public static int SolveCubic(float a, float b, float c, out float r0, out float r1, out float r2) { float p = b - a * a / 3; float p3 = p * p * p; float q = a * (2 * a * a - 9 * b) / 27 + c; float d = q * q + 4 * p3 / 27; float s = a / -3; if (d >= 0) { float z = MathF.Sqrt(d); float u = (-q + z) / 2; float v = (-q - z) / 2; u = MathF.Cbrt(u); v = MathF.Cbrt(v); r0 = s + u + v; Unsafe.SkipInit(out r1); Unsafe.SkipInit(out r2); return(1); } else { float u = MathF.Sqrt(p / -3); float v = MathF.Acos(-MathF.Sqrt(-27 / p3) * q / 2) / 3; float m = MathF.Cos(v); float n = MathF.Cos(v - MathF.PI / 2) * 1.732050808f; r0 = s + u * 2 * m; r1 = s + u * (-m - n); r2 = s + u * (-m + n); return(3); } }
/// <summary> /// Inverse formula for <see cref="RadiusToIntensity"/> /// </summary> public float IntensityToRadius(float totalIntensity, float slope, float maxIntensity) { // max radius to avoid being capped by max-intensity var r0 = maxIntensity / slope; // volume at r0 var v0 = RadiusToIntensity(r0, slope); if (totalIntensity <= v0) { // maxIntensity is a non-issue, can use simple inverse formula return(MathF.Cbrt(3 * totalIntensity / (slope * MathF.PI))); } return(r0 * (MathF.Sqrt(12 * totalIntensity / v0 - 3) / 6 + 0.5f)); }
public static void CbrtTest() { var result = 0.0f; var value = 0.0f; for (var iteration = 0; iteration < MathTests.Iterations; iteration++) { result += MathF.Cbrt(value); value += cbrtDelta; } var diff = MathF.Abs(cbrtExpectedResult - result); if (float.IsNaN(result) || (diff > MathTests.SingleEpsilon)) { throw new Exception($"Expected Result {cbrtExpectedResult,10:g9}; Actual Result {result,10:g9}"); } }
// From Linear to oklab public static Vector4 RgbAToOkLab(Vector4 c) { var l = 0.4122214708f * c.X + 0.5363325363f * c.Y + 0.0514459929f * c.Z; var m = 0.2119034982f * c.X + 0.6806995451f * c.Y + 0.1073969566f * c.Z; var s = 0.0883024619f * c.X + 0.2817188376f * c.Y + 0.6299787005f * c.Z; var l1 = MathF.Cbrt(l); var m1 = MathF.Cbrt(m); var s1 = MathF.Cbrt(s); return(new Vector4( 0.2104542553f * l1 + 0.7936177850f * m1 - 0.0040720468f * s1, 1.9779984951f * l1 - 2.4285922050f * m1 + 0.4505937099f * s1, 0.0259040371f * l1 + 0.7827717662f * m1 - 0.8086757660f * s1, c.W )); }
public static ref float cbrt(ref float src) { src = MathF.Cbrt(src); return(ref src); }
public static float cbrt(float src) => MathF.Cbrt(src);
/// <inheritdoc cref="MathF.Cbrt(float)"/> public static float Cbrt(this float value) => MathF.Cbrt(value);
public Test(Mode modeParam, TextWriter errorOutParam, TextWriter infoOutParam, Table table) { _table = table; _mode = modeParam; _errorOut = errorOutParam; _infoOut = infoOutParam; _failedOperations = new HashSet <string>(); // Validate parsing, this whole program expects little endian { uint val = 1234567891; if (Convert.ToUInt32(ToBinary(Convert.ToUInt32(ToBinary(val), 2)), 2) != val) { ReportError($"{nameof(ToBinary)} and back failed"); } } for (int testIndex = 0; testIndex < _table.Data.Length; testIndex++) { for (int testResult = 0; testResult < (_table.Data[testIndex].results?.Length ?? 