Solving 10385 - Duathlon (Ternary search)

[and.git] / 11448 - Who said crisis / bigint-2007.07.07 / BigInteger.cc

/*
* Matt McCutchen's Big Integer Library
*/

#include "BigInteger.hh"

// MANAGEMENT

// Assignment operator
void BigInteger::operator =(const BigInteger &x) {
        // Calls like a = a have no effect
        if (this == &x)
                return;
        // Copy sign
        sign = x.sign;
        // Copy the rest
        BigUnsigned::operator =(x);
}

// Constructor from an array of blocks and a sign
BigInteger::BigInteger(const Blk *b, Index l, Sign s) : BigUnsigned(b, l) {
        switch (s) {
                case zero:
                case positive:
                case negative:
                sign = (len == 0) ? zero : s;
                break;
                default:
                throw "BigInteger::BigInteger(Blk *, Index, Sign): Invalid sign";
        }
}

// Constructor from a BigUnsigned and a sign
BigInteger::BigInteger(const BigUnsigned &x, Sign s) : BigUnsigned(x) {
        switch (s) {
                case zero:
                case positive:
                case negative:
                sign = (len == 0) ? zero : s;
                break;
                default:
                throw "BigInteger::BigInteger(Blk *, Index, Sign): Invalid sign";
        }
}

/*
* The steps for construction of a BigInteger
* from an integral value x are as follows:
* 1. If x is zero, create an empty BigInteger and stop.
* 2. Allocate a one-block number array.
* 3. If x is positive (or of an unsigned type), set the
*    sign of the BigInteger to positive.
* 4. If x is of a signed type and is negative, set the
*    sign of the BigInteger to negative.
* 5. If x is of a signed type, convert x (or -x if x < 0)
*    to the unsigned type of the same length.
* 6. Expand x (or the result of step 5) to a Blk,
*    and store it in the number array.
*
* See remarks in `BigUnsigned.cc' and `NumberlikeArray.hh'
* about new handling of zero-length arrays.
*/

BigInteger::BigInteger(unsigned long x) {
        if (x == 0)
                sign = zero; // NumberlikeArray did the rest
        else {
                cap = 1;
                blk = new Blk[1];
                sign = positive;
                len = 1;
                blk[0] = Blk(x);
        }
}

BigInteger::BigInteger(long x) {
        if (x > 0) {
                cap = 1;
                blk = new Blk[1];
                sign = positive;
                len = 1;
                blk[0] = Blk(x);
        } else if (x < 0) {
                cap = 1;
                blk = new Blk[1];
                sign = negative;
                len = 1;
                blk[0] = Blk(-x);
        } else
        sign = zero;
}

BigInteger::BigInteger(unsigned int x) {
        if (x == 0)
                sign = zero;
        else {
                cap = 1;
                blk = new Blk[1];
                sign = positive;
                len = 1;
                blk[0] = Blk(x);
        }
}

BigInteger::BigInteger(int x) {
        if (x > 0) {
                cap = 1;
                blk = new Blk[1];
                sign = positive;
                len = 1;
                blk[0] = Blk(x);
        } else if (x < 0) {
                cap = 1;
                blk = new Blk[1];
                sign = negative;
                len = 1;
                blk[0] = Blk(-x);
        } else
        sign = zero;
}

BigInteger::BigInteger(unsigned short x) {
        if (x == 0)
                sign = zero;
        else {
                cap = 1;
                blk = new Blk[1];
                sign = positive;
                len = 1;
                blk[0] = Blk(x);
        }
}

BigInteger::BigInteger(short x) {
        if (x > 0) {
                cap = 1;
                blk = new Blk[1];
                sign = positive;
                len = 1;
                blk[0] = Blk(x);
        } else if (x < 0) {
                cap = 1;
                blk = new Blk[1];
                sign = negative;
                len = 1;
                blk[0] = Blk(-x);
        } else
        sign = zero;
}

