docs: remove C# Implementation Considerations sections, clean up temp scripts, reorganize test files

- Remove 'C# Implementation Considerations' sections from 34 indicator .md files
- Delete 29 temp PowerShell scripts (_fix_mojibake.ps1, _hex_scan.ps1, etc.)
- Move test files into tests/ subdirectories for consistent project structure
- Add trader-focused bullet points to indicator documentation

lib/trends_IIR/rema/tests/Rema.Quantower.Tests.cs

@@ -0,0 +1,207 @@
+using TradingPlatform.BusinessLayer;
+
+namespace QuanTAlib.Tests;
+
+public class RemaIndicatorTests
+{
+    [Fact]
+    public void RemaIndicator_Constructor_SetsDefaults()
+    {
+        var indicator = new RemaIndicator();
+
+        Assert.Equal(10, indicator.Period);
+        Assert.Equal(0.5, indicator.Lambda);
+        Assert.Equal(SourceType.Close, indicator.Source);
+        Assert.True(indicator.ShowColdValues);
+        Assert.Equal("REMA - Regularized Exponential Moving Average", indicator.Name);
+        Assert.False(indicator.SeparateWindow);
+        Assert.True(indicator.OnBackGround);
+    }
+
+    [Fact]
+    public void RemaIndicator_MinHistoryDepths_EqualsZero()
+    {
+        var indicator = new RemaIndicator { Period = 20 };
+
+        Assert.Equal(0, RemaIndicator.MinHistoryDepths);
+        Assert.Equal(0, ((IWatchlistIndicator)indicator).MinHistoryDepths);
+    }
+
+    [Fact]
+    public void RemaIndicator_ShortName_IncludesPeriodLambdaAndSource()
+    {
+        var indicator = new RemaIndicator { Period = 15, Lambda = 0.7 };
+
+        Assert.Contains("REMA", indicator.ShortName, StringComparison.Ordinal);
+        Assert.Contains("15", indicator.ShortName, StringComparison.Ordinal);
+        Assert.Contains("0.70", indicator.ShortName, StringComparison.Ordinal);
+    }
+
+    [Fact]
+    public void RemaIndicator_Initialize_CreatesInternalRema()
+    {
+        var indicator = new RemaIndicator { Period = 10, Lambda = 0.5 };
+
+        // Initialize should not throw
+        indicator.Initialize();
+
+        // After init, line series should exist
+        Assert.Single(indicator.LinesSeries);
+    }
+
+    [Fact]
+    public void RemaIndicator_ProcessUpdate_HistoricalBar_ComputesValue()
+    {
+        var indicator = new RemaIndicator { Period = 3, Lambda = 0.5 };
+        indicator.Initialize();
+
+        // Add historical data
+        var now = DateTime.UtcNow;
+        indicator.HistoricalData.AddBar(now, 100, 105, 95, 102);
+
+        // Process update
+        var args = new UpdateArgs(UpdateReason.HistoricalBar);
+        indicator.ProcessUpdate(args);
+
+        // Line series should have a value
+        Assert.Equal(1, indicator.LinesSeries[0].Count);
+        Assert.True(double.IsFinite(indicator.LinesSeries[0].GetValue(0)));
+    }
+
+    [Fact]
+    public void RemaIndicator_ProcessUpdate_NewBar_ComputesValue()
+    {
+        var indicator = new RemaIndicator { Period = 3, Lambda = 0.5 };
+        indicator.Initialize();
+
+        // Add historical data
+        var now = DateTime.UtcNow;
+        indicator.HistoricalData.AddBar(now, 100, 105, 95, 102);
+        indicator.HistoricalData.AddBar(now.AddMinutes(1), 102, 108, 100, 106);
+
+        // Process first update
+        indicator.ProcessUpdate(new UpdateArgs(UpdateReason.HistoricalBar));
+        indicator.ProcessUpdate(new UpdateArgs(UpdateReason.NewBar));
+
+        // Line series should have values
+        Assert.Equal(2, indicator.LinesSeries[0].Count);
+    }
+
+    [Fact]
+    public void RemaIndicator_ProcessUpdate_NewTick_ProcessesWithoutError()
+    {
+        var indicator = new RemaIndicator { Period = 3, Lambda = 0.5 };
+        indicator.Initialize();
+
+        // Add historical data
+        var now = DateTime.UtcNow;
+        indicator.HistoricalData.AddBar(now, 100, 105, 95, 102);
+
+        // Process historical bar first
+        indicator.ProcessUpdate(new UpdateArgs(UpdateReason.HistoricalBar));
+        double firstValue = indicator.LinesSeries[0].GetValue(0);
+
+        // Update with new tick (same bar data - simulates intrabar update)
+        indicator.ProcessUpdate(new UpdateArgs(UpdateReason.NewTick));
+        double secondValue = indicator.LinesSeries[0].GetValue(0);
+
+        // Both values should be finite
+        Assert.True(double.IsFinite(firstValue));
+        Assert.True(double.IsFinite(secondValue));
+    }
+
+    [Fact]
+    public void RemaIndicator_MultipleUpdates_ProducesCorrectRemaSequence()
+    {
+        var indicator = new RemaIndicator { Period = 3, Lambda = 0.5 };
+        indicator.Initialize();
+
+        var now = DateTime.UtcNow;
+        double[] closes = { 100, 102, 104, 103, 105, 107, 106 };
+
+        foreach (var close in closes)
+        {
+            indicator.HistoricalData.AddBar(now, close, close + 2, close - 2, close);
+            indicator.ProcessUpdate(new UpdateArgs(UpdateReason.HistoricalBar));
+            now = now.AddMinutes(1);
+        }
+
+        // All values should be finite
+        for (int i = 0; i < closes.Length; i++)
+        {
+            Assert.True(double.IsFinite(indicator.LinesSeries[0].GetValue(closes.Length - 1 - i)));
+        }
+
+        // REMA should be smoothing the values
