cfloating-pointlanguage-lawyerterminologyfma

Terminology: why "floating multiply-add" instead of "fused multiply-add"?


C11 (and newer):

7.12.13 Floating multiply-add

IEEE 754-2008:

fused multiply add, fusedMultiplyAdd

Wikipedia:

fused multiply-add

Why C11 (and newer) uses "floating multiply-add" instead of "fused multiply-add"?

Where this "floating" comes from?


Solution

  • This is most likely a mistake from the technical report which introduced these arithmetic operations to the language

    With some detective work we may dig down to the root source of C11's "Floating multiply-add" and identify a discrepancy that very much hints at this naming being just an oversight. WG14's N1154 (Extension for the programming language C to support decimal floating-point arithmetic) from 2006 idiomatically describe the operation as a fused multiply-add arithmetic operation:

    9 Arithmetic Operations

    [...]

    9.2 Functions

    The decimal floating point operations square root, min, max, fused multiply-add and remainder, which are defined in IEEE 754R, are implemented as library functions.

    Only to replace (arguably by mistake) fused by floating in the library synopsis for the associated function prototypes. An oversight arguably easily missed in review of the library synopsis as f in the abbreviated fmad names in the containing function prototypes could easily be misinterpreted as "floating" as opposed to its actual meaning "fused".

    10 Library

    10.1 Decimal mathematics <math.h>

    The list of elementary functions specified in the mathematics library is extended to handle decimal floating-point types. These include functions specified in 7.12.4, 7.12.5, 7.12.6, 7.12.7, 7.12.8, 7.12.9, 7.12.10, 7.12.11, 7.12.12, and 7.12.13

    [...]

    Suggested changes to C99:

    Add the following list of function prototypes to the synopsis of the respective subclauses:

    [...]

    7.12.13 Floating multiply-add

    _Decimal64 fmad64(_Decimal64 x, _Decimal64 y, _Decimal64 z);
    _Decimal32 fmad32(_Decimal32 x, _Decimal32 y, _Decimal32 z); 
    _Decimal128 fmad128(_Decimal128 x, _Decimal128 y, _Decimal128 z);