mirror of
https://github.com/mihakralj/QuanTAlib.git
synced 2026-08-06 04:57:44 +00:00
Miha Kralj
361 lines
12 KiB
C#
361 lines
12 KiB
C#
using System;
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using Xunit;
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using Xunit.Abstractions;
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namespace QuanTAlib.Tests;
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/// <summary>
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/// Validates the behavioral differences between .NET's Math.Atan2 and PineScript's custom atan2 implementation.
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///
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/// PineScript's atan2 uses a numerically stable algorithm:
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/// 1. If |x| > |y|: angle = atan(|y|/|x|)
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/// 2. If |y| >= |x|: angle = π/2 - atan(|x|/|y|)
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/// 3. Then applies quadrant correction based on sign of x and y
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///
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/// Math.Atan2 follows the standard IEEE convention: atan2(y, x) returns the angle
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/// in radians between the positive x-axis and the point (x, y).
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///
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/// Both return values in the range [-π, π], but they can differ in edge cases
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/// and have different numerical stability characteristics.
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/// </summary>
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public class Atan2ValidationTests
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{
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private readonly ITestOutputHelper _output;
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public Atan2ValidationTests(ITestOutputHelper output)
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{
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_output = output;
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}
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/// <summary>
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/// PineScript-style atan2 implementation for comparison.
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/// This is a direct port of the algorithm from ht_phasor.pine.
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/// </summary>
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private static double PineScriptAtan2(double y, double x)
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{
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if (y == 0.0 && x == 0.0)
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{
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throw new ArgumentException("atan2: Both y and x cannot be zero", nameof(y));
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}
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double ay = Math.Abs(y);
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double ax = Math.Abs(x);
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double angle;
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if (ax > ay)
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{
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angle = Math.Atan(ay / ax);
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}
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else
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{
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angle = (Math.PI / 2.0) - Math.Atan(ax / ay);
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}
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if (x < 0.0)
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{
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angle = Math.PI - angle;
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}
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if (y < 0.0)
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{
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angle = -angle;
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}
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return angle;
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}
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[Fact]
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public void Atan2_StandardQuadrant1_BothMatch()
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{
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// First quadrant: x > 0, y > 0
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double y = 1.0, x = 1.0;
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double dotNet = Math.Atan2(y, x);
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double pine = PineScriptAtan2(y, x);
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_output.WriteLine($"Q1: Math.Atan2({y}, {x}) = {dotNet:F15}");
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_output.WriteLine($"Q1: PineAtan2({y}, {x}) = {pine:F15}");
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_output.WriteLine($"Q1: Difference = {Math.Abs(dotNet - pine):E}");
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Assert.Equal(dotNet, pine, precision: 14);
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}
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[Fact]
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public void Atan2_StandardQuadrant2_BothMatch()
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{
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// Second quadrant: x < 0, y > 0
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double y = 1.0, x = -1.0;
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double dotNet = Math.Atan2(y, x);
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double pine = PineScriptAtan2(y, x);
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_output.WriteLine($"Q2: Math.Atan2({y}, {x}) = {dotNet:F15}");
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_output.WriteLine($"Q2: PineAtan2({y}, {x}) = {pine:F15}");
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_output.WriteLine($"Q2: Difference = {Math.Abs(dotNet - pine):E}");
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Assert.Equal(dotNet, pine, precision: 14);
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}
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[Fact]
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public void Atan2_StandardQuadrant3_BothMatch()
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{
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// Third quadrant: x < 0, y < 0
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double y = -1.0, x = -1.0;
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double dotNet = Math.Atan2(y, x);
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double pine = PineScriptAtan2(y, x);
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_output.WriteLine($"Q3: Math.Atan2({y}, {x}) = {dotNet:F15}");
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_output.WriteLine($"Q3: PineAtan2({y}, {x}) = {pine:F15}");
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_output.WriteLine($"Q3: Difference = {Math.Abs(dotNet - pine):E}");
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Assert.Equal(dotNet, pine, precision: 14);
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}
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[Fact]
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public void Atan2_StandardQuadrant4_BothMatch()
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{
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// Fourth quadrant: x > 0, y < 0
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double y = -1.0, x = 1.0;
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double dotNet = Math.Atan2(y, x);
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double pine = PineScriptAtan2(y, x);
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_output.WriteLine($"Q4: Math.Atan2({y}, {x}) = {dotNet:F15}");
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_output.WriteLine($"Q4: PineAtan2({y}, {x}) = {pine:F15}");
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_output.WriteLine($"Q4: Difference = {Math.Abs(dotNet - pine):E}");
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Assert.Equal(dotNet, pine, precision: 14);
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}
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[Fact]
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public void Atan2_AxisAligned_PositiveY()
