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45 lines
1.6 KiB
Python
45 lines
1.6 KiB
Python
###############################################################################
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# Top contributors (to current version):
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# Alex Ozdemir, Anjiang-Wei
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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) 2009-2024 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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# An example of solving floating-point problems with cvc5's Python API.
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#
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# This example shows to create floating-point types, variables and expressions,
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# and how to create rounding mode constants by solving toy problems. The
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# example also shows making special values (such as NaN and +oo) and converting
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# an IEEE 754-2008 bit-vector to a floating-point number.
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##
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from cvc5.pythonic import *
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if __name__ == "__main__":
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x, y, z = FPs("x y z", Float32())
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set_default_rounding_mode(RoundNearestTiesToEven())
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# FP addition is *not* commutative. This finds a counterexample.
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assert not is_tautology(fpEQ(x + y, y + x))
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# Without NaN or infinities, it is commutative. This proof succeeds.
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assert is_tautology(
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Implies(
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Not(Or(fpIsNaN(x), fpIsNaN(y), fpIsInf(x), fpIsInf(y))), fpEQ(x + y, y + x)
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)
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)
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pi = FPVal(+3.14, Float32())
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# FP addition is *not* associative in the range (-pi, pi).
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assert not is_tautology(
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Implies(
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And(x >= -pi, x <= pi, y >= -pi, y <= pi, z >= -pi, z <= pi),
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fpEQ((x + y) + z, x + (y + z)),
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)
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)
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