Floating-Point Rounding Routines

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Many of the rounding routines in the Delphi Run-Time Library (RTL) use the currently set rounding mode for the FPU (floating-point unit) or SSE register, for 32-bit or 64-bit, respectively. Some RTL routines have their own rounding mode or algorithm. The tables on this page present more detail about some of the various rounding routines.

Rounding Routines

The following table summarizes the rounding functions available in the RTL:

Name	Argument type	Return type	Has digit parameter?	Range of digit parameter	Rounding mode	Notes
System.Round (built-in)	Extended	Int64			Current RoundMode setting
System.Trunc (built-in)	Extended	Int64			Always rmTruncate (Truncate toward Zero)	Same as Int. Return type is integer.
System.Int (built-in)	Extended for 32bit Double for 64bit	Extended for 32bit Double for 64bit			Always rmTruncate (Truncate toward Zero)	Same as Trunc. Return type is floating-point number.
System.Math.RoundTo	Extended	Extended	Yes	-20 .. +20 no default value.	Always rmNearest (Banker's round)
System.Math.SimpleRoundTo	Single Double Extended	Single Double Extended	Yes	-37 .. +37 -2 is default value.	Always "Round half away from zero"	SimpleRoundTo is the traditional "Round off" that was learned at school.
System.Math.Ceil	Single Double Extended	Integer			Always rmUp (the smallest following integer number)
System.Math.Floor	Single Double Extended	Integer			Always rmDown (the largest previous integer number)
Data.FmtBcd.BCDRoundTo	TBcd	TBcd	Yes	Integer	Current RoundMode
FMTBcd.BCDRoundAt (Deprecated)	String	String	Yes	SmallInt	Always "Round half away from zero"	Deprecated function.  Use BcdRoundTo.

Examples of Positive Numbers

The following table gives examples of rounding positive numbers:

Name	Rounding Mode	0.4	0.5	0.6	1.4	1.5	1.6
System.Round(x)	rmNearest	0	0	1	1	2	2
	rmDown	0	0	0	1	1	1
	rmUp	1	1	1	2	2	2
	rmTruncate	0	0	0	1	1	1
System.Trunc(x)		0	0	0	1	1	1
System.Int(X)		0.0	0.0	0.0	1.0	1.0	1.0
Math.RoundTo(x, 0)		0.0	0.0	1.0	1.0	2.0	2.0
Math.SimpleRoundTo(x,0)		0.0	1.0	1.0	1.0	2.0	2.0
Math.Ceil(x)		1	1	1	2	2	2
Math.Floor(x)		0	0	0	1	1	1
FMTBcd.BCDRoundTo(x,0)	rmNearest	0	0	1	1	2	2
	rmDown	0	0	0	1	1	1
	rmUp	1	1	1	2	2	2
	rmTruncate	0	0	0	1	1	1
FmtBcd.RoundAt(x,0) (Deprecated)		'0'	'1'	'1'	'1'	'2'	'2'

Examples of Negative Numbers

The following table gives examples of rounding negative numbers:

Name	Rounding Mode	-0.4	-0.5	-0.6	-1.4	-1.5	-1.6
System.Round(x)	rmNearest	0	0	-1	-1	-2	-2
	rmDown	-1	-1	-1	-2	-2	-2
	rmUp	0	0	0	-1	-1	-1
	rmTruncate	0	0	0	-1	-1	-1
System.Trunc(x)		0	0	0	-1	-1	-1
System.Int(X)		0.0	0.0	0.0	-1.0	-1.0	-1.0
Math.RoundTo(x,0)		0.0	0.0	-1.0	-1.0	-2.0	-2.0
Math.SimpleRoundTo(x,0)		0.0	-1.0	-1.0	-1.0	-2.0	-2.0
Math.Ceil(x)		0	0	0	-1	-1	-1
Math.Floor(x)		-1	-1	-1	-2	-2	-2
FMTBcd.BCDRoundTo(x,0)	rmNearest	0	0	-1	-1	-2	-2
	rmDown	-1	-1	-1	-2	-2	-2
	rmUp	0	0	0	-1	-1	-1
	rmTruncate	0	0	0	-1	-1	-1
FmtBcd.RoundAt(x,0) (Deprecated)		'-0'	'-1'	'-1'	'-1'	'-2'	'-2'

Examples of the Digit Parameter with RoundTo and SimpleRoundTo

The digit (D) indicates the power of ten to which you want the given value to be rounded. The digit can be any value in the range from –20 through 20. The examples here use D = 0, -1 ... -5.

Name	0	-1	-2	-3	-4	-5
Math.RoundTo(2.15625, D)	2.0	2.2	2.16	2.156	2.1562	2.15625
Math.SimpleRoundTo(2.15625, D)	2.0	2.2	2.16	2.156	2.1563	2.15625

See Also

• About Floating-Point Arithmetic
• Floating-Point Comparison Routines

• Floating-Point Number Control Routines
• System.Math.SetFPURoundMode
• System.Math.SetSSERoundMode
• System.Math.SetRoundMode
• System.Round

Code Examples

• SetRoundMode (Delphi)
• SystemRound (Delphi)