Task: Modular arithmetic

C: #include <stdio.h>

struct ModularArithmetic {
    int value;
    int modulus;
};

struct ModularArithmetic make(const int value, const int modulus) {
    struct ModularArithmetic r = { value % modulus, modulus };
    return r;
}

struct ModularArithmetic add(const struct ModularArithmetic a, const struct ModularArithmetic b) {
    return make(a.value + b.value, a.modulus);
}

struct ModularArithmetic addi(const struct ModularArithmetic a, const int v) {
    return make(a.value + v, a.modulus);
}

struct ModularArithmetic mul(const struct ModularArithmetic a, const struct ModularArithmetic b) {
    return make(a.value * b.value, a.modulus);
}

struct ModularArithmetic pow(const struct ModularArithmetic b, int pow) {
    struct ModularArithmetic r = make(1, b.modulus);
    while (pow-- > 0) {
        r = mul(r, b);
    }
    return r;
}

void print(const struct ModularArithmetic v) {
    printf("ModularArithmetic(%d, %d)", v.value, v.modulus);
}

struct ModularArithmetic f(const struct ModularArithmetic x) {
    return addi(add(pow(x, 100), x), 1);
}

int main() {
    struct ModularArithmetic input = make(10, 13);
    struct ModularArithmetic output = f(input);

    printf("f(");
    print(input);
    printf(") = ");
    print(output);
    printf("\n");

    return 0;
}










Fortran: module modular_arithmetic
  implicit none

  type :: modular
     integer :: val
     integer :: modulus
  end type modular

  interface operator(+)
     module procedure modular_modular_add
     module procedure modular_integer_add
  end interface operator(+)

  interface operator(**)
     module procedure modular_integer_pow
  end interface operator(**)

contains

  function modular_modular_add (a, b) result (c)
    type(modular), intent(in) :: a
    type(modular), intent(in) :: b
    type(modular) :: c

    if (a%modulus /= b%modulus) error stop
    c%val = modulo (a%val + b%val, a%modulus)
    c%modulus = a%modulus
  end function modular_modular_add

  function modular_integer_add (a, i) result (c)
    type(modular), intent(in) :: a
    integer, intent(in) :: i
    type(modular) :: c

    c%val = modulo (a%val + i, a%modulus)
    c%modulus = a%modulus
  end function modular_integer_add

  function modular_integer_pow (a, i) result (c)
    type(modular), intent(in) :: a
    integer, intent(in) :: i
    type(modular) :: c

    
    
    
    

    integer :: modulus
    integer :: base
    integer :: exponent

    modulus = a%modulus
    exponent = i

    if (modulus < 1) error stop
    if (exponent < 0) error stop

    c%modulus = modulus
    if (modulus == 1) then
       c%val = 0
    else
       c%val = 1
       base = modulo (a%val, modulus)
       do while (exponent > 0)
          if (modulo (exponent, 2) /= 0) then
             c%val = modulo (c%val * base, modulus)
          end if
          exponent = exponent / 2
          base = modulo (base * base, modulus)
       end do
    end if
  end function modular_integer_pow

end module modular_arithmetic




#define f(x) ((x)**100 + (x) + 1)

program modular_arithmetic_task
  use, intrinsic :: iso_fortran_env
  use, non_intrinsic :: modular_arithmetic
  implicit none

  type(modular) :: x, y

  x = modular(10, 13)
  y = f(x)

  write (*, '("    modulus 13:  ", I0)') y%val
  write (*, '("floating point:  ", E55.50)') f(10.0_real64)

end program modular_arithmetic_task