CPROJ(3P)

💖 CPROJ(3P) — the POSIX Programmer's Manual, but make it make sense 💖

okay bestie, so this one lives in the POSIX Programmer's Manual, and before we even get into it there's a whole PROLOG moment we gotta get through, because it's important, fr.

🚨 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.

ngl that's the classic "your mileage may vary, go check your own system" disclaimer and you should actually listen to it 💅

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✨ NAME ✨

cproj, cprojf, cprojl — complex projection functions

like, they project complex numbers. onto a sphere. we'll get there 🦋

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🎀 SYNOPSIS 🎀

#include <complex.h>

double complex cproj(double complex z);
float complex cprojf(float complex z);
long double complex cprojl(long double complex z);

three versions, three precisions, one vibe. pick your double, your float, or your long double and go off 👑

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🌸 DESCRIPTION 🌸

So first thing first, 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: if this page and the ISO C standard ever beef, the standard wins. periodt.

Now the actual tea: these functions shall compute a projection of z onto the Riemann sphere. z projects to z, except that all complex infinities (even those with one infinite part and one NaN part) project to positive infinity on the real axis. So like, every infinity gets squished into one single infinity. no cap.

If z has an infinite part, then cproj(z) shall be equivalent to:

INFINITY + I * copysign(0.0, cimag(z))

the way that copysign keeps the sign of the imaginary part but zeroes out the magnitude... it's giving "I remember your sign, bestie, but the rest is not your business" 😭

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💫 RETURN VALUE 💫

These functions shall return the value of the projection onto the Riemann sphere.

that's it. that's the return. iconic behaviour honestly 🫶

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🙈 ERRORS 🙈

No errors are defined.

the following sections are informative. iykyk.

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🍓 EXAMPLES 🍓

None.

literally none. we're all just vibing on theory today 🧚

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💜 APPLICATION USAGE 💜

None.

also none. the RATIONALE is where the plot is, keep scrolling ⬇️

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🌈 RATIONALE 🌈

okay so THIS is the good part, get comfy ✨

Two topologies are commonly used in complex mathematics: the complex plane with its continuum of infinities, and the Riemann sphere with its single infinity. The complex plane is better suited for transcendental functions, the Riemann sphere for algebraic functions. The complex types with their multiplicity of infinities provide a useful (though imperfect) model for the complex plane.

The cproj() function helps model the Riemann sphere by mapping all infinities to one, and should be used just before any operation, especially comparisons, that might give spurious results for any of the other infinities. So like, do the projection first, then compare, bestie. otherwise your comparisons are gonna be a mess and not in a cute way 💀

Note that a complex value with one infinite part and one NaN part is regarded as an infinity, not a NaN, because if one part is infinite, the complex value is infinite independent of the value of the other part. For the same reason, cabs() returns an infinity if its argument has an infinite part and a NaN part.

so yeah: one infinite part = the whole thing is infinite. that's the rule. not up for debate 🎀

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🦋 FUTURE DIRECTIONS 🦋

None.

the future is bright, but it holds no new directions for cproj 💅

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⭐ SEE ALSO ⭐

• carg()
• cimag()
• conj()
• creal()

And the Base Definitions volume of POSIX.1‐2017, <complex.h>

go read those next, bestie, they're the supporting cast and they ate 🔥

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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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and that's the whole page, bestie 🫶 courtesy of IEEE/The Open Group, 2017 — CPROJ(3P), projecting all your infinities into one since forever. slay 💖✨