mirror of
https://github.com/danbulant/Cosmos
synced 2026-05-19 12:30:32 +00:00
594 lines
17 KiB
C#
594 lines
17 KiB
C#
using System;
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using Cosmos.Debug.Kernel;
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using Cosmos.IL2CPU.Plugs;
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namespace Cosmos.System.Plugs.System
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{
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[Plug(Target = typeof(Math))]
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public static class MathImpl
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{
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internal static Debugger mDebugger = new Debugger("System", "Math Plugs");
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#region Internal Constants
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private const double sq2p1 = 2.414213562373095048802e0F;
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private const double sq2m1 = .414213562373095048802e0F;
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private const double pio2 = 1.570796326794896619231e0F;
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private const double pio4 = .785398163397448309615e0F;
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private const double log2e = 1.4426950408889634073599247F;
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private const double sqrt2 = 1.4142135623730950488016887F;
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private const double ln2 = 6.93147180559945286227e-01F;
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private const double atan_p4 = .161536412982230228262e2F;
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private const double atan_p3 = .26842548195503973794141e3F;
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private const double atan_p2 = .11530293515404850115428136e4F;
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private const double atan_p1 = .178040631643319697105464587e4F;
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private const double atan_p0 = .89678597403663861959987488e3F;
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private const double atan_q4 = .5895697050844462222791e2F;
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private const double atan_q3 = .536265374031215315104235e3F;
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private const double atan_q2 = .16667838148816337184521798e4F;
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private const double atan_q1 = .207933497444540981287275926e4F;
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private const double atan_q0 = .89678597403663861962481162e3F;
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#endregion
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public const double PI = 3.1415926535897932384626433832795;
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public const double E = 2.71828182845904523536;
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#region Abs
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public static double Abs(double value)
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{
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if (value < 0)
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{
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return -value;
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}
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else
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{
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return value;
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}
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}
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public static float Abs(float value)
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{
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if (value < 0)
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{
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return -value;
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}
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else
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{
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return value;
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}
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}
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#endregion
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#region Acos
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public static double Acos(double x)
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{
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if ((x > 1.0) || (x < -1.0))
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throw new ArgumentOutOfRangeException("Domain error");
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return (pio2 - Asin(x));
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}
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#endregion
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#region Asin
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public static double Asin(double x)
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{
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if (x > 1.0F)
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{
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throw new ArgumentOutOfRangeException("Domain error");
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}
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double sign = 1F, temp;
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if (x < 0.0F)
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{
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x = -x;
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sign = -1.0F;
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}
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temp = Sqrt(1.0F - (x * x));
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if (x > 0.7)
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{
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temp = pio2 - Atan(temp / x);
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}
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else
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{
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temp = Atan(x / temp);
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}
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return (sign * temp);
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}
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#endregion
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#region Atan
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public static double Atan(double x)
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{
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return ((x > 0F) ? atans(x) : (-atans(-x)));
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}
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#endregion
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#region Atan2
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public static double Atan2(double x, double y)
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{
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if ((x + y) == x)
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{
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if ((x == 0F) & (y == 0F))
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return 0F;
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if (x >= 0.0F)
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return pio2;
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return (-pio2);
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}
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if (y < 0.0F)
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{
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if (x >= 0.0F)
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return ((pio2 * 2) - atans((-x) / y));
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return (((-pio2) * 2) + atans(x / y));
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}
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if (x > 0.0F)
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{
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return (atans(x / y));
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}
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return (-atans((-x) / y));
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//return (((x + y) == x) ? (((x == 0F) & (y == 0F)) ? 0F : ((x >= 0F) ? pio2 : (-pio2))) : ((y < 0F) ? ((x >= 0F) ? ((pio2 * 2) - atans((-x) / y)) : (((-pio2) * 2) + atans(x / y))) : ((x > 0F) ? atans(x / y) : -atans((-x) / y))));
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}
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#endregion
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#region Ceiling
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public static double Ceiling(double a)
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{
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// should be using assembler for bigger values than int or long max
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if (a == Double.NaN || a == Double.NegativeInfinity || a == Double.PositiveInfinity)
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return a;
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int i = (a - (int)a > 0) ? (int)(a + 1) : (int)a;
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return i;
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}
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#endregion
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#region Cos
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public static double Cos(double x)
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{
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// First we need to anchor it to a valid range.
