Merge cc94905930 into 6750f0e3db

I'm an idiot.

X10D.Tests/src/IO/UInt16Tests.cs

@@ -1,4 +1,4 @@
-using NUnit.Framework;
+using NUnit.Framework;
 using X10D.IO;
 
 namespace X10D.Tests.IO;

X10D.Tests/src/IO/UInt32Tests.cs

@@ -1,4 +1,4 @@
-using NUnit.Framework;
+using NUnit.Framework;
 using X10D.IO;
 
 namespace X10D.Tests.IO;

X10D.Tests/src/IO/UInt64Tests.cs

@@ -1,4 +1,4 @@
-using NUnit.Framework;
+using NUnit.Framework;
 using X10D.IO;
 
 namespace X10D.Tests.IO;

X10D.Tests/src/Math/UInt32Tests.cs

@@ -1,4 +1,4 @@
-using NUnit.Framework;
+using NUnit.Framework;
 using X10D.Math;
 
 namespace X10D.Tests.Math;

X10D.Tests/src/Math/UInt64Tests.cs

@@ -1,4 +1,4 @@
-using NUnit.Framework;
+using NUnit.Framework;
 using X10D.Math;
 
 namespace X10D.Tests.Math;

X10D/src/Collections/BinaryIntegerExtensions.cs

@@ -0,0 +1,89 @@
+#if NET7_0_OR_GREATER
+using System.Diagnostics.Contracts;
+using System.Numerics;
+using System.Runtime.CompilerServices;
+using System.Runtime.Intrinsics.X86;
+using X10D.CompilerServices;
+
+namespace X10D.Collections;
+
+/// <summary>
+///     Collection-related extension methods for <see cref="IBinaryInteger{T}" />.
+/// </summary>
+public static class BinaryIntegerExtensions
+{
+    /// <summary>
+    ///     Unpacks this integer into a boolean list, treating it as a bit field.
+    /// </summary>
+    /// <param name="value">The value to unpack.</param>
+    /// <returns>An array of <see cref="bool" /> with a length equal to the size of <typeparamref name="TInteger" />.</returns>
+    [Pure]
+    [MethodImpl(CompilerResources.MaxOptimization)]
+    public static bool[] Unpack<TInteger>(this TInteger value)
+        where TInteger : unmanaged, IBinaryInteger<TInteger>
+    {
+        unsafe
+        {
+            var buffer = new bool[sizeof(TInteger) * 8];
+            value.Unpack(buffer);
+            return buffer;
+        }
+    }
+
+    /// <summary>
+    ///     Unpacks this integer into a boolean list, treating it as a bit field.
+    /// </summary>
+    /// <param name="value">The value to unpack.</param>
+    /// <param name="destination">When this method returns, contains the unpacked booleans from <paramref name="value" />.</param>
+    /// <exception cref="ArgumentException"><paramref name="destination" /> is not large enough to contain the result.</exception>
+    [MethodImpl(CompilerResources.MaxOptimization)]
+    public static void Unpack<TInteger>(this TInteger value, Span<bool> destination)
+        where TInteger : unmanaged, IBinaryInteger<TInteger>
+    {
+        unsafe
+        {
+            if (destination.Length < sizeof(TInteger) * 8)
+            {
+                throw new ArgumentException(ExceptionMessages.DestinationSpanLengthTooShort, nameof(destination));
+            }
+        }
+
+        switch (value)
+        {
+            case byte valueByte when Sse3.IsSupported:
+                valueByte.UnpackInternal_Ssse3(destination);
+                break;
+
+            case int valueInt32 when Avx2.IsSupported:
+                valueInt32.UnpackInternal_Ssse3(destination);
+                break;
+
+            case int valueInt32 when Sse3.IsSupported:
+                valueInt32.UnpackInternal_Ssse3(destination);
+                break;
+
+            case short valueInt16 when Sse3.IsSupported:
+                valueInt16.UnpackInternal_Ssse3(destination);
+                break;
+
+            default:
+                UnpackInternal_Fallback(value, destination);
+                break;
+        }
+    }
+
+    [MethodImpl(CompilerResources.MaxOptimization)]
+    internal static void UnpackInternal_Fallback<TInteger>(this TInteger value, Span<bool> destination)
+        where TInteger : unmanaged, IBinaryInteger<TInteger>
+    {
+        unsafe
+        {
+            int bitCount = sizeof(TInteger) * 8;
+            for (var index = 0; index < bitCount; index++)
+            {
+                destination[index] = (value & (TInteger.One << index)) != TInteger.Zero;
+            }
+        }
+    }
+}
+#endif

X10D/src/Collections/ByteExtensions.cs

@@ -1,5 +1,7 @@
+#if !NET7_0_OR_GREATER
 using System.Diagnostics.CodeAnalysis;
 using System.Diagnostics.Contracts;
+#endif
 using System.Runtime.CompilerServices;
 using System.Runtime.Intrinsics;
 using System.Runtime.Intrinsics.X86;
@@ -14,6 +16,7 @@ public static class ByteExtensions
 {
     private const int Size = sizeof(byte) * 8;
 