+        // Last REMA value should be between first and last close
+        double lastRema = indicator.LinesSeries[0].GetValue(0);
+        Assert.True(lastRema >= 100 && lastRema <= 110);
+    }
+
+    [Fact]
+    public void RemaIndicator_DifferentSourceTypes_Work()
+    {
+        var sources = new[] { SourceType.Open, SourceType.High, SourceType.Low, SourceType.Close, SourceType.HL2, SourceType.HLC3 };
+
+        foreach (var source in sources)
+        {
+            var indicator = new RemaIndicator { Period = 3, Lambda = 0.5, Source = source };
+            indicator.Initialize();
+
+            var now = DateTime.UtcNow;
+            indicator.HistoricalData.AddBar(now, 100, 110, 90, 105);
+            indicator.ProcessUpdate(new UpdateArgs(UpdateReason.HistoricalBar));
+
+            Assert.True(double.IsFinite(indicator.LinesSeries[0].GetValue(0)),
+                $"Source {source} should produce finite value");
+        }
+    }
+
+    [Fact]
+    public void RemaIndicator_Period_CanBeChanged()
+    {
+        var indicator = new RemaIndicator { Period = 5 };
+        Assert.Equal(5, indicator.Period);
+
+        indicator.Period = 20;
+        Assert.Equal(20, indicator.Period);
+        Assert.Equal(0, RemaIndicator.MinHistoryDepths);
+    }
+
+    [Fact]
+    public void RemaIndicator_Lambda_CanBeChanged()
+    {
+        var indicator = new RemaIndicator { Lambda = 0.5 };
+        Assert.Equal(0.5, indicator.Lambda);
+
+        indicator.Lambda = 0.8;
+        Assert.Equal(0.8, indicator.Lambda);
+    }
+
+    [Fact]
+    public void RemaIndicator_DifferentLambdaValues_ProduceDifferentResults()
+    {
+        var now = DateTime.UtcNow;
+        double[] closes = { 100, 102, 104, 103, 105, 107, 106 };
+
+        var indicator1 = new RemaIndicator { Period = 3, Lambda = 0.3 };
+        var indicator2 = new RemaIndicator { Period = 3, Lambda = 0.7 };
+        indicator1.Initialize();
+        indicator2.Initialize();
+
+        foreach (var close in closes)
+        {
+            indicator1.HistoricalData.AddBar(now, close, close + 2, close - 2, close);
+            indicator2.HistoricalData.AddBar(now, close, close + 2, close - 2, close);
+            indicator1.ProcessUpdate(new UpdateArgs(UpdateReason.HistoricalBar));
+            indicator2.ProcessUpdate(new UpdateArgs(UpdateReason.HistoricalBar));
+            now = now.AddMinutes(1);
+        }
+
+        // Different lambda values should produce different results
+        double result1 = indicator1.LinesSeries[0].GetValue(0);
+        double result2 = indicator2.LinesSeries[0].GetValue(0);
+
+        Assert.NotEqual(result1, result2);
+    }
+}

lib/trends_IIR/rema/tests/Rema.Tests.cs

@@ -0,0 +1,702 @@
+namespace QuanTAlib.Tests;
+
+public class RemaTests
+{
+    [Fact]
+    public void Rema_Constructor_Period_ValidatesInput()
+    {
+        Assert.Throws<ArgumentOutOfRangeException>(() => new Rema(0));
+        Assert.Throws<ArgumentOutOfRangeException>(() => new Rema(-1));
+
+        var rema = new Rema(10);
+        Assert.NotNull(rema);
+    }
+
+    [Fact]
+    public void Rema_Constructor_Lambda_ValidatesInput()
+    {
+        Assert.Throws<ArgumentOutOfRangeException>(() => new Rema(10, -0.1));
+        Assert.Throws<ArgumentOutOfRangeException>(() => new Rema(10, 1.1));
+
+        var rema1 = new Rema(10, 0.0);
+        var rema2 = new Rema(10, 1.0);
+        var rema3 = new Rema(10, 0.5);
+        Assert.NotNull(rema1);
+        Assert.NotNull(rema2);
+        Assert.NotNull(rema3);
+    }
+
+    [Fact]
+    public void Rema_Calc_ReturnsValue()
+    {
+        var rema = new Rema(10);
+
+        Assert.Equal(0, rema.Last.Value);
+
+        TValue result = rema.Update(new TValue(DateTime.UtcNow, 100));
+
+        Assert.True(result.Value > 0);
+        Assert.Equal(result.Value, rema.Last.Value);
+    }
+
+    [Fact]
+    public void Rema_Calc_IsNew_AcceptsParameter()
+    {
+        var rema = new Rema(10);
+
+        rema.Update(new TValue(DateTime.UtcNow, 100), isNew: true);
+        double value1 = rema.Last.Value;
+
+        rema.Update(new TValue(DateTime.UtcNow, 105), isNew: true);
+        double value2 = rema.Last.Value;
+
+        // Values should change with new bars
+        Assert.NotEqual(value1, value2);
+    }
+
+    [Fact]
+    public void Rema_Calc_IsNew_False_UpdatesValue()
+    {
+        var rema = new Rema(10);
+
+        rema.Update(new TValue(DateTime.UtcNow, 100));
+        rema.Update(new TValue(DateTime.UtcNow, 110), isNew: true);
+        double beforeUpdate = rema.Last.Value;
+
+        rema.Update(new TValue(DateTime.UtcNow, 120), isNew: false);
+        double afterUpdate = rema.Last.Value;
+
+        // Update should change the value
+        Assert.NotEqual(beforeUpdate, afterUpdate);
+    }
+
+    [Fact]
+    public void Rema_Reset_ClearsState()
+    {
+        var rema = new Rema(10);
+
+        rema.Update(new TValue(DateTime.UtcNow, 100));
+        rema.Update(new TValue(DateTime.UtcNow, 105));
+        double valueBefore = rema.Last.Value;
+
+        rema.Reset();
+
+        Assert.Equal(0, rema.Last.Value);
+
+        // After reset, should accept new values
