Add functions for smallest and largest representable fixed point (#606)

* Add functions for smallest and largest representable fixed point

Implements #594

* New line.

* Apply suggestions from code review

Co-authored-by: Mariia Mykhailova <[email protected]>

Co-authored-by: Mariia Mykhailova <[email protected]>

Author: msoeken

Numerics/src/FixedPoint/Math.qs

@@ -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));
+    }
+
+}

Numerics/tests/FixedPointTests.qs

@@ -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));
+            }
+        }
+    }
 }