//
// Math.NET Numerics, part of the Math.NET Project
// http://numerics.mathdotnet.com
// http://github.com/mathnet/mathnet-numerics
//
// Copyright (c) 2009-2013 Math.NET
//
// Permission is hereby granted, free of charge, to any person
// obtaining a copy of this software and associated documentation
// files (the "Software"), to deal in the Software without
// restriction, including without limitation the rights to use,
// copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following
// conditions:
//
// The above copyright notice and this permission notice shall be
// included in all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
// OTHER DEALINGS IN THE SOFTWARE.
//
namespace IStation.Numerics
{
public static partial class Precision
{
///
/// Compares two doubles and determines which double is bigger.
/// a < b -> -1; a ~= b (almost equal according to parameter) -> 0; a > b -> +1.
///
/// The first value.
/// The second value.
/// The absolute accuracy required for being almost equal.
public static int CompareTo(this double a, double b, double maximumAbsoluteError)
{
// NANs are equal to nothing,
// not even themselves, and thus they're not bigger or
// smaller than anything either
if (double.IsNaN(a) || double.IsNaN(b))
{
return a.CompareTo(b);
}
// If A or B are infinity (positive or negative) then
// only return true if first is smaller
if (double.IsInfinity(a) || double.IsInfinity(b))
{
return a.CompareTo(b);
}
// If the numbers are equal to within the number of decimal places
// then there's technically no difference
if (AlmostEqual(a, b, maximumAbsoluteError))
{
return 0;
}
// The numbers differ by more than the decimal places, so
// we can check the normal way to see if the first is
// larger than the second.
return a.CompareTo(b);
}
///
/// Compares two doubles and determines which double is bigger.
/// a < b -> -1; a ~= b (almost equal according to parameter) -> 0; a > b -> +1.
///
/// The first value.
/// The second value.
/// The number of decimal places on which the values must be compared. Must be 1 or larger.
public static int CompareTo(this double a, double b, int decimalPlaces)
{
// NANs are equal to nothing,
// not even themselves, and thus they're not bigger or
// smaller than anything either
if (double.IsNaN(a) || double.IsNaN(b))
{
return a.CompareTo(b);
}
// If A or B are infinity (positive or negative) then
// only return true if first is smaller
if (double.IsInfinity(a) || double.IsInfinity(b))
{
return a.CompareTo(b);
}
// If the numbers are equal to within the number of decimal places
// then there's technically no difference
if (AlmostEqual(a, b, decimalPlaces))
{
return 0;
}
// The numbers differ by more than the decimal places, so
// we can check the normal way to see if the first is
// larger than the second.
return a.CompareTo(b);
}
///
/// Compares two doubles and determines which double is bigger.
/// a < b -> -1; a ~= b (almost equal according to parameter) -> 0; a > b -> +1.
///
/// The first value.
/// The second value.
/// The relative accuracy required for being almost equal.
public static int CompareToRelative(this double a, double b, double maximumError)
{
// NANs are equal to nothing,
// not even themselves, and thus they're not bigger or
// smaller than anything either
if (double.IsNaN(a) || double.IsNaN(b))
{
return a.CompareTo(b);
}
// If A or B are infinity (positive or negative) then
// only return true if first is smaller
if (double.IsInfinity(a) || double.IsInfinity(b))
{
return a.CompareTo(b);
}
// If the numbers are equal to within the number of decimal places
// then there's technically no difference
if (AlmostEqualRelative(a, b, maximumError))
{
return 0;
}
// The numbers differ by more than the decimal places, so
// we can check the normal way to see if the first is
// larger than the second.
return a.CompareTo(b);
}
///
/// Compares two doubles and determines which double is bigger.
/// a < b -> -1; a ~= b (almost equal according to parameter) -> 0; a > b -> +1.
///
/// The first value.
/// The second value.
