// Licensed to the .NET Foundation under one or more agreements. // The .NET Foundation licenses this file to you under the MIT license. // See the LICENSE file in the project root for more information. /*============================================================ ** ** ** ** Purpose: Some floating-point math operations ** ** ===========================================================*/ namespace System { //This class contains only static members and doesn't require serialization. using System; using System.Runtime; using System.Runtime.CompilerServices; using System.Runtime.ConstrainedExecution; using System.Runtime.Versioning; using System.Diagnostics.Contracts; public static class Math { private static double doubleRoundLimit = 1e16d; private const int maxRoundingDigits = 15; // This table is required for the Round function which can specify the number of digits to round to private static double[] roundPower10Double = new double[] { 1E0, 1E1, 1E2, 1E3, 1E4, 1E5, 1E6, 1E7, 1E8, 1E9, 1E10, 1E11, 1E12, 1E13, 1E14, 1E15 }; public const double PI = 3.14159265358979323846; public const double E = 2.7182818284590452354; [System.Security.SecuritySafeCritical] // auto-generated [MethodImplAttribute(MethodImplOptions.InternalCall)] public static extern double Acos(double d); [System.Security.SecuritySafeCritical] // auto-generated [MethodImplAttribute(MethodImplOptions.InternalCall)] public static extern double Asin(double d); [System.Security.SecuritySafeCritical] // auto-generated [MethodImplAttribute(MethodImplOptions.InternalCall)] public static extern double Atan(double d); [System.Security.SecuritySafeCritical] // auto-generated [MethodImplAttribute(MethodImplOptions.InternalCall)] public static extern double Atan2(double y,double x); public static Decimal Ceiling(Decimal d) { return Decimal.Ceiling(d); } [System.Security.SecuritySafeCritical] // auto-generated [MethodImplAttribute(MethodImplOptions.InternalCall)] public static extern double Ceiling(double a); [System.Security.SecuritySafeCritical] // auto-generated [MethodImplAttribute(MethodImplOptions.InternalCall)] public static extern double Cos (double d); [System.Security.SecuritySafeCritical] // auto-generated [MethodImplAttribute(MethodImplOptions.InternalCall)] public static extern double Cosh(double value); public static Decimal Floor(Decimal d) { return Decimal.Floor(d); } [System.Security.SecuritySafeCritical] // auto-generated [MethodImplAttribute(MethodImplOptions.InternalCall)] public static extern double Floor(double d); [System.Security.SecuritySafeCritical] // auto-generated private static unsafe double InternalRound(double value, int digits, MidpointRounding mode) { if (Abs(value) < doubleRoundLimit) { Double power10 = roundPower10Double[digits]; value *= power10; if (mode == MidpointRounding.AwayFromZero) { double fraction = SplitFractionDouble(&value); if (Abs(fraction) >= 0.5d) { value += Sign(fraction); } } else { // On X86 this can be inlined to just a few instructions value = Round(value); } value /= power10; } return value; } [System.Security.SecuritySafeCritical] // auto-generated private unsafe static double InternalTruncate(double d) { SplitFractionDouble(&d); return d; } [System.Security.SecuritySafeCritical] // auto-generated [MethodImplAttribute(MethodImplOptions.InternalCall)] public static extern double Sin(double a); [System.Security.SecuritySafeCritical] // auto-generated [MethodImplAttribute(MethodImplOptions.InternalCall)] public static extern double Tan(double a); [System.Security.SecuritySafeCritical] // auto-generated [MethodImplAttribute(MethodImplOptions.InternalCall)] public static extern double Sinh(double value); [System.Security.SecuritySafeCritical] // auto-generated [MethodImplAttribute(MethodImplOptions.InternalCall)] public static extern double Tanh(double value); [System.Security.SecuritySafeCritical] // auto-generated [MethodImplAttribute(MethodImplOptions.InternalCall)] public static extern double Round(double a); public static double Round(double value, int digits) { if ((digits < 0) || (digits > maxRoundingDigits)) throw new ArgumentOutOfRangeException("digits", Environment.GetResourceString("ArgumentOutOfRange_RoundingDigits")); Contract.EndContractBlock(); return InternalRound(value, digits, MidpointRounding.ToEven); } public static double Round(double value, MidpointRounding mode) { return Round(value, 0, mode); } public static