- Additional debug / verification of flight perf stuff

- Replaced usages of Vector3.Zero() by our own method that *actually* set the vector components to zero, fixes a few inconsistencies/bugs in the flight perf implementations (including a few that exist in stock)
- Added ULP based FP equality comparer methods

Author: gotmachine

KSPCommunityFixes/Library/Numerics.cs

@@ -1,6 +1,7 @@
 using System;
 using System.Linq;
 using System.Runtime.CompilerServices;
+using System.Runtime.InteropServices;
 using UnityEngine;
 using Random = System.Random;
 
@@ -9,13 +10,21 @@ namespace KSPCommunityFixes.Library
     internal static class Numerics
     {
         [MethodImpl(MethodImplOptions.AggressiveInlining)]
-        public static void Zero(ref this Vector3 v)
+        public static void MutateZero(ref this Vector3 v)
         {
             v.x = 0f; 
             v.y = 0f; 
             v.z = 0f;
         }
 
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static void MutateZero(ref this Vector3d v)
+        {
+            v.x = 0.0;
+            v.y = 0.0;
+            v.z = 0.0;
+        }
+
         [MethodImpl(MethodImplOptions.AggressiveInlining)]
         public static void CopyFrom(ref this Vector3d v, Vector3 other)
         {
@@ -412,6 +421,158 @@ public static unsafe double FastPow(double value, double exponent)
             long tmp2 = (long)(b_faction * (tmp - 4606921280493453312L)) + 4606921280493453312L;
             return r * *(double*)&tmp2;
         }
+
+        // ULP equality helpers from https://github.com/nunit/nunit/blob/a39e8297b4e9ad279679430021af7a83f3091d59/src/NUnitFramework/framework/Constraints/FloatingPointNumerics.cs
+
+        /// <summary>Union of a floating point variable and an integer</summary>
+        [StructLayout(LayoutKind.Explicit)]
+        private struct FloatIntUnion
+        {
+            /// <summary>The union's value as a floating point variable</summary>
+            [FieldOffset(0)]
+            public float Float;
+
+            /// <summary>The union's value as an integer</summary>
+            [FieldOffset(0)]
+            public int Int;
+
+            /// <summary>The union's value as an unsigned integer</summary>
+            [FieldOffset(0)]
+            public uint UInt;
+        }
+
+        /// <summary>Union of a double precision floating point variable and a long</summary>
+        [StructLayout(LayoutKind.Explicit)]
+        private struct DoubleLongUnion
+        {
+            /// <summary>The union's value as a double precision floating point variable</summary>
+            [FieldOffset(0)]
+            public double Double;
+
+            /// <summary>The union's value as a long</summary>
+            [FieldOffset(0)]
+            public long Long;
+
+            /// <summary>The union's value as an unsigned long</summary>
+            [FieldOffset(0)]
+            public ulong ULong;
+        }
+
+        /// <summary>Compares two floating point values for equality</summary>
+        /// <param name="left">First floating point value to be compared</param>
+        /// <param name="right">Second floating point value t be compared</param>
+        /// <param name="maxUlps">
+        ///   Maximum number of representable floating point values that are allowed to
+        ///   be between the left and the right floating point values
+        /// </param>
+        /// <returns>True if both numbers are equal or close to being equal</returns>
+        /// <remarks>
+        ///   <para>
+        ///     Floating point values can only represent a finite subset of natural numbers.
+        ///     For example, the values 2.00000000 and 2.00000024 can be stored in a float,
+        ///     but nothing between them.
+        ///   </para>
+        ///   <para>
+        ///     This comparison will count how many possible floating point values are between
+        ///     the left and the right number. If the number of possible values between both
+        ///     numbers is less than or equal to maxUlps, then the numbers are considered as
+        ///     being equal.
+        ///   </para>
+        ///   <para>
+        ///     Implementation partially follows the code outlined here:
+        ///     http://www.anttirt.net/2007/08/19/proper-floating-point-comparisons/
+        ///   </para>
+        /// </remarks>
+        public static bool AlmostEqual(float left, float right, int maxUlps)
+        {
+            FloatIntUnion leftUnion = new FloatIntUnion();
