Terminology
In this question I am calling "floating point number" "decimal number" to prevent ambiguation with the float
/double
Java primitive data types. The term "decimal" has no relationship with "base 10".
Background
I am expressing a decimal number of any base in this way:
class Decimal{
int[] digits;
int exponent;
int base;
int signum;
}
which approximately expresses this double
value:
public double toDouble(){
if(signum == 0) return 0d;
double out = 0d;
for(int i = digits.length - 1, j = 0; i >= 0; i--, j++){
out += digits[i] * Math.pow(base, j + exponent);
}
return out * signum;
}
I am aware that some conversions are not possible. For example, it is not possible to convert 0.1 (base 3)
to base 10, because it is a recurring decimal. Similarly, converting 0.1 (base 9)
to base 3 is not possible, but covnerting 0.3 (base 3)
is possible. There are probably other cases that I have not considered.
The traditional way
The traditional way (by hand) of change of base, for integers, from base 10 to base 2, is to divide the number by the exponents of 2, and from base 2 to base 10 is to multiply the digits by respective exponents of 2. Changing from base x to base y usually involves converting to base 10 as an intermediate.
First question: Argument validation
Therefore, my first question is, if I were to implement the method public Decimal Decimal.changeBase(int newBase)
, how can I validate whether newBase
can be made without resulting in recurring decimals (which is incompatible with the design of the int[] digits
field, since I don't plan to make an int recurringOffset
field just for this.
Second question: Implementation
Hence, how to implement this? I instinctively feel that this question is much easier to solve if the first question is solved.
Third question: What about recurring number output:
I don't plan to make an
int recurringOffset
field just for this.
For the sake of future readers, this question should also be asked.
For example, according to Wolfram|Alpha:
0.1 (base 4) = 0.[2...] (base 9)
How can this be calculated (by hand, if by programming sounds too complicated)?
I think that a data structure like this can represent this decimal number:
class Decimal{
int[] constDigits;
int exponent;
int base;
int signum;
@Nullable @NonEmpty int[] appendRecurring;
}
For example, 61/55
can be expressed like this:
{
constDigits: [1, 1], // 11
exponent: -1, // 11e-1
base: 10,
signum: 1, // positive
appendRecurring: [0, 9]
}
Not a homework question
I am not looking for any libraries. Please do not answer this question with reference to any libraries. (Because I'm writing this class just for fun, OK?)