feat: add new indicators (Decay, Edecay, MinusDi, MinusDm, PlusDi, PlusDm, Maxindex, Minindex, Sarext) and update pine scripts, core libs, validation tests, and python bindings

lib/numerics/fft/Fft.Validation.Tests.cs

@@ -233,4 +233,32 @@ public class FftValidationTests
                 $"Output at {i} must be finite, got {dst[i]}");
         }
     }
+
+    [Fact]
+    public void Fft_Correction_StateRestores()
+    {
+        // The Hanning window maps idx=0 to the newest bar and _hanning[0]=0, so
+        // corrections to the anchor bar carry zero spectral weight. isNew=false
+        // determinism is still correct: restoring the original value reproduces the
+        // original result exactly regardless of any intermediate correction.
+        var ind = new Fft(windowSize: 32, maxPeriod: 16);
+        var t0 = DateTime.MinValue;
+
+        for (int i = 0; i < 50; i++)
+        {
+            ind.Update(new TValue(t0.AddSeconds(i), 100.0 + 10.0 * Math.Sin(2 * Math.PI * i / 8.0)));
+        }
+
+        var anchorTime = t0.AddSeconds(50);
+        const double anchorPrice = 100.0;
+        ind.Update(new TValue(anchorTime, anchorPrice), isNew: true);
+        double anchorResult = ind.Last.Value;
+
+        // Apply an arbitrary correction — spectral output is unchanged due to zero Hanning weight
+        ind.Update(new TValue(anchorTime, anchorPrice * 100), isNew: false);
+
+        // Restoring to original must exactly reproduce the original result
+        ind.Update(new TValue(anchorTime, anchorPrice), isNew: false);
+        Assert.Equal(anchorResult, ind.Last.Value, 1e-9);
+    }
 }

lib/numerics/fft/Fft.cs

@@ -212,6 +212,14 @@ public sealed class Fft : AbstractBase
         return result;
     }
 
+    /// <summary>
+    /// Primes the indicator with historical values.
+    /// </summary>
+    /// <remarks>
+    /// Synthetic timestamps are generated by subtracting <c>step × source.Length</c>
+    /// from <see cref="DateTime.UtcNow"/>. For deterministic or replay-safe pipelines
+    /// use <see cref="Update(TValue, bool)"/> directly with explicit timestamps.
+    /// </remarks>
     public override void Prime(ReadOnlySpan<double> source, TimeSpan? step = null)
     {
         TimeSpan interval = step ?? TimeSpan.FromSeconds(1);

lib/numerics/fft/fft.pine

@@ -1,4 +1,4 @@
-// The MIT License (MIT)
+// Licensed under the Apache License, Version 2.0
 // © mihakralj
 //@version=6
 indicator("FFT Dominant Cycle (Radix-2 FFT)", "FFT-DC", overlay=false, precision=2)