// CONVERTERS
/*
* The steps for conversion of a BigInteger to an
* integral type are as follows:
* 1. If the BigInteger is zero, return zero.
* 2. If the BigInteger is positive:
*    3. If it is more than one block long or its lowest
*       block has bits set out of the range of the target
*       type, throw an exception.
*    4. Otherwise, convert the lowest block to the
*       target type and return it.
* 5. If the BigInteger is negative:
*    6. If the target type is unsigned, throw an exception.
*    7. If it is more than one block long or its lowest
*       block has bits set out of the range of the target
*       type, throw an exception.
*    8. Otherwise, convert the lowest block to the
*       target type, negate it, and return it.
*/

namespace {
        // These masks are used to test whether a Blk has bits
        // set out of the range of a smaller integral type.  Note
        // that this range is not considered to include the sign bit.
        const BigUnsigned::Blk  lMask = ~0 >> 1;
        const BigUnsigned::Blk uiMask = (unsigned int)(~0);
        const BigUnsigned::Blk  iMask = uiMask >> 1;
        const BigUnsigned::Blk usMask = (unsigned short)(~0);
        const BigUnsigned::Blk  sMask = usMask >> 1;
}

BigInteger::operator unsigned long() const {
        switch (sign) {
                case zero:
                return 0;
                case positive:
                if (len == 1)
                        return blk[0];
                else
                        throw "BigInteger operator unsigned long() const: Value is too big for an unsigned long";
                case negative:
                throw "BigInteger operator unsigned long() const: Cannot convert a negative integer to an unsigned type";
                default:
                throw "BigInteger: Internal error";
        }
}

BigInteger::operator long() const {
        switch (sign) {
                case zero:
                return 0;
                case positive:
                if (len == 1 && (blk[0] & ~lMask) == 0)
                        return long(blk[0]);
                else
                        throw "BigInteger operator long() const: Value is too big for a long";
                case negative:
                if (len == 1 && (blk[0] & ~lMask) == 0)
                        return -long(blk[0]);
                else
                        throw "BigInteger operator long() const: Value is too big for a long";
                default:
                throw "BigInteger: Internal error";
        }
}

BigInteger::operator unsigned int() const {
        switch (sign) {
                case zero:
                return 0;
                case positive:
                if (len == 1 && (blk[0] & ~uiMask) == 0)
                        return (unsigned int)(blk[0]);
                else
                        throw "BigInteger operator unsigned int() const: Value is too big for an unsigned int";
                case negative:
                throw "BigInteger operator unsigned int() const: Cannot convert a negative integer to an unsigned type";
                default:
                throw "BigInteger: Internal error";
        }
}

BigInteger::operator int() const {
        switch (sign) {
                case zero:
                return 0;
                case positive:
                if (len == 1 && (blk[0] & ~iMask) == 0)
                        return int(blk[0]);
                else
                        throw "BigInteger operator int() const: Value is too big for an int";
                case negative:
                if (len == 1 && (blk[0] & ~iMask) == 0)
                        return -int(blk[0]);
                else
                        throw "BigInteger operator int() const: Value is too big for an int";
                default:
                throw "BigInteger: Internal error";
        }
}

BigInteger::operator unsigned short() const {
        switch (sign) {
                case zero:
                return 0;
                case positive:
                if (len == 1 && (blk[0] & ~usMask) == 0)
                        return (unsigned short)(blk[0]);
                else
                        throw "BigInteger operator unsigned short() const: Value is too big for an unsigned short";
                case negative:
                throw "BigInteger operator unsigned short() const: Cannot convert a negative integer to an unsigned type";
                default:
                throw "BigInteger: Internal error";
        }
}

BigInteger::operator short() const {
        switch (sign) {
                case zero:
                return 0;
                case positive:
                if (len == 1 && (blk[0] & ~sMask) == 0)
                        return short(blk[0]);
                else
                        throw "BigInteger operator short() const: Value is too big for a short";
                case negative:
                if (len == 1 && (blk[0] & ~sMask) == 0)
                        return -short(blk[0]);
                else
                        throw "BigInteger operator short() const: Value is too big for a short";
                default:
                throw "BigInteger: Internal error";
        }
}

// COMPARISON
BigInteger::CmpRes BigInteger::compareTo(const BigInteger &x) const {
        // A greater sign implies a greater number
        if (sign < x.sign)
                return less;
        else if (sign > x.sign)
                return greater;
        else switch (sign) {
                // If the signs are the same...
                case zero:
                return equal; // Two zeros are equal
                case positive:
                // Compare the magnitudes
                return BigUnsigned::compareTo(x);
                case negative:
                // Compare the magnitudes, but return the opposite result
                return CmpRes(-BigUnsigned::compareTo(x));
                default:
                throw "BigInteger: Internal error";
        }
}

// PUT-HERE OPERATIONS
// These do some messing around to determine the sign of the result,
// then call one of BigUnsigned's put-heres.

