System.Double struct
This article provides supplementary remarks to the reference documentation for this API.
The Double value type represents a double-precision 64-bit number with values ranging from negative 1.79769313486232e308 to positive 1.79769313486232e308, as well as positive or negative zero, PositiveInfinity, NegativeInfinity, and not a number (NaN). It is intended to represent values that are extremely large (such as distances between planets or galaxies) or extremely small (such as the molecular mass of a substance in kilograms) and that often are imprecise (such as the distance from earth to another solar system). The Double type complies with the IEC 60559:1989 (IEEE 754) standard for binary floating-point arithmetic.
Floating-point representation and precision
The Double data type stores double-precision floating-point values in a 64-bit binary format, as shown in the following table:
| Part | Bits |
|---|---|
| Significand or mantissa | 0-51 |
| Exponent | 52-62 |
| Sign (0 = Positive, 1 = Negative) | 63 |
Just as decimal fractions are unable to precisely represent some fractional values (such as 1/3 or Math.PI), binary fractions are unable to represent some fractional values. For example, 1/10, which is represented precisely by .1 as a decimal fraction, is represented by .001100110011 as a binary fraction, with the pattern "0011" repeating to infinity. In this case, the floating-point value provides an imprecise representation of the number that it represents. Performing additional mathematical operations on the original floating-point value often tends to increase its lack of precision. For example, if we compare the result of multiplying .1 by 10 and adding .1 to .1 nine times, we see that addition, because it has involved eight more operations, has produced the less precise result. Note that this disparity is apparent only if we display the two Double values by using the "R" standard numeric format string, which if necessary displays all 17 digits of precision supported by the Double type.
using System;
public class Example13
{
public static void Main()
{
Double value = .1;
Double result1 = value * 10;
Double result2 = 0;
for (int ctr = 1; ctr <= 10; ctr++)
result2 += value;
Console.WriteLine(".1 * 10: {0:R}", result1);
Console.WriteLine(".1 Added 10 times: {0:R}", result2);
}
}
// The example displays the following output:
// .1 * 10: 1
// .1 Added 10 times: 0.99999999999999989
let value = 0.1
let result1 = value * 10.
let mutable result2 = 0.
for i = 1 to 10 do
result2 <- result2 + value
printfn $".1 * 10: {result1:R}"
printfn $".1 Added 10 times: {result2:R}"
// The example displays the following output:
// .1 * 10: 1
// .1 Added 10 times: 0.99999999999999989
Module Example14
Public Sub Main()
Dim value As Double = 0.1
Dim result1 As Double = value * 10
Dim result2 As Double
For ctr As Integer = 1 To 10
result2 += value
Next
Console.WriteLine(".1 * 10: {0:R}", result1)
Console.WriteLine(".1 Added 10 times: {0:R}", result2)
End Sub
End Module
' The example displays the following output:
' .1 * 10: 1
' .1 Added 10 times: 0.99999999999999989
Because some numbers cannot be represented exactly as fractional binary values, floating-point numbers can only approximate real numbers.
All floating-point numbers also have a limited number of significant digits, which also determines how accurately a floating-point value approximates a real number. A Double value has up to 15 decimal digits of precision, although a maximum of 17 digits is maintained internally. This means that some floating-point operations may lack the precision to change a floating point value. The following example provides an illustration. It defines a very large floating-point value, and then adds the product of Double.Epsilon and one quadrillion to it. The product, however, is too small to modify the original floating-point value. Its least significant digit is thousandths, whereas the most significant digit in the product is 10-309.
using System;
public class Example14
{
public static void Main()
{
Double value = 123456789012.34567;
Double additional = Double.Epsilon * 1e15;
Console.WriteLine("{0} + {1} = {2}", value, additional,
value + additional);
}
}
// The example displays the following output:
// 123456789012.346 + 4.94065645841247E-309 = 123456789012.346
open System
let value = 123456789012.34567
let additional = Double.Epsilon * 1e15
printfn $"{value} + {additional} = {value + additional}"
// The example displays the following output:
// 123456789012.346 + 4.94065645841247E-309 = 123456789012.346
Module Example15
Public Sub Main()
Dim value As Double = 123456789012.34567
Dim additional As Double = Double.Epsilon * 1.0E+15
Console.WriteLine("{0} + {1} = {2}", value, additional,
value + additional)
End Sub
End Module
' The example displays the following output:
' 123456789012.346 + 4.94065645841247E-309 = 123456789012.346
The limited precision of a floating-point number has several consequences:
Two floating-point numbers that appear equal for a particular precision might not compare equal because their least significant digits are different. In the following example, a series of numbers are added together, and their total is compared with their expected total. Although the two values appear to be the same, a call to the
Equalsmethod indicates that they are not.using System; public class Example10 { public static void Main() { Double[] values = { 10.0, 2.88, 2.88, 2.88, 9.0 }; Double result = 27.64; Double total = 0; foreach (var value in values) total += value; if (total.Equals(result)) Console.WriteLine("The sum of the values equals the total."); else Console.WriteLine("The sum of the values ({0}) does not equal the total ({1}).", total, result); } } // The example displays the following output: // The sum of the values (36.64) does not equal the total (36.64). // // If the index items in the Console.WriteLine statement are changed to {0:R}, // the example displays the following output: // The sum of the values (27.639999999999997) does not equal the total (27.64).let values = [ 10.0; 2.88; 2.88; 2.88; 9.0 ] let result = 27.64 let total = List.sum values if total.Equals result then printfn "The sum of the values equals the total." else printfn $"The sum of the values ({total}) does not equal the total ({result})." // The example displays the following output: // The sum of the values (36.64) does not equal the total (36.64). // // If the index items in the Console.WriteLine statement are changed to {0:R}, // the example displays the following output: // The sum of the values (27.639999999999997) does not equal the total (27.64).Module Example11 Public Sub Main() Dim values() As Double = {10.0, 2.88, 2.88, 2.88, 9.0} Dim result As Double = 27.64 Dim total As Double For Each value In values total += value Next If total.Equals(result) Then Console.WriteLine("The sum of the values equals the total.") Else Console.WriteLine("The sum of the values ({0}) does not equal the total ({1}).", total, result) End If End Sub End Module ' The example displays the following output: ' The sum of the values (36.64) does not equal the total (36.64). ' ' If the index items in the Console.WriteLine statement are changed to {0:R}, ' the example displays the following output: ' The sum of the values (27.639999999999997) does not equal the total (27.64).If you change the format items in the Console.WriteLine(String, Object, Object) statement from
{0}and{1}to{0:R}and{1:R}to display all significant digits of the two Double values, it is clear that the two values are unequal because of a loss of precision during the addition operations. In this case, the issue can be resolved by calling the Math.Round(Double, Int32) method to round the Double values to the desired precision before performing the comparison.A mathematical or comparison operation that uses a floating-point number might not yield the same result if a decimal number is used, because the binary floating-point number might not equal the decimal number. A previous example illustrated this by displaying the result of multiplying .1 by 10 and adding .1 times.
When accuracy in numeric operations with fractional values is important, you can use the Decimal rather than the Double type. When accuracy in numeric operations with integral values beyond the range of the Int64 or UInt64 types is important, use the BigInteger type.
A value might not round-trip if a floating-point number is involved. A value is said to round-trip if an operation converts an original floating-point number to another form, an inverse operation transforms the converted form back to a floating-point number, and the final floating-point number is not equal to the original floating-point number. The round trip might fail because one or more least significant digits are lost or changed in a conversion. In the following example, three Double values are converted to strings and saved in a file. As the output shows, however, even though the values appear to be identical, the restored values are not equal to the original values.
