Probably done for today. Added a start to some caching optimizations.

Base/Extensions/FormattingExtensions.cs

@@ -0,0 +1,32 @@
+namespace Graphing.Extensions;
+
+public static class FormattingExtensions
+{
+    private static readonly string[] sizeUnits =
+    [
+        " bytes",
+        " KB",
+        " MB",
+        " GB",
+        " TB",
+        " PB",
+    ];
+
+    public static string FormatAsBytes(this long bytes)
+    {
+        double val = bytes;
+        int unitIndex = 0;
+
+        while (val > 1024)
+        {
+            unitIndex++;
+            val /= 1024;
+        }
+
+        string result;
+        if (unitIndex == 0) result = val.ToString("0");
+        else result = val.ToString("0.00");
+
+        return result + sizeUnits[unitIndex];
+    }
+}

Base/Forms/GraphForm.Designer.cs

@@ -39,6 +39,8 @@
             MenuEquations = new ToolStripMenuItem();
             MenuEquationsDerivative = new ToolStripMenuItem();
             MenuEquationsIntegral = new ToolStripMenuItem();
+            MenuMisc = new ToolStripMenuItem();
+            MenuMiscCaches = new ToolStripMenuItem();
             GraphMenu.SuspendLayout();
             SuspendLayout();
             // 
@@ -58,7 +60,7 @@
             // GraphMenu
             // 
             GraphMenu.ImageScalingSize = new Size(32, 32);
-            GraphMenu.Items.AddRange(new ToolStripItem[] { MenuViewport, MenuColors, MenuEquations });
+            GraphMenu.Items.AddRange(new ToolStripItem[] { MenuViewport, MenuColors, MenuEquations, MenuMisc });
             GraphMenu.Location = new Point(0, 0);
             GraphMenu.Name = "GraphMenu";
             GraphMenu.Size = new Size(1449, 42);
@@ -125,6 +127,20 @@
             MenuEquationsIntegral.Size = new Size(360, 44);
             MenuEquationsIntegral.Text = "Compute Integral";
             // 
+            // MenuMisc
+            // 
+            MenuMisc.DropDownItems.AddRange(new ToolStripItem[] { MenuMiscCaches });
+            MenuMisc.Name = "MenuMisc";
+            MenuMisc.Size = new Size(83, 38);
+            MenuMisc.Text = "Misc";
+            // 
+            // MenuMiscCaches
+            // 
+            MenuMiscCaches.Name = "MenuMiscCaches";
+            MenuMiscCaches.Size = new Size(359, 44);
+            MenuMiscCaches.Text = "View Caches";
+            MenuMiscCaches.Click += MenuMiscCaches_Click;
+            // 
             // GraphForm
             // 
             AutoScaleDimensions = new SizeF(13F, 32F);
@@ -154,5 +170,7 @@
         private ToolStripMenuItem MenuEquations;
         private ToolStripMenuItem MenuEquationsDerivative;
         private ToolStripMenuItem MenuEquationsIntegral;
+        private ToolStripMenuItem MenuMisc;
+        private ToolStripMenuItem MenuMiscCaches;
     }
 }

Base/Forms/GraphForm.cs

@@ -1,4 +1,6 @@
-using Graphing.Graphables;
+using Graphing.Extensions;
+using Graphing.Graphables;
+using System.Text;
 
 namespace Graphing.Forms;
 
@@ -346,7 +348,7 @@ public partial class GraphForm : Form
         static double Integrate(EquationDelegate e, double lower, double upper)
         {
             // TODO: a better rendering method could make this much faster.
-            const double step = 1e-1;
+            const double step = 1e-2;
 
             double factor = 1;
             if (upper < lower)
@@ -364,4 +366,33 @@ public partial class GraphForm : Form
             return sum * factor;
         }
     }
+
+    private void MenuMiscCaches_Click(object? sender, EventArgs e)
+    {
+        // TODO: Replace with a form with a pie chart of the use by equation
+        //       and the ability to reset them.
+        StringBuilder message = new();
+        long total = 0;
+        foreach (Graphable able in ables)
+        {
+            if (able is Equation equ)
+            {
+                long size = equ.GetCacheBytes();
+                message.AppendLine($"{able.Name}: {size.FormatAsBytes()}");
+
+                total += size;
+            }
+        }
+
+        message.AppendLine($"\nTotal: {total.FormatAsBytes()}\n\nClick \"No\" to erase caches.");
+
+        DialogResult result = MessageBox.Show(message.ToString(), "Graph Caches", MessageBoxButtons.YesNo, MessageBoxIcon.Information);
+        if (result == DialogResult.No)
+        {
+            foreach (Graphable able in ables)
+            {
+                if (able is Equation equ) equ.EraseCache();
+            }
+        }
+    }
 }

