406 lines
11 KiB
C++
406 lines
11 KiB
C++
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#include "BigInteger.hh"
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void BigInteger::operator =(const BigInteger &x) {
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// Calls like a = a have no effect
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if (this == &x)
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return;
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// Copy sign
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sign = x.sign;
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// Copy the rest
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mag = x.mag;
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}
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BigInteger::BigInteger(const Blk *b, Index blen, Sign s) : mag(b, blen) {
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switch (s) {
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case zero:
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if (!mag.isZero())
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throw "BigInteger::BigInteger(const Blk *, Index, Sign): Cannot use a sign of zero with a nonzero magnitude";
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sign = zero;
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break;
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case positive:
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case negative:
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// If the magnitude is zero, force the sign to zero.
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sign = mag.isZero() ? zero : s;
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break;
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default:
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/* g++ seems to be optimizing out this case on the assumption
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* that the sign is a valid member of the enumeration. Oh well. */
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throw "BigInteger::BigInteger(const Blk *, Index, Sign): Invalid sign";
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}
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}
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BigInteger::BigInteger(const BigUnsigned &x, Sign s) : mag(x) {
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switch (s) {
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case zero:
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if (!mag.isZero())
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throw "BigInteger::BigInteger(const BigUnsigned &, Sign): Cannot use a sign of zero with a nonzero magnitude";
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sign = zero;
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break;
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case positive:
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case negative:
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// If the magnitude is zero, force the sign to zero.
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sign = mag.isZero() ? zero : s;
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break;
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default:
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/* g++ seems to be optimizing out this case on the assumption
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* that the sign is a valid member of the enumeration. Oh well. */
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throw "BigInteger::BigInteger(const BigUnsigned &, Sign): Invalid sign";
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}
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}
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/* CONSTRUCTION FROM PRIMITIVE INTEGERS
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* Same idea as in BigUnsigned.cc, except that negative input results in a
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* negative BigInteger instead of an exception. */
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// Done longhand to let us use initialization.
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BigInteger::BigInteger(unsigned long x) : mag(x) { sign = mag.isZero() ? zero : positive; }
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BigInteger::BigInteger(unsigned int x) : mag(x) { sign = mag.isZero() ? zero : positive; }
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BigInteger::BigInteger(unsigned short x) : mag(x) { sign = mag.isZero() ? zero : positive; }
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// For signed input, determine the desired magnitude and sign separately.
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namespace {
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template <class X, class UX>
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BigInteger::Blk magOf(X x) {
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/* UX(...) cast needed to stop short(-2^15), which negates to
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* itself, from sign-extending in the conversion to Blk. */
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return BigInteger::Blk(x < 0 ? UX(-x) : x);
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}
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template <class X>
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BigInteger::Sign signOf(X x) {
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return (x == 0) ? BigInteger::zero
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: (x > 0) ? BigInteger::positive
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: BigInteger::negative;
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}
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}
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BigInteger::BigInteger(long x) : sign(signOf(x)), mag(magOf<long , unsigned long >(x)) {}
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BigInteger::BigInteger(int x) : sign(signOf(x)), mag(magOf<int , unsigned int >(x)) {}
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BigInteger::BigInteger(short x) : sign(signOf(x)), mag(magOf<short, unsigned short>(x)) {}
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// CONVERSION TO PRIMITIVE INTEGERS
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/* Reuse BigUnsigned's conversion to an unsigned primitive integer.
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* The friend is a separate function rather than
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* BigInteger::convertToUnsignedPrimitive to avoid requiring BigUnsigned to
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* declare BigInteger. */
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template <class X>
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inline X convertBigUnsignedToPrimitiveAccess(const BigUnsigned &a) {
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return a.convertToPrimitive<X>();
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}
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template <class X>
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X BigInteger::convertToUnsignedPrimitive() const {
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if (sign == negative)
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throw "BigInteger::to<Primitive>: "
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"Cannot convert a negative integer to an unsigned type";
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else
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return convertBigUnsignedToPrimitiveAccess<X>(mag);
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}
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/* Similar to BigUnsigned::convertToPrimitive, but split into two cases for
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* nonnegative and negative numbers. */
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template <class X, class UX>
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X BigInteger::convertToSignedPrimitive() const {
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if (sign == zero)
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return 0;
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else if (mag.getLength() == 1) {
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// The single block might fit in an X. Try the conversion.