+#if !NET7_0_OR_GREATER
     /// <summary>
     ///     Unpacks this 8-bit unsigned integer into a boolean list, treating it as a bit field.
     /// </summary>
@@ -51,6 +54,7 @@ public static class ByteExtensions
 
         UnpackInternal_Fallback(value, destination);
     }
+#endif
 
     [MethodImpl(CompilerResources.MaxOptimization)]
     internal static void UnpackInternal_Fallback(this byte value, Span<bool> destination)

X10D/src/Collections/Int16Extensions.cs

@@ -1,5 +1,7 @@
+#if !NET7_0_OR_GREATER
 using System.Diagnostics.CodeAnalysis;
 using System.Diagnostics.Contracts;
+#endif
 using System.Runtime.CompilerServices;
 using System.Runtime.Intrinsics;
 using System.Runtime.Intrinsics.X86;
@@ -14,6 +16,7 @@ public static class Int16Extensions
 {
     private const int Size = sizeof(short) * 8;
 
+#if !NET7_0_OR_GREATER
     /// <summary>
     ///     Unpacks this 16-bit signed integer into a boolean list, treating it as a bit field.
     /// </summary>
@@ -51,6 +54,7 @@ public static class Int16Extensions
 
         UnpackInternal_Fallback(value, destination);
     }
+#endif
 
     [MethodImpl(CompilerResources.MaxOptimization)]
     internal static void UnpackInternal_Fallback(this short value, Span<bool> destination)

X10D/src/Collections/Int32Extensions.cs

@@ -1,5 +1,7 @@
+#if !NET7_0_OR_GREATER
 using System.Diagnostics.CodeAnalysis;
 using System.Diagnostics.Contracts;
+#endif
 using System.Runtime.CompilerServices;
 using System.Runtime.Intrinsics;
 using System.Runtime.Intrinsics.X86;
@@ -14,6 +16,7 @@ public static class Int32Extensions
 {
     private const int Size = sizeof(int) * 8;
 
+#if !NET7_0_OR_GREATER
     /// <summary>
     ///     Unpacks this 32-bit signed integer into a boolean list, treating it as a bit field.
     /// </summary>
@@ -57,6 +60,7 @@ public static class Int32Extensions
 
         UnpackInternal_Fallback(value, destination);
     }
+#endif
 
     [MethodImpl(CompilerResources.MaxOptimization)]
     internal static void UnpackInternal_Fallback(this int value, Span<bool> destination)

X10D/src/Collections/Int64Extensions.cs

@@ -1,3 +1,4 @@
+#if !NET7_0_OR_GREATER
 using System.Diagnostics.Contracts;
 
 namespace X10D.Collections;
@@ -41,3 +42,4 @@ public static class Int64Extensions
         }
     }
 }
+#endif

X10D/src/IO/DoubleExtensions.cs

@@ -1,4 +1,4 @@
-using System.Buffers.Binary;
+using System.Buffers.Binary;
 using System.Diagnostics.Contracts;
 using System.Runtime.InteropServices;
 

X10D/src/IO/Int16Extensions.cs

@@ -1,4 +1,4 @@
-using System.Buffers.Binary;
+using System.Buffers.Binary;
 using System.Diagnostics.Contracts;
 
 namespace X10D.IO;

X10D/src/IO/Int32Extensions.cs

@@ -1,4 +1,4 @@
-using System.Buffers.Binary;
+using System.Buffers.Binary;
 using System.Diagnostics.Contracts;
 
 namespace X10D.IO;

X10D/src/IO/Int64Extensions.cs

@@ -1,4 +1,4 @@
-using System.Buffers.Binary;
+using System.Buffers.Binary;
 using System.Diagnostics.Contracts;
 
 namespace X10D.IO;

X10D/src/IO/SingleExtensions.cs

@@ -1,4 +1,4 @@
-using System.Buffers.Binary;
+using System.Buffers.Binary;
 using System.Diagnostics.Contracts;
 #if !NET5_0_OR_GREATER
 using System.Runtime.InteropServices;

X10D/src/IO/UInt16Extensions.cs

@@ -1,4 +1,4 @@
-using System.Buffers.Binary;
+using System.Buffers.Binary;
 using System.Diagnostics.Contracts;
 
 namespace X10D.IO;

X10D/src/IO/UInt32Extensions.cs

@@ -1,4 +1,4 @@
-using System.Buffers.Binary;
+using System.Buffers.Binary;
 using System.Diagnostics.Contracts;
 
 namespace X10D.IO;

X10D/src/IO/UInt64Extensions.cs

@@ -1,4 +1,4 @@
-using System.Buffers.Binary;
+using System.Buffers.Binary;
 using System.Diagnostics.Contracts;
 
 namespace X10D.IO;