+        rema.Update(new TValue(DateTime.UtcNow, 50));
+        Assert.NotEqual(0, rema.Last.Value);
+        Assert.NotEqual(valueBefore, rema.Last.Value);
+    }
+
+    [Fact]
+    public void Rema_Properties_Accessible()
+    {
+        var rema = new Rema(10);
+
+        Assert.Equal(0, rema.Last.Value);
+        Assert.False(rema.IsHot);
+
+        rema.Update(new TValue(DateTime.UtcNow, 100));
+
+        Assert.NotEqual(0, rema.Last.Value);
+    }
+
+    [Fact]
+    public void Rema_IsHot_BecomesTrueAfterWarmup()
+    {
+        var rema = new Rema(10);
+
+        // Initially IsHot should be false
+        Assert.False(rema.IsHot);
+
+        int steps = 0;
+        while (!rema.IsHot && steps < 1000)
+        {
+            rema.Update(new TValue(DateTime.UtcNow, 100));
+            steps++;
+        }
+
+        Assert.True(rema.IsHot);
+        Assert.True(steps > 0);
+        // Similar to EMA, should become hot around 15 bars for period 10
+        Assert.InRange(steps, 14, 17);
+    }
+
+    [Fact]
+    public void Rema_IsHot_IsPeriodDependent()
+    {
+        int[] periods = [10, 20, 50];
+        int[] expectedSteps = new int[periods.Length];
+
+        for (int i = 0; i < periods.Length; i++)
+        {
+            int period = periods[i];
+            var rema = new Rema(period);
+
+            int steps = 0;
+            while (!rema.IsHot && steps < 500)
+            {
+                rema.Update(new TValue(DateTime.UtcNow, 100));
+                steps++;
+            }
+
+            expectedSteps[i] = steps;
+        }
+
+        // Verify warmup times increase with period
+        Assert.True(expectedSteps[0] < expectedSteps[1], $"Period 10 ({expectedSteps[0]}) should be less than Period 20 ({expectedSteps[1]})");
+        Assert.True(expectedSteps[1] < expectedSteps[2], $"Period 20 ({expectedSteps[1]}) should be less than Period 50 ({expectedSteps[2]})");
+    }
+
+    [Fact]
+    public void Rema_Lambda1_ApproachesEma()
+    {
+        // With lambda=1, REMA should behave similarly to EMA
+        var rema = new Rema(10, lambda: 1.0);
+        var ema = new Ema(10);
+
+        var gbm = new GBM(startPrice: 100.0, mu: 0.02, sigma: 0.1, seed: 42);
+
+        for (int i = 0; i < 100; i++)
+        {
+            var bar = gbm.Next(isNew: true);
+            var input = new TValue(bar.Time, bar.Close);
+            rema.Update(input);
+            ema.Update(input);
+        }
+
+        // With lambda=1, REMA should be very close to EMA
+        Assert.Equal(ema.Last.Value, rema.Last.Value, 1e-6);
+    }
+
+    [Fact]
+    public void Rema_Lambda0_MaxRegularization()
+    {
+        // With lambda=0, REMA uses pure momentum continuation
+        var rema0 = new Rema(10, lambda: 0.0);
+        var rema05 = new Rema(10, lambda: 0.5);
+        var rema1 = new Rema(10, lambda: 1.0);
+
+        var gbm = new GBM(startPrice: 100.0, mu: 0.02, sigma: 0.1, seed: 42);
+
+        for (int i = 0; i < 50; i++)
+        {
+            var bar = gbm.Next(isNew: true);
+            var input = new TValue(bar.Time, bar.Close);
+            rema0.Update(input);
+            rema05.Update(input);
+            rema1.Update(input);
+        }
+
+        // All should produce finite values
+        Assert.True(double.IsFinite(rema0.Last.Value));
+        Assert.True(double.IsFinite(rema05.Last.Value));
+        Assert.True(double.IsFinite(rema1.Last.Value));
+
+        // They should generally differ (lambda affects behavior)
+        // Note: exact equality is unlikely with different lambdas
+    }
+
+    [Fact]
+    public void Rema_IterativeCorrections_RestoreToOriginalState()
+    {
+        var rema = new Rema(10);
+        var gbm = new GBM(startPrice: 100.0, mu: 0.02, sigma: 0.1);
+
+        // Feed 10 new values
+        TValue tenthInput = default;
+        for (int i = 0; i < 10; i++)
+        {
+            var bar = gbm.Next(isNew: true);
+            tenthInput = new TValue(bar.Time, bar.Close);
+            rema.Update(tenthInput, isNew: true);
+        }
+
+        // Remember state after 10 values
+        double remaAfterTen = rema.Last.Value;
+
+        // Generate 9 corrections with isNew=false (different values)
+        for (int i = 0; i < 9; i++)
+        {
+            var bar = gbm.Next(isNew: false);
+            rema.Update(new TValue(bar.Time, bar.Close), isNew: false);
+        }
+
+        // Feed the remembered 10th input again with isNew=false
+        TValue finalRema = rema.Update(tenthInput, isNew: false);
+
+        // Should match the original state after 10 values
+        Assert.Equal(remaAfterTen, finalRema.Value, 1e-10);
+    }
+
+    [Fact]
+    public void Rema_BatchCalc_MatchesIterativeCalc()
+    {
+        var remaIterative = new Rema(10);
+        var remaBatch = new Rema(10);
+        var gbm = new GBM(startPrice: 100.0, mu: 0.02, sigma: 0.1);
+
+        // Generate data
+        var series = new TSeries();
+        for (int i = 0; i < 100; i++)
+        {
+            var bar = gbm.Next(isNew: true);
+            series.Add(bar.Time, bar.Close);
+        }
+
+        Assert.True(series.Count > 0);
+
+        // Calculate iteratively
+        var iterativeResults = new TSeries();
