IsZeroEpsilon

Function IsZeroEpsilon( const A : Extended; Epsilon : Extended): Boolean

Example

procedure ScriptEvent(var Value: variant);
begin
  Value := IsZeroEpsilon(0.0004, 0.001);
end;

Usage

IsZeroEpsilon tests whether an Extended value is within an explicit tolerance of zero.

Parameters

Name	Type	Description
A	Extended, const	Value whose magnitude is tested.
Epsilon	Extended	Allowed absolute magnitude. Use a finite positive value for predictable explicit behaviour.

Returns

True when Abs(A) <= Epsilon after Velox has resolved the epsilon sentinel; otherwise False.

Behaviour

For a finite positive epsilon, positive and negative values at or inside the boundary return True. Values outside it return False. The supplied tolerance uses the same units as A and is absolute rather than percentage-based.

Errors

The function does not validate the epsilon. Conversion of nonnumeric arguments to Extended can raise before it is entered.

Usage notes

Store a domain epsilon with its unit and rationale. If the rule is relative to the value's size, calculate the relative threshold explicitly before calling or use a comparison designed for that rule.

Additional Technical Info

IsZeroEpsilon tests whether an Extended value lies within an explicit absolute tolerance of zero. The example returns True. It is source-reviewed and is not executed by the documentation workflow.

Implementation

The Velox wrapper calls System.Math.IsZero(A, Epsilon) using the Extended overload. A supplied Epsilon of zero is not an exact-zero request: Delphi replaces it with the platform's ExtendedResolution before performing the inclusive comparison.

Edge cases and quirks

• Epsilon = 0 selects the platform default (1E-16 for true 80-bit Extended, otherwise 1E-12 in current Delphi), so a small nonzero value can still return True.
• A negative epsilon returns False even for zero. Validate the tolerance instead of using a negative number to mean "disabled".
• NaN returns False for any ordinary epsilon.
• An infinite positive epsilon makes every finite value pass and can also make infinity pass under the floating-point comparison. Reject it as a configuration tolerance.
• An epsilon supplied as NaN makes the comparison false.
• A finite explicit epsilon makes the rule clearer across architectures, although input evaluation still uses the platform's Extended representation.

Side effects

None.

Performance and concurrency

The operation is constant-time, allocation-free and re-entrant.

Related entries

• IsZero uses the calculated platform default.
• CompareValueEpsilon compares two values with an explicit tolerance.
• LessThanValueEpsilon applies the same comparison family to ordering.

External references

• Embarcadero System.Math.IsZero
• Free Pascal IsZero — general compatibility reference; Delphi's inclusive implementation is authoritative here.

Created 2026-07-15