Author: Ernesto De Spirito
How can I round a number "normally"? Can I round the thousands? Can I round the
third digit after the decimal point?
Answer:
Integer rounding
The Round function that comes with Delphi performs what is called "banker's
rounding", meaning that a number with a fractional part of 0.5 is rounded sometimes
up and sometimes down, always towards the nearest even number. This means that for
example Round(3.5) gives 4 while Round(2.5) gives 2. Here goes a set of functions
for rounding numbers, including RoundN which rounds a number "normally" (i.e.
RoundN(3.5) is 4 and RoundN(2.5) is 3).
1 function Sgn(X: Extended): Integer;
2 // Returns -1, 0 or 1 according to the
3 // sign of the argument
4 begin
5 if X < 0 then
6 Result := -1
7 else if X = 0 then
8 Result := 0
9 else
10 Result := 1;
11 end;
12
13 function RoundUp(X: Extended): Extended;
14 // Returns the first integer greater than or
15 // equal to a given number in absolute value
16 // (sign is preserved).
17 // RoundUp(3.3) = 4 RoundUp(-3.3) = -4
18 begin
19 Result := Int(X) + Sgn(Frac(X));
20 end;
21
22 function RoundDn(X: Extended): Extended;
23 // Returns the first integer less than or
24 // equal to a given number in absolute
25 // value (sign is preserved).
26 // RoundDn(3.7) = 3 RoundDn(-3.7) = -3
27 begin
28 Result := Int(X);
29 end;
30
31 function RoundN(X: Extended): Extended;
32 // Rounds a number "normally": if the fractional
33 // part is >= 0.5 the number is rounded up (see RoundUp)
34 // Otherwise, if the fractional part is < 0.5, the
35 // number is rounded down (see RoundDn).
36 // RoundN(3.5) = 4 RoundN(-3.5) = -4
37 // RoundN(3.1) = 3 RoundN(-3.1) = -3
38 begin
39 (*
40 if Abs(Frac(X)) >= 0.5 then
41 Result := RoundUp(X)
42 else
43 Result := RoundDn(X);
44 *)
45 Result := Int(X) + Int(Frac(X) * 2);
46 end;
47
48 function Fix(X: Extended): Extended;
49 // Returns the first integer less than or
50 // equal to a given number.
51 // Int(3.7) = 3 Int(-3.7) = -3
52 // Fix(3.7) = 3 Fix(-3.1) = -4
53 begin
54 if (X >= 0) or (Frac(X) = 0) then
55 Result := Int(X)
56 else
57 Result := Int(X) - 1;
58 end;
59
60 function RoundDnX(X: Extended): Extended;
61 // Returns the first integer less than or
62 // equal to a given number.
63 // RoundDnX(3.7) = 3 RoundDnX(-3.7) = -3
64 // RoundDnX(3.7) = 3 RoundDnX(-3.1) = -4
65 begin
66 Result := Fix(X);
67 end;
68
69 function RoundUpX(X: Extended): Extended;
70 // Returns the first integer greater than or
71 // equal to a given number.
72 // RoundUpX(3.1) = 4 RoundUpX(-3.7) = -3
73 begin
74 Result := Fix(X) + Abs(Sgn(Frac(X)))
75 end;
76
77 function RoundX(X: Extended): Extended;
78 // Rounds a number "normally", but taking the sign into
79 // account: if the fractional part is >= 0.5 the number
80 // is rounded up (see RoundUpX)
81 // Otherwise, if the fractional part is < 0.5, the
82 // number is rounded down (see RoundDnX).
83 // RoundX(3.5) = 4 RoundX(-3.5) = -3
84 begin
85 (*
86 if Abs(Frac(X)) >= 0.5 then
87 Result := RoundUpX(X)
88 else
89 Result := RoundDnX(X);
90 *)
91 Result := Fix(X + 0.5);
92 end;
Rounding to a decimal digit
The functions we've just presented above always round to the last integer digit,
but sometimes we need to round for example to the second decimal or to the
thousands, millions or billions. You can overload the RoundN function with this
version that takes an extra parameter to indicate the digit to be round:
93 function RoundN(x: Extended; d: Integer): Extended;
94 // RoundN(123.456, 0) = 123.00
95 // RoundN(123.456, 2) = 123.46
96 // RoundN(123456, -3) = 123000
97 const
98 t: array[0..12] of int64 = (1, 10, 100, 1000, 10000, 100000,
99 1000000, 10000000, 100000000, 1000000000, 10000000000,
100 100000000000, 1000000000000);
101 begin
102 if Abs(d) > 12 then
103 raise ERangeError.Create('RoundN: Value must be in -12..12');
104 if d = 0 then
105 Result := Int(x) + Int(Frac(x) * 2)
106 else if d > 0 then
107 begin
108 x := x * t[d];
109 Result := (Int(x) + Int(Frac(x) * 2)) / t[d];
110 end
111 else
112 begin // d < 0
113 x := x / t[-d];
114 Result := (Int(x) + Int(Frac(x) * 2)) * t[-d];
115 end;
116 end;
Copyright (c) 2001 Ernesto De Spiritomailto:edspirito@latiumsoftware.com
Visit: http://www.latiumsoftware.com/delphi-newsletter.php
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