fmaf

fmaf refers to the single-precision fused multiply-add operation in floating-point arithmetic. It computes the expression (x * y) + z with a single rounding, using one IEEE 754-compliant result rather than performing the multiplication and addition as separate steps that produce two roundings.

In the C standard library, fmaf is defined as a function that takes three float arguments and returns a float: float fmaf(float x, float y, float z). It provides the fused multiply-add operation at the single-precision level, complementing the double-precision fma function for double types and the long double variant fmal. Many compilers expose fmaf under the math library and also map it to hardware FMA instructions where available.

The main advantages of fmaf are improved numerical accuracy and potential performance benefits. By performing the multiplication and addition with one rounding, it minimizes rounding errors that arise from separate operations, making it especially useful in polynomial evaluation, dot products, and other numerically sensitive computations. Hardware that includes an FMA unit can execute fmaf efficiently, often with better throughput than separate multiply-then-add instructions. Conversely, on platforms without native FMA support, an implementation may emulate fmaf, which can involve additional overhead and may not perfectly match the precision of true fused hardware.

Use of fmaf is common in numerical software that prioritizes precision and performance for single-precision arithmetic. It is part of the broader family of fused multiply-add operations, alongside the double-precision and extended-precision variants, which share the same mathematical principle but operate on different data types.