This article provides supplementary remarks to the reference documentation for this API.
The Single value type represents a single-precision 32-bit number with values ranging from negative 3.402823e38 to positive 3.402823e38, 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 Single type complies with the IEC 60559:1989 (IEEE 754) standard for binary floating-point arithmetic.
System.Single provides methods to compare instances of this type, to convert the value of an instance to its string representation, and to convert the string representation of a number to an instance of this type. For information about how format specification codes control the string representation of value types, see Formatting Types, Standard Numeric Format Strings, and Custom Numeric Format Strings.
Floating-point representation and precisionThe Single data type stores single-precision floating-point values in a 32-bit binary format, as shown in the following table:
Part Bits Significand or mantissa 0-22 Exponent 23-30 Sign (0 = positive, 1 = negative) 31Just 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, 2/10, which is represented precisely by .2 as a decimal fraction, is represented by .0011111001001100 as a binary fraction, with the pattern "1100" 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 increases its lack of precision. For example, if you compare the results of multiplying .3 by 10 and adding .3 to .3 nine times, you will see that addition produces the less precise result, because it involves eight more operations than multiplication. Note that this disparity is apparent only if you display the two Single values by using the "R" standard numeric format string, which, if necessary, displays all 9 digits of precision supported by the Single type.
using System;
public class Example12
{
public static void Main()
{
Single value = .2f;
Single result1 = value * 10f;
Single result2 = 0f;
for (int ctr = 1; ctr <= 10; ctr++)
result2 += value;
Console.WriteLine($".2 * 10: {result1:R}");
Console.WriteLine($".2 Added 10 times: {result2:R}");
}
}
// The example displays the following output:
// .2 * 10: 2
// .2 Added 10 times: 2.00000024
let value = 0.2f
let result1 = value * 10f
let mutable result2 = 0f
for _ = 1 to 10 do
result2 <- result2 + value
printfn $".2 * 10: {result1:R}"
printfn $".2 Added 10 times: {result2:R}"
// The example displays the following output:
// .2 * 10: 2
// .2 Added 10 times: 2.00000024
Module Example13
Public Sub Main()
Dim value As Single = 0.2
Dim result1 As Single = value * 10
Dim result2 As Single
For ctr As Integer = 1 To 10
result2 += value
Next
Console.WriteLine(".2 * 10: {0:R}", result1)
Console.WriteLine(".2 Added 10 times: {0:R}", result2)
End Sub
End Module
' The example displays the following output:
' .2 * 10: 2
' .2 Added 10 times: 2.00000024
Because some numbers cannot be represented exactly as fractional binary values, floating-point numbers can only approximate real numbers.
All floating-point numbers have a limited number of significant digits, which also determines how accurately a floating-point value approximates a real number. A Single value has up to 7 decimal digits of precision, although a maximum of 9 digits is maintained internally. This means that some floating-point operations may lack the precision to change a floating-point value. The following example defines a large single-precision floating-point value, and then adds the product of Single.Epsilon and one quadrillion to it. However, the product is too small to modify the original floating-point value. Its least significant digit is thousandths, whereas the most significant digit in the product is 10-30.
using System;
public class Example13
{
public static void Main()
{
Single value = 123.456f;
Single additional = Single.Epsilon * 1e15f;
Console.WriteLine($"{value} + {additional} = {value + additional}");
}
}
// The example displays the following output:
// 123.456 + 1.401298E-30 = 123.456
open System
let value = 123.456f
let additional = Single.Epsilon * 1e15f
printfn $"{value} + {additional} = {value + additional}"
// The example displays the following output:
// 123.456 + 1.401298E-30 = 123.456
Module Example
Public Sub Main()
Dim value As Single = 123.456
Dim additional As Single = Single.Epsilon * 1e15
Console.WriteLine($"{value} + {additional} = {value + additional}")
End Sub
End Module
' The example displays the following output:
' 123.456 + 1.401298E-30 = 123.456
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 Equals method indicates that they are not.
using System;
public class Example9
{
public static void Main()
{
Single[] values = { 10.01f, 2.88f, 2.88f, 2.88f, 9.0f };
Single result = 27.65f;
Single total = 0f;
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 ({total}) does not equal the total ({result}).");
}
}
// The example displays the following output:
// The sum of the values (27.65) does not equal the total (27.65).
//
// 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 (27.6500015) does not equal the total (27.65).
let values = [| 10.01f; 2.88f; 2.88f; 2.88f; 9f |]
let result = 27.65f
let mutable total = 0f
for value in values do
total <- total + value
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 (27.65) does not equal the total (27.65).
//
// 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 (27.6500015) does not equal the total (27.65).
Module Example10
Public Sub Main()
Dim values() As Single = {10.01, 2.88, 2.88, 2.88, 9.0}
Dim result As Single = 27.65
Dim total As Single
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 (27.65) does not equal the total (27.65).
'
' 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 Single 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 Single 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 .3 by 10 and adding .3 to .3 nine times.
When accuracy in numeric operations with fractional values is important, use the Decimal type instead of the Single 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 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 Single values are converted to strings and saved in a file. If you run this example on .NET Framework, even though the values appear to be identical, the restored values are not equal to the original values. (This has since been addressed in .NET, where the values round-trip correctly.)
