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Sqrt

function Sqrt(E: Extended): Extended;

Example​

procedure ScriptEvent(var Value: variant);
begin
  Value := Sqrt(144); // 12
end;

Usage​

Sqrt returns the principal square root of an Extended floating-point value.

Parameters

NameTypeDescription
EExtendedRadicand. Use a finite value greater than or equal to zero for an ordinary real result.

Returns

The Extended principal square root. The result is approximate unless the value is exactly representable in binary floating point.

Additional Technical Info​

Sqrt returns the principal square root of an Extended floating-point value. For a positive finite input, it returns the non-negative value which, when squared, approximates the input.

This is the PascalScript standard function and delegates directly to Delphi's System.Sqrt. The example is fictional and source-reviewed only.

Implementation

  1. The modified PascalScript compiler declares Sqrt in its standard Math group.
  2. Runtime selector 17 reads the argument through Stack.GetReal.
  3. Delphi System.Sqrt performs the platform operation and returns an Extended.
  4. PascalScript stores the result through Stack.SetReal.

The product project targets both Win32 and Win64 and currently defaults to Win64. Win32 terminates at x87 FSQRT; Win64 uses the RTL's SSE/double-precision square-root path because Extended aliases Double. There is no Velox domain check or exception wrapper.

Edge cases and quirks

  • Sqrt(0) is zero. IEEE square root can retain the sign of negative zero even though positive and negative zero compare equal.
  • A negative finite value has no real square root. It causes an invalid floating-point condition rather than returning a complex number.
  • Positive infinity returns positive infinity under normal IEEE behaviour.
  • NaN remains non-numeric and can propagate or signal according to its form and the active floating-point environment.
  • Results that feed equality or threshold logic should be compared with an appropriate tolerance because input and output can both be rounded.
  • Extended precision depends on the Delphi target; common 64-bit targets alias it to Double.

Errors and side effects

The function is pure. With floating-point invalid exceptions unmasked, a negative radicand can raise into the script; with the condition masked, the hardware can return NaN. Velox does not normalize these alternatives, so scripts should validate E >= 0 when invalid input is possible.

Performance

Sqrt is a direct square-root operation and is preferable to NthRoot(2, E) for clarity, zero-domain support and avoiding logarithm/exponentiation error.

Related entries

  • NthRoot calculates other roots for strictly positive values.
  • Power raises a value to an integer exponent.
  • Abs removes a sign but does not calculate a root.

External references

Created 2026-07-15