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tk-yoshimuratk-yoshimura
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update fp64 code
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-60033
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‎ErrorFunctionFP64/Properties/AssemblyInfo.cs‎

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using System.Reflection;
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using System.Runtime.CompilerServices;
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using System.Runtime.InteropServices;
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[assembly: AssemblyTitle("ErrorFunctionFP64")]

‎ErrorFunctionFP64Tests/ErrorSummary.cs‎

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using ErrorFunctionFP64;
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using Microsoft.VisualStudio.TestTools.UnitTesting;
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using MultiPrecision;
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namespace ErrorFunctionFP64Tests {
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[TestClass()]
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public class ErrorSummary {
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[TestMethod()]
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public void PlotErf() {
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using StreamWriter sw = new("../../../../results/erf_approx.csv");
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sw.WriteLine("x,y_expected,y_actual,error(abs),error(rate)");
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MultiPrecision<Pow2.N8> maxrateerror = 0;
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for (double x = -10; x <= 10; x += 1d / 1024) {
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double actual = ErrorFunction.Erf((double)x);
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MultiPrecision<Pow2.N8> expetected = MultiPrecision<Pow2.N8>.Erf(x);
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MultiPrecision<Pow2.N8> error = MultiPrecision<Pow2.N8>.Abs(expetected - actual);
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MultiPrecision<Pow2.N8> rateerror = (error != 0) ? error / MultiPrecision<Pow2.N8>.Abs(expetected) : 0;
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if (double.IsNormal(actual)) {
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maxrateerror = MultiPrecision<Pow2.N8>.Max(rateerror, maxrateerror);
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}
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sw.WriteLine($"{x},{expetected:e20},{actual},{error:e8},{rateerror:e8}");
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}
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Console.WriteLine($"max error (rate): {maxrateerror:e8}");
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}
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[TestMethod()]
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public void PlotErfc() {
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using StreamWriter sw = new("../../../../results/erfc_approx.csv");
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sw.WriteLine("x,y_expected,y_actual,error(abs),error(rate)");
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MultiPrecision<Pow2.N8> maxrateerror = 0;
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for (double x = -10; x <= 30; x += 1d / 1024) {
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double actual = ErrorFunction.Erfc((double)x);
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MultiPrecision<Pow2.N8> expetected = MultiPrecision<Pow2.N8>.Erfc(x);
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MultiPrecision<Pow2.N8> error = MultiPrecision<Pow2.N8>.Abs(expetected - actual);
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MultiPrecision<Pow2.N8> rateerror = (error != 0) ? error / MultiPrecision<Pow2.N8>.Abs(expetected) : 0;
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if (double.IsNormal(actual)) {
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maxrateerror = MultiPrecision<Pow2.N8>.Max(rateerror, maxrateerror);
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}
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sw.WriteLine($"{x},{expetected:e20},{actual},{error:e8},{rateerror:e8}");
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}
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Console.WriteLine($"max error (rate): {maxrateerror:e8}");
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}
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[TestMethod()]
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public void PlotInverseErf() {
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using StreamWriter sw = new("../../../../results/inverf_approx.csv");
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sw.WriteLine("x,y_expected,y_actual,error(abs),error(rate)");
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MultiPrecision<Pow2.N8> maxrateerror = 0;
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for (double x = -1023d / 1024; x < 1; x += 1d / 1024) {
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double actual = ErrorFunction.InverseErf((double)x);
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MultiPrecision<Pow2.N8> expetected = MultiPrecision<Pow2.N8>.InverseErf(x);
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MultiPrecision<Pow2.N8> error = MultiPrecision<Pow2.N8>.Abs(expetected - actual);
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MultiPrecision<Pow2.N8> rateerror = (error != 0) ? error / MultiPrecision<Pow2.N8>.Abs(expetected) : 0;
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if (double.IsNormal(actual)) {
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maxrateerror = MultiPrecision<Pow2.N8>.Max(rateerror, maxrateerror);
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}
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sw.WriteLine($"{x},{expetected:e20},{actual},{error:e8},{rateerror:e8}");
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}
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Console.WriteLine($"max error (rate): {maxrateerror:e8}");
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}
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[TestMethod()]
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public void PlotInverseErfc() {
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using StreamWriter sw = new("../../../../results/inverfc_approx.csv");
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sw.WriteLine("x,y_expected,y_actual,error(abs),error(rate)");
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MultiPrecision<Pow2.N8> maxrateerror = 0;
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for (double x = Math.ScaleB(1, -1024); x < Math.ScaleB(1, -10); x *= 2) {
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double actual = ErrorFunction.InverseErfc((double)x);
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MultiPrecision<Pow2.N8> expetected = MultiPrecision<Pow2.N8>.InverseErfc(x);
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MultiPrecision<Pow2.N8> error = MultiPrecision<Pow2.N8>.Abs(expetected - actual);
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MultiPrecision<Pow2.N8> rateerror = (error != 0) ? error / MultiPrecision<Pow2.N8>.Abs(expetected) : 0;
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if (double.IsNormal(actual)) {
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maxrateerror = MultiPrecision<Pow2.N8>.Max(rateerror, maxrateerror);
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}
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sw.WriteLine($"{x},{expetected:e20},{actual},{error:e8},{rateerror:e8}");
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}
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for (double x = 1d / 1024; x < 2; x += 1d / 1024) {
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double actual = ErrorFunction.InverseErfc((double)x);
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MultiPrecision<Pow2.N8> expetected = MultiPrecision<Pow2.N8>.InverseErfc(x);
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MultiPrecision<Pow2.N8> error = MultiPrecision<Pow2.N8>.Abs(expetected - actual);
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MultiPrecision<Pow2.N8> rateerror = (error != 0) ? error / MultiPrecision<Pow2.N8>.Abs(expetected) : 0;
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if (double.IsNormal(actual)) {
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maxrateerror = MultiPrecision<Pow2.N8>.Max(rateerror, maxrateerror);
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}
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sw.WriteLine($"{x},{expetected:e20},{actual},{error:e8},{rateerror:e8}");
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}
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Console.WriteLine($"max error (rate): {maxrateerror:e8}");
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}
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}
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}

