Specifications

These are some basic specifications.

apa::bint : Bitwise Not (~)

• The bitwise not (~) of bint is the same as Python’s not operator, or in general it performs a 2’s complement conversion.

  \[y = -(x+1)\]

  In bint This will be equivalent to adding 1 for the number member, then flipping the sign member to negative.

apa::bint’s bitwise logical &, |, ^ operators

• The other bitwise logical operators of bint (&, |, ^) applies a special 2’s complement conversion to negative bint parameters before applying the operators.

  If the output is negative we then again applies a special 2’s complement conversion.

  This special 2’s complement conversion is different from the bint::operator~, it involves padding the operands and the sign does not flip here.

  In general the output of these operators should be the same as python3’s bitwise logical operators.

apa::bint : Division

• The division operator of bint is more similar to C/C++ than in python. bint don’t apply a floor function to the quotient, instead it stops calculating the value after the decimal.

  To show the difference here is an example:

  • C/C++ & bint division output:

    \[-9/4 = -2\]

  • Python3 floor division output:

    \[-9//4 = -3\]

apa::bint : Modulo

• Since the division of bint is more similar to C/C++ the modulo output of bint in some cases for negative numbers will be different to the output of python’s modulo.

  • C/C++ & bint modulo output:

    \[-9 \ mod \ 4 = -1\]

  • Python3 modulo output:

    \[-9 \ mod \ 4 = 3\]

  This is because python uses the floor division to get the mod:

  \[remainder = a - b \lfloor a/b\rfloor\]

  To achieve a python similar modulo result in C++ we can use this operation instead:

    template<typename T>
    constexpr T mod(T num, T mod) {
        return ((num % mod) + mod) % mod;
    }
  

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