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FMA(3P) POSIX Programmer's Manual FMA(3P)PROLOGThis manual page is part of the POSIX Programmer's Manual. The Linux implementation of this interface may dif- fer (consult the corresponding Linux manual page for details of Linux behavior), or the interface may not be implemented on Linux.NAMEfma, fmaf, fmal - floating-point multiply-addSYNOPSIS#include<math.h>doublefma(doublex,doubley,doublez);floatfmaf(floatx,floaty,floatz);longdoublefmal(longdoublex,longdoubley,longdoublez);DESCRIPTIONThese 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 seterrnoto zero and callfeclearex-cept(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.RETURNVALUEUpon successful completion, these functions shall return (x*y) +z, rounded as one ternary operation. Ifxoryare NaN, a NaN shall be returned. Ifxmultiplied 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 ofxandyis 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 ofxandyis infinite, the other is zero, andzis a NaN, a NaN shall be returned and a domain error may occur. Ifx*yis not 0*Inf nor Inf*0 andzis a NaN, a NaN shall be returned.ERRORSThese functions shall fail if: Domain Error 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 excep- tion 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 excep- tion shall be raised. These functions may fail if: Domain Error 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 excep- tion 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.Thefollowingsectionsareinformative.EXAMPLESNone.APPLICATIONUSAGEOn error, the expressions (math_errhandling & MATH_ERRNO) and (math_errhandling & MATH_ERREXCEPT) are indepen- dent of each other, but at least one of them must be non-zero.RATIONALEIn 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.FUTUREDIRECTIONSNone.SEEALSOfeclearexcept(),fetestexcept(), the Base Definitions volume of IEEE Std 1003.1-2001, Section 4.18, Treatment of Error Conditions for Mathematical Functions,<math.h>COPYRIGHTPortions of this text are reprinted and reproduced in electronic form from IEEE Std 1003.1, 2003 Edition, Stan- dard for Information Technology -- Portable Operating System Interface (POSIX), The Open Group Base Specifica- tions 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 Stan- dard, 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 2003 FMA(3P)