+        foreach (var item in series)
+        {
+            iterativeResults.Add(remaIterative.Update(item));
+        }
+
+        // Calculate batch
+        var batchResults = remaBatch.Update(series);
+
+        // Compare
+        Assert.Equal(iterativeResults.Count, batchResults.Count);
+        for (int i = 0; i < iterativeResults.Count; i++)
+        {
+            Assert.Equal(iterativeResults[i].Value, batchResults[i].Value, 1e-10);
+            Assert.Equal(iterativeResults[i].Time, batchResults[i].Time);
+        }
+    }
+
+    [Fact]
+    public void Rema_NaN_Input_UsesLastValidValue()
+    {
+        var rema = new Rema(10);
+
+        // Feed some valid values
+        rema.Update(new TValue(DateTime.UtcNow, 100));
+        rema.Update(new TValue(DateTime.UtcNow, 110));
+
+        // Feed NaN - should use last valid value (110)
+        var resultAfterNaN = rema.Update(new TValue(DateTime.UtcNow, double.NaN));
+
+        // Result should be finite (not NaN)
+        Assert.True(double.IsFinite(resultAfterNaN.Value));
+        Assert.NotEqual(0, resultAfterNaN.Value);
+    }
+
+    [Fact]
+    public void Rema_Infinity_Input_UsesLastValidValue()
+    {
+        var rema = new Rema(10);
+
+        // Feed some valid values
+        rema.Update(new TValue(DateTime.UtcNow, 100));
+        rema.Update(new TValue(DateTime.UtcNow, 110));
+
+        // Feed positive infinity - should use last valid value
+        var resultAfterPosInf = rema.Update(new TValue(DateTime.UtcNow, double.PositiveInfinity));
+        Assert.True(double.IsFinite(resultAfterPosInf.Value));
+
+        // Feed negative infinity - should use last valid value
+        var resultAfterNegInf = rema.Update(new TValue(DateTime.UtcNow, double.NegativeInfinity));
+        Assert.True(double.IsFinite(resultAfterNegInf.Value));
+    }
+
+    [Fact]
+    public void Rema_MultipleNaN_ContinuesWithLastValid()
+    {
+        var rema = new Rema(10);
+
+        // Feed valid values
+        rema.Update(new TValue(DateTime.UtcNow, 100));
+        rema.Update(new TValue(DateTime.UtcNow, 110));
+        rema.Update(new TValue(DateTime.UtcNow, 120));
+
+        // Feed multiple NaN values
+        var r1 = rema.Update(new TValue(DateTime.UtcNow, double.NaN));
+        var r2 = rema.Update(new TValue(DateTime.UtcNow, double.NaN));
+        var r3 = rema.Update(new TValue(DateTime.UtcNow, double.NaN));
+
+        // All results should be finite
+        Assert.True(double.IsFinite(r1.Value));
+        Assert.True(double.IsFinite(r2.Value));
+        Assert.True(double.IsFinite(r3.Value));
+    }
+
+    [Fact]
+    public void Rema_BatchCalc_HandlesNaN()
+    {
+        var rema = new Rema(10);
+
+        // Create series with NaN values interspersed
+        var series = new TSeries();
+        series.Add(DateTime.UtcNow.Ticks, 100);
+        series.Add(DateTime.UtcNow.Ticks + 1, 110);
+        series.Add(DateTime.UtcNow.Ticks + 2, double.NaN);
+        series.Add(DateTime.UtcNow.Ticks + 3, 120);
+        series.Add(DateTime.UtcNow.Ticks + 4, double.PositiveInfinity);
+        series.Add(DateTime.UtcNow.Ticks + 5, 130);
+
+        var results = rema.Update(series);
+
+        // All results should be finite
+        foreach (var result in results)
+        {
+            Assert.True(double.IsFinite(result.Value), $"Expected finite value but got {result.Value}");
+        }
+    }
+
+    [Fact]
+    public void Rema_Reset_ClearsLastValidValue()
+    {
+        var rema = new Rema(10);
+
+        // Feed values including NaN
+        rema.Update(new TValue(DateTime.UtcNow, 100));
+        rema.Update(new TValue(DateTime.UtcNow, double.NaN));
+
+        // Reset
+        rema.Reset();
+
+        // After reset, first valid value should establish new baseline
+        var result = rema.Update(new TValue(DateTime.UtcNow, 50));
+        Assert.Equal(50.0, result.Value, 1e-10);
+    }
+
+    // ============== Span API Tests ==============
+
+    [Fact]
+    public void Rema_SpanBatch_Period_ValidatesInput()
+    {
+        double[] source = [1, 2, 3, 4, 5];
+        double[] output = new double[5];
+        double[] wrongSizeOutput = new double[3];
+
+        // Period must be > 0
+        Assert.Throws<ArgumentException>(() => Rema.Batch(source.AsSpan(), output.AsSpan(), 0));
+        Assert.Throws<ArgumentException>(() => Rema.Batch(source.AsSpan(), output.AsSpan(), -1));
+
+        // Output must be same length as source
+        Assert.Throws<ArgumentException>(() => Rema.Batch(source.AsSpan(), wrongSizeOutput.AsSpan(), 3));
+    }
+
+    [Fact]
+    public void Rema_SpanBatch_Lambda_ValidatesInput()
+    {
+        double[] source = [1, 2, 3, 4, 5];
+        double[] output = new double[5];
+
+        // Lambda must be >= 0 and <= 1
+        Assert.Throws<ArgumentOutOfRangeException>(() => Rema.Batch(source.AsSpan(), output.AsSpan(), 3, -0.1));
+        Assert.Throws<ArgumentOutOfRangeException>(() => Rema.Batch(source.AsSpan(), output.AsSpan(), 3, 1.1));
+    }
+
+    [Fact]
+    public void Rema_SpanBatch_MatchesTSeriesBatch()
+    {
+        var series = new TSeries();
+        double[] source = new double[100];
+        double[] output = new double[100];
+
