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

^[CX] 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.1-2024 defers to the ISO C standard.

These functions shall compute the value of x raised to the power y, x^y. 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 ^[MX]  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, ^[MXX]  and is not representable,  a range error may occur, and pow(), powf(), and powl() shall return ^[MXX]  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 ^[CX]  pole  error may occur and pow(), powf(), and powl() shall return ±HUGE_VAL, ±HUGE_VALF, and ±HUGE_VALL, respectively. ^[MX]  On systems that support the IEC 60559 Floating-Point option, if x is ±0:

• If y is an odd integer, a pole error shall occur and pow(), powf(), and powl() shall return ±HUGE_VAL, ±HUGE_VALF, and ±HUGE_VALL, respectively.

• If y is finite and is not an odd integer, a pole error shall occur and pow(), powf(), and powl() shall return HUGE_VAL, HUGE_VALF, and HUGE_VALL, respectively.

• If y is -Inf, a pole error may occur and pow(), powf(), and powl() shall return HUGE_VAL, HUGE_VALF, and HUGE_VALL, respectively.

^[MX] 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.

^[MXX] 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

^[MX] 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.

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

XBD 4.23 Treatment of Error Conditions for Mathematical Functions, <math.h>

CHANGE HISTORY

First released in Issue 1. Derived from Issue 1 of the SVID.

Issue 5

The DESCRIPTION is updated to indicate how an application should check for an error. This text was previously published in the APPLICATION USAGE section.

Issue 6

The normative text is updated to avoid use of the term "must" for application requirements.

The powf() and powl() functions are added for alignment with the ISO/IEC 9899:1999 standard.

The DESCRIPTION, RETURN VALUE, ERRORS, and APPLICATION USAGE sections are revised to align with the ISO/IEC 9899:1999 standard.

IEC 60559:1989 standard floating-point extensions over the ISO/IEC 9899:1999 standard are marked.

IEEE Std 1003.1-2001/Cor 1-2002, item XSH/TC1/D6/42 is applied, correcting the third paragraph in the RETURN VALUE section.

Issue 7

ISO/IEC 9899:1999 standard, Technical Corrigendum 2 #51 (SD5-XSH-ERN-81) is applied.

POSIX.1-2008, Technical Corrigendum 1, XSH/TC1-2008/0443 [68], XSH/TC1-2008/0444 [148], and XSH/TC1-2008/0445 [68] are applied.

Issue 8

Austin Group Defect 1302 is applied, aligning these functions with the ISO/IEC 9899:2018 standard.