// See remarks about aliased calls in BigUnsigned.cc .
#define DOTR_ALIASED(cond, op) \
        if (cond) { \
                BigInteger tmpThis; \
                tmpThis.op; \
                *this = tmpThis; \
                return; \
        }

// Addition
void BigInteger::add(const BigInteger &a, const BigInteger &b) {
        DOTR_ALIASED(this == &a || this == &b, add(a, b));
        // If one argument is zero, copy the other.
        if (a.sign == zero)
                operator =(b);
        else if (b.sign == zero)
                operator =(a);
        // If the arguments have the same sign, take the
        // common sign and add their magnitudes.
        else if (a.sign == b.sign) {
                sign = a.sign;
                BigUnsigned::add(a, b);
        } else {
                // Otherwise, their magnitudes must be compared.
                switch (a.BigUnsigned::compareTo(b)) {
                        // If their magnitudes are the same, copy zero.
                        case equal:
                        len = 0;
                        sign = zero;
                        break;
                        // Otherwise, take the sign of the greater, and subtract
                        // the lesser magnitude from the greater magnitude.
                        case greater:
                        sign = a.sign;
                        BigUnsigned::subtract(a, b);
                        break;
                        case less:
                        sign = b.sign;
                        BigUnsigned::subtract(b, a);
                        break;
                }
        }
}

// Subtraction
void BigInteger::subtract(const BigInteger &a, const BigInteger &b) {
        // Notice that this routine is identical to BigInteger::add,
        // if one replaces b.sign by its opposite.
        DOTR_ALIASED(this == &a || this == &b, subtract(a, b));
        // If a is zero, copy b and flip its sign.  If b is zero, copy a.
        if (a.sign == zero) {
                BigUnsigned::operator =(b);
                // Take the negative of _b_'s, sign, not ours.
                // Bug pointed out by Sam Larkin on 2005.03.30.
                sign = Sign(-b.sign);
        } else if (b.sign == zero)
                operator =(a);
        // If their signs differ, take a.sign and add the magnitudes.
        else if (a.sign != b.sign) {
                sign = a.sign;
                BigUnsigned::add(a, b);
        } else {
                // Otherwise, their magnitudes must be compared.
                switch (a.BigUnsigned::compareTo(b)) {
                        // If their magnitudes are the same, copy zero.
                        case equal:
                        len = 0;
                        sign = zero;
                        break;
                        // If a's magnitude is greater, take a.sign and
                        // subtract a from b.
                        case greater:
                        sign = a.sign;
                        BigUnsigned::subtract(a, b);
                        break;
                        // If b's magnitude is greater, take the opposite
                        // of b.sign and subtract b from a.
                        case less:
                        sign = Sign(-b.sign);
                        BigUnsigned::subtract(b, a);
                        break;
                }
        }
}

// Multiplication
void BigInteger::multiply(const BigInteger &a, const BigInteger &b) {
        DOTR_ALIASED(this == &a || this == &b, multiply(a, b));
        // If one object is zero, copy zero and return.
        if (a.sign == zero || b.sign == zero) {
                sign = zero;
                len = 0;
                return;
        }
        // If the signs of the arguments are the same, the result
        // is positive, otherwise it is negative.
        sign = (a.sign == b.sign) ? positive : negative;
        // Multiply the magnitudes.
        BigUnsigned::multiply(a, b);
}