using System; using System.IO; public class Example11 { public static void Main() { StreamWriter sw = new StreamWriter(@".\Doubles.dat"); Double[] values = { 2.2 / 1.01, 1.0 / 3, Math.PI }; for (int ctr = 0; ctr < values.Length; ctr++) { sw.Write(values[ctr].ToString()); if (ctr != values.Length - 1) sw.Write("|"); } sw.Close(); Double[] restoredValues = new Double[values.Length]; StreamReader sr = new StreamReader(@".\Doubles.dat"); string temp = sr.ReadToEnd(); string[] tempStrings = temp.Split('|'); for (int ctr = 0; ctr < tempStrings.Length; ctr++) restoredValues[ctr] = Double.Parse(tempStrings[ctr]); for (int ctr = 0; ctr < values.Length; ctr++) Console.WriteLine("{0} {2} {1}", values[ctr], restoredValues[ctr], values[ctr].Equals(restoredValues[ctr]) ? "=" : "<>"); } } // The example displays the following output: // 2.17821782178218 <> 2.17821782178218 // 0.333333333333333 <> 0.333333333333333 // 3.14159265358979 <> 3.14159265358979open System open System.IO let values = [ 2.2 / 1.01; 1. / 3.; Math.PI ] using (new StreamWriter(@".\Doubles.dat")) (fun sw -> for i = 0 to values.Length - 1 do sw.Write(string values[i]) if i <> values.Length - 1 then sw.Write "|") using (new StreamReader(@".\Doubles.dat")) (fun sr -> let temp = sr.ReadToEnd() let tempStrings = temp.Split '|' let restoredValues = [ for i = 0 to tempStrings.Length - 1 do Double.Parse tempStrings[i] ] for i = 0 to values.Length - 1 do printfn $"""{values[i]} {if values[ i ].Equals restoredValues[i] then "=" else "<>"} {restoredValues[i]}""") // The example displays the following output: // 2.17821782178218 <> 2.17821782178218 // 0.333333333333333 <> 0.333333333333333 // 3.14159265358979 <> 3.14159265358979Imports System.IO Module Example12 Public Sub Main() Dim sw As New StreamWriter(".\Doubles.dat") Dim values() As Double = {2.2 / 1.01, 1.0 / 3, Math.PI} For ctr As Integer = 0 To values.Length - 1 sw.Write(values(ctr).ToString()) If ctr <> values.Length - 1 Then sw.Write("|") Next sw.Close() Dim restoredValues(values.Length - 1) As Double Dim sr As New StreamReader(".\Doubles.dat") Dim temp As String = sr.ReadToEnd() Dim tempStrings() As String = temp.Split("|"c) For ctr As Integer = 0 To tempStrings.Length - 1 restoredValues(ctr) = Double.Parse(tempStrings(ctr)) Next For ctr As Integer = 0 To values.Length - 1 Console.WriteLine("{0} {2} {1}", values(ctr), restoredValues(ctr), If(values(ctr).Equals(restoredValues(ctr)), "=", "<>")) Next End Sub End Module ' The example displays the following output: ' 2.17821782178218 <> 2.17821782178218 ' 0.333333333333333 <> 0.333333333333333 ' 3.14159265358979 <> 3.14159265358979In this case, the values can be successfully round-tripped by using the "G17" standard numeric format string to preserve the full precision of Double values, as the following example shows.
using System; using System.IO; public class Example12 { public static void Main() { StreamWriter sw = new StreamWriter(@".\Doubles.dat"); Double[] values = { 2.2 / 1.01, 1.0 / 3, Math.PI }; for (int ctr = 0; ctr < values.Length; ctr++) sw.Write("{0:G17}{1}", values[ctr], ctr < values.Length - 1 ? "|" : ""); sw.Close(); Double[] restoredValues = new Double[values.Length]; StreamReader sr = new StreamReader(@".\Doubles.dat"); string temp = sr.ReadToEnd(); string[] tempStrings = temp.Split('|'); for (int ctr = 0; ctr < tempStrings.Length; ctr++) restoredValues[ctr] = Double.Parse(tempStrings[ctr]); for (int ctr = 0; ctr < values.Length; ctr++) Console.WriteLine("{0} {2} {1}", values[ctr], restoredValues[ctr], values[ctr].Equals(restoredValues[ctr]) ? "=" : "<>"); } } // The example displays the following output: // 2.17821782178218 = 2.17821782178218 // 0.333333333333333 = 0.333333333333333 // 3.14159265358979 = 3.14159265358979open System open System.IO let values = [ 2.2 / 1.01; 1. / 3.; Math.PI ] using (new StreamWriter(@".\Doubles.dat")) (fun sw -> for i = 0 to values.Length - 1 do sw.Write $"""{values[i]:G17}{if i < values.Length - 1 then "|" else ""}""") using (new StreamReader(@".\Doubles.dat")) (fun sr -> let temp = sr.ReadToEnd() let tempStrings = temp.Split '|' let restoredValues = [ for i = 0 to tempStrings.Length - 1 do Double.Parse tempStrings[i] ] for i = 0 to values.Length - 1 do printfn $"""{restoredValues[i]} {if values[i].Equals restoredValues[i] then "=" else "<>"} {values[i]}""") // The example displays the following output: // 2.17821782178218 = 2.17821782178218 // 0.333333333333333 = 0.333333333333333 // 3.14159265358979 = 3.14159265358979Imports System.IO Module Example13 Public Sub Main() Dim sw As New StreamWriter(".\Doubles.dat") Dim values() As Double = {2.2 / 1.01, 1.0 / 3, Math.PI} For ctr As Integer = 0 To values.Length - 1 sw.Write("{0:G17}{1}", values(ctr), If(ctr < values.Length - 1, "|", "")) Next sw.Close() Dim restoredValues(values.Length - 1) As Double Dim sr As New StreamReader(".\Doubles.dat") Dim temp As String = sr.ReadToEnd() Dim tempStrings() As String = temp.Split("|"c) For ctr As Integer = 0 To tempStrings.Length - 1 restoredValues(ctr) = Double.Parse(tempStrings(ctr)) Next For ctr As Integer = 0 To values.Length - 1 Console.WriteLine("{0} {2} {1}", values(ctr), restoredValues(ctr), If(values(ctr).Equals(restoredValues(ctr)), "=", "<>")) Next End Sub End Module ' The example displays the following output: ' 2.17821782178218 = 2.17821782178218 ' 0.333333333333333 = 0.333333333333333 ' 3.14159265358979 = 3.14159265358979Single values have less precision than Double values. A Single value that is converted to a seemingly equivalent Double often does not equal the Double value because of differences in precision. In the following example, the result of identical division operations is assigned to a Double and a Single value. After the Single value is cast to a Double, a comparison of the two values shows that they are unequal.
using System; public class Example9 { public static void Main() { Double value1 = 1 / 3.0; Single sValue2 = 1 / 3.0f; Double value2 = (Double)sValue2; Console.WriteLine("{0:R} = {1:R}: {2}", value1, value2, value1.Equals(value2)); } } // The example displays the following output: // 0.33333333333333331 = 0.3333333432674408: Falseopen System let value1 = 1. / 3. let sValue2 = 1f /3f let value2 = double sValue2 printfn $"{value1:R} = {value2:R}: {value1.Equals value2}" // The example displays the following output: // 0.33333333333333331 = 0.3333333432674408: FalseModule Example10 Public Sub Main() Dim value1 As Double = 1 / 3 Dim sValue2 As Single = 1 / 3 Dim value2 As Double = CDbl(sValue2) Console.WriteLine("{0} = {1}: {2}", value1, value2, value1.Equals(value2)) End Sub End Module ' The example displays the following output: ' 0.33333333333333331 = 0.3333333432674408: FalseTo avoid this problem, use either the Double in place of the Single data type, or use the Round method so that both values have the same precision.
In addition, the result of arithmetic and assignment operations with Double values may differ slightly by platform because of the loss of precision of the Double type. For example, the result of assigning a literal Double value may differ in the 32-bit and 64-bit versions of .NET. The following example illustrates this difference when the literal value -4.42330604244772E-305 and a variable whose value is -4.42330604244772E-305 are assigned to a Double variable. Note that the result of the Parse(String) method in this case does not suffer from a loss of precision.
double value = -4.42330604244772E-305;
double fromLiteral = -4.42330604244772E-305;
double fromVariable = value;
double fromParse = Double.Parse("-4.42330604244772E-305");
Console.WriteLine("Double value from literal: {0,29:R}", fromLiteral);
Console.WriteLine("Double value from variable: {0,28:R}", fromVariable);
Console.WriteLine("Double value from Parse method: {0,24:R}", fromParse);
// On 32-bit versions of the .NET Framework, the output is:
// Double value from literal: -4.42330604244772E-305
// Double value from variable: -4.42330604244772E-305
// Double value from Parse method: -4.42330604244772E-305
//
// On other versions of the .NET Framework, the output is:
// Double value from literal: -4.4233060424477198E-305
// Double value from variable: -4.4233060424477198E-305
// Double value from Parse method: -4.42330604244772E-305
let value = -4.42330604244772E-305
let fromLiteral = -4.42330604244772E-305
let fromVariable = value
let fromParse = Double.Parse "-4.42330604244772E-305"
printfn $"Double value from literal: {fromLiteral,29:R}"
printfn $"Double value from variable: {fromVariable,28:R}"
printfn $"Double value from Parse method: {fromParse,24:R}"
// On 32-bit versions of the .NET Framework, the output is:
// Double value from literal: -4.42330604244772E-305
// Double value from variable: -4.42330604244772E-305
// Double value from Parse method: -4.42330604244772E-305
//
// On other versions of the .NET Framework, the output is:
// Double value from literal: -4.4233060424477198E-305
// Double value from variable: -4.4233060424477198E-305
// Double value from Parse method: -4.42330604244772E-305
Dim value As Double = -4.4233060424477198E-305
Dim fromLiteral As Double = -4.4233060424477198E-305
Dim fromVariable As Double = value
Dim fromParse As Double = Double.Parse("-4.42330604244772E-305")
Console.WriteLine("Double value from literal: {0,29:R}", fromLiteral)
Console.WriteLine("Double value from variable: {0,28:R}", fromVariable)
Console.WriteLine("Double value from Parse method: {0,24:R}", fromParse)
' On 32-bit versions of the .NET Framework, the output is:
' Double value from literal: -4.42330604244772E-305
' Double value from variable: -4.42330604244772E-305
' Double value from Parse method: -4.42330604244772E-305
'
' On other versions of the .NET Framework, the output is:
' Double value from literal: -4.4233060424477198E-305
' Double value from variable: -4.4233060424477198E-305
' Double value from Parse method: -4.42330604244772E-305
Test for equality
To be considered equal, two Double values must represent identical values. However, because of differences in precision between values, or because of a loss of precision by one or both values, floating-point values that are expected to be identical often turn out to be unequal because of differences in their least significant digits. As a result, calls to the Equals method to determine whether two values are equal, or calls to the CompareTo method to determine the relationship between two Double values, often yield unexpected results. This is evident in the following example, where two apparently equal Double values turn out to be unequal because the first has 15 digits of precision, while the second has 17.