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Blk b = mag.getBlock(0);
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if (sign == positive) {
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X x = X(b);
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if (x >= 0 && Blk(x) == b)
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return x;
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} else {
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X x = -X(b);
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/* UX(...) needed to avoid rejecting conversion of
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* -2^15 to a short. */
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if (x < 0 && Blk(UX(-x)) == b)
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return x;
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}
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// Otherwise fall through.
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}
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throw "BigInteger::to<Primitive>: "
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"Value is too big to fit in the requested type";
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}
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unsigned long BigInteger::toUnsignedLong () const { return convertToUnsignedPrimitive<unsigned long > (); }
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unsigned int BigInteger::toUnsignedInt () const { return convertToUnsignedPrimitive<unsigned int > (); }
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unsigned short BigInteger::toUnsignedShort() const { return convertToUnsignedPrimitive<unsigned short> (); }
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long BigInteger::toLong () const { return convertToSignedPrimitive <long , unsigned long> (); }
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int BigInteger::toInt () const { return convertToSignedPrimitive <int , unsigned int> (); }
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short BigInteger::toShort () const { return convertToSignedPrimitive <short, unsigned short>(); }
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// COMPARISON
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BigInteger::CmpRes BigInteger::compareTo(const BigInteger &x) const {
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// A greater sign implies a greater number
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if (sign < x.sign)
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return less;
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else if (sign > x.sign)
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return greater;
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else switch (sign) {
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// If the signs are the same...
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case zero:
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return equal; // Two zeros are equal
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case positive:
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// Compare the magnitudes
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return mag.compareTo(x.mag);
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case negative:
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// Compare the magnitudes, but return the opposite result
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return CmpRes(-mag.compareTo(x.mag));
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default:
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throw "BigInteger internal error";
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}
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}
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/* COPY-LESS OPERATIONS
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* These do some messing around to determine the sign of the result,
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* then call one of BigUnsigned's copy-less operations. */
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// See remarks about aliased calls in BigUnsigned.cc .
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#define DTRT_ALIASED(cond, op) \
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if (cond) { \
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BigInteger tmpThis; \
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tmpThis.op; \
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*this = tmpThis; \
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return; \
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}
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void BigInteger::add(const BigInteger &a, const BigInteger &b) {
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DTRT_ALIASED(this == &a || this == &b, add(a, b));
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// If one argument is zero, copy the other.
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if (a.sign == zero)
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operator =(b);
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else if (b.sign == zero)
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operator =(a);
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// If the arguments have the same sign, take the
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// common sign and add their magnitudes.
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else if (a.sign == b.sign) {
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sign = a.sign;
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mag.add(a.mag, b.mag);
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} else {
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// Otherwise, their magnitudes must be compared.
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switch (a.mag.compareTo(b.mag)) {
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case equal:
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// If their magnitudes are the same, copy zero.
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mag = 0;
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sign = zero;
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break;
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// Otherwise, take the sign of the greater, and subtract
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// the lesser magnitude from the greater magnitude.
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case greater:
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sign = a.sign;
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mag.subtract(a.mag, b.mag);
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break;
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case less:
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sign = b.sign;
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mag.subtract(b.mag, a.mag);
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break;
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}
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}
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}
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void BigInteger::subtract(const BigInteger &a, const BigInteger &b) {
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// Notice that this routine is identical to BigInteger::add,
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// if one replaces b.sign by its opposite.
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DTRT_ALIASED(this == &a || this == &b, subtract(a, b));
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// If a is zero, copy b and flip its sign. If b is zero, copy a.
