diff --git a/src/libraries/System.Private.CoreLib/src/System.Private.CoreLib.Shared.projitems b/src/libraries/System.Private.CoreLib/src/System.Private.CoreLib.Shared.projitems
index d527a4cf583216..7e8c3aefe04104 100644
--- a/src/libraries/System.Private.CoreLib/src/System.Private.CoreLib.Shared.projitems
+++ b/src/libraries/System.Private.CoreLib/src/System.Private.CoreLib.Shared.projitems
@@ -530,6 +530,7 @@
     <Compile Include="$(MSBuildThisFileDirectory)System\Numerics\Matrix4x4.cs" />
     <Compile Include="$(MSBuildThisFileDirectory)System\Numerics\Plane.cs" />
     <Compile Include="$(MSBuildThisFileDirectory)System\Numerics\Quaternion.cs" />
+    <Compile Include="$(MSBuildThisFileDirectory)System\Numerics\TotalOrderIeee754Comparer.cs" />
     <Compile Include="$(MSBuildThisFileDirectory)System\Numerics\Vector.cs" />
     <Compile Include="$(MSBuildThisFileDirectory)System\Numerics\Vector_1.cs" />
     <Compile Include="$(MSBuildThisFileDirectory)System\Numerics\Vector2.cs" />
diff --git a/src/libraries/System.Private.CoreLib/src/System/Numerics/TotalOrderIeee754Comparer.cs b/src/libraries/System.Private.CoreLib/src/System/Numerics/TotalOrderIeee754Comparer.cs
new file mode 100644
index 00000000000000..d461168433634a
--- /dev/null
+++ b/src/libraries/System.Private.CoreLib/src/System/Numerics/TotalOrderIeee754Comparer.cs
@@ -0,0 +1,233 @@
+// Licensed to the .NET Foundation under one or more agreements.
+// The .NET Foundation licenses this file to you under the MIT license.
+
+using System.Collections.Generic;
+using System.Diagnostics.CodeAnalysis;
+using System.Runtime.CompilerServices;
+
+namespace System.Numerics
+{
+    /// <summary>
+    /// Represents a comparison operation that compares floating-point numbers
+    /// with IEEE 754 totalOrder semantic.
+    /// </summary>
+    /// <typeparam name="T">The type of the numbers to be compared, must be an IEEE 754 floating-point type.</typeparam>
+    public readonly struct TotalOrderIeee754Comparer<T> : IComparer<T>, IEqualityComparer<T>, IEquatable<TotalOrderIeee754Comparer<T>>
+        where T : IFloatingPointIeee754<T>?
+    {
+        /// <summary>
+        /// Compares two numbers with IEEE 754 totalOrder semantic and returns
+        /// a value indicating whether one is less than, equal to, or greater than the other.
+        /// </summary>
+        /// <param name="x">The first number to compare.</param>
+        /// <param name="y">The second number to compare.</param>
+        /// <returns>
+        /// A signed integer that indicates the relative
+        /// values of <paramref name="x"/> and <paramref name="y"/>, as shown in the following table.
+        /// <list type="table">
+        ///   <listheader>
+        ///     <term> Value</term>
+        ///     <description> Meaning</description>
+        ///   </listheader>
+        ///   <item>
+        ///     <term> Less than zero</term>
+        ///     <description><paramref name = "x" /> is less than <paramref name="y" /></description>
+        ///   </item>
+        ///   <item>
+        ///     <term> Zero</term>
+        ///     <description><paramref name = "x" /> equals <paramref name="y" /></description>
+        ///   </item>
+        ///   <item>
+        ///     <term> Greater than zero</term>
+        ///     <description><paramref name = "x" /> is greater than <paramref name="y" /></description>
+        ///   </item>
+        /// </list>
+        /// </returns>
+        /// <remarks>
+        /// IEEE 754 specification defines totalOrder as &lt;= semantic.
+        /// totalOrder(x,y) is <see langword="true"/> when the result of this method is less than or equal to 0.