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{
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// On positive Y-axis: x = 0, y > 0 → π/2
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double y = 1.0, x = 0.0;
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double dotNet = Math.Atan2(y, x);
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double pine = PineScriptAtan2(y, x);
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double expected = Math.PI / 2.0;
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_output.WriteLine($"Positive Y-axis: Math.Atan2({y}, {x}) = {dotNet:F15}");
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_output.WriteLine($"Positive Y-axis: PineAtan2({y}, {x}) = {pine:F15}");
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_output.WriteLine($"Expected: π/2 = {expected:F15}");
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Assert.Equal(expected, dotNet, precision: 14);
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Assert.Equal(expected, pine, precision: 14);
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}
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[Fact]
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public void Atan2_AxisAligned_NegativeY()
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{
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// On negative Y-axis: x = 0, y < 0 → -π/2
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double y = -1.0, x = 0.0;
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double dotNet = Math.Atan2(y, x);
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double pine = PineScriptAtan2(y, x);
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double expected = -Math.PI / 2.0;
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_output.WriteLine($"Negative Y-axis: Math.Atan2({y}, {x}) = {dotNet:F15}");
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_output.WriteLine($"Negative Y-axis: PineAtan2({y}, {x}) = {pine:F15}");
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_output.WriteLine($"Expected: -π/2 = {expected:F15}");
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Assert.Equal(expected, dotNet, precision: 14);
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Assert.Equal(expected, pine, precision: 14);
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}
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[Fact]
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public void Atan2_AxisAligned_PositiveX()
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{
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// On positive X-axis: x > 0, y = 0 → 0
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double y = 0.0, x = 1.0;
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double dotNet = Math.Atan2(y, x);
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double pine = PineScriptAtan2(y, x);
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double expected = 0.0;
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_output.WriteLine($"Positive X-axis: Math.Atan2({y}, {x}) = {dotNet:F15}");
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_output.WriteLine($"Positive X-axis: PineAtan2({y}, {x}) = {pine:F15}");
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_output.WriteLine($"Expected: 0 = {expected:F15}");
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Assert.Equal(expected, dotNet, precision: 14);
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Assert.Equal(expected, pine, precision: 14);
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}
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[Fact]
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public void Atan2_AxisAligned_NegativeX()
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{
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// On negative X-axis: x < 0, y = 0 → π
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double y = 0.0, x = -1.0;
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double dotNet = Math.Atan2(y, x);
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double pine = PineScriptAtan2(y, x);
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double expected = Math.PI;
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_output.WriteLine($"Negative X-axis: Math.Atan2({y}, {x}) = {dotNet:F15}");
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_output.WriteLine($"Negative X-axis: PineAtan2({y}, {x}) = {pine:F15}");
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_output.WriteLine($"Expected: π = {expected:F15}");
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Assert.Equal(expected, dotNet, precision: 14);
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Assert.Equal(expected, pine, precision: 14);
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}
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[Fact]
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public void Atan2_Origin_DotNetReturnsZero_PineThrows()
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{
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// Origin: x = 0, y = 0
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// Math.Atan2 returns 0 (by convention)
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// PineScript throws an error
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double y = 0.0, x = 0.0;
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double dotNet = Math.Atan2(y, x);
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_output.WriteLine($"Origin: Math.Atan2({y}, {x}) = {dotNet:F15}");
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_output.WriteLine("Origin: PineScript throws ArgumentException");
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Assert.Equal(0.0, dotNet);
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Assert.Throws<ArgumentException>(() => PineScriptAtan2(y, x));
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}
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[Fact]
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public void Atan2_VerySmallValues_NumericalStability()
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{
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// Test numerical stability with very small values
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double y = 1e-300, x = 1e-300;
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double dotNet = Math.Atan2(y, x);
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double pine = PineScriptAtan2(y, x);
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double expected = Math.PI / 4.0; // 45 degrees
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_output.WriteLine($"Small values: Math.Atan2({y:E}, {x:E}) = {dotNet:F15}");
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_output.WriteLine($"Small values: PineAtan2({y:E}, {x:E}) = {pine:F15}");
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_output.WriteLine($"Expected: π/4 = {expected:F15}");
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_output.WriteLine($"Difference = {Math.Abs(dotNet - pine):E}");
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// Both should handle small values well
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Assert.Equal(expected, dotNet, precision: 10);
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Assert.Equal(expected, pine, precision: 10);
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}
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[Fact]
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public void Atan2_VeryLargeValues_NumericalStability()
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{
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// Test numerical stability with very large values
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double y = 1e300, x = 1e300;
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double dotNet = Math.Atan2(y, x);
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double pine = PineScriptAtan2(y, x);
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double expected = Math.PI / 4.0; // 45 degrees
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_output.WriteLine($"Large values: Math.Atan2({y:E}, {x:E}) = {dotNet:F15}");
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_output.WriteLine($"Large values: PineAtan2({y:E}, {x:E}) = {pine:F15}");
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_output.WriteLine($"Expected: π/4 = {expected:F15}");
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_output.WriteLine($"Difference = {Math.Abs(dotNet - pine):E}");
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Assert.Equal(expected, dotNet, precision: 10);
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Assert.Equal(expected, pine, precision: 10);
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}
