LessThanValue

Function LessThanValue( const A, B : Extended): Boolean

Example

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

Usage

LessThanValue tests whether one Extended value orders below another after Velox's default-tolerance comparison.

Parameters

Name	Type	Description
A	Extended, const	Left-hand value.
B	Extended, const	Right-hand value.

Returns

Values within the default tolerance return False.

Behaviour

For ordinary finite operands well outside the tolerance, the result matches A < B. At or within the inclusive tolerance boundary, the operands classify as same and this function returns False.

Errors

There is no ordinary data-dependent exception. Nonnumeric script inputs can fail conversion to Extended before entry.

Usage notes

Use this when near-equal floating values should not order below one another under Velox's default machine tolerance. Use LessThanValueEpsilon when the allowed band is part of the interface or business rule.

Additional Technical Info

LessThanValue reports whether A orders below B after applying Delphi's calculated default floating-point tolerance. It does not perform the raw expression A < B.

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

Implementation

Velox calls Delphi CompareValue for Extended operands and compares its result with the internal LessThan constant. The underlying routine first tests approximate equality. With default epsilon, its tolerance is based on the smaller operand magnitude and ExtendedResolution, with a minimum of that resolution.

Edge cases and quirks

• The platform's Extended resolution affects the default band: current true 80-bit builds use 1E-16, while builds where Extended aliases Double use 1E-12.
• A slightly smaller A can return False when its difference from B is within tolerance.
• A NaN in either position does not classify as less than through CompareValue; this function returns False. That does not mean the operands are equal.
• Equal same-signed infinities also return False, although the underlying relationship can be the greater/unordered branch rather than same.
• This is an absolute-tolerance comparison derived from floating magnitude, not a decimal rounding or currency-minor-unit rule.

Side effects

None.

Performance and concurrency

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

Related entries

• CompareValue exposes all three underlying relationships.
• LessThanValueEpsilon supplies a tolerance.
• IsZero uses the related default-resolution zero test.

External references

• Embarcadero System.Math.CompareValue
• Free Pascal CompareValue — compatible background; Delphi defines Velox's exact tolerance and platform behaviour.

Created 2026-07-15