FileMaker Pro Custom Functions

/* CUSTOM FUNCTION: BaseConvert ( string ; baseFrom ; baseTo ) © 2008 Debi Fuchs of Aptworks Consulting, debi@aptworks.com Convert a number (up to 10 billion) from one base to another. EXAMPLES: BaseConvert( "F1"; 16; 2 ) // --> "11110001" BaseConvert( -5; 10; 2 ) // --> "-101" BaseConvert( 255; 10; 16 ) // --> "FF" BaseConvert( "-101" ; 2; 10 ) // --> "-5" BaseConvert( -101 ; 2; 10 ) // --> -5 BaseConvert( "FF"; 16; 10 ) // --> "255" BaseConvert( "-101" ; 16; 2 ) // --> "-100000001" BaseConvert( "-101" ; 2; 16 ) // --> "-5" BaseConvert( "FF"; 16; 2 ) // --> "11111111" IMPLEMENTATION: See comments. No helper functions are required. Limit is set at 10^10 so that the math does not break down, as log calculations on large numbers can be incorrect. LAST MODIFIED: 14-AUG-2008 by Debi Fuchs of Aptworks Consulting */ Case( // Simulate an "out of range" error if either base is out of range baseFrom < 2 or baseFrom > 36 or baseTo < 2 or baseTo > 36; Evaluate("Factorial(-1)"); // Return a null value if the string is null; string = ""; ""; // Return a 0 value if the string represents 0; string = 0 or string = "0"; Case( baseTo=10; 0; "0" ); // If the string represents a negative number, subtract from // 0 the result of calling the function again on the positive version. GetAsNumber(string) = string and string + 0 < 0; 0 - BaseConvert( Abs( GetAsNumber( string ) ); baseFrom; baseTo ); // If the string otherwise begins with a "minus" symbol, // return the result of appending a negative sign with the result of // calling the function again on the postive version of the string. Left( string; 1 ) = "-"; 0-BaseConvert( Right( string; Length( string ) - 1 ); baseFrom; baseTo ); // Simulate an "out of range" error if string is a number but is either // a base10 number greater than 10 billion, or a non-integer, or // contains characters other than the digits for BaseFrom GetAsNumber(string) = string and ( (baseFrom=10 and GetAsNumber(string)> 10^10) or GetAsNumber(string)<>Int(string) or Let( [ sci_not_pos = Position(string; "e+"; 0; 1); partial_string = Case( sci_not_pos; Left( string; sci_not_pos - 1 ); string ) ]; Filter( partial_string; Left(".0123456789"; baseFrom+1) ) <> partial_string ) ); Evaluate("Factorial(-1)"); // Simulate an "out of range" error if string is a non-number and contains // characters outside of the digits for BaseFrom GetAsNumber(string) <> string and ( Filter( string; Left("0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"; baseFrom) ) <> string ); Evaluate("Factorial(-1)"); // Calculate the integer that the string represents. This is either the // original string as a number (if we're converting from base 10), or // the the sum of 1) the product of the first "digit" times a power // the target base and 2) the result of recursing on the remaining // "digits" in the string. Let( base10Int = Case( // If the baseFrom is 10, then the base10 version is (clearly) the // numeric version of our original string. baseFrom = 10; GetAsNumber( string ); // If the string is a number then calculate the first digit, // multiply it by a power of baseFrom, and add the result of // recursing on the remainder. (The number might contain scientific // notation, so we can't use each character of digit as a number). GetAsNumber(string) = string; Let( [ new_string_length = Int( Log( string ) ) + 1; power_of_10 = 10 ^ ( new_string_length - 1 ); power_of_x = baseFrom ^ ( new_string_length - 1 ); first_digit = Int( string / power_of_10 ); first_digit_char = Middle( "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"; first_digit + 1; 1 ); remaining = string - first_digit * power_of_10 ]; first_digit_char*power_of_x + BaseConvert (remaining; baseFrom; 10) ); // If the string is not a number then calculate the number representing // the first character, multiply it by a power of baseFrom, and add the result // of recursing on the remainder. ( ( Position( "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"; Left( string; 1 ); 0; 1 ) - 1 ) * baseFrom ^ ( Length( string ) - 1) ) + BaseConvert( Right( string; Length( string ) - 1 ); baseFrom; 10 ) ); // Return either the base10Int from above (if base10), use it to calculate // its representation in the new base, throwing an error on integers that // are too large to deal with reliably. Case( // Simulate an "out of range" error if the base10Int is too large for the math // to work out base10Int > 10^10; Evaluate("Factorial(-1)"); // Return the base10Int from above if the target base is 10. baseTo = 10; base10Int; // Otherwise, calculate the new string as follows: Determine // the first digit of the new string; Then append it together // with 1) any subequent zeros, and 2) the result of recursing // on the remainder using a "fromBase" of 10. Let( [ new_string_length = Int( Log( base10Int ) / Log( baseTo ) ) + 1; power_of_y = baseTo ^ ( new_string_length - 1 ); first_digit = Int( base10Int / power_of_y ); first_digit_char = Middle( "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"; first_digit + 1; 1 ); remaining = base10Int - first_digit * power_of_y; zero_digits_following = Case( remaining = 0; new_string_length - 1; new_string_length - Int( Log( remaining ) / Log( baseTo ) ) - 2 ); zero_chars = Left( "000000000000000000000000000000000000000000000000000" & "000000000000000000000000000000000000000000000000000" & "000000000000000000000000000000000000000000000000000"; zero_digits_following ) ]; first_digit_char & zero_chars & Case( remaining > 0; BaseConvert( remaining; 10; baseTo ) ) ) ) ) )
 Then copy & paste into FileMaker Advanced's Edit Custom Function window.