using System;
public class Example
{
public static void Main()
{
double value1 = .333333333333333;
double value2 = 1.0/3;
Console.WriteLine("{0:R} = {1:R}: {2}", value1, value2, value1.Equals(value2));
}
}
// The example displays the following output:
// 0.333333333333333 = 0.33333333333333331: False
open System
let value1 = 0.333333333333333
let value2 = 1. / 3.
printfn $"{value1:R} = {value2:R}: {value1.Equals value2}"
// The example displays the following output:
// 0.333333333333333 = 0.33333333333333331: False
Module Example1
Public Sub Main()
Dim value1 As Double = 0.333333333333333
Dim value2 As Double = 1 / 3
Console.WriteLine("{0:R} = {1:R}: {2}", value1, value2, value1.Equals(value2))
End Sub
End Module
' The example displays the following output:
' 0.333333333333333 = 0.33333333333333331: False
Calculated values that follow different code paths and that are manipulated in different ways often prove to be unequal. In the following example, one Double value is squared, and then the square root is calculated to restore the original value. A second Double is multiplied by 3.51 and squared before the square root of the result is divided by 3.51 to restore the original value. Although the two values appear to be identical, a call to the Equals(Double) method indicates that they are not equal. Using the "R" standard format string to return a result string that displays all the significant digits of each Double value shows that the second value is .0000000000001 less than the first.
using System;
public class Example1
{
public static void Main()
{
double value1 = 100.10142;
value1 = Math.Sqrt(Math.Pow(value1, 2));
double value2 = Math.Pow(value1 * 3.51, 2);
value2 = Math.Sqrt(value2) / 3.51;
Console.WriteLine("{0} = {1}: {2}\n",
value1, value2, value1.Equals(value2));
Console.WriteLine("{0:R} = {1:R}", value1, value2);
}
}
// The example displays the following output:
// 100.10142 = 100.10142: False
//
// 100.10142 = 100.10141999999999
open System
let value1 =
Math.Pow(100.10142, 2)
|> sqrt
let value2 =
let v = pown (value1 * 3.51) 2
(Math.Sqrt v) / 3.51
printfn $"{value1} = {value2}: {value1.Equals value2}\n"
printfn $"{value1:R} = {value2:R}"
// The example displays the following output:
// 100.10142 = 100.10142: False
//
// 100.10142 = 100.10141999999999
Module Example2
Public Sub Main()
Dim value1 As Double = 100.10142
value1 = Math.Sqrt(Math.Pow(value1, 2))
Dim value2 As Double = Math.Pow(value1 * 3.51, 2)
value2 = Math.Sqrt(value2) / 3.51
Console.WriteLine("{0} = {1}: {2}",
value1, value2, value1.Equals(value2))
Console.WriteLine()
Console.WriteLine("{0:R} = {1:R}", value1, value2)
End Sub
End Module
' The example displays the following output:
' 100.10142 = 100.10142: False
'
' 100.10142 = 100.10141999999999
In cases where a loss of precision is likely to affect the result of a comparison, you can adopt any of the following alternatives to calling the Equals or CompareTo method:
Call the Math.Round method to ensure that both values have the same precision. The following example modifies a previous example to use this approach so that two fractional values are equivalent.
using System; public class Example2 { public static void Main() { double value1 = .333333333333333; double value2 = 1.0 / 3; int precision = 7; value1 = Math.Round(value1, precision); value2 = Math.Round(value2, precision); Console.WriteLine("{0:R} = {1:R}: {2}", value1, value2, value1.Equals(value2)); } } // The example displays the following output: // 0.3333333 = 0.3333333: Trueopen System let v1 = 0.333333333333333 let v2 = 1. / 3. let precision = 7 let value1 = Math.Round(v1, precision) let value2 = Math.Round(v2, precision) printfn $"{value1:R} = {value2:R}: {value1.Equals value2}" // The example displays the following output: // 0.3333333 = 0.3333333: TrueModule Example3 Public Sub Main() Dim value1 As Double = 0.333333333333333 Dim value2 As Double = 1 / 3 Dim precision As Integer = 7 value1 = Math.Round(value1, precision) value2 = Math.Round(value2, precision) Console.WriteLine("{0:R} = {1:R}: {2}", value1, value2, value1.Equals(value2)) End Sub End Module ' The example displays the following output: ' 0.3333333 = 0.3333333: TrueThe problem of precision still applies to rounding of midpoint values. For more information, see the Math.Round(Double, Int32, MidpointRounding) method.
Test for approximate equality rather than equality. This requires that you define either an absolute amount by which the two values can differ but still be equal, or that you define a relative amount by which the smaller value can diverge from the larger value.
Warning
Double.Epsilon is sometimes used as an absolute measure of the distance between two Double values when testing for equality. However, Double.Epsilon measures the smallest possible value that can be added to, or subtracted from, a Double whose value is zero. For most positive and negative Double values, the value of Double.Epsilon is too small to be detected. Therefore, except for values that are zero, we do not recommend its use in tests for equality.
The following example uses the latter approach to define an
IsApproximatelyEqualmethod that tests the relative difference between two values. It also contrasts the result of calls to theIsApproximatelyEqualmethod and the Equals(Double) method.using System; public class Example3 { public static void Main() { double one1 = .1 * 10; double one2 = 0; for (int ctr = 1; ctr <= 10; ctr++) one2 += .1; Console.WriteLine("{0:R} = {1:R}: {2}", one1, one2, one1.Equals(one2)); Console.WriteLine("{0:R} is approximately equal to {1:R}: {2}", one1, one2, IsApproximatelyEqual(one1, one2, .000000001)); } static bool IsApproximatelyEqual(double value1, double value2, double epsilon) { // If they are equal anyway, just return True. if (value1.Equals(value2)) return true; // Handle NaN, Infinity. if (Double.IsInfinity(value1) | Double.IsNaN(value1)) return value1.Equals(value2); else if (Double.IsInfinity(value2) | Double.IsNaN(value2)) return value1.Equals(value2); // Handle zero to avoid division by zero double divisor = Math.Max(value1, value2); if (divisor.Equals(0)) divisor = Math.Min(value1, value2); return Math.Abs((value1 - value2) / divisor) <= epsilon; } } // The example displays the following output: // 1 = 0.99999999999999989: False // 1 is approximately equal to 0.99999999999999989: Trueopen System let isApproximatelyEqual (value1: double) (value2: double) (epsilon: double) = // If they are equal anyway, just return True. if value1.Equals value2 then true else // Handle NaN, Infinity. if Double.IsInfinity value1 || Double.IsNaN value1 then value1.Equals value2 elif Double.IsInfinity value2 || Double.IsNaN value2 then value1.Equals value2 else // Handle zero to avoid division by zero let divisor = max value1 value2 let divisor = if divisor.Equals 0 then min value1 value2 else divisor abs ((value1 - value2) / divisor) <= epsilon let one1 = 0.1 * 10. let mutable one2 = 0. for _ = 1 to 10 do one2 <- one2 + 0.1 printfn $"{one1:R} = {one2:R}: {one1.Equals one2}" printfn $"{one1:R} is approximately equal to {one2:R}: {isApproximatelyEqual one1 one2 0.000000001}" // The example displays the following output: // 1 = 0.99999999999999989: False // 1 is approximately equal to 0.99999999999999989: TrueModule Example4 Public Sub Main() Dim one1 As Double = 0.1 * 10 Dim one2 As Double = 0 For ctr As Integer = 1 To 10 one2 += 0.1 Next Console.WriteLine("{0:R} = {1:R}: {2}", one1, one2, one1.Equals(one2)) Console.WriteLine("{0:R} is approximately equal to {1:R}: {2}", one1, one2, IsApproximatelyEqual(one1, one2, 0.000000001)) End Sub Function IsApproximatelyEqual(value1 As Double, value2 As Double, epsilon As Double) As Boolean ' If they are equal anyway, just return True. If value1.Equals(value2) Then Return True ' Handle NaN, Infinity. If Double.IsInfinity(value1) Or Double.IsNaN(value1) Then Return value1.Equals(value2) ElseIf Double.IsInfinity(value2) Or Double.IsNaN(value2) Then Return value1.Equals(value2) End If ' Handle zero to avoid division by zero Dim divisor As Double = Math.Max(value1, value2) If divisor.Equals(0) Then divisor = Math.Min(value1, value2) End If Return Math.Abs((value1 - value2) / divisor) <= epsilon End Function End Module ' The example displays the following output: ' 1 = 0.99999999999999989: False ' 1 is approximately equal to 0.99999999999999989: True
Floating-point values and exceptions
Unlike operations with integral types, which throw exceptions in cases of overflow or illegal operations such as division by zero, operations with floating-point values do not throw exceptions. Instead, in exceptional situations, the result of a floating-point operation is zero, positive infinity, negative infinity, or not a number (NaN):
If the result of a floating-point operation is too small for the destination format, the result is zero. This can occur when two very small numbers are multiplied, as the following example shows.
