atan function

Synopsis

$atan(number)
$atan(y x)

Technical

With one argument, atan() returns the principal arc tangent of number in radians, using the C library's atan() function. Every finite real number is in its domain; the result is between -pi/2 and pi/2. Positive and negative infinity produce positive and negative pi/2, respectively. The input is a tangent value, not an angle in degrees.

With two arguments, this same EPIC function calls the library's atan2(y, x). It determines the angle of the point (x, y), using both signs to select a quadrant; the result is between -pi and pi radians. The first argument is y, and the second is x. This form handles a zero x without first dividing by it. There is no separate C built-in named atan2.

The normal rules about number arguments apply. Arguments are converted with atof(), accepting decimal fractions and scientific notation. Nonnumeric arguments convert to zero, and numeric prefixes can be accepted even when followed by nonnumeric text. Missing input returns the empty string. Additional words after the second argument are ignored. See tan() for tangent calculation.

Returns

The calculation uses C double values, and the result string is formatted with %.50g, rather than being limited to six decimal places. The floating_point_math and floating_point_precision settings do not change this calculation or formatting. Additional displayed rounding digits do not imply 50 digits of accuracy.

The handler clears errno before converting its arguments, then checks it after the library calculation. It returns DOM for a reported domain error, RANGE for a reported range error, and the empty string for another reported error. Very small subnormal inputs to the one-argument form, or an underflowing result in the two-argument form, can cause platform-dependent range errors. Only errno is checked; floating-point exception flags are not. A conversion error can also affect this handler's error result because it does not clear errno between conversion and calculation.

Examples

The approximate examples describe the numeric value; the returned string may contain more digits.

Source

source/functions.c registers atan and implements both forms in function_atan(), using the shared error-return macro. include/functions.h defines argument conversion and formatting. The C/POSIX specifications for atan and atan2 define library ranges and error reporting.