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while (x > (2 * PI))
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{
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x -= (2 * PI);
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}
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if (x < 0)
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x = -x;
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byte quadrand = 0;
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if ((x > (PI / 2F)) && (x < (PI)))
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{
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quadrand = 1;
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x = PI - x;
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}
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if ((x > (PI)) && (x < ((3F * PI) / 2)))
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{
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quadrand = 2;
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x = x - PI;
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}
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if ((x > ((3F * PI) / 2)))
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{
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quadrand = 3;
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x = (2F * PI) - x;
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}
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const double c1 = 0.9999999999999999999999914771;
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const double c2 = -0.4999999999999999999991637437;
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const double c3 = 0.04166666666666666665319411988;
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const double c4 = -0.00138888888888888880310186415;
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const double c5 = 0.00002480158730158702330045157;
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const double c6 = -0.000000275573192239332256421489;
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const double c7 = 0.000000002087675698165412591559;
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const double c8 = -0.0000000000114707451267755432394;
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const double c9 = 0.0000000000000477945439406649917;
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const double c10 = -0.00000000000000015612263428827781;
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const double c11 = 0.00000000000000000039912654507924;
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double x2 = x * x;
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if (quadrand == 0 || quadrand == 3)
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{
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return (c1 + (x2 * (c2 + (x2 * (c3 + (x2 * (c4 + (x2 * (c5 + (x2 * (c6 + (x2 * (c7 + (x2 * (c8 + (x2 * (c9 + (x2 * (c10 + (x2 * c11))))))))))))))))))));
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}
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else
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{
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return -(c1 + (x2 * (c2 + (x2 * (c3 + (x2 * (c4 + (x2 * (c5 + (x2 * (c6 + (x2 * (c7 + (x2 * (c8 + (x2 * (c9 + (x2 * (c10 + (x2 * c11))))))))))))))))))));
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}
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}
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#endregion
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#region Cosh
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public static double Cosh(double x)
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{
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if (x < 0.0F)
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x = -x;
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return ((x == 0F) ? 1F : ((x <= (ln2 / 2)) ? (1 + (_power((Exp(x) - 1), 2) / (2 * Exp(x)))) : ((x <= 22F) ? ((Exp(x) + (1 / Exp(x))) / 2) : (0.5F * (Exp(x) + Exp(-x))))));
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}
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#endregion
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#region Exp
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public static double Exp(double x)
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{
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double c;
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int n = 1;
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double ex = 1F;
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double m = 1F;
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while (x > 10.000F)
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{
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m *= 22026.4657948067;
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x -= 10F;
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}
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while (x > 01.000F)
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{
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m *= E;
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x -= 1F;
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}
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while (x > 00.100F)
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{
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m *= 1.10517091807565; ;
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x -= 0.1F;
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}
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while (x > 00.010F)
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{
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m *= 1.01005016708417;
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x -= 0.01F;
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}
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for (int y = 1; y <= 4; y++)
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{
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c = _power(x, y);
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ex += c / (double)n;
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n *= (y + 1);
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}
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return ex * m;
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}
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#endregion
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#region Floor
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public static double Floor(double a)
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{
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// should be using assembler for bigger values than int or long max
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if (a == Double.NaN || a == Double.NegativeInfinity || a == Double.PositiveInfinity)
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return a;
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int i = (a - (int)a < 0) ? (int)(a - 1) : (int)a;
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return i;
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}
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#endregion
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#region Log (base e)
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public static double Log(double x)
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{
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return Log(x, E);
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}
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#endregion
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#region Log (base specified)
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public static double Log(double x, double newBase)
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{
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if (x == 0.0F)
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{
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return double.NegativeInfinity;
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}
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if ((x < 1.0F) && (newBase < 1.0F))
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{
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throw new ArgumentOutOfRangeException("can't compute Log");
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}
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double partial = 0.5F;
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double integer = 0F;
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double fractional = 0.0F;
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while (x < 1.0F)
