ERFC(3P)

💖 ERFC(3P) — the complementary error function glow-up 💖

okay bestie, welcome to the POSIX Programmer's Manual page for erfc, erfcf, and erfcl — yes, the complementary error functions, and yes, they're kind of iconic. 🫶

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✨ PROLOG ✨

okay so first things first, 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. like, check before you commit, bestie. 🙈

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🌸 NAME 🌸

erfc, erfcf, erfcl — complementary error functions 💅

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✨ SYNOPSIS ✨

#include <math.h>

double erfc(double x);
float erfcf(float x);
long double erfcl(long double x);

three functions, three float sizes, all slaying in their own lane. 🎀

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💜 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. no cap, the ISO C standard is the main character here and POSIX is just vibing alongside it. 👑

These functions shall compute the complementary error function 1.0 - erf(x). that's it. that's the whole job. ✨

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. it's giving "vibe check your floating point exceptions before you freak out." 🔥

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🦋 RETURN VALUE 🦋

Upon successful completion, these functions shall return the value of the complementary error function. periodt. ✨

If the correct value would cause underflow, and is not representable, a range error may occur, and erfc(), erfcf(), and erfcl() shall return 0.0, or (if the IEC 60559 Floating-Point option is not supported) an implementation-defined value no greater in magnitude than DBL_MIN, FLT_MIN, and LDBL_MIN, respectively. so like... very smol. 💀

If x is NaN, a NaN shall be returned.

If x is ±0, +1 shall be returned.

If x is -Inf, +2 shall be returned.

If x is +Inf, +0 shall be returned.

honestly? the edge case table ate. no crumbs. 🌈

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😭 ERRORS 😭

These functions may fail if:

• 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. (aka, the fun bonus lore section, not the legally binding part 🎀)

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🎀 EXAMPLES 🎀

None. bestie there is literally nothing here. empty. void. the silence is deafening. 🙈

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💅 APPLICATION USAGE 💅

The erfc() function is provided because of the extreme loss of relative accuracy if erf(x) is called for large x and the result subtracted from 1.0. like yes, you could do 1.0 - erf(x) yourself but for big x the accuracy just evaporates 😭 so erfc() said "not on my watch."

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. they're not besties, they don't text each other, but one of them has to show up to the function. 🫶

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🧚 RATIONALE 🧚

None. iconic of them to say nothing and still be correct. ✨

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💜 FUTURE DIRECTIONS 💜

None. the future is... unchanged. slay. 💅

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🌟 SEE ALSO 🌟

• erf()
• feclearexcept()
• fetestexcept()
• isnan()

The Base Definitions volume of POSIX.1‐2017, Section 4.20, Treatment of Error Conditions for Mathematical Functions, <math.h> 🌸

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⭐ 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 .

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 .

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ngl if you spot a typo it's probably from the man page conversion pipeline, not from the math. report it at the link above, bestie. 🫶

okay that's the whole page, you understood all of it, I'm so proud of you, go forth and compute your complementary error functions responsibly. 👑✨

IEEE/The Open Group — 2017 — ERFC(3P) 💖