/*
* DIVISION WITH REMAINDER
* Please read the comments before the definition of
* `BigUnsigned::divideWithRemainder' in `BigUnsigned.cc' for lots of
* information you should know before reading this function.
*
* Following Knuth, I decree that x / y is to be
* 0 if y==0 and floor(real-number x / y) if y!=0.
* Then x % y shall be x - y*(integer x / y).
*
* Note that x = y * (x / y) + (x % y) always holds.
* In addition, (x % y) is from 0 to y - 1 if y > 0,
* and from -(|y| - 1) to 0 if y < 0.  (x % y) = x if y = 0.
*
* Examples: (q = a / b, r = a % b)
*       a       b       q       r
*       ===     ===     ===     ===
*       4       3       1       1
*       -4      3       -2      2
*       4       -3      -2      -2
*       -4      -3      1       -1
*/
void BigInteger::divideWithRemainder(const BigInteger &b, BigInteger &q) {
        // Defend against aliased calls;
        // same idea as in BigUnsigned::divideWithRemainder .
        if (this == &q)
                throw "BigInteger::divideWithRemainder: Cannot write quotient and remainder into the same variable";
        if (this == &b || &q == &b) {
                BigInteger tmpB(b);
                divideWithRemainder(tmpB, q);
                return;
        }
        
        // Division by zero gives quotient 0 and remainder *this
        if (b.sign == zero) {
                q.len = 0;
                q.sign = zero;
                return;
        }
        // 0 / b gives quotient 0 and remainder 0
        if (sign == zero) {
                q.len = 0;
                q.sign = zero;
                return;
        }
        
        // Here *this != 0, b != 0.
        
        // Do the operands have the same sign?
        if (sign == b.sign) {
                // Yes: easy case.  Quotient is zero or positive.
                q.sign = positive;
        } else {
                // No: harder case.  Quotient is negative.
                q.sign = negative;
                // Decrease the magnitude of the dividend by one.
                BigUnsigned::operator --();
                /*
                * We tinker with the dividend before and with the
                * quotient and remainder after so that the result
                * comes out right.  To see why it works, consider the following
                * list of examples, where A is the magnitude-decreased
                * a, Q and R are the results of BigUnsigned division
                * with remainder on A and |b|, and q and r are the
                * final results we want:
                *
                *       a       A       b       Q       R       q       r
                *       -3      -2      3       0       2       -1      0
                *       -4      -3      3       1       0       -2      2
                *       -5      -4      3       1       1       -2      1
                *       -6      -5      3       1       2       -2      0
                *
                * It appears that we need a total of 3 corrections:
                * Decrease the magnitude of a to get A.  Increase the
                * magnitude of Q to get q (and make it negative).
                * Find r = (b - 1) - R and give it the desired sign.
                */
        }
        
        // Divide the magnitudes.
        BigUnsigned::divideWithRemainder(b, q);
        
        if (sign != b.sign) {
                // More for the harder case (as described):
                // Increase the magnitude of the quotient by one.
                q.BigUnsigned::operator ++();
                // Modify the remainder.
                BigUnsigned temp(*this);
                BigUnsigned::subtract(b, temp);
                BigUnsigned::operator --();
        }
        
        // Sign of the remainder is always the sign of the divisor b.
        sign = b.sign;
        
        // Set signs to zero as necessary.  (Thanks David Allen!)
        if (len == 0)
                sign = zero;
        if (q.len == 0)
                q.sign = zero;
        
        // WHEW!!!
}

// Negation
void BigInteger::negate(const BigInteger &a) {
        DOTR_ALIASED(this == &a, negate(a));
        // Copy a's magnitude
        BigUnsigned::operator =(a);
        // Copy the opposite of a.sign
        sign = Sign(-a.sign);
}

// INCREMENT/DECREMENT OPERATORS

// Prefix increment
void BigInteger::operator ++() {
        switch (sign) {
                case zero:
                allocate(1);
                sign = positive;
                len = 1;
                blk[0] = 1;
                break;
                case positive:
                BigUnsigned::operator ++();
                break;
                case negative:
                BigUnsigned::operator --();
                if (len == 0)
                        sign = zero;
                break;
        }
}

// Postfix increment: same as prefix
void BigInteger::operator ++(int) {
        operator ++();
}

// Prefix decrement
void BigInteger::operator --() {
        switch (sign) {
                case zero:
                allocate(1);
                sign = negative;
                len = 1;
                blk[0] = 1;
                break;
                case negative:
                BigUnsigned::operator ++();
                break;
                case positive:
                BigUnsigned::operator --();
                if (len == 0)
                        sign = zero;
                break;
        }
}

// Postfix decrement: same as prefix
void BigInteger::operator --(int) {
        operator --();
}