0); testResult++) { var result = _table.Data[testIndex].results[testResult]; var asFloat = To <uint, float>(result.i); if (asFloat != result.f && !NaNAndBitsMatch(asFloat, result.f)) { ReportError($"FAILED PARSING {ToBinary(result.i)} to value {result.f.ToString("G9", CultureInfo.InvariantCulture)}, expected {ToBinary(result.f)}"); } } } for (int testIndex = 0; testIndex < _table.Data.Length; testIndex++) { float value = To <uint, float>(_table.Data[testIndex].initialValue); // Certain operations are funneling tests into specific ranges of values // so we aren't just using them as is, that is dVal's purpose in this code StartValidation(value); Validate(testIndex, "BIN", value); Validate(testIndex, "+", value + 0.1735f); Validate(testIndex, "-", value - 17f); Validate(testIndex, "*", value * 7.7757f); Validate(testIndex, "/", value / 0.3353f); Validate(testIndex, "%", value % 7.0f); // MATHF Validate(testIndex, nameof(MathF.Abs), MathF.Abs(value)); Validate(testIndex, nameof(MathF.Acos), MathF.Acos(value % 1f)); Validate(testIndex, nameof(MathF.Acosh), MathF.Acosh(1f + MathF.Abs(value))); Validate(testIndex, nameof(MathF.Asin), MathF.Asin(value % 1f)); Validate(testIndex, nameof(MathF.Asinh), MathF.Asinh(value)); Validate(testIndex, nameof(MathF.Atan), MathF.Atan(value)); Validate(testIndex, nameof(MathF.Atan2), MathF.Atan2(value, 0.17f)); Validate(testIndex, nameof(MathF.Atanh), MathF.Atanh(value % 1f)); Validate(testIndex, nameof(MathF.Cbrt), MathF.Cbrt(value)); Validate(testIndex, nameof(MathF.Ceiling), MathF.Ceiling(value)); Validate(testIndex, nameof(MathF.Cos), MathF.Cos(value)); Validate(testIndex, nameof(MathF.Cosh), MathF.Cosh(value % 2f)); Validate(testIndex, nameof(MathF.Exp), MathF.Exp(1f / value)); Validate(testIndex, nameof(MathF.Floor), MathF.Floor(value)); Validate(testIndex, nameof(MathF.FusedMultiplyAdd), MathF.FusedMultiplyAdd(value, 1.33f, -1.5f)); Validate(testIndex, nameof(MathF.IEEERemainder), MathF.IEEERemainder(value, 25.78f)); Validate(testIndex, nameof(MathF.Log), MathF.Log(MathF.Abs(value))); Validate(testIndex, nameof(MathF.Log) + "(x,y)", MathF.Log(MathF.Abs(value), 4f)); Validate(testIndex, nameof(MathF.Log2), MathF.Log2(MathF.Abs(value))); Validate(testIndex, nameof(MathF.Log10), MathF.Log10(MathF.Abs(value))); Validate(testIndex, nameof(MathF.Pow), MathF.Pow(MathF.Abs(value) % 1E+23f, 1.7f)); Validate(testIndex, nameof(MathF.ScaleB), MathF.ScaleB(value % 1E+23f, 2)); Validate(testIndex, nameof(MathF.Sin), MathF.Sin(value)); Validate(testIndex, nameof(MathF.Sinh), MathF.Sinh(value % 2f)); Validate(testIndex, nameof(MathF.Sqrt), MathF.Sqrt(MathF.Abs(value))); Validate(testIndex, nameof(MathF.Tan), MathF.Tan(value)); Validate(testIndex, nameof(MathF.Tanh), MathF.Tanh(value)); Validate(testIndex, nameof(MathF.Max), MathF.Max(value, 0.9f)); Validate(testIndex, nameof(MathF.MaxMagnitude), MathF.MaxMagnitude(value, -0.7f)); Validate(testIndex, nameof(MathF.Min), MathF.Min(value, 307f)); Validate(testIndex, nameof(MathF.MinMagnitude), MathF.MinMagnitude(value, -8.89f)); Validate(testIndex, nameof(MathF.Round), MathF.Round(value)); if (float.IsNaN(value) == false) { Validate(testIndex, nameof(MathF.Sign), MathF.Sign(value)); } Validate(testIndex, nameof(MathF.Truncate), MathF.Truncate(value)); // MATH double valueAsDouble = value; Validate(testIndex, $"D.