using System; public class Example6 { public static void Main() { Double value1 = 1.1632875981534209e-225; Double value2 = 9.1642346778e-175; Double result = value1 * value2; Console.WriteLine("{0} * {1} = {2}", value1, value2, result); Console.WriteLine("{0} = 0: {1}", result, result.Equals(0.0)); } } // The example displays the following output: // 1.16328759815342E-225 * 9.1642346778E-175 = 0 // 0 = 0: Truelet value1 = 1.1632875981534209e-225 let value2 = 9.1642346778e-175 let result = value1 * value2 printfn $"{value1} * {value2} = {result}" printfn $"{result} = 0: {result.Equals 0.0}" // The example displays the following output: // 1.16328759815342E-225 * 9.1642346778E-175 = 0 // 0 = 0: TrueModule Example7 Public Sub Main() Dim value1 As Double = 1.1632875981534209E-225 Dim value2 As Double = 9.1642346778E-175 Dim result As Double = value1 * value2 Console.WriteLine("{0} * {1} = {2}", value1, value2, result) Console.WriteLine("{0} = 0: {1}", result, result.Equals(0.0)) End Sub End Module ' The example displays the following output: ' 1.16328759815342E-225 * 9.1642346778E-175 = 0 ' 0 = 0: TrueIf the magnitude of the result of a floating-point operation exceeds the range of the destination format, the result of the operation is PositiveInfinity or NegativeInfinity, as appropriate for the sign of the result. The result of an operation that overflows Double.MaxValue is PositiveInfinity, and the result of an operation that overflows Double.MinValue is NegativeInfinity, as the following example shows.
using System; public class Example7 { public static void Main() { Double value1 = 4.565e153; Double value2 = 6.9375e172; Double result = value1 * value2; Console.WriteLine("PositiveInfinity: {0}", Double.IsPositiveInfinity(result)); Console.WriteLine("NegativeInfinity: {0}\n", Double.IsNegativeInfinity(result)); value1 = -value1; result = value1 * value2; Console.WriteLine("PositiveInfinity: {0}", Double.IsPositiveInfinity(result)); Console.WriteLine("NegativeInfinity: {0}", Double.IsNegativeInfinity(result)); } } // The example displays the following output: // PositiveInfinity: True // NegativeInfinity: False // // PositiveInfinity: False // NegativeInfinity: Trueopen System let value1 = 4.565e153 let value2 = 6.9375e172 let result = value1 * value2 printfn $"PositiveInfinity: {Double.IsPositiveInfinity result}" printfn $"NegativeInfinity: {Double.IsNegativeInfinity result}\n" let value3 = - value1 let result2 = value2 * value3 printfn $"PositiveInfinity: {Double.IsPositiveInfinity result2}" printfn $"NegativeInfinity: {Double.IsNegativeInfinity result2}" // The example displays the following output: // PositiveInfinity: True // NegativeInfinity: False // // PositiveInfinity: False // NegativeInfinity: TrueModule Example8 Public Sub Main() Dim value1 As Double = 4.565E+153 Dim value2 As Double = 6.9375E+172 Dim result As Double = value1 * value2 Console.WriteLine("PositiveInfinity: {0}", Double.IsPositiveInfinity(result)) Console.WriteLine("NegativeInfinity: {0}", Double.IsNegativeInfinity(result)) Console.WriteLine() value1 = -value1 result = value1 * value2 Console.WriteLine("PositiveInfinity: {0}", Double.IsPositiveInfinity(result)) Console.WriteLine("NegativeInfinity: {0}", Double.IsNegativeInfinity(result)) End Sub End Module ' The example displays the following output: ' PositiveInfinity: True ' NegativeInfinity: False ' ' PositiveInfinity: False ' NegativeInfinity: TruePositiveInfinity also results from a division by zero with a positive dividend, and NegativeInfinity results from a division by zero with a negative dividend.
If a floating-point operation is invalid, the result of the operation is NaN. For example, NaN results from the following operations:
Division by zero with a dividend of zero. Note that other cases of division by zero result in either PositiveInfinity or NegativeInfinity.
Any floating-point operation with an invalid input. For example, calling the Math.Sqrt method with a negative value returns NaN, as does calling the Math.Acos method with a value that is greater than one or less than negative one.
Any operation with an argument whose value is Double.NaN.
Type conversions
The Double structure does not define any explicit or implicit conversion operators; instead, conversions are implemented by the compiler.
The conversion of the value of any primitive numeric type to a Double is a widening conversion and therefore does not require an explicit cast operator or call to a conversion method unless a compiler explicitly requires it. For example, the C# compiler requires a casting operator for conversions from Decimal to Double, while the Visual Basic compiler does not. The following example converts the minimum or maximum value of other primitive numeric types to a Double.
using System;
public class Example4
{
public static void Main()
{
dynamic[] values = { Byte.MinValue, Byte.MaxValue, Decimal.MinValue,
Decimal.MaxValue, Int16.MinValue, Int16.MaxValue,
Int32.MinValue, Int32.MaxValue, Int64.MinValue,
Int64.MaxValue, SByte.MinValue, SByte.MaxValue,
Single.MinValue, Single.MaxValue, UInt16.MinValue,
UInt16.MaxValue, UInt32.MinValue, UInt32.MaxValue,
UInt64.MinValue, UInt64.MaxValue };
double dblValue;
foreach (var value in values)
{
if (value.GetType() == typeof(Decimal))
dblValue = (Double)value;
else
dblValue = value;
Console.WriteLine("{0} ({1}) --> {2:R} ({3})",
value, value.GetType().Name,
dblValue, dblValue.GetType().Name);
}
}
}
// The example displays the following output:
// 0 (Byte) --> 0 (Double)
// 255 (Byte) --> 255 (Double)
// -79228162514264337593543950335 (Decimal) --> -7.9228162514264338E+28 (Double)
// 79228162514264337593543950335 (Decimal) --> 7.9228162514264338E+28 (Double)
// -32768 (Int16) --> -32768 (Double)
// 32767 (Int16) --> 32767 (Double)
// -2147483648 (Int32) --> -2147483648 (Double)
// 2147483647 (Int32) --> 2147483647 (Double)
// -9223372036854775808 (Int64) --> -9.2233720368547758E+18 (Double)
// 9223372036854775807 (Int64) --> 9.2233720368547758E+18 (Double)
// -128 (SByte) --> -128 (Double)
// 127 (SByte) --> 127 (Double)
// -3.402823E+38 (Single) --> -3.4028234663852886E+38 (Double)
// 3.402823E+38 (Single) --> 3.4028234663852886E+38 (Double)
// 0 (UInt16) --> 0 (Double)
// 65535 (UInt16) --> 65535 (Double)
// 0 (UInt32) --> 0 (Double)
// 4294967295 (UInt32) --> 4294967295 (Double)
// 0 (UInt64) --> 0 (Double)
// 18446744073709551615 (UInt64) --> 1.8446744073709552E+19 (Double)
open System
let values: obj[] =
[| Byte.MinValue; Byte.MaxValue; Decimal.MinValue
Decimal.MaxValue; Int16.MinValue; Int16.MaxValue
Int32.MinValue; Int32.MaxValue; Int64.MinValue
Int64.MaxValue; SByte.MinValue; SByte.MaxValue
Single.MinValue; Single.MaxValue; UInt16.MinValue
UInt16.MaxValue; UInt32.MinValue, UInt32.MaxValue
UInt64.MinValue; UInt64.MaxValue |]
for value in values do
let dblValue = value :?> double
printfn $"{value} ({value.GetType().Name}) --> {dblValue:R} ({dblValue.GetType().Name})"
// The example displays the following output:
// 0 (Byte) --> 0 (Double)
// 255 (Byte) --> 255 (Double)
// -79228162514264337593543950335 (Decimal) --> -7.9228162514264338E+28 (Double)
// 79228162514264337593543950335 (Decimal) --> 7.9228162514264338E+28 (Double)
// -32768 (Int16) --> -32768 (Double)
// 32767 (Int16) --> 32767 (Double)
// -2147483648 (Int32) --> -2147483648 (Double)