StreamWriter sw = new(@"./Singles.dat");
float[] values = { 3.2f / 1.11f, 1.0f / 3f, (float)Math.PI };
for (int ctr = 0; ctr < values.Length; ctr++)
{
sw.Write(values[ctr].ToString());
if (ctr != values.Length - 1)
sw.Write("|");
}
sw.Close();
float[] restoredValues = new float[values.Length];
StreamReader sr = new(@"./Singles.dat");
string temp = sr.ReadToEnd();
string[] tempStrings = temp.Split('|');
for (int ctr = 0; ctr < tempStrings.Length; ctr++)
restoredValues[ctr] = float.Parse(tempStrings[ctr]);
for (int ctr = 0; ctr < values.Length; ctr++)
Console.WriteLine($"{values[ctr]} {(values[ctr].Equals(restoredValues[ctr]) ? "=" : "<>")} {restoredValues[ctr]}");
// The example displays the following output:
// 2.882883 <> 2.882883
// 0.3333333 <> 0.3333333
// 3.141593 <> 3.141593
open System
open System.IO
let values = [| 3.2f / 1.11f; 1f / 3f; MathF.PI |]
do
use sw = new StreamWriter(@".\Singles.dat")
for i = 0 to values.Length - 1 do
sw.Write(string values[i])
if i <> values.Length - 1 then
sw.Write "|"
let restoredValues =
use sr = new StreamReader(@".\Singles.dat")
sr.ReadToEnd().Split '|'
|> Array.map Single.Parse
for i = 0 to values.Length - 1 do
printfn $"""{values[i]} {if values[i].Equals restoredValues[i] then "=" else "<>"} {restoredValues[i]}"""
// The example displays the following output:
// 2.882883 <> 2.882883
// 0.3333333 <> 0.3333333
// 3.141593 <> 3.141593
Imports System.IO
Module Example11
Public Sub Main()
Dim sw As New StreamWriter(".\Singles.dat")
Dim values() As Single = {3.2 / 1.11, 1.0 / 3, CSng(Math.PI)}
For ctr As Integer = 0 To values.Length - 1
sw.Write(values(ctr).ToString())
If ctr <> values.Length - 1 Then sw.Write("|")
Next
sw.Close()
Dim restoredValues(values.Length - 1) As Single
Dim sr As New StreamReader(".\Singles.dat")
Dim temp As String = sr.ReadToEnd()
Dim tempStrings() As String = temp.Split("|"c)
For ctr As Integer = 0 To tempStrings.Length - 1
restoredValues(ctr) = Single.Parse(tempStrings(ctr))
Next
For ctr As Integer = 0 To values.Length - 1
Console.WriteLine("{0} {2} {1}", values(ctr),
restoredValues(ctr),
If(values(ctr).Equals(restoredValues(ctr)), "=", "<>"))
Next
End Sub
End Module
' The example displays the following output:
' 2.882883 <> 2.882883
' 0.3333333 <> 0.3333333
' 3.141593 <> 3.141593
If you're targeting .NET Framework, the values can be successfully round-tripped by using the "G9" standard numeric format string to preserve the full precision of Single values.
Single values have less precision than Double values. A Single value that is converted to a seemingly equivalent Double often does not equal the Double value because of differences in precision. In the following example, the result of identical division operations is assigned to a Double value and a Single value. After the Single value is cast to a Double, a comparison of the two values shows that they are unequal.
using System;
public class Example9
{
public static void Main()
{
Double value1 = 1 / 3.0;
Single sValue2 = 1 / 3.0f;
Double value2 = (Double)sValue2;
Console.WriteLine($"{value1:R} = {value2:R}: {value1.Equals(value2)}");
}
}
// The example displays the following output:
// 0.33333333333333331 = 0.3333333432674408: False
open System
let value1 = 1. / 3.
let sValue2 = 1f /3f
let value2 = double sValue2
printfn $"{value1:R} = {value2:R}: {value1.Equals value2}"
// The example displays the following output:
// 0.33333333333333331 = 0.3333333432674408: False
Module Example10
Public Sub Main()
Dim value1 As Double = 1 / 3
Dim sValue2 As Single = 1 / 3
Dim value2 As Double = CDbl(sValue2)
Console.WriteLine("{0} = {1}: {2}", value1, value2, value1.Equals(value2))
End Sub
End Module
' The example displays the following output:
' 0.33333333333333331 = 0.3333333432674408: False
To avoid this problem, either use the Double data type in place of the Single data type, or use the Round method so that both values have the same precision.
To be considered equal, two Single values must represent identical values. However, because of differences in precision between values, or because of a loss of precision by one or both values, floating-point values that are expected to be identical often turn out to be unequal due to differences in their least significant digits. As a result, calls to the Equals method to determine whether two values are equal, or calls to the CompareTo method to determine the relationship between two Single values, often yield unexpected results. This is evident in the following example, where two apparently equal Single values turn out to be unequal, because the first value has 7 digits of precision, whereas the second value has 9.
using System;
public class Example
{
public static void Main()
{
float value1 = .3333333f;
float value2 = 1.0f/3;
Console.WriteLine($"{value1:R} = {value2:R}: {value1.Equals(value2)}");
}
}
// The example displays the following output:
// 0.3333333 = 0.333333343: False
let value1 = 0.3333333f
let value2 = 1f / 3f
printfn $"{value1:R} = {value2:R}: {value1.Equals value2}"
// The example displays the following output:
// 0.3333333 = 0.333333343: False
Module Example1
Public Sub Main()
Dim value1 As Single = 0.3333333
Dim value2 As Single = 1 / 3
Console.WriteLine("{0:R} = {1:R}: {2}", value1, value2, value1.Equals(value2))
End Sub
End Module
' The example displays the following output:
' 0.3333333 = 0.333333343: False
Calculated values that follow different code paths and that are manipulated in different ways often prove to be unequal. In the following example, one Single value is squared, and then the square root is calculated to restore the original value. A second Single is multiplied by 3.51 and squared before the square root of the result is divided by 3.51 to restore the original value. Although the two values appear to be identical, a call to the Equals(Single) method indicates that they are not equal. Using the "G9" standard format string to return a result string that displays all the significant digits of each Single value shows that the second value is .0000000000001 less than the first.
using System;
public class Example1
{
public static void Main()
{
float value1 = 10.201438f;
value1 = (float)Math.Sqrt((float)Math.Pow(value1, 2));
float value2 = (float)Math.Pow((float)value1 * 3.51f, 2);
value2 = ((float)Math.Sqrt(value2)) / 3.51f;
Console.WriteLine($"{value1} = {value2}: {value1.Equals(value2)}");
Console.WriteLine();
Console.WriteLine($"{value1:G9} = {value2:G9}");
}
}
// The example displays the following output:
// 10.20144 = 10.20144: False
//
// 10.201438 = 10.2014389
let value1 =
10.201438f ** 2f
|> sqrt
let value2 =
((value1 * 3.51f) ** 2f |> sqrt) / 3.51f
printfn $"{value1} = {value2}: {value1.Equals value2}\n"
printfn $"{value1:G9} = {value2:G9}"
// The example displays the following output:
// 10.20144 = 10.20144: False
//
// 10.201438 = 10.2014389
Module Example2
Public Sub Main()
Dim value1 As Single = 10.201438
value1 = CSng(Math.Sqrt(CSng(Math.Pow(value1, 2))))
Dim value2 As Single = CSng(Math.Pow(value1 * CSng(3.51), 2))
value2 = CSng(Math.Sqrt(value2) / CSng(3.51))
Console.WriteLine("{0} = {1}: {2}",
value1, value2, value1.Equals(value2))
Console.WriteLine()
Console.WriteLine("{0:G9} = {1:G9}", value1, value2)
End Sub
End Module
' The example displays the following output:
' 10.20144 = 10.20144: False
'
' 10.201438 = 10.2014389
In cases where a loss of precision is likely to affect the result of a comparison, you can use the following techniques instead of calling the Equals or CompareTo method:
Call the Math.Round method to ensure that both values have the same precision. The following example modifies a previous example to use this approach so that two fractional values are equivalent.
