
			$$ = Interval{$2, $4}
		}
	}
	| VREG			{ $$.Get($1) }
	| vexp '+' vexp		{ $$ = $3.vadd($1) }
	| dexp '+' vexp		{ $$ = $3.vadd(Interval{$1, $1}) }
	| vexp '+' dexp		{ $$ = Interval{$3, $3}.vadd($1) }
	| vexp '-' vexp		{ $$ = $3.vsub($1) }
	| dexp '-' vexp		{ $$ = $3.vsub(Interval{$1, $1}) }
	| vexp '-' dexp		{ $$ = Interval{$3, $3}.vsub($1) }
	| vexp '*' vexp		{ $$ = $3.vmul($1) }
	| dexp '*' vexp		{ $$ = $3.vmul(Interval{$1, $1}) }
	| vexp '*' dexp		{ $$ = Interval{$3, $3}.vmul($1) }
	| vexp '/' vexp		{
		if $3.dcheck() {
			yylex.Error("divisor interval contains 0")
		}
		$$ = $3.vdiv($1)
	}
	| dexp '/' vexp		{
		if $3.dcheck() {
			yylex.Error("divisor interval contains 0")
		}
		$$ = $3.vdiv(Interval{$1, $1})
	}
	| vexp '/' dexp		{
		if $3 == 0 {
			yylex.Error("divisor interval contains 0")
		}
		$$ = Interval{$3, $3}.vdiv($1)
	}
	| '-' vexp %prec UMINUS	{ $$ = $2.vneg() }
	| '(' vexp ')'		{ $$ = $2 }
	;

%%

func (i Interval) String() string {
	return fmt.Sprint("(", i.lo, ",", i.hi, ")")
}

func hilo(a, b, c, d Number) (v Interval) {
	if a > b {
		v.hi = a
		v.lo = b
	} else {
		v.hi = b
		v.lo = a
	}
	if c > d {
		if c > v.hi { v.hi = c }
		if d < v.lo { v.lo = d }
	} else {
		if d > v.hi { v.hi = d }
		if c < v.lo { v.lo = c }
	}
	return
}

func (v Interval) vmul(a Interval) Interval {
	return hilo(a.lo*v.hi, a.lo*v.lo, a.hi*v.hi, a.hi*v.lo)
}

func (v Interval) dcheck() bool {
	return v.hi >= 0 && v.lo <= 0
}

func (v Interval) vdiv(a Interval) Interval {
	return hilo(a.lo/v.hi, a.lo/v.lo, a.hi/v.hi, a.hi/v.lo)
}

func (v Interval) vadd(a Interval) Interval {
	return Interval{a.lo + v.lo, a.hi + v.hi}
}

func (v Interval) vsub(a Interval) Interval {
	return Interval{a.lo - v.lo, a.hi - v.hi}
}

func (v Interval) vneg() Interval {
	return Interval{lo: -v.hi, hi: -v.lo}
}

func (n *Number) Set(key rune) { nreg[key] = *n }
func (n *Number) Get(key rune) { *n = nreg[key] }

func (n *Interval) Set(key rune) { ireg[key] = *n }
func (n *Interval) Get(key rune) { *n = ireg[key] }