Editing Multiply–accumulate operation (section)

==In floating-point arithmetic==
When done with [[integer]]s, the operation is typically exact (computed [[modular arithmetic|modulo]] some [[power of two]]). However, [[Floating-point arithmetic|floating-point]] numbers have only a certain amount of mathematical [[arithmetic precision|precision]]. That is, digital floating-point arithmetic is generally not [[associativity|associative]] or [[distributivity|distributive]]. (See {{slink|Floating-point arithmetic#Accuracy problems}}.)
Therefore, it makes a difference to the result whether the multiply–add is performed with two roundings, or in one operation with a single rounding (a fused multiply–add). [[IEEE 754-2008]] specifies that it must be performed with one rounding, yielding a more accurate result.<ref>{{cite web |url=https://developer.nvidia.com/sites/default/files/akamai/cuda/files/NVIDIA-CUDA-Floating-Point.pdf |title=Precision & Performance: Floating Point and IEEE 754 Compliance for NVIDIA GPUs |publisher=nvidia |first1=Nathan |last1=Whitehead |first2=Alex |last2=Fit-Florea |year=2011 |access-date=2013-08-31}}</ref>