X10D/src/Math/BigIntegerExtensions.cs

@@ -10,6 +10,7 @@ namespace X10D.Math;
 /// </summary>
 public static class BigIntegerExtensions
 {
+#if !NET7_0_OR_GREATER
     /// <summary>
     ///     Returns the number of digits in the current integer.
     /// </summary>
@@ -42,6 +43,7 @@ public static class BigIntegerExtensions
         BigInteger root = BigInteger.Abs(value).Mod(9);
         return (int)(root == 0 ? 9 : root);
     }
+#endif
 
     /// <summary>
     ///     Returns the factorial of the current 64-bit signed integer.
@@ -170,6 +172,7 @@ public static class BigIntegerExtensions
         return value * other / value.GreatestCommonFactor(other);
     }
 
+#if !NET7_0_OR_GREATER
     /// <summary>
     ///     Performs a modulo operation which supports a negative dividend.
     /// </summary>
@@ -191,6 +194,7 @@ public static class BigIntegerExtensions
         BigInteger r = dividend % divisor;
         return r < 0 ? r + divisor : r;
     }
+#endif
 
     /// <summary>
     ///     Returns the multiplicative persistence of a specified value.

X10D/src/Math/BinaryIntegerExtensions.cs

@@ -0,0 +1,52 @@
+#if NET7_0_OR_GREATER
+using System.Diagnostics.Contracts;
+using System.Numerics;
+using System.Runtime.CompilerServices;
+using X10D.CompilerServices;
+
+namespace X10D.Math;
+
+/// <summary>
+///     Math-related extension methods for <see cref="IBinaryInteger{TSelf}" />.
+/// </summary>
+public static class BinaryIntegerExtensions
+{
+    /// <summary>
+    ///     Returns the number of digits in the current binary integer.
+    /// </summary>
+    /// <param name="value">The value whose digit count to compute.</param>
+    /// <returns>The number of digits in <paramref name="value" />.</returns>
+    [Pure]
+    [MethodImpl(CompilerResources.MaxOptimization)]
+    public static int CountDigits<TInteger>(this TInteger value)
+        where TInteger : IBinaryInteger<TInteger>
+    {
+        if (TInteger.IsZero(value))
+        {
+            return 1;
+        }
+
+        return 1 + (int)System.Math.Floor(System.Math.Log10(System.Math.Abs(double.CreateChecked(value))));
+    }
+
+    /// <summary>
+    ///     Computes the digital root of this integer.
+    /// </summary>
+    /// <param name="value">The value whose digital root to compute.</param>
+    /// <returns>The digital root of <paramref name="value" />.</returns>
+    /// <remarks>The digital root is defined as the recursive sum of digits until that result is a single digit.</remarks>
+    /// <remarks>
+    ///     <para>The digital root is defined as the recursive sum of digits until that result is a single digit.</para>
+    ///     <para>For example, the digital root of 239 is 5: <c>2 + 3 + 9 = 14</c>, then <c>1 + 4 = 5</c>.</para>
+    /// </remarks>
+    [Pure]
+    [MethodImpl(CompilerResources.MaxOptimization)]
+    public static int DigitalRoot<TInteger>(this TInteger value)
+        where TInteger : IBinaryInteger<TInteger>
+    {
+        var nine = TInteger.CreateChecked(9);
+        TInteger root = TInteger.Abs(value).Mod(nine);
+        return int.CreateChecked(root == TInteger.Zero ? nine : root);
+    }
+}
+#endif

X10D/src/Math/ByteExtensions.cs

@@ -9,6 +9,7 @@ namespace X10D.Math;
 /// </summary>
 public static class ByteExtensions
 {
+#if !NET7_0_OR_GREATER
     /// <summary>
     ///     Returns the number of digits in the current 8-bit unsigned integer.
     /// </summary>
@@ -41,6 +42,7 @@ public static class ByteExtensions
         int root = value % 9;
         return (byte)(root == 0 ? 9 : root);
     }
+#endif
 
     /// <summary>
     ///     Returns the factorial of the current 8-bit unsigned integer.

X10D/src/Math/Int16Extensions.cs

@@ -9,6 +9,7 @@ namespace X10D.Math;
 /// </summary>
 public static class Int16Extensions
 {
+#if !NET7_0_OR_GREATER
     /// <summary>
     ///     Returns the number of digits in the current 16-bit signed integer.
     /// </summary>
@@ -40,6 +41,7 @@ public static class Int16Extensions
         short root = System.Math.Abs(value).Mod(9);
         return root < 1 ? (short)(9 - root) : root;
     }
+#endif
 
     /// <summary>
     ///     Returns the factorial of the current 16-bit signed integer.
@@ -140,6 +142,7 @@ public static class Int16Extensions
         return (short)((long)value).LowestCommonMultiple(other);
     }
 
+#if !NET7_0_OR_GREATER
     /// <summary>
     ///     Performs a modulo operation which supports a negative dividend.
     /// </summary>
@@ -161,6 +164,7 @@ public static class Int16Extensions
         int r = dividend % divisor;
         return (short)(r < 0 ? r + divisor : r);
     }
+#endif
 
     /// <summary>
     ///     Returns the multiplicative persistence of a specified value.

