Euler Tools

Assortment of Ada functions to solve Project Euler problems.

Euler Tools is an Ada 2022 library of functions that contains usual mathematical functions and non-usual numeric functions, like concatenation of numbers, palindrome checking or the length (number of digits) of a number.

New functions are added to the library from each solved problem: common functionality that can be abstracted, and possibly reused in other problems, becomes an Euler Tools function.

For example, to solve problem 3 you need to deal with prime numbers and to check if a given number evenly divides another one. Also, to reduce the search space, divisors checked start with the squared root of a number. Thus, three functions are used from Euler Tools: Square_Root, Is_Divisor and Is_Prime.

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Current Status and Future Plans

Euler Tools is currently in its very early stage.

New functions are being added very often, some are re-implemented, some optimized, or specifications change according to some criteria. But to make things clear, the set of unit tests included in the library can be used to understand a function specification.

New Ada 2022 features are expected to be supported by compilers soon. Some features are really interesting to Euler Tools, like parallel blocks, and it will be used as they are available.

Ada pre- and post-conditions are used in some function specifications. The plan is to improve and generalize its use. SPARK is also planned to be used.

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Installation

Build

Use Alire to get and compile the library:

alr get euler_tools
cd euler_tools*
alr build

Unit tests

To compile and run the unit tests:

cd tests
alr build
./bin/euler_tools_tests

Traceability matrix of functions vs unit tests is provided here.

Examples

The directory examples contains solutions to some problems.

To compile these tests:

cd examples
alr build

Then check the bin directory to run the provided examples.

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Design

Euler Package

Main component of Euler Tools is a generic package, Euler_Package (<>), that can be instantiated with any integer type, from Integer to Long_Long_Long_Integer.

Some instantiations are provided as separate packages:

• package Euler_Tools is new Euler_Package (Integer)
• package Euler_Tools_Int1 is new Euler_Package (Long_Integer)
• package Euler_Tools_Int2 is new Euler_Package (Long_Long_Integer)
• package Euler_Tools_Int3 is new Euler_Package (Long_Long_Long_Integer)

Each platform provides different representation of type, ranging from 32 or 64 bits for Integer, or 128 bits for Long_Long_Long_Integer.

Each package provides also the Integer_Type that has been used to instantiate Euler_Package (<>). This is a convenient type to easily change from one package to another without having to rewrite the integer type used. For example, you can start solving a problem with Euler_Tools:

  with Text_IO;     use Text_IO;
  with Euler_Tools; use Euler_Tools;

  procedure Problem_42 is
     Answer : Integer_Type := Factorial (12);
  begin
     Put_Line ("Answer:" & Answer'Image);
  end Problem_42;

If later on you realize that Integer is not big enough, the you can try with a longer type simply by replacing the Euler package:

   with Text_IO;          use Text_IO;
   with Euler_Tools_Int3; use Euler_Tools_Int3;

   procedure Problem_42 is
      Answer : Integer_Type := Factorial (33);
   begin
      Put_Line ("Answer:" & Answer'Image);
   end Problem_42;

Other Packages

Other packages included in Euler Tools are:

• Euler_Calendar, that provides a function to get the weekday of a date (YYYY/MM/DD).
• Euler_Text, that implements a function that return a number written out in words.

Additional Types

Solving mathematical problems usually require not only Integer_Type, but more complex types. Euler Tools contains the following types for your convenience:

• List_Type is a list of Integer_Type. It is a doubly linked list, so elements can be visited in both directions (see Ada.Containers.Doubly_Linked_Lists).
• Set_Type is a set of Integer_Type. You can Insert new numbers, Include possibly repeated numbers, make it an Empty_Set, get the Length (cardinality) of a set, etc. It is an ordered set, so elements of a set are always visited in order (see Ada.Containers.Ordered_Sets).
• Numeral_Type is range 0 .. 9 (4 bits long), a subtype used in other types.
• Crumbled_Natural is an arbitrary long natural number composed as a vector of numerals. Contrast with Ada 2022 package Ada.Numerics.Big_Numbers.Big_Integers.
• Decimal_Division_Type is used to perform arbitrary precision divisions. For example, problem 26 requires really long divisions (spoiler: recurring cycle of $1/n$ contains 982 digits, for some $n<1000$).

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Contributions

Please feel free to

• Use Euler Tools to solve Project Euler or other mathematical problems: send us the link to you work and we'll it include in this section.
• Send contributions, ideas and suggestions to improve Euler Tools functions or implementations.

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License

MIT (c) 2023 Francesc Rocher