Base converting

unit baseConvert;

// for exceptions
{$mode objfpc}

// P U B L I C ======================================================== //
interface
 
const
    /// list of symbols for integer representations
    digits = '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ';

function intToBaseStr(value: longword; const base: cardinal = 10): string;
function baseStrToInt(const value: string; const base: cardinal = 10): longword;

function baseToBase(
        const value: string;
        const interpretation: cardinal = 10;
        const base: cardinal = 10
    ): string;
 

// P R I V A T E ====================================================== //
implementation
 
uses
    // math unit for inRange and divMod routines
    math,
    // sysutils unit for ERangeError exception
    sysutils;

resourceString
    /// base not within range of available symbols
    errInvalidBase = '↯ b = %0:d! ⇒ b ∉ [%1:d, %2:d]';
    /// supplied character not within domain
    errInvalidSymbol = '↯ v(''%0:s'')↑; b = %1:d';
 
(**
    \brief expresses the value in the desired base
    
    \param value the value to convert
    \param base
    
    \return a string representing the number in given base
*)
function intToBaseStr(value: longword; const base: cardinal = 10): string;
var
    remainder: longword;
begin
    // validity of the base
    if not inRange(base, 2, length(digits)) then
    begin
        raise eRangeError.createFmt(errInvalidBase, [base, 2, length(digits)]);
    end;
    
    // decomposing the value: reverse Horner-scheme
    // The repeat-statement takes the value 0 into account.
    result := emptyStr;
    repeat
    begin
        divMod(value, base, value, remainder);
        // prepend value: intermediate results are read backwards
        result := digits[remainder + 1] + result;
    end
    until value = 0;
end;
 
(**
    \brief transforms the string of a number
           expressed in the parameter base
           into the equivalent integer
    
    \param value the representation of the integer
    \param base assume string is in given base
    
    If the string is empty, the result is 0.
    
    Caution:
    No verification of integer overflows.
    Reasonable values have to be used.
    
    \return the integer
*)
function baseStrToInt(const value: string; const base: cardinal = 10): longword;
var
    symbol: char;
    // beware, cardinal is _non-negative_
    digit: cardinal;
begin
    result := 0;
    // Horner-scheme
    for symbol in value do
    begin
        // determine ordinal value of current symbol
        digit := pos(symbol, digits);
        // If symbol wasn't found, pos returns 0.
        // Or possibly the symbol isn't known in the base.
        if not inRange(digit, 1, base) then
        begin
            raise eRangeError.createFmt(errInvalidSymbol, [symbol, base]);
        end;
        // e.g. the symbol '0' is the _first_ character in digits
        // thus the pos function returned 1 => here we subtract one
        dec(digit);
        result := result * base + digit;
    end;
end;
 
(**
    \brief direct conversion of number expressed in one base to another
    
    \param value the value to convert from
    \param interpretation the base to interpret the value as
    \param base the base to convert to
*)
function baseToBase(
        const value: string;
        const interpretation: cardinal = 10;
        const base: cardinal = 10
    ): string;
begin
    // the case interpretation = base
    // intentionally does not have special treatment for unit tests
    result := intToBaseStr(baseStrToInt(value, interpretation), base);
end;

// end of unit
end.

#: baseconvert:errinvalidbase
msgid "\342\206\257\302\240b\302\240= %0:d!\302\240\342\207\222 b\302\240\342\210\211\302\240[%1:d, %2:d]"
msgstr "Base %0:d is invalid. It must be between %1:d and %2:d."

#: baseconvert:errinvalidsymbol
msgid "\342\206\257\302\240v('%0:s')\342\206\221; b\302\240= %1:d"
msgstr "The symbol '%0:s' has an unacceptable value for base = %1:d."

#: baseconvert:errinvalidbase
msgid "\342\206\257\302\240b\302\240= %0:d!\302\240\342\207\222 b\302\240\342\210\211\302\240[%1:d, %2:d]"
msgstr "Die Basis %0:d ist ungültig. Sie muß zwischen %1:d und %2:d sein."

#: baseconvert:errinvalidsymbol
msgid "\342\206\257\302\240v('%0:s')\342\206\221; b\302\240= %1:d"
msgstr "Der Zeichenwert von '%0:s' ist ungültig für Zahlen der Basis %1:d."

#: baseconvert:errinvalidbase
msgid "\342\206\257\302\240b\302\240= %0:d!\302\240\342\207\222 b\302\240\342\210\211\302\240[%1:d, %2:d]"
msgstr "Base %0:d invalide, elle doit être comprise entre %1:d et %2:d."

#: baseconvert:errinvalidsymbol
msgid "\342\206\257\302\240v('%0:s')\342\206\221; b\302\240= %1:d"
msgstr "Mauvais chiffre '%0:s' dans la valeur, base = %1:d."