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Pi

function Pi: Extended;

Example​

procedure ScriptEvent(var Value: variant);
begin
  Value := 2 * Pi * 10; // circumference for radius 10
end;

Usage​

Returns Velox's Extended floating-point approximation of the mathematical constant pi.

Parameters

Pi has no parameters. In Pascal syntax it can be called without parentheses.

Returns

An Extended approximation beginning 3.1415926535897932385. The mathematical value is irrational, so every finite binary floating-point representation is necessarily approximate.

Additional Technical Info​

Pi returns Delphi's floating-point approximation of the mathematical constant pi, the ratio of a circle's circumference to its diameter. It is also useful when converting between degrees and radians.

This is a zero-argument PascalScript standard function. The example is fictional and source-reviewed only.

Implementation

  1. The modified PascalScript compiler declares Pi in its standard Math group.
  2. Runtime selector 21 evaluates Delphi's intrinsic System.Pi.
  3. PascalScript writes that value to its real return slot.

There is no lookup, configuration read or recalculation from another constant.

Usage

Radians := Degrees * Pi / 180;
Degrees := Radians * 180 / Pi;

Keep units explicit in variable names because Sin and Cos accept radians only.

Edge cases and precision

  • The returned value is approximate; do not compare a derived floating-point calculation with an expected value using exact equality.
  • Extended precision depends on the Delphi compilation target. It is an 80-bit extended type on the Win32 target, but aliases Double on common 64-bit Delphi targets.
  • Repeated calls have no accumulating state. Store it only for readability or to avoid repeating a larger derived expression.

Errors and side effects

Pi is pure, deterministic for a given build target and has no expected error path or side effect.

Related entries

  • Sin accepts an angle in radians.
  • Cos accepts an angle in radians.

External references

Created 2026-07-15