ZeCalculator

ZeCalculator is a C++20 library for parsing and computing mathematical expressions and objects.

Features

• Parse and compute math objects defined through a simple equation of the type <object declaration> = <math expression>
  • Multi-variable functions e.g. f(x, y) = cos(x) * sin(y)
  • Global Variables: functions without arguments, e.g. my_var = f(1, 1)
  • Global constants: simple valued e.g. my_constant = 1.2
• Handle elegantly wrong math expressions
  • No exceptions (only used when the user does something wrong)
  • Give meaningful error messages: what went wrong, on what part of the equation
• Has no dependencies for easy packaging
• Fast repetitive evaluation of math objects.
• Know dependencies between objects (which object calls which other objects)

Example code

#include <zecalculator/zecalculator.h>
#include <zecalculator/test-utils/print-utils.h>

using namespace zc;
using namespace tl;
using namespace std;

double square(double x) { return x * x; }

int main()
{
  rpn::MathWorld world;

  // Notes about adding a math object to a math world:
  // - Each added object exists only within the math world that creates it
  // - Adding a math object returns a DynMathObject reference that is essentially an expected<variant, error>
  //   with some helper functions.
  //   - the variant contains all the possible objects: function, sequence, global constant, cpp function
  //   - the error expresses what went wrong in adding the object / parsing the equation
  rpn::DynMathObject& obj1 = world.new_object();

  // Assign a one parameter function named "f"
  // Note that 'my_constant' is only defined later
  // - this function's state will be updated once 'my_constant' is defined
  // - (re)defining objects within a math world can potentially modify every other objects
  obj1 = "f(x) = x + my_constant + cos(math::pi)";

  // We can query the direct dependencies of any object: name, type, and where in the equation
  // Note: only Function and Sequence instances with a valid equation return a non-empty set
  assert(bool(obj1.direct_dependencies()
              == deps::Deps{{"my_constant", {deps::Dep::VARIABLE, {11}}},
                            {"cos", {deps::Dep::FUNCTION, {25}}},
                            {"math::pi", {deps::Dep::VARIABLE, {29}}}}));

  // the expected should hold an error since 'my_constant' is undefined at this point
  assert(not obj1.has_value()
         and obj1.error()
               == Error::undefined_variable(parsing::tokens::Text{"my_constant", 11},
                                            "f(x) = x + my_constant + cos(math::pi)"));

  rpn::DynMathObject& obj2 = world.new_object();

  // Assign a global constant called "my_constant" with an initial value of 3.0
  obj2 = "my_constant = 3.0";

  // now that 'my_constant' is defined, 'obj1' gets modified to properly hold a function
  // Note that assigning to an object in the MathWorld may affect any other object
  // -> Assigning to objects is NOT thread-safe
  assert(obj1.holds<rpn::Function>());

  // We can evaluate 'obj1'
  // note: we could also do it when 'my_constant' was undefined,
  //       in that case the result would be the same error as above
  expected<double, Error> eval = obj1(1.0);

  // Notes:
  // - We know the expression is correct, otherwise the call `.value()` will throw
  // - The error can be recovered with '.error()`
  // - To know if the result is correct
  //   - call `.has_value()`
  //   - use the `bool()` operator on 'eval'
  assert(eval.value() == 3);

  // add a single argument function 'g' to the world
  world.new_object() = "g(z) = 2*z + my_constant";

  // assign a new equation to 'obj1'
  // - Now it's the Fibonacci sequence called 'u'
  // - we can force the parser to interpret it as a sequence
  //   - unneeded here, just for demo
  //   - the object will contain an error if the equation doesn't fit with the type asked for
  //     - even if the equation is a valid e.g. a GlobalConstant expression
  obj1 = As<rpn::Sequence>{"u(n) = 0 ; 1 ; u(n-1) + u(n-2)"};

  // should hold a Sequence now
  assert(obj1.holds<rpn::Sequence>());

  // evaluate function again and get the new value
  assert(obj1(10).value() == 55);

  // C++ double(double...) functions can also be registered in a world
  auto& obj3 = world.new_object();
  obj3 = CppFunction{"square", square};

  assert(world.evaluate("square(2)").value() == 4.);

  // ======================================================================================

  // the underlying objects can be retrieved either by using the fact that
  // DynMathObject publicly inherits expected<variant, error> or the 'value_as' helper function:
  // - "value" prefix just like expected::value, i.e. can throw
  // - "value_as" as a wrapper to std::get<>(expected::value), can throw for two different reasons
  //   - the expected has an error
  //   - the alternative asked is not the actual one held by the variant
  [[maybe_unused]] rpn::Sequence& u = obj1.value_as<rpn::Sequence>();
  [[maybe_unused]] GlobalConstant& my_constant = obj2.value_as<GlobalConstant>();

  // each specific math object has extra public methods that may prove useful

  return 0;
}

More examples of what the library can do are in the test folder.

Documentation

Classes within header files are fully documented.

