Is there a standard name for the function $f_m(x,y) = mx + y$? When formalizing the base-$m$ positional numeral system, the function $$f_m : \mathbb{N} \times \mathbb{N} \rightarrow \mathbb{N}$$ $$x,y \mapsto mx + y$$ is extremely useful. For example, observe that $$365 = f_{10}(f_{10}(3,6),5).$$

Question. Is there an accepted name for the function $f_m$ either in general, or else in the the case $m=2$, or in the case $m = 10$, or else in the case $m=2^{64}$?

Motivation. I have plans to use the function $f_{2^{64}}$ in the context of a term-rewriting system that's designed to implement basic arithmetic on a standard $64$-bit computer. More generally, the idea is to specify a whole family of term-rewriting systems based on $f_m$, one for each possible value of $m$. By choosing $m := 2^n$, where $n$ is the native word size of the target architecture, it should be possible to obtain a system that implements arithmetic with large integers relatively efficiently, and whose correctness is extremely easy to prove (because every step involves rewriting some terms based on accepted and provably correct principles of mathematics.) To do this, I have to pick a name for this function, and I guess it's better to use the standard name if there is one.

The inverse of the function you gave $$f_m: \mathbb{N} \to \mathbb{N} \times \mathbb{N}$$ $$a \mapsto (b,r) \backepsilon a=bm + r $$
is called Euclidean division so logically your function should be called Euclidean multiplication.  Though i've never heard that term used. 