/// The number of decimal places on which the values must be compared. Must be 1 or larger.
public static int CompareToRelative(this double a, double b, int decimalPlaces)
{
// NANs are equal to nothing,
// not even themselves, and thus they're not bigger or
// smaller than anything either
if (double.IsNaN(a) || double.IsNaN(b))
{
return a.CompareTo(b);
}
// If A or B are infinity (positive or negative) then
// only return true if first is smaller
if (double.IsInfinity(a) || double.IsInfinity(b))
{
return a.CompareTo(b);
}
// If the numbers are equal to within the number of decimal places
// then there's technically no difference
if (AlmostEqualRelative(a, b, decimalPlaces))
{
return 0;
}
// The numbers differ by more than the decimal places, so
// we can check the normal way to see if the first is
// larger than the second.
return a.CompareTo(b);
}
///
/// Compares two doubles and determines which double is bigger.
/// a < b -> -1; a ~= b (almost equal according to parameter) -> 0; a > b -> +1.
///
/// The first value.
/// The second value.
/// The maximum error in terms of Units in Last Place (ulps), i.e. the maximum number of decimals that may be different. Must be 1 or larger.
public static int CompareToNumbersBetween(this double a, double b, long maxNumbersBetween)
{
// NANs are equal to nothing,
// not even themselves, and thus they're not bigger or
// smaller than anything either
if (double.IsNaN(a) || double.IsNaN(b))
{
return a.CompareTo(b);
}
// If A or B are infinity (positive or negative) then
// only return true if first is smaller
if (double.IsInfinity(a) || double.IsInfinity(b))
{
return a.CompareTo(b);
}
// If the numbers are equal to within the tolerance then
// there's technically no difference
if (AlmostEqualNumbersBetween(a, b, maxNumbersBetween))
{
return 0;
}
return a.CompareTo(b);
}
///
/// Compares two doubles and determines if the first value is larger than the second
/// value to within the specified number of decimal places or not.
///
///
///
/// The values are equal if the difference between the two numbers is smaller than 10^(-numberOfDecimalPlaces). We divide by
/// two so that we have half the range on each side of the numbers, e.g. if == 2, then 0.01 will equal between
/// 0.005 and 0.015, but not 0.02 and not 0.00
///
///
/// The first value.
/// The second value.
/// The number of decimal places.
/// true if the first value is larger than the second value; otherwise false.
public static bool IsLarger(this double a, double b, int decimalPlaces)
{
// If A or B are a NAN, return false. NANs are equal to nothing,
// not even themselves, and thus they're not bigger or
// smaller than anything either
if (double.IsNaN(a) || double.IsNaN(b))
{
return false;
}
return CompareTo(a, b, decimalPlaces) > 0;
}
///
/// Compares two doubles and determines if the first value is larger than the second
/// value to within the specified number of decimal places or not.
///
///
///
/// The values are equal if the difference between the two numbers is smaller than 10^(-numberOfDecimalPlaces). We divide by
/// two so that we have half the range on each side of the numbers, e.g. if == 2, then 0.01 will equal between
/// 0.005 and 0.015, but not 0.02 and not 0.00
///
///
/// The first value.
/// The second value.
/// The number of decimal places.
/// true if the first value is larger than the second value; otherwise false.
public static bool IsLarger(this float a, float b, int decimalPlaces)
{
// If A or B are a NAN, return false. NANs are equal to nothing,
// not even themselves, and thus they're not bigger or
// smaller than anything either
if (float.IsNaN(a) || float.IsNaN(b))
{
return false;
}
return CompareTo(a, b, decimalPlaces) > 0;
}
///
/// Compares two doubles and determines if the first value is larger than the second
/// value to within the specified number of decimal places or not.
///
/// The first value.
/// The second value.
/// The absolute accuracy required for being almost equal.
/// true if the first value is larger than the second value; otherwise false.
public static bool IsLarger(this double a, double b, double maximumAbsoluteError)
{
// If A or B are a NAN, return false. NANs are equal to nothing,
// not even themselves, and thus they're not bigger or
// smaller than anything either
if (double.IsNaN(a) || double.IsNaN(b))
{
return false;
}
return CompareTo(a, b, maximumAbsoluteError) > 0;
}
///
/// Compares two doubles and determines if the first value is larger than the second
/// value to within the specified number of decimal places or not.
