Comparison of approaches for rounding to an integer: what changed

Revision 1 to 2. Removed lines have a minus sign; added lines have a plus sign.

Old	New		Line
1	1		Real numbers can be converted to integers in many ways. Here's a comparison some of them.
2	2
3	3		``` pascal
4	4		program ComparisonOfApproachesForRoundingToInteger(input,output);
5	5		// Comparison of approaches for rounding to an integer
6	6
7	7		uses SysUtils,Math;
8	8
9	9		function RoundISO7185(x:real):integer;
10	10		// If x is positive or zero, round(x) shall be equivalent to trunc(x+0 .5) ;
11	11		// otherwise, round(x) shall be equivalent to trunc(x-0.5)
12	12		begin
13	13		If x >= 0 then result := trunc(x+0.5)
14	14		else result := trunc(x-0.5);
15	15		end;
16	16
17	17		var
18	18		r1,r2,r3,r4:real;
19	19		fmt : string;
20	20		begin
21	21		r1 := 1.3;
22	22		r2 := 1.6;
23	23		r3 := 3.5;
24	24		r4 := 4.5;
25	25		fmt := '%10s%10s%10s%10s%10s%10s%10s';
26	26		WriteLn(format(fmt,['Value','Write:x:0','Trunc','Round','ISO7185','Floor','Ceil']));
27	27		fmt := '%10d%10d%10d%10d%10d';
28	28		write (r1:10:1,r1:10:0);
29	29		WriteLn(format(fmt,[Trunc(r1),Round(r1),RoundISO7185(r1),floor(r1),ceil(r1)]));
30	30		write (r2:10:1,r2:10:0);
31	31		WriteLn(format(fmt,[Trunc(r2),Round(r2),RoundISO7185(r2),floor(r2),ceil(r2)]));
32	32		write (r3:10:1,r3:10:0);
33	33		WriteLn(format(fmt,[Trunc(r3),Round(r3),RoundISO7185(r3),floor(r3),ceil(r3)]));
34	34		write (r4:10:1,r4:10:0);
35	35		WriteLn(format(fmt,[Trunc(r4),Round(r4),RoundISO7185(r4),floor(r4),ceil(r4)]));
36	36		r1 := r1 *-1;
37	37		r2 := r2 *-1;
38	38		r3 := r3 *-1;
39	39		r4 := r4 *-1;
40	40		write (r1:10:1,r1:10:0);
41	41		WriteLn(format(fmt,[Trunc(r1),Round(r1),RoundISO7185(r1),floor(r1),ceil(r1)]));
42	42		write (r2:10:1,r2:10:0);
43	43		WriteLn(format(fmt,[Trunc(r2),Round(r2),RoundISO7185(r2),floor(r2),ceil(r2)]));
44	44		write (r3:10:1,r3:10:0);
45	45		WriteLn(format(fmt,[Trunc(r3),Round(r3),RoundISO7185(r3),floor(r3),ceil(r3)]));
46	46		write (r4:10:1,r4:10:0);
47	47		WriteLn(format(fmt,[Trunc(r4),Round(r4),RoundISO7185(r4),floor(r4),ceil(r4)]));
48	48		Readln;
49	49		end.
50	50		```
51	51
52		-	~~` Output:`\~~
53		-	~~` Value Write:x:0 Trunc Round ISO7185 Floor Ceil`\~~
54		-	~~` 1.3 1 1 1 1 1 2`\~~
55		-	~~` 1.6 2 1 2 2 1 2`\~~
56		-	~~` 3.5 4 3 4 4 3 4`\~~
57		-	~~` 4.5 5 4 4 5 4 5`\~~
58		-	~~` -1.3 -1 -1 -1 -1 -2 -1`\~~
59		-	~~` -1.6 -2 -1 -2 -2 -2 -1`\~~
60		-	~~` -3.5 -4 -3 -4 -4 -4 -3`\~~
61		-	~~` -4.5 -5 -4 -4 -5 -5 -4`~~
	52	+	```text
	53	+	Output:
	54	+	Value Write:x:0 Trunc Round ISO7185 Floor Ceil
	55	+	1.3 1 1 1 1 1 2
	56	+	1.6 2 1 2 2 1 2
	57	+	3.5 4 3 4 4 3 4
	58	+	4.5 5 4 4 5 4 5
	59	+	-1.3 -1 -1 -1 -1 -2 -1
	60	+	-1.6 -2 -1 -2 -2 -2 -1
	61	+	-3.5 -4 -3 -4 -4 -4 -3
	62	+	-4.5 -5 -4 -4 -5 -5 -4
	63	+	```
62	64
63	65		## See also
64	66
65	67		- [[Round\|round]]
66	68		- [[Trunc\|trunc]] - round towards zero
67	69		- [`math.ceil`](https://www.freepascal.org/docs-html/rtl/math/ceil.html) - round up
68	70		- [`math.floor`](https://www.freepascal.org/docs-html/rtl/math/floor.html) - round down
69	71
70	72		- [[Format function]]
71	73
72	74		---
73	75		From the Free Pascal wiki, page "Comparison of approaches for rounding to an integer", as it stood on 2022-08-06 after a change by Kai Burghardt, out of the wiki's dump of 2024-05-26. Copyright stays with the author who wrote it, according to the old wiki's [[Licensing]] page. If you have concerns about this material, [message the admin](/wiki-contact).

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