The Open Group Base Specifications Issue 7
IEEE Std 1003.1, 2013 Edition
Copyright © 2001-2013 The IEEE and The Open Group

#### 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

> [CX] 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. [MX] 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
>   [MX] 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
>   [MX] 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
>   [MX] 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, fetestexcept

> XBD Treatment of Error Conditions for Mathematical Functions, <math.h>

#### CHANGE HISTORY

> First released in Issue 6. Derived from the ISO/IEC 9899:1999 standard.

#### Issue 7

> ISO/IEC 9899:1999 standard, Technical Corrigendum 2 #57 (SD5-XSH-ERN-69) is applied, adding a ``may fail'' range error for non-MX systems.

End of informative text.

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