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
|
/******************************************************************************
* 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 cvc5's cpp API
*
* This example shows 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.
*/
#include <cvc5/cvc5.h>
#include <iostream>
#include <cassert>
using namespace std;
using namespace cvc5::api;
int main()
{
Solver solver;
solver.setOption("produce-models", "true");
// Make single precision floating-point variables
Sort fpt32 = solver.mkFloatingPointSort(8, 24);
Term a = solver.mkConst(fpt32, "a");
Term b = solver.mkConst(fpt32, "b");
Term c = solver.mkConst(fpt32, "c");
Term d = solver.mkConst(fpt32, "d");
Term e = solver.mkConst(fpt32, "e");
// Assert that floating-point addition is not associative:
// (a + (b + c)) != ((a + b) + c)
Term rm = solver.mkRoundingMode(ROUND_NEAREST_TIES_TO_EVEN);
Term lhs = solver.mkTerm(
FLOATINGPOINT_ADD, rm, a, solver.mkTerm(FLOATINGPOINT_ADD, rm, b, c));
Term rhs = solver.mkTerm(
FLOATINGPOINT_ADD, rm, solver.mkTerm(FLOATINGPOINT_ADD, rm, a, b), c);
solver.assertFormula(solver.mkTerm(NOT, solver.mkTerm(EQUAL, a, b)));
Result r = solver.checkSat(); // result is sat
assert (r.isSat());
cout << "a = " << solver.getValue(a) << endl;
cout << "b = " << solver.getValue(b) << endl;
cout << "c = " << solver.getValue(c) << endl;
// Now, let's restrict `a` to be either NaN or positive infinity
Term nan = solver.mkNaN(8, 24);
Term inf = solver.mkPosInf(8, 24);
solver.assertFormula(solver.mkTerm(
OR, solver.mkTerm(EQUAL, a, inf), solver.mkTerm(EQUAL, a, nan)));
r = solver.checkSat(); // result is sat
assert (r.isSat());
cout << "a = " << solver.getValue(a) << endl;
cout << "b = " << solver.getValue(b) << endl;
cout << "c = " << solver.getValue(c) << endl;
// 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.
Term rtp = solver.mkRoundingMode(ROUND_TOWARD_POSITIVE);
Term rtn = solver.mkRoundingMode(ROUND_TOWARD_NEGATIVE);
Op op = solver.mkOp(FLOATINGPOINT_TO_SBV, 16); // (_ fp.to_sbv 16)
lhs = solver.mkTerm(op, rtp, d);
rhs = solver.mkTerm(op, rtn, d);
solver.assertFormula(solver.mkTerm(FLOATINGPOINT_ISN, d));
solver.assertFormula(solver.mkTerm(NOT, solver.mkTerm(EQUAL, lhs, rhs)));
r = solver.checkSat(); // result is sat
assert (r.isSat());
// Convert the result to a rational and print it
Term val = solver.getValue(d);
Term realVal = solver.getValue(solver.mkTerm(FLOATINGPOINT_TO_REAL, val));
cout << "d = " << val << " = " << realVal << endl;
cout << "((_ fp.to_sbv 16) RTP d) = " << solver.getValue(lhs) << endl;
cout << "((_ fp.to_sbv 16) RTN d) = " << solver.getValue(rhs) << endl;
// For our final trick, let's try to find a floating-point number between
// positive zero and the smallest positive floating-point number
Term zero = solver.mkPosZero(8, 24);
Term smallest = solver.mkFloatingPoint(8, 24, solver.mkBitVector(32, 0b001));
solver.assertFormula(
solver.mkTerm(AND,
solver.mkTerm(FLOATINGPOINT_LT, zero, e),
solver.mkTerm(FLOATINGPOINT_LT, e, smallest)));
r = solver.checkSat(); // result is unsat
assert (!r.isSat());
}
|