X10D/src/Math/Int32Extensions.cs

@@ -9,6 +9,7 @@ namespace X10D.Math;
 /// </summary>
 public static class Int32Extensions
 {
+#if !NET7_0_OR_GREATER
     /// <summary>
     ///     Returns the number of digits in the current 32-bit signed integer.
     /// </summary>
@@ -40,6 +41,7 @@ public static class Int32Extensions
         int root = System.Math.Abs(value).Mod(9);
         return root < 1 ? 9 - root : root;
     }
+#endif
 
     /// <summary>
     ///     Returns the factorial of the current 32-bit signed integer.
@@ -140,6 +142,7 @@ public static class Int32Extensions
         return (int)((long)value).LowestCommonMultiple(other);
     }
 
+#if !NET7_0_OR_GREATER
     /// <summary>
     ///     Performs a modulo operation which supports a negative dividend.
     /// </summary>
@@ -161,6 +164,7 @@ public static class Int32Extensions
         int r = dividend % divisor;
         return r < 0 ? r + divisor : r;
     }
+#endif
 
     /// <summary>
     ///     Returns the multiplicative persistence of a specified value.

X10D/src/Math/Int64Extensions.cs

@@ -9,6 +9,7 @@ namespace X10D.Math;
 /// </summary>
 public static class Int64Extensions
 {
+#if !NET7_0_OR_GREATER
     /// <summary>
     ///     Returns the number of digits in the current 64-bit signed integer.
     /// </summary>
@@ -40,6 +41,7 @@ public static class Int64Extensions
         long root = System.Math.Abs(value).Mod(9L);
         return root < 1L ? 9L - root : root;
     }
+#endif
 
     /// <summary>
     ///     Returns the factorial of the current 64-bit signed integer.
@@ -179,6 +181,7 @@ public static class Int64Extensions
         return value * other / value.GreatestCommonFactor(other);
     }
 
+#if !NET7_0_OR_GREATER
     /// <summary>
     ///     Performs a modulo operation which supports a negative dividend.
     /// </summary>
@@ -200,6 +203,7 @@ public static class Int64Extensions
         long r = dividend % divisor;
         return r < 0 ? r + divisor : r;
     }
+#endif
 
     /// <summary>
     ///     Returns the multiplicative persistence of a specified value.

X10D/src/Math/MathUtility.cs

@@ -1,4 +1,5 @@
 using System.Diagnostics.Contracts;
+using System.Numerics;
 using System.Runtime.CompilerServices;
 using X10D.CompilerServices;
 
@@ -12,34 +13,6 @@ public static class MathUtility
     private const double DefaultGamma = 2.2;
     private const float DefaultGammaF = 2.2f;
 
-    /// <summary>
-    ///     Applies a simple bias function to value.
-    /// </summary>
-    /// <param name="value">The value to which the bias function will be applied.</param>
-    /// <param name="bias">The bias value. Valid values range from 0-1.</param>
-    /// <returns>The biased result.</returns>
-    /// <remarks>
-    ///     If <paramref name="bias" /> is less than 0.5, <paramref name="value" /> will be shifted downward; otherwise, upward.
-    /// </remarks>
-    public static float Bias(float value, float bias)
-    {
-        return value / ((1.0f / bias - 2.0f) * (1.0f - value) + 1.0f);
-    }
-
-    /// <summary>
-    ///     Applies a simple bias function to value.
-    /// </summary>
-    /// <param name="value">The value to which the bias function will be applied.</param>
-    /// <param name="bias">The bias value. Valid values range from 0-1.</param>
-    /// <returns>The biased result.</returns>
-    /// <remarks>
-    ///     If <paramref name="bias" /> is less than 0.5, <paramref name="value" /> will be shifted downward; otherwise, upward.
-    /// </remarks>
-    public static double Bias(double value, double bias)
-    {
-        return value / ((1.0 / bias - 2.0) * (1.0 - value) + 1.0);
-    }
-
     /// <summary>
     ///     Calculates exponential decay for a value.
     /// </summary>
@@ -154,6 +127,35 @@ public static class MathUtility
         return (alpha - start) / (end - start);
     }
 
+#if !NET7_0_OR_GREATER
+    /// <summary>
+    ///     Applies a simple bias function to value.
+    /// </summary>
+    /// <param name="value">The value to which the bias function will be applied.</param>
+    /// <param name="bias">The bias value. Valid values range from 0-1.</param>
+    /// <returns>The biased result.</returns>
+    /// <remarks>
+    ///     If <paramref name="bias" /> is less than 0.5, <paramref name="value" /> will be shifted downward; otherwise, upward.
+    /// </remarks>
+    public static float Bias(float value, float bias)
+    {
+        return value / ((1.0f / bias - 2.0f) * (1.0f - value) + 1.0f);
+    }
+
+    /// <summary>
+    ///     Applies a simple bias function to value.
+    /// </summary>
+    /// <param name="value">The value to which the bias function will be applied.</param>
+    /// <param name="bias">The bias value. Valid values range from 0-1.</param>
+    /// <returns>The biased result.</returns>
+    /// <remarks>
+    ///     If <paramref name="bias" /> is less than 0.5, <paramref name="value" /> will be shifted downward; otherwise, upward.
+    /// </remarks>
+    public static double Bias(double value, double bias)
+    {
+        return value / ((1.0 / bias - 2.0) * (1.0 - value) + 1.0);
+    }
+
     /// <summary>
     ///     Linearly interpolates from one value to a target using a specified alpha.
     /// </summary>
@@ -190,6 +192,93 @@ public static class MathUtility
         return ((1.0 - alpha) * value) + (alpha * target);
     }
 