using System;
public class Example2
{
public static void Main()
{
float value1 = .3333333f;
float value2 = 1.0f / 3;
int precision = 7;
value1 = (float)Math.Round(value1, precision);
value2 = (float)Math.Round(value2, precision);
Console.WriteLine($"{value1:R} = {value2:R}: {value1.Equals(value2)}");
}
}
// The example displays the following output:
// 0.3333333 = 0.3333333: True
open System
let value1 = 0.3333333f
let value2 = 1f / 3f
let precision = 7
let value1r = Math.Round(float value1, precision) |> float32
let value2r = Math.Round(float value2, precision) |> float32
printfn $"{value1:R} = {value2:R}: {value1.Equals value2}"
// The example displays the following output:
// 0.3333333 = 0.3333333: True
Module Example3
Public Sub Main()
Dim value1 As Single = 0.3333333
Dim value2 As Single = 1 / 3
Dim precision As Integer = 7
value1 = CSng(Math.Round(value1, precision))
value2 = CSng(Math.Round(value2, precision))
Console.WriteLine("{0:R} = {1:R}: {2}", value1, value2, value1.Equals(value2))
End Sub
End Module
' The example displays the following output:
' 0.3333333 = 0.3333333: True
The problem of precision still applies to rounding of midpoint values. For more information, see the Math.Round(Double, Int32, MidpointRounding) method.
Test for approximate equality instead of equality. This technique requires that you define either an absolute amount by which the two values can differ but still be equal, or that you define a relative amount by which the smaller value can diverge from the larger value.
Warning
Single.Epsilon is sometimes used as an absolute measure of the distance between two Single values when testing for equality. However, Single.Epsilon measures the smallest possible value that can be added to, or subtracted from, a Single whose value is zero. For most positive and negative Single values, the value of Single.Epsilon is too small to be detected. Therefore, except for values that are zero, we do not recommend its use in tests for equality.
The following example uses the latter approach to define an IsApproximatelyEqual method that tests the relative difference between two values. It also contrasts the result of calls to the IsApproximatelyEqual method and the Equals(Single) method.
using System;
public class Example3
{
public static void Main()
{
float one1 = .1f * 10;
float one2 = 0f;
for (int ctr = 1; ctr <= 10; ctr++)
one2 += .1f;
Console.WriteLine($"{one1:R} = {one2:R}: {one1.Equals(one2)}");
Console.WriteLine($"{one1:R} is approximately equal to {one2:R}: " +
$"{IsApproximatelyEqual(one1, one2, .000001f)}");
float negativeOne1 = -1 * one1;
float negativeOne2 = -1 * one2;
Console.WriteLine($"{negativeOne1:R} = {negativeOne2:R}: {negativeOne1.Equals(negativeOne2)}");
Console.WriteLine($"{negativeOne1:R} is approximately equal to {negativeOne2:R}: " +
$"{IsApproximatelyEqual(negativeOne1, negativeOne2, .000001f)}");
}
static bool IsApproximatelyEqual(float value1, float value2, float 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 = 1.00000012: False
// 1 is approximately equal to 1.00000012: True
// -1 is approximately equal to -1.00000012: True
open System
let isApproximatelyEqual value1 value2 epsilon =
// If they are equal anyway, just return True.
if value1.Equals value2 then
true
// Handle NaN, Infinity.
elif Single.IsInfinity value1 || Single.IsNaN value1 then
value1.Equals value2
elif Single.IsInfinity value2 || Single.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 = 0.1f * 10f
let mutable one2 = 0f
for _ = 1 to 10 do
one2 <- one2 + 0.1f
printfn $"{one1:R} = {one2:R}: {one1.Equals one2}"
printfn $"{one1:R} is approximately equal to {one2:R}: {isApproximatelyEqual one1 one2 0.000001f}"
// The example displays the following output:
// 1 = 1.00000012: False
// 1 is approximately equal to 1.00000012: True
Module Example4
Public Sub Main()
Dim one1 As Single = 0.1 * 10
Dim one2 As Single = 0
For ctr As Integer = 1 To 10
one2 += CSng(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, 0.000001))
End Sub
Function IsApproximatelyEqual(value1 As Single, value2 As Single,
epsilon As Single) As Boolean
' If they are equal anyway, just return True.
If value1.Equals(value2) Then Return True
' Handle NaN, Infinity.
If Single.IsInfinity(value1) Or Single.IsNaN(value1) Then
Return value1.Equals(value2)
ElseIf Single.IsInfinity(value2) Or Single.IsNaN(value2) Then
Return value1.Equals(value2)
End If
' Handle zero to avoid division by zero
Dim divisor As Single = 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 = 1.00000012: False
' 1 is approximately equal to 1.00000012: True
Operations with floating-point values do not throw exceptions, unlike operations with integral types, which throw exceptions in cases of illegal operations such as division by zero or overflow. Instead, in these 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 floating-point numbers are multiplied, as the following example shows.
using System;
public class Example6
{
public static void Main()
{
float value1 = 1.163287e-36f;
float value2 = 9.164234e-25f;
float result = value1 * value2;
Console.WriteLine($"{value1} * {value2} = {result}");
Console.WriteLine($"{result} = 0: {result.Equals(0.0f)}");
}
}
// The example displays the following output:
// 1.163287E-36 * 9.164234E-25 = 0
// 0 = 0: True
let value1 = 1.163287e-36f
let value2 = 9.164234e-25f
let result = value1 * value2
printfn $"{value1} * {value2} = {result}"
printfn $"{result} = 0: {result.Equals(0f)}"
// The example displays the following output:
// 1.163287E-36 * 9.164234E-25 = 0
// 0 = 0: True
Module Example7
Public Sub Main()
Dim value1 As Single = 1.163287E-36
Dim value2 As Single = 9.164234E-25
Dim result As Single = value1 * value2
Console.WriteLine("{0} * {1} = {2:R}", value1, value2, result)
Console.WriteLine("{0} = 0: {1}", result, result.Equals(0))
End Sub
End Module
' The example displays the following output:
' 1.163287E-36 * 9.164234E-25 = 0
' 0 = 0: True
If the magnitude of the result of a floating-point operation exceeds the range of the destination format, the result of the operation is PositiveInfinity or NegativeInfinity, as appropriate for the sign of the result. The result of an operation that overflows Single.MaxValue is PositiveInfinity, and the result of an operation that overflows Single.MinValue is NegativeInfinity, as the following example shows.