+        /// </remarks>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public int Compare(T? x, T? y)
+        {
+            if (typeof(T) == typeof(float))
+            {
+                return CompareIntegerSemantic(BitConverter.SingleToInt32Bits((float)(object)x!), BitConverter.SingleToInt32Bits((float)(object)y!));
+            }
+            else if (typeof(T) == typeof(double))
+            {
+                return CompareIntegerSemantic(BitConverter.DoubleToInt64Bits((double)(object)x!), BitConverter.DoubleToInt64Bits((double)(object)y!));
+            }
+            else if (typeof(T) == typeof(Half))
+            {
+                return CompareIntegerSemantic(BitConverter.HalfToInt16Bits((Half)(object)x!), BitConverter.HalfToInt16Bits((Half)(object)y!));
+            }
+            else
+            {
+                return CompareGeneric(x, y);
+            }
+
+            static int CompareIntegerSemantic<TInteger>(TInteger x, TInteger y)
+                where TInteger : struct, IBinaryInteger<TInteger>, ISignedNumber<TInteger>
+            {
+                // In IEEE 754 binary floating-point representation, a number is represented as Sign|Exponent|Significand
+                // Normal numbers has an implicit 1. in front of the significand, so value with larger exponent will have larger absolute value
+                // Inf and NaN are defined as Exponent=All 1s, while Inf has Significand=0, sNaN has Significand=0xxx and qNaN has Significand=1xxx
+                // This also satisfies totalOrder definition which is +x < +Inf < +sNaN < +qNaN
+
+                // The order of NaNs of same category and same sign is implementation defined,
+                // here we define it as the order of exponent bits to simplify comparison
+
+                // Negative values are represented in sign-magnitude, instead of two's complement like integers
+                // Just negating the comparison result when both numbers are negative is enough
+
+                return (TInteger.IsNegative(x) && TInteger.IsNegative(y)) ? y.CompareTo(x) : x.CompareTo(y);
+            }
+
+            static int CompareGeneric(T? x, T? y)
+            {
+                // IComparer contract is null < value
+
+                if (x is null)
+                {
+                    return (y is null) ? 0 : -1;
+                }
+                else if (y is null)
+                {
+                    return 1;
+                }
+
+                // If < or > returns true, the result satisfies definition of totalOrder too
+
+                if (x < y)
+                {
+                    return -1;
+                }
+                else if (x > y)
+                {
+                    return 1;
+                }
+                else if (x == y)
+                {
+                    if (T.IsZero(x)) // only zeros are equal to zeros
+                    {
+                        // IEEE 754 numbers are either positive or negative. Skip check for the opposite.
+
+                        if (T.IsNegative(x))
+                        {
+                            return T.IsNegative(y) ? 0 : -1;
+                        }
+                        else
+                        {
+                            return T.IsPositive(y) ? 0 : 1;
+                        }
+                    }
+                    else
+                    {
+                        // Equivalant values are compared by their exponent parts,
+                        // and the value with smaller exponent is considered closer to zero.
+
+                        // This only applies to IEEE 754 decimals. Consider to add support if decimals are added into .NET.
