SameValueEpsilon

Function SameValueEpsilon( const A, B : Extended; Epsilon : Extended): Boolean

Example

procedure ScriptEvent(var Value: variant);
begin
  Value := SameValueEpsilon(10.0, 10.04, 0.05);
end;

Usage

SameValueEpsilon tests whether two Extended values differ by no more than an explicit tolerance.

Parameters

Name	Type	Description
A	Extended, const	First value.
B	Extended, const	Second value.
Epsilon	Extended	Maximum absolute difference accepted as same. Zero selects Velox's calculated default.

Returns

For finite operands and a positive finite epsilon, True when the absolute difference is less than or equal to Epsilon; otherwise False.

Behaviour

The boundary is inclusive. Epsilon is expressed in the same numeric units as the operands and is not automatically converted to an absolute value. A zero epsilon means default approximate equality, not exact equality.

Errors

The Velox function does not reject negative, infinite or NaN epsilon values with an exception. Validate the tolerance before calling. Values that cannot convert to Extended can fail before entry.

Usage notes

For conventional approximate equality, require a positive finite epsilon derived from the data domain and finite operands. For monetary values, prefer explicit decimal rounding or minor-unit comparison.

Additional Technical Info

SameValueEpsilon performs approximate equality for two Extended values using the supplied absolute tolerance.

The example returns True. It is source-reviewed and is not executed by the documentation workflow.

Implementation

vxCommonNumber.SameValueEpsilon delegates directly to the Extended overload of System.Math.SameValue(A, B, Epsilon). Current source compares the non-negative directional difference with the supplied epsilon. Only an epsilon equal to zero is replaced by Delphi's magnitude-scaled default.

Edge cases and quirks

• A negative epsilon returns False even for equal finite values because 0 <= negative is false.
• A NaN epsilon returns False for all operands.
• With positive-infinite epsilon, every finite pair returns True.
• A NaN operand returns False regardless of ordinary epsilon.
• Equal same-signed infinities return False because their difference is NaN, even when epsilon is infinite.
• Opposite infinities return True when epsilon is positive infinity, because their directional difference is infinity.
• Passing zero reintroduces the platform-dependent ExtendedResolution and magnitude scaling documented by SameValue.
• Parameter conversion remains platform-dependent because Extended can be 80-bit or an alias of Double.

Side effects

None.

Performance and concurrency

The operation is constant-time, allocates no managed data and uses no shared mutable state.

Related entries

• SameValue calculates a default tolerance.
• CompareValueEpsilon returns a three-way result using this same equality test.
• IsZeroEpsilon compares one value with zero using an explicit tolerance.

External references

• Embarcadero System.Math.SameValue
• Free Pascal SameValue - compatibility context; current Delphi source defines invalid-epsilon and exceptional-value results.

Created 2026-07-15