Precision Class |
Utilities for working with floating point numbers.
Inheritance HierarchyNamespace: Altaxo.Calc
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3179.0 (4.8.3179.0)
SyntaxC#
public static class Precision
The Precision type exposes the following members.
Methods| Name | Description | |
|---|---|---|
 | AlmostEqual(Complex, Complex) | Checks whether two Complex numbers are almost equal. |
| AlmostEqual(Complex32, Complex32) | Checks whether two Complex numbers are almost equal. |
| AlmostEqual(Double, Double) | Checks whether two real numbers are almost equal. |
| AlmostEqual(Single, Single) | Checks whether two real numbers are almost equal. |
| AlmostEqual(Complex, Complex, Double) | Compares two complex and determines if they are equal within the specified maximum error. |
| AlmostEqual(Complex, Complex, Int32) | Compares two doubles and determines if they are equal to within the specified number of decimal places or not, using the number of decimal places as an absolute measure. |
| AlmostEqual(Complex32, Complex32, Double) | Compares two complex and determines if they are equal within the specified maximum error. |
| AlmostEqual(Complex32, Complex32, Int32) | Compares two doubles and determines if they are equal to within the specified number of decimal places or not, using the number of decimal places as an absolute measure. |
| AlmostEqual(Double, Double, Double) | Compares two doubles and determines if they are equal within the specified maximum error. |
| AlmostEqual(Double, Double, Int32) | Compares two doubles and determines if they are equal to within the specified number of decimal places or not, using the number of decimal places as an absolute measure. |
| AlmostEqual(Single, Single, Double) | Compares two complex and determines if they are equal within the specified maximum error. |
| AlmostEqual(Single, Single, Int32) | Compares two doubles and determines if they are equal to within the specified number of decimal places or not, using the number of decimal places as an absolute measure. |
| AlmostEqualT(MatrixT, MatrixT, Double) | Compares two matrices and determines if they are equal within the specified maximum error. |
| AlmostEqualT(MatrixT, MatrixT, Int32) | Compares two matrices and determines if they are equal to within the specified number of decimal places or not, using the number of decimal places as an absolute measure. |
| AlmostEqualT(VectorT, VectorT, Double) | Compares two vectors and determines if they are equal within the specified maximum error. |
| AlmostEqualT(VectorT, VectorT, Int32) | Compares two vectors and determines if they are equal to within the specified number of decimal places or not, using the number of decimal places as an absolute measure. |
| AlmostEqualNorm(Double, Double, Double, Double) | Compares two doubles and determines if they are equal within the specified maximum absolute error. |
| AlmostEqualNorm(Double, Double, Double, Int32) | Compares two doubles and determines if they are equal to within the specified number of decimal places or not, using the number of decimal places as an absolute measure. |
| AlmostEqualNormT(T, T, Double) | Compares two doubles and determines if they are equal within the specified maximum absolute error. |
| AlmostEqualNormT(T, T, Int32) | Compares two doubles and determines if they are equal to within the specified number of decimal places or not, using the number of decimal places as an absolute measure. |
| AlmostEqualNormRelative(Double, Double, Double, Double) | Compares two doubles and determines if they are equal within the specified maximum error. |
| AlmostEqualNormRelative(Double, Double, Double, Int32) | Compares two doubles and determines if they are equal to within the specified number of decimal places or not. If the numbers are very close to zero an absolute difference is compared, otherwise the relative difference is compared. |
| AlmostEqualNormRelativeT(T, T, Double) | Compares two doubles and determines if they are equal within the specified maximum error. |
| AlmostEqualNormRelativeT(T, T, Int32) | Compares two doubles and determines if they are equal to within the specified number of decimal places or not. If the numbers are very close to zero an absolute difference is compared, otherwise the relative difference is compared. |
| AlmostEqualNumbersBetween(Double, Double, Int64) | Compares two doubles and determines if they are equal to within the tolerance or not. Equality comparison is based on the binary representation. |
| AlmostEqualNumbersBetween(Single, Single, Int32) | Compares two floats and determines if they are equal to within the tolerance or not. Equality comparison is based on the binary representation. |
| AlmostEqualRelative(Complex, Complex) | Checks whether two Complex numbers are almost equal. |
