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# atan(+Y, +X, -Result)

Computes the arc tangent function of two variables and unifies the resulting value with Result.
*Y*
- A number.
*X*
- A number.
*Result*
- A variable, float or breal.

## Description

This predicate is used by the ECLiPSe compiler to expand evaluable
arithmetic expressions. So the call to atan(Y, X, Result) is
equivalent to
Result is atan(Y, X)

which should be preferred for portability.
It is similar to calculating the arc tangent of Y/X, except that the
signs of both arguments are used to determine the quadrant of the result.
The result lies in the interval -pi..pi. The operation is valid even if
X is zero, in which case the result is pi/2 or -pi/2. One application
is the conversion of cartesian to polar coordinates, where this function
computes the angle component (in radians).

In coroutining mode, if X or Y is uninstantiated, the call to atan/3 is
delayed until both variables are instantiated.

### Modes and Determinism

### Exceptions

*(4) instantiation fault *
- X or Y is not instantiated (non-coroutining mode only).
*(24) number expected *
- Number is not of a numeric type.

## Examples

Success:
atan( 0.0, -1.0, Result). (gives Result = 3.141592)
atan( 1.0, -1.0, Result). (gives Result = 2.356194)
atan( 1.0, 0.0, Result). (gives Result = 1.570796)
atan( 1.0, 1.0, Result). (gives Result = 0.785398)
atan( 0.0, 0.0, Result). (gives Result = 0.0)
atan(-1.0, 1.0, Result). (gives Result = -0.785398)
atan(-1.0, 0.0, Result). (gives Result = -1.570796)
atan(-1.0, -1.0, Result). (gives Result = -2.356194)
atan(-0.0, -1.0, Result). (gives Result = -3.141592)
atan( 7.0, 7.0, Result). (gives Result = 0.785398)
Fail:
atan(1.55741, 0.0, 1).
Error:
atan(A, 0.0, 6.0). (Error 4).
atan(1 + 0.55741, 1.0, R). (Error 24).

## See Also

is / 2