  Recent technological advances allow us to view chemical mass-action systems
as analog computers. In this context, the inputs to a computation are encoded
as initial values of certain chemical species while the outputs are the
limiting values of other chemical species. In this paper, we design chemical
systems that carry out the elementary arithmetic computations of:
identification, inversion, $m$th roots (for $m \ge 2$), addition,
multiplication, absolute difference, rectified subtraction over non-negative
real numbers, and partial real inversion over real numbers. We prove that these
``elementary modules'' have a speed of computation that is independent of the
inputs to the computation. Moreover, we prove that finite sequences of such
elementary modules, running in parallel, can carry out composite arithmetic
over real numbers, also at a rate that is independent of inputs. Furthermore,
we show that the speed of a composite computation is precisely the speed of the
slowest elementary step. Specifically, the scale of the composite computation,
i.e. the number of elementary steps involved in the composite, does not affect
the overall asymptotic speed -- a feature of the parallel computing nature of
our algorithm. Our proofs require the careful mathematical analysis of certain
non-autonomous systems, and we believe this analysis will be useful in
different areas of applied mathematics, dynamical systems, and the theory of
computation. We close with a discussion on future research directions,
including numerous important open theoretical questions pertaining to the field
of computation with reaction networks.
