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/******************************************************************************
* Top contributors (to current version):
* Aina Niemetz, Mudathir Mohamed, Andres Noetzli
*
* This file is part of the cvc5 project.
*
* Copyright (c) 2009-2025 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 Java 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.
*/
import static io.github.cvc5.Kind.*;
import io.github.cvc5.*;
public class FloatingPointArith
{
public static void main(String[] args) throws CVC5ApiException
{
TermManager tm = new TermManager();
Solver solver = new Solver(tm);
{
solver.setOption("incremental", "true");
solver.setOption("produce-models", "true");
// Make single precision floating-point variables
Sort fpt32 = tm.mkFloatingPointSort(8, 24);
Term a = tm.mkConst(fpt32, "a");
Term b = tm.mkConst(fpt32, "b");
Term c = tm.mkConst(fpt32, "c");
Term d = tm.mkConst(fpt32, "d");
Term e = tm.mkConst(fpt32, "e");
// Rounding mode
Term rm = tm.mkRoundingMode(RoundingMode.ROUND_NEAREST_TIES_TO_EVEN);
System.out.println("Show that fused multiplication and addition `(fp.fma RM a b c)`");
System.out.println("is different from `(fp.add RM (fp.mul a b) c)`:");
solver.push(1);
Term fma = tm.mkTerm(Kind.FLOATINGPOINT_FMA, new Term[] {rm, a, b, c});
Term mul = tm.mkTerm(Kind.FLOATINGPOINT_MULT, rm, a, b);
Term add = tm.mkTerm(Kind.FLOATINGPOINT_ADD, rm, mul, c);
solver.assertFormula(tm.mkTerm(Kind.DISTINCT, fma, add));
Result r = solver.checkSat(); // result is sat
System.out.println("Expect sat: " + r);
System.out.println("Value of `a`: " + solver.getValue(a));
System.out.println("Value of `b`: " + solver.getValue(b));
System.out.println("Value of `c`: " + solver.getValue(c));
System.out.println("Value of `(fp.fma RNE a b c)`: " + solver.getValue(fma));
System.out.println("Value of `(fp.add RNE (fp.mul a b) c)`: " + solver.getValue(add));
System.out.println();
solver.pop(1);
System.out.println("Show that floating-point addition is not associative:");
System.out.println("(a + (b + c)) != ((a + b) + c)");
Term lhs =
tm.mkTerm(Kind.FLOATINGPOINT_ADD, rm, a, tm.mkTerm(Kind.FLOATINGPOINT_ADD, rm, b, c));
Term rhs =
tm.mkTerm(Kind.FLOATINGPOINT_ADD, rm, tm.mkTerm(Kind.FLOATINGPOINT_ADD, rm, a, b), c);
solver.assertFormula(tm.mkTerm(Kind.NOT, tm.mkTerm(Kind.EQUAL, a, b)));
r = solver.checkSat(); // result is sat
assert r.isSat();
System.out.println("Value of `a`: " + solver.getValue(a));
System.out.println("Value of `b`: " + solver.getValue(b));
System.out.println("Value of `c`: " + solver.getValue(c));
System.out.println("Now, restrict `a` to be either NaN or positive infinity:");
Term nan = tm.mkFloatingPointNaN(8, 24);
Term inf = tm.mkFloatingPointPosInf(8, 24);
solver.assertFormula(
tm.mkTerm(Kind.OR, tm.mkTerm(Kind.EQUAL, a, inf), tm.mkTerm(Kind.EQUAL, a, nan)));
r = solver.checkSat(); // result is sat
assert r.isSat();
System.out.println("Value of `a`: " + solver.getValue(a));
System.out.println("Value of `b`: " + solver.getValue(b));
System.out.println("Value of `c`: " + solver.getValue(c));
System.out.println("Now, try to find a (normal) floating-point number that rounds");
System.out.println("to different integer values for different rounding modes:");
Term rtp = tm.mkRoundingMode(RoundingMode.ROUND_TOWARD_POSITIVE);
Term rtn = tm.mkRoundingMode(RoundingMode.ROUND_TOWARD_NEGATIVE);
Op op = tm.mkOp(Kind.FLOATINGPOINT_TO_UBV, 16); // (_ fp.to_ubv 16)
lhs = tm.mkTerm(op, rtp, d);
rhs = tm.mkTerm(op, rtn, d);
solver.assertFormula(tm.mkTerm(Kind.FLOATINGPOINT_IS_NORMAL, d));
solver.assertFormula(tm.mkTerm(Kind.NOT, tm.mkTerm(Kind.EQUAL, lhs, rhs)));
r = solver.checkSat(); // result is sat
assert r.isSat();
System.out.println("Get value of `d` as floating-point, bit-vector and real:");
Term val = solver.getValue(d);
System.out.println("Value of `d`: " + val);
System.out.println("Value of `((_ fp.to_ubv 16) RTP d)`: " + solver.getValue(lhs));
System.out.println("Value of `((_ fp.to_ubv 16) RTN d)`: " + solver.getValue(rhs));
System.out.println("Value of `(fp.to_real d)`: "
+ solver.getValue(tm.mkTerm(Kind.FLOATINGPOINT_TO_REAL, val)));
System.out.println("Finally, try to find a floating-point number between positive");
System.out.println("zero and the smallest positive floating-point number:");
Term zero = tm.mkFloatingPointPosZero(8, 24);
Term smallest = tm.mkFloatingPoint(8, 24, tm.mkBitVector(32, 0b001));
solver.assertFormula(tm.mkTerm(Kind.AND,
tm.mkTerm(Kind.FLOATINGPOINT_LT, zero, e),
tm.mkTerm(Kind.FLOATINGPOINT_LT, e, smallest)));
r = solver.checkSat(); // result is unsat
assert !r.isSat();
}
Context.deletePointers();
}
}
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