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Difference between revisions of "Floating Point Rounding"

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== Solution ==
 
== Solution ==
  
Use one of the procedures erlang:round, ceiling, floor and erlang:trunc. Note, the standard Erlang distribution does not come with either floor or ceiling, but they can be easily implemented in terms of erlang:trunc:
+
Use one of the functions round/1, ceiling/1, floor/1 and trunc/1. Note, the standard Erlang distribution does not come with either floor/1 or ceiling/1, but they can be easily implemented in terms of trunc/1
  
 
<code>
 
<code>
floor(X) ->
+
floor(X) when X < 0 ->
     T = erlang:trunc(X),
+
     T = trunc(X),
     case (X - T) of
+
     case X - T == 0 of
         Neg when Neg < 0 -> T - 1;
+
         true -> T;
         Pos when Pos > 0 -> T;
+
         false -> T - 1
        _ -> T
+
    end;
     end.
+
floor(X) ->  
 +
     trunc(X).
  
 +
 +
ceiling(X) when X < 0 ->
 +
    trunc(X);
 
ceiling(X) ->
 
ceiling(X) ->
     T = erlang:trunc(X),
+
     T = trunc(X),
     case (X - T) of
+
     case X - T == 0 of
         Neg when Neg < 0 -> T;
+
         true -> T;
         Pos when Pos > 0 -> T + 1;
+
         false -> T + 1
        _ -> T
+
 
     end.
 
     end.
 +
  
 
1> floor(-4.3).
 
1> floor(-4.3).
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2> ceiling(-4.3).
 
2> ceiling(-4.3).
 
-4
 
-4
3> erlang:trunc(-4.3).
+
3> trunc(-4.3).
 
-4
 
-4
4> erlang:round(-4.3).
+
4> round(-4.3).
 
-4
 
-4
 
5> floor(3.5).
 
5> floor(3.5).
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6> ceiling(3.5).
 
6> ceiling(3.5).
 
4
 
4
7> erlang:trunc(3.5).
+
7> trunc(3.5).
 
3
 
3
8> erlang:round(3.5).
+
8> round(3.5).
 
4
 
4
9> erlang:round(7).
+
9> round(7).
 
7
 
7
 
</code>
 
</code>
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The procedures all return integers.  
 
The procedures all return integers.  
  
erlang:round returns the closest integer to x, rounding to even when x is halfway between two integers.  
+
round/1 returns the closest integer to x, rounding to even when x is halfway between two integers.
floor returns the largest integer not larger than x.  
+
trunc/1 returns the integer closest to x whose absolute value is not larger than the absolute value of x.  
ceiling returns the smallest integer not smaller than x.  
+
floor/1 returns the largest integer not larger than x.  
erlang:trunc returns the integer closest to x whose absolute value is not larger than the absolute value of x.  
+
ceiling/1 returns the smallest integer not smaller than x.  
  
If the number given to one of the procedures is inexact?, then the result will also be inexact.  
+
For the floor and ceiling functions implemented above, T will always be less than or equal to X.  We just need to check if there is a difference between the two in which case we will either increase or decrease the truncation depending if we want to floor or ceiling X.
  
See Also
+
''(Correction to floor/1 and ceiling/1 to check for negative or positive values. 2009-11-21 seetho)''
  
 
Further general information on math and rounding is available from:  
 
Further general information on math and rounding is available from:  
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[[Category:CookBook]]
+
[[Category:CookBook]][[Category:NumberRecipes]]

Revision as of 19:25, 20 November 2009

Problem

You need to round a floating-point number to an integer.

Solution

Use one of the functions round/1, ceiling/1, floor/1 and trunc/1. Note, the standard Erlang distribution does not come with either floor/1 or ceiling/1, but they can be easily implemented in terms of trunc/1

floor(X) when X < 0 ->
    T = trunc(X),
    case X - T == 0 of
        true -> T;
        false -> T - 1
    end;
floor(X) -> 
    trunc(X).


ceiling(X) when X < 0 ->
    trunc(X);
ceiling(X) ->
    T = trunc(X),
    case X - T == 0 of
        true -> T;
        false -> T + 1
    end.


1> floor(-4.3).
-5
2> ceiling(-4.3).
-4
3> trunc(-4.3).
-4
4> round(-4.3).
-4
5> floor(3.5).
3
6> ceiling(3.5).
4
7> trunc(3.5).
3
8> round(3.5).
4
9> round(7).
7

The procedures all return integers.

round/1 returns the closest integer to x, rounding to even when x is halfway between two integers. trunc/1 returns the integer closest to x whose absolute value is not larger than the absolute value of x. floor/1 returns the largest integer not larger than x. ceiling/1 returns the smallest integer not smaller than x.

For the floor and ceiling functions implemented above, T will always be less than or equal to X. We just need to check if there is a difference between the two in which case we will either increase or decrease the truncation depending if we want to floor or ceiling X.

(Correction to floor/1 and ceiling/1 to check for negative or positive values. 2009-11-21 seetho)

Further general information on math and rounding is available from:

MathWorld definition of the Floor Function. MathWorld definition of the Ceiling Function