// 2147483647 (Int32) --> 2147483647 (Double)
// -9223372036854775808 (Int64) --> -9.2233720368547758E+18 (Double)
// 9223372036854775807 (Int64) --> 9.2233720368547758E+18 (Double)
// -128 (SByte) --> -128 (Double)
// 127 (SByte) --> 127 (Double)
// -3.402823E+38 (Single) --> -3.4028234663852886E+38 (Double)
// 3.402823E+38 (Single) --> 3.4028234663852886E+38 (Double)
// 0 (UInt16) --> 0 (Double)
// 65535 (UInt16) --> 65535 (Double)
// 0 (UInt32) --> 0 (Double)
// 4294967295 (UInt32) --> 4294967295 (Double)
// 0 (UInt64) --> 0 (Double)
// 18446744073709551615 (UInt64) --> 1.8446744073709552E+19 (Double)
Module Example5
Public Sub Main()
Dim values() As Object = {Byte.MinValue, Byte.MaxValue, Decimal.MinValue,
Decimal.MaxValue, Int16.MinValue, Int16.MaxValue,
Int32.MinValue, Int32.MaxValue, Int64.MinValue,
Int64.MaxValue, SByte.MinValue, SByte.MaxValue,
Single.MinValue, Single.MaxValue, UInt16.MinValue,
UInt16.MaxValue, UInt32.MinValue, UInt32.MaxValue,
UInt64.MinValue, UInt64.MaxValue}
Dim dblValue As Double
For Each value In values
dblValue = value
Console.WriteLine("{0} ({1}) --> {2:R} ({3})",
value, value.GetType().Name,
dblValue, dblValue.GetType().Name)
Next
End Sub
End Module
' The example displays the following output:
' 0 (Byte) --> 0 (Double)
' 255 (Byte) --> 255 (Double)
' -79228162514264337593543950335 (Decimal) --> -7.9228162514264338E+28 (Double)
' 79228162514264337593543950335 (Decimal) --> 7.9228162514264338E+28 (Double)
' -32768 (Int16) --> -32768 (Double)
' 32767 (Int16) --> 32767 (Double)
' -2147483648 (Int32) --> -2147483648 (Double)
' 2147483647 (Int32) --> 2147483647 (Double)
' -9223372036854775808 (Int64) --> -9.2233720368547758E+18 (Double)
' 9223372036854775807 (Int64) --> 9.2233720368547758E+18 (Double)
' -128 (SByte) --> -128 (Double)
' 127 (SByte) --> 127 (Double)
' -3.402823E+38 (Single) --> -3.4028234663852886E+38 (Double)
' 3.402823E+38 (Single) --> 3.4028234663852886E+38 (Double)
' 0 (UInt16) --> 0 (Double)
' 65535 (UInt16) --> 65535 (Double)
' 0 (UInt32) --> 0 (Double)
' 4294967295 (UInt32) --> 4294967295 (Double)
' 0 (UInt64) --> 0 (Double)
' 18446744073709551615 (UInt64) --> 1.8446744073709552E+19 (Double)
In addition, the Single values Single.NaN, Single.PositiveInfinity, and Single.NegativeInfinity convert to Double.NaN, Double.PositiveInfinity, and Double.NegativeInfinity, respectively.
Note that the conversion of the value of some numeric types to a Double value can involve a loss of precision. As the example illustrates, a loss of precision is possible when converting Decimal, Int64, and UInt64 values to Double values.
The conversion of a Double value to a value of any other primitive numeric data type is a narrowing conversion and requires a cast operator (in C#), a conversion method (in Visual Basic), or a call to a Convert method. Values that are outside the range of the target data type, which are defined by the target type's MinValue and MaxValue properties, behave as shown in the following table.
| Target type | Result |
|---|---|
| Any integral type | An OverflowException exception if the conversion occurs in a checked context. If the conversion occurs in an unchecked context (the default in C#), the conversion operation succeeds but the value overflows. |
| Decimal | An OverflowException exception. |
| Single | Single.NegativeInfinity for negative values. Single.PositiveInfinity for positive values. |
In addition, Double.NaN, Double.PositiveInfinity, and Double.NegativeInfinity throw an OverflowException for conversions to integers in a checked context, but these values overflow when converted to integers in an unchecked context. For conversions to Decimal, they always throw an OverflowException. For conversions to Single, they convert to Single.NaN, Single.PositiveInfinity, and Single.NegativeInfinity, respectively.
A loss of precision may result from converting a Double value to another numeric type. In the case of converting to any of the integral types, as the output from the example shows, the fractional component is lost when the Double value is either rounded (as in Visual Basic) or truncated (as in C#). For conversions to Decimal and Single values, the Double value may not have a precise representation in the target data type.
The following example converts a number of Double values to several other numeric types. The conversions occur in a checked context in Visual Basic (the default), in C# (because of the checked keyword), and in F# (because of the Checked module). The output from the example shows the result for conversions in both a checked an unchecked context. You can perform conversions in an unchecked context in Visual Basic by compiling with the /removeintchecks+ compiler switch, in C# by commenting out the checked statement, and in F# by commenting out the open Checked statement.
using System;
public class Example5
{
public static void Main()
{
Double[] values = { Double.MinValue, -67890.1234, -12345.6789,
12345.6789, 67890.1234, Double.MaxValue,
Double.NaN, Double.PositiveInfinity,
Double.NegativeInfinity };
checked
{
foreach (var value in values)
{
try
{
Int64 lValue = (long)value;
Console.WriteLine("{0} ({1}) --> {2} (0x{2:X16}) ({3})",
value, value.GetType().Name,
lValue, lValue.GetType().Name);
}
catch (OverflowException)
{
Console.WriteLine("Unable to convert {0} to Int64.", value);
}
try
{
UInt64 ulValue = (ulong)value;
Console.WriteLine("{0} ({1}) --> {2} (0x{2:X16}) ({3})",
value, value.GetType().Name,
ulValue, ulValue.GetType().Name);
}
catch (OverflowException)
{
Console.WriteLine("Unable to convert {0} to UInt64.", value);
}
try
{
Decimal dValue = (decimal)value;
Console.WriteLine("{0} ({1}) --> {2} ({3})",
value, value.GetType().Name,
dValue, dValue.GetType().Name);
}
catch (OverflowException)
{
Console.WriteLine("Unable to convert {0} to Decimal.", value);
}
try
{
Single sValue = (float)value;
Console.WriteLine("{0} ({1}) --> {2} ({3})",
value, value.GetType().Name,
sValue, sValue.GetType().Name);
}
catch (OverflowException)
{
Console.WriteLine("Unable to convert {0} to Single.", value);
}
Console.WriteLine();
}
}
}
}
// The example displays the following output for conversions performed
// in a checked context:
// Unable to convert -1.79769313486232E+308 to Int64.
// Unable to convert -1.79769313486232E+308 to UInt64.
// Unable to convert -1.79769313486232E+308 to Decimal.
// -1.79769313486232E+308 (Double) --> -Infinity (Single)
//
// -67890.1234 (Double) --> -67890 (0xFFFFFFFFFFFEF6CE) (Int64)
// Unable to convert -67890.1234 to UInt64.
// -67890.1234 (Double) --> -67890.1234 (Decimal)
// -67890.1234 (Double) --> -67890.13 (Single)
//
// -12345.6789 (Double) --> -12345 (0xFFFFFFFFFFFFCFC7) (Int64)
// Unable to convert -12345.6789 to UInt64.
// -12345.6789 (Double) --> -12345.6789 (Decimal)
// -12345.6789 (Double) --> -12345.68 (Single)
//
// 12345.6789 (Double) --> 12345 (0x0000000000003039) (Int64)
// 12345.6789 (Double) --> 12345 (0x0000000000003039) (UInt64)
// 12345.6789 (Double) --> 12345.6789 (Decimal)
// 12345.6789 (Double) --> 12345.68 (Single)
//
// 67890.1234 (Double) --> 67890 (0x0000000000010932) (Int64)
// 67890.1234 (Double) --> 67890 (0x0000000000010932) (UInt64)
// 67890.1234 (Double) --> 67890.1234 (Decimal)
// 67890.1234 (Double) --> 67890.13 (Single)
//
// Unable to convert 1.79769313486232E+308 to Int64.
