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Add functions for smallest and largest representable fixed point #606

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msoeken merged 3 commits into from
Jul 18, 2022
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Add functions for smallest and largest representable fixed point #606

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Add functions for smallest and largest representable fixed point
msoeken Jul 13, 2022
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msoeken Jul 13, 2022
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msoeken Jul 14, 2022
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38 changes: 38 additions & 0 deletions Numerics/src/FixedPoint/Math.qs
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Original file line number Diff line number Diff line change
@@ -0,0 +1,38 @@
// Copyright (c) Microsoft Corporation.
// Licensed under the MIT License.

namespace Microsoft.Quantum.Math {
open Microsoft.Quantum.Convert;

/// # Summary
/// Returns the smallest representable number for specific fixed point dimensions.
///
/// # Input
/// ## integerBits
/// Number of integer bits (including the sign bit).
/// ## fractionalBits
/// Number of fractional bits.
///
/// # Remark
/// The value can be computed as $-2^{p-1}$, where $p$ is the number of integer bits.
function SmallestFixedPoint(integerBits : Int, fractionalBits : Int) : Double {
return -PowD(2.0, IntAsDouble(integerBits - 1));
}

/// # Summary
/// Returns the largest representable number for specific fixed point dimensions.
///
/// # Input
/// ## integerBits
/// Number of integer bits (including the sign bit).
/// ## fractionalBits
/// Number of fractional bits.
///
/// # Remark
/// The value can be computed as $2^{p-1} - 2^{-q}$, where $p$
/// is the number of integer bits and $q$ is the number of fractional bits.
function LargestFixedPoint(integerBits : Int, fractionalBits : Int) : Double {
return PowD(2.0, IntAsDouble(integerBits - 1)) - PowD(2.0, -IntAsDouble(fractionalBits));
}

}
12 changes: 12 additions & 0 deletions Numerics/tests/FixedPointTests.qs
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Expand Up @@ -435,4 +435,16 @@ namespace Microsoft.Quantum.Tests {
}
}
}

@Test("QuantumSimulator")
operation TestFixedPointLimits() : Unit {
for numBits in 1..6 {
for integerBits in 0..numBits {
let fractionalBits = numBits - integerBits;

NearEqualityFactD(SmallestFixedPoint(integerBits, fractionalBits), BoolArrayAsFixedPoint(integerBits, [false, size = numBits] w/ numBits - 1 <- true));
NearEqualityFactD(LargestFixedPoint(integerBits, fractionalBits), BoolArrayAsFixedPoint(integerBits, [true, size = numBits] w/ numBits - 1 <- false));
}
}
}
}