using System;
public class Example7
{
public static void Main()
{
float value1 = 3.065e35f;
float value2 = 6.9375e32f;
float result = value1 * value2;
Console.WriteLine($"PositiveInfinity: {Single.IsPositiveInfinity(result)}");
Console.WriteLine($"NegativeInfinity: {Single.IsNegativeInfinity(result)}");
Console.WriteLine();
value1 = -value1;
result = value1 * value2;
Console.WriteLine($"PositiveInfinity: {Single.IsPositiveInfinity(result)}");
Console.WriteLine($"NegativeInfinity: {Single.IsNegativeInfinity(result)}");
}
}
// The example displays the following output:
// PositiveInfinity: True
// NegativeInfinity: False
//
// PositiveInfinity: False
// NegativeInfinity: True
open System
let value1 = 3.065e35f
let value2 = 6.9375e32f
let result = value1 * value2
printfn $"PositiveInfinity: {Single.IsPositiveInfinity result}"
printfn $"NegativeInfinity: {Single.IsNegativeInfinity result}\n"
let value3 = -value1
let result2 = value3 * value2
printfn $"PositiveInfinity: {Single.IsPositiveInfinity result}"
printfn $"NegativeInfinity: {Single.IsNegativeInfinity result}"
// The example displays the following output:
// PositiveInfinity: True
// NegativeInfinity: False
//
// PositiveInfinity: False
// NegativeInfinity: True
Module Example8
Public Sub Main()
Dim value1 As Single = 3.065E+35
Dim value2 As Single = 6.9375E+32
Dim result As Single = value1 * value2
Console.WriteLine("PositiveInfinity: {0}",
Single.IsPositiveInfinity(result))
Console.WriteLine("NegativeInfinity: {0}",
Single.IsNegativeInfinity(result))
Console.WriteLine()
value1 = -value1
result = value1 * value2
Console.WriteLine("PositiveInfinity: {0}",
Single.IsPositiveInfinity(result))
Console.WriteLine("NegativeInfinity: {0}",
Single.IsNegativeInfinity(result))
End Sub
End Module
' The example displays the following output:
' PositiveInfinity: True
' NegativeInfinity: False
'
' PositiveInfinity: False
' NegativeInfinity: True
PositiveInfinity 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:
The Single structure does not define any explicit or implicit conversion operators; instead, conversions are implemented by the compiler.
The following table lists the possible conversions of a value of the other primitive numeric types to a Single value, It also indicates whether the conversion is widening or narrowing and whether the resulting Single may have less precision than the original value.
The following example converts the minimum or maximum value of other primitive numeric types to a Single value.
using System;
public class Example4
{
public static void Main()
{
dynamic[] values = { Byte.MinValue, Byte.MaxValue, Decimal.MinValue,
Decimal.MaxValue, Double.MinValue, Double.MaxValue,
Int16.MinValue, Int16.MaxValue, Int32.MinValue,
Int32.MaxValue, Int64.MinValue, Int64.MaxValue,
SByte.MinValue, SByte.MaxValue, UInt16.MinValue,
UInt16.MaxValue, UInt32.MinValue, UInt32.MaxValue,
UInt64.MinValue, UInt64.MaxValue };
float sngValue;
foreach (var value in values)
{
if (value.GetType() == typeof(Decimal) ||
value.GetType() == typeof(Double))
sngValue = (float)value;
else
sngValue = value;
Console.WriteLine($"{value} ({value.GetType().Name}) --> {sngValue:R} ({sngValue.GetType().Name})");
}
}
}
// The example displays the following output:
// 0 (Byte) --> 0 (Single)
// 255 (Byte) --> 255 (Single)
// -79228162514264337593543950335 (Decimal) --> -7.92281625E+28 (Single)
// 79228162514264337593543950335 (Decimal) --> 7.92281625E+28 (Single)
// -1.79769313486232E+308 (Double) --> -Infinity (Single)
// 1.79769313486232E+308 (Double) --> Infinity (Single)
// -32768 (Int16) --> -32768 (Single)
// 32767 (Int16) --> 32767 (Single)
// -2147483648 (Int32) --> -2.14748365E+09 (Single)
// 2147483647 (Int32) --> 2.14748365E+09 (Single)
// -9223372036854775808 (Int64) --> -9.223372E+18 (Single)
// 9223372036854775807 (Int64) --> 9.223372E+18 (Single)
// -128 (SByte) --> -128 (Single)
// 127 (SByte) --> 127 (Single)
// 0 (UInt16) --> 0 (Single)
// 65535 (UInt16) --> 65535 (Single)
// 0 (UInt32) --> 0 (Single)
// 4294967295 (UInt32) --> 4.2949673E+09 (Single)
// 0 (UInt64) --> 0 (Single)
// 18446744073709551615 (UInt64) --> 1.84467441E+19 (Single)
open System
let values: obj list =
[ Byte.MinValue; Byte.MaxValue; Decimal.MinValue
Decimal.MaxValue; Double.MinValue; Double.MaxValue
Int16.MinValue; Int16.MaxValue; Int32.MinValue
Int32.MaxValue; Int64.MinValue; Int64.MaxValue
SByte.MinValue; SByte.MaxValue; UInt16.MinValue
UInt16.MaxValue; UInt32.MinValue; UInt32.MaxValue
UInt64.MinValue; UInt64.MaxValue ]
for value in values do
let sngValue =
match value with
| :? byte as v -> float32 v
| :? decimal as v -> float32 v
| :? double as v -> float32 v
| :? int16 as v -> float32 v
| :? int as v -> float32 v
| :? int64 as v -> float32 v
| :? int8 as v -> float32 v
| :? uint16 as v -> float32 v
| :? uint as v -> float32 v
| :? uint64 as v -> float32 v
| _ -> raise (NotImplementedException "Unknown Type")
printfn $"{value} ({value.GetType().Name}) --> {sngValue:R} ({sngValue.GetType().Name})"
// The example displays the following output:
// 0 (Byte) --> 0 (Single)
// 255 (Byte) --> 255 (Single)
// -79228162514264337593543950335 (Decimal) --> -7.92281625E+28 (Single)
// 79228162514264337593543950335 (Decimal) --> 7.92281625E+28 (Single)
// -1.79769313486232E+308 (Double) --> -Infinity (Single)
// 1.79769313486232E+308 (Double) --> Infinity (Single)
