CheckedArithmetic

This package aims to make it easier to detect overflow in numeric computations. It exports two macros, @check and @checked, as well as functions accumulatortype and acc. Packages can add support for their own types to interact appropriately with these tools.

@checked converts arithmetic operators to their checked variants. For example,

@checked z = x + y

rewrites this expression as

z = Base.Checked.checked_add(x, y)

Note that this macro only operates at the level of surface syntax, i.e.,

@checked z = f(x) + f(y)

will not detect overflow caused by f.

The Base.Checked module defines numerous checked operations. These can be specialized for custom types.

@check performs an operation in two different ways, checking that both approaches agree. @check is primarily useful in tests.

For example,

d = @check ssd(a, b)

would perform ssd(a, b) with the inputs as given, and also compute ssd(asafe, bsafe) where asafe and bsafe are "safer" variants of a and b. It then tests whether the result obtained from the "safe" arguments is consistent with the result obtained from a and b. If the two differ to within the precision of the "ordinary" (unsafe) result, an error is thrown. Optionally, you can supply keywords accepted by isapprox:

@check foo(a) atol=1e-12

Packages can specialize CheckedArithmetic.safearg to control how asafe and bsafe are generated. To guard against oversights, safearg must be explicitly defined for each numeric type---the fallback method for safearg(::Number) is to throw an error.

These functions are useful for writing overflow-safe algorithms. accumulatortype(T) or accumulatortype(T1, T2...) takes types as input arguments and returns a type suitable for limited-risk arithmetic operations. acc(x) is just shorthand for convert(accumulatortype(typeof(x)), x).

You can also specialize on the operation. For example,

julia> accumulatortype(+, UInt8)
UInt64

julia> accumulatortype(-, UInt8)
Int64

If you're computing a sum-of-squares and want to make sure you algorithm is (reasonably) safe for an input array of UInt8 numbers, you might want to write that as

function sumsquares(A::AbstractArray)
    s = zero(accumulatortype(eltype(A)))
    for a in A
        s += acc(a)^2
    end
    return s
end