Which is a good C++ BigInteger class for programmi

Question

I was just wondering which will the best BigInteger class in C++ for programming contests which do not allow external libraries?

Mainly I was looking for a class which could be used in my code( I will of course write it on my own, on similar grounds ).

The primary factors which I think are important are( according to their importance ):

1. Arbitrary length numbers and their operations should be supported.

2. Should be as small as possible, code-wise. Usually there's a limit on the size of the source code which can be submitted to ~50KB, so the code should be ( much )smaller than that.

3. Should be as fast as possible. I read somewhere that bigInt classes take O( log( n ) ) time, so this should have a similiar complexity. What I mean is that it should be as fast as possible.

Answer 1

So far I've only needed unsigned integer big numbers for codechef, but codechef only gives 2KB, so I don't have the full implementation up there anywhere, just the members needed for that problem. My code also assumes that long long has at least twice as many bits as a unsigned, though that's pretty safe. The only real trick to it is that different biguint classes may have different data lengths. Here's summaries of the more interesting functions.

#define BIG_LEN()  (data.size()>rhs.data.size()?data.size():rhs.data.size())
    //the length of data or rhs.data, whichever is bigger
#define SML_LEN()  (data.size()<rhs.data.size()?data.size():rhs.data.size())
    //the length of data or rhs.data, whichever is smaller
const unsigned char baselut[256]={ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                                   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                                   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                                   0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 0, 0, 0, 0, 0,
                                   0,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,
                                  25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,
                                  41,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,
                                  25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40
                                  };
const unsigned char base64lut[256]={ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                                     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
                                     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,62, 0, 0, 0,63,
                                    52,53,54,55,56,57,58,59,60,61, 0, 0, 0, 0, 0, 0,
                                     0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13,14,
                                    15,16,17,18,19,20,21,22,23,24,25, 0, 0, 0, 0, 0,
                                     0,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,
                                    41,42,43,44,45,46,47,48,49,50,51, 0, 0, 0, 0, 0
                                    };
    //lookup tables for creating from strings

void add(unsigned int amount, unsigned int index)
    adds amount at index with carry, simplifies other members
void sub(unsigned int amount, unsigned int index)
    subtracts amount at index with borrow, simplifies other members
biguint& operator+=(const biguint& rhs)
    resize data to BIG_LEN()
    int carry = 0
    for each element i in data up to SML_LEN()
        data[i] += rhs.data[i] + carry
        carry = ((data[i]<rhs[i]+carry || (carry && rhs[i]+carry==0)) ? 1u : 0u);
   if data.length > rhs.length
       add(carry, SML_LEN())
biguint& operator*=(const biguint& rhs) 
    biguint lhs = *this;
    resize data to data.length + rhs.length
    zero out data
    for each element j in lhs
        long long t = lhs[j]
        for each element i in rhs (and j+i<data.size)
            t*=rhs[i];
            add(t&UINT_MAX, k);
            if (k+1<data.size())
                add(t>>uint_bits, k+1);
//note this was public, so I could do both at the same time when needed
//operator /= and %= both just call this
//I have never needed to divide by a biguint yet.
biguint& div(unsigned int rhs, unsigned int & mod) 
    long long carry = 0
    for each element i from data length to zero
        carry = (carry << uint_bits) | data[i]
        data[i] = carry/rhs;
        carry %= rhs
    mod = carry
//I have never needed to shift by a biguint yet
biguint& operator<<=(unsigned int rhs) 
    resize to have enough room, always at least 1 bigger
    const unsigned int bigshift = rhs/uint_bits;
    const unsigned int lilshift = rhs%uint_bits;
    const unsigned int carry_shift = (uint_bits-lilshift)%32;
    for each element i from bigshift to zero
         t = data[i-bigshift] << lilshift;
         t |= data[i-bigshift-1] >> carry_shift;
         data[i] = t;
    if bigshift < data.size
        data[bigshift] = data[0] << lilshift
    zero each element i from 0 to bigshift
std::ofstream& operator<<(std::ofstream& out, biguint num)
    unsigned int mod
    vector reverse
    do 
        num.div(10,mod);
        push back mod onto reverse
    while num greater than 0
    print out elements of reverse in reverse
std::ifstream& operator>>(std::ifstream& in, biguint num)
    char next
    do
        in.get(next) 
    while next is whitespace
    num = 0
    do 
        num = num * 10 + next
    while in.get(next) and next is digit
//these are handy for initializing to known values.
//I also have constructors that simply call these
biguint& assign(const char* rhs, unsigned int base)
    for each char c in rhs
        data *= base
        add(baselut[c], 0)
biguint& assign(const char* rhs, std::integral_constant<unsigned int, 64> base)
    for each char c in rhs
        data *= base
        add(base64lut[c], 0)
//despite being 3 times as much, code, the hex version is _way_ faster.
biguint& assign(const char* rhs, std::integral_constant<unsigned int, 16>) 
    if first two characters are "0x" skip them
    unsigned int len = strlen(rhs);
    grow(len/4+1);
    zero out data
    const unsigned int hex_per_int = uint_bits/4;
    if (len > hex_per_int*data.size()) { //calculate where first digit goes
        rhs += len-hex_per_int*data.size();
        len = hex_per_int*data.size();
    }
    for(unsigned int i=len; i --> 0; ) { //place each digit directly in it's place
        unsigned int t = (unsigned int)(baselut[*(rhs++)]) << (i%hex_per_int)*4u;
        data[i/hex_per_int] |= t;
    }

I also made specializations for multiplication, divide, modulo, shifts and others for std::integral_constant<unsigned int, Value>, which made massive improvements to my serializing and deserializing functions amongst others.