// Unable to convert 1.79769313486232E+308 to UInt64.
// Unable to convert 1.79769313486232E+308 to Decimal.
// 1.79769313486232E+308 (Double) --> Infinity (Single)
//
// Unable to convert NaN to Int64.
// Unable to convert NaN to UInt64.
// Unable to convert NaN to Decimal.
// NaN (Double) --> NaN (Single)
//
// Unable to convert Infinity to Int64.
// Unable to convert Infinity to UInt64.
// Unable to convert Infinity to Decimal.
// Infinity (Double) --> Infinity (Single)
//
// Unable to convert -Infinity to Int64.
// Unable to convert -Infinity to UInt64.
// Unable to convert -Infinity to Decimal.
// -Infinity (Double) --> -Infinity (Single)
// The example displays the following output for conversions performed
// in an unchecked context:
// -1.79769313486232E+308 (Double) --> -9223372036854775808 (0x8000000000000000) (Int64)
// -1.79769313486232E+308 (Double) --> 9223372036854775808 (0x8000000000000000) (UInt64)
// Unable to convert -1.79769313486232E+308 to Decimal.
// -1.79769313486232E+308 (Double) --> -Infinity (Single)
//
// -67890.1234 (Double) --> -67890 (0xFFFFFFFFFFFEF6CE) (Int64)
// -67890.1234 (Double) --> 18446744073709483726 (0xFFFFFFFFFFFEF6CE) (UInt64)
// -67890.1234 (Double) --> -67890.1234 (Decimal)
// -67890.1234 (Double) --> -67890.13 (Single)
//
// -12345.6789 (Double) --> -12345 (0xFFFFFFFFFFFFCFC7) (Int64)
// -12345.6789 (Double) --> 18446744073709539271 (0xFFFFFFFFFFFFCFC7) (UInt64)
// -12345.6789 (Double) --> -12345.6789 (Decimal)
// -12345.6789 (Double) --> -12345.68 (Single)
//
// 12345.6789 (Double) --> 12345 (0x0000000000003039) (Int64)
// 12345.6789 (Double) --> 12345 (0x0000000000003039) (UInt64)
// 12345.6789 (Double) --> 12345.6789 (Decimal)
// 12345.6789 (Double) --> 12345.68 (Single)
//
// 67890.1234 (Double) --> 67890 (0x0000000000010932) (Int64)
// 67890.1234 (Double) --> 67890 (0x0000000000010932) (UInt64)
// 67890.1234 (Double) --> 67890.1234 (Decimal)
// 67890.1234 (Double) --> 67890.13 (Single)
//
// 1.79769313486232E+308 (Double) --> -9223372036854775808 (0x8000000000000000) (Int64)
// 1.79769313486232E+308 (Double) --> 0 (0x0000000000000000) (UInt64)
// Unable to convert 1.79769313486232E+308 to Decimal.
// 1.79769313486232E+308 (Double) --> Infinity (Single)
//
// NaN (Double) --> -9223372036854775808 (0x8000000000000000) (Int64)
// NaN (Double) --> 0 (0x0000000000000000) (UInt64)
// Unable to convert NaN to Decimal.
// NaN (Double) --> NaN (Single)
//
// Infinity (Double) --> -9223372036854775808 (0x8000000000000000) (Int64)
// Infinity (Double) --> 0 (0x0000000000000000) (UInt64)
// Unable to convert Infinity to Decimal.
// Infinity (Double) --> Infinity (Single)
//
// -Infinity (Double) --> -9223372036854775808 (0x8000000000000000) (Int64)
// -Infinity (Double) --> 9223372036854775808 (0x8000000000000000) (UInt64)
// Unable to convert -Infinity to Decimal.
// -Infinity (Double) --> -Infinity (Single)
open System
open Checked
let values =
[| Double.MinValue; -67890.1234; -12345.6789
12345.6789; 67890.1234; Double.MaxValue
Double.NaN; Double.PositiveInfinity;
Double.NegativeInfinity |]
for value in values do
try
let lValue = int64 value
printfn $"{value} ({value.GetType().Name}) --> {lValue} (0x{lValue:X16}) ({lValue.GetType().Name})"
with :? OverflowException ->
printfn $"Unable to convert {value} to Int64."
try
let ulValue = uint64 value
printfn $"{value} ({value.GetType().Name}) --> {ulValue} (0x{ulValue:X16}) ({ulValue.GetType().Name})"
with :? OverflowException ->
printfn $"Unable to convert {value} to UInt64."
try
let dValue = decimal value
printfn $"{value} ({value.GetType().Name}) --> {dValue} ({dValue.GetType().Name})"
with :? OverflowException ->
printfn $"Unable to convert {value} to Decimal."
try
let sValue = float32 value
printfn $"{value} ({value.GetType().Name}) --> {sValue} ({sValue.GetType().Name})"
with :? OverflowException ->
printfn $"Unable to convert {value} to Single."
printfn ""
// The example displays the following output for conversions performed
// in a checked context:
// Unable to convert -1.79769313486232E+308 to Int64.
// Unable to convert -1.79769313486232E+308 to UInt64.
// Unable to convert -1.79769313486232E+308 to Decimal.
// -1.79769313486232E+308 (Double) --> -Infinity (Single)
//
// -67890.1234 (Double) --> -67890 (0xFFFFFFFFFFFEF6CE) (Int64)
// Unable to convert -67890.1234 to UInt64.
// -67890.1234 (Double) --> -67890.1234 (Decimal)
// -67890.1234 (Double) --> -67890.13 (Single)
//
// -12345.6789 (Double) --> -12345 (0xFFFFFFFFFFFFCFC7) (Int64)
// Unable to convert -12345.6789 to UInt64.
// -12345.6789 (Double) --> -12345.6789 (Decimal)
// -12345.6789 (Double) --> -12345.68 (Single)
//
// 12345.6789 (Double) --> 12345 (0x0000000000003039) (Int64)
// 12345.6789 (Double) --> 12345 (0x0000000000003039) (UInt64)
// 12345.6789 (Double) --> 12345.6789 (Decimal)
// 12345.6789 (Double) --> 12345.68 (Single)
//
// 67890.1234 (Double) --> 67890 (0x0000000000010932) (Int64)
// 67890.1234 (Double) --> 67890 (0x0000000000010932) (UInt64)
// 67890.1234 (Double) --> 67890.1234 (Decimal)
// 67890.1234 (Double) --> 67890.13 (Single)
//
// Unable to convert 1.79769313486232E+308 to Int64.
// Unable to convert 1.79769313486232E+308 to UInt64.
// Unable to convert 1.79769313486232E+308 to Decimal.
// 1.79769313486232E+308 (Double) --> Infinity (Single)
//
// Unable to convert NaN to Int64.
// Unable to convert NaN to UInt64.
// Unable to convert NaN to Decimal.
// NaN (Double) --> NaN (Single)
//
// Unable to convert Infinity to Int64.
// Unable to convert Infinity to UInt64.
// Unable to convert Infinity to Decimal.
// Infinity (Double) --> Infinity (Single)
//
// Unable to convert -Infinity to Int64.
// Unable to convert -Infinity to UInt64.
// Unable to convert -Infinity to Decimal.
// -Infinity (Double) --> -Infinity (Single)
// The example displays the following output for conversions performed
// in an unchecked context:
// -1.79769313486232E+308 (Double) --> -9223372036854775808 (0x8000000000000000) (Int64)
// -1.79769313486232E+308 (Double) --> 9223372036854775808 (0x8000000000000000) (UInt64)
// Unable to convert -1.79769313486232E+308 to Decimal.
// -1.79769313486232E+308 (Double) --> -Infinity (Single)
//
// -67890.1234 (Double) --> -67890 (0xFFFFFFFFFFFEF6CE) (Int64)
// -67890.1234 (Double) --> 18446744073709483726 (0xFFFFFFFFFFFEF6CE) (UInt64)
// -67890.1234 (Double) --> -67890.1234 (Decimal)
// -67890.1234 (Double) --> -67890.13 (Single)
//
// -12345.6789 (Double) --> -12345 (0xFFFFFFFFFFFFCFC7) (Int64)
// -12345.6789 (Double) --> 18446744073709539271 (0xFFFFFFFFFFFFCFC7) (UInt64)
// -12345.6789 (Double) --> -12345.6789 (Decimal)
// -12345.6789 (Double) --> -12345.68 (Single)
//
// 12345.6789 (Double) --> 12345 (0x0000000000003039) (Int64)
// 12345.6789 (Double) --> 12345 (0x0000000000003039) (UInt64)
// 12345.6789 (Double) --> 12345.6789 (Decimal)
// 12345.6789 (Double) --> 12345.68 (Single)
//
// 67890.1234 (Double) --> 67890 (0x0000000000010932) (Int64)
// 67890.1234 (Double) --> 67890 (0x0000000000010932) (UInt64)
// 67890.1234 (Double) --> 67890.1234 (Decimal)
// 67890.1234 (Double) --> 67890.13 (Single)
//
// 1.79769313486232E+308 (Double) --> -9223372036854775808 (0x8000000000000000) (Int64)
// 1.79769313486232E+308 (Double) --> 0 (0x0000000000000000) (UInt64)
// Unable to convert 1.79769313486232E+308 to Decimal.