///
/// The first value.
/// The second value.
/// The absolute accuracy required for being almost equal.
/// true if the first value is larger than the second value; otherwise false.
public static bool IsLarger(this float a, float b, double maximumAbsoluteError)
{
// If A or B are a NAN, return false. NANs are equal to nothing,
// not even themselves, and thus they're not bigger or
// smaller than anything either
if (float.IsNaN(a) || float.IsNaN(b))
{
return false;
}
return CompareTo(a, b, maximumAbsoluteError) > 0;
}
///
/// Compares two doubles and determines if the first value is larger than the second
/// value to within the specified number of decimal places or not.
///
///
///
/// The values are equal if the difference between the two numbers is smaller than 10^(-numberOfDecimalPlaces). We divide by
/// two so that we have half the range on each side of the numbers, e.g. if == 2, then 0.01 will equal between
/// 0.005 and 0.015, but not 0.02 and not 0.00
///
///
/// The first value.
/// The second value.
/// The number of decimal places.
/// true if the first value is larger than the second value; otherwise false.
public static bool IsLargerRelative(this double a, double b, int decimalPlaces)
{
// If A or B are a NAN, return false. NANs are equal to nothing,
// not even themselves, and thus they're not bigger or
// smaller than anything either
if (double.IsNaN(a) || double.IsNaN(b))
{
return false;
}
return CompareToRelative(a, b, decimalPlaces) > 0;
}
///
/// Compares two doubles and determines if the first value is larger than the second
/// value to within the specified number of decimal places or not.
///
///
///
/// The values are equal if the difference between the two numbers is smaller than 10^(-numberOfDecimalPlaces). We divide by
/// two so that we have half the range on each side of the numbers, e.g. if == 2, then 0.01 will equal between
/// 0.005 and 0.015, but not 0.02 and not 0.00
///
///
/// The first value.
/// The second value.
/// The number of decimal places.
/// true if the first value is larger than the second value; otherwise false.
public static bool IsLargerRelative(this float a, float b, int decimalPlaces)
{
// If A or B are a NAN, return false. NANs are equal to nothing,
// not even themselves, and thus they're not bigger or
// smaller than anything either
if (float.IsNaN(a) || float.IsNaN(b))
{
return false;
}
return CompareToRelative(a, b, decimalPlaces) > 0;
}
///
/// Compares two doubles and determines if the first value is larger than the second
/// value to within the specified number of decimal places or not.
///
/// The first value.
/// The second value.
/// The relative accuracy required for being almost equal.
/// true if the first value is larger than the second value; otherwise false.
public static bool IsLargerRelative(this double a, double b, double maximumError)
{
// If A or B are a NAN, return false. NANs are equal to nothing,
// not even themselves, and thus they're not bigger or
// smaller than anything either
if (double.IsNaN(a) || double.IsNaN(b))
{
return false;
}
return CompareToRelative(a, b, maximumError) > 0;
}
///
/// Compares two doubles and determines if the first value is larger than the second
/// value to within the specified number of decimal places or not.
///
/// The first value.
/// The second value.
/// The relative accuracy required for being almost equal.
/// true if the first value is larger than the second value; otherwise false.
public static bool IsLargerRelative(this float a, float b, double maximumError)
{
// If A or B are a NAN, return false. NANs are equal to nothing,
// not even themselves, and thus they're not bigger or
// smaller than anything either
if (float.IsNaN(a) || float.IsNaN(b))
{
return false;
}
return CompareToRelative(a, b, maximumError) > 0;
}
///
/// Compares two doubles and determines if the first value is larger than the second
/// value to within the tolerance or not. Equality comparison is based on the binary representation.
///
/// The first value.
/// The second value.
/// The maximum number of floating point values for which the two values are considered equal. Must be 1 or larger.