// -32768 (Int16) --> -32768 (Single)
// 32767 (Int16) --> 32767 (Single)
// -2147483648 (Int32) --> -2.14748365E+09 (Single)
// 2147483647 (Int32) --> 2.14748365E+09 (Single)
// -9223372036854775808 (Int64) --> -9.223372E+18 (Single)
// 9223372036854775807 (Int64) --> 9.223372E+18 (Single)
// -128 (SByte) --> -128 (Single)
// 127 (SByte) --> 127 (Single)
// 0 (UInt16) --> 0 (Single)
// 65535 (UInt16) --> 65535 (Single)
// 0 (UInt32) --> 0 (Single)
// 4294967295 (UInt32) --> 4.2949673E+09 (Single)
// 0 (UInt64) --> 0 (Single)
// 18446744073709551615 (UInt64) --> 1.84467441E+19 (Single)
Module Example5
Public Sub Main()
Dim values() As Object = {Byte.MinValue, Byte.MaxValue, Decimal.MinValue,
Decimal.MaxValue, Double.MinValue, Double.MaxValue,
Int16.MinValue, Int16.MaxValue, Int32.MinValue,
Int32.MaxValue, Int64.MinValue, Int64.MaxValue,
SByte.MinValue, SByte.MaxValue, UInt16.MinValue,
UInt16.MaxValue, UInt32.MinValue, UInt32.MaxValue,
UInt64.MinValue, UInt64.MaxValue}
Dim sngValue As Single
For Each value In values
If value.GetType() = GetType(Double) Then
sngValue = CSng(value)
Else
sngValue = value
End If
Console.WriteLine("{0} ({1}) --> {2:R} ({3})",
value, value.GetType().Name,
sngValue, sngValue.GetType().Name)
Next
End Sub
End Module
' The example displays the following output:
' 0 (Byte) --> 0 (Single)
' 255 (Byte) --> 255 (Single)
' -79228162514264337593543950335 (Decimal) --> -7.92281625E+28 (Single)
' 79228162514264337593543950335 (Decimal) --> 7.92281625E+28 (Single)
' -1.79769313486232E+308 (Double) --> -Infinity (Single)
' 1.79769313486232E+308 (Double) --> Infinity (Single)
' -32768 (Int16) --> -32768 (Single)
' 32767 (Int16) --> 32767 (Single)
' -2147483648 (Int32) --> -2.14748365E+09 (Single)
' 2147483647 (Int32) --> 2.14748365E+09 (Single)
' -9223372036854775808 (Int64) --> -9.223372E+18 (Single)
' 9223372036854775807 (Int64) --> 9.223372E+18 (Single)
' -128 (SByte) --> -128 (Single)
' 127 (SByte) --> 127 (Single)
' 0 (UInt16) --> 0 (Single)
' 65535 (UInt16) --> 65535 (Single)
' 0 (UInt32) --> 0 (Single)
' 4294967295 (UInt32) --> 4.2949673E+09 (Single)
' 0 (UInt64) --> 0 (Single)
' 18446744073709551615 (UInt64) --> 1.84467441E+19 (Single)
In addition, the Double values Double.NaN, Double.PositiveInfinity, and Double.NegativeInfinity convert to Single.NaN, Single.PositiveInfinity, and Single.NegativeInfinity, respectively.
Note that the conversion of the value of some numeric types to a Single value can involve a loss of precision. As the example illustrates, a loss of precision is possible when converting Decimal, Double, Int32, Int64, UInt32, and UInt64 values to Single values.
The conversion of a Single value to a Double is a widening conversion. The conversion may result in a loss of precision if the Double type does not have a precise representation for the Single value.
The conversion of a Single value to a value of any primitive numeric data type other than a Double is a narrowing conversion and requires a cast operator (in C#) or a conversion method (in Visual Basic). 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.
If the conversion occurs in an unchecked context (the default in C#), the conversion operation succeeds but the value overflows.
Decimal An OverflowException exception,In addition, Single.NaN, Single.PositiveInfinity, and Single.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 Double, they convert to Double.NaN, Double.PositiveInfinity, and Double.NegativeInfinity, respectively.
Note that a loss of precision may result from converting a Single value to another numeric type. In the case of converting non-integral Single values, as the output from the example shows, the fractional component is lost when the Single value is either rounded (as in Visual Basic) or truncated (as in C# and F#). For conversions to Decimal values, the Single value may not have a precise representation in the target data type.
The following example converts a number of Single 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 open Checked statement). 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()
{
float[] values = { Single.MinValue, -67890.1234f, -12345.6789f,
12345.6789f, 67890.1234f, Single.MaxValue,
Single.NaN, Single.PositiveInfinity,
Single.NegativeInfinity };
checked
{
foreach (var value in values)
{
try
{
Int64 lValue = (long)value;
Console.WriteLine($"{value} ({value.GetType().Name}) --> {lValue} (0x{lValue:X16}) ({lValue.GetType().Name})");
}
catch (OverflowException)
{
Console.WriteLine($"Unable to convert {value} to Int64.");
}
try
{
UInt64 ulValue = (ulong)value;
Console.WriteLine($"{value} ({value.GetType().Name}) --> {ulValue} (0x{ulValue:X16}) ({ulValue.GetType().Name})");
}
catch (OverflowException)
{
Console.WriteLine($"Unable to convert {value} to UInt64.");
}
try
{
Decimal dValue = (decimal)value;
Console.WriteLine($"{value} ({value.GetType().Name}) --> {dValue} ({dValue.GetType().Name})");
}
catch (OverflowException)
{
Console.WriteLine($"Unable to convert {value} to Decimal.");
}
Double dblValue = value;
Console.WriteLine($"{value} ({value.GetType().Name}) --> {dblValue} ({dblValue.GetType().Name})");
Console.WriteLine();
}
}
}
}
// The example displays the following output for conversions performed
// in a checked context:
// Unable to convert -3.402823E+38 to Int64.