{nameof(Math.Abs)}", Math.Abs(valueAsDouble)); Validate(testIndex, $"D.{nameof(Math.Acos)}", Math.Acos(valueAsDouble % 1d)); Validate(testIndex, $"D.{nameof(Math.Acosh)}", Math.Acosh(1d + Math.Abs(valueAsDouble))); Validate(testIndex, $"D.{nameof(Math.Asin)}", Math.Asin(valueAsDouble % 1d)); Validate(testIndex, $"D.{nameof(Math.Asinh)}", Math.Asinh(valueAsDouble)); Validate(testIndex, $"D.{nameof(Math.Atan)}", Math.Atan(valueAsDouble)); Validate(testIndex, $"D.{nameof(Math.Atan2)}", Math.Atan2(valueAsDouble, 0.17d)); Validate(testIndex, $"D.{nameof(Math.Atanh)}", Math.Atanh(valueAsDouble % 1d)); Validate(testIndex, $"D.{nameof(Math.Cbrt)}", Math.Cbrt(valueAsDouble)); Validate(testIndex, $"D.{nameof(Math.Ceiling)}", Math.Ceiling(valueAsDouble)); Validate(testIndex, $"D.{nameof(Math.Cos)}", Math.Cos(valueAsDouble)); Validate(testIndex, $"D.{nameof(Math.Cosh)}", Math.Cosh(valueAsDouble % 2d)); Validate(testIndex, $"D.{nameof(Math.Exp)}", Math.Exp(1d / valueAsDouble)); Validate(testIndex, $"D.{nameof(Math.Floor)}", Math.Floor(valueAsDouble)); Validate(testIndex, $"D.{nameof(Math.FusedMultiplyAdd)}", Math.FusedMultiplyAdd(valueAsDouble, 1.33d, -1.5d)); Validate(testIndex, $"D.{nameof(Math.IEEERemainder)}", Math.IEEERemainder(valueAsDouble, 25.78d)); Validate(testIndex, $"D.{nameof(Math.Log)}", Math.Log(Math.Abs(valueAsDouble))); Validate(testIndex, $"D.{nameof(Math.Log)}" + "(x,y)", Math.Log(Math.Abs(valueAsDouble), 4d)); Validate(testIndex, $"D.{nameof(Math.Log2)}", Math.Log2(Math.Abs(valueAsDouble))); Validate(testIndex, $"D.{nameof(Math.Log10)}", Math.Log10(Math.Abs(valueAsDouble))); Validate(testIndex, $"D.{nameof(Math.Pow)}", Math.Pow(Math.Abs(valueAsDouble) % 1E+23d, 1.7d)); Validate(testIndex, $"D.{nameof(Math.ScaleB)}", Math.ScaleB(valueAsDouble % 1E+23d, 2)); Validate(testIndex, $"D.{nameof(Math.Sin)}", Math.Sin(valueAsDouble)); Validate(testIndex, $"D.{nameof(Math.Sinh)}", Math.Sinh(valueAsDouble % 2d)); Validate(testIndex, $"D.{nameof(Math.Sqrt)}", Math.Sqrt(Math.Abs(valueAsDouble))); Validate(testIndex, $"D.{nameof(Math.Tan)}", Math.Tan(valueAsDouble)); Validate(testIndex, $"D.{nameof(Math.Tanh)}", Math.Tanh(valueAsDouble)); Validate(testIndex, $"D.{nameof(Math.Max)}", Math.Max(valueAsDouble, 0.9d)); Validate(testIndex, $"D.{nameof(Math.MaxMagnitude)}", Math.MaxMagnitude(valueAsDouble, -0.7d)); Validate(testIndex, $"D.{nameof(Math.Min)}", Math.Min(valueAsDouble, 307d)); Validate(testIndex, $"D.{nameof(Math.MinMagnitude)}", Math.MinMagnitude(valueAsDouble, -8.89d)); Validate(testIndex, $"D.{nameof(Math.Round)}", Math.Round(valueAsDouble)); if (float.IsNaN(value) == false) { Validate(testIndex, $"D.{nameof(Math.Sign)}", Math.Sign(valueAsDouble)); } Validate(testIndex, $"D.{nameof(Math.Truncate)}", Math.Truncate(valueAsDouble)); } }