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
|
/******************************************************************************
* Top contributors (to current version):
* Andres Noetzli
*
* This file is part of the cvc5 project.
*
* Copyright (c) 2009-2021 by the authors listed in the file AUTHORS
* in the top-level source directory and their institutional affiliations.
* All rights reserved. See the file COPYING in the top-level source
* directory for licensing information.
* ****************************************************************************
*
* An example of solving floating-point problems with CVC4's Java API
*
* This example shows how to check whether CVC4 was built with floating-point
* support, how to create floating-point types, variables and expressions, and
* how to create rounding mode constants by solving toy problems. The example
* also shows making special values (such as NaN and +oo) and converting an
* IEEE 754-2008 bit-vector to a floating-point number.
*/
import edu.stanford.CVC4.*;
import java.util.Iterator;
public class FloatingPointArith {
public static void main(String[] args) {
System.loadLibrary("cvc4jni");
// Test whether CVC4 was built with floating-point support
ExprManager em = new ExprManager();
SmtEngine smt = new SmtEngine(em);
// Enable the model production
smt.setOption("produce-models", new SExpr(true));
// Make single precision floating-point variables
FloatingPointType fpt32 = em.mkFloatingPointType(8, 24);
Expr a = em.mkVar("a", fpt32);
Expr b = em.mkVar("b", fpt32);
Expr c = em.mkVar("c", fpt32);
Expr d = em.mkVar("d", fpt32);
Expr e = em.mkVar("e", fpt32);
// Assert that floating-point addition is not associative:
// (a + (b + c)) != ((a + b) + c)
Expr rm = em.mkConst(RoundingMode.roundNearestTiesToEven);
Expr lhs = em.mkExpr(Kind.FLOATINGPOINT_ADD,
rm,
a,
em.mkExpr(Kind.FLOATINGPOINT_ADD, rm, b, c));
Expr rhs = em.mkExpr(Kind.FLOATINGPOINT_ADD,
rm,
em.mkExpr(Kind.FLOATINGPOINT_ADD, rm, a, b),
c);
smt.assertFormula(em.mkExpr(Kind.NOT, em.mkExpr(Kind.EQUAL, a, b)));
Result r = smt.checkSat(); // result is sat
assert r.isSat() == Result.Sat.SAT;
System.out.println("a = " + smt.getValue(a));
System.out.println("b = " + smt.getValue(b));
System.out.println("c = " + smt.getValue(c));
// Now, let's restrict `a` to be either NaN or positive infinity
FloatingPointSize fps32 = new FloatingPointSize(8, 24);
Expr nan = em.mkConst(FloatingPoint.makeNaN(fps32));
Expr inf = em.mkConst(FloatingPoint.makeInf(fps32, /* sign */ true));
smt.assertFormula(em.mkExpr(
Kind.OR, em.mkExpr(Kind.EQUAL, a, inf), em.mkExpr(Kind.EQUAL, a, nan)));
r = smt.checkSat(); // result is sat
assert r.isSat() == Result.Sat.SAT;
System.out.println("a = " + smt.getValue(a));
System.out.println("b = " + smt.getValue(b));
System.out.println("c = " + smt.getValue(c));
// And now for something completely different. Let's try to find a (normal)
// floating-point number that rounds to different integer values for
// different rounding modes.
Expr rtp = em.mkConst(RoundingMode.roundTowardPositive);
Expr rtn = em.mkConst(RoundingMode.roundTowardNegative);
Expr op = em.mkConst(new FloatingPointToSBV(16)); // (_ fp.to_sbv 16)
lhs = em.mkExpr(op, rtp, d);
rhs = em.mkExpr(op, rtn, d);
smt.assertFormula(em.mkExpr(Kind.FLOATINGPOINT_ISN, d));
smt.assertFormula(em.mkExpr(Kind.NOT, em.mkExpr(Kind.EQUAL, lhs, rhs)));
r = smt.checkSat(); // result is sat
assert r.isSat() == Result.Sat.SAT;
// Convert the result to a rational and print it
Expr val = smt.getValue(d);
Rational realVal =
val.getConstFloatingPoint().convertToRationalTotal(new Rational(0));
System.out.println("d = " + val + " = " + realVal);
System.out.println("((_ fp.to_sbv 16) RTP d) = " + smt.getValue(lhs));
System.out.println("((_ fp.to_sbv 16) RTN d) = " + smt.getValue(rhs));
// For our final trick, let's try to find a floating-point number between
// positive zero and the smallest positive floating-point number
Expr zero = em.mkConst(FloatingPoint.makeZero(fps32, /* sign */ true));
Expr smallest =
em.mkConst(new FloatingPoint(8, 24, new BitVector(32, 0b001)));
smt.assertFormula(em.mkExpr(Kind.AND,
em.mkExpr(Kind.FLOATINGPOINT_LT, zero, e),
em.mkExpr(Kind.FLOATINGPOINT_LT, e, smallest)));
r = smt.checkSat(); // result is unsat
assert r.isSat() == Result.Sat.UNSAT;
}
}
|