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{
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integer -= 1F;
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x *= newBase;
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}
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while (x >= newBase)
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{
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integer += 1F;
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x /= newBase;
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}
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x *= x;
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while (partial >= 2.22045e-016)
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{
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if (x >= newBase)
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{
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fractional += partial;
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x = x / newBase;
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}
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partial *= 0.5F;
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x *= x;
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}
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return (integer + fractional);
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}
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#endregion
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#region Log10
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public static double Log10(double x)
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{
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return Log(x, 10F);
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}
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#endregion
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#region Pow
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public static double Pow(double x, double y)
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{
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if (x <= 0.0F)
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{
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double temp = 0F;
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long l;
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if (x == 0.0F && y <= 0.0F)
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throw new ArgumentException();
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l = (long)Floor(y);
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if (l != y)
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temp = Exp(y * Log(-x));
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if ((l % 2) == 1)
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temp = -temp;
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return (temp);
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}
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return (Exp(y * Log(x)));
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//if (y == 0)
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//{
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// return 1;
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//}
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//else if (y == 1)
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//{
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// return x;
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//}
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//else
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//{
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// double xResult = x;
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// for (int i = 2; i <= y; i++)
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// {
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// xResult = xResult * x;
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// }
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// return xResult;
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//}
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}
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#endregion
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#region Round
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public static double Round(double d)
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{
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return ((Math.Floor(d) % 2 == 0) ? Math.Floor(d) : Math.Ceiling(d));
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}
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#endregion
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#region Sin
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public static double Sin(double x)
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{
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// First we need to anchor it to a valid range.
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while (x > (2 * PI))
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{
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x -= (2 * PI);
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}
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return Cos((PI / 2.0F) - x);
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}
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#endregion
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#region Sinh
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public static double Sinh(double x)
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{
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if (x < 0F)
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x = -x;
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if (x <= 22F)
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{
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double Ex_1 = Tanh(x / 2) * (Exp(x) + 1);
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return ((Ex_1 + (Ex_1 / (Ex_1 - 1))) / 2);
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}
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else
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{
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return (Exp(x) / 2);
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}
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}
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#endregion
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#region Sqrt
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public static double Sqrt(double x)
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{
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double i = 0;
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double x1 = 0.0F;
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double x2 = 0.0F;
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if (x == 0F)
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return 0F;
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while ((i * i) <= x)
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{
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i += 0.1F;
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}
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x1 = i;
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// this originally used another variable here,
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// but the use of i was done, thus it's faster
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// to re-use the variable.
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for (i = 0; i < 10; i++)
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{
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x2 = x;
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x2 /= x1;
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x2 += x1;
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x2 /= 2;
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x1 = x2;
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}
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return x2;
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}
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#endregion
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#region Tan
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public static double Tan(double x)
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{
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// First we need to anchor it to a valid range.
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while (x > (2 * PI))
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{
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x -= (2 * PI);