| AlmostEqualRelative(Complex32, Complex32) | Checks whether two Complex numbers are almost equal. |
| AlmostEqualRelative(Double, Double) | Checks whether two real numbers are almost equal. |
| AlmostEqualRelative(Single, Single) | Checks whether two real numbers are almost equal. |
| AlmostEqualRelative(Complex, Complex, Double) | Compares two complex and determines if they are equal within the specified maximum error. |
| AlmostEqualRelative(Complex, Complex, Int32) | Compares two doubles and determines if they are equal to within the specified number of decimal places or not. If the numbers are very close to zero an absolute difference is compared, otherwise the relative difference is compared. |
| AlmostEqualRelative(Complex32, Complex32, Double) | Compares two complex and determines if they are equal within the specified maximum error. |
| AlmostEqualRelative(Complex32, Complex32, Int32) | Compares two doubles and determines if they are equal to within the specified number of decimal places or not. If the numbers are very close to zero an absolute difference is compared, otherwise the relative difference is compared. |
| AlmostEqualRelative(Double, Double, Double) | Compares two doubles and determines if they are equal within the specified maximum error. |
| AlmostEqualRelative(Double, Double, Int32) | Compares two doubles and determines if they are equal to within the specified number of decimal places or not. If the numbers are very close to zero an absolute difference is compared, otherwise the relative difference is compared. |
| AlmostEqualRelative(Single, Single, Double) | Compares two complex and determines if they are equal within the specified maximum error. |
| AlmostEqualRelative(Single, Single, Int32) | Compares two doubles and determines if they are equal to within the specified number of decimal places or not. If the numbers are very close to zero an absolute difference is compared, otherwise the relative difference is compared. |
| AlmostEqualRelativeT(MatrixT, MatrixT, Double) | Compares two matrices and determines if they are equal within the specified maximum error. |
| AlmostEqualRelativeT(MatrixT, MatrixT, Int32) | Compares two matrices and determines if they are equal to within the specified number of decimal places or not. If the numbers are very close to zero an absolute difference is compared, otherwise the relative difference is compared. |
| AlmostEqualRelativeT(VectorT, VectorT, Double) | Compares two vectors and determines if they are equal within the specified maximum error. |
| AlmostEqualRelativeT(VectorT, VectorT, Int32) | Compares two vectors and determines if they are equal to within the specified number of decimal places or not. If the numbers are very close to zero an absolute difference is compared, otherwise the relative difference is compared. |
| CoerceZero(Double) | Forces small numbers near zero to zero. |
| CoerceZero(Double, Double) | Forces small numbers near zero to zero, according to the specified absolute accuracy. |
| CoerceZero(Double, Int32) | Forces small numbers near zero to zero, according to the specified absolute accuracy. |
| CoerceZero(Double, Int64) | Forces small numbers near zero to zero, according to the specified absolute accuracy. |
| CompareTo(Double, Double, Double) | Compares two doubles and determines which double is bigger. a < b -> -1; a ~= b (almost equal according to parameter) -> 0; a > b -> +1. |
| CompareTo(Double, Double, Int32) | Compares two doubles and determines which double is bigger. a < b -> -1; a ~= b (almost equal according to parameter) -> 0; a > b -> +1. |
| CompareToNumbersBetween | Compares two doubles and determines which double is bigger. a < b -> -1; a ~= b (almost equal according to parameter) -> 0; a > b -> +1. |
| CompareToRelative(Double, Double, Double) | Compares two doubles and determines which double is bigger. a < b -> -1; a ~= b (almost equal according to parameter) -> 0; a > b -> +1. |
| CompareToRelative(Double, Double, Int32) | Compares two doubles and determines which double is bigger. a < b -> -1; a ~= b (almost equal according to parameter) -> 0; a > b -> +1. |
| Decrement | Decrements a floating point number to the next smaller number representable by the data type. |
| EpsilonOf(Double) | Evaluates the minimum distance to the next distinguishable number near the argument value. |
| EpsilonOf(Single) | Evaluates the minimum distance to the next distinguishable number near the argument value. |
| Increment | Increments a floating point number to the next bigger number representable by the data type. |
| IsFinite | Checks if a given double values is finite, i.e. neither NaN nor inifnity |
| IsLarger(Double, Double, Double) | 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. |
