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26 lines
766 B
Python
26 lines
766 B
Python
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, is 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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