/// true if the first value is larger than the second value; otherwise false.
public static bool IsLargerNumbersBetween(this double a, double b, long maxNumbersBetween)
{
// If A or B are a NAN, return false. NANs are equal to nothing,
// not even themselves, and thus they're not bigger or
// smaller than anything either
if (double.IsNaN(a) || double.IsNaN(b))
{
return false;
}
return CompareToNumbersBetween(a, b, maxNumbersBetween) > 0;
}
///
/// Compares two doubles and determines if the first value is larger than the second
/// value to within the tolerance or not. Equality comparison is based on the binary representation.
///
/// The first value.
/// The second value.
/// The maximum number of floating point values for which the two values are considered equal. Must be 1 or larger.
/// true if the first value is larger than the second value; otherwise false.
public static bool IsLargerNumbersBetween(this float a, float b, long maxNumbersBetween)
{
// If A or B are a NAN, return false. NANs are equal to nothing,
// not even themselves, and thus they're not bigger or
// smaller than anything either
if (float.IsNaN(a) || float.IsNaN(b))
{
return false;
}
return CompareToNumbersBetween(a, b, maxNumbersBetween) > 0;
}
///
/// Compares two doubles and determines if the first value is smaller than the second
/// value to within the specified number of decimal places or not.
///
///
///
/// The values are equal if the difference between the two numbers is smaller than 10^(-numberOfDecimalPlaces). We divide by
/// two so that we have half the range on each side of thg. if == 2, then 0.01 will equal between
/// 0.005 and 0.015, but not 0.02 and not 0.00
///
///
/// The first value.
/// The second value.
/// The number of decimal places.
/// true if the first value is smaller than the second value; otherwise false.
public static bool IsSmaller(this double a, double b, int decimalPlaces)
{
// If A or B are a NAN, return false. NANs are equal to nothing,
// not even themselves, and thus they're not bigger or
// smaller than anything either
if (double.IsNaN(a) || double.IsNaN(b))
{
return false;
}
return CompareTo(a, b, decimalPlaces) < 0;
}
///
/// Compares two doubles and determines if the first value is smaller than the second
/// value to within the specified number of decimal places or not.
///
///
///
/// The values are equal if the difference between the two numbers is smaller than 10^(-numberOfDecimalPlaces). We divide by
/// two so that we have half the range on each side of thg. if == 2, then 0.01 will equal between
/// 0.005 and 0.015, but not 0.02 and not 0.00
///
///
/// The first value.
/// The second value.
/// The number of decimal places.
/// true if the first value is smaller than the second value; otherwise false.
public static bool IsSmaller(this float a, float b, int decimalPlaces)
{
// If A or B are a NAN, return false. NANs are equal to nothing,
// not even themselves, and thus they're not bigger or
// smaller than anything either
if (float.IsNaN(a) || float.IsNaN(b))
{
return false;
}
return CompareTo(a, b, decimalPlaces) < 0;
}
///
/// Compares two doubles and determines if the first value is smaller than the second
/// value to within the specified number of decimal places or not.
///
/// The first value.
/// The second value.
/// The absolute accuracy required for being almost equal.
/// true if the first value is smaller than the second value; otherwise false.
public static bool IsSmaller(this double a, double b, double maximumAbsoluteError)
{
// If A or B are a NAN, return false. NANs are equal to nothing,
// not even themselves, and thus they're not bigger or
// smaller than anything either
if (double.IsNaN(a) || double.IsNaN(b))
{
return false;
}
return CompareTo(a, b, maximumAbsoluteError) < 0;
}
///
/// Compares two doubles and determines if the first value is smaller than the second
/// value to within the specified number of decimal places or not.
///
/// The first value.
/// The second value.
/// The absolute accuracy required for being almost equal.
/// true if the first value is smaller than the second value; otherwise false.
public static bool IsSmaller(this float a, float b, double maximumAbsoluteError)
{
// If A or B are a NAN, return false. NANs are equal to nothing,
// not even themselves, and thus they're not bigger or
// smaller than anything either
if (float.IsNaN(a) || float.IsNaN(b))
{
return false;
}
return CompareTo(a, b, maximumAbsoluteError) < 0;
}
///
/// Compares two doubles and determines if the first value is smaller than the second
/// value to within the specified number of decimal places or not.