+    /// <summary>
+    ///     Performs smooth Hermite interpolation from one value to a target using a specified alpha.
+    /// </summary>
+    /// <param name="value">The interpolation source.</param>
+    /// <param name="target">The interpolation target.</param>
+    /// <param name="alpha">The interpolation alpha.</param>
+    /// <returns>The interpolation result.</returns>
+    public static float SmoothStep(float value, float target, float alpha)
+    {
+        alpha = System.Math.Clamp(alpha, 0.0f, 1.0f);
+        alpha = -2.0f * alpha * alpha * alpha + 3.0f * alpha * alpha;
+        return target * alpha + value * (1.0f - alpha);
+    }
+
+    /// <summary>
+    ///     Performs smooth Hermite interpolation from one value to a target using a specified alpha.
+    /// </summary>
+    /// <param name="value">The interpolation source.</param>
+    /// <param name="target">The interpolation target.</param>
+    /// <param name="alpha">The interpolation alpha.</param>
+    /// <returns>The interpolation result.</returns>
+    public static double SmoothStep(double value, double target, double alpha)
+    {
+        alpha = System.Math.Clamp(alpha, 0.0, 1.0);
+        alpha = -2.0 * alpha * alpha * alpha + 3.0 * alpha * alpha;
+        return target * alpha + value * (1.0 - alpha);
+    }
+
+    /// <summary>
+    ///     Converts a value from being a percentage of one range, to being the same percentage in a new range.
+    /// </summary>
+    /// <param name="value">The value to convert.</param>
+    /// <param name="oldMin">The old minimum value.</param>
+    /// <param name="oldMax">The old maximum value.</param>
+    /// <param name="newMin">The new minimum value.</param>
+    /// <param name="newMax">The new maximum value.</param>
+    /// <returns>The scaled value.</returns>
+    [Pure]
+    [MethodImpl(CompilerResources.MaxOptimization)]
+    public static float ScaleRange(float value, float oldMin, float oldMax, float newMin, float newMax)
+    {
+        float oldRange = oldMax - oldMin;
+        float newRange = newMax - newMin;
+        float alpha = (value - oldMin) / oldRange;
+        return (alpha * newRange) + newMin;
+    }
+
+    /// <summary>
+    ///     Converts a value from being a percentage of one range, to being the same percentage in a new range.
+    /// </summary>
+    /// <param name="value">The value to convert.</param>
+    /// <param name="oldMin">The old minimum value.</param>
+    /// <param name="oldMax">The old maximum value.</param>
+    /// <param name="newMin">The new minimum value.</param>
+    /// <param name="newMax">The new maximum value.</param>
+    /// <returns>The scaled value.</returns>
+    [Pure]
+    [MethodImpl(CompilerResources.MaxOptimization)]
+    public static double ScaleRange(double value, double oldMin, double oldMax, double newMin, double newMax)
+    {
+        double oldRange = oldMax - oldMin;
+        double newRange = newMax - newMin;
+        double alpha = (value - oldMin) / oldRange;
+        return (alpha * newRange) + newMin;
+    }
+
+    /// <summary>
+    ///     Returns the incremental sawtooth wave of a given value.
+    /// </summary>
+    /// <param name="value">The value to calculate.</param>
+    /// <returns>The sawtooth wave of the given value.</returns>
+    public static float Sawtooth(float value)
+    {
+        return (value - MathF.Floor(value));
+    }
+
+    /// <summary>
+    ///     Returns the incremental sawtooth wave of a given value.
+    /// </summary>
+    /// <param name="value">The value to calculate.</param>
+    /// <returns>The sawtooth wave of the given value.</returns>
+    public static double Sawtooth(double value)
+    {
+        return (value - System.Math.Floor(value));
+    }
+#endif
+
     /// <summary>
     ///     Converts a linear value to a gamma-encoded value using a gamma value of <c>2.2</c>.
     /// </summary>
@@ -272,64 +361,6 @@ public static class MathUtility
         return Unsafe.As<bool, int>(ref result);
     }
 
