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Sin

function Sin(E: Extended): Extended;

Example​

procedure ScriptEvent(var Value: variant);
begin
  Value := Sin(Pi / 2); // approximately 1
end;

Usage​

Returns the sine of an Extended angle expressed in radians.

Parameters

NameTypeDescription
EExtendedAngle in radians. Convert degrees with Degrees * Pi / 180 before calling.

Returns

An Extended approximation of the sine. Results near zero should normally be compared with a tolerance rather than exact equality; for example, Sin(Pi) need not be stored as exact zero.

Additional Technical Info​

Sin returns the sine of an angle expressed in radians. For finite input, the mathematical result is in the interval -1 through 1, subject to floating-point approximation.

This is the PascalScript standard function and delegates directly to Delphi's System.Sin. It does not interpret degrees. The example is fictional and source-reviewed only.

Implementation

  1. The modified PascalScript compiler declares Sin in its standard Math group.
  2. Runtime selector 15 obtains the argument through Stack.GetReal.
  3. Delphi System.Sin performs the target-specific trigonometric calculation.
  4. PascalScript stores the real result without a Velox transformation.

The product project targets both Win32 and Win64 and currently defaults to Win64. The Win32 RTL path ultimately uses the x87 sine instruction; the Win64 path treats Extended as Double and uses the RTL's double-precision range-reduction implementation.

Edge cases and quirks

  • Input is in radians, not degrees. One complete revolution is 2 * Pi.
  • Sine is odd: within rounding error, Sin(-E) equals -Sin(E).
  • Very large finite angles lose useful low-order phase information and require range reduction, so accuracy can be materially worse than for a small equivalent angle.
  • On Win32, x87 FSIN has a finite argument-reduction limit. Outside its supported approximately +/-2^63-radian range it sets its C2 status flag and leaves the operand unchanged; this wrapper does not inspect C2, so it can return the original huge value rather than a result in -1 through 1. Reduce large angles before calling.
  • Positive infinity, negative infinity and NaN do not have a finite sine. They can produce NaN and an invalid floating-point condition.
  • Extended has target-dependent precision; a 64-bit Delphi target commonly treats it as Double.

Errors and side effects

The function is pure. For ordinary finite input it has no external side effects and no Velox-specific error path. Whether an invalid floating-point condition returns a special IEEE value or raises depends on the active process exception mask; the PascalScript dispatch does not catch it.

Performance

Each call performs a real trigonometric operation. Calculate an invariant angle once rather than repeatedly inside a high-volume mapping loop.

Related entries

  • Cos returns the cosine of a radian angle.
  • Pi supplies the circle constant used for angle conversion.

External references

Created 2026-07-15