FMA(3POSIX)

💖 FMA(3POSIX) — the POSIX Programmer's Manual, bestie edition 💖

okay so this one lives in the POSIX Programmer's Manual (yes the whole manual, not just this page, iykyk). anyway hi, welcome, let's get into it 🫶

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🌸 PROLOG 🌸

bestie real talk before we even start: this manual page is part of the POSIX Programmer's Manual. The Linux implementation of this interface may differ (so like, go consult the corresponding Linux manual page for details of Linux behavior), or honestly the interface might just not be implemented on Linux at all. vibe check your platform first, fr fr 💅

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✨ NAME ✨

fma, fmaf, fmal — floating-point multiply-add 👑

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🎀 SYNOPSIS 🎀

#include <math.h>

double fma(double x, double y, double z);
float fmaf(float x, float y, float z);
long double fmal(long double x, long double y, long double z);

three flavors, same energy 🦋

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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. (not us starting drama with ISO C, we would never 😭)

These functions shall compute (x * y) + z, rounded as one ternary operation. The way that means it shall compute the value (as if) to infinite precision and round once to the result format, according to the rounding mode characterized by the value of FLT_ROUNDS. one rounding. one. periodt ✨

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. that's the little pre-flight ritual bestie, do it every time 🧚

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🔥 RETURN VALUE 🔥

Upon successful completion, these functions shall return (x * y) + z, rounded as one ternary operation. slay 💅

If the result overflows or underflows, a range error may occur. On systems that support the IEC 60559 Floating-Point option, if the result overflows a range error shall occur. (may vs shall, the eternal academic weapons-grade distinction, love that for us)

If x or y are NaN, a NaN shall be returned. 🫠

If x multiplied by y is an exact infinity and z is also an infinity but with the opposite sign, a domain error shall occur, and either a NaN (if supported), or an implementation-defined value shall be returned. infinity minus infinity is not giving what you want it to give 💀

If one of x and y is infinite, the other is zero, and z is not a NaN, a domain error shall occur, and either a NaN (if supported), or an implementation-defined value shall be returned. Inf * 0 bestie? no. not today 🙈

If one of x and y is infinite, the other is zero, and z is a NaN, a NaN shall be returned and a domain error may occur.

If x*y is not 0*Inf nor Inf*0 and z is a NaN, a NaN shall be returned.

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💅 ERRORS 💅

These functions shall fail if:

• Domain Error — The value of x*y+z is invalid, or the value x*y is invalid and z is not a NaN.
  • 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.
• 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:

• Domain Error — The value x*y is invalid and z is a NaN.
  • 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.
• 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.
• 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.

The following sections are informative. (i.e. gossip, not law 💅)

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🌈 EXAMPLES 🌈

None.

not one single example. she simply said "figure it out" and honestly? iconic. 💀

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🦋 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. like two besties who don't need to match outfits but you cannot show up with neither, okurrr 🎀

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⭐ RATIONALE ⭐

In many cases, clever use of floating (fused) multiply-add leads to much improved code; but its unexpected use by the compiler can undermine carefully written code. (not the compiler sneaking in an fma behind your back and ruining your whole carefully-crafted numerical situation 😭 the audacity) The FP_CONTRACT macro can be used to disallow use of floating multiply-add; and the fma() function guarantees its use where desired. Many current machines provide hardware floating multiply-add instructions; software implementation can be used for others. either way, you're eating 🍓

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💜 FUTURE DIRECTIONS 💜

None.

nothing coming. she's already perfect. periodt.

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🌸 SEE ALSO 🌸

• feclearexcept()
• fetestexcept()
• 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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okay that's the whole page bestie, every flag, every NaN, every [EDOM] accounted for, no cap 🫶 this edition came to you from IEEE/The Open Group, 2017, and that's the whole FMA(3POSIX) situation. go forth and round exactly once 💖✨🎀