// Unable to convert -3.402823E+38 to UInt64.
// Unable to convert -3.402823E+38 to Decimal.
// -3.402823E+38 (Single) --> -3.40282346638529E+38 (Double)
//
// -67890.13 (Single) --> -67890 (0xFFFFFFFFFFFEF6CE) (Int64)
// Unable to convert -67890.13 to UInt64.
// -67890.13 (Single) --> -67890.12 (Decimal)
// -67890.13 (Single) --> -67890.125 (Double)
//
// -12345.68 (Single) --> -12345 (0xFFFFFFFFFFFFCFC7) (Int64)
// Unable to convert -12345.68 to UInt64.
// -12345.68 (Single) --> -12345.68 (Decimal)
// -12345.68 (Single) --> -12345.6787109375 (Double)
//
// 12345.68 (Single) --> 12345 (0x0000000000003039) (Int64)
// 12345.68 (Single) --> 12345 (0x0000000000003039) (UInt64)
// 12345.68 (Single) --> 12345.68 (Decimal)
// 12345.68 (Single) --> 12345.6787109375 (Double)
//
// 67890.13 (Single) --> 67890 (0x0000000000010932) (Int64)
// 67890.13 (Single) --> 67890 (0x0000000000010932) (UInt64)
// 67890.13 (Single) --> 67890.12 (Decimal)
// 67890.13 (Single) --> 67890.125 (Double)
//
// Unable to convert 3.402823E+38 to Int64.
// Unable to convert 3.402823E+38 to UInt64.
// Unable to convert 3.402823E+38 to Decimal.
// 3.402823E+38 (Single) --> 3.40282346638529E+38 (Double)
//
// Unable to convert NaN to Int64.
// Unable to convert NaN to UInt64.
// Unable to convert NaN to Decimal.
// NaN (Single) --> NaN (Double)
//
// Unable to convert Infinity to Int64.
// Unable to convert Infinity to UInt64.
// Unable to convert Infinity to Decimal.
// Infinity (Single) --> Infinity (Double)
//
// Unable to convert -Infinity to Int64.
// Unable to convert -Infinity to UInt64.
// Unable to convert -Infinity to Decimal.
// -Infinity (Single) --> -Infinity (Double)
// The example displays the following output for conversions performed
// in an unchecked context:
// -3.402823E+38 (Single) --> -9223372036854775808 (0x8000000000000000) (Int64)
// -3.402823E+38 (Single) --> 9223372036854775808 (0x8000000000000000) (UInt64)
// Unable to convert -3.402823E+38 to Decimal.
// -3.402823E+38 (Single) --> -3.40282346638529E+38 (Double)
//
// -67890.13 (Single) --> -67890 (0xFFFFFFFFFFFEF6CE) (Int64)
// -67890.13 (Single) --> 18446744073709483726 (0xFFFFFFFFFFFEF6CE) (UInt64)
// -67890.13 (Single) --> -67890.12 (Decimal)
// -67890.13 (Single) --> -67890.125 (Double)
//
// -12345.68 (Single) --> -12345 (0xFFFFFFFFFFFFCFC7) (Int64)
// -12345.68 (Single) --> 18446744073709539271 (0xFFFFFFFFFFFFCFC7) (UInt64)
// -12345.68 (Single) --> -12345.68 (Decimal)
// -12345.68 (Single) --> -12345.6787109375 (Double)
//
// 12345.68 (Single) --> 12345 (0x0000000000003039) (Int64)
// 12345.68 (Single) --> 12345 (0x0000000000003039) (UInt64)
// 12345.68 (Single) --> 12345.68 (Decimal)
// 12345.68 (Single) --> 12345.6787109375 (Double)
//
// 67890.13 (Single) --> 67890 (0x0000000000010932) (Int64)
// 67890.13 (Single) --> 67890 (0x0000000000010932) (UInt64)
// 67890.13 (Single) --> 67890.12 (Decimal)
// 67890.13 (Single) --> 67890.125 (Double)
//
// 3.402823E+38 (Single) --> -9223372036854775808 (0x8000000000000000) (Int64)
// 3.402823E+38 (Single) --> 0 (0x0000000000000000) (UInt64)
// Unable to convert 3.402823E+38 to Decimal.
// 3.402823E+38 (Single) --> 3.40282346638529E+38 (Double)
//
// NaN (Single) --> -9223372036854775808 (0x8000000000000000) (Int64)
// NaN (Single) --> 0 (0x0000000000000000) (UInt64)
// Unable to convert NaN to Decimal.
// NaN (Single) --> NaN (Double)
//
// Infinity (Single) --> -9223372036854775808 (0x8000000000000000) (Int64)
// Infinity (Single) --> 0 (0x0000000000000000) (UInt64)
// Unable to convert Infinity to Decimal.
// Infinity (Single) --> Infinity (Double)
//
// -Infinity (Single) --> -9223372036854775808 (0x8000000000000000) (Int64)
// -Infinity (Single) --> 9223372036854775808 (0x8000000000000000) (UInt64)
// Unable to convert -Infinity to Decimal.
// -Infinity (Single) --> -Infinity (Double)
open System
open Checked
let values =
[ Single.MinValue; -67890.1234f; -12345.6789f
12345.6789f; 67890.1234f; Single.MaxValue
Single.NaN; Single.PositiveInfinity
Single.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."
let dblValue = double value
printfn $"{value} ({value.GetType().Name}) --> {dblValue} ({dblValue.GetType().Name})\n"
// The example displays the following output for conversions performed
// in a checked context:
// Unable to convert -3.402823E+38 to Int64.
// Unable to convert -3.402823E+38 to UInt64.
// Unable to convert -3.402823E+38 to Decimal.
// -3.402823E+38 (Single) --> -3.40282346638529E+38 (Double)
//
// -67890.13 (Single) --> -67890 (0xFFFFFFFFFFFEF6CE) (Int64)
// Unable to convert -67890.13 to UInt64.