+                        return 0;
+                    }
+                }
+                else
+                {
+                    // One or two of the values are NaN
+                    // totalOrder defines that -qNaN < -sNaN < x < +sNaN < + qNaN
+
+                    static int CompareSignificand(T x, T y)
+                    {
+                        // IEEE 754 totalOrder only defines the order of NaN type bit (the first bit of significand)
+                        // To match the integer semantic comparison above, here we compare all the significand bits
+                        // Revisit this if decimals are added
+
+                        // Leave the space for custom floating-point type that has variable significand length
+
+                        int xSignificandBits = x!.GetSignificandBitLength();
+                        int ySignificandBits = y!.GetSignificandBitLength();
+
+                        if (xSignificandBits == ySignificandBits)
+                        {
+                            // Prevent stack overflow for huge numbers
+                            const int StackAllocThreshold = 256;
+
+                            int xSignificandLength = x.GetSignificandByteCount();
+                            int ySignificandLength = y.GetSignificandByteCount();
+
+                            Span<byte> significandX = xSignificandLength <= StackAllocThreshold ? stackalloc byte[xSignificandLength] : new byte[xSignificandLength];
+                            Span<byte> significandY = ySignificandLength <= StackAllocThreshold ? stackalloc byte[ySignificandLength] : new byte[ySignificandLength];
+
+                            x.WriteSignificandBigEndian(significandX);
+                            y.WriteSignificandBigEndian(significandY);
+
+                            return significandX.SequenceCompareTo(significandY);
+                        }
+                        else
+                        {
+                            return xSignificandBits.CompareTo(ySignificandBits);
+                        }
+                    }
+
+                    if (T.IsNaN(x))
+                    {
+                        if (T.IsNaN(y))
+                        {
+                            if (T.IsNegative(x))
+                            {
+                                return T.IsPositive(y) ? -1 : CompareSignificand(y, x);
+                            }
+                            else
+                            {
+                                return T.IsNegative(y) ? 1 : CompareSignificand(x, y);
+                            }
+                        }
+                        else
+                        {
+                            return T.IsPositive(x) ? 1 : -1;
+                        }
+                    }
+                    else if (T.IsNaN(y))
+                    {
+                        return T.IsPositive(y) ? -1 : 1;
+                    }
+                    else
+                    {
+                        // T does not correctly implement IEEE754 semantics
+                        ThrowHelper.ThrowArgumentException(ExceptionResource.Argument_InvalidArgumentForComparison);
+                        return 0; // unreachable
+                    }
+                }
+            }
+        }
+
+        /// <summary>
+        /// Determines whether the specified numbers are equal.
+        /// </summary>
+        /// <param name="x">The first number of type <typeparamref name="T"/> to compare.</param>
+        /// <param name="y">The second number of type <typeparamref name="T"/> to compare.</param>
+        /// <returns><see langword="true"/> if the specified numbers are equal; otherwise, <see langword="false"/>.</returns>
+        /// <remarks>
+        /// There is no corresponding equals semantic with totalOrder defined by IEEE 754 specification.
+        /// This method returns <see langword="true"/> when <see cref="Compare(T?, T?)"/> returns 0.
+        /// </remarks>
+        public bool Equals(T? x, T? y) => Compare(x, y) == 0;
+
+        /// <summary>
+        /// Returns a hash code for the specified number.
+        /// </summary>
+        /// <param name="obj">The number for which a hash code is to be returned.</param>
+        /// <returns>A hash code for the specified number.</returns>
+        public int GetHashCode([DisallowNull] T obj)
+        {
+            ArgumentNullException.ThrowIfNull(obj, nameof(obj));
+            return obj.GetHashCode();
+        }
+
+        public bool Equals(TotalOrderIeee754Comparer<T> other) => true;
+
+        public override bool Equals([NotNullWhen(true)] object? obj) => obj is TotalOrderIeee754Comparer<T>;
+
+        public override int GetHashCode() => EqualityComparer<T>.Default.GetHashCode();
+    }
+}
diff --git a/src/libraries/System.Runtime/ref/System.Runtime.cs b/src/libraries/System.Runtime/ref/System.Runtime.cs
index 6ad2debb088229..d52f990054fcb2 100644
--- a/src/libraries/System.Runtime/ref/System.Runtime.cs
+++ b/src/libraries/System.Runtime/ref/System.Runtime.cs
@@ -10530,6 +10530,15 @@ public partial interface IUnaryPlusOperators<TSelf, TResult> where TSelf : Syste
     public partial interface IUnsignedNumber<TSelf> : System.Numerics.INumberBase<TSelf> where TSelf : System.Numerics.IUnsignedNumber<TSelf>?
     {
     }
+    public readonly partial struct TotalOrderIeee754Comparer<T> : System.Collections.Generic.IComparer<T>, System.Collections.Generic.IEqualityComparer<T>, System.IEquatable<System.Numerics.TotalOrderIeee754Comparer<T>> where T : System.Numerics.IFloatingPointIeee754<T>?