+        var gbm = new GBM(startPrice: 100.0, mu: 0.02, sigma: 0.1, seed: 42);
+        for (int i = 0; i < 100; i++)
+        {
+            var bar = gbm.Next(isNew: true);
+            source[i] = bar.Close;
+            series.Add(bar.Time, bar.Close);
+        }
+
+        // Calculate with TSeries API
+        var tseriesResult = Rema.Batch(series, 10);
+
+        // Calculate with Span API
+        Rema.Batch(source.AsSpan(), output.AsSpan(), 10);
+
+        // Compare results
+        for (int i = 0; i < 100; i++)
+        {
+            Assert.Equal(tseriesResult[i].Value, output[i], 1e-9);
+        }
+    }
+
+    [Fact]
+    public void Rema_SpanBatch_DifferentLambdas()
+    {
+        double[] source = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100];
+        double[] output0 = new double[10];
+        double[] output05 = new double[10];
+        double[] output1 = new double[10];
+
+        Rema.Batch(source.AsSpan(), output0.AsSpan(), 5, 0.0);
+        Rema.Batch(source.AsSpan(), output05.AsSpan(), 5, 0.5);
+        Rema.Batch(source.AsSpan(), output1.AsSpan(), 5, 1.0);
+
+        // All should produce finite results
+        for (int i = 0; i < 10; i++)
+        {
+            Assert.True(double.IsFinite(output0[i]));
+            Assert.True(double.IsFinite(output05[i]));
+            Assert.True(double.IsFinite(output1[i]));
+        }
+    }
+
+    [Fact]
+    public void Rema_SpanBatch_ZeroAllocation()
+    {
+        double[] source = new double[10000];
+        double[] output = new double[10000];
+
+        var gbm = new GBM(startPrice: 100, mu: 0.05, sigma: 0.2, seed: 42);
+        for (int i = 0; i < source.Length; i++)
+        {
+            source[i] = gbm.Next().Close;
+        }
+
+        // Warm up
+        Rema.Batch(source.AsSpan(), output.AsSpan(), 100);
+
+        // This test verifies the method runs without throwing
+        Assert.True(double.IsFinite(output[^1]));
+    }
+
+    [Fact]
+    public void Rema_SpanBatch_HandlesNaN()
+    {
+        double[] source = [100, 110, double.NaN, 120, 130];
+        double[] output = new double[5];
+
+        Rema.Batch(source.AsSpan(), output.AsSpan(), 3);
+
+        // All outputs should be finite
+        foreach (var val in output)
+        {
+            Assert.True(double.IsFinite(val), $"Expected finite value but got {val}");
+        }
+    }
+
+    [Fact]
+    public void Chainability_Works()
+    {
+        var source = new TSeries();
+        var rema = new Rema(source, 10);
+
+        source.Add(new TValue(DateTime.UtcNow, 100));
+        Assert.Equal(100, rema.Last.Value, 1e-10);
+    }
+
+    [Fact]
+    public void Prime_SetsStateCorrectly()
+    {
+        var rema = new Rema(5);
+        double[] history = [10, 20, 30, 40, 50];
+
+        rema.Prime(history);
+
+        // Verify against a fresh REMA fed with same data
+        var verifyRema = new Rema(5);
+        foreach (var val in history)
+        {
+            verifyRema.Update(new TValue(DateTime.UtcNow, val));
+        }
+
+        Assert.Equal(verifyRema.Last.Value, rema.Last.Value, 1e-10);
+        Assert.Equal(verifyRema.IsHot, rema.IsHot);
+
+        // Verify it continues correctly
+        rema.Update(new TValue(DateTime.UtcNow, 60));
+        verifyRema.Update(new TValue(DateTime.UtcNow, 60));
+        Assert.Equal(verifyRema.Last.Value, rema.Last.Value, 1e-10);
+    }
+
+    [Fact]
+    public void Prime_HandlesNaN_InHistory()
+    {
+        var rema = new Rema(5);
+        double[] history = [10, 20, double.NaN, 40, 50];
+
+        rema.Prime(history);
+
+        var verifyRema = new Rema(5);
+        foreach (var val in history)
+        {
+            verifyRema.Update(new TValue(DateTime.UtcNow, val));
+        }
+
+        Assert.Equal(verifyRema.Last.Value, rema.Last.Value, 1e-10);
+    }
+
+    [Fact]
+    public void Prime_AllNaNs_ReturnsNaN()
+    {
+        var rema = new Rema(5);
+        double[] history = [double.NaN, double.NaN, double.NaN];
+
+        rema.Prime(history);
+
+        Assert.True(double.IsNaN(rema.Last.Value));
+    }
+
+    [Fact]
+    public void Calculate_ReturnsCorrectResultsAndHotIndicator()
+    {
+        var series = new TSeries();
+        for (int i = 1; i <= 20; i++)
+        {
+            series.Add(DateTime.UtcNow, i * 10);
+        }
+
+        var (results, indicator) = Rema.Calculate(series, 5);
+
+        // Check results
+        Assert.Equal(20, results.Count);
+
+        // Verify against standard calculation
+        var verifyRema = new Rema(5);
+        var verifyResults = verifyRema.Update(series);
+
+        Assert.Equal(verifyResults.Last.Value, results.Last.Value, 1e-10);
+        Assert.Equal(verifyRema.Last.Value, indicator.Last.Value, 1e-10);
+
+        // Check indicator state
+        Assert.True(indicator.IsHot);
+
+        // Verify indicator continues correctly
+        indicator.Update(new TValue(DateTime.UtcNow, 210));
+        verifyRema.Update(new TValue(DateTime.UtcNow, 210));
+        Assert.Equal(verifyRema.Last.Value, indicator.Last.Value, 1e-10);
+    }
+
+    [Fact]
+    public void Rema_Batch_AllNaNs_ReturnsNaN()
+    {
+        double[] source = [double.NaN, double.NaN, double.NaN];