-    /// <summary>
-    ///     Returns the incremental sawtooth wave of a given value.
-    /// </summary>
-    /// <param name="value">The value to calculate.</param>
-    /// <returns>The sawtooth wave of the given value.</returns>
-    public static float Sawtooth(float value)
-    {
-        return (value - MathF.Floor(value));
-    }
-
-    /// <summary>
-    ///     Returns the incremental sawtooth wave of a given value.
-    /// </summary>
-    /// <param name="value">The value to calculate.</param>
-    /// <returns>The sawtooth wave of the given value.</returns>
-    public static double Sawtooth(double value)
-    {
-        return (value - System.Math.Floor(value));
-    }
-
-    /// <summary>
-    ///     Converts a value from being a percentage of one range, to being the same percentage in a new range.
-    /// </summary>
-    /// <param name="value">The value to convert.</param>
-    /// <param name="oldMin">The old minimum value.</param>
-    /// <param name="oldMax">The old maximum value.</param>
-    /// <param name="newMin">The new minimum value.</param>
-    /// <param name="newMax">The new maximum value.</param>
-    /// <returns>The scaled value.</returns>
-    [Pure]
-    [MethodImpl(CompilerResources.MaxOptimization)]
-    public static float ScaleRange(float value, float oldMin, float oldMax, float newMin, float newMax)
-    {
-        float oldRange = oldMax - oldMin;
-        float newRange = newMax - newMin;
-        float alpha = (value - oldMin) / oldRange;
-        return (alpha * newRange) + newMin;
-    }
-
-    /// <summary>
-    ///     Converts a value from being a percentage of one range, to being the same percentage in a new range.
-    /// </summary>
-    /// <param name="value">The value to convert.</param>
-    /// <param name="oldMin">The old minimum value.</param>
-    /// <param name="oldMax">The old maximum value.</param>
-    /// <param name="newMin">The new minimum value.</param>
-    /// <param name="newMax">The new maximum value.</param>
-    /// <returns>The scaled value.</returns>
-    [Pure]
-    [MethodImpl(CompilerResources.MaxOptimization)]
-    public static double ScaleRange(double value, double oldMin, double oldMax, double newMin, double newMax)
-    {
-        double oldRange = oldMax - oldMin;
-        double newRange = newMax - newMin;
-        double alpha = (value - oldMin) / oldRange;
-        return (alpha * newRange) + newMin;
-    }
-
     /// <summary>
     ///     Calculates the sigmoid function for the given input value.
     /// </summary>
@@ -358,18 +389,71 @@ public static class MathUtility
         return 1.0f / (1.0f + System.Math.Exp(-value));
     }
 
+#if NET7_0_OR_GREATER
     /// <summary>
-    ///     Performs smooth Hermite interpolation from one value to a target using a specified alpha.
+    ///     Applies a simple bias function to value.
+    /// </summary>
+    /// <param name="value">The value to which the bias function will be applied.</param>
+    /// <param name="bias">The bias value. Valid values range from 0-1.</param>
+    /// <returns>The biased result.</returns>
+    /// <remarks>
+    ///     If <paramref name="bias" /> is less than 0.5, <paramref name="value" /> will be shifted downward; otherwise, upward.
+    /// </remarks>
+    public static TNumber Bias<TNumber>(TNumber value, TNumber bias)
+        where TNumber : INumber<TNumber>
+    {
+        TNumber identity = TNumber.MultiplicativeIdentity;
+        return value / ((identity / bias - TNumber.CreateChecked(2)) * (identity - value) + identity);
+    }
+
+    /// <summary>
+    ///     Linearly interpolates from one value to a target using a specified alpha.
     /// </summary>
     /// <param name="value">The interpolation source.</param>
     /// <param name="target">The interpolation target.</param>
     /// <param name="alpha">The interpolation alpha.</param>
-    /// <returns>The interpolation result.</returns>
-    public static float SmoothStep(float value, float target, float alpha)
+    /// <returns>
+    ///     The interpolation result as determined by <c>(1 - alpha) * value + alpha * target</c>.
+    /// </returns>
+    [Pure]
+    [MethodImpl(CompilerResources.MaxOptimization)]
+    public static TNumber Lerp<TNumber>(TNumber value, TNumber target, TNumber alpha)
+        where TNumber : INumber<TNumber>
     {
-        alpha = System.Math.Clamp(alpha, 0.0f, 1.0f);
-        alpha = -2.0f * alpha * alpha * alpha + 3.0f * alpha * alpha;
-        return target * alpha + value * (1.0f - alpha);
+        // rookie mistake: a + t * (b - a)
+        // "precise" method: (1 - t) * a + t * b
+        return ((TNumber.MultiplicativeIdentity - alpha) * value) + (alpha * target);
+    }
+
+    /// <summary>
+    ///     Returns the incremental sawtooth wave of a given value.
+    /// </summary>
+    /// <param name="value">The value to calculate.</param>
+    /// <returns>The sawtooth wave of the given value.</returns>
+    public static TNumber Sawtooth<TNumber>(TNumber value)
+        where TNumber : IFloatingPoint<TNumber>
+    {
+        return (value - TNumber.Floor(value));
+    }
+
+    /// <summary>
+    ///     Converts a value from being a percentage of one range, to being the same percentage in a new range.
+    /// </summary>
+    /// <param name="value">The value to convert.</param>
+    /// <param name="oldMin">The old minimum value.</param>
+    /// <param name="oldMax">The old maximum value.</param>
+    /// <param name="newMin">The new minimum value.</param>
+    /// <param name="newMax">The new maximum value.</param>
+    /// <returns>The scaled value.</returns>
+    [Pure]
+    [MethodImpl(CompilerResources.MaxOptimization)]
+    public static TNumber ScaleRange<TNumber>(TNumber value, TNumber oldMin, TNumber oldMax, TNumber newMin, TNumber newMax)
+        where TNumber : INumber<TNumber>
+    {
+        TNumber oldRange = oldMax - oldMin;
+        TNumber newRange = newMax - newMin;
+        TNumber alpha = (value - oldMin) / oldRange;
+        return (alpha * newRange) + newMin;
     }
 
