|
// Licensed to the .NET Foundation under one or more agreements.
// The .NET Foundation licenses this file to you under the MIT license.
using System.Buffers.Binary;
using System.Diagnostics;
using System.Diagnostics.CodeAnalysis;
using System.Globalization;
using System.Numerics;
using System.Runtime.CompilerServices;
using System.Runtime.InteropServices;
using System.Runtime.Versioning;
namespace System
{
/// <summary>
/// Represents a double-precision floating-point number.
/// </summary>
[Serializable]
[StructLayout(LayoutKind.Sequential)]
[TypeForwardedFrom("mscorlib, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089")]
public readonly struct Double
: IComparable,
IConvertible,
ISpanFormattable,
IComparable<double>,
IEquatable<double>,
IBinaryFloatingPointIeee754<double>,
IMinMaxValue<double>,
IUtf8SpanFormattable,
IBinaryFloatParseAndFormatInfo<double>
{
private readonly double m_value; // Do not rename (binary serialization)
//
// Public Constants
//
public const double MinValue = -1.7976931348623157E+308;
public const double MaxValue = 1.7976931348623157E+308;
// Note Epsilon should be a double whose hex representation is 0x1
// on little endian machines.
public const double Epsilon = 4.9406564584124654E-324;
public const double NegativeInfinity = (double)-1.0 / (double)(0.0);
public const double PositiveInfinity = (double)1.0 / (double)(0.0);
public const double NaN = (double)0.0 / (double)0.0;
/// <summary>Represents the additive identity (0).</summary>
internal const double AdditiveIdentity = 0.0;
/// <summary>Represents the multiplicative identity (1).</summary>
internal const double MultiplicativeIdentity = 1.0;
/// <summary>Represents the number one (1).</summary>
internal const double One = 1.0;
/// <summary>Represents the number zero (0).</summary>
internal const double Zero = 0.0;
/// <summary>Represents the number negative one (-1).</summary>
internal const double NegativeOne = -1.0;
/// <summary>Represents the number negative zero (-0).</summary>
public const double NegativeZero = -0.0;
/// <summary>Represents the natural logarithmic base, specified by the constant, e.</summary>
/// <remarks>Euler's number is approximately 2.7182818284590452354.</remarks>
public const double E = Math.E;
/// <summary>Represents the ratio of the circumference of a circle to its diameter, specified by the constant, PI.</summary>
/// <remarks>Pi is approximately 3.1415926535897932385.</remarks>
public const double Pi = Math.PI;
/// <summary>Represents the number of radians in one turn, specified by the constant, Tau.</summary>
/// <remarks>Tau is approximately 6.2831853071795864769.</remarks>
public const double Tau = Math.Tau;
//
// Constants for manipulating the private bit-representation
//
internal const ulong SignMask = 0x8000_0000_0000_0000;
internal const int SignShift = 63;
internal const byte ShiftedSignMask = (byte)(SignMask >> SignShift);
internal const ulong BiasedExponentMask = 0x7FF0_0000_0000_0000;
internal const int BiasedExponentShift = 52;
internal const int BiasedExponentLength = 11;
internal const ushort ShiftedExponentMask = (ushort)(BiasedExponentMask >> BiasedExponentShift);
internal const ulong TrailingSignificandMask = 0x000F_FFFF_FFFF_FFFF;
internal const byte MinSign = 0;
internal const byte MaxSign = 1;
internal const ushort MinBiasedExponent = 0x0000;
internal const ushort MaxBiasedExponent = 0x07FF;
internal const ushort ExponentBias = 1023;
internal const short MinExponent = -1022;
internal const short MaxExponent = +1023;
internal const ulong MinTrailingSignificand = 0x0000_0000_0000_0000;
internal const ulong MaxTrailingSignificand = 0x000F_FFFF_FFFF_FFFF;
internal const int TrailingSignificandLength = 52;
internal const int SignificandLength = TrailingSignificandLength + 1;
// Constants representing the private bit-representation for various default values
internal const ulong PositiveZeroBits = 0x0000_0000_0000_0000;
internal const ulong NegativeZeroBits = 0x8000_0000_0000_0000;
internal const ulong EpsilonBits = 0x0000_0000_0000_0001;
internal const ulong PositiveInfinityBits = 0x7FF0_0000_0000_0000;
internal const ulong NegativeInfinityBits = 0xFFF0_0000_0000_0000;
internal const ulong SmallestNormalBits = 0x0010_0000_0000_0000;
internal ushort BiasedExponent
{
get
{
ulong bits = BitConverter.DoubleToUInt64Bits(m_value);
return ExtractBiasedExponentFromBits(bits);
}
}
internal short Exponent
{
get
{
return (short)(BiasedExponent - ExponentBias);
}
}
internal ulong Significand
{
get
{
return TrailingSignificand | ((BiasedExponent != 0) ? (1UL << BiasedExponentShift) : 0UL);
}
}
internal ulong TrailingSignificand
{
get
{
ulong bits = BitConverter.DoubleToUInt64Bits(m_value);
return ExtractTrailingSignificandFromBits(bits);
}
}
internal static ushort ExtractBiasedExponentFromBits(ulong bits)
{
return (ushort)((bits >> BiasedExponentShift) & ShiftedExponentMask);
}
internal static ulong ExtractTrailingSignificandFromBits(ulong bits)
{
return bits & TrailingSignificandMask;
}
/// <summary>Determines whether the specified value is finite (zero, subnormal, or normal).</summary>
/// <remarks>This effectively checks the value is not NaN and not infinite.</remarks>
[NonVersionable]
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static bool IsFinite(double d)
{
ulong bits = BitConverter.DoubleToUInt64Bits(d);
return (~bits & PositiveInfinityBits) != 0;
}
/// <summary>Determines whether the specified value is infinite.</summary>
[NonVersionable]
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static bool IsInfinity(double d)
{
ulong bits = BitConverter.DoubleToUInt64Bits(d);
return (bits & ~SignMask) == PositiveInfinityBits;
}
/// <summary>Determines whether the specified value is NaN.</summary>
[NonVersionable]
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static bool IsNaN(double d)
{
// A NaN will never equal itself so this is an
// easy and efficient way to check for NaN.
#pragma warning disable CS1718
return d != d;
#pragma warning restore CS1718
}
[NonVersionable]
[MethodImpl(MethodImplOptions.AggressiveInlining)]
internal static bool IsNaNOrZero(double d)
{
ulong bits = BitConverter.DoubleToUInt64Bits(d);
return ((bits - 1) & ~SignMask) >= PositiveInfinityBits;
}
/// <summary>Determines whether the specified value is negative.</summary>
[NonVersionable]
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static bool IsNegative(double d)
{
return BitConverter.DoubleToInt64Bits(d) < 0;
}
/// <summary>Determines whether the specified value is negative infinity.</summary>
[NonVersionable]
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static bool IsNegativeInfinity(double d)
{
return d == NegativeInfinity;
}
/// <summary>Determines whether the specified value is normal (finite, but not zero or subnormal).</summary>
/// <remarks>This effectively checks the value is not NaN, not infinite, not subnormal, and not zero.</remarks>
[NonVersionable]
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static bool IsNormal(double d)
{
ulong bits = BitConverter.DoubleToUInt64Bits(d);
return ((bits & ~SignMask) - SmallestNormalBits) < (PositiveInfinityBits - SmallestNormalBits);
}
/// <summary>Determines whether the specified value is positive infinity.</summary>
[NonVersionable]
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static bool IsPositiveInfinity(double d)
{
return d == PositiveInfinity;
}
/// <summary>Determines whether the specified value is subnormal (finite, but not zero or normal).</summary>
/// <remarks>This effectively checks the value is not NaN, not infinite, not normal, and not zero.</remarks>
[NonVersionable]
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static bool IsSubnormal(double d)
{
ulong bits = BitConverter.DoubleToUInt64Bits(d);
return ((bits & ~SignMask) - 1) < MaxTrailingSignificand;
}
[NonVersionable]
[MethodImpl(MethodImplOptions.AggressiveInlining)]
internal static bool IsZero(double d)
{
return d == 0;
}
// Compares this object to another object, returning an instance of System.Relation.
// Null is considered less than any instance.
//
// If object is not of type Double, this method throws an ArgumentException.
//
// Returns a value less than zero if this object
//
public int CompareTo(object? value)
{
if (value is not double other)
{
return (value is null) ? 1 : throw new ArgumentException(SR.Arg_MustBeDouble);
}
return CompareTo(other);
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public int CompareTo(double value)
{
if (m_value < value)
{
return -1;
}
if (m_value > value)
{
return 1;
}
if (m_value == value)
{
return 0;
}
if (IsNaN(m_value))
{
return IsNaN(value) ? 0 : -1;
}
Debug.Assert(IsNaN(value));
return 1;
}
// True if obj is another Double with the same value as the current instance. This is
// a method of object equality, that only returns true if obj is also a double.
public override bool Equals([NotNullWhen(true)] object? obj)
{
return (obj is double other) && Equals(other);
}
/// <inheritdoc cref="IEqualityOperators{TSelf, TOther, TResult}.op_Equality(TSelf, TOther)" />
[NonVersionable]
public static bool operator ==(double left, double right) => left == right;
/// <inheritdoc cref="IEqualityOperators{TSelf, TOther, TResult}.op_Inequality(TSelf, TOther)" />
[NonVersionable]
public static bool operator !=(double left, double right) => left != right;
/// <inheritdoc cref="IComparisonOperators{TSelf, TOther, TResult}.op_LessThan(TSelf, TOther)" />
[NonVersionable]
public static bool operator <(double left, double right) => left < right;
/// <inheritdoc cref="IComparisonOperators{TSelf, TOther, TResult}.op_GreaterThan(TSelf, TOther)" />
[NonVersionable]
public static bool operator >(double left, double right) => left > right;
/// <inheritdoc cref="IComparisonOperators{TSelf, TOther, TResult}.op_LessThanOrEqual(TSelf, TOther)" />
[NonVersionable]
public static bool operator <=(double left, double right) => left <= right;
/// <inheritdoc cref="IComparisonOperators{TSelf, TOther, TResult}.op_GreaterThanOrEqual(TSelf, TOther)" />
[NonVersionable]
public static bool operator >=(double left, double right) => left >= right;
public bool Equals(double obj)
{
if (obj == m_value)
{
return true;
}
return IsNaN(obj) && IsNaN(m_value);
}
// The hashcode for a double is the absolute value of the integer representation
// of that double.