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[Fact]
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public void Atan2_AspectRatioExtreme_TallVector()
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{
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// PineScript algorithm switches behavior when |y| > |x|
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// Test with y >> x
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double y = 1000.0, x = 1.0;
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double dotNet = Math.Atan2(y, x);
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double pine = PineScriptAtan2(y, x);
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_output.WriteLine($"Tall vector: Math.Atan2({y}, {x}) = {dotNet:F15}");
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_output.WriteLine($"Tall vector: PineAtan2({y}, {x}) = {pine:F15}");
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_output.WriteLine($"Difference = {Math.Abs(dotNet - pine):E}");
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// Should be very close to π/2
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Assert.True(Math.Abs(dotNet - pine) < 1e-12, $"Difference {Math.Abs(dotNet - pine):E} exceeds tolerance");
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}
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[Fact]
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public void Atan2_AspectRatioExtreme_WideVector()
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{
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// Test with x >> y
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double y = 1.0, x = 1000.0;
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double dotNet = Math.Atan2(y, x);
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double pine = PineScriptAtan2(y, x);
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_output.WriteLine($"Wide vector: Math.Atan2({y}, {x}) = {dotNet:F15}");
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_output.WriteLine($"Wide vector: PineAtan2({y}, {x}) = {pine:F15}");
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_output.WriteLine($"Difference = {Math.Abs(dotNet - pine):E}");
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// Should be very close to 0
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Assert.True(Math.Abs(dotNet - pine) < 1e-12, $"Difference {Math.Abs(dotNet - pine):E} exceeds tolerance");
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}
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[Theory]
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[InlineData(0.5, 0.866025403784439)] // 30 degrees
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[InlineData(0.707106781186548, 0.707106781186548)] // 45 degrees
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[InlineData(0.866025403784439, 0.5)] // 60 degrees
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public void Atan2_CommonAngles_Match(double y, double x)
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{
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double dotNet = Math.Atan2(y, x);
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double pine = PineScriptAtan2(y, x);
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_output.WriteLine($"Math.Atan2({y}, {x}) = {dotNet:F15} rad = {dotNet * 180 / Math.PI:F10}°");
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_output.WriteLine($"PineAtan2({y}, {x}) = {pine:F15} rad = {pine * 180 / Math.PI:F10}°");
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_output.WriteLine($"Difference = {Math.Abs(dotNet - pine):E}");
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Assert.Equal(dotNet, pine, precision: 13);
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}
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[Fact]
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public void Atan2_FullCircle_360DegreesSweep()
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{
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// Sweep through 360 degrees and verify both implementations match
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const int steps = 360;
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double maxDiff = 0;
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int maxDiffStep = 0;
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for (int i = 0; i < steps; i++)
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{
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double angle = i * 2.0 * Math.PI / steps;
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double y = Math.Sin(angle);
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double x = Math.Cos(angle);
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// Skip origin (angle = 0 with x=1, y=0 is fine, but need to handle numerical zeros)
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if (Math.Abs(x) < 1e-15 && Math.Abs(y) < 1e-15)
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{
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continue;
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}
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double dotNet = Math.Atan2(y, x);
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double pine = PineScriptAtan2(y, x);
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double diff = Math.Abs(dotNet - pine);
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if (diff > maxDiff)
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{
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maxDiff = diff;
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maxDiffStep = i;
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}
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}
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_output.WriteLine($"Full circle sweep: {steps} steps");
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_output.WriteLine($"Maximum difference: {maxDiff:E} at step {maxDiffStep} ({maxDiffStep}°)");
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// Expect very small differences
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Assert.True(maxDiff < 1e-14, $"Maximum difference {maxDiff:E} exceeds tolerance");
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}
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[Fact]
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public void Summary_ImplementationDifferences()
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{
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_output.WriteLine("=== Math.Atan2 vs PineScript atan2 Summary ===");
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_output.WriteLine("");
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_output.WriteLine("1. Origin handling:");
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_output.WriteLine(" - Math.Atan2(0, 0) returns 0");
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_output.WriteLine(" - PineScript throws an error");
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_output.WriteLine("");
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_output.WriteLine("2. Algorithm:");
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_output.WriteLine(" - Math.Atan2: IEEE standard implementation");
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_output.WriteLine(" - PineScript: Uses |y|/|x| or |x|/|y| based on which is larger");
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_output.WriteLine(" This avoids division by very small numbers");
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_output.WriteLine("");
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_output.WriteLine("3. Numerical stability:");
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_output.WriteLine(" - Both handle extreme values well");
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_output.WriteLine(" - PineScript's approach may be slightly more stable for extreme aspect ratios");
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_output.WriteLine("");
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_output.WriteLine("4. Recommendation:");
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_output.WriteLine(" - Use Math.Atan2 for general purposes (standard, well-tested)");
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_output.WriteLine(" - PineScript algorithm adds ~zero benefit in .NET");
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_output.WriteLine(" - Only difference is origin handling (error vs 0)");
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Assert.True(true); // This is a documentation test
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}
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}
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