FMA(3P) POSIX Programmer's Manual FMA(3P)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.
NAME
fma, fmaf, fmal — floating-point multiply-add
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);
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.1‐2008
defers to the ISO C standard.
These functions shall compute (x * y) + z, rounded as one ternary oper‐
ation: they shall compute the value (as if) to infinite precision and
round once to the result format, according to the rounding mode charac‐
terized by the value of FLT_ROUNDS.
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 (x * y) + z,
rounded as one ternary operation.
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.
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.
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 imple‐
mentation-defined value shall be returned.
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.
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.
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
In many cases, clever use of floating (fused) multiply-add leads to
much improved code; but its unexpected use by the compiler can under‐
mine carefully written code. The FP_CONTRACT macro can be used to dis‐
allow 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 oth‐
ers.
FUTURE DIRECTIONS
None.
SEE ALSOfeclearexcept(), fetestexcept()
The Base Definitions volume of POSIX.1‐2008, Section 4.19, Treatment of
Error Conditions for Mathematical Functions, <math.h>
COPYRIGHT
Portions of this text are reprinted and reproduced in electronic form
from IEEE Std 1003.1, 2013 Edition, Standard for Information Technology
-- Portable Operating System Interface (POSIX), The Open Group Base
Specifications Issue 7, Copyright (C) 2013 by the Institute of Electri‐
cal and Electronics Engineers, Inc and The Open Group. (This is
POSIX.1-2008 with the 2013 Technical Corrigendum 1 applied.) 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.unix.org/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.ker‐
nel.org/doc/man-pages/reporting_bugs.html .
IEEE/The Open Group 2013 FMA(3P)