// -67890.13 (Single) --> -67890.12 (Decimal)
// -67890.13 (Single) --> -67890.125 (Double)
//
// -12345.68 (Single) --> -12345 (0xFFFFFFFFFFFFCFC7) (Int64)
// Unable to convert -12345.68 to UInt64.
// -12345.68 (Single) --> -12345.68 (Decimal)
// -12345.68 (Single) --> -12345.6787109375 (Double)
//
// 12345.68 (Single) --> 12345 (0x0000000000003039) (Int64)
// 12345.68 (Single) --> 12345 (0x0000000000003039) (UInt64)
// 12345.68 (Single) --> 12345.68 (Decimal)
// 12345.68 (Single) --> 12345.6787109375 (Double)
//
// 67890.13 (Single) --> 67890 (0x0000000000010932) (Int64)
// 67890.13 (Single) --> 67890 (0x0000000000010932) (UInt64)
// 67890.13 (Single) --> 67890.12 (Decimal)
// 67890.13 (Single) --> 67890.125 (Double)
//
// Unable to convert 3.402823E+38 to Int64.
// Unable to convert 3.402823E+38 to UInt64.
// Unable to convert 3.402823E+38 to Decimal.
// 3.402823E+38 (Single) --> 3.40282346638529E+38 (Double)
//
// Unable to convert NaN to Int64.
// Unable to convert NaN to UInt64.
// Unable to convert NaN to Decimal.
// NaN (Single) --> NaN (Double)
//
// Unable to convert Infinity to Int64.
// Unable to convert Infinity to UInt64.
// Unable to convert Infinity to Decimal.
// Infinity (Single) --> Infinity (Double)
//
// Unable to convert -Infinity to Int64.
// Unable to convert -Infinity to UInt64.
// Unable to convert -Infinity to Decimal.
// -Infinity (Single) --> -Infinity (Double)
// The example displays the following output for conversions performed
// in an unchecked context:
// -3.402823E+38 (Single) --> -9223372036854775808 (0x8000000000000000) (Int64)
// -3.402823E+38 (Single) --> 9223372036854775808 (0x8000000000000000) (UInt64)
// Unable to convert -3.402823E+38 to Decimal.
// -3.402823E+38 (Single) --> -3.40282346638529E+38 (Double)
//
// -67890.13 (Single) --> -67890 (0xFFFFFFFFFFFEF6CE) (Int64)
// -67890.13 (Single) --> 18446744073709483726 (0xFFFFFFFFFFFEF6CE) (UInt64)
// -67890.13 (Single) --> -67890.12 (Decimal)
// -67890.13 (Single) --> -67890.125 (Double)
//
// -12345.68 (Single) --> -12345 (0xFFFFFFFFFFFFCFC7) (Int64)
// -12345.68 (Single) --> 18446744073709539271 (0xFFFFFFFFFFFFCFC7) (UInt64)
// -12345.68 (Single) --> -12345.68 (Decimal)
// -12345.68 (Single) --> -12345.6787109375 (Double)
//
// 12345.68 (Single) --> 12345 (0x0000000000003039) (Int64)
// 12345.68 (Single) --> 12345 (0x0000000000003039) (UInt64)
// 12345.68 (Single) --> 12345.68 (Decimal)
// 12345.68 (Single) --> 12345.6787109375 (Double)
//
// 67890.13 (Single) --> 67890 (0x0000000000010932) (Int64)
// 67890.13 (Single) --> 67890 (0x0000000000010932) (UInt64)
// 67890.13 (Single) --> 67890.12 (Decimal)
// 67890.13 (Single) --> 67890.125 (Double)
//
// 3.402823E+38 (Single) --> -9223372036854775808 (0x8000000000000000) (Int64)
// 3.402823E+38 (Single) --> 0 (0x0000000000000000) (UInt64)
// Unable to convert 3.402823E+38 to Decimal.
// 3.402823E+38 (Single) --> 3.40282346638529E+38 (Double)
//
// NaN (Single) --> -9223372036854775808 (0x8000000000000000) (Int64)
// NaN (Single) --> 0 (0x0000000000000000) (UInt64)
// Unable to convert NaN to Decimal.
// NaN (Single) --> NaN (Double)
//
// Infinity (Single) --> -9223372036854775808 (0x8000000000000000) (Int64)
// Infinity (Single) --> 0 (0x0000000000000000) (UInt64)
// Unable to convert Infinity to Decimal.
// Infinity (Single) --> Infinity (Double)
//
// -Infinity (Single) --> -9223372036854775808 (0x8000000000000000) (Int64)
// -Infinity (Single) --> 9223372036854775808 (0x8000000000000000) (UInt64)
// Unable to convert -Infinity to Decimal.
// -Infinity (Single) --> -Infinity (Double)
Module Example6
Public Sub Main()
Dim values() As Single = {Single.MinValue, -67890.1234, -12345.6789,
12345.6789, 67890.1234, Single.MaxValue,
Single.NaN, Single.PositiveInfinity,
Single.NegativeInfinity}
For Each value In values
Try
Dim lValue As Long = 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
Dim dblValue As Double = value
Console.WriteLine("{0} ({1}) --> {2} ({3})",
value, value.GetType().Name,
dblValue, dblValue.GetType().Name)
Console.WriteLine()
Next
End Sub
End Module
' The example displays the following output for conversions performed
' in a checked context:
' Unable to convert -3.402823E+38 to Int64.
' Unable to convert -3.402823E+38 to UInt64.
' Unable to convert -3.402823E+38 to Decimal.
' -3.402823E+38 (Single) --> -3.40282346638529E+38 (Double)
'
' -67890.13 (Single) --> -67890 (0xFFFFFFFFFFFEF6CE) (Int64)
' Unable to convert -67890.13 to UInt64.
' -67890.13 (Single) --> -67890.12 (Decimal)
' -67890.13 (Single) --> -67890.125 (Double)
'
' -12345.68 (Single) --> -12346 (0xFFFFFFFFFFFFCFC6) (Int64)
' Unable to convert -12345.68 to UInt64.
' -12345.68 (Single) --> -12345.68 (Decimal)
' -12345.68 (Single) --> -12345.6787109375 (Double)
'
' 12345.68 (Single) --> 12346 (0x000000000000303A) (Int64)
' 12345.68 (Single) --> 12346 (0x000000000000303A) (UInt64)
' 12345.68 (Single) --> 12345.68 (Decimal)
' 12345.68 (Single) --> 12345.6787109375 (Double)
'
' 67890.13 (Single) --> 67890 (0x0000000000010932) (Int64)
' 67890.13 (Single) --> 67890 (0x0000000000010932) (UInt64)
' 67890.13 (Single) --> 67890.12 (Decimal)
' 67890.13 (Single) --> 67890.125 (Double)
'
' Unable to convert 3.402823E+38 to Int64.
