New section: Checked arithmetic

[hyrodium]

• SaferIntegers.jl
• CheckedArithmetic.jl

[KronosTheLate]

Nice. The introduction could include examples to showcase the issue, such as:

"""
Some operations throw overflow warnings:

julia> factorial(21)  # Explicit overflow warning
ERROR: OverflowError: 21 is too large to look up in the table; consider using `factorial(big(21))` instead
Stacktrace:
 [1] factorial_lookup
   @ Base ./combinatorics.jl:19 [inlined]
 [2] factorial(n::Int64)
   @ Base ./combinatorics.jl:27
 [3] top-level scope
   @ REPL[28]:1

julia> parse(Int32, bitstring(typemax(Int64)))
ERROR: OverflowError: overflow parsing "0111111111111111111111111111111111111111111111111111111111111111"
Stacktrace:
 [1] tryparse_internal(::Type{Int32}, s::String, startpos::Int64, endpos::Int64, base_::Int64, raise::Bool)
   @ Base ./parse.jl:169
 [2] parse(::Type{Int32}, s::String; base::Nothing)
   @ Base ./parse.jl:254
 [3] parse(::Type{Int32}, s::String)
   @ Base ./parse.jl:253
 [4] top-level scope
   @ REPL[35]:1

However, these check slow down computation, and are therefore not done for simple operations like addition and exponentiation, as it would slow down all such computations:

julia> typemax(Int) + 1
-9223372036854775808

julia> 10 ^ round(log10(typemax(Int)), RoundUp)  # log10 returns float, no problem
1.0e19

julia> 10 ^ round(Int, log10(typemax(Int)), RoundUp)  # integer exponent and base -> integer result -> overflow
-8446744073709551616

Some issues can be solved by using BigInt and BigFloat, but there are still no guarantees. If you want to guarantee that overflow never occurs in your program, there are packages that can help. Options include:
"""