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122 lines
4.6 KiB
Python
122 lines
4.6 KiB
Python
#!/usr/bin/env python
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###############################################################################
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# Top contributors (to current version):
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# Aina Niemetz, Makai Mann, Mathias Preiner
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#
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# This file is part of the cvc5 project.
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#
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# Copyright (c) 2009-2025 by the authors listed in the file AUTHORS
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# in the top-level source directory and their institutional affiliations.
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# All rights reserved. See the file COPYING in the top-level source
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# directory for licensing information.
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# #############################################################################
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#
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# A simple demonstration of the solving capabilities of the cvc5
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# floating point solver through the Python API contributed by Eva
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# Darulova. This requires building cvc5 with symfpu.
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##
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import cvc5
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from cvc5 import Kind, RoundingMode
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if __name__ == "__main__":
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tm = cvc5.TermManager()
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slv = cvc5.Solver(tm)
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slv.setOption("produce-models", "true")
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slv.setLogic("QF_FP")
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# single 32-bit precision
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fp32 = tm.mkFloatingPointSort(8, 24)
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# rounding mode
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rm = tm.mkRoundingMode(RoundingMode.ROUND_NEAREST_TIES_TO_EVEN)
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# create a few single-precision variables
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a = tm.mkConst(fp32, 'a')
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b = tm.mkConst(fp32, 'b')
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c = tm.mkConst(fp32, 'c')
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d = tm.mkConst(fp32, 'd')
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e = tm.mkConst(fp32, 'e')
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print("Show that fused multiplication and addition `(fp.fma RM a b c)`")
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print("is different from `(fp.add RM (fp.mul a b) c)`:")
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slv.push()
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fma = tm.mkTerm(Kind.FLOATINGPOINT_FMA, rm, a, b, c)
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mul = tm.mkTerm(Kind.FLOATINGPOINT_MULT, rm, a, b)
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add = tm.mkTerm(Kind.FLOATINGPOINT_ADD, rm, mul, c)
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slv.assertFormula(tm.mkTerm(Kind.DISTINCT, fma, add))
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print("Expect SAT.")
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print("cvc5:", slv.checkSat())
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print(f'Value of `a`: {slv.getValue(a)}')
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print(f'Value of `b`: {slv.getValue(b)}')
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print(f'Value of `c`: {slv.getValue(c)}')
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print(f'Value of `(fp.fma RNE a b c)`: {slv.getValue(fma)}')
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print(f'Value of `(fp.add RNE (fp.mul a b) c)`: {slv.getValue(add)}')
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print();
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slv.pop();
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print("Show that floating-point addition is not associative:")
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print("(a + (b + c)) != ((a + b) + c)")
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slv.push()
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slv.assertFormula(tm.mkTerm(
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Kind.DISTINCT,
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tm.mkTerm(Kind.FLOATINGPOINT_ADD,
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rm, a, tm.mkTerm(Kind.FLOATINGPOINT_ADD, rm, b, c)),
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tm.mkTerm(Kind.FLOATINGPOINT_ADD,
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rm, tm.mkTerm(Kind.FLOATINGPOINT_ADD, rm, a, b), c)))
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print("Expect SAT.")
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print("cvc5:", slv.checkSat())
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print(f'Value of `a`: {slv.getValue(a)}')
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print(f'Value of `b`: {slv.getValue(b)}')
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print(f'Value of `c`: {slv.getValue(c)}')
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print()
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print("Now, restrict `a` to be either NaN or positive infinity:")
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nan = tm.mkFloatingPointNaN(8, 24)
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inf = tm.mkFloatingPointPosInf(8, 24)
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slv.assertFormula(tm.mkTerm(
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Kind.OR, tm.mkTerm(Kind.EQUAL, a, inf), tm.mkTerm(Kind.EQUAL, a, nan)))
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print("Expect SAT.")
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print("cvc5:", slv.checkSat())
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print(f'Value of `a`: {slv.getValue(a)}')
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print(f'Value of `b`: {slv.getValue(b)}')
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print(f'Value of `c`: {slv.getValue(c)}')
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print()
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slv.pop(1)
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print("Now, try to find a (normal) floating-point number that rounds")
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print("to different integer values for different rounding modes:")
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slv.push()
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rtp = tm.mkRoundingMode(RoundingMode.ROUND_TOWARD_POSITIVE)
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rtn = tm.mkRoundingMode(RoundingMode.ROUND_TOWARD_NEGATIVE)
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op = tm.mkOp(Kind.FLOATINGPOINT_TO_UBV, 16) # (_ fp.to_ubv 16)
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lhs = tm.mkTerm(op, rtp, d)
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rhs = tm.mkTerm(op, rtn, d)
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slv.assertFormula(tm.mkTerm(Kind.FLOATINGPOINT_IS_NORMAL, d))
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slv.assertFormula(tm.mkTerm(Kind.NOT, tm.mkTerm(Kind.EQUAL, lhs, rhs)))
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print("Expect SAT.")
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print("cvc5:", slv.checkSat())
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print("Get value of `d` as floating-point, bit-vector and real:")
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val = slv.getValue(d)
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print(f'Value of `d`: {val}')
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print(f'Value of `((_ fp.to_ubv 16) RTP d)`: {slv.getValue(lhs)}')
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print(f'Value of `((_ fp.to_ubv 16) RTN d)`: {slv.getValue(rhs)}')
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print(f'Value of `(fp.to_real d)`: {slv.getValue(tm.mkTerm(Kind.FLOATINGPOINT_TO_REAL, val))}')
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print()
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slv.pop()
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print("Finally, try to find a floating-point number between positive")
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print("zero and the smallest positive floating-point number:")
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zero = tm.mkFloatingPointPosZero(8, 24)
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smallest = tm.mkFloatingPoint(8, 24, tm.mkBitVector(32, 0b001))
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slv.assertFormula(tm.mkTerm(
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Kind.AND, tm.mkTerm(Kind.FLOATINGPOINT_LT, zero, e),
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tm.mkTerm(Kind.FLOATINGPOINT_LT, e, smallest)))
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print("Expect UNSAT.")
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print("cvc5:", slv.checkSat())
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