     /// <summary>
@@ -379,10 +463,16 @@ public static class MathUtility
     /// <param name="target">The interpolation target.</param>
     /// <param name="alpha">The interpolation alpha.</param>
     /// <returns>The interpolation result.</returns>
-    public static double SmoothStep(double value, double target, double alpha)
+    public static TNumber SmoothStep<TNumber>(TNumber value, TNumber target, TNumber alpha)
+        where TNumber : INumber<TNumber>
     {
-        alpha = System.Math.Clamp(alpha, 0.0, 1.0);
-        alpha = -2.0 * alpha * alpha * alpha + 3.0 * alpha * alpha;
-        return target * alpha + value * (1.0 - alpha);
+        TNumber one = TNumber.One;
+        TNumber two = one + one;
+        TNumber three = two + one;
+
+        alpha = TNumber.Clamp(alpha, TNumber.Zero, TNumber.One);
+        alpha = -two * alpha * alpha * alpha + three * alpha * alpha;
+        return target * alpha + value * (one - alpha);
     }
+#endif
 }

X10D/src/Math/NumberExtensions.cs

@@ -0,0 +1,104 @@
+#if NET7_0_OR_GREATER
+using System.Diagnostics.Contracts;
+using System.Numerics;
+using System.Runtime.CompilerServices;
+using X10D.CompilerServices;
+
+namespace X10D.Math;
+
+/// <summary>
+///     Math-related extension methods for <see cref="INumber{TSelf}" />.
+/// </summary>
+public static class NumberExtensions
+{
+    /// <summary>
+    ///     Returns a value indicating whether the current value is evenly divisible by 2.
+    /// </summary>
+    /// <param name="value">The value whose parity to check.</param>
+    /// <returns>
+    ///     <see langword="true" /> if <paramref name="value" /> is evenly divisible by 2, or <see langword="false" />
+    ///     otherwise.
+    /// </returns>
+    [Pure]
+    [MethodImpl(CompilerResources.MaxOptimization)]
+    public static bool IsEven<TNumber>(this TNumber value)
+        where TNumber : INumber<TNumber>
+    {
+        return value % TNumber.CreateChecked(2) == TNumber.Zero;
+    }
+
+    /// <summary>
+    ///     Returns a value indicating whether the current value is not evenly divisible by 2.
+    /// </summary>
+    /// <param name="value">The value whose parity to check.</param>
+    /// <returns>
+    ///     <see langword="true" /> if <paramref name="value" /> is not evenly divisible by 2, or <see langword="false" />
+    ///     otherwise.
+    /// </returns>
+    [Pure]
+    [MethodImpl(CompilerResources.MaxOptimization)]
+    public static bool IsOdd<TNumber>(this TNumber value)
+        where TNumber : INumber<TNumber>
+    {
+        return !value.IsEven();
+    }
+
+    /// <summary>
+    ///     Performs a modulo operation which supports a negative dividend.
+    /// </summary>
+    /// <param name="dividend">The dividend.</param>
+    /// <param name="divisor">The divisor.</param>
+    /// <returns>The result of <c>dividend mod divisor</c>.</returns>
+    /// <remarks>
+    ///     The <c>%</c> operator (commonly called the modulo operator) in C# is not defined to be modulo, but is instead
+    ///     remainder. This quirk inherently makes it difficult to use modulo in a negative context, as <c>x % y</c> where x is
+    ///     negative will return a negative value, akin to <c>-(x % y)</c>, even if precedence is forced. This method provides a
+    ///     modulo operation which supports negative dividends.
+    /// </remarks>
+    /// <author>ShreevatsaR, https://stackoverflow.com/a/1082938/1467293</author>
+    /// <license>CC-BY-SA 2.5</license>
+    [Pure]
+    [MethodImpl(CompilerResources.MaxOptimization)]
+    public static TNumber Mod<TNumber>(this TNumber dividend, TNumber divisor)
+        where TNumber : INumber<TNumber>
+    {
+        TNumber r = dividend % divisor;
+        return r < TNumber.Zero ? r + divisor : r;
+    }
+
+    /// <summary>
+    ///     Returns an integer that indicates the sign of this number.
+    /// </summary>
+    /// <param name="value">A signed number.</param>
+    /// <returns>
+    ///     A number that indicates the sign of <paramref name="value" />, as shown in the following table.
+    ///
+    ///     <list type="table">
+    ///         <listheader>
+    ///             <term>Return value</term>
+    ///             <description>Meaning</description>
+    ///         </listheader>
+    ///
+    ///         <item>
+    ///             <term>-1</term>
+    ///             <description><paramref name="value" /> is less than zero.</description>
+    ///         </item>
+    ///         <item>
+    ///             <term>0</term>
+    ///             <description><paramref name="value" /> is equal to zero.</description>
+    ///         </item>
+    ///         <item>
+    ///             <term>1</term>
+    ///             <description><paramref name="value" /> is greater than zero.</description>
+    ///         </item>
+    ///     </list>
+    /// </returns>
+    [Pure]
+    [MethodImpl(CompilerResources.MaxOptimization)]
+    public static int Sign<TNumber>(this TNumber value)
+        where TNumber : INumber<TNumber>
+    {
+        return TNumber.Sign(value);
+    }
+}
+#endif