///
/// The first value.
/// The second value.
/// The number of decimal places.
/// true if the first value is smaller than the second value; otherwise false.
public static bool IsSmallerRelative(this double a, double b, int decimalPlaces)
{
// If A or B are a NAN, return false. NANs are equal to nothing,
// not even themselves, and thus they're not bigger or
// smaller than anything either
if (double.IsNaN(a) || double.IsNaN(b))
{
return false;
}
return CompareToRelative(a, b, decimalPlaces) < 0;
}
///
/// Compares two doubles and determines if the first value is smaller than the second
/// value to within the specified number of decimal places or not.
///
/// The first value.
/// The second value.
/// The number of decimal places.
/// true if the first value is smaller than the second value; otherwise false.
public static bool IsSmallerRelative(this float a, float b, int decimalPlaces)
{
// If A or B are a NAN, return false. NANs are equal to nothing,
// not even themselves, and thus they're not bigger or
// smaller than anything either
if (float.IsNaN(a) || float.IsNaN(b))
{
return false;
}
return CompareToRelative(a, b, decimalPlaces) < 0;
}
///
/// Compares two doubles and determines if the first value is smaller than the second
/// value to within the specified number of decimal places or not.
///
/// The first value.
/// The second value.
/// The relative accuracy required for being almost equal.
/// true if the first value is smaller than the second value; otherwise false.
public static bool IsSmallerRelative(this double a, double b, double maximumError)
{
// If A or B are a NAN, return false. NANs are equal to nothing,
// not even themselves, and thus they're not bigger or
// smaller than anything either
if (double.IsNaN(a) || double.IsNaN(b))
{
return false;
}
return CompareToRelative(a, b, maximumError) < 0;
}
///
/// Compares two doubles and determines if the first value is smaller than the second
/// value to within the specified number of decimal places or not.
///
/// The first value.
/// The second value.
/// The relative accuracy required for being almost equal.
/// true if the first value is smaller than the second value; otherwise false.
public static bool IsSmallerRelative(this float a, float b, double maximumError)
{
// If A or B are a NAN, return false. NANs are equal to nothing,
// not even themselves, and thus they're not bigger or
// smaller than anything either
if (float.IsNaN(a) || float.IsNaN(b))
{
return false;
}
return CompareToRelative(a, b, maximumError) < 0;
}
///
/// Compares two doubles and determines if the first value is smaller than the second
/// value to within the tolerance or not. Equality comparison is based on the binary representation.
///
/// The first value.
/// The second value.
/// The maximum number of floating point values for which the two values are considered equal. Must be 1 or larger.
/// true if the first value is smaller than the second value; otherwise false.
public static bool IsSmallerNumbersBetween(this double a, double b, long maxNumbersBetween)
{
// If A or B are a NAN, return false. NANs are equal to nothing,
// not even themselves, and thus they're not bigger or
// smaller than anything either
if (double.IsNaN(a) || double.IsNaN(b))
{
return false;
}
return CompareToNumbersBetween(a, b, maxNumbersBetween) < 0;
}
///
/// Compares two doubles and determines if the first value is smaller than the second
/// value to within the tolerance or not. Equality comparison is based on the binary representation.
///
/// The first value.
/// The second value.
/// The maximum number of floating point values for which the two values are considered equal. Must be 1 or larger.
/// true if the first value is smaller than the second value; otherwise false.
public static bool IsSmallerNumbersBetween(this float a, float b, long maxNumbersBetween)
{
// If A or B are a NAN, return false. NANs are equal to nothing,
// not even themselves, and thus they're not bigger or
// smaller than anything either
if (float.IsNaN(a) || float.IsNaN(b))
{
return false;
}
return CompareToNumbersBetween(a, b, maxNumbersBetween) < 0;
}
///
/// Checks if a given double values is finite, i.e. neither NaN nor inifnity
///
/// The value to be checked fo finitenes.
public static bool IsFinite(this double value)
{
return !double.IsNaN(value) && !double.IsInfinity(value);
}
}
}