+    {
+        public int Compare(T? x, T? y) { throw null; }
+        public bool Equals(System.Numerics.TotalOrderIeee754Comparer<T> other) { throw null; }
+        public override bool Equals([System.Diagnostics.CodeAnalysis.NotNullWhenAttribute(true)] object? obj) { throw null; }
+        public bool Equals(T? x, T? y) { throw null; }
+        public override int GetHashCode() { throw null; }
+        public int GetHashCode([System.Diagnostics.CodeAnalysis.DisallowNullAttribute] T obj) { throw null; }
+    }
 }
 namespace System.Reflection
 {
diff --git a/src/libraries/System.Runtime/tests/System.Runtime.Tests.csproj b/src/libraries/System.Runtime/tests/System.Runtime.Tests.csproj
index fc6859854dc2e6..91d560c81a8d8c 100644
--- a/src/libraries/System.Runtime/tests/System.Runtime.Tests.csproj
+++ b/src/libraries/System.Runtime/tests/System.Runtime.Tests.csproj
@@ -113,6 +113,7 @@
     <Compile Include="System\NullReferenceExceptionTests.cs" />
     <Compile Include="System\Numerics\IExponentialFunctionsTests.cs" />
     <Compile Include="System\Numerics\IFloatingPointTests.cs" />
+    <Compile Include="System\Numerics\TotalOrderIeee754ComparerTests.cs" />
     <Compile Include="System\ObjectTests.cs" />
     <Compile Include="System\ObjectDisposedExceptionTests.cs" />
     <Compile Include="System\ObsoleteAttributeTests.cs" />
diff --git a/src/libraries/System.Runtime/tests/System/Numerics/TotalOrderIeee754ComparerTests.cs b/src/libraries/System.Runtime/tests/System/Numerics/TotalOrderIeee754ComparerTests.cs
new file mode 100644
index 00000000000000..454a60dff8e641
--- /dev/null
+++ b/src/libraries/System.Runtime/tests/System/Numerics/TotalOrderIeee754ComparerTests.cs
@@ -0,0 +1,104 @@
+// Licensed to the .NET Foundation under one or more agreements.
+// The .NET Foundation licenses this file to you under the MIT license.
+
+using System.Collections.Generic;
+using System.Numerics;
+using System.Runtime.InteropServices;
+using Xunit;
+
+namespace System.Runtime.Tests
+{
+    public sealed class TotalOrderIeee754ComparerTests
+    {
+        public static IEnumerable<object[]> SingleTestData
+        {
+            get
+            {
+                yield return new object[] { 0.0f, 0.0f, 0 };
+                yield return new object[] { -0.0f, -0.0f, 0 };
+                yield return new object[] { 0.0f, -0.0f, 1 };
+                yield return new object[] { -0.0f, 0.0f, -1 };
+                yield return new object[] { 0.0f, 1.0f, -1 };
+                yield return new object[] { float.PositiveInfinity, 1.0f, 1 };
+                yield return new object[] { BitConverter.UInt32BitsToSingle(0xFFC00000), float.NegativeInfinity, -1 };
+                yield return new object[] { BitConverter.UInt32BitsToSingle(0xFFC00000), -1.0f, -1 };
+                yield return new object[] { BitConverter.UInt32BitsToSingle(0x7FC00000), 1.0f, 1 };
+                yield return new object[] { BitConverter.UInt32BitsToSingle(0x7FC00000), float.PositiveInfinity, 1 };
+                yield return new object[] { float.NaN, float.NaN, 0 };
+                yield return new object[] { BitConverter.UInt32BitsToSingle(0xFFC00000), BitConverter.UInt32BitsToSingle(0x7FC00000), -1 };
+                yield return new object[] { BitConverter.UInt32BitsToSingle(0x7FC00000), BitConverter.UInt32BitsToSingle(0x7FC00001), -1 }; // implementation defined, not part of IEEE 754 totalOrder
+            }
+        }
+
+        [Theory]
+        [MemberData(nameof(SingleTestData))]
+        public void TotalOrderTestSingle(float x, float y, int result)
+        {
+            var comparer = new TotalOrderIeee754Comparer<float>();
+            Assert.Equal(result, Math.Sign(comparer.Compare(x, y)));
+        }