Overview:

1. The entry-point class is MathWorld

   rpn::MathWorld mathworld;

   • Within the same MathWorld instance, objects can "see" and "talk" to each other.
   • Every instance of MathWorld is filled with the usual functions and constants, see builtin.h.
   • Stores its objects in a container of zc::DynMathObject
     • Does not invalidate references to unaffected zc::DynMathObject instances it contains when growing/shrinking
     • When adding an object, the math world returns a zc::DynMathObject&, and that can be used as a "permanent handle"

       rpn::DynMathObject& obj = mathworld.new_object();

2. DynMathObject is essentially (inherits) an std::expected<std::variant<alternative...>, zc::Error>
   • Has the std::expected public methods
     • bool has_value() to know if it's currently holding an std::variant
     • zc::Error error() to retrieve the error, when it's in an error state
     • std::variant<alternative...>& value() to retrieve the variant (with check)
     • std::variant<alternative...>& operator * () to retrieve the variant (without check)
   • Some extra helper methods
     • bool holds<T> to know if it's in a good state, and the variant holds the alternative T
     • T& value_as<T> to retrieve a specific alternative of the variant
   • Can be assigned, using operator =, equations or math objects.
     • CppFunction

       double square(double x) { return x * x; }
       // ...
       obj = zc::CppFunction{"square", square};

     • Function

       // automatic type deduction
       obj = "f(x) = cos(x)";
       // or force type
       obj = As<rpn::Function>{"f(x) = cos(x)"};

     • Sequence

       // needs forcing the type, automatic type deduction would otherwise deduce a zc::Function
       obj = As<rpn::Sequence>{"u(n) = n"};
       // or sequence with first values, the last expression is the generic expression
       obj = "fibonacci(n) = 0 ; 1 ; fibonacci(n-1) + fibonacci(n-2)"

     • GlobalConstant

       // defined through an equation of type "name = number"
       obj = "pi = 3.14";
       // or assigned directly without the need of parsing
       obj = zc::GlobalConstant{"pi", 3.14};

   • Can be evaluated

     tl::expected<double, zc::Error> res1 = obj(1.0);
     tl::expected<double, zc::Error> res2 = obj.evaluate(12.0);

3. Error messages when expressions have faulty syntax or semantics are expressed through the zc::Error class:
   • If it is known, gives what part of the equation raised the error with the token member, of the type zc::tokens::Text
   • If it is known, gives the type of error.
4. Two namespaces are offered, that express the underlying representation of the parsed math objects
   • zc::fast::: using the abstract syntax tree representation (AST)
   • zc::rpn::: using reverse polish notation (RPN) / postfix notation in a flat representation in memory.
     • Generated from the fast representation, but the time taken by the extra step is negligible (see results of the test "AST/FAST/RPN creation speed")
     • Has faster evaluation

Benchmarks

There is for now one benchmark defined in the tests, called "parametric function benchmark" in the file test/function_test.cpp, that computes the average evaluation time of the function f(x) = 3*cos(t*x) + 2*sin(x/t) + 4, where t is a global constant, in ast vs rpn vs c++.

The current results are (AMD Ryzen 5950X, -march=native -O3 compile flags)

• g++ 13.2.1 + libstdc++ + ld.bfd 2.41.0
  • ast: 270ns ± 5ns
  • rpn: 135ns ± 5ns
  • c++: 75ns ± 5ns
• clang++ 17.0.6 + libc++ + ld.lld 17.0.6
  • ast: 245ns ± 5ns
  • rpn: 140ns ± 5ns
  • c++: 75ns ± 5ns

Benchmark code snippet

"parametric function benchmark"_test = []<class StructType>()
{
  constexpr auto duration = nanoseconds(500ms);
  {
    constexpr parsing::Type type = std::is_same_v<StructType, FAST_TEST> ? parsing::Type::FAST : parsing::Type::RPN;
    constexpr std::string_view data_type_str_v = std::is_same_v<StructType, FAST_TEST> ? "FAST" : "RPN";

    MathWorld<type> world;
    auto& t = world.add("t = 1").template value_as<GlobalConstant>();
    auto& f = world.add("f(x) =3*cos(t*x) + 2*sin(x/t) + 4").template value_as<Function<type>>();

    double x = 0;
    double res = 0;
    size_t iterations =
      loop_call_for(duration, [&]{
        res += f(x).value();
        x++;
        t += 1;
    });
    std::cout << "Avg zc::Function<" << data_type_str_v << "> eval time: "
              << duration_cast<nanoseconds>(duration / iterations).count() << "ns"
              << std::endl;
    std::cout << "dummy val: " << res << std::endl;
  }
  {
    double cpp_t = 1;
    auto cpp_f = [&](double x) {
      return 3*cos(cpp_t*x) + 2*sin(x/cpp_t) + 4;
    };

    double x = 0;
    double res = 0;
    size_t iterations =
      loop_call_for(duration, [&]{
        res += cpp_f(x);
        iterations++;
        x++;
        cpp_t++;
    });
    std::cout << "Avg C++ function eval time: " << duration_cast<nanoseconds>(duration/iterations).count() << "ns" << std::endl;
    std::cout << "dummy val: " << res << std::endl;

  }

} | std::tuple<FAST_TEST, RPN_TEST>{};

How to build

The project uses the meson build system. Being header-only, it does not have a shared library to build: downstream projects only need the headers

How to run tests

To build tests

git clone https://github.com/AdelKS/ZeCalculator
cd ZeCalculator
meson setup build -D test=true
cd build
meson compile

Once the library is built, all tests can simply be run with

meson test

in the build folder.

How to install

Once the library is built (see above), you can install it by running

meson install

in the build folder.