IntroductionThis library is intended as a drop-in replacement for all built-in
integer types in any program which must:be demonstrably and verifiably correct.detect every user error such as input, assignment, etc.be efficient as possible subject to the constraints above.ProblemArithmetic operations in C/C++ are NOT guaranteed to yield a correct
mathematical result. This feature is inherited from the early days of C.
The behavior of int, unsigned int and others
were designed to map closely to the underlying hardware. Computer hardware
implements these types as a fixed number of bits. When the result of
arithmetic operations exceeds this number of bits, the result will not be
arithmetically correct. The following example illustrates just one example
where this causes problems.int f(int x, int y){
// this returns an invalid result for some legal values of x and y !
return x + y;
}
It is incumbent upon the C/C++ programmer to guarantee that this
behavior does not result in incorrect or unexpected operation of the
program. There are no language facilities which implement such a
guarantee. A programmer needs to examine each expression individually to
know that his program will not return an invalid result. There are a
number of ways to do this. In the above instance,
INT32-C seems to recommend the following
approach:int f(int x, int y){
if (((y > 0) && (x > (INT_MAX - y)))
|| ((y < 0) && (x < (INT_MIN - y)))) {
/* Handle error */
}
return x + y;
}
This will indeed trap the error. However, it would be tedious and
laborious for a programmer to alter his code in this manner. Altering code
in this way for all arithmetic operations would likely render the code
unreadable and add another source of potential programming errors. This
approach is clearly not functional when the expression is even a little
more complex as is shown in the following example.int f(int x, int y, int z){
// this returns an invalid result for some legal values of x and y !
return x + y * z;
}
This example addresses only the problem of undefined/erroneous
behavior related to overflow of the addition operation as applied to the
type int. Similar problems occur with other built-in integer
types such as unsigned, long, etc. And it also
applies to other operations such as subtraction, multiplication etc. .
C/C++ often automatically and silently converts some integer types to
others in the course of implementing binary operations. Sometimes such
conversions can silently change arithmetic values which inject errors. The
C/C++ standards designate some behavior such as right shifting a negative
number as "implementation defined behavior". These days machines usually
do what the programmer expects - but such behavior is not guaranteed.
Relying on such behavior will create a program which cannot be guaranteed
to be portable. And then there is undefined behavior. In this case,
compiler writer is under no obligation to do anything in particular.
Sometimes this will unexpectedly break the program. At the very least, the
program is rendered non-portable. Finally there is the case of behavior
that is arithmetically wrong to begin with - for example divide by zero.
Some runtime environments will just terminate the program, others may
throw some sort of exception. In any case, the execution has failed in a
manner from which there is no recovery.All of the above conditions are obstacles to creation of a program
which will never fail. The Safe Numerics Library addresses all of these
conditions, at least as far as integer operations are concerned.Since the problems and their solution are similar, we'll confine the
current discussion to just the one example shown above.SolutionThis library implements special versions of int,
unsigned, etc. which behave exactly like the original ones
except that the results of these
operations are guaranteed to be either to be arithmetically correct or
invoke an error. Using this library, the above example would be rendered
as:#include <boost/safe_numerics/safe_integer.hpp>
using namespace boost::numeric;
safe<int> f(safe<int> x, safe<int> y){
return x + y; // throw exception if correct result cannot be returned
}
Library code in this document resides in the namespace
boost::numeric. This namespace has generally been
eliminated from text, code and examples in order to improve
readability of the text.The addition expression is checked at runtime or (if possible) at
compile time to trap any possible errors resulting in incorrect arithmetic
behavior. Arithmetic expressions will not produce an erroneous result.
Instead, one and only one of the following is guaranteed to occur.the expression will yield the correct mathematical
resultthe expression will emit a compilation error.the expression will invoke a runtime exception.In other words, the library absolutely
guarantees that no integer arithmetic expression will yield incorrect
results.How It WorksThe library implements special versions of int,
unsigned, etc. Named safe<int>,
safe<unsigned int> etc. These behave exactly like the
underlying types except that expressions
using these types fulfill the above guarantee. These "safe" types are
meant to be "drop-in" replacements for the built-in types of the same
name. So things which are legal - such as assignment of a
signed to unsigned value - are not trapped at
compile time as they are legal C/C++ code. Instead, they are checked at
runtime to trap the case where this (legal) operation would lead to an
arithmetically incorrect result.Note that the library addresses arithmetical errors generated by
straightforward C/C++ expressions. Some of these arithmetic errors are
defined as conforming to the C/C++ standards while others are not. So
characterizing this library as only addressing undefined behavior of C/C++
numeric expressions would be misleading.Facilities particular to C++14 are employed to minimize any runtime
overhead. In many cases there is no runtime overhead at all. In other
cases, a program using the library can be slightly altered to achieve the
above guarantee without any runtime overhead.Additional FeaturesOperation of safe types is determined by template parameters which
specify a pair of policy
classes which specify the behavior for type promotion and error
handling. In addition to the usage serving as a drop-in replacement for
standard integer types, users of the library can:Select or define an exception policy class to specify handling
of exceptions.Throw exception on runtime, trap at compile time if
possible.Trap at compile time all operations which could possibly
fail at runtime.Specify custom functions which should be called in case
errors are detected at runtime.Select or define a promotion policy class to alter the C/C++
type promotion rules. This can be used to Use C/C++ native type promotion rules so that, except
for throwing/trapping of exceptions on operations resulting in
incorrect arithmetic behavior, programs will operate
identically when using/not using safe types. This might be
used if safe types are only enabled during debug and
testing.Replace C/C++ native promotion rules with ones which are
arithmetically equivalent but minimize the need for runtime
checking of arithmetic results. Such a policy will effectively
change the semantics of a C++ program. It's not really C++ any
more. The program cannot be expected to function the same as
when normal integer types are used.Replace C/C++ native promotion rules with ones which
emulate other machine architectures. This is designed to
permit the testing of C/C++ code destined to be run on another
machine on one's development platform. Such a situation often
occurs while developing code for embedded systems.Enforce other program requirements using bounded integer
types. The library includes the types for ranges and literals.
Operations which violate these requirements will be trapped at
either compile time or runtime and not silently return invalid
values. These types can be used to improve program correctness and
performance.RequirementsThis library is composed entirely of C++ Headers. It requires a
compiler compatible with the C++14 standard.The following Boost Libraries must be installed in order to use this
librarymp11integerconfigtriboolenable_ifThe Safe Numerics library is delivered with an exhaustive
suite of test programs.ScopeThis library currently applies only to built-in integer types.
Analogous issues arise for floating point types but they are not currently
addressed by this version of the library. User or library defined types
such as arbitrary precision integers can also have this problem. Extension
of this library to these other types is not currently under development
but may be addressed in the future. This is one reason why the library
name is "safe numeric" rather than "safe integer" library.