+        double[] output = new double[3];
+
+        Rema.Batch(source.AsSpan(), output.AsSpan(), 5);
+
+        // Should be all NaNs, not 0s
+        foreach (var val in output)
+        {
+            Assert.True(double.IsNaN(val), $"Expected NaN but got {val}");
+        }
+    }
+
+    [Fact]
+    public void Rema_AllModes_ProduceSameResult()
+    {
+        // Arrange
+        int period = 10;
+        double lambda = 0.5;
+        var gbm = new GBM(startPrice: 100, mu: 0.05, sigma: 0.2, seed: 123);
+        var bars = gbm.Fetch(1000, DateTime.UtcNow.Ticks, TimeSpan.FromMinutes(1));
+        var series = bars.Close;
+
+        // 1. Batch Mode
+        var batchSeries = Rema.Batch(series, period, lambda);
+        double expected = batchSeries.Last.Value;
+
+        // 2. Span Mode
+        var tValues = series.Values.ToArray();
+        var spanInput = new ReadOnlySpan<double>(tValues);
+        var spanOutput = new double[tValues.Length];
+        Rema.Batch(spanInput, spanOutput, period, lambda);
+        double spanResult = spanOutput[^1];
+
+        // 3. Streaming Mode
+        var streamingInd = new Rema(period, lambda);
+        for (int i = 0; i < series.Count; i++)
+        {
+            streamingInd.Update(series[i]);
+        }
+        double streamingResult = streamingInd.Last.Value;
+
+        // 4. Eventing Mode
+        var pubSource = new TSeries();
+        var eventingInd = new Rema(pubSource, period, lambda);
+        for (int i = 0; i < series.Count; i++)
+        {
+            pubSource.Add(series[i]);
+        }
+        double eventingResult = eventingInd.Last.Value;
+
+        // Assert
+        Assert.Equal(expected, spanResult, precision: 9);
+        Assert.Equal(expected, streamingResult, precision: 9);
+        Assert.Equal(expected, eventingResult, precision: 9);
+    }
+
+    [Fact]
+    public void Rema_AllModes_ProduceSameResult_AfterResyncInterval()
+    {
+        // This guards against implementation drift between CalculateCore (batch/span)
+        // and Update(TValue) (streaming/eventing) when internal counters wrap/reset.
+        int period = 10;
+        double lambda = 0.5;
+        int count = 12050; // > ResyncInterval (10,000)
+
+        var gbm = new GBM(startPrice: 100, mu: 0.05, sigma: 0.2, seed: 321);
+        var bars = gbm.Fetch(count, DateTime.UtcNow.Ticks, TimeSpan.FromMinutes(1));
+        var series = bars.Close;
+
+        // 1. Batch Mode
+        var batchSeries = Rema.Batch(series, period, lambda);
+        double expected = batchSeries.Last.Value;
+
+        // 2. Span Mode
+        var tValues = series.Values.ToArray();
+        var spanInput = new ReadOnlySpan<double>(tValues);
+        var spanOutput = new double[tValues.Length];
+        Rema.Batch(spanInput, spanOutput, period, lambda);
+        double spanResult = spanOutput[^1];
+
+        // 3. Streaming Mode
+        var streamingInd = new Rema(period, lambda);
+        for (int i = 0; i < series.Count; i++)
+        {
+            streamingInd.Update(series[i]);
+        }
+
+        double streamingResult = streamingInd.Last.Value;
+
+        // 4. Eventing Mode
+        var pubSource = new TSeries();
+        var eventingInd = new Rema(pubSource, period, lambda);
+        for (int i = 0; i < series.Count; i++)
+        {
+            pubSource.Add(series[i]);
+        }
+
+        double eventingResult = eventingInd.Last.Value;
+
+        Assert.Equal(expected, spanResult, precision: 9);
+        Assert.Equal(expected, streamingResult, precision: 9);
+        Assert.Equal(expected, eventingResult, precision: 9);
+    }
+
+    [Fact]
+    public void Prime_ThenUpdate_StateWorksCorrectly()
+    {
+        var rema = new Rema(5);
+        double[] history = [10, 20, 30, 40, 50];
+
+        rema.Prime(history);
+        double afterPrime = rema.Last.Value;
+
+        // After Prime, an isNew=true should advance the state
+        rema.Update(new TValue(DateTime.UtcNow, 60), isNew: true);
+        double afterNewBar = rema.Last.Value;
+
+        // Values should be different
+        Assert.NotEqual(afterPrime, afterNewBar);
+
+        // isNew=false with a different value should recalculate from previous state
+        rema.Update(new TValue(DateTime.UtcNow, 70), isNew: false);
+        double afterCorrection = rema.Last.Value;
+
+        // Correction with 70 should give different result than 60
+        Assert.NotEqual(afterNewBar, afterCorrection);
+
+        // isNew=false with original value (60) should restore to afterNewBar
+        rema.Update(new TValue(DateTime.UtcNow, 60), isNew: false);
+        Assert.Equal(afterNewBar, rema.Last.Value, 1e-10);
+    }
+}

lib/trends_IIR/rema/tests/Rema.Validation.Tests.cs

@@ -0,0 +1,354 @@
+using Xunit.Abstractions;
+
+using OoplesFinance.StockIndicators;
+using OoplesFinance.StockIndicators.Models;
+
+namespace QuanTAlib.Tests;
+
+/// <summary>
+/// Validation tests for REMA (Regularized Exponential Moving Average).
+/// Since REMA is a custom indicator not found in external libraries like TA-Lib, Skender, Tulip, or Ooples,
+/// these tests validate internal consistency across different calculation modes and against known mathematical properties.
