Tutorial 8: Custom Units for Dimensionless Counters

This tutorial demonstrates how to use mp-units to create strongly-typed wrappers for common dimensionless counters in business and logistics, such as units and cartons. These are not related to physics, but benefit from type safety and automatic conversions.

Scenario

A small electronics factory produces light bulbs. The production line outputs 3 units every minute, operates 14 hours per day, 5 days per week. Products are packed into cartons (1 carton = 12 units). For shipping, each truck can carry a fixed number of cartons.

Your task

1. Define custom dimensionless units for unit and carton with fixed compile-time scaling (1 carton = 12 units).
2. Given:
   • Production rate: 3 * unit / min
   • Working hours per day: 14 * h
   • Working days per week: 5
   • Truck capacity: 60 * carton / truck
3. Calculate:
   • Total weekly production in units and cartons
   • Number of cartons needed for weekly production (every carton should be full of goods)
   • Number of trucks required for shipment
4. Use strongly-typed quantities and automatic conversions for all calculations. Show how type safety prevents scaling errors.

// ce-embed height=650 compiler=clang2110 flags="-std=c++23 -stdlib=libc++ -O3"
#include <mp-units/core.h>
#include <mp-units/systems/si.h>
#include <iostream>

namespace electronics {

// TODO: replace with strongly typed units
constexpr int unit = 1;
constexpr int carton = 12 * unit;
constexpr int truck = 1;

}

int main()
{
  using namespace electronics;
  using namespace mp_units;
  using namespace mp_units::si::unit_symbols;

  quantity production_rate = 3. * unit / min;
  quantity hours_per_day = 14 * h;
  quantity days_per_week = 5;
  quantity truck_capacity = 60 * carton / truck;

  quantity weekly_production = production_rate * hours_per_day * days_per_week;

  std::cout << "Weekly production:\n"
            // TODO: use correct units below
            << "- " << weekly_production.numerical_value_in(one) << " unit\n"
            << "- " << weekly_production.numerical_value_in(one) / carton << " carton\n";

  // TODO: use mp-units math functions instead
  quantity cartons_needed = std::floor((weekly_production / carton).numerical_value_in(one));
  std::cout << "Cartons needed for packaging: " << cartons_needed << "\n";

  quantity trucks_needed = std::ceil((weekly_production / truck_capacity).numerical_value_in(one));
  std::cout << "Trucks needed for shipment: " << trucks_needed << "\n";

  // TODO: the below should not compile
  quantity bad1 = 1 * unit + 1;
  quantity bad2 = 1 * unit + 1 * truck;
}

Solution

#include <mp-units/core.h>
#include <mp-units/systems/si.h>
#include <iostream>

namespace electronics {

inline constexpr struct unit final : mp_units::named_unit<"unit", kind_of<dimensionless>> {} unit;
inline constexpr struct carton final : mp_units::named_unit<"carton", mp_units::mag<12> * unit> {} carton;
inline constexpr struct truck final : mp_units::named_unit<"truck", kind_of<dimensionless>> {} truck;

}

int main()
{
  using namespace electronics;
  using namespace mp_units;
  using namespace mp_units::si::unit_symbols;

  quantity production_rate = 3 * unit / min;
  quantity hours_per_day = 14 * h;
  quantity days_per_week = 5;
  quantity truck_capacity = 60 * carton / truck;

  quantity weekly_production = production_rate * hours_per_day * days_per_week;

  std::cout << "Weekly production:\n"
            << "- " << weekly_production.in(unit) << "\n"
            << "- " << weekly_production.in(carton) << "\n";

  quantity cartons_needed = floor<carton>(weekly_production);
  std::cout << "Cartons needed for packaging: " << cartons_needed << "\n";

  quantity trucks_needed = ceil<truck>(weekly_production / truck_capacity);
  std::cout << "Trucks needed for shipment: " << trucks_needed << "\n";

  // quantity bad1 = 1 * unit + 1;          // does not compile
  // quantity bad2 = 1 * unit + 1 * truck;  // does not compile
}

Takeaways

• Strongly-typed wrappers for dimensionless counters prevent scaling and mixing errors.
• Automatic conversions make calculations safe and clear.
• This approach is valuable in production, logistics, and order processing domains.
• mp-units is not limited to physics—use it for any domain where numeric confusion is possible.