POW(3P)

📦 version 2017a, in alpine 3.22, alpine 3.23, alpine 3.24, arch rolling, nixpkgs unstable, opensuse-leap 16.0

✨ POW(3P) — power function ✨

okay bestie, sit down, hydrate, because we're doing exponents today 💅 this is the POSIX Programmer's Manual page for pow, powf and powl, and yes it is a LOT of edge cases, but they're all iconic and we're getting through every single one together 🫶

🌸 PROLOG 🌸

This manual page is part of the POSIX Programmer's Manual. The Linux implementation of this interface may differ (consult the corresponding Linux manual page for details of Linux behavior), or the interface may not be implemented on Linux.

so like. heads up. Linux might do its own thing. read the Linux page too, no cap 🧚

🎀 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);

three flavors, one vibe. double, float, long double, pick your fighter ✨

🦋 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.

translation: ISO C is the referee here, this page is just the hype woman 🫶

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.

okay this one matters bestie. negative base? then y has to be an integer. that's the deal. 💀

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.

so the vibe check is: clear everything, call the function, check everything. if errno ain't zero, or that fetestexcept call ain't zero, something went down 🌈

🔥 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.

okay now the iconic list of special cases. this is the part everyone skips and then gets surprised by. we do not skip. 💅

  • 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.

and one more, tucked at the end:

If the correct value would cause underflow, and is representable, a range error may occur and the correct value shall be returned.

slay. every single one of them, accounted for. 👑

💀 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.

ngl the "shall fail" vs "may fail" split is the whole tea here. same pole error shows up in BOTH lists. that's not a typo, that's the spec. periodt. 🙈

The following sections are informative.

🍓 EXAMPLES 🍓

None.

(not me having zero examples to show you 😭 the spec said none and we respect the spec)

🧚 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.

so like, they don't talk to each other, they're independent queens 💅 but at least one of them has to be non-zero. that's the rule.

⭐ 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>

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 .

Any typographical or formatting errors that appear in this page are most likely to have been introduced during the conversion of the source files to man page format. To report such errors, see https://www.kernel.org/doc/man-pages/reporting_bugs.html .

and that's the whole page bestie 🫶 this one's brought to you by IEEE/The Open Group, 2017, and it's the POW(3P) page — go forth and raise things to powers responsibly, mwah 💖✨

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