[MethodImpl(MethodImplOptions.AggressiveInlining)] // 64-bit constants make the IL unusually large that makes the inliner to reject the method
public override int GetHashCode()
{
ulong bits = BitConverter.DoubleToUInt64Bits(m_value);
if (IsNaNOrZero(m_value))
{
// Ensure that all NaNs and both zeros have the same hash code
bits &= PositiveInfinityBits;
}
return unchecked((int)bits) ^ ((int)(bits >> 32));
}
public override string ToString()
{
return Number.FormatDouble(m_value, null, NumberFormatInfo.CurrentInfo);
}
public string ToString([StringSyntax(StringSyntaxAttribute.NumericFormat)] string? format)
{
return Number.FormatDouble(m_value, format, NumberFormatInfo.CurrentInfo);
}
public string ToString(IFormatProvider? provider)
{
return Number.FormatDouble(m_value, null, NumberFormatInfo.GetInstance(provider));
}
public string ToString([StringSyntax(StringSyntaxAttribute.NumericFormat)] string? format, IFormatProvider? provider)
{
return Number.FormatDouble(m_value, format, NumberFormatInfo.GetInstance(provider));
}
public bool TryFormat(Span<char> destination, out int charsWritten, [StringSyntax(StringSyntaxAttribute.NumericFormat)] ReadOnlySpan<char> format = default, IFormatProvider? provider = null)
{
return Number.TryFormatDouble(m_value, format, NumberFormatInfo.GetInstance(provider), destination, out charsWritten);
}
/// <inheritdoc cref="IUtf8SpanFormattable.TryFormat" />
public bool TryFormat(Span<byte> utf8Destination, out int bytesWritten, [StringSyntax(StringSyntaxAttribute.NumericFormat)] ReadOnlySpan<char> format = default, IFormatProvider? provider = null)
{
return Number.TryFormatDouble(m_value, format, NumberFormatInfo.GetInstance(provider), utf8Destination, out bytesWritten);
}
public static double Parse(string s) => Parse(s, NumberStyles.Float | NumberStyles.AllowThousands, provider: null);
public static double Parse(string s, NumberStyles style) => Parse(s, style, provider: null);
public static double Parse(string s, IFormatProvider? provider) => Parse(s, NumberStyles.Float | NumberStyles.AllowThousands, provider);
public static double Parse(string s, NumberStyles style, IFormatProvider? provider)
{
if (s is null)
{
ThrowHelper.ThrowArgumentNullException(ExceptionArgument.s);
}
return Parse(s.AsSpan(), style, provider);
}
// Parses a double from a String in the given style. If
// a NumberFormatInfo isn't specified, the current culture's
// NumberFormatInfo is assumed.
//
// This method will not throw an OverflowException, but will return
// PositiveInfinity or NegativeInfinity for a number that is too
// large or too small.
public static double Parse(ReadOnlySpan<char> s, NumberStyles style = NumberStyles.Float | NumberStyles.AllowThousands, IFormatProvider? provider = null)
{
NumberFormatInfo.ValidateParseStyleFloatingPoint(style);
return Number.ParseFloat<char, double>(s, style, NumberFormatInfo.GetInstance(provider));
}
public static bool TryParse([NotNullWhen(true)] string? s, out double result) => TryParse(s, NumberStyles.Float | NumberStyles.AllowThousands, provider: null, out result);
public static bool TryParse(ReadOnlySpan<char> s, out double result) => TryParse(s, NumberStyles.Float | NumberStyles.AllowThousands, provider: null, out result);
/// <summary>Tries to convert a UTF-8 character span containing the string representation of a number to its double-precision floating-point number equivalent.</summary>
/// <param name="utf8Text">A read-only UTF-8 character span that contains the number to convert.</param>
/// <param name="result">When this method returns, contains a double-precision floating-point number equivalent of the numeric value or symbol contained in <paramref name="utf8Text" /> if the conversion succeeded or zero if the conversion failed. The conversion fails if the <paramref name="utf8Text" /> is <see cref="ReadOnlySpan{T}.Empty" /> or is not in a valid format. This parameter is passed uninitialized; any value originally supplied in result will be overwritten.</param>
/// <returns><c>true</c> if <paramref name="utf8Text" /> was converted successfully; otherwise, false.</returns>
public static bool TryParse(ReadOnlySpan<byte> utf8Text, out double result) => TryParse(utf8Text, NumberStyles.Float | NumberStyles.AllowThousands, provider: null, out result);
public static bool TryParse([NotNullWhen(true)] string? s, NumberStyles style, IFormatProvider? provider, out double result)
{
NumberFormatInfo.ValidateParseStyleFloatingPoint(style);
if (s == null)
{
result = 0;
return false;
}
return Number.TryParseFloat(s.AsSpan(), style, NumberFormatInfo.GetInstance(provider), out result);
}
public static bool TryParse(ReadOnlySpan<char> s, NumberStyles style, IFormatProvider? provider, out double result)
{
NumberFormatInfo.ValidateParseStyleFloatingPoint(style);
return Number.TryParseFloat(s, style, NumberFormatInfo.GetInstance(provider), out result);
}
//
// IConvertible implementation
//
public TypeCode GetTypeCode()
{
return TypeCode.Double;
}
bool IConvertible.ToBoolean(IFormatProvider? provider)
{
return Convert.ToBoolean(m_value);
}
char IConvertible.ToChar(IFormatProvider? provider)
{
throw new InvalidCastException(SR.Format(SR.InvalidCast_FromTo, "Double", "Char"));
}
sbyte IConvertible.ToSByte(IFormatProvider? provider)
{
return Convert.ToSByte(m_value);
}
byte IConvertible.ToByte(IFormatProvider? provider)
{
return Convert.ToByte(m_value);
}
short IConvertible.ToInt16(IFormatProvider? provider)
{
return Convert.ToInt16(m_value);
}
ushort IConvertible.ToUInt16(IFormatProvider? provider)
{
return Convert.ToUInt16(m_value);
}
int IConvertible.ToInt32(IFormatProvider? provider)
{
return Convert.ToInt32(m_value);
}
uint IConvertible.ToUInt32(IFormatProvider? provider)
{
return Convert.ToUInt32(m_value);
}
long IConvertible.ToInt64(IFormatProvider? provider)
{
return Convert.ToInt64(m_value);
}
ulong IConvertible.ToUInt64(IFormatProvider? provider)
{
return Convert.ToUInt64(m_value);
}
float IConvertible.ToSingle(IFormatProvider? provider)
{
return Convert.ToSingle(m_value);
}
double IConvertible.ToDouble(IFormatProvider? provider)
{
return m_value;
}
decimal IConvertible.ToDecimal(IFormatProvider? provider)
{
return Convert.ToDecimal(m_value);
}
DateTime IConvertible.ToDateTime(IFormatProvider? provider)
{
throw new InvalidCastException(SR.Format(SR.InvalidCast_FromTo, "Double", "DateTime"));
}
object IConvertible.ToType(Type type, IFormatProvider? provider)
{
return Convert.DefaultToType((IConvertible)this, type, provider);
}
//
// IAdditionOperators
//
/// <inheritdoc cref="IAdditionOperators{TSelf, TOther, TResult}.op_Addition(TSelf, TOther)" />
static double IAdditionOperators<double, double, double>.operator +(double left, double right) => left + right;
//
// IAdditiveIdentity
//
/// <inheritdoc cref="IAdditiveIdentity{TSelf, TResult}.AdditiveIdentity" />
static double IAdditiveIdentity<double, double>.AdditiveIdentity => AdditiveIdentity;
//
// IBinaryNumber
//
/// <inheritdoc cref="IBinaryNumber{TSelf}.AllBitsSet" />
static double IBinaryNumber<double>.AllBitsSet => BitConverter.UInt64BitsToDouble(0xFFFF_FFFF_FFFF_FFFF);
/// <inheritdoc cref="IBinaryNumber{TSelf}.IsPow2(TSelf)" />
public static bool IsPow2(double value)
{
ulong bits = BitConverter.DoubleToUInt64Bits(value);
if ((long)bits <= 0)
{
// Zero and negative values cannot be powers of 2
return false;
}
ushort biasedExponent = ExtractBiasedExponentFromBits(bits);
ulong trailingSignificand = ExtractTrailingSignificandFromBits(bits);
if (biasedExponent == MinBiasedExponent)
{
// Subnormal values have 1 bit set when they're powers of 2
return ulong.PopCount(trailingSignificand) == 1;
}
else if (biasedExponent == MaxBiasedExponent)
{
// NaN and Infinite values cannot be powers of 2
return false;
}
// Normal values have 0 bits set when they're powers of 2
return trailingSignificand == MinTrailingSignificand;
}
/// <inheritdoc cref="IBinaryNumber{TSelf}.Log2(TSelf)" />
[Intrinsic]
public static double Log2(double value) => Math.Log2(value);
//
// IBitwiseOperators
//
/// <inheritdoc cref="IBitwiseOperators{TSelf, TOther, TResult}.op_BitwiseAnd(TSelf, TOther)" />
static double IBitwiseOperators<double, double, double>.operator &(double left, double right)
{
ulong bits = BitConverter.DoubleToUInt64Bits(left) & BitConverter.DoubleToUInt64Bits(right);
return BitConverter.UInt64BitsToDouble(bits);
}
/// <inheritdoc cref="IBitwiseOperators{TSelf, TOther, TResult}.op_BitwiseOr(TSelf, TOther)" />
static double IBitwiseOperators<double, double, double>.operator |(double left, double right)
{
ulong bits = BitConverter.DoubleToUInt64Bits(left) | BitConverter.DoubleToUInt64Bits(right);
return BitConverter.UInt64BitsToDouble(bits);
}
/// <inheritdoc cref="IBitwiseOperators{TSelf, TOther, TResult}.op_ExclusiveOr(TSelf, TOther)" />
static double IBitwiseOperators<double, double, double>.operator ^(double left, double right)
