hypot

You can use the hypot function to compute the length of the hypotenuse of a right triangle.

double_t hypot(double_t x, double_t y);

x

Any floating-point number.

y

Any floating-point number.

DESCRIPTION

The hypot function computes the square root of the sum of the squares of its arguments. This is an ANSI standard C library function.

$hypot(x,y)\; =\; SQRTx$²+y²

The function hypot performs its computation without undeserved overflow or underflow. For example, if $x$²+y² is greater than the maximum representable value
of the data type but the square root of $x$²+y² is not, then no overflow occurs.

EXCEPTIONS

When x and y are finite and nonzero, either the result of $hypot(x,y)$ is exact or it raises one of the following exceptions:

• inexact (if the result must be rounded or an overflow or underflow occurs)
• overflow (if the result is outside the range of the data type)
• underflow (if the result is inexact and must be represented as a denormalized number or 0)

SPECIAL CASES

Table 10-40 shows the results when one of the arguments to the hypot 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 hypot function

Operation	Result	Exceptions raised
$hypot(+0,y)$	|y|	None
$hypot(x,+0)$	|x|	None
$hypot(-0,y)$	|y|	None
$hypot(x,-0)$	|x|	None
$hypot(NaN,y)$	NaN	None[65]
$hypot(x,NaN)$	NaN	None[65]
$hypot(NaN,\pm$ )		None
$hypot(\pm$ ,NaN)		None
$hypot(+$ ,y)	+	None
$hypot(x,+$ )	+	None
$hypot(-$ ,y)	+	None
$hypot(x,-$ )	+	None

EXAMPLES

z = hypot(2.0, 2.0); /* z = sqrt(8.0)  2.82843. The inexact 
                        exception is raised. */

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