| IsLarger(Double, Double, Int32) | 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. |
| IsLarger(Single, Single, Double) | 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. |
| IsLarger(Single, Single, Int32) | 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. |
| IsLargerNumbersBetween(Double, Double, Int64) | 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. |
| IsLargerNumbersBetween(Single, Single, Int64) | 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. |
| IsLargerRelative(Double, Double, Double) | 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. |
| IsLargerRelative(Double, Double, Int32) | 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. |
| IsLargerRelative(Single, Single, Double) | 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. |
| IsLargerRelative(Single, Single, Int32) | 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. |
| IsSmaller(Double, Double, Double) | 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. |
| IsSmaller(Double, Double, Int32) | 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. |
| IsSmaller(Single, Single, Double) | 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. |
| IsSmaller(Single, Single, Int32) | 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. |
| IsSmallerNumbersBetween(Double, Double, Int64) | 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. |
| IsSmallerNumbersBetween(Single, Single, Int64) | 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. |
| IsSmallerRelative(Double, Double, Double) | 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. |
| IsSmallerRelative(Double, Double, Int32) | 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. |
| IsSmallerRelative(Single, Single, Double) | 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. |
| IsSmallerRelative(Single, Single, Int32) | 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. |
| ListAlmostEqual(IListComplex32, IListComplex32, Double) | Compares two lists of doubles and determines if they are equal within the specified maximum error. |
| ListAlmostEqual(IListComplex32, IListComplex32, Int32) | Compares two lists of doubles and determines if they are equal within the specified maximum error. |
| ListAlmostEqual(IListDouble, IListDouble, Double) | Compares two lists of doubles and determines if they are equal within the specified maximum error. |
| ListAlmostEqual(IListDouble, IListDouble, Int32) | Compares two lists of doubles and determines if they are equal within the specified maximum error. |
| ListAlmostEqual(IListComplex, IListComplex, Double) | Compares two lists of doubles and determines if they are equal within the specified maximum error. |
| ListAlmostEqual(IListComplex, IListComplex, Int32) | Compares two lists of doubles and determines if they are equal within the specified maximum error. |
| ListAlmostEqual(IListSingle, IListSingle, Double) | Compares two lists of doubles and determines if they are equal within the specified maximum error. |
| ListAlmostEqual(IListSingle, IListSingle, Int32) | Compares two lists of doubles and determines if they are equal within the specified maximum error. |
| ListAlmostEqualNormT | Compares two lists of doubles and determines if they are equal within the specified maximum error. |
| ListAlmostEqualNormRelativeT | Compares two lists of doubles and determines if they are equal within the specified maximum error. |
| ListAlmostEqualRelative(IListComplex32, IListComplex32, Double) | Compares two lists of doubles and determines if they are equal within the specified maximum error. |
| ListAlmostEqualRelative(IListComplex32, IListComplex32, Int32) | Compares two lists of doubles and determines if they are equal within the specified maximum error. |
| ListAlmostEqualRelative(IListDouble, IListDouble, Double) | Compares two lists of doubles and determines if they are equal within the specified maximum error. |
| ListAlmostEqualRelative(IListDouble, IListDouble, Int32) | Compares two lists of doubles and determines if they are equal within the specified maximum error. |
| ListAlmostEqualRelative(IListComplex, IListComplex, Double) | Compares two lists of doubles and determines if they are equal within the specified maximum error. |
| ListAlmostEqualRelative(IListComplex, IListComplex, Int32) | Compares two lists of doubles and determines if they are equal within the specified maximum error. |
| ListAlmostEqualRelative(IListSingle, IListSingle, Double) | Compares two lists of doubles and determines if they are equal within the specified maximum error. |
| ListAlmostEqualRelative(IListSingle, IListSingle, Int32) | Compares two lists of doubles and determines if they are equal within the specified maximum error. |
| Magnitude(Double) | Returns the magnitude of the number. |
| Magnitude(Single) | Returns the magnitude of the number. |
