LessThanValueEpsilon

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

Example

procedure ScriptEvent(var Value: variant);
begin
  Value := LessThanValueEpsilon(9.5, 10.0, 0.01);
end;

Usage

LessThanValueEpsilon tests whether one Extended value orders below another after an explicit-tolerance comparison.

Parameters

Name	Type	Description
A	Extended, const	Left-hand value.
B	Extended, const	Right-hand value.
Epsilon	Extended	Allowed absolute difference before the values are treated as same. Use a finite positive value.

Returns

A difference less than or equal to a valid positive epsilon returns False because the values classify as same.

Behaviour

With a finite positive epsilon, this operation provides a tolerance-aware strict ordering: A must be below the lower edge of B's tolerance band to return True. It is an absolute band in the same unit as the operands.

Errors

The function does not validate epsilon or finiteness. Nonnumeric argument conversion can raise before entry.

Usage notes

Validate epsilon when it comes from configuration and document its unit. If the rule is "less than after rounding to N decimal places", perform that domain rounding explicitly; an absolute binary floating band is not the same rule.

Additional Technical Info

LessThanValueEpsilon reports whether A orders below B after first applying the supplied absolute tolerance. The example returns True because the difference is greater than 0.01. It is source-reviewed and is not executed by the documentation workflow.

Implementation

The Velox wrapper calls the Delphi Extended CompareValue overload and tests for the internal LessThan constant. Delphi performs its inclusive SameValue test before evaluating A < B.

Edge cases and quirks

• A difference exactly equal to epsilon is same, so the result is False.
• Epsilon = 0 selects Delphi's calculated, platform-dependent default tolerance rather than exact < semantics.
• With a negative epsilon, even equal values fail the same-value test; ordinary A < B pairs still return True. This makes the predicate internally inconsistent as a tolerance rule, so reject negative values.
• A very large or infinite positive epsilon can make widely separated finite values classify as same and return False.
• A NaN operand never classifies as less than through the underlying comparison and this function returns False.
• Equal same-signed infinities also return False; do not infer equality from that Boolean alone.
• Operand evaluation remains platform-dependent Extended arithmetic even when the epsilon is explicit.

Side effects

None.

Performance and concurrency

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

Related entries

• CompareValueEpsilon exposes the three-way relationship.
• LessThanValue uses the calculated default tolerance.
• IsZeroEpsilon applies an explicit band around zero.

External references

• Embarcadero System.Math.CompareValue
• Free Pascal CompareValue — compatibility reference; current Delphi behaviour is authoritative for Velox.

Created 2026-07-15