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Cos

function Cos(E: Extended): Extended;

Example​

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

Usage​

Returns the cosine 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 cosine. Do not normally test the result for exact equality: even values such as Cos(Pi / 2) can be a very small non-zero number after range reduction and rounding.

Additional Technical Info​

Cos returns the cosine 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.Cos. It does not interpret degrees. The example is fictional and source-reviewed only.

Implementation

  1. The modified PascalScript compiler declares Cos in its standard Math group.
  2. Runtime selector 16 obtains an Extended through Stack.GetReal.
  3. Delphi System.Cos performs the platform-specific trigonometric calculation and PascalScript stores the returned real value.

The product project targets both Win32 and Win64 and currently defaults to Win64. The Win32 RTL path ultimately uses the x87 cosine instruction; the Win64 path treats Extended as Double and uses the RTL's double-precision range-reduction implementation. No Velox wrapper alters the argument or result.

Edge cases and quirks

  • Input is in radians, not degrees. One complete revolution is 2 * Pi.
  • Cosine is even: within rounding error, Cos(-E) equals Cos(E).
  • Very large finite angles require range reduction. Their low-order angle information may already have been lost in the input, so accuracy can be much worse than for a small equivalent angle.
  • On Win32, x87 FCOS 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 cosine. 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 or other floating-point condition returns a special IEEE value or raises depends on the process's active floating-point exception mask; the PascalScript dispatch does not catch it.

Performance

Each call performs a real trigonometric operation. Avoid recomputing the same invariant angle inside a high-volume record loop when the value can be calculated once and reused.

Related entries

  • Sin returns the sine of a radian angle.
  • Pi supplies the circle constant used for angle conversion.

External references

Created 2026-07-15