| MaximumMatchingFloatingPointNumber | Returns the floating point number that will match the value with the tolerance on the maximum size (i.e. the result is always bigger than the value) |
| MinimumMatchingFloatingPointNumber | Returns the floating point number that will match the value with the tolerance on the minimum size (i.e. the result is always smaller than the value) |
| NumbersBetween | Evaluates the count of numbers between two double numbers |
| PositiveEpsilonOf(Double) | Evaluates the minimum distance to the next distinguishable number near the argument value. |
| PositiveEpsilonOf(Single) | Evaluates the minimum distance to the next distinguishable number near the argument value. |
| RangeOfMatchingFloatingPointNumbers | Determines the range of floating point numbers that will match the specified value with the given tolerance. |
| RangeOfMatchingNumbers | Determines the range of ulps that will match the specified value with the given tolerance. |
 | Round(BigInteger, Int32) | Round to the number closest to 10^(-decimals). Negative decimals to round within the integer part. |
| Round(Decimal, Int32) | Round to the number closest to 10^(-decimals). Negative decimals to round within the integer part. |
| Round(Double, Int32) | Round to the number closest to 10^(-decimals). Negative decimals to round within the integer part. |
| Round(Int16, Int32) | Round to the number closest to 10^(-decimals). Negative decimals to round within the integer part. |
| Round(Int32, Int32) | Round to the number closest to 10^(-decimals). Negative decimals to round within the integer part. |
| Round(Int64, Int32) | Round to the number closest to 10^(-decimals). Negative decimals to round within the integer part. |
| Round(Single, Int32) | Round to the number closest to 10^(-decimals). Negative decimals to round within the integer part. |
| Round(UInt16, Int32) | Round to the number closest to 10^(-decimals). Negative decimals to round within the integer part. |
| Round(UInt32, Int32) | Round to the number closest to 10^(-decimals). Negative decimals to round within the integer part. |
| Round(UInt64, Int32) | Round to the number closest to 10^(-decimals). Negative decimals to round within the integer part. |
| RoundToMultiple(Decimal, Decimal) | Round to a multiple of the provided positive basis. |
| RoundToMultiple(Double, Double) | Round to a multiple of the provided positive basis. |
| RoundToMultiple(Single, Single) | Round to a multiple of the provided positive basis. |
| RoundToPower(Double, Double) | Round to a multiple of the provided positive basis. |
| RoundToPower(Single, Single) | Round to a multiple of the provided positive basis. |
| ScaleUnitMagnitude | Returns the number divided by it's magnitude, effectively returning a number between -10 and 10. |
Fields| Name | Description | |
|---|---|---|
  | DoubleDecimalPlaces | The number of significant decimal places of double-precision floating numbers (64 bit). |
| DoublePrecision | Standard epsilon, the maximum relative precision of IEEE 754 double-precision floating numbers (64 bit). According to the definition of Prof. Demmel and used in LAPACK and Scilab. |
| MachineEpsilon | Actual double precision machine epsilon, the smallest number that can be subtracted from 1, yielding a results different than 1. This is also known as unit roundoff error. According to the definition of Prof. Demmel. On a standard machine this is equivalent to `DoublePrecision`. |
| PositiveDoublePrecision | Standard epsilon, the maximum relative precision of IEEE 754 double-precision floating numbers (64 bit). According to the definition of Prof. Higham and used in the ISO C standard and MATLAB. |
| PositiveMachineEpsilon | Actual double precision machine epsilon, the smallest number that can be added to 1, yielding a results different than 1. This is also known as unit roundoff error. According to the definition of Prof. Higham. On a standard machine this is equivalent to `PositiveDoublePrecision`. |
| PositiveSinglePrecision | Standard epsilon, the maximum relative precision of IEEE 754 single-precision floating numbers (32 bit). According to the definition of Prof. Higham and used in the ISO C standard and MATLAB. |
| SingleDecimalPlaces | The number of significant decimal places of single-precision floating numbers (32 bit). |
| SinglePrecision | Standard epsilon, the maximum relative precision of IEEE 754 single-precision floating numbers (32 bit). According to the definition of Prof. Demmel and used in LAPACK and Scilab. |
RemarksUseful links:
- http://docs.sun.com/source/806-3568/ncg_goldberg.html#689 - What every computer scientist should know about floating-point arithmetic
- http://en.wikipedia.org/wiki/Machine_epsilon - Gives the definition of machine epsilon
See Also