X10D/src/Math/SByteExtensions.cs

@@ -10,6 +10,7 @@ namespace X10D.Math;
 [CLSCompliant(false)]
 public static class SByteExtensions
 {
+#if !NET7_0_OR_GREATER
     /// <summary>
     ///     Returns the number of digits in the current 8-bit signed integer.
     /// </summary>
@@ -41,6 +42,7 @@ public static class SByteExtensions
         int root = System.Math.Abs(value).Mod(9);
         return (sbyte)(root < 1 ? 9 - root : root);
     }
+#endif
 
     /// <summary>
     ///     Returns the factorial of the current 8-bit signed integer.
@@ -141,6 +143,7 @@ public static class SByteExtensions
         return (sbyte)((long)value).LowestCommonMultiple(other);
     }
 
+#if !NET7_0_OR_GREATER
     /// <summary>
     ///     Performs a modulo operation which supports a negative dividend.
     /// </summary>
@@ -162,6 +165,7 @@ public static class SByteExtensions
         int r = dividend % divisor;
         return (sbyte)(r < 0 ? r + divisor : r);
     }
+#endif
 
     /// <summary>
     ///     Returns the multiplicative persistence of a specified value.

X10D/src/Math/UInt16Extensions.cs

@@ -10,6 +10,7 @@ namespace X10D.Math;
 [CLSCompliant(false)]
 public static class UInt16Extensions
 {
+#if !NET7_0_OR_GREATER
     /// <summary>
     ///     Returns the number of digits in the current 16-bit signed integer.
     /// </summary>
@@ -41,6 +42,7 @@ public static class UInt16Extensions
         var root = (ushort)(value % 9);
         return (ushort)(root == 0 ? 9 : root);
     }
+#endif
 
     /// <summary>
     ///     Returns the factorial of the current 16-bit unsigned integer.

X10D/src/Math/UInt32Extensions.cs

@@ -10,6 +10,7 @@ namespace X10D.Math;
 [CLSCompliant(false)]
 public static class UInt32Extensions
 {
+#if !NET7_0_OR_GREATER
     /// <summary>
     ///     Returns the number of digits in the current 32-bit unsigned integer.
     /// </summary>
@@ -41,6 +42,7 @@ public static class UInt32Extensions
         uint root = value % 9;
         return root == 0 ? 9 : root;
     }
+#endif
 
     /// <summary>
     ///     Returns the factorial of the current 32-bit unsigned integer.

X10D/src/Math/UInt64Extensions.cs

@@ -10,6 +10,7 @@ namespace X10D.Math;
 [CLSCompliant(false)]
 public static class UInt64Extensions
 {
+#if !NET7_0_OR_GREATER
     /// <summary>
     ///     Returns the number of digits in the current 64-bit unsigned integer.
     /// </summary>
@@ -41,6 +42,7 @@ public static class UInt64Extensions
         ulong root = value % 9;
         return root == 0 ? 9 : root;
     }
+#endif
 
     /// <summary>
     ///     Returns the factorial of the current 64-bit unsigned integer.

X10D/src/Time/Int16Extensions.cs

@@ -32,7 +32,7 @@ public static class Int16Extensions
             value++;
         }
 
-        return value.Mod(4) == 0 && (value.Mod(100) != 0 || value.Mod(400) == 0);
+        return value.Mod((short)4) == 0 && (value.Mod((short)100) != 0 || value.Mod((short)400) == 0);
     }
 
     /// <summary>

X10D/src/Time/SByteExtensions.cs

@@ -33,7 +33,7 @@ public static class SByteExtensions
             value++;
         }
 
-        return value.Mod(4) == 0 && value.Mod(100) != 0; // mod 400 not required, sbyte.MaxValue is 127 anyway
+        return value.Mod((sbyte)4) == 0 && value.Mod((sbyte)100) != 0; // mod 400 not required, sbyte.MaxValue is 127 anyway
     }
 
     /// <summary>