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Round2BR

function Round2BR(aValue: Extended; aDP: Integer): Extended;

Example​

procedure ScriptEvent(var Value: variant);
begin
  Value := Round2BR(12.25, 1); // normally 12.2: scaled 122.5 ties to even 122
end;

Usage​

Round2BR rounds at a decimal position by scaling through Double and applying Velox nearest-even Round.

Parameters

NameTypeDescription
aValueExtendedValue to round.
aDPIntegerDecimal-place scale: positive for fractional digits, zero for units and negative for tens/hundreds while scaling remains valid.

Returns

An Extended rescaled result. Under default nearest/even rounding:

CallTypical result
Round2BR(12.25, 1)12.2 because 122.5 -> 122
Round2BR(12.35, 1)potentially 12.4, subject to binary representation of the scaled midpoint
Round2BR(155, -1)160 because 15.5 -> 16
Round2BR(145, -1)140 because 14.5 -> 14

Additional Technical Info​

Round2BR scales an Extended value by a power of ten, deliberately assigns the scaled value to Delphi Real (the modern Double alias), rounds that Double to Int64 with System.Round, then divides by the scale.

Under the default rounding mode it uses banker's/nearest-even rounding. The intentional Double conversion changes precision before rounding and was added to address a particular decimal-boundary case in product code; it does not make binary floating point decimal-exact. The example is fictional and source-reviewed only.

Implementation

Nominator := Power(10, aDP);
x := aValue * Nominator; // x: Real (Double)
Result := Round(x) / Nominator;

Power is the native Velox wrapper over System.Math.Power. Round here is Delphi System.Round returning Int64, not the PascalScript Round wrapper with unchecked 32-bit narrowing.

Edge cases and quirks

  • Midpoint behavior follows the active floating-point rounding mode. Nearest/even is the normal default but is not forced here.
  • On Win32, assigning scaled Extended to Real loses 80-bit precision before rounding. On Win64, Extended already aliases Double.
  • Decimal literals and their scaled values may fall just above or below the mathematical midpoint in binary; the apparent last decimal digit alone is not a guarantee.
  • Extreme positive aDP can overflow during scaling or push Round(x) outside Int64. Extreme negative aDP can underflow the scale and make final division invalid.
  • The Power target-specific extreme-exponent behavior is inherited.
  • NaN/infinity and invalid conversions propagate according to Delphi's floating-point exception handling.

Performance and side effects

The function is pure and constant-time. It performs power/scaling, a precision conversion and an integer conversion on every call.

Related entries

  • Round2 uses a non-standard six-tenths threshold.
  • Round2Up uses text and midpoint-away-from-zero semantics for supported input.
  • RoundAs dispatches to this function with token ROUND2BR.

External references

Created 2026-07-15