{
ulong bits = BitConverter.DoubleToUInt64Bits(left) ^ BitConverter.DoubleToUInt64Bits(right);
return BitConverter.UInt64BitsToDouble(bits);
}
/// <inheritdoc cref="IBitwiseOperators{TSelf, TOther, TResult}.op_OnesComplement(TSelf)" />
static double IBitwiseOperators<double, double, double>.operator ~(double value)
{
ulong bits = ~BitConverter.DoubleToUInt64Bits(value);
return BitConverter.UInt64BitsToDouble(bits);
}
//
// IDecrementOperators
//
/// <inheritdoc cref="IDecrementOperators{TSelf}.op_Decrement(TSelf)" />
static double IDecrementOperators<double>.operator --(double value) => --value;
//
// IDivisionOperators
//
/// <inheritdoc cref="IDivisionOperators{TSelf, TOther, TResult}.op_Division(TSelf, TOther)" />
static double IDivisionOperators<double, double, double>.operator /(double left, double right) => left / right;
//
// IExponentialFunctions
//
/// <inheritdoc cref="IExponentialFunctions{TSelf}.Exp" />
[Intrinsic]
public static double Exp(double x) => Math.Exp(x);
/// <inheritdoc cref="IExponentialFunctions{TSelf}.ExpM1(TSelf)" />
public static double ExpM1(double x) => Math.Exp(x) - 1;
/// <inheritdoc cref="IExponentialFunctions{TSelf}.Exp2(TSelf)" />
public static double Exp2(double x) => Math.Pow(2, x);
/// <inheritdoc cref="IExponentialFunctions{TSelf}.Exp2M1(TSelf)" />
public static double Exp2M1(double x) => Math.Pow(2, x) - 1;
/// <inheritdoc cref="IExponentialFunctions{TSelf}.Exp10(TSelf)" />
public static double Exp10(double x) => Math.Pow(10, x);
/// <inheritdoc cref="IExponentialFunctions{TSelf}.Exp10M1(TSelf)" />
public static double Exp10M1(double x) => Math.Pow(10, x) - 1;
//
// IFloatingPoint
//
/// <inheritdoc cref="IFloatingPoint{TSelf}.Ceiling(TSelf)" />
[Intrinsic]
public static double Ceiling(double x) => Math.Ceiling(x);
/// <inheritdoc cref="IFloatingPoint{TSelf}.ConvertToInteger{TInteger}(TSelf)" />
[Intrinsic]
public static TInteger ConvertToInteger<TInteger>(double value)
where TInteger : IBinaryInteger<TInteger> => TInteger.CreateSaturating(value);
/// <inheritdoc cref="IFloatingPoint{TSelf}.ConvertToIntegerNative{TInteger}(TSelf)" />
[Intrinsic]
public static TInteger ConvertToIntegerNative<TInteger>(double value)
where TInteger : IBinaryInteger<TInteger>
{
#if !MONO
if (typeof(TInteger).IsPrimitive)
{
// We need this to be recursive so indirect calls (delegates
// for example) produce the same result as direct invocation
return ConvertToIntegerNative<TInteger>(value);
}
#endif
return TInteger.CreateSaturating(value);
}
/// <inheritdoc cref="IFloatingPoint{TSelf}.Floor(TSelf)" />
[Intrinsic]
public static double Floor(double x) => Math.Floor(x);
/// <inheritdoc cref="IFloatingPoint{TSelf}.Round(TSelf)" />
[Intrinsic]
public static double Round(double x) => Math.Round(x);
/// <inheritdoc cref="IFloatingPoint{TSelf}.Round(TSelf, int)" />
public static double Round(double x, int digits) => Math.Round(x, digits);
/// <inheritdoc cref="IFloatingPoint{TSelf}.Round(TSelf, MidpointRounding)" />
public static double Round(double x, MidpointRounding mode) => Math.Round(x, mode);
/// <inheritdoc cref="IFloatingPoint{TSelf}.Round(TSelf, int, MidpointRounding)" />
public static double Round(double x, int digits, MidpointRounding mode) => Math.Round(x, digits, mode);
/// <inheritdoc cref="IFloatingPoint{TSelf}.Truncate(TSelf)" />
[Intrinsic]
public static double Truncate(double x) => Math.Truncate(x);
/// <inheritdoc cref="IFloatingPoint{TSelf}.GetExponentByteCount()" />
int IFloatingPoint<double>.GetExponentByteCount() => sizeof(short);
/// <inheritdoc cref="IFloatingPoint{TSelf}.GetExponentShortestBitLength()" />
int IFloatingPoint<double>.GetExponentShortestBitLength()
{
short exponent = Exponent;
if (exponent >= 0)
{
return (sizeof(short) * 8) - short.LeadingZeroCount(exponent);
}
else
{
return (sizeof(short) * 8) + 1 - short.LeadingZeroCount((short)(~exponent));
}
}
/// <inheritdoc cref="IFloatingPoint{TSelf}.GetSignificandByteCount()" />
int IFloatingPoint<double>.GetSignificandByteCount() => sizeof(ulong);
/// <inheritdoc cref="IFloatingPoint{TSelf}.GetSignificandBitLength()" />
int IFloatingPoint<double>.GetSignificandBitLength() => 53;
/// <inheritdoc cref="IFloatingPoint{TSelf}.TryWriteExponentBigEndian(Span{byte}, out int)" />
bool IFloatingPoint<double>.TryWriteExponentBigEndian(Span<byte> destination, out int bytesWritten)
{
if (destination.Length >= sizeof(short))
{
short exponent = Exponent;
if (BitConverter.IsLittleEndian)
{
exponent = BinaryPrimitives.ReverseEndianness(exponent);
}
Unsafe.WriteUnaligned(ref MemoryMarshal.GetReference(destination), exponent);
bytesWritten = sizeof(short);
return true;
}
else
{
bytesWritten = 0;
return false;
}
}
/// <inheritdoc cref="IFloatingPoint{TSelf}.TryWriteExponentLittleEndian(Span{byte}, out int)" />
bool IFloatingPoint<double>.TryWriteExponentLittleEndian(Span<byte> destination, out int bytesWritten)
{
if (destination.Length >= sizeof(short))
{
short exponent = Exponent;
if (!BitConverter.IsLittleEndian)
{
exponent = BinaryPrimitives.ReverseEndianness(exponent);
}
Unsafe.WriteUnaligned(ref MemoryMarshal.GetReference(destination), exponent);
bytesWritten = sizeof(short);
return true;
}
else
{
bytesWritten = 0;
return false;
}
}
/// <inheritdoc cref="IFloatingPoint{TSelf}.TryWriteSignificandBigEndian(Span{byte}, out int)" />
bool IFloatingPoint<double>.TryWriteSignificandBigEndian(Span<byte> destination, out int bytesWritten)
{
if (destination.Length >= sizeof(ulong))
{
ulong significand = Significand;
if (BitConverter.IsLittleEndian)
{
significand = BinaryPrimitives.ReverseEndianness(significand);
}
Unsafe.WriteUnaligned(ref MemoryMarshal.GetReference(destination), significand);
bytesWritten = sizeof(ulong);
return true;
}
else
{
bytesWritten = 0;
return false;
}
}
/// <inheritdoc cref="IFloatingPoint{TSelf}.TryWriteSignificandLittleEndian(Span{byte}, out int)" />
bool IFloatingPoint<double>.TryWriteSignificandLittleEndian(Span<byte> destination, out int bytesWritten)
{
if (destination.Length >= sizeof(ulong))
{
ulong significand = Significand;
if (!BitConverter.IsLittleEndian)
{
significand = BinaryPrimitives.ReverseEndianness(significand);
}
Unsafe.WriteUnaligned(ref MemoryMarshal.GetReference(destination), significand);
bytesWritten = sizeof(ulong);
return true;
}
else
{
bytesWritten = 0;
return false;
}
}
//
// IFloatingPointConstants
//
/// <inheritdoc cref="IFloatingPointConstants{TSelf}.E" />
static double IFloatingPointConstants<double>.E => Math.E;
/// <inheritdoc cref="IFloatingPointConstants{TSelf}.Pi" />
static double IFloatingPointConstants<double>.Pi => Pi;
/// <inheritdoc cref="IFloatingPointConstants{TSelf}.Tau" />
static double IFloatingPointConstants<double>.Tau => Tau;
//
// IFloatingPointIeee754
//
/// <inheritdoc cref="IFloatingPointIeee754{TSelf}.Epsilon" />
static double IFloatingPointIeee754<double>.Epsilon => Epsilon;
/// <inheritdoc cref="IFloatingPointIeee754{TSelf}.NaN" />
static double IFloatingPointIeee754<double>.NaN => NaN;
/// <inheritdoc cref="IFloatingPointIeee754{TSelf}.NegativeInfinity" />
static double IFloatingPointIeee754<double>.NegativeInfinity => NegativeInfinity;
/// <inheritdoc cref="IFloatingPointIeee754{TSelf}.NegativeZero" />
static double IFloatingPointIeee754<double>.NegativeZero => NegativeZero;
/// <inheritdoc cref="IFloatingPointIeee754{TSelf}.PositiveInfinity" />
static double IFloatingPointIeee754<double>.PositiveInfinity => PositiveInfinity;
/// <inheritdoc cref="IFloatingPointIeee754{TSelf}.Atan2(TSelf, TSelf)" />
[Intrinsic]
public static double Atan2(double y, double x) => Math.Atan2(y, x);
/// <inheritdoc cref="IFloatingPointIeee754{TSelf}.Atan2Pi(TSelf, TSelf)" />
public static double Atan2Pi(double y, double x) => Atan2(y, x) / Pi;
/// <inheritdoc cref="IFloatingPointIeee754{TSelf}.BitDecrement(TSelf)" />
public static double BitDecrement(double x) => Math.BitDecrement(x);
/// <inheritdoc cref="IFloatingPointIeee754{TSelf}.BitIncrement(TSelf)" />
public static double BitIncrement(double x) => Math.BitIncrement(x);
/// <inheritdoc cref="IFloatingPointIeee754{TSelf}.FusedMultiplyAdd(TSelf, TSelf, TSelf)" />
[Intrinsic]
public static double FusedMultiplyAdd(double left, double right, double addend) => Math.FusedMultiplyAdd(left, right, addend);
/// <inheritdoc cref="IFloatingPointIeee754{TSelf}.Ieee754Remainder(TSelf, TSelf)" />
public static double Ieee754Remainder(double left, double right) => Math.IEEERemainder(left, right);
/// <inheritdoc cref="IFloatingPointIeee754{TSelf}.ILogB(TSelf)" />
public static int ILogB(double x) => Math.ILogB(x);
/// <inheritdoc cref="IFloatingPointIeee754{TSelf}.Lerp(TSelf, TSelf, TSelf)" />
public static double Lerp(double value1, double value2, double amount) => (value1 * (1.0 - amount)) + (value2 * amount);
/// <inheritdoc cref="IFloatingPointIeee754{TSelf}.ReciprocalEstimate(TSelf)" />
