```FMA(3P)                   POSIX Programmer's Manual                  FMA(3P)
```

## PROLOG         top

```       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         top

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

## SYNOPSIS         top

```       #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         top

```       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
operation: they 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.

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         top

```       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
implementation-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         top

```       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         top

```       None.
```

## APPLICATION USAGE         top

```       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         top

```       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. 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.
```

## FUTURE DIRECTIONS         top

```       None.
```

```       feclearexcept(3p), fetestexcept(3p)

The Base Definitions volume of POSIX.1‐2008, Section 4.19, Treatment
of Error Conditions for Mathematical Functions, math.h(0p)
```

```       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 Electrical 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 .