atan2

You can use the atan2 function to compute the arc tangent of a real number divided by another real number.

double_t atan2 (double_t y, double_t x);

y

Any floating-point number.

x

Any floating-point number.

DESCRIPTION

The atan2 function returns the arc tangent of its first argument divided by its second argument. The return value is expressed in radians in the range [-∫, +∫], using the signs of its operands to determine the quadrant.

$atan2(y,x)\; =\; arctan(y/x)\; =\; z$ such that $tan(z)\; =\; y/x$

EXCEPTIONS

When x and y are finite and nonzero, the result of $atan2(y,x)$ might raise one of the following exceptions:

• inexact (if either x or y is any finite, nonzero value)
• underflow (if the result is inexact and must be represented as a denormalized number or 0)

SPECIAL CASES

Table 10-26 shows the results when one of the arguments to the atan2 function is a zero, a NaN, or an Infinity. In this table, x and y are finite, nonzero floating-point numbers.

Special cases for the atan2 function

Operation	Result	Exceptions raised
$atan2(+0,x)$	+0 x > 0	None
	+∫ x < 0	None
$atan2(y,+0)$	+∫/2 y > 0	None
	-∫/2 y < 0	None
$atan2(\pm 0,+0)$	±0	None
$atan2(-0,x)$	$-0$ x > 0	Inexact
	-∫ x < 0	Inexact
$atan2(y,-0)$	+∫/2 y > 0	None
	-∫/2 y < 0	None
$atan2(\pm 0,-0)$	±∫	Inexact
$atan2(NaN,x)$	NaN[47]	None[48]
$atan2(y,NaN)$	NaN	None
$atan2(+$ ,x)	∫/2	Inexact
$atan2(y,+$ )	±0	None
$atan2(\pm$ ,+ )	±3∫/4	Inexact
$atan2(-$ ,x)	-∫/2	Inexact
$atan2(y,-$ )	±∫	None
$atan2(\pm$ ,- )	±3∫/4	Inexact

EXAMPLES

z = atan2(1.0, 1.0); /* z = arctan 1/1 = arctan 1 = ∫/4. The 
                        inexact exception is raised. */
z = atan2(3.5, 0.0); /* z = arctan 3.5/0 = arctan    = ∫/2 */

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[47] If both arguments are NaNs, it is undefined which one atan2 returns.

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[48] If the NaN is a signaling NaN, the invalid exception is raised.