[Intrinsic]
public static double ReciprocalEstimate(double x) => Math.ReciprocalEstimate(x);
/// <inheritdoc cref="IFloatingPointIeee754{TSelf}.ReciprocalSqrtEstimate(TSelf)" />
[Intrinsic]
public static double ReciprocalSqrtEstimate(double x) => Math.ReciprocalSqrtEstimate(x);
/// <inheritdoc cref="IFloatingPointIeee754{TSelf}.ScaleB(TSelf, int)" />
public static double ScaleB(double x, int n) => Math.ScaleB(x, n);
// /// <inheritdoc cref="IFloatingPointIeee754{TSelf}.Compound(TSelf, TSelf)" />
// public static double Compound(double x, double n) => Math.Compound(x, n);
//
// IHyperbolicFunctions
//
/// <inheritdoc cref="IHyperbolicFunctions{TSelf}.Acosh(TSelf)" />
[Intrinsic]
public static double Acosh(double x) => Math.Acosh(x);
/// <inheritdoc cref="IHyperbolicFunctions{TSelf}.Asinh(TSelf)" />
[Intrinsic]
public static double Asinh(double x) => Math.Asinh(x);
/// <inheritdoc cref="IHyperbolicFunctions{TSelf}.Atanh(TSelf)" />
[Intrinsic]
public static double Atanh(double x) => Math.Atanh(x);
/// <inheritdoc cref="IHyperbolicFunctions{TSelf}.Cosh(TSelf)" />
[Intrinsic]
public static double Cosh(double x) => Math.Cosh(x);
/// <inheritdoc cref="IHyperbolicFunctions{TSelf}.Sinh(TSelf)" />
[Intrinsic]
public static double Sinh(double x) => Math.Sinh(x);
/// <inheritdoc cref="IHyperbolicFunctions{TSelf}.Tanh(TSelf)" />
[Intrinsic]
public static double Tanh(double x) => Math.Tanh(x);
//
// IIncrementOperators
//
/// <inheritdoc cref="IIncrementOperators{TSelf}.op_Increment(TSelf)" />
static double IIncrementOperators<double>.operator ++(double value) => ++value;
//
// ILogarithmicFunctions
//
/// <inheritdoc cref="ILogarithmicFunctions{TSelf}.Log(TSelf)" />
[Intrinsic]
public static double Log(double x) => Math.Log(x);
/// <inheritdoc cref="ILogarithmicFunctions{TSelf}.Log(TSelf, TSelf)" />
public static double Log(double x, double newBase) => Math.Log(x, newBase);
/// <inheritdoc cref="ILogarithmicFunctions{TSelf}.LogP1(TSelf)" />
public static double LogP1(double x) => Math.Log(x + 1);
/// <inheritdoc cref="ILogarithmicFunctions{TSelf}.Log2P1(TSelf)" />
public static double Log2P1(double x) => Math.Log2(x + 1);
/// <inheritdoc cref="ILogarithmicFunctions{TSelf}.Log10(TSelf)" />
[Intrinsic]
public static double Log10(double x) => Math.Log10(x);
/// <inheritdoc cref="ILogarithmicFunctions{TSelf}.Log10P1(TSelf)" />
public static double Log10P1(double x) => Math.Log10(x + 1);
//
// IMinMaxValue
//
/// <inheritdoc cref="IMinMaxValue{TSelf}.MinValue" />
static double IMinMaxValue<double>.MinValue => MinValue;
/// <inheritdoc cref="IMinMaxValue{TSelf}.MaxValue" />
static double IMinMaxValue<double>.MaxValue => MaxValue;
//
// IModulusOperators
//
/// <inheritdoc cref="IModulusOperators{TSelf, TOther, TResult}.op_Modulus(TSelf, TOther)" />
static double IModulusOperators<double, double, double>.operator %(double left, double right) => left % right;
//
// IMultiplicativeIdentity
//
/// <inheritdoc cref="IMultiplicativeIdentity{TSelf, TResult}.MultiplicativeIdentity" />
static double IMultiplicativeIdentity<double, double>.MultiplicativeIdentity => MultiplicativeIdentity;
//
// IMultiplyOperators
//
/// <inheritdoc cref="IMultiplyOperators{TSelf, TOther, TResult}.op_Multiply(TSelf, TOther)" />
static double IMultiplyOperators<double, double, double>.operator *(double left, double right) => left * right;
//
// INumber
//
/// <inheritdoc cref="INumber{TSelf}.Clamp(TSelf, TSelf, TSelf)" />
public static double Clamp(double value, double min, double max) => Math.Clamp(value, min, max);
/// <inheritdoc cref="INumber{TSelf}.CopySign(TSelf, TSelf)" />
public static double CopySign(double value, double sign) => Math.CopySign(value, sign);
/// <inheritdoc cref="INumber{TSelf}.Max(TSelf, TSelf)" />
[Intrinsic]
public static double Max(double x, double y) => Math.Max(x, y);
/// <inheritdoc cref="INumber{TSelf}.MaxNumber(TSelf, TSelf)" />
[Intrinsic]
public static double MaxNumber(double x, double y)
{
// This matches the IEEE 754:2019 `maximumNumber` function
//
// It does not propagate NaN inputs back to the caller and
// otherwise returns the larger of the inputs. It
// treats +0 as larger than -0 as per the specification.
if (x != y)
{
if (!IsNaN(y))
{
return y < x ? x : y;
}
return x;
}
return IsNegative(y) ? x : y;
}
/// <inheritdoc cref="INumber{TSelf}.Min(TSelf, TSelf)" />
[Intrinsic]
public static double Min(double x, double y) => Math.Min(x, y);
/// <inheritdoc cref="INumber{TSelf}.MinNumber(TSelf, TSelf)" />
[Intrinsic]
public static double MinNumber(double x, double y)
{
// This matches the IEEE 754:2019 `minimumNumber` function
//
// It does not propagate NaN inputs back to the caller and
// otherwise returns the larger of the inputs. It
// treats +0 as larger than -0 as per the specification.
if (x != y)
{
if (!IsNaN(y))
{
return x < y ? x : y;
}
return x;
}
return IsNegative(x) ? x : y;
}
/// <inheritdoc cref="INumber{TSelf}.Sign(TSelf)" />
public static int Sign(double value) => Math.Sign(value);
//
// INumberBase
//
/// <inheritdoc cref="INumberBase{TSelf}.One" />
static double INumberBase<double>.One => One;
/// <inheritdoc cref="INumberBase{TSelf}.Radix" />
static int INumberBase<double>.Radix => 2;
/// <inheritdoc cref="INumberBase{TSelf}.Zero" />
static double INumberBase<double>.Zero => Zero;
/// <inheritdoc cref="INumberBase{TSelf}.Abs(TSelf)" />
[Intrinsic]
public static double Abs(double value) => Math.Abs(value);
/// <inheritdoc cref="INumberBase{TSelf}.CreateChecked{TOther}(TOther)" />
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static double CreateChecked<TOther>(TOther value)
where TOther : INumberBase<TOther>
{
double result;
if (typeof(TOther) == typeof(double))
{
result = (double)(object)value;
}
else if (!TryConvertFrom(value, out result) && !TOther.TryConvertToChecked(value, out result))
{
ThrowHelper.ThrowNotSupportedException();
}
return result;
}
/// <inheritdoc cref="INumberBase{TSelf}.CreateSaturating{TOther}(TOther)" />
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static double CreateSaturating<TOther>(TOther value)
where TOther : INumberBase<TOther>
{
double result;
if (typeof(TOther) == typeof(double))
{
result = (double)(object)value;
}
else if (!TryConvertFrom(value, out result) && !TOther.TryConvertToSaturating(value, out result))
{
ThrowHelper.ThrowNotSupportedException();
}
return result;
}
/// <inheritdoc cref="INumberBase{TSelf}.CreateTruncating{TOther}(TOther)" />
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static double CreateTruncating<TOther>(TOther value)
where TOther : INumberBase<TOther>
{
double result;
if (typeof(TOther) == typeof(double))
{
result = (double)(object)value;
}
else if (!TryConvertFrom(value, out result) && !TOther.TryConvertToTruncating(value, out result))
{
ThrowHelper.ThrowNotSupportedException();
}
return result;
}
/// <inheritdoc cref="INumberBase{TSelf}.IsCanonical(TSelf)" />
static bool INumberBase<double>.IsCanonical(double value) => true;
/// <inheritdoc cref="INumberBase{TSelf}.IsComplexNumber(TSelf)" />
static bool INumberBase<double>.IsComplexNumber(double value) => false;
/// <inheritdoc cref="INumberBase{TSelf}.IsEvenInteger(TSelf)" />
public static bool IsEvenInteger(double value) => IsInteger(value) && (Abs(value % 2) == 0);
/// <inheritdoc cref="INumberBase{TSelf}.IsImaginaryNumber(TSelf)" />
static bool INumberBase<double>.IsImaginaryNumber(double value) => false;
/// <inheritdoc cref="INumberBase{TSelf}.IsInteger(TSelf)" />
public static bool IsInteger(double value) => IsFinite(value) && (value == Truncate(value));
/// <inheritdoc cref="INumberBase{TSelf}.IsOddInteger(TSelf)" />
public static bool IsOddInteger(double value) => IsInteger(value) && (Abs(value % 2) == 1);
/// <inheritdoc cref="INumberBase{TSelf}.IsPositive(TSelf)" />
public static bool IsPositive(double value) => BitConverter.DoubleToInt64Bits(value) >= 0;
/// <inheritdoc cref="INumberBase{TSelf}.IsRealNumber(TSelf)" />
public static bool IsRealNumber(double value)
{
// A NaN will never equal itself so this is an
// easy and efficient way to check for a real number.
#pragma warning disable CS1718
return value == value;
#pragma warning restore CS1718
}
/// <inheritdoc cref="INumberBase{TSelf}.IsZero(TSelf)" />
static bool INumberBase<double>.IsZero(double value) => IsZero(value);
/// <inheritdoc cref="INumberBase{TSelf}.MaxMagnitude(TSelf, TSelf)" />
[Intrinsic]
public static double MaxMagnitude(double x, double y) => Math.MaxMagnitude(x, y);
/// <inheritdoc cref="INumberBase{TSelf}.MaxMagnitudeNumber(TSelf, TSelf)" />
[Intrinsic]
public static double MaxMagnitudeNumber(double x, double y)
{
// This matches the IEEE 754:2019 `maximumMagnitudeNumber` function
//
// It does not propagate NaN inputs back to the caller and
// otherwise returns the input with a larger magnitude.
