# 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(doublex, doubley, doublez); float fmaf(floatx, floaty, floatz); long double fmal(long doublex, long doubley, long doublez);

# 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 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

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

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.- 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 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

None.# SEE ALSO

*,*

*feclearexcept*()*The Base Definitions volume of POSIX.1‐2008,*

*fetestexcept*()*Section 4.19*,

*Treatment of Error Conditions for Mathematical Functions*,

**<math.h>**