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Round2

function Round2(aValue: Extended; aDP: Integer): Extended;

Example​

procedure ScriptEvent(var Value: variant);
begin
  Value := Round2(1.265625, 1); // 1.3; the first discarded digit is 6
end;

Usage​

Round2 rounds at a decimal position with a non-standard six-tenths threshold using scaled truncation.

Parameters

NameTypeDescription
aValueExtendedValue to round.
aDPIntegerDecimal-place scale. Positive values address fractional places; zero addresses units; negative values can address tens/hundreds while the scale remains finite.

Returns

The rescaled Extended result. Examples:

CallResult/reason
Round2(1.25, 1)1.2; discarded digit 5 does not increment
Round2(1.265625, 1)1.3; first discarded digit 6 increments
Round2(-1.25, 1)-1.2; 5 remains toward zero
Round2(-1.265625, 1)-1.3; first discarded digit 6 moves away from zero
Round2(155, -1)150
Round2(156, -1)160

Additional Technical Info​

Round2 scales a value to a requested decimal position, truncates it, and increments/decrements the retained integer only when the first discarded digit is 6 through 9.

Despite its name, this is not conventional half-up or nearest rounding: a discarded 5 does not round away from zero. The threshold is effectively six-tenths at the scaled position. The example is fictional and source-reviewed only.

Implementation

Nominator := Power(10, aDP);
x := aValue * Nominator;
Result := (Trunc(x) + (Trunc(Frac(x) * 10) div 6)) / Nominator;

The two Trunc calls here are native Delphi Int64 operations inside vxCommonNumber, not the PascalScript Trunc wrapper with 32-bit narrowing.

Edge cases and quirks

  • Only the first discarded decimal digit affects the increment. For example, a scaled fraction near 0.5999 still truncates its first digit to 5 and does not round.
  • Binary floating representation can place an intended decimal boundary just below/above 5 or 6.
  • Scaling uses the custom Power implementation and inherits its overflow, underflow, target and extreme-exponent behavior.
  • If x cannot be converted by Delphi Trunc to Int64, a floating invalid-operation error propagates.
  • If Nominator underflows to zero, final division can raise or produce a special value according to the floating exception mask.
  • The operation is locale-independent but not decimal-exact; it uses binary Extended arithmetic.

Performance and side effects

The function is pure and constant-time. It performs exponentiation/scaling plus two integer conversions, so cache a repeated invariant scale/result if used in a high-volume loop.

Related entries

  • Round2BR uses Double plus Delphi nearest/even rounding.
  • Round2Up uses textual midpoint-away-from-zero logic.
  • RoundAs selects among these named algorithms.

External references

Created 2026-07-15