+            FloatIntUnion rightUnion = new FloatIntUnion();
+
+            leftUnion.Float = left;
+            rightUnion.Float = right;
+
+            uint leftSignMask = (leftUnion.UInt >> 31);
+            uint rightSignMask = (rightUnion.UInt >> 31);
+
+            uint leftTemp = ((0x80000000 - leftUnion.UInt) & leftSignMask);
+            leftUnion.UInt = leftTemp | (leftUnion.UInt & ~leftSignMask);
+
+            uint rightTemp = ((0x80000000 - rightUnion.UInt) & rightSignMask);
+            rightUnion.UInt = rightTemp | (rightUnion.UInt & ~rightSignMask);
+
+            if (leftSignMask != rightSignMask) // Overflow possible, check each against zero
+            {
+                // This check is specifically used to trap the case of 0 == -0
+                // In IEEE floating point maths, -0 is converted to Float.MinValue, which cannot be used with
+                // Math.Abs(...) below due to overflow issues. This should only match the 0 == -0 condition.
+                if (left == right)
+                    return true;
+
+                if (Math.Abs(leftUnion.Int) > maxUlps || Math.Abs(rightUnion.Int) > maxUlps)
+                    return false;
+            }
+
+            // Either they have the same sign or both are very close to zero
+            return Math.Abs(leftUnion.Int - rightUnion.Int) <= maxUlps;
+        }
+
+        /// <summary>Compares two double precision floating point values for equality</summary>
+        /// <param name="left">First double precision floating point value to be compared</param>
+        /// <param name="right">Second double precision floating point value t be compared</param>
+        /// <param name="maxUlps">
+        ///   Maximum number of representable double precision floating point values that are
+        ///   allowed to be between the left and the right double precision floating point values
+        /// </param>
+        /// <returns>True if both numbers are equal or close to being equal</returns>
+        /// <remarks>
+        ///   <para>
+        ///     Double precision floating point values can only represent a limited series of
+        ///     natural numbers. For example, the values 2.0000000000000000 and 2.0000000000000004
+        ///     can be stored in a double, but nothing between them.
+        ///   </para>
+        ///   <para>
+        ///     This comparison will count how many possible double precision floating point
+        ///     values are between the left and the right number. If the number of possible
+        ///     values between both numbers is less than or equal to maxUlps, then the numbers
+        ///     are considered as being equal.
+        ///   </para>
+        ///   <para>
+        ///     Implementation partially follows the code outlined here:
+        ///     http://www.anttirt.net/2007/08/19/proper-floating-point-comparisons/
+        ///   </para>
+        /// </remarks>
+        public static bool AlmostEqual(double left, double right, long maxUlps)
+        {
+            DoubleLongUnion leftUnion = new DoubleLongUnion();
+            DoubleLongUnion rightUnion = new DoubleLongUnion();
+
+            leftUnion.Double = left;
+            rightUnion.Double = right;
+
+            ulong leftSignMask = (leftUnion.ULong >> 63);
+            ulong rightSignMask = (rightUnion.ULong >> 63);
+
+            ulong leftTemp = ((0x8000000000000000 - leftUnion.ULong) & leftSignMask);
+            leftUnion.ULong = leftTemp | (leftUnion.ULong & ~leftSignMask);
+
+            ulong rightTemp = ((0x8000000000000000 - rightUnion.ULong) & rightSignMask);
+            rightUnion.ULong = rightTemp | (rightUnion.ULong & ~rightSignMask);
+
+            if (leftSignMask != rightSignMask) // Overflow possible, check each against zero
+            {
+                // This check is specifically used to trap the case of 0 == -0
+                // In IEEE floating point maths, -0 is converted to Double.MinValue, which cannot be used with
+                // Math.Abs(...) below due to overflow issues. This should only match the 0 == -0 condition.
+                if (left == right)
+                    return true;
+
+                if (Math.Abs(leftUnion.Long) > maxUlps || Math.Abs(rightUnion.Long) > maxUlps)
+                    return false;
+            }
+
+            // Either they have the same sign or both are very close to zero
+            return Math.Abs(leftUnion.Long - rightUnion.Long) <= maxUlps;
+        }
     }
 
     /// <summary>