// 1.79769313486232E+308 (Double) --> Infinity (Single)
//
// NaN (Double) --> -9223372036854775808 (0x8000000000000000) (Int64)
// NaN (Double) --> 0 (0x0000000000000000) (UInt64)
// Unable to convert NaN to Decimal.
// NaN (Double) --> NaN (Single)
//
// Infinity (Double) --> -9223372036854775808 (0x8000000000000000) (Int64)
// Infinity (Double) --> 0 (0x0000000000000000) (UInt64)
// Unable to convert Infinity to Decimal.
// Infinity (Double) --> Infinity (Single)
//
// -Infinity (Double) --> -9223372036854775808 (0x8000000000000000) (Int64)
// -Infinity (Double) --> 9223372036854775808 (0x8000000000000000) (UInt64)
// Unable to convert -Infinity to Decimal.
// -Infinity (Double) --> -Infinity (Single)
Module Example6
Public Sub Main()
Dim values() As Double = {Double.MinValue, -67890.1234, -12345.6789,
12345.6789, 67890.1234, Double.MaxValue,
Double.NaN, Double.PositiveInfinity,
Double.NegativeInfinity}
For Each value In values
Try
Dim lValue As Int64 = CLng(value)
Console.WriteLine("{0} ({1}) --> {2} (0x{2:X16}) ({3})",
value, value.GetType().Name,
lValue, lValue.GetType().Name)
Catch e As OverflowException
Console.WriteLine("Unable to convert {0} to Int64.", value)
End Try
Try
Dim ulValue As UInt64 = CULng(value)
Console.WriteLine("{0} ({1}) --> {2} (0x{2:X16}) ({3})",
value, value.GetType().Name,
ulValue, ulValue.GetType().Name)
Catch e As OverflowException
Console.WriteLine("Unable to convert {0} to UInt64.", value)
End Try
Try
Dim dValue As Decimal = CDec(value)
Console.WriteLine("{0} ({1}) --> {2} ({3})",
value, value.GetType().Name,
dValue, dValue.GetType().Name)
Catch e As OverflowException
Console.WriteLine("Unable to convert {0} to Decimal.", value)
End Try
Try
Dim sValue As Single = CSng(value)
Console.WriteLine("{0} ({1}) --> {2} ({3})",
value, value.GetType().Name,
sValue, sValue.GetType().Name)
Catch e As OverflowException
Console.WriteLine("Unable to convert {0} to Single.", value)
End Try
Console.WriteLine()
Next
End Sub
End Module
' The example displays the following output for conversions performed
' in a checked context:
' Unable to convert -1.79769313486232E+308 to Int64.
' Unable to convert -1.79769313486232E+308 to UInt64.
' Unable to convert -1.79769313486232E+308 to Decimal.
' -1.79769313486232E+308 (Double) --> -Infinity (Single)
'
' -67890.1234 (Double) --> -67890 (0xFFFFFFFFFFFEF6CE) (Int64)
' Unable to convert -67890.1234 to UInt64.
' -67890.1234 (Double) --> -67890.1234 (Decimal)
' -67890.1234 (Double) --> -67890.13 (Single)
'
' -12345.6789 (Double) --> -12346 (0xFFFFFFFFFFFFCFC6) (Int64)
' Unable to convert -12345.6789 to UInt64.
' -12345.6789 (Double) --> -12345.6789 (Decimal)
' -12345.6789 (Double) --> -12345.68 (Single)
'
' 12345.6789 (Double) --> 12346 (0x000000000000303A) (Int64)
' 12345.6789 (Double) --> 12346 (0x000000000000303A) (UInt64)
' 12345.6789 (Double) --> 12345.6789 (Decimal)
' 12345.6789 (Double) --> 12345.68 (Single)
'
' 67890.1234 (Double) --> 67890 (0x0000000000010932) (Int64)
' 67890.1234 (Double) --> 67890 (0x0000000000010932) (UInt64)
' 67890.1234 (Double) --> 67890.1234 (Decimal)
' 67890.1234 (Double) --> 67890.13 (Single)
'
' Unable to convert 1.79769313486232E+308 to Int64.
' Unable to convert 1.79769313486232E+308 to UInt64.
' Unable to convert 1.79769313486232E+308 to Decimal.
' 1.79769313486232E+308 (Double) --> Infinity (Single)
'
' Unable to convert NaN to Int64.
' Unable to convert NaN to UInt64.
' Unable to convert NaN to Decimal.
' NaN (Double) --> NaN (Single)
'
' Unable to convert Infinity to Int64.
' Unable to convert Infinity to UInt64.
' Unable to convert Infinity to Decimal.
' Infinity (Double) --> Infinity (Single)
'
' Unable to convert -Infinity to Int64.
' Unable to convert -Infinity to UInt64.
' Unable to convert -Infinity to Decimal.
' -Infinity (Double) --> -Infinity (Single)
' The example displays the following output for conversions performed
' in an unchecked context:
' -1.79769313486232E+308 (Double) --> -9223372036854775808 (0x8000000000000000) (Int64)
' -1.79769313486232E+308 (Double) --> 9223372036854775808 (0x8000000000000000) (UInt64)
' Unable to convert -1.79769313486232E+308 to Decimal.
' -1.79769313486232E+308 (Double) --> -Infinity (Single)
'
' -67890.1234 (Double) --> -67890 (0xFFFFFFFFFFFEF6CE) (Int64)
' -67890.1234 (Double) --> 18446744073709483726 (0xFFFFFFFFFFFEF6CE) (UInt64)
' -67890.1234 (Double) --> -67890.1234 (Decimal)
' -67890.1234 (Double) --> -67890.13 (Single)
'
' -12345.6789 (Double) --> -12346 (0xFFFFFFFFFFFFCFC6) (Int64)
' -12345.6789 (Double) --> 18446744073709539270 (0xFFFFFFFFFFFFCFC6) (UInt64)
' -12345.6789 (Double) --> -12345.6789 (Decimal)
' -12345.6789 (Double) --> -12345.68 (Single)
'
' 12345.6789 (Double) --> 12346 (0x000000000000303A) (Int64)
' 12345.6789 (Double) --> 12346 (0x000000000000303A) (UInt64)
' 12345.6789 (Double) --> 12345.6789 (Decimal)
' 12345.6789 (Double) --> 12345.68 (Single)
'
' 67890.1234 (Double) --> 67890 (0x0000000000010932) (Int64)
' 67890.1234 (Double) --> 67890 (0x0000000000010932) (UInt64)
' 67890.1234 (Double) --> 67890.1234 (Decimal)
' 67890.1234 (Double) --> 67890.13 (Single)
'
' 1.79769313486232E+308 (Double) --> -9223372036854775808 (0x8000000000000000) (Int64)
' 1.79769313486232E+308 (Double) --> 0 (0x0000000000000000) (UInt64)
' Unable to convert 1.79769313486232E+308 to Decimal.
' 1.79769313486232E+308 (Double) --> Infinity (Single)
'
' NaN (Double) --> -9223372036854775808 (0x8000000000000000) (Int64)
' NaN (Double) --> 0 (0x0000000000000000) (UInt64)
' Unable to convert NaN to Decimal.
' NaN (Double) --> NaN (Single)
'
' Infinity (Double) --> -9223372036854775808 (0x8000000000000000) (Int64)
' Infinity (Double) --> 0 (0x0000000000000000) (UInt64)
' Unable to convert Infinity to Decimal.
' Infinity (Double) --> Infinity (Single)
'
' -Infinity (Double) --> -9223372036854775808 (0x8000000000000000) (Int64)
' -Infinity (Double) --> 9223372036854775808 (0x8000000000000000) (UInt64)
' Unable to convert -Infinity to Decimal.
' -Infinity (Double) --> -Infinity (Single)
For more information on the conversion of numeric types, see Type Conversion in .NET and Type Conversion Tables.
Floating-point functionality
The Double structure and related types provide methods to perform operations in the following areas:
Comparison of values. You can call the Equals method to determine whether two Double values are equal, or the CompareTo method to determine the relationship between two values.