// It treats +0 as larger than -0 as per the specification.
double ax = Abs(x);
double ay = Abs(y);
if ((ax > ay) || IsNaN(ay))
{
return x;
}
if (ax == ay)
{
return IsNegative(x) ? y : x;
}
return y;
}
/// <inheritdoc cref="INumberBase{TSelf}.MinMagnitude(TSelf, TSelf)" />
[Intrinsic]
public static double MinMagnitude(double x, double y) => Math.MinMagnitude(x, y);
/// <inheritdoc cref="INumberBase{TSelf}.MinMagnitudeNumber(TSelf, TSelf)" />
[Intrinsic]
public static double MinMagnitudeNumber(double x, double y)
{
// This matches the IEEE 754:2019 `minimumMagnitudeNumber` function
//
// It does not propagate NaN inputs back to the caller and
// otherwise returns the input with a larger magnitude.
// It treats +0 as larger than -0 as per the specification.
double ax = Abs(x);
double ay = Abs(y);
if ((ax < ay) || IsNaN(ay))
{
return x;
}
if (ax == ay)
{
return IsNegative(x) ? x : y;
}
return y;
}
/// <inheritdoc cref="INumberBase{TSelf}.MultiplyAddEstimate(TSelf, TSelf, TSelf)" />
[Intrinsic]
public static double MultiplyAddEstimate(double left, double right, double addend)
{
#if MONO
return (left * right) + addend;
#else
return MultiplyAddEstimate(left, right, addend);
#endif
}
/// <inheritdoc cref="INumberBase{TSelf}.TryConvertFromChecked{TOther}(TOther, out TSelf)" />
[MethodImpl(MethodImplOptions.AggressiveInlining)]
static bool INumberBase<double>.TryConvertFromChecked<TOther>(TOther value, out double result)
{
return TryConvertFrom(value, out result);
}
/// <inheritdoc cref="INumberBase{TSelf}.TryConvertFromSaturating{TOther}(TOther, out TSelf)" />
[MethodImpl(MethodImplOptions.AggressiveInlining)]
static bool INumberBase<double>.TryConvertFromSaturating<TOther>(TOther value, out double result)
{
return TryConvertFrom(value, out result);
}
/// <inheritdoc cref="INumberBase{TSelf}.TryConvertFromTruncating{TOther}(TOther, out TSelf)" />
[MethodImpl(MethodImplOptions.AggressiveInlining)]
static bool INumberBase<double>.TryConvertFromTruncating<TOther>(TOther value, out double result)
{
return TryConvertFrom(value, out result);
}
private static bool TryConvertFrom<TOther>(TOther value, out double result)
where TOther : INumberBase<TOther>
{
// In order to reduce overall code duplication and improve the inlinabilty of these
// methods for the corelib types we have `ConvertFrom` handle the same sign and
// `ConvertTo` handle the opposite sign. However, since there is an uneven split
// between signed and unsigned types, the one that handles unsigned will also
// handle `Decimal`.
//
// That is, `ConvertFrom` for `double` will handle the other signed types and
// `ConvertTo` will handle the unsigned types
if (typeof(TOther) == typeof(Half))
{
Half actualValue = (Half)(object)value;
result = (double)actualValue;
return true;
}
else if (typeof(TOther) == typeof(short))
{
short actualValue = (short)(object)value;
result = actualValue;
return true;
}
else if (typeof(TOther) == typeof(int))
{
int actualValue = (int)(object)value;
result = actualValue;
return true;
}
else if (typeof(TOther) == typeof(long))
{
long actualValue = (long)(object)value;
result = actualValue;
return true;
}
else if (typeof(TOther) == typeof(Int128))
{
Int128 actualValue = (Int128)(object)value;
result = (double)actualValue;
return true;
}
else if (typeof(TOther) == typeof(nint))
{
nint actualValue = (nint)(object)value;
result = actualValue;
return true;
}
else if (typeof(TOther) == typeof(sbyte))
{
sbyte actualValue = (sbyte)(object)value;
result = actualValue;
return true;
}
else if (typeof(TOther) == typeof(float))
{
float actualValue = (float)(object)value;
result = actualValue;
return true;
}
else
{
result = default;
return false;
}
}
/// <inheritdoc cref="INumberBase{TSelf}.TryConvertToChecked{TOther}(TSelf, out TOther)" />
[MethodImpl(MethodImplOptions.AggressiveInlining)]
static bool INumberBase<double>.TryConvertToChecked<TOther>(double value, [MaybeNullWhen(false)] out TOther result)
{
// In order to reduce overall code duplication and improve the inlinabilty of these
// methods for the corelib types we have `ConvertFrom` handle the same sign and
// `ConvertTo` handle the opposite sign. However, since there is an uneven split
// between signed and unsigned types, the one that handles unsigned will also
// handle `Decimal`.
//
// That is, `ConvertFrom` for `double` will handle the other signed types and
// `ConvertTo` will handle the unsigned types
if (typeof(TOther) == typeof(byte))
{
byte actualResult = checked((byte)value);
result = (TOther)(object)actualResult;
return true;
}
else if (typeof(TOther) == typeof(char))
{
char actualResult = checked((char)value);
result = (TOther)(object)actualResult;
return true;
}
else if (typeof(TOther) == typeof(decimal))
{
decimal actualResult = checked((decimal)value);
result = (TOther)(object)actualResult;
return true;
}
else if (typeof(TOther) == typeof(ushort))
{
ushort actualResult = checked((ushort)value);
result = (TOther)(object)actualResult;
return true;
}
else if (typeof(TOther) == typeof(uint))
{
uint actualResult = checked((uint)value);
result = (TOther)(object)actualResult;
return true;
}
else if (typeof(TOther) == typeof(ulong))
{
ulong actualResult = checked((ulong)value);
result = (TOther)(object)actualResult;
return true;
}
else if (typeof(TOther) == typeof(UInt128))
{
UInt128 actualResult = checked((UInt128)value);
result = (TOther)(object)actualResult;
return true;
}
else if (typeof(TOther) == typeof(nuint))
{
nuint actualResult = checked((nuint)value);
result = (TOther)(object)actualResult;
return true;
}
else
{
result = default;
return false;
}
}
/// <inheritdoc cref="INumberBase{TSelf}.TryConvertToSaturating{TOther}(TSelf, out TOther)" />
[MethodImpl(MethodImplOptions.AggressiveInlining)]
static bool INumberBase<double>.TryConvertToSaturating<TOther>(double value, [MaybeNullWhen(false)] out TOther result)
{
return TryConvertTo(value, out result);
}
/// <inheritdoc cref="INumberBase{TSelf}.TryConvertToTruncating{TOther}(TSelf, out TOther)" />
[MethodImpl(MethodImplOptions.AggressiveInlining)]
static bool INumberBase<double>.TryConvertToTruncating<TOther>(double value, [MaybeNullWhen(false)] out TOther result)
{
return TryConvertTo(value, out result);
}
private static bool TryConvertTo<TOther>(double value, [MaybeNullWhen(false)] out TOther result)
where TOther : INumberBase<TOther>
{
// In order to reduce overall code duplication and improve the inlinabilty of these
// methods for the corelib types we have `ConvertFrom` handle the same sign and
// `ConvertTo` handle the opposite sign. However, since there is an uneven split
// between signed and unsigned types, the one that handles unsigned will also
// handle `Decimal`.
//
// That is, `ConvertFrom` for `double` will handle the other signed types and
// `ConvertTo` will handle the unsigned types
if (typeof(TOther) == typeof(byte))
{
byte actualResult = (value >= byte.MaxValue) ? byte.MaxValue :
(value <= byte.MinValue) ? byte.MinValue : (byte)value;
result = (TOther)(object)actualResult;
return true;
}
else if (typeof(TOther) == typeof(char))
{
char actualResult = (value >= char.MaxValue) ? char.MaxValue :
(value <= char.MinValue) ? char.MinValue : (char)value;
result = (TOther)(object)actualResult;
return true;
}
else if (typeof(TOther) == typeof(decimal))
{
decimal actualResult = (value >= +79228162514264337593543950336.0) ? decimal.MaxValue :
(value <= -79228162514264337593543950336.0) ? decimal.MinValue :
IsNaN(value) ? 0.0m : (decimal)value;
result = (TOther)(object)actualResult;
return true;
}
else if (typeof(TOther) == typeof(ushort))
{
ushort actualResult = (value >= ushort.MaxValue) ? ushort.MaxValue :
(value <= ushort.MinValue) ? ushort.MinValue : (ushort)value;
result = (TOther)(object)actualResult;
return true;
}
else if (typeof(TOther) == typeof(uint))
{
uint actualResult = (value >= uint.MaxValue) ? uint.MaxValue :
(value <= uint.MinValue) ? uint.MinValue : (uint)value;
result = (TOther)(object)actualResult;
return true;
}
else if (typeof(TOther) == typeof(ulong))
{
ulong actualResult = (value >= ulong.MaxValue) ? ulong.MaxValue :
(value <= ulong.MinValue) ? ulong.MinValue :
IsNaN(value) ? 0 : (ulong)value;
result = (TOther)(object)actualResult;
return true;
}
else if (typeof(TOther) == typeof(UInt128))
{
UInt128 actualResult = (value >= 340282366920938463463374607431768211455.0) ? UInt128.MaxValue :
(value <= 0.0) ? UInt128.MinValue : (UInt128)value;
result = (TOther)(object)actualResult;
return true;
}
else if (typeof(TOther) == typeof(nuint))
{
#if TARGET_64BIT
nuint actualResult = (value >= ulong.MaxValue) ? unchecked((nuint)ulong.MaxValue) :
(value <= ulong.MinValue) ? unchecked((nuint)ulong.MinValue) : (nuint)value;
result = (TOther)(object)actualResult;
return true;
#else
nuint actualResult = (value >= uint.MaxValue) ? uint.MaxValue :
(value <= uint.MinValue) ? uint.MinValue : (nuint)value;
result = (TOther)(object)actualResult;
return true;
#endif
}
else
{
result = default;
return false;
}
}
//
// IParsable
//
/// <inheritdoc cref="IParsable{TSelf}.TryParse(string?, IFormatProvider?, out TSelf)" />
public static bool TryParse([NotNullWhen(true)] string? s, IFormatProvider? provider, out double result) => TryParse(s, NumberStyles.Float | NumberStyles.AllowThousands, provider, out result);
//
// IPowerFunctions
//
/// <inheritdoc cref="IPowerFunctions{TSelf}.Pow(TSelf, TSelf)" />
[Intrinsic]
public static double Pow(double x, double y) => Math.Pow(x, y);
//
// IRootFunctions
//
/// <inheritdoc cref="IRootFunctions{TSelf}.Cbrt(TSelf)" />
[Intrinsic]
public static double Cbrt(double x) => Math.Cbrt(x);
/// <inheritdoc cref="IRootFunctions{TSelf}.Hypot(TSelf, TSelf)" />
public static double Hypot(double x, double y)
{
// This code is based on `hypot` from amd/aocl-libm-ose
// Copyright (C) 2008-2020 Advanced Micro Devices, Inc. All rights reserved.
