IEEE Std 1003.1, 2013 Edition

Copyright © 2001-2013 The IEEE and The Open Group

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

#include <math.h>

double fma(doublex, doubley, doublez);

float fmaf(floatx, floaty, floatz);

long double fmal(long doublex, long doubley, long doublez);

^{[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

errnoto zero and callfeclearexcept(FE_ALL_EXCEPT) before calling these functions. On return, iferrnois non-zero orfetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has occurred.

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

xoryare NaN, a NaN shall be returned.If

xmultiplied byyis an exact infinity andzis 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

xandyis infinite, the other is zero, andzis 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

xandyis infinite, the other is zero, andzis a NaN, a NaN shall be returned and a domain error may occur.If

x*yis not 0*Inf nor Inf*0 andzis a NaN, a NaN shall be returned.

These functions shall fail if:

- Domain Error
^{[MX]}The value ofx*y+zis invalid, or the valuex*yis invalid andzis not a NaN.If the integer expression (

math_errhandling& MATH_ERRNO) is non-zero, thenerrnoshall 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, thenerrnoshall 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 valuex*yis invalid andzis a NaN.If the integer expression (

math_errhandling& MATH_ERRNO) is non-zero, thenerrnoshall 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, thenerrnoshall 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, thenerrnoshall be set to [ERANGE]. If the integer expression (math_errhandling& MATH_ERREXCEPT) is non-zero, then the overflow floating-point exception shall be raised.

None.

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.

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 thefma() function guarantees its use where desired. Many current machines provide hardware floating multiply-add instructions; software implementation can be used for others.

None.

XBD

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

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

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.

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