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数学和数学之间的差异。floor()。truncate()

What is the difference between Math.Floor() and Math.Truncate() in .NET?

2016年12月09日33分06秒

Math.Floor rounds down, Math.Ceiling rounds up, and Math.Truncate rounds towards zero. Thus, Math.Truncate is like Math.Floor for positive numbers, and like Math.Ceiling for negative numbers. Here's the reference.

For completeness, Math.Round rounds to the nearest integer. If the number is exactly midway between two integers, then it rounds towards the even one. Reference.

See also: Pax Diablo's answer. Highly recommended!

2016年12月08日33分06秒

Follow these links for the MSDN descriptions of:

  • Math.Floor, which rounds down towards negative infinity.
  • Math.Ceiling, which rounds up towards positive infinity.
  • Math.Truncate, which rounds up or down towards zero.
  • Math.Round, which rounds to the nearest integer or specified number of decimal places. You can specify the behavior if it's exactly equidistant between two possibilities, such as rounding so that the final digit is even ("Round(2.5,MidpointRounding.ToEven)" becoming 2) or so that it's further away from zero ("Round(2.5,MidpointRounding.AwayFromZero)" becoming 3).

The following diagram and table may help:

-3        -2        -1         0         1         2         3
 +--|------+---------+----|----+--|------+----|----+-------|-+
    a                     b       c           d            e

                       a=-2.7  b=-0.5  c=0.3  d=1.5  e=2.8
                       ======  ======  =====  =====  =====
Floor                    -3      -1      0      1      2
Ceiling                  -2       0      1      2      3
Truncate                 -2       0      0      1      2
Round (ToEven)           -3       0      0      2      3
Round (AwayFromZero)     -3      -1      0      2      3

Note that Round is a lot more powerful than it seems, simply because it can round to a specific number of decimal places. All the others round to zero decimals always. For example:

n = 3.145;
a = System.Math.Round (n, 2, MidpointRounding.ToEven);       // 3.14
b = System.Math.Round (n, 2, MidpointRounding.AwayFromZero); // 3.15

With the other functions, you have to use multiply/divide trickery to achieve the same effect:

c = System.Math.Truncate (n * 100) / 100;                    // 3.14
d = System.Math.Ceiling (n * 100) / 100;                     // 3.15

2016年12月08日33分06秒

Some examples:

Round(1.5) = 2
Round(2.5) = 2
Round(1.5, MidpointRounding.AwayFromZero) = 2
Round(2.5, MidpointRounding.AwayFromZero) = 3
Round(1.55, 1) = 1.6
Round(1.65, 1) = 1.6
Round(1.55, 1, MidpointRounding.AwayFromZero) = 1.6
Round(1.65, 1, MidpointRounding.AwayFromZero) = 1.7

Truncate(2.10) = 2
Truncate(2.00) = 2
Truncate(1.90) = 1
Truncate(1.80) = 1

2016年12月08日33分06秒

Math.Floor() rounds toward negative infinity

Math.Truncate rounds up or down towards zero.

For example:

Math.Floor(-3.4)     = -4
Math.Truncate(-3.4)  = -3

2016年12月08日33分06秒

Math.Floor() rounds "toward negative infinity" in compliance to IEEE Standard 754 section 4.

Math.Truncate() rounds " to the nearest integer towards zero."

2016年12月08日33分06秒

They are functionally equivalent with positive numbers. The difference is in how they handle negative numbers.

For example:

Math.Floor(2.5) = 2
Math.Truncate(2.5) = 2

Math.Floor(-2.5) = -3
Math.Truncate(-2.5) = -2

http://msdn.microsoft.com/en-us/library/e0b5f0xb.aspx

http://msdn.microsoft.com/en-us/library/c2eabd70.aspx

P.S. Beware of Math.Round it may not be what you expect: http://dnfug.com/Web/blogs/mperera/archive/2007/12/26/issue-with-math-round-in-c.aspx

To get the "standard" rounding result use:

float myFloat = 4.5;
Console.WriteLine( Math.Round(myFloat) ); // writes 4
Console.WriteLine( Math.Round(myFloat, 0, MidpointRounding.AwayFromZero) ) //writes 5
Console.WriteLine( myFloat.ToString("F0") ); // writes 5

2016年12月08日33分06秒

Math.Floor() -Returns the largest integer less than or equal to the specified double-precision floating-point number.

Math.Round() -Rounds a value to the nearest integer or to the specified number of fractional digits.

2016年12月08日33分06秒

math.floor()

Returns the largest integer less than or equal to the specified number.

https://msdn.microsoft.com/en-us/library/system.math.floor.aspx

math.truncate()

Calculates the integral part of a number.

https://msdn.microsoft.com/en-us/library/system.math.truncate(v=vs.110).aspx

2016年12月08日33分06秒