//
// Licensed under the BSD 3-Clause "New" or "Revised" License
// See THIRD-PARTY-NOTICES.TXT for the full license text
double result;
if (IsFinite(x) && IsFinite(y))
{
double ax = Abs(x);
double ay = Abs(y);
if (ax == 0.0f)
{
result = ay;
}
else if (ay == 0.0f)
{
result = ax;
}
else
{
ulong xBits = BitConverter.DoubleToUInt64Bits(ax);
ulong yBits = BitConverter.DoubleToUInt64Bits(ay);
uint xExp = (uint)((xBits >> BiasedExponentShift) & ShiftedExponentMask);
uint yExp = (uint)((yBits >> BiasedExponentShift) & ShiftedExponentMask);
int expDiff = (int)(xExp - yExp);
double expFix = 1.0;
if ((expDiff <= (SignificandLength + 1)) && (expDiff >= (-SignificandLength - 1)))
{
if ((xExp > (ExponentBias + 500)) || (yExp > (ExponentBias + 500)))
{
// To prevent overflow, scale down by 2^+600
expFix = 4.149515568880993E+180;
xBits -= 0x2580000000000000;
yBits -= 0x2580000000000000;
}
else if ((xExp < (ExponentBias - 500)) || (yExp < (ExponentBias - 500)))
{
// To prevent underflow, scale up by 2^-600
expFix = 2.409919865102884E-181;
xBits += 0x2580000000000000;
yBits += 0x2580000000000000;
// For subnormal values, do an additional fixing up changing the
// adjustment to scale up by 2^601 instead and then subtract a
// correction of 2^601 to account for the implicit bit.
if (xExp == 0) // x is subnormal
{
xBits += 0x0010000000000000;
ax = BitConverter.UInt64BitsToDouble(xBits);
ax -= 9.232978617785736E-128;
xBits = BitConverter.DoubleToUInt64Bits(ax);
}
if (yExp == 0) // y is subnormal
{
yBits += 0x0010000000000000;
ay = BitConverter.UInt64BitsToDouble(yBits);
ay -= 9.232978617785736E-128;
yBits = BitConverter.DoubleToUInt64Bits(ay);
}
}
ax = BitConverter.UInt64BitsToDouble(xBits);
ay = BitConverter.UInt64BitsToDouble(yBits);
if (ax < ay)
{
// Sort so ax is greater than ay
double tmp = ax;
ax = ay;
ay = tmp;
ulong tmpBits = xBits;
xBits = yBits;
yBits = tmpBits;
}
Debug.Assert(ax >= ay);
// Split ax and ay into a head and tail portion
double xHead = BitConverter.UInt64BitsToDouble(xBits & 0xFFFF_FFFF_F800_0000);
double yHead = BitConverter.UInt64BitsToDouble(yBits & 0xFFFF_FFFF_F800_0000);
double xTail = ax - xHead;
double yTail = ay - yHead;
// Compute (x * x) + (y * y) with extra precision
//
// This includes taking into account expFix which may
// cause an underflow or overflow, but if it does that
// will still be the correct result.
double xx = ax * ax;
double yy = ay * ay;
double rHead = xx + yy;
double rTail = (xx - rHead) + yy;
rTail += (xHead * xHead) - xx;
rTail += 2 * xHead * xTail;
rTail += xTail * xTail;
if (expDiff == 0)
{
// We only need to do extra accounting when ax and ay have equal exponents
rTail += (yHead * yHead) - yy;
rTail += 2 * yHead * yTail;
rTail += yTail * yTail;
}
result = Sqrt(rHead + rTail) * expFix;
}
else
{
// x or y is insignificant compared to the other
result = ax + ay;
}
}
}
else if (IsInfinity(x) || IsInfinity(y))
{
// IEEE 754 requires that we return +Infinity
// even if one of the inputs is NaN
result = PositiveInfinity;
}
else
{
// IEEE 754 requires that we return NaN
// if either input is NaN and neither is Infinity
result = NaN;
}
return result;
}
/// <inheritdoc cref="IRootFunctions{TSelf}.RootN(TSelf, int)" />
public static double RootN(double x, int n)
{
double result;
if (n > 0)
{
if (n == 2)
{
result = (x != 0.0) ? Sqrt(x) : 0.0;
}
else if (n == 3)
{
result = Cbrt(x);
}
else
{
result = PositiveN(x, n);
}
}
else if (n < 0)
{
result = NegativeN(x, n);
}
else
{
Debug.Assert(n == 0);
result = NaN;
}
return result;
static double PositiveN(double x, int n)
{
double result;
if (IsFinite(x))
{
if (x != 0)
{
if ((x > 0) || IsOddInteger(n))
{
result = Pow(Abs(x), 1.0 / n);
result = CopySign(result, x);
}
else
{
result = NaN;
}
}
else if (IsEvenInteger(n))
{
result = 0.0;
}
else
{
result = CopySign(0.0, x);
}
}
else if (IsNaN(x))
{
result = NaN;
}
else if (x > 0)
{
Debug.Assert(IsPositiveInfinity(x));
result = PositiveInfinity;
}
else
{
Debug.Assert(IsNegativeInfinity(x));
result = int.IsOddInteger(n) ? NegativeInfinity : NaN;
}
return result;
}
static double NegativeN(double x, int n)
{
double result;
if (IsFinite(x))
{
if (x != 0)
{
if ((x > 0) || IsOddInteger(n))
{
result = Pow(Abs(x), 1.0 / n);
result = CopySign(result, x);
}
else
{
result = NaN;
}
}
else if (IsEvenInteger(n))
{
result = PositiveInfinity;
}
else
{
result = CopySign(PositiveInfinity, x);
}
}
else if (IsNaN(x))
{
result = NaN;
}
else if (x > 0)
{
Debug.Assert(IsPositiveInfinity(x));
result = 0.0;
}
else
{
Debug.Assert(IsNegativeInfinity(x));
result = int.IsOddInteger(n) ? -0.0 : NaN;
}
return result;
}
}
/// <inheritdoc cref="IRootFunctions{TSelf}.Sqrt(TSelf)" />
[Intrinsic]
public static double Sqrt(double x) => Math.Sqrt(x);
//
// ISignedNumber
//
/// <inheritdoc cref="ISignedNumber{TSelf}.NegativeOne" />
static double ISignedNumber<double>.NegativeOne => NegativeOne;
//
// ISpanParsable
//
/// <inheritdoc cref="ISpanParsable{TSelf}.Parse(ReadOnlySpan{char}, IFormatProvider?)" />
public static double Parse(ReadOnlySpan<char> s, IFormatProvider? provider) => Parse(s, NumberStyles.Float | NumberStyles.AllowThousands, provider);
/// <inheritdoc cref="ISpanParsable{TSelf}.TryParse(ReadOnlySpan{char}, IFormatProvider?, out TSelf)" />
public static bool TryParse(ReadOnlySpan<char> s, IFormatProvider? provider, out double result) => TryParse(s, NumberStyles.Float | NumberStyles.AllowThousands, provider, out result);
//
// ISubtractionOperators
//
/// <inheritdoc cref="ISubtractionOperators{TSelf, TOther, TResult}.op_Subtraction(TSelf, TOther)" />
static double ISubtractionOperators<double, double, double>.operator -(double left, double right) => left - right;
//
// ITrigonometricFunctions
//
/// <inheritdoc cref="ITrigonometricFunctions{TSelf}.Acos(TSelf)" />
[Intrinsic]
public static double Acos(double x) => Math.Acos(x);
/// <inheritdoc cref="ITrigonometricFunctions{TSelf}.AcosPi(TSelf)" />
public static double AcosPi(double x)
{
return Acos(x) / Pi;
}
/// <inheritdoc cref="ITrigonometricFunctions{TSelf}.Asin(TSelf)" />
[Intrinsic]
public static double Asin(double x) => Math.Asin(x);
/// <inheritdoc cref="ITrigonometricFunctions{TSelf}.AsinPi(TSelf)" />
public static double AsinPi(double x)
{
return Asin(x) / Pi;
}
/// <inheritdoc cref="ITrigonometricFunctions{TSelf}.Atan(TSelf)" />
[Intrinsic]
public static double Atan(double x) => Math.Atan(x);
/// <inheritdoc cref="ITrigonometricFunctions{TSelf}.AtanPi(TSelf)" />
public static double AtanPi(double x)
{
return Atan(x) / Pi;
}
/// <inheritdoc cref="ITrigonometricFunctions{TSelf}.Cos(TSelf)" />
[Intrinsic]
public static double Cos(double x) => Math.Cos(x);
/// <inheritdoc cref="ITrigonometricFunctions{TSelf}.CosPi(TSelf)" />
public static double CosPi(double x)
{
// This code is based on `cospi` from amd/aocl-libm-ose
// Copyright (C) 2008-2020 Advanced Micro Devices, Inc. All rights reserved.
