Legacy Document

pow

You can use the pow function to raise a real number to the power of some other real number.

double_t pow (double_t x, double_t y);

x

Any floating-point number.

y

Any floating-point number.

DESCRIPTION

The pow function computes x to the y power. This is an ANSI standard C library function.

$pow(x,y)\; =\; xy$

Use the function call pow(x,y) instead of the expression

exp(y * log(x))

The call pow(x,y) produces a more exact result.

There are some differences between this implementation and the behavior of the pow function in a SANE implementation. For example, in SANE pow(NAN,0) returns a NaN, whereas in PowerPC Numerics, pow(NAN,0) returns a 1.

EXCEPTIONS

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

• inexact (if y is not an integer or an underflow or overflow occurs)
• invalid (if x is negative and y is not an integer)
• 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 10-11 shows the results when one of the arguments to the pow function is a zero, a NaN, or an Infinity, plus other special cases for the pow function. In this table, x and y are finite, nonzero floating-point numbers.

Special cases for the pow function

Operation	Result	Exceptions raised
$pow(x,y)$ for x < 0	NaN if y is not integer	Invalid
	$xy$ if y is integer	None
$pow(+0,y)$	\xB10 if y is odd integer > 0	None
	+0 if y > 0 but not odd integer	None
	\xB1 if y is odd integer < 0	Divide-by-zero
	+ if y < 0 but not odd integer	Divide-by-zero
$pow(x,+0)$	+1	None
$pow(-0,y)$	\xB10 if y is odd integer > 0	None
	+0 if y > 0 but not odd integer	None
	\xB1 if y is odd integer < 0	Divide-by-zero
	+ if y < 0 but not odd integer	Divide-by-zero
$pow(x,-0)$	+1	None
$pow(NaN,y)$	NaN if y 0	None[32]
	+1 if y = 0	None[32]
$pow(x,NaN)$	NaN	None[32]
$pow(+$ ,y)	+ if y > 0	None
	+0 if y < 0	None
	+1 if y = 0	None
$pow(x,+$ )	+ if |x| > 1	None
	+0 if |x| < 1	None
	NaN if |x| = 1	Invalid
$pow(-$ ,y)	$-$ if y is odd integer > 0	None
	+ if y > 0 but not odd integer	None
	$-0$ if y is odd integer < 0	None
	+0 if y < 0 but not odd integer	None
	+1 if y = 0	None
$pow(x,-$ )	+0 if |x| > 1	None
	+ if |x| < 1	None
	NaN if |x| = 1	Invalid

EXAMPLES

z = pow(NAN, 0);     /* z = 1 */

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