‎README.md‎

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@@ -81,13 +81,7 @@ Let N be the recursion times (Fn+4(z) to Fn(z)), and N until convergence is as f
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![erfc convergence bitwise](https://github.com/tk-yoshimura/ErrorFunctionApproximation/blob/main/figures/erfc_convergence_bitswise.svg)
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## Double Precision (IEEE 754) Approx
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### Taylor Series
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[C# code](https://github.com/tk-yoshimura/ErrorFunctionApproximation/blob/main/ErrorFunctionApproximation/ErrorFunction.cs)
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[erf result](https://github.com/tk-yoshimura/ErrorFunctionApproximation/blob/main/results/erf_approx.csv)
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[erfc result](https://github.com/tk-yoshimura/ErrorFunctionApproximation/blob/main/results/erfc_approx.csv)
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[inverse erf result](https://github.com/tk-yoshimura/ErrorFunctionApproximation/blob/main/results/inverf_approx.csv)
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[inverse erfc result](https://github.com/tk-yoshimura/ErrorFunctionApproximation/blob/main/results/inverfc_approx.csv)
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[C# code](https://github.com/tk-yoshimura/ErrorFunctionApproximation/blob/main/ErrorFunctionFP64/ErrorFunction.cs)
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The following is used to approximate the error of machine epsilon in the entire domain.
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![erfc az diff](https://github.com/tk-yoshimura/ErrorFunctionApproximation/blob/main/figures/erfc_diff.svg)
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A(z) taylor series (z0=1.5)
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![erfc az 12](https://github.com/tk-yoshimura/ErrorFunctionApproximation/blob/main/figures/erfc_approx_az_12.svg)
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A(z) taylor series (z0=2.5)
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![erfc az 23](https://github.com/tk-yoshimura/ErrorFunctionApproximation/blob/main/figures/erfc_approx_az_23.svg)
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A(z) taylor series (z0=3.5)
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![erfc az 34](https://github.com/tk-yoshimura/ErrorFunctionApproximation/blob/main/figures/erfc_approx_az_34.svg)
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4 to 27.25:
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![erfc x20](https://github.com/tk-yoshimura/ErrorFunctionApproximation/blob/main/figures/erfc_approx_x20.svg)
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larger 27.25:
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![erfc tolarge](https://github.com/tk-yoshimura/ErrorFunctionApproximation/blob/main/figures/erfc_approx_tolarge.svg)
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### Pade Approximant Base
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![pade definition](https://github.com/tk-yoshimura/ErrorFunctionApproximation/blob/main/figures/pade_definition.svg)
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[C# code](https://github.com/tk-yoshimura/ErrorFunctionApproximation/blob/main/ErrorFunctionApproximation/ErrorFunctionMarkII.cs)
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[pade erf precision16](https://github.com/tk-yoshimura/ErrorFunctionApproximation/blob/main/results/pade_erf_e16.txt)
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[pade erf precision32](https://github.com/tk-yoshimura/ErrorFunctionApproximation/blob/main/results/pade_erf_e32.txt)

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