+
+        public static IEnumerable<object[]> DoubleTestData
+        {
+            get
+            {
+                yield return new object[] { 0.0, 0.0, 0 };
+                yield return new object[] { -0.0, -0.0, 0 };
+                yield return new object[] { 0.0, -0.0, 1 };
+                yield return new object[] { -0.0, 0.0, -1 };
+                yield return new object[] { 0.0, 1.0, -1 };
+                yield return new object[] { double.PositiveInfinity, 1.0, 1 };
+                yield return new object[] { BitConverter.UInt64BitsToDouble(0xFFF80000_00000000), double.NegativeInfinity, -1 };
+                yield return new object[] { BitConverter.UInt64BitsToDouble(0xFFF80000_00000000), -1.0, -1 };
+                yield return new object[] { BitConverter.UInt64BitsToDouble(0x7FF80000_00000000), 1.0, 1 };
+                yield return new object[] { BitConverter.UInt64BitsToDouble(0x7FF80000_00000000), double.PositiveInfinity, 1 };
+                yield return new object[] { double.NaN, double.NaN, 0 };
+                yield return new object[] { BitConverter.UInt64BitsToDouble(0xFFF80000_00000000), BitConverter.UInt64BitsToDouble(0x7FF80000_00000000), -1 };
+                yield return new object[] { BitConverter.UInt64BitsToDouble(0x7FF80000_00000000), BitConverter.UInt64BitsToDouble(0x7FF80000_00000001), -1 }; // implementation defined, not part of IEEE 754 totalOrder
+            }
+        }
+
+        [Theory]
+        [MemberData(nameof(DoubleTestData))]
+        public void TotalOrderTestDouble(double x, double y, int result)
+        {
+            var comparer = new TotalOrderIeee754Comparer<double>();
+            Assert.Equal(result, Math.Sign(comparer.Compare(x, y)));
+        }
+        public static IEnumerable<object[]> HalfTestData
+        {
+            get
+            {
+                yield return new object[] { (Half)0.0, (Half)0.0, 0 };
+                yield return new object[] { (Half)(-0.0), (Half)(-0.0), 0 };
+                yield return new object[] { (Half)0.0, (Half)(-0.0), 1 };
+                yield return new object[] { (Half)(-0.0), (Half)0.0, -1 };
+                yield return new object[] { (Half)0.0, (Half)1.0, -1 };
+                yield return new object[] { Half.PositiveInfinity, (Half)1.0, 1 };
+                yield return new object[] { BitConverter.UInt16BitsToHalf(0xFE00), Half.NegativeInfinity, -1 };
+                yield return new object[] { BitConverter.UInt16BitsToHalf(0xFE00), (Half)(-1.0), -1 };
+                yield return new object[] { BitConverter.UInt16BitsToHalf(0x7E00), (Half)1.0, 1 };
+                yield return new object[] { BitConverter.UInt16BitsToHalf(0x7E00), Half.PositiveInfinity, 1 };
+                yield return new object[] { Half.NaN, Half.NaN, 0 };
+                yield return new object[] { BitConverter.UInt16BitsToHalf(0xFE00), BitConverter.UInt16BitsToHalf(0x7E00), -1 };
+                yield return new object[] { BitConverter.UInt16BitsToHalf(0x7E00), BitConverter.UInt16BitsToHalf(0x7E01), -1 }; // implementation defined, not part of IEEE 754 totalOrder
+            }
+        }
+
+        [Theory]
+        [MemberData(nameof(HalfTestData))]
+        public void TotalOrderTestHalf(Half x, Half y, int result)
+        {
+            var comparer = new TotalOrderIeee754Comparer<Half>();
+            Assert.Equal(result, Math.Sign(comparer.Compare(x, y)));
+        }
+
+        [Theory]
+        [MemberData(nameof(SingleTestData))]
+        public void TotalOrderTestNFloat(float x, float y, int result)
+        {
+            var comparer = new TotalOrderIeee754Comparer<NFloat>();
+            Assert.Equal(result, Math.Sign(comparer.Compare(x, y)));
+        }
+    }
+}