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}
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byte octant = (byte)Floor(x * (1 / (PI / 4)));
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switch (octant)
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{
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case 0:
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x = x * (4 / PI);
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break;
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case 1:
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x = ((PI / 2) - x) * (4 / PI);
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break;
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case 2:
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x = (x - (PI / 2)) * (4 / PI);
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break;
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case 3:
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x = (PI - x) * (4 / PI);
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break;
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case 4:
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x = (x - PI) * (4 / PI);
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break;
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case 5:
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x = ((3.5 * PI) - x) * (4 / PI);
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break;
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case 6:
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x = (x - (3.5 * PI)) * (4 / PI);
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break;
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case 7:
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x = ((2 * PI) - x) * (4 / PI);
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break;
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}
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const double c1 = 4130240.588996024013440146267;
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const double c2 = -349781.8562517381616631012487;
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const double c3 = 6170.317758142494245331944348;
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const double c4 = -27.94920941380194872760036319;
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const double c5 = 0.0175143807040383602666563058;
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const double c6 = 5258785.647179987798541780825;
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const double c7 = -1526650.549072940686776259893;
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const double c8 = 54962.51616062905361152230566;
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const double c9 = -497.495460280917265024506937;
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double x2 = x * x;
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if (octant == 0 || octant == 4)
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{
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return ((x * (c1 + (x2 * (c2 + (x2 * (c3 + (x2 * (c4 + (x2 * c5))))))))) / (c6 + (x2 * (c7 + (x2 * (c8 + (x2 * (c9 + x2))))))));
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}
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else if (octant == 1 || octant == 5)
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{
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return (1 / ((x * (c1 + (x2 * (c2 + (x2 * (c3 + (x2 * (c4 + (x2 * c5))))))))) / (c6 + (x2 * (c7 + (x2 * (c8 + (x2 * (c9 + x2)))))))));
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}
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else if (octant == 2 || octant == 6)
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{
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return (-1 / ((x * (c1 + (x2 * (c2 + (x2 * (c3 + (x2 * (c4 + (x2 * c5))))))))) / (c6 + (x2 * (c7 + (x2 * (c8 + (x2 * (c9 + x2)))))))));
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}
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else // octant == 3 || octant == 7
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{
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return -((x * (c1 + (x2 * (c2 + (x2 * (c3 + (x2 * (c4 + (x2 * c5))))))))) / (c6 + (x2 * (c7 + (x2 * (c8 + (x2 * (c9 + x2))))))));
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}
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}
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#endregion
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#region Tanh
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public static double Tanh(double x)
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{
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return (expm1(2F * x) / (expm1(2F * x) + 2F));
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}
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#endregion
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#region Truncate
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public static double Truncate(double x)
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{
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return ((x == 0) ? 0F : ((x > 0F) ? Floor(x) : Ceiling(x)));
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}
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#endregion
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//#region Factorial (only used in Sin(), not plug )
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//public static int Factorial(int n)
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//{
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// if (n == 0)
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// return 1;
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// else
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// return n * Factorial(n - 1);
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//}
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//#endregion
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#region Internaly used functions
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#region expm1
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private static double expm1(double x)
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{
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double u = Exp(x);
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return ((u == 1.0F) ? x : ((u - 1.0F == -1.0F) ? -1.0F : ((u - 1.0F) * x / Log(u))));
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}
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#endregion
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#region _power
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private static double _power(double x, int c)
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{
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if (c == 0)
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return 1.0F;
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int _c;
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double ret = x;
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if (c >= 0f)
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{
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for (_c = 1; _c < c; _c++)
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ret *= ret;
|
|
}
|
|
else
|
|
{
|
|
for (_c = 1; _c < c; _c++)
|
|
ret /= ret;
|
|
}
|
|
|
|
return ret;
|
|
}
|
|
#endregion
|
|
|
|
#region atans
|
|
private static double atans(double x)
|
|
{
|
|
if (x < sq2m1)
|
|
{
|
|
return atanx(x);
|
|
}
|
|
else if (x > sq2p1)
|
|
{
|
|
return (pio2 - atanx(1.0F / x));
|
|
}
|
|
else
|
|
{
|
|
return (pio4 + atanx((x - 1.0F) / (x + 1.0F)));
|
|
}
|
|
}
|
|
#endregion
|
|
|
|
#region atanx
|
|
private static double atanx(double x)
|
|
{
|
|
double argsq, value;
|
|
|
|
/* get denormalized add in following if range arg**10 is much smaller
|
|
than q1, so check for that case
|
|
*/
|
|
if ((x > -.01) && (x < .01))
|
|
{
|
|
value = (atan_p0 / atan_q0);
|
|
}
|
|
else
|
|
{
|
|
argsq = x * x;
|
|
value = ((((atan_p4 * argsq + atan_p3) * argsq + atan_p2) * argsq + atan_p1) * argsq + atan_p0) / (((((argsq + atan_q4) * argsq + atan_q3) * argsq + atan_q2) * argsq + atan_q1) * argsq + atan_q0);
|
|
}
|
|
return value * x;
|
|
|
|
//if (-.01 < arg && arg < .01)
|
|
// value = p0 / q0;
|
|
//double ArgSquared = x * x;
|
|
//return
|
|
// (((((atan_p4 * ArgSquared + atan_p3) * ArgSquared + atan_p2) * ArgSquared + atan_p1) * ArgSquared + atan_p0)
|
|
// /
|
|
// (((((ArgSquared + atan_q4) * ArgSquared + atan_q3) * ArgSquared + atan_q2) * ArgSquared + atan_q1) * ArgSquared + atan_q0) * x);
|
|
}
|
|
#endregion
|
|
|
|
#endregion
|
|
}
|
|
}
|