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Round2Up

function Round2Up(aValue: Extended; aDP: Integer): Extended;

Example​

procedure ScriptEvent(var Value: variant);
begin
  Value := Round2Up(-12.25, 1); // normally -12.3: midpoint away from zero
end;

Usage​

Round2Up rounds decimal text at a requested place with midpoint values away from zero before reparsing it.

Parameters

NameTypeDescription
aValueExtendedValue converted to text and rounded.
aDPIntegerIntended number of fractional decimal digits to retain. Use a non-negative value only.

Returns

For supported ordinary dot-decimal text, the value rounded at aDP digits with a first discarded digit of 5..9 incrementing the retained magnitude. Fewer existing fractional digits return the original binary value unchanged rather than padding zeros.

Additional Technical Info​

Round2Up converts the value to general-format decimal text, edits digits to implement a 5-through-9 increment, then reparses the text. It removes a negative sign while editing, so midpoint rounding is away from zero for both signs.

The implementation assumes a literal dot decimal separator and ordinary non-exponent decimal text. Formatting and parsing do not even use the same settings source, which makes locale and scientific notation important correctness hazards. The example is fictional and source-reviewed only.

Implementation

  1. Result starts as the original aValue.
  2. Unqualified SysUtils.FloatToStr(aValue) formats through process-global FormatSettings in general format.
  3. A leading - is remembered and removed.
  4. The code searches for literal .. No dot, or no digits beyond the requested place, returns the original value.
  5. The dot is removed and the first discarded character is inspected.
  6. 5..9 recursively increments the preceding digit and zeroes digits to its right; 0..4 only zeroes from the discarded digit onward.
  7. A carry can insert a new leading 1; the decimal position is adjusted.
  8. The literal dot and sign are restored.
  9. vxStrToFloat reparses using a newly created Windows system-default TFormatSettings.

Locale and representation defects

  • A comma-decimal FloatToStr result contains no literal dot, so the function silently returns the unrounded original value.
  • Formatting uses mutable process-global FormatSettings, while parsing uses fresh LOCALE_SYSTEM_DEFAULT settings. If they differ, text produced by one side can be misread or rejected by the other.
  • FloatToStr uses general format and can emit exponent notation for very large/small values. The digit mutators do not understand E, exponent signs or exponent digits; they can overwrite those characters, calculate with a nondigit, return the original due no dot or produce malformed/wrong text.
  • The operation rounds the formatted decimal representation, whose significant digits are already limited, rather than the full binary Extended value.

Other edge cases and quirks

  • Negative aDP is not validated. It indexes into characters to the left of the decimal and can access position zero/negative under enabled range checking, raise ERangeError, or produce an accidental/non-general integer-place result. Use Round2BR for documented negative-place scaling.
  • NaN/infinity text normally has no dot and therefore returns the original special value unchanged.
  • An exact carry such as supported text 99.95 at one place becomes 100.0 through recursive digit increment.
  • -0 sign preservation depends on FloatToStr; a no-dot representation returns the original value.
  • Final StrToFloat failures propagate as EConvertError.

Performance and side effects

The function has no external side effect, but allocates and mutates multiple strings and creates locale settings on parse. It is slower and less stable than direct arithmetic in a high-volume loop.

Related entries

  • Round2BR uses scaled Double nearest/even rounding without text/locale conversion.
  • Round2 uses a six-tenths arithmetic threshold.
  • RoundAs selects this function with token ROUND2UP.

External references

Created 2026-07-15