+/// </summary>
+public sealed class RemaValidationTests : IDisposable
+{
+    private readonly ValidationTestData _testData;
+    private readonly ITestOutputHelper _output;
+    private bool _disposed;
+
+    public RemaValidationTests(ITestOutputHelper output)
+    {
+        _output = output;
+        _testData = new ValidationTestData();
+    }
+
+    public void Dispose()
+    {
+        Dispose(true);
+    }
+
+    private void Dispose(bool disposing)
+    {
+        if (_disposed)
+        {
+            return;
+        }
+
+        _disposed = true;
+
+        if (disposing)
+        {
+            _testData?.Dispose();
+        }
+    }
+
+    [Fact]
+    public void Validate_Lambda1_MatchesEma_Batch()
+    {
+        // When lambda=1, REMA should produce results very close to EMA
+        int[] periods = { 5, 10, 20, 50 };
+
+        foreach (var period in periods)
+        {
+            var rema = new Rema(period, lambda: 1.0);
+            var ema = new Ema(period);
+
+            var remaResult = rema.Update(_testData.Data);
+            var emaResult = ema.Update(_testData.Data);
+
+            // Compare last 100 records - they should be very close
+            int compareCount = Math.Min(100, remaResult.Count);
+            int startIdx = remaResult.Count - compareCount;
+
+            for (int i = startIdx; i < remaResult.Count; i++)
+            {
+                Assert.Equal(emaResult[i].Value, remaResult[i].Value, 1e-8);
+            }
+        }
+        _output.WriteLine("REMA(lambda=1) Batch validated successfully against EMA");
+    }
+
+    [Fact]
+    public void Validate_Lambda1_MatchesEma_Streaming()
+    {
+        int[] periods = { 5, 10, 20, 50 };
+
+        foreach (var period in periods)
+        {
+            var rema = new Rema(period, lambda: 1.0);
+            var ema = new Ema(period);
+
+            var remaResults = new List<double>();
+            var emaResults = new List<double>();
+
+            foreach (var item in _testData.Data)
+            {
+                remaResults.Add(rema.Update(item).Value);
+                emaResults.Add(ema.Update(item).Value);
+            }
+
+            // Compare last 100 records
+            int compareCount = Math.Min(100, remaResults.Count);
+            int startIdx = remaResults.Count - compareCount;
+
+            for (int i = startIdx; i < remaResults.Count; i++)
+            {
+                Assert.Equal(emaResults[i], remaResults[i], 1e-8);
+            }
+        }
+        _output.WriteLine("REMA(lambda=1) Streaming validated successfully against EMA");
+    }
+
+    [Fact]
+    public void Validate_Lambda1_MatchesEma_Span()
+    {
+        int[] periods = { 5, 10, 20, 50 };
+        double[] sourceData = _testData.RawData.ToArray();
+
+        foreach (var period in periods)
+        {
+            double[] remaOutput = new double[sourceData.Length];
+            double[] emaOutput = new double[sourceData.Length];
+
+            Rema.Batch(sourceData.AsSpan(), remaOutput.AsSpan(), period, lambda: 1.0);
+            Ema.Batch(sourceData.AsSpan(), emaOutput.AsSpan(), period);
+
+            // Compare last 100 records
+            int compareCount = Math.Min(100, sourceData.Length);
+            int startIdx = sourceData.Length - compareCount;
+
+            for (int i = startIdx; i < sourceData.Length; i++)
+            {
+                Assert.Equal(emaOutput[i], remaOutput[i], 1e-8);
+            }
+        }
+        _output.WriteLine("REMA(lambda=1) Span validated successfully against EMA");
+    }
+
+    [Fact]
+    public void Validate_BatchStreamingSpan_Consistency()
+    {
+        // Validate that all three modes produce identical results
+        int[] periods = { 5, 10, 20, 50 };
+        double[] lambdas = { 0.0, 0.25, 0.5, 0.75, 1.0 };
+
+        double[] sourceData = _testData.RawData.ToArray();
+
+        foreach (var period in periods)
+        {
+            foreach (var lambda in lambdas)
+            {
+                // Batch (TSeries)
+                var remaBatch = new Rema(period, lambda);
+                var batchResult = remaBatch.Update(_testData.Data);
+
+                // Streaming
+                var remaStream = new Rema(period, lambda);
+                var streamResults = new List<double>();
+                foreach (var item in _testData.Data)
+                {
+                    streamResults.Add(remaStream.Update(item).Value);
+                }
+
+                // Span
+                double[] spanOutput = new double[sourceData.Length];
+                Rema.Batch(sourceData.AsSpan(), spanOutput.AsSpan(), period, lambda);
+
+                // Compare all three
+                int compareCount = Math.Min(100, sourceData.Length);
+                int startIdx = sourceData.Length - compareCount;
+
+                for (int i = startIdx; i < sourceData.Length; i++)
+                {
+                    Assert.Equal(batchResult[i].Value, streamResults[i], 1e-10);
+                    Assert.Equal(batchResult[i].Value, spanOutput[i], 1e-10);
+                }
+            }
+        }
+        _output.WriteLine("REMA Batch/Streaming/Span consistency validated successfully");
+    }
+
+    [Fact]
+    public void Validate_SmoothingBehavior()
+    {
+        // Validate that lower lambda produces smoother output (less variance)
+        int period = 10;
+        double[] sourceData = _testData.RawData.ToArray();
+
+        double[] output0 = new double[sourceData.Length];
+        double[] output05 = new double[sourceData.Length];
+        double[] output1 = new double[sourceData.Length];
+
+        Rema.Batch(sourceData.AsSpan(), output0.AsSpan(), period, lambda: 0.0);
+        Rema.Batch(sourceData.AsSpan(), output05.AsSpan(), period, lambda: 0.5);
+        Rema.Batch(sourceData.AsSpan(), output1.AsSpan(), period, lambda: 1.0);
+
+        // Calculate variance of differences (measure of smoothness)
+        // Skip warmup period
+        int startIdx = period * 3;
+        int len = sourceData.Length - startIdx;
+