//
// Licensed under the BSD 3-Clause "New" or "Revised" License
// See THIRD-PARTY-NOTICES.TXT for the full license text
double result;
if (IsFinite(x))
{
double ax = Abs(x);
if (ax < 4_503_599_627_370_496.0) // |x| < 2^52
{
if (ax > 0.25)
{
long integral = (long)ax;
double fractional = ax - integral;
double sign = long.IsOddInteger(integral) ? -1.0 : +1.0;
if (fractional <= 0.25)
{
if (fractional != 0.00)
{
result = sign * CosForIntervalPiBy4(fractional * Pi, 0.0);
}
else
{
result = sign;
}
}
else if (fractional <= 0.50)
{
if (fractional != 0.50)
{
result = sign * SinForIntervalPiBy4((0.5 - fractional) * Pi, 0.0);
}
else
{
result = 0.0;
}
}
else if (fractional <= 0.75)
{
result = -sign * SinForIntervalPiBy4((fractional - 0.5) * Pi, 0.0);
}
else
{
result = -sign * CosForIntervalPiBy4((1.0 - fractional) * Pi, 0.0);
}
}
else if (ax >= 6.103515625E-05) // |x| >= 2^-14
{
result = CosForIntervalPiBy4(x * Pi, 0.0);
}
else if (ax >= 7.450580596923828E-09) // |x| >= 2^-27
{
double value = x * Pi;
result = 1.0 - (value * value * 0.5);
}
else
{
result = 1.0;
}
}
else if (ax < 9_007_199_254_740_992.0) // |x| < 2^53
{
// x is an integer
long bits = BitConverter.DoubleToInt64Bits(ax);
result = long.IsOddInteger(bits) ? -1.0 : +1.0;
}
else
{
// x is an even integer
result = 1.0;
}
}
else
{
result = NaN;
}
return result;
}
/// <inheritdoc cref="ITrigonometricFunctions{TSelf}.DegreesToRadians(TSelf)" />
public static double DegreesToRadians(double degrees)
{
// NOTE: Don't change the algorithm without consulting the DIM
// which elaborates on why this implementation was chosen
return (degrees * Pi) / 180.0;
}
/// <inheritdoc cref="ITrigonometricFunctions{TSelf}.RadiansToDegrees(TSelf)" />
public static double RadiansToDegrees(double radians)
{
// NOTE: Don't change the algorithm without consulting the DIM
// which elaborates on why this implementation was chosen
return (radians * 180.0) / Pi;
}
/// <inheritdoc cref="ITrigonometricFunctions{TSelf}.Sin(TSelf)" />
[Intrinsic]
public static double Sin(double x) => Math.Sin(x);
/// <inheritdoc cref="ITrigonometricFunctions{TSelf}.SinCos(TSelf)" />
public static (double Sin, double Cos) SinCos(double x) => Math.SinCos(x);
/// <inheritdoc cref="ITrigonometricFunctions{TSelf}.SinCos(TSelf)" />
public static (double SinPi, double CosPi) SinCosPi(double x)
{
// This code is based on `cospi` and `sinpi` from amd/aocl-libm-ose
// Copyright (C) 2008-2020 Advanced Micro Devices, Inc. All rights reserved.
//
// Licensed under the BSD 3-Clause "New" or "Revised" License
// See THIRD-PARTY-NOTICES.TXT for the full license text
double sinPi;
double cosPi;
if (IsFinite(x))
{
double ax = Abs(x);
if (ax < 4_503_599_627_370_496.0) // |x| < 2^52
{
if (ax > 0.25)
{
long integral = (long)ax;
double fractional = ax - integral;
double sign = long.IsOddInteger(integral) ? -1.0 : +1.0;
double sinSign = ((x > 0.0) ? +1.0 : -1.0) * sign;
double cosSign = sign;
if (fractional <= 0.25)
{
if (fractional != 0.00)
{
double value = fractional * Pi;
sinPi = sinSign * SinForIntervalPiBy4(value, 0.0);
cosPi = cosSign * CosForIntervalPiBy4(value, 0.0);
}
else
{
sinPi = x * 0.0;
cosPi = cosSign;
}
}
else if (fractional <= 0.50)
{
if (fractional != 0.50)
{
double value = (0.5 - fractional) * Pi;
sinPi = sinSign * CosForIntervalPiBy4(value, 0.0);
cosPi = cosSign * SinForIntervalPiBy4(value, 0.0);
}
else
{
sinPi = sinSign;
cosPi = 0.0;
}
}
else if (fractional <= 0.75)
{
double value = (fractional - 0.5) * Pi;
sinPi = +sinSign * CosForIntervalPiBy4(value, 0.0);
cosPi = -cosSign * SinForIntervalPiBy4(value, 0.0);
}
else
{
double value = (1.0 - fractional) * Pi;
sinPi = +sinSign * SinForIntervalPiBy4(value, 0.0);
cosPi = -cosSign * CosForIntervalPiBy4(value, 0.0);
}
}
else if (ax >= 1.220703125E-4) // |x| >= 2^-13
{
double value = x * Pi;
sinPi = SinForIntervalPiBy4(value, 0.0);
cosPi = CosForIntervalPiBy4(value, 0.0);
}
else if (ax >= 7.450580596923828E-09) // |x| >= 2^-27
{
double value = x * Pi;
double valueSq = value * value;
sinPi = value - (valueSq * value * (1.0 / 6.0));
cosPi = 1.0 - (valueSq * 0.5);
}
else
{
sinPi = x * Pi;
cosPi = 1.0;
}
}
else if (ax < 9_007_199_254_740_992.0) // |x| < 2^53
{
// x is an integer
sinPi = x * 0.0;
long bits = BitConverter.DoubleToInt64Bits(ax);
cosPi = long.IsOddInteger(bits) ? -1.0 : +1.0;
}
else
{
// x is an even integer
sinPi = x * 0.0;
cosPi = 1.0;
}
}
else
{
sinPi = NaN;
cosPi = NaN;
}
return (sinPi, cosPi);
}
/// <inheritdoc cref="ITrigonometricFunctions{TSelf}.SinPi(TSelf)" />
public static double SinPi(double x)
{
// This code is based on `sinpi` from amd/aocl-libm-ose
// Copyright (C) 2008-2020 Advanced Micro Devices, Inc. All rights reserved.
//
// Licensed under the BSD 3-Clause "New" or "Revised" License
// See THIRD-PARTY-NOTICES.TXT for the full license text
double result;
if (IsFinite(x))
{
double ax = Abs(x);
if (ax < 4_503_599_627_370_496.0) // |x| < 2^52
{
if (ax > 0.25)
{
long integral = (long)ax;
double fractional = ax - integral;
double sign = ((x > 0.0) ? +1.0 : -1.0) * (long.IsOddInteger(integral) ? -1.0 : +1.0);
if (fractional <= 0.25)
{
if (fractional != 0.00)
{
result = sign * SinForIntervalPiBy4(fractional * Pi, 0.0);
}
else
{
result = x * 0.0;
}
}
else if (fractional <= 0.50)
{
if (fractional != 0.50)
{
result = sign * CosForIntervalPiBy4((0.5 - fractional) * Pi, 0.0);
}
else
{
result = sign;
}
}
else if (fractional <= 0.75)
{
result = sign * CosForIntervalPiBy4((fractional - 0.5) * Pi, 0.0);
}
else
{
result = sign * SinForIntervalPiBy4((1.0 - fractional) * Pi, 0.0);
}
}
else if (ax >= 1.220703125E-4) // |x| >= 2^-13
{
result = SinForIntervalPiBy4(x * Pi, 0.0);
}
else if (ax >= 7.450580596923828E-09) // |x| >= 2^-27
{
double value = x * Pi;
result = value - (value * value * value * (1.0 / 6.0));
}
else
{
result = x * Pi;
}
}
else
{
// x is an integer
result = x * 0.0;
}
}
else
{
result = NaN;
}
return result;
}
/// <inheritdoc cref="ITrigonometricFunctions{TSelf}.Tan(TSelf)" />
[Intrinsic]
public static double Tan(double x) => Math.Tan(x);
/// <inheritdoc cref="ITrigonometricFunctions{TSelf}.TanPi(TSelf)" />
public static double TanPi(double x)
{
// This code is based on `tanpi` from amd/aocl-libm-ose
// Copyright (C) 2008-2020 Advanced Micro Devices, Inc. All rights reserved.
//
// Licensed under the BSD 3-Clause "New" or "Revised" License
// See THIRD-PARTY-NOTICES.TXT for the full license text
double result;
if (IsFinite(x))
{
double ax = Abs(x);
double sign = (x > 0.0) ? +1.0 : -1.0;
if (ax < 4_503_599_627_370_496.0) // |x| < 2^52
{
if (ax > 0.25)
{
long integral = (long)ax;
double fractional = ax - integral;
if (fractional <= 0.25)
{
if (fractional != 0.00)
{
result = sign * TanForIntervalPiBy4(fractional * Pi, 0.0, isReciprocal: false);
}
else
{
result = sign * (long.IsOddInteger(integral) ? -0.0 : +0.0);
}
}
else if (fractional <= 0.50)
{
if (fractional != 0.50)
{
result = -sign * TanForIntervalPiBy4((0.5 - fractional) * Pi, 0.0, isReciprocal: true);
}
else
{
result = +sign * (long.IsOddInteger(integral) ? NegativeInfinity : PositiveInfinity);
}
}
else if (fractional <= 0.75)
{
result = +sign * TanForIntervalPiBy4((fractional - 0.5) * Pi, 0.0, isReciprocal: true);
}
else
{
result = -sign * TanForIntervalPiBy4((1.0 - fractional) * Pi, 0.0, isReciprocal: false);
}
}
else if (ax >= 6.103515625E-05) // |x| >= 2^-14
{
result = TanForIntervalPiBy4(x * Pi, 0.0, isReciprocal: false);
}
else if (ax >= 7.450580596923828E-09) // |x| >= 2^-27
{
double value = x * Pi;
result = value + (value * value * value * (1.0 / 3.0));
}
else
{
result = x * Pi;
}
}
else if (ax < 9_007_199_254_740_992.0) // |x| < 2^53
{
// x is an integer
long bits = BitConverter.DoubleToInt64Bits(ax);
result = sign * (long.IsOddInteger(bits) ? -0.0 : +0.0);
}
else
{
// x is an even integer
result = sign * 0.0;
}
}
else
{
result = NaN;
}
return result;
}
//
// IUnaryNegationOperators
//
/// <inheritdoc cref="IUnaryNegationOperators{TSelf, TResult}.op_UnaryNegation(TSelf)" />
static double IUnaryNegationOperators<double, double>.operator -(double value) => -value;
//
// IUnaryPlusOperators
//
/// <inheritdoc cref="IUnaryPlusOperators{TSelf, TResult}.op_UnaryPlus(TSelf)" />
static double IUnaryPlusOperators<double, double>.operator +(double value) => (double)(+value);
//
// IUtf8SpanParsable
//
/// <inheritdoc cref="INumberBase{TSelf}.Parse(ReadOnlySpan{byte}, NumberStyles, IFormatProvider?)" />
public static double Parse(ReadOnlySpan<byte> utf8Text, NumberStyles style = NumberStyles.Float | NumberStyles.AllowThousands, IFormatProvider? provider = null)
{
NumberFormatInfo.ValidateParseStyleInteger(style);
return Number.ParseFloat<byte, double>(utf8Text, style, NumberFormatInfo.GetInstance(provider));
}
/// <inheritdoc cref="INumberBase{TSelf}.TryParse(ReadOnlySpan{byte}, NumberStyles, IFormatProvider?, out TSelf)" />