double Round(double value, int digits, MidpointRounding mode) { if ((digits < 0) || (digits > maxRoundingDigits)) throw new ArgumentOutOfRangeException("digits", Environment.GetResourceString("ArgumentOutOfRange_RoundingDigits")); if (mode < MidpointRounding.ToEven || mode > MidpointRounding.AwayFromZero) { throw new ArgumentException(Environment.GetResourceString("Argument_InvalidEnumValue", mode, "MidpointRounding"), "mode"); } Contract.EndContractBlock(); return InternalRound(value, digits, mode); } public static Decimal Round(Decimal d) { return Decimal.Round(d,0); } public static Decimal Round(Decimal d, int decimals) { return Decimal.Round(d,decimals); } public static Decimal Round(Decimal d, MidpointRounding mode) { return Decimal.Round(d, 0, mode); } public static Decimal Round(Decimal d, int decimals, MidpointRounding mode) { return Decimal.Round(d, decimals, mode); } [System.Security.SecurityCritical] // auto-generated [MethodImplAttribute(MethodImplOptions.InternalCall)] private static unsafe extern double SplitFractionDouble(double* value); public static Decimal Truncate(Decimal d) { return Decimal.Truncate(d); } public static double Truncate(double d) { return InternalTruncate(d); } [System.Security.SecuritySafeCritical] // auto-generated [ReliabilityContract(Consistency.WillNotCorruptState, Cer.Success)] [MethodImplAttribute(MethodImplOptions.InternalCall)] public static extern double Sqrt(double d); [System.Security.SecuritySafeCritical] // auto-generated [MethodImplAttribute(MethodImplOptions.InternalCall)] public static extern double Log (double d); [System.Security.SecuritySafeCritical] // auto-generated [MethodImplAttribute(MethodImplOptions.InternalCall)] public static extern double Log10(double d); [System.Security.SecuritySafeCritical] // auto-generated [MethodImplAttribute(MethodImplOptions.InternalCall)] public static extern double Exp(double d); [System.Security.SecuritySafeCritical] // auto-generated [MethodImplAttribute(MethodImplOptions.InternalCall)] public static extern double Pow(double x, double y); public static double IEEERemainder(double x, double y) { if (Double.IsNaN(x)) { return x; // IEEE 754-2008: NaN payload must be preserved } if (Double.IsNaN(y)) { return y; // IEEE 754-2008: NaN payload must be preserved } double regularMod = x % y; if (Double.IsNaN(regularMod)) { return Double.NaN; } if (regularMod == 0) { if (Double.IsNegative(x)) { return Double.NegativeZero; } } double alternativeResult; alternativeResult = regularMod - (Math.Abs(y) * Math.Sign(x)); if (Math.Abs(alternativeResult) == Math.Abs(regularMod)) { double divisionResult = x/y; double roundedResult = Math.Round(divisionResult); if (Math.Abs(roundedResult) > Math.Abs(divisionResult)) { return alternativeResult; } else { return regularMod; } } if (Math.Abs(alternativeResult) < Math.Abs(regularMod)) { return alternativeResult; } else { return regularMod; } } /*================================Abs========================================= **Returns the absolute value of it's argument. ============================================================================*/ [CLSCompliant(false)] public static sbyte Abs(sbyte value) { if (value >= 0) return value; else return AbsHelper(value); } private static sbyte AbsHelper(sbyte value) { Contract.Requires(value < 0, "AbsHelper should only be called for negative values! (workaround for JIT inlining)"); if (value == SByte.MinValue) throw new OverflowException(Environment.GetResourceString("Overflow_NegateTwosCompNum")); Contract.EndContractBlock(); return ((sbyte)(-value)); } public static short Abs(short value) { if (value >= 0) return value; else return AbsHelper(value); } private static short AbsHelper(short value) { Contract.Requires(value < 0, "AbsHelper should only be called for negative values! (workaround for JIT inlining)"); if (value == Int16.MinValue) throw new OverflowException(Environment.GetResourceString("Overflow_NegateTwosCompNum")); Contract.EndContractBlock(); return (short) -value; } public static int Abs(int value) { if (value >= 0) return value; else return AbsHelper(value); } private static int AbsHelper(int value) { Contract.Requires(value < 0, "AbsHelper should only be called for negative values! (workaround for JIT inlining)"); if (value == Int32.MinValue) throw new OverflowException(Environment.GetResourceString("Overflow_NegateTwosCompNum")); Contract.EndContractBlock(); return -value; } public static long Abs(long value) { if (value >= 0) return value; else return AbsHelper(value); } private static long AbsHelper(long value) { Contract.Requires(value < 0, "AbsHelper should only be called for negative values! (workaround for JIT inlining)"); if (value == Int64.MinValue) throw new OverflowException(Environment.GetResourceString("Overflow_NegateTwosCompNum")); Contract.EndContractBlock(); return -value; } [System.Security.SecuritySafeCritical] // auto-generated [MethodImplAttribute(MethodImplOptions.InternalCall)] extern public static float Abs(float value); // This is special code to handle NaN (We need to make sure NaN's aren't // negated). In CSharp, the else clause here should always be taken if // value is NaN, since the normal case is taken if and only if value < 0. // To illustrate this completely, a compiler has translated this into: // "load value; load 0; bge; ret -value ; ret value". // The bge command branches for comparisons with the unordered NaN. So // it runs the else case, which returns +value instead of negating it. // return (value < 0) ? -value : value; [System.Security.SecuritySafeCritical] // auto-generated [MethodImplAttribute(MethodImplOptions.InternalCall)] extern public static double Abs(double value); // This is special code to handle NaN (We need to make sure NaN's aren't // negated). In CSharp, the else clause here should always be taken if // value is NaN, since the normal case is taken if and only if value < 0. // To illustrate this completely, a compiler has translated this into: // "load value; load 0; bge; ret -value ; ret value". // The bge command branches for comparisons with the unordered NaN. So // it runs the else case, which returns +value instead of negating it. // return (value < 0) ? -value : value; public static Decimal Abs(Decimal value) { return Decimal.Abs(value); } /*================================MAX========================================= **Returns the larger of val1 and val2 ============================================================================*/ [CLSCompliant(false)] [ReliabilityContract(Consistency.WillNotCorruptState, Cer.Success)] [System.Runtime.Versioning.NonVersionable] public static sbyte Max(sbyte val1, sbyte val2) { return (val1>=val2)?val1:val2; } [ReliabilityContract(Consistency.WillNotCorruptState, Cer.Success)] [System.Runtime.Versioning.NonVersionable] public static byte Max(byte val1, byte val2) { return (val1>=val2)?val1:val2; } [ReliabilityContract(Consistency.WillNotCorruptState, Cer.Success)] [System.Runtime.Versioning.NonVersionable] public static short Max(short val1, short val2) { return (val1>=val2)?val1:val2; } [CLSCompliant(false)] [ReliabilityContract(Consistency.WillNotCorruptState, Cer.Success)] [System.Runtime.Versioning.NonVersionable] public static ushort Max(ushort val1, ushort val2) { return (val1>=val2)?val1:val2; } [ReliabilityContract(Consistency.WillNotCorruptState, Cer.Success)] [System.Runtime.Versioning.NonVersionable] public static int Max(int val1, int val2) { return (val1>=val2)?val1:val2; } [CLSCompliant(false)] [ReliabilityContract(Consistency.WillNotCorruptState, Cer.Success)] [System.Runtime.Versioning.NonVersionable] public static uint Max(uint val1, uint val2) { return (val1>=val2)?val1:val2; } [ReliabilityContract(Consistency.WillNotCorruptState, Cer.Success)] [System.Runtime.Versioning.NonVersionable] public static long Max(long val1, long val2) { return (val1>=val2)?val1:val2; } [CLSCompliant(false)] [ReliabilityContract(Consistency.WillNotCorruptState, Cer.Success)] [System.Runtime.Versioning.NonVersionable] public static ulong Max(ulong val1, ulong val2) { return (val1>=val2)?val1:val2; } [ReliabilityContract(Consistency.WillNotCorruptState, Cer.Success)] public static float Max(float val1, float val2) { if (val1 > val2) return val1; if (Single.IsNaN(val1)) return val1; return val2; } [ReliabilityContract(Consistency.WillNotCorruptState, Cer.Success)] public static double Max(double val1, double val2) { if (val1 > val2) return val1; if (Double.IsNaN(val1)) return val1; return val2; } [ReliabilityContract(Consistency.WillNotCorruptState, Cer.Success)] public static Decimal Max(Decimal val1, Decimal val2) { return Decimal.Max(val1,val2); } /*================================MIN========================================= **Returns the smaller of val1 and val2. ============================================================================*/ [CLSCompliant(false)] [ReliabilityContract(Consistency.WillNotCorruptState, Cer.Success)] [System.Runtime.Versioning.NonVersionable] public static sbyte Min(sbyte val1, sbyte val2) { return (val1<=val2)?val1:val2; } [ReliabilityContract(Consistency.WillNotCorruptState, Cer.Success)] [System.Runtime.Versioning.NonVersionable] public static byte Min(byte val1, byte val2) { return (val1<=val2)?val1:val2; } [ReliabilityContract(Consistency.WillNotCorruptState, Cer.Success)] [System.Runtime.Versioning.NonVersionable] public static short Min(short val1, short val2) { return (val1<=val2)?val1:val2; } [CLSCompliant(false)] [ReliabilityContract(Consistency.WillNotCorruptState, Cer.Success)] [System.Runtime.Versioning.NonVersionable] public static ushort Min(ushort val1, ushort val2) { return (val1<=val2)?val1:val2; } [ReliabilityContract(Consistency.WillNotCorruptState, Cer.Success)] [System.Runtime.Versioning.NonVersionable] public static int Min(int val1, int val2) { return (val1<=val2)?val1:val2; } [CLSCompliant(false)] [ReliabilityContract(Consistency.WillNotCorruptState, Cer.Success)] [System.Runtime.Versioning.NonVersionable] public static uint Min(uint val1, uint val2) { return (val1<=val2)?val1:val2; } [ReliabilityContract(Consistency.WillNotCorruptState, Cer.Success)] [System.Runtime.Versioning.NonVersionable] public static long Min(long val1, long val2) { return (val1<=val2)?val1:val2; } [CLSCompliant(false)] [ReliabilityContract(Consistency.WillNotCorruptState, Cer.Success)] [System.Runtime.Versioning.NonVersionable] public static ulong Min(ulong val1, ulong val2) { return (val1<=val2)?val1:val2; } [ReliabilityContract(Consistency.WillNotCorruptState, Cer.Success)] public static float Min(float val1, float val2) { if (val1 < val2) return val1; if (Single.IsNaN(val1)) return val1; return val2; } [ReliabilityContract(Consistency.WillNotCorruptState, Cer.Success)] public static double Min(double val1, double val2) { if (val1 < val2) return val1; if (Double.IsNaN(val1)) return val1; return val2; } [ReliabilityContract(Consistency.WillNotCorruptState, Cer.Success)] public static Decimal Min(Decimal val1, Decimal val2) { return Decimal.Min(val1,val2); } /*=====================================Log====================================== ** ==============================================================================*/ public static double Log(double a, double newBase) { if (Double.IsNaN(a)) { return a; // IEEE 754-2008: NaN payload must be preserved } if (Double.IsNaN(newBase)) { return newBase; // IEEE 754-2008: NaN payload must be preserved } if (newBase == 1) return Double.NaN; if (a != 1 && (newBase == 0 || Double.IsPositiveInfinity(newBase))) return Double.NaN; return (Log(a)/Log(newBase)); } // Sign function for VB. Returns -1, 0, or 1 if the sign of the number // is negative, 0, or positive. Throws for floating point NaN's. [CLSCompliant(false)] public static int Sign(sbyte value) { if (value < 0) return -1; else if (value > 0) return 1; else return 0; } // Sign function for VB. Returns -1, 0, or 1 if the sign of the number // is negative, 0, or positive. Throws for floating point NaN's. public static int Sign(short value) { if (value < 0) return -1; else if (value > 0) return 1; else return 0; } // Sign function for VB. Returns -1, 0, or 1 if the sign of the number // is negative, 0, or positive. Throws for floating point NaN's. public static int Sign(int value) { if (value < 0) return -1; else if (value > 0) return 1; else return 0; } public static int Sign(long value) { if (value < 0) return -1; else if (value > 0) return 1; else return 0; } public static int Sign (float value) { if (value < 0) return -1; else if (value > 0) return 1; else if (value == 0) return 0; throw new ArithmeticException(Environment.GetResourceString("Arithmetic_NaN")); } public static int Sign(double value) { if (value < 0) return -1; else if (value > 0) return 1; else if (value == 0) return 0; throw new ArithmeticException(Environment.GetResourceString("Arithmetic_NaN")); } public static int Sign(Decimal value) { if (value < 0) return -1; else if (value > 0) return 1; else return 0; } public static long BigMul(int a, int b) { return ((long)a) * b; } public static int DivRem(int a, int b, out int result) { result = a%b; return a/b; } public static long DivRem(long a, long b, out long result) { result = a%b; return a/b; } } }