The Double structure also supports a complete set of comparison operators. For example, you can test for equality or inequality, or determine whether one value is greater than or equal to another. If one of the operands is a numeric type other than a Double, it is converted to a Double before performing the comparison.
Warning
Because of differences in precision, two Double values that you expect to be equal may turn out to be unequal, which affects the result of the comparison. See the Test for equality section for more information about comparing two Double values.
You can also call the IsNaN, IsInfinity, IsPositiveInfinity, and IsNegativeInfinity methods to test for these special values.
Mathematical operations. Common arithmetic operations, such as addition, subtraction, multiplication, and division, are implemented by language compilers and Common Intermediate Language (CIL) instructions, rather than by Double methods. If one of the operands in a mathematical operation is a numeric type other than a Double, it is converted to a Double before performing the operation. The result of the operation is also a Double value.
Other mathematical operations can be performed by calling
static(Sharedin Visual Basic) methods in the System.Math class. It includes additional methods commonly used for arithmetic (such as Math.Abs, Math.Sign, and Math.Sqrt), geometry (such as Math.Cos and Math.Sin), and calculus (such as Math.Log).You can also manipulate the individual bits in a Double value. The BitConverter.DoubleToInt64Bits method preserves a Double value's bit pattern in a 64-bit integer. The BitConverter.GetBytes(Double) method returns its bit pattern in a byte array.
Rounding. Rounding is often used as a technique for reducing the impact of differences between values caused by problems of floating-point representation and precision. You can round a Double value by calling the Math.Round method.
Formatting. You can convert a Double value to its string representation by calling the ToString method or by using the composite formatting feature. For information about how format strings control the string representation of floating-point values, see the Standard Numeric Format Strings and Custom Numeric Format Strings topics.
Parsing strings. You can convert the string representation of a floating-point value to a Double value by calling either the Parse or TryParse method. If the parse operation fails, the Parse method throws an exception, whereas the TryParse method returns
false.Type conversion. The Double structure provides an explicit interface implementation for the IConvertible interface, which supports conversion between any two standard .NET data types. Language compilers also support the implicit conversion of values of all other standard numeric types to Double values. Conversion of a value of any standard numeric type to a Double is a widening conversion and does not require the user of a casting operator or conversion method,
However, conversion of Int64 and Single values can involve a loss of precision. The following table lists the differences in precision for each of these types:
Type Maximum precision Internal precision Double 15 17 Int64 19 decimal digits 19 decimal digits Single 7 decimal digits 9 decimal digits The problem of precision most frequently affects Single values that are converted to Double values. In the following example, two values produced by identical division operations are unequal because one of the values is a single-precision floating point value converted to a Double.
using System; public class Example13 { public static void Main() { Double value = .1; Double result1 = value * 10; Double result2 = 0; for (int ctr = 1; ctr <= 10; ctr++) result2 += value; Console.WriteLine(".1 * 10: {0:R}", result1); Console.WriteLine(".1 Added 10 times: {0:R}", result2); } } // The example displays the following output: // .1 * 10: 1 // .1 Added 10 times: 0.99999999999999989let value = 0.1 let result1 = value * 10. let mutable result2 = 0. for i = 1 to 10 do result2 <- result2 + value printfn $".1 * 10: {result1:R}" printfn $".1 Added 10 times: {result2:R}" // The example displays the following output: // .1 * 10: 1 // .1 Added 10 times: 0.99999999999999989Module Example14 Public Sub Main() Dim value As Double = 0.1 Dim result1 As Double = value * 10 Dim result2 As Double For ctr As Integer = 1 To 10 result2 += value Next Console.WriteLine(".1 * 10: {0:R}", result1) Console.WriteLine(".1 Added 10 times: {0:R}", result2) End Sub End Module ' The example displays the following output: ' .1 * 10: 1 ' .1 Added 10 times: 0.99999999999999989
Examples
The following code example illustrates the use of Double:
// The Temperature class stores the temperature as a Double
// and delegates most of the functionality to the Double
// implementation.
public class Temperature : IComparable, IFormattable
{
// IComparable.CompareTo implementation.
public int CompareTo(object obj) {
if (obj == null) return 1;
Temperature temp = obj as Temperature;
if (obj != null)
return m_value.CompareTo(temp.m_value);
else
throw new ArgumentException("object is not a Temperature");
}
// IFormattable.ToString implementation.
public string ToString(string format, IFormatProvider provider) {
if( format != null ) {
if( format.Equals("F") ) {
return String.Format("{0}'F", this.Value.ToString());
}
if( format.Equals("C") ) {
return String.Format("{0}'C", this.Celsius.ToString());
}
}
return m_value.ToString(format, provider);
}
// Parses the temperature from a string in the form
// [ws][sign]digits['F|'C][ws]
public static Temperature Parse(string s, NumberStyles styles, IFormatProvider provider) {
Temperature temp = new Temperature();
if( s.TrimEnd(null).EndsWith("'F") ) {
temp.Value = Double.Parse( s.Remove(s.LastIndexOf('\''), 2), styles, provider);
}
else if( s.TrimEnd(null).EndsWith("'C") ) {
temp.Celsius = Double.Parse( s.Remove(s.LastIndexOf('\''), 2), styles, provider);
}
else {
temp.Value = Double.Parse(s, styles, provider);
}
return temp;
}
// The value holder
protected double m_value;
public double Value {
get {
return m_value;
}
set {
m_value = value;
}
}
public double Celsius {
get {
return (m_value-32.0)/1.8;
}
set {
m_value = 1.8*value+32.0;
}
}
}
// The Temperature class stores the temperature as a Double
// and delegates most of the functionality to the Double
// implementation.
type Temperature() =
member val Value = 0. with get, set
member this.Celsius
with get () = (this.Value - 32.) / 1.8
and set (value) =
this.Value <- 1.8 * value + 32.
// Parses the temperature from a string in the form
// [ws][sign]digits['F|'C][ws]
static member Parse(s: string, styles: NumberStyles, provider: IFormatProvider) =
let temp = Temperature()
if s.TrimEnd(null).EndsWith "'F" then
temp.Value <- Double.Parse(s.Remove(s.LastIndexOf '\'', 2), styles, provider)
elif s.TrimEnd(null).EndsWith "'C" then
temp.Celsius <- Double.Parse(s.Remove(s.LastIndexOf '\'', 2), styles, provider)
else
temp.Value <- Double.Parse(s, styles, provider)
temp
interface IComparable with
// IComparable.CompareTo implementation.
member this.CompareTo(obj: obj) =
match obj with
| null -> 1
| :? Temperature as temp ->
this.Value.CompareTo temp.Value
| _ ->
invalidArg "obj" "object is not a Temperature"
interface IFormattable with
// IFormattable.ToString implementation.
member this.ToString(format: string, provider: IFormatProvider) =
match format with
| "F" ->
$"{this.Value}'F"
| "C" ->
$"{this.Celsius}'C"
| _ ->
this.Value.ToString(format, provider)
' Temperature class stores the value as Double
' and delegates most of the functionality
' to the Double implementation.
Public Class Temperature
Implements IComparable, IFormattable
Public Overloads Function CompareTo(ByVal obj As Object) As Integer _
Implements IComparable.CompareTo
If TypeOf obj Is Temperature Then
Dim temp As Temperature = CType(obj, Temperature)
Return m_value.CompareTo(temp.m_value)
End If
Throw New ArgumentException("object is not a Temperature")
End Function
Public Overloads Function ToString(ByVal format As String, ByVal provider As IFormatProvider) As String _
Implements IFormattable.ToString
If Not (format Is Nothing) Then
If format.Equals("F") Then
Return [String].Format("{0}'F", Me.Value.ToString())
End If
If format.Equals("C") Then
Return [String].Format("{0}'C", Me.Celsius.ToString())
End If
End If
Return m_value.ToString(format, provider)
End Function
' Parses the temperature from a string in form
' [ws][sign]digits['F|'C][ws]
Public Shared Function Parse(ByVal s As String, ByVal styles As NumberStyles, ByVal provider As IFormatProvider) As Temperature
Dim temp As New Temperature()
If s.TrimEnd().EndsWith("'F") Then
temp.Value = Double.Parse(s.Remove(s.LastIndexOf("'"c), 2), styles, provider)
Else
If s.TrimEnd().EndsWith("'C") Then
temp.Celsius = Double.Parse(s.Remove(s.LastIndexOf("'"c), 2), styles, provider)
Else
temp.Value = Double.Parse(s, styles, provider)
End If
End If
Return temp
End Function
' The value holder
Protected m_value As Double
Public Property Value() As Double
Get
Return m_value
End Get
Set(ByVal Value As Double)
m_value = Value
End Set
End Property
Public Property Celsius() As Double
Get
Return (m_value - 32) / 1.8
End Get
Set(ByVal Value As Double)
m_value = Value * 1.8 + 32
End Set
End Property
End Class
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