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NAME
pow, powf, powl — power function
SYNOPSIS
#include <math.h>
double pow(double x, double y);
float powf(float x, float y);
long double powl(long double x, long double y);
DESCRIPTION
The functionality described on this reference page is aligned with the ISO C standard. Any conflict
between the requirements described here and the ISO C standard is unintentional. This volume of
POSIX.1‐2017 defers to the ISO C standard.
These functions shall compute the value of x raised to the power y, xy. If x is negative, the
application shall ensure that y is an integer value.
An application wishing to check for error situations should set errno to zero and call
feclearexcept(FE_ALL_EXCEPT) before calling these functions. On return, if errno is non-zero or
fetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has occurred.
RETURN VALUE
Upon successful completion, these functions shall return the value of x raised to the power y.
For finite values of x < 0, and finite non-integer values of y, a domain error shall occur and either a
NaN (if representable), or an implementation-defined value shall be returned.
If the correct value would cause overflow, a range error shall occur and pow(), powf(), and powl() shall
return ±HUGE_VAL, ±HUGE_VALF, and ±HUGE_VALL, respectively, with the same sign as the correct value of
the function.
If the correct value would cause underflow, and is not representable, a range error may occur, and pow(),
powf(), and powl() shall return 0.0, or (if IEC 60559 Floating-Point is not supported) an implementation-
defined value no greater in magnitude than DBL_MIN, FLT_MIN, and LDBL_MIN, respectively.
For y < 0, if x is zero, a pole error may occur and pow(), powf(), and powl() shall return ±HUGE_VAL,
±HUGE_VALF, and ±HUGE_VALL, respectively. On systems that support the IEC 60559 Floating-Point option,
if x is ±0, a pole error shall occur and pow(), powf(), and powl() shall return ±HUGE_VAL, ±HUGE_VALF,
and ±HUGE_VALL, respectively if y is an odd integer, or HUGE_VAL, HUGE_VALF, and HUGE_VALL, respectively
if y is not an odd integer.
If x or y is a NaN, a NaN shall be returned (unless specified elsewhere in this description).
For any value of y (including NaN), if x is +1, 1.0 shall be returned.
For any value of x (including NaN), if y is ±0, 1.0 shall be returned.
For any odd integer value of y > 0, if x is ±0, ±0 shall be returned.
For y > 0 and not an odd integer, if x is ±0, +0 shall be returned.
If x is -1, and y is ±Inf, 1.0 shall be returned.
For |x| < 1, if y is -Inf, +Inf shall be returned.
For |x| > 1, if y is -Inf, +0 shall be returned.
For |x| < 1, if y is +Inf, +0 shall be returned.
For |x| > 1, if y is +Inf, +Inf shall be returned.
For y an odd integer < 0, if x is -Inf, -0 shall be returned.
For y < 0 and not an odd integer, if x is -Inf, +0 shall be returned.
For y an odd integer > 0, if x is -Inf, -Inf shall be returned.
For y > 0 and not an odd integer, if x is -Inf, +Inf shall be returned.
For y < 0, if x is +Inf, +0 shall be returned.
For y > 0, if x is +Inf, +Inf shall be returned.
If the correct value would cause underflow, and is representable, a range error may occur and the correct
value shall be returned.
ERRORS
These functions shall fail if:
Domain Error
The value of x is negative and y is a finite non-integer.
If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then errno shall be
set to [EDOM]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero,
then the invalid floating-point exception shall be raised.
Pole Error The value of x is zero and y is negative.
If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then errno shall be
set to [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero,
then the divide-by-zero floating-point exception shall be raised.
Range Error The result overflows.
If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then errno shall be
set to [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero,
then the overflow floating-point exception shall be raised.
These functions may fail if:
Pole Error The value of x is zero and y is negative.
If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then errno shall be
set to [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero,
then the divide-by-zero floating-point exception shall be raised.
Range Error The result underflows.
If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then errno shall be
set to [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero,
then the underflow floating-point exception shall be raised.
The following sections are informative.
EXAMPLES
None.
APPLICATION USAGE
On error, the expressions (math_errhandling & MATH_ERRNO) and (math_errhandling & MATH_ERREXCEPT) are
independent of each other, but at least one of them must be non-zero.
RATIONALE
None.
FUTURE DIRECTIONS
None.
SEE ALSO
exp(), feclearexcept(), fetestexcept(), isnan()
The Base Definitions volume of POSIX.1‐2017, Section 4.20, Treatment of Error Conditions for Mathematical
Functions, <math.h>
COPYRIGHT
Portions of this text are reprinted and reproduced in electronic form from IEEE Std 1003.1-2017, Standard
for Information Technology -- Portable Operating System Interface (POSIX), The Open Group Base
Specifications Issue 7, 2018 Edition, Copyright (C) 2018 by the Institute of Electrical and Electronics
Engineers, Inc and The Open Group. In the event of any discrepancy between this version and the original
IEEE and The Open Group Standard, the original IEEE and The Open Group Standard is the referee document.
The original Standard can be obtained online at http://www.opengroup.org/unix/online.html .
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