Base/Graphables/Equation.cs

@@ -8,23 +8,33 @@ public class Equation : Graphable
 
     private readonly EquationDelegate equ;
 
+    private readonly List<Float2> cache;
+
     public Equation(EquationDelegate equ)
     {
         equationNum++;
         Name = $"Equation {equationNum}";
 
         this.equ = equ;
+        cache = [];
     }
 
     public override IEnumerable<Line2d> GetItemsToRender(in GraphForm graph)
     {
+        const int step = 10;
+        double epsilon = Math.Abs(graph.ScreenSpaceToGraphSpace(new Int2(0, 0)).x
+                                - graph.ScreenSpaceToGraphSpace(new Int2(step / 2, 0)).x) / 5;
+
         List<Line2d> lines = [];
+
+        bool addedToDictionary = false;
         double previousX = graph.MinVisibleGraph.x;
-        double previousY = equ(previousX);
-        for (int i = 1; i < graph.ClientRectangle.Width; i += 10)
+        double previousY = GetFromCache(previousX, epsilon, ref addedToDictionary);
+
+        for (int i = 1; i < graph.ClientRectangle.Width; i += step)
         {
             double currentX = graph.ScreenSpaceToGraphSpace(new Int2(i, 0)).x;
-            double currentY = equ(currentX);
+            double currentY = GetFromCache(currentX, epsilon, ref addedToDictionary);
             if (Math.Abs(currentY - previousY) <= 10)
             {
                 lines.Add(new Line2d(new Float2(previousX, previousY), new Float2(currentX, currentY)));
@@ -32,10 +42,50 @@ public class Equation : Graphable
             previousX = currentX;
             previousY = currentY;
         }
+
+        if (addedToDictionary) cache.Sort((a, b) => a.y.CompareTo(b.y));
+
         return lines;
     }
 
     public EquationDelegate GetDelegate() => equ;
+
+    public void EraseCache() => cache.Clear();
+    private double GetFromCache(double x, double epsilon, ref bool addedToDictionary)
+    {
+        (double dist, double nearest) = NearestCachedPoint(x);
+        if (dist < epsilon) return nearest;
+        else
+        {
+            addedToDictionary = true;
+            double result = equ(x);
+            cache.Add(new(x, result));
+            // TODO: Rather than sorting the whole list when we add a single number,
+            //       we could just insert it.
+            return result;
+        }
+    }
+
+    private (double dist, double y) NearestCachedPoint(double x)
+    {
+        // TODO: Replace with a binary search system.
+        double closestDist = double.PositiveInfinity;
+        double closest = 0;
+
+        foreach (Float2 p in cache)
+        {
+            double dist = Math.Abs(x - p.x);
+            if (dist < closestDist)
+            {
+                closestDist = dist;
+                closest = p.y;
+            }
+        }
+
+        return (closestDist, closest);
+    }
+
+    public long GetCacheBytes() => cache.Count * 16;
 }
 
 public delegate double EquationDelegate(double x);

Testing/Program.cs

@@ -13,7 +13,8 @@ internal static class Program
         Application.SetHighDpiMode(HighDpiMode.PerMonitorV2);
 
         GraphForm graph = new("One Of The Graphing Calculators Of All Time");
-        graph.Graph(new Equation(Math.Cos));
+        graph.Graph(new Equation(x => Math.Pow(2, x)));
+        graph.Graph(new Equation(Math.Log2));
 
         Application.Run(graph);
     }

Testing/Testing.csproj

@@ -1,7 +1,6 @@
 <Project Sdk="Microsoft.NET.Sdk">
 
   <PropertyGroup>
-    <OutputType>WinExe</OutputType>
     <TargetFramework>net8.0-windows</TargetFramework>
     <Nullable>enable</Nullable>
     <UseWindowsForms>true</UseWindowsForms>
@@ -9,6 +8,14 @@
     <RootNamespace>Graphing.Testing</RootNamespace>
     <AssemblyName>ThatOneNerd.Graphing.Testing</AssemblyName>
   </PropertyGroup>
+    
+  <PropertyGroup Condition="'$(Configuration)|$(Platform)'=='Debug|AnyCPU'">
+    <OutputType>Exe</OutputType>
+  </PropertyGroup>
+
+  <PropertyGroup Condition="'$(Configuration)|$(Platform)'=='Release|AnyCPU'">
+    <OutputType>WinExe</OutputType>
+  </PropertyGroup>
 
   <ItemGroup>
     <ProjectReference Include="..\Base\Base.csproj" />