' Unable to convert 3.402823E+38 to UInt64.
' Unable to convert 3.402823E+38 to Decimal.
' 3.402823E+38 (Single) --> 3.40282346638529E+38 (Double)
'
' Unable to convert NaN to Int64.
' Unable to convert NaN to UInt64.
' Unable to convert NaN to Decimal.
' NaN (Single) --> NaN (Double)
'
' Unable to convert Infinity to Int64.
' Unable to convert Infinity to UInt64.
' Unable to convert Infinity to Decimal.
' Infinity (Single) --> Infinity (Double)
'
' Unable to convert -Infinity to Int64.
' Unable to convert -Infinity to UInt64.
' Unable to convert -Infinity to Decimal.
' -Infinity (Single) --> -Infinity (Double)
' The example displays the following output for conversions performed
' in an unchecked context:
' -3.402823E+38 (Single) --> -9223372036854775808 (0x8000000000000000) (Int64)
' -3.402823E+38 (Single) --> 9223372036854775808 (0x8000000000000000) (UInt64)
' Unable to convert -3.402823E+38 to Decimal.
' -3.402823E+38 (Single) --> -3.40282346638529E+38 (Double)
'
' -67890.13 (Single) --> -67890 (0xFFFFFFFFFFFEF6CE) (Int64)
' -67890.13 (Single) --> 18446744073709483726 (0xFFFFFFFFFFFEF6CE) (UInt64)
' -67890.13 (Single) --> -67890.12 (Decimal)
' -67890.13 (Single) --> -67890.125 (Double)
'
' -12345.68 (Single) --> -12346 (0xFFFFFFFFFFFFCFC6) (Int64)
' -12345.68 (Single) --> 18446744073709539270 (0xFFFFFFFFFFFFCFC6) (UInt64)
' -12345.68 (Single) --> -12345.68 (Decimal)
' -12345.68 (Single) --> -12345.6787109375 (Double)
'
' 12345.68 (Single) --> 12346 (0x000000000000303A) (Int64)
' 12345.68 (Single) --> 12346 (0x000000000000303A) (UInt64)
' 12345.68 (Single) --> 12345.68 (Decimal)
' 12345.68 (Single) --> 12345.6787109375 (Double)
'
' 67890.13 (Single) --> 67890 (0x0000000000010932) (Int64)
' 67890.13 (Single) --> 67890 (0x0000000000010932) (UInt64)
' 67890.13 (Single) --> 67890.12 (Decimal)
' 67890.13 (Single) --> 67890.125 (Double)
'
' 3.402823E+38 (Single) --> -9223372036854775808 (0x8000000000000000) (Int64)
' 3.402823E+38 (Single) --> 0 (0x0000000000000000) (UInt64)
' Unable to convert 3.402823E+38 to Decimal.
' 3.402823E+38 (Single) --> 3.40282346638529E+38 (Double)
'
' NaN (Single) --> -9223372036854775808 (0x8000000000000000) (Int64)
' NaN (Single) --> 0 (0x0000000000000000) (UInt64)
' Unable to convert NaN to Decimal.
' NaN (Single) --> NaN (Double)
'
' Infinity (Single) --> -9223372036854775808 (0x8000000000000000) (Int64)
' Infinity (Single) --> 0 (0x0000000000000000) (UInt64)
' Unable to convert Infinity to Decimal.
' Infinity (Single) --> Infinity (Double)
'
' -Infinity (Single) --> -9223372036854775808 (0x8000000000000000) (Int64)
' -Infinity (Single) --> 9223372036854775808 (0x8000000000000000) (UInt64)
' Unable to convert -Infinity to Decimal.
' -Infinity (Single) --> -Infinity (Double)
For more information on the conversion of numeric types, see Type Conversion in .NET and Type Conversion Tables.
Floating-point functionalityThe Single structure and related types provide methods to perform the following categories of operations:
Comparison of values. You can call the Equals method to determine whether two Single values are equal, or the CompareTo method to determine the relationship between two values.
The Single 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 value. If one of the operands is a Double, the Single value is converted to a Double before performing the comparison. If one of the operands is an integral type, it is converted to a Single before performing the comparison. Although these are widening conversions, they may involve a loss of precision.
Warning
Because of differences in precision, two Single 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 Single 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 Single methods. If the other operand in a mathematical operation is a Double, the Single is converted to a Double before performing the operation, and the result of the operation is also a Double value. If the other operand is an integral type, it is converted to a Single before performing the operation, and the result of the operation is also a Single value.
You can perform other mathematical operations by calling static (Shared in Visual Basic) methods in the System.Math class. These include 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). In all cases, the Single value is converted to a Double.
You can also manipulate the individual bits in a Single value. The BitConverter.GetBytes(Single) method returns its bit pattern in a byte array. By passing that byte array to the BitConverter.ToInt32 method, you can also preserve the Single value's bit pattern in a 32-bit integer.
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 Single value by calling the Math.Round method. However, note that the Single value is converted to a Double before the method is called, and the conversion can involve a loss of precision.
Formatting. You can convert a Single 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 Standard Numeric Format Strings and Custom Numeric Format Strings.
Parsing strings. You can convert the string representation of a floating-point value to a Single value by calling 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 Single 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 for all other standard numeric types except for the conversion of Double to Single values. Conversion of a value of any standard numeric type other than a Double to a Single is a widening conversion and does not require the use of a casting operator or conversion method.
However, conversion of 32-bit and 64-bit integer values can involve a loss of precision. The following table lists the differences in precision for 32-bit, 64-bit, and Double types:
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 that is converted to a Double.
using System;
public class Example8
{
public static void Main()
{
Double value1 = 1 / 3.0;
Single sValue2 = 1 / 3.0f;
Double value2 = (Double)sValue2;
Console.WriteLine($"{value1:R} = {value2:R}: {value1.Equals(value2)}");
}
}
// The example displays the following output:
// 0.33333333333333331 = 0.3333333432674408: False
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: False
Module Example9
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: False
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