public static bool TryParse(ReadOnlySpan<byte> utf8Text, NumberStyles style, IFormatProvider? provider, out double result)
{
NumberFormatInfo.ValidateParseStyleInteger(style);
return Number.TryParseFloat(utf8Text, style, NumberFormatInfo.GetInstance(provider), out result);
}
/// <inheritdoc cref="IUtf8SpanParsable{TSelf}.Parse(ReadOnlySpan{byte}, IFormatProvider?)" />
public static double Parse(ReadOnlySpan<byte> utf8Text, IFormatProvider? provider) => Parse(utf8Text, NumberStyles.Float | NumberStyles.AllowThousands, provider);
/// <inheritdoc cref="IUtf8SpanParsable{TSelf}.TryParse(ReadOnlySpan{byte}, IFormatProvider?, out TSelf)" />
public static bool TryParse(ReadOnlySpan<byte> utf8Text, IFormatProvider? provider, out double result) => TryParse(utf8Text, NumberStyles.Float | NumberStyles.AllowThousands, provider, out result);
//
// IBinaryFloatParseAndFormatInfo
//
static int IBinaryFloatParseAndFormatInfo<double>.NumberBufferLength => Number.DoubleNumberBufferLength;
static ulong IBinaryFloatParseAndFormatInfo<double>.ZeroBits => 0;
static ulong IBinaryFloatParseAndFormatInfo<double>.InfinityBits => 0x7FF00000_00000000;
static ulong IBinaryFloatParseAndFormatInfo<double>.NormalMantissaMask => (1UL << SignificandLength) - 1;
static ulong IBinaryFloatParseAndFormatInfo<double>.DenormalMantissaMask => TrailingSignificandMask;
static int IBinaryFloatParseAndFormatInfo<double>.MinBinaryExponent => 1 - MaxExponent;
static int IBinaryFloatParseAndFormatInfo<double>.MaxBinaryExponent => MaxExponent;
static int IBinaryFloatParseAndFormatInfo<double>.MinDecimalExponent => -324;
static int IBinaryFloatParseAndFormatInfo<double>.MaxDecimalExponent => 309;
static int IBinaryFloatParseAndFormatInfo<double>.ExponentBias => ExponentBias;
static ushort IBinaryFloatParseAndFormatInfo<double>.ExponentBits => 11;
static int IBinaryFloatParseAndFormatInfo<double>.OverflowDecimalExponent => (MaxExponent + (2 * SignificandLength)) / 3;
static int IBinaryFloatParseAndFormatInfo<double>.InfinityExponent => 0x7FF;
static ushort IBinaryFloatParseAndFormatInfo<double>.NormalMantissaBits => SignificandLength;
static ushort IBinaryFloatParseAndFormatInfo<double>.DenormalMantissaBits => TrailingSignificandLength;
static int IBinaryFloatParseAndFormatInfo<double>.MinFastFloatDecimalExponent => -342;
static int IBinaryFloatParseAndFormatInfo<double>.MaxFastFloatDecimalExponent => 308;
static int IBinaryFloatParseAndFormatInfo<double>.MinExponentRoundToEven => -4;
static int IBinaryFloatParseAndFormatInfo<double>.MaxExponentRoundToEven => 23;
static int IBinaryFloatParseAndFormatInfo<double>.MaxExponentFastPath => 22;
static ulong IBinaryFloatParseAndFormatInfo<double>.MaxMantissaFastPath => 2UL << TrailingSignificandLength;
static double IBinaryFloatParseAndFormatInfo<double>.BitsToFloat(ulong bits) => BitConverter.UInt64BitsToDouble(bits);
static ulong IBinaryFloatParseAndFormatInfo<double>.FloatToBits(double value) => BitConverter.DoubleToUInt64Bits(value);
//
// Helpers
//
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private static double CosForIntervalPiBy4(double x, double xTail)
{
// This code is based on `cos_piby4` from amd/aocl-libm-ose
// Copyright (C) 2008-2020 Advanced Micro Devices, Inc. All rights reserved.
//
// Licensed under the BSD 3-Clause "New" or "Revised" License
// See THIRD-PARTY-NOTICES.TXT for the full license text
// Taylor series for cos(x) is: 1 - (x^2 / 2!) + (x^4 / 4!) - (x^6 / 6!) ...
//
// Then define f(xx) where xx = (x * x)
// and f(xx) = 1 - (xx / 2!) + (xx^2 / 4!) - (xx^3 / 6!) ...
//
// We use a minimax approximation of (f(xx) - 1 + (xx / 2)) / (xx * xx)
// because this produces an expansion in even powers of x.
//
// If xTail is non-zero, we subtract a correction term g(x, xTail) = (x * xTail)
// to the result, where g(x, xTail) is an approximation to sin(x) * sin(xTail)
//
// This is valid because xTail is tiny relative to x.
const double C1 = +0.41666666666666665390037E-1; // approx: +1 / 4!
const double C2 = -0.13888888888887398280412E-2; // approx: -1 / 6!
const double C3 = +0.248015872987670414957399E-4; // approx: +1 / 8!
const double C4 = -0.275573172723441909470836E-6; // approx: -1 / 10!
const double C5 = +0.208761463822329611076335E-8; // approx: +1 / 12!
const double C6 = -0.113826398067944859590880E-10; // approx: -1 / 14!
double xx = x * x;
double tmp1 = 0.5 * xx;
double tmp2 = 1.0 - tmp1;
double result = C6;
result = (result * xx) + C5;
result = (result * xx) + C4;
result = (result * xx) + C3;
result = (result * xx) + C2;
result = (result * xx) + C1;
result *= (xx * xx);
result += 1.0 - tmp2 - tmp1 - (x * xTail);
result += tmp2;
return result;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private static double SinForIntervalPiBy4(double x, double xTail)
{
// This code is based on `sin_piby4` from amd/aocl-libm-ose
// Copyright (C) 2008-2020 Advanced Micro Devices, Inc. All rights reserved.
//
// Licensed under the BSD 3-Clause "New" or "Revised" License
// See THIRD-PARTY-NOTICES.TXT for the full license text
// Taylor series for sin(x) is x - (x^3 / 3!) + (x^5 / 5!) - (x^7 / 7!) ...
// Which can be expressed as x * (1 - (x^2 / 3!) + (x^4 /5!) - (x^6 /7!) ...)
//
// Then define f(xx) where xx = (x * x)
// and f(xx) = 1 - (xx / 3!) + (xx^2 / 5!) - (xx^3 / 7!) ...
//
// We use a minimax approximation of (f(xx) - 1) / xx
// because this produces an expansion in even powers of x.
//
// If xTail is non-zero, we add a correction term g(x, xTail) = (1 - xx / 2) * xTail
// to the result, where g(x, xTail) is an approximation to cos(x) * sin(xTail)
//
// This is valid because xTail is tiny relative to x.
const double C1 = -0.166666666666666646259241729; // approx: -1 / 3!
const double C2 = +0.833333333333095043065222816E-2; // approx: +1 / 5!
const double C3 = -0.19841269836761125688538679E-3; // approx: -1 / 7!
const double C4 = +0.275573161037288022676895908448E-5; // approx: +1 / 9!
const double C5 = -0.25051132068021699772257377197E-7; // approx: -1 / 11!
const double C6 = +0.159181443044859136852668200E-9; // approx: +1 / 13!
double xx = x * x;
double xxx = xx * x;
double result = C6;
result = (result * xx) + C5;
result = (result * xx) + C4;
result = (result * xx) + C3;
result = (result * xx) + C2;
if (xTail == 0.0)
{
result = (xx * result) + C1;
result = (xxx * result) + x;
}
else
{
result = x - ((xx * ((0.5 * xTail) - (xxx * result))) - xTail - (xxx * C1));
}
return result;
}
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private static double TanForIntervalPiBy4(double x, double xTail, bool isReciprocal)
{
// This code is based on `tan_piby4` from amd/aocl-libm-ose
// Copyright (C) 2008-2020 Advanced Micro Devices, Inc. All rights reserved.
//
// Licensed under the BSD 3-Clause "New" or "Revised" License
// See THIRD-PARTY-NOTICES.TXT for the full license text
// In order to maintain relative precision transform using the identity:
// tan((pi / 4) - x) = (1 - tan(x)) / (1 + tan(x)) for arguments close to (pi / 4).
//
// Similarly use tan(x - (pi / 4)) = (tan(x) - 1) / (tan(x) + 1) close to (-pi / 4).
const double PiBy4Head = 7.85398163397448278999E-01;
const double PiBy4Tail = 3.06161699786838240164E-17;
int transform = 0;
if (x > +0.68)
{
transform = 1;
x = (PiBy4Head - x) + (PiBy4Tail - xTail);
xTail = 0.0;
}
else if (x < -0.68)
{
transform = -1;
x = (PiBy4Head + x) + (PiBy4Tail + xTail);
xTail = 0.0;
}
// Core Remez [2, 3] approximation to tan(x + xTail) on the interval [0, 0.68].
double tmp1 = (x * x) + (2.0 * x * xTail);
double denominator = -0.232371494088563558304549252913E-3;
denominator = +0.260656620398645407524064091208E-1 + (denominator * tmp1);
denominator = -0.515658515729031149329237816945E+0 + (denominator * tmp1);
denominator = +0.111713747927937668539901657944E+1 + (denominator * tmp1);
double numerator = +0.224044448537022097264602535574E-3;
numerator = -0.229345080057565662883358588111E-1 + (numerator * tmp1);
numerator = +0.372379159759792203640806338901E+0 + (numerator * tmp1);
double tmp2 = x * tmp1;
tmp2 *= numerator / denominator;
tmp2 += xTail;
// Reconstruct tan(x) in the transformed case
double result = x + tmp2;
if (transform != 0)
{
if (isReciprocal)
{
result = (transform * (2 * result / (result - 1))) - 1.0;
}
else
{
result = transform * (1.0 - (2 * result / (1 + result)));
}
}
else if (isReciprocal)
{
// Compute -1.0 / (x + tmp2) accurately
ulong bits = BitConverter.DoubleToUInt64Bits(result);
bits &= 0xFFFFFFFF00000000;
double z1 = BitConverter.UInt64BitsToDouble(bits);
double z2 = tmp2 - (z1 - x);
double reciprocal = -1.0 / result;
bits = BitConverter.DoubleToUInt64Bits(reciprocal);
bits &= 0xFFFFFFFF00000000;
double reciprocalHead = BitConverter.UInt64BitsToDouble(bits);
result = reciprocalHead + (reciprocal * (1.0 + (reciprocalHead * z1) + (reciprocalHead * z2)));
}
return result;
}
}
}
|