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1.14 |
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29-Jul-2017 |
riastradh |
Clarify compile-time and run-time arithmetic safety assertions.
This is an experiment with a handful of macros for writing the
checks, most of which are compile-time:
MUL_OK(t, a, b) Does a*b avoid overflow in type t?
ADD_OK(t, a, b) Does a + b avoid overflow in type t?
TOOMANY(t, x, b, m) Are there more than m b-element blocks in x in type t?
(I.e., does ceiling(x/b) > m?)
Addenda that might make sense but are not needed here:
MUL(t, a, b, &p) Set p = a*b and return 0, or return ERANGE if overflow.
ADD(t, a, b, &s) Set s = a+b and return 0, or return ERANGE if overflow.
Example:
uint32_t a = ..., b = ..., y = ..., z = ..., x, w;
/* input validation */
error = MUL(size_t, a, b, &x);
if (error)
fail;
if (TOOMANY(uint32_t, x, BLKSIZ, MAX_NBLK))
fail;
y = HOWMANY(x, BLKSIZ);
if (z > Z_MAX)
fail;
...
/* internal computation */
__CTASSERT(MUL_OK(uint32_t, Z_MAX, MAX_NBLK));
w = z*y;
Obvious shortcomings:
1. Nothing checks your ctassert matches your subsequent arithmetic.
(Maybe we could have BOUNDED_MUL(t, x, xmax, y, ymax) with a
ctassert inside.)
2. Nothing flows the bounds needed by the arithmetic you use back
into candidate definitions of X_MAX/Y_MAX.
But at least the reviewer's job is only to make sure that (a) the
MUL_OK matches the *, and (b) the bounds in the assertion match the
bounds on the inputs -- in particular, the reviewer need not derive
the bounds from the context, only confirm they are supported by the
paths to it.
This is not meant to be a general-purpose proof assistant, or even a
special-purpose one like gfverif <http://gfverif.cryptojedi.org/>.
Rather, it is an experiment in adding a modicum of compile-time
verification with a simple C API change.
This also is not intended to serve as trapping arithmetic on
overflow. The goal here is to enable writing the program with
explicit checks on input and compile-time annotations on computation
to gain confident that overflow won't happen in the computation.
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