+        double var0 = CalculateDiffVariance(output0, startIdx, len);
+        double var05 = CalculateDiffVariance(output05, startIdx, len);
+        double var1 = CalculateDiffVariance(output1, startIdx, len);
+
+        // Lower lambda should generally produce smoother (lower variance) output
+        // Note: This is a statistical property that may not always hold for all data
+        _output.WriteLine($"Variance of differences - lambda=0: {var0:F6}, lambda=0.5: {var05:F6}, lambda=1: {var1:F6}");
+
+        // At minimum, all should produce finite positive variance
+        Assert.True(double.IsFinite(var0) && var0 > 0);
+        Assert.True(double.IsFinite(var05) && var05 > 0);
+        Assert.True(double.IsFinite(var1) && var1 > 0);
+    }
+
+    [Fact]
+    public void Validate_PrimeConsistency()
+    {
+        // Validate that Prime produces same state as streaming through same data
+        int[] periods = { 5, 10, 20 };
+        double[] lambdas = { 0.0, 0.5, 1.0 };
+
+        double[] sourceData = _testData.RawData.Span.Slice(0, 100).ToArray();
+
+        foreach (var period in periods)
+        {
+            foreach (var lambda in lambdas)
+            {
+                // Via Prime
+                var remaPrime = new Rema(period, lambda);
+                remaPrime.Prime(sourceData);
+
+                // Via streaming
+                var remaStream = new Rema(period, lambda);
+                foreach (var val in sourceData)
+                {
+                    remaStream.Update(new TValue(DateTime.UtcNow, val));
+                }
+
+                Assert.Equal(remaStream.Last.Value, remaPrime.Last.Value, 1e-10);
+                Assert.Equal(remaStream.IsHot, remaPrime.IsHot);
+
+                // Verify they continue correctly
+                double nextVal = sourceData[^1] * 1.05; // 5% increase
+                remaPrime.Update(new TValue(DateTime.UtcNow, nextVal));
+                remaStream.Update(new TValue(DateTime.UtcNow, nextVal));
+
+                Assert.Equal(remaStream.Last.Value, remaPrime.Last.Value, 1e-10);
+            }
+        }
+        _output.WriteLine("REMA Prime consistency validated successfully");
+    }
+
+    [Fact]
+    public void Validate_ConstantInput_ConvergesToInput()
+    {
+        // With constant input, REMA should converge to that value when lambda > 0
+        // Note: lambda=0 is pure momentum and may not converge to constant value
+        double constantValue = 100.0;
+        int[] periods = { 5, 10, 20 };
+        double[] lambdas = { 0.5, 1.0 }; // Exclude lambda=0 (pure momentum)
+
+        foreach (var period in periods)
+        {
+            foreach (var lambda in lambdas)
+            {
+                var rema = new Rema(period, lambda);
+
+                // Feed constant values until well past warmup
+                for (int i = 0; i < period * 10; i++)
+                {
+                    rema.Update(new TValue(DateTime.UtcNow, constantValue));
+                }
+
+                // Should converge to the constant value (within tolerance)
+                Assert.Equal(constantValue, rema.Last.Value, 1e-4);
+            }
+        }
+        _output.WriteLine("REMA constant input convergence validated successfully");
+    }
+
+    [Fact]
+    public void Validate_BarCorrection_Consistency()
+    {
+        // Validate that bar correction (isNew=false) works correctly
+        int period = 10;
+        double lambda = 0.5;
+        var gbm = new GBM(startPrice: 100.0, mu: 0.02, sigma: 0.1, seed: 42);
+
+        var rema = new Rema(period, lambda);
+
+        // Feed 20 bars
+        for (int i = 0; i < 20; i++)
+        {
+            var bar = gbm.Next(isNew: true);
+            rema.Update(new TValue(bar.Time, bar.Close), isNew: true);
+        }
+
+        double valueAfter20 = rema.Last.Value;
+
+        // Apply 5 corrections
+        for (int i = 0; i < 5; i++)
+        {
+            var bar = gbm.Next(isNew: false);
+            rema.Update(new TValue(bar.Time, bar.Close), isNew: false);
+        }
+
+        // The value should have changed
+        Assert.NotEqual(valueAfter20, rema.Last.Value);
+
+        // Now restore by using the same correction with original value
+        // We need to track the original 20th bar value for this
+        // Since we can't easily do that, we just verify the mechanism works
+        Assert.True(double.IsFinite(rema.Last.Value));
+
+        _output.WriteLine("REMA bar correction consistency validated successfully");
+    }
+
+    private static double CalculateDiffVariance(double[] values, int startIdx, int count)
+    {
+        if (count < 2)
+        {
+            return 0;
+        }
+
+        // Calculate differences
+        double sumDiff = 0;
+        double sumDiffSq = 0;
+        int n = 0;
+
+        for (int i = startIdx + 1; i < startIdx + count && i < values.Length; i++)
+        {
+            double diff = values[i] - values[i - 1];
+            sumDiff += diff;
+            sumDiffSq += diff * diff;
+            n++;
+        }
+
+        if (n < 2)
+        {
+            return 0;
+        }
+
+        double mean = sumDiff / n;
+        double variance = (sumDiffSq / n) - (mean * mean);
+        return Math.Max(0, variance); // Ensure non-negative due to floating point
+    }
+
+    [Fact]
+    public void Rema_MatchesOoples_Structural()
+    {
+        var gbm = new GBM(startPrice: 100.0, mu: 0.02, sigma: 0.15, seed: 42);
+        var bars = gbm.Fetch(500, DateTime.UtcNow.Ticks, TimeSpan.FromMinutes(1));
+        var ooplesData = bars.Select(b => new TickerData
+        {
+            Date = new DateTime(b.Time, DateTimeKind.Utc),
+            Open = b.Open, High = b.High, Low = b.Low,
+            Close = b.Close, Volume = b.Volume
+        }).ToList();
+        var result = new StockData(ooplesData).CalculateRegularizedExponentialMovingAverage();
+        var values = result.CustomValuesList;
+        int finiteCount = values.Count(v => double.IsFinite(v));
+        Assert.True(finiteCount > 100, $"Expected >100 finite values, got {finiteCount}");
+    }
+}