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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);

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

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:

If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then

Domain Error The value of x*y+zis invalid, or the valuex*yis invalid andzis not a NaN.If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then errnoshall 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 errnoshall 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*yis invalid andzis a NaN.If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then errnoshall 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. errnoshall be set to [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the underflow floating-point exception shall be raised.

The following sections are informative.

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.

feclearexcept() ,fetestexcept() , the Base Definitions volume of IEEE Std 1003.1-2001, Section 4.18, Treatment of Error Conditions for Mathematical Functions,<math.h>

Portions of this text are reprinted and reproduced in electronic form from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology -- Portable Operating System Interface (POSIX), The Open Group Base Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of Electrical and Electronics Engineers, Inc and The Open Group. 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.opengroup.org/unix/online.html .

IEEE/The Open Group |
FMA (P) | 2003 |