  Research project "Platform-independent approach to formal specification and
verification of standard mathematical functions" is aimed onto a development of
an incremental combined approach to the specification and verification of the
standard mathematical functions like sqrt, cos, sin, etc. Platform-independence
means that we attempt to design a relatively simple axiomatization of the
computer arithmetic in terms of real, rational, and integer arithmetic (i.e.
the fields R and Q of real and rational numbers, the ring Z of integers) but
don't specify neither base of the computer arithmetic, nor a format of numbers'
representation. Incrementality means that we start with the most
straightforward specification of the simplest easy to verify algorithm in real
numbers and finish with a realistic specification and a verification of an
algorithm in computer arithmetic. We call our approach combined because we
start with a manual (pen-and-paper) verification of some selected algorithm in
real numbers, then use these algorithm and verification as a draft and
proof-outlines for the algorithm in computer arithmetic and its manual
verification, and finish with a computer-aided validation of our manual proofs
with some proof-assistant system (to avoid appeals to "obviousness" that are
very common in human-carried proofs). In the paper we present first steps
towards a platform-independent incremental combined approach to specification
and verification of the standard functions cos and sin that implement
mathematical trigonometric functions cos and sin.