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if (a.sign == zero) {
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mag = b.mag;
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// Take the negative of _b_'s, sign, not ours.
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// Bug pointed out by Sam Larkin on 2005.03.30.
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sign = Sign(-b.sign);
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} else if (b.sign == zero)
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operator =(a);
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// If their signs differ, take a.sign and add the magnitudes.
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else if (a.sign != b.sign) {
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sign = a.sign;
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mag.add(a.mag, b.mag);
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} else {
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// Otherwise, their magnitudes must be compared.
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switch (a.mag.compareTo(b.mag)) {
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// If their magnitudes are the same, copy zero.
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case equal:
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mag = 0;
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sign = zero;
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break;
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// If a's magnitude is greater, take a.sign and
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// subtract a from b.
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case greater:
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sign = a.sign;
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mag.subtract(a.mag, b.mag);
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break;
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// If b's magnitude is greater, take the opposite
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// of b.sign and subtract b from a.
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case less:
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sign = Sign(-b.sign);
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mag.subtract(b.mag, a.mag);
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break;
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}
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}
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}
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void BigInteger::multiply(const BigInteger &a, const BigInteger &b) {
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DTRT_ALIASED(this == &a || this == &b, multiply(a, b));
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// If one object is zero, copy zero and return.
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if (a.sign == zero || b.sign == zero) {
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sign = zero;
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mag = 0;
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return;
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}
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// If the signs of the arguments are the same, the result
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// is positive, otherwise it is negative.
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sign = (a.sign == b.sign) ? positive : negative;
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// Multiply the magnitudes.
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mag.multiply(a.mag, b.mag);
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}
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/*
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* DIVISION WITH REMAINDER
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* Please read the comments before the definition of
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* `BigUnsigned::divideWithRemainder' in `BigUnsigned.cc' for lots of
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* information you should know before reading this function.
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*
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* Following Knuth, I decree that x / y is to be
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* 0 if y==0 and floor(real-number x / y) if y!=0.
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* Then x % y shall be x - y*(integer x / y).
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*
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* Note that x = y * (x / y) + (x % y) always holds.
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* In addition, (x % y) is from 0 to y - 1 if y > 0,
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* and from -(|y| - 1) to 0 if y < 0. (x % y) = x if y = 0.
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*
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* Examples: (q = a / b, r = a % b)
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* a b q r
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* === === === ===
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* 4 3 1 1
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* -4 3 -2 2
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* 4 -3 -2 -2
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* -4 -3 1 -1
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*/
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void BigInteger::divideWithRemainder(const BigInteger &b, BigInteger &q) {
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// Defend against aliased calls;
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// same idea as in BigUnsigned::divideWithRemainder .
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if (this == &q)
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throw "BigInteger::divideWithRemainder: Cannot write quotient and remainder into the same variable";
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if (this == &b || &q == &b) {
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BigInteger tmpB(b);
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divideWithRemainder(tmpB, q);
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return;
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}
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// Division by zero gives quotient 0 and remainder *this
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if (b.sign == zero) {
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q.mag = 0;
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q.sign = zero;
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return;
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}
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// 0 / b gives quotient 0 and remainder 0
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if (sign == zero) {
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q.mag = 0;
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q.sign = zero;
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return;
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}
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// Here *this != 0, b != 0.
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// Do the operands have the same sign?
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if (sign == b.sign) {
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// Yes: easy case. Quotient is zero or positive.
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q.sign = positive;
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} else {
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// No: harder case. Quotient is negative.
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q.sign = negative;
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// Decrease the magnitude of the dividend by one.
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mag--;
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/*
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* We tinker with the dividend before and with the
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* quotient and remainder after so that the result
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* comes out right. To see why it works, consider the following
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* list of examples, where A is the magnitude-decreased
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* a, Q and R are the results of BigUnsigned division
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* with remainder on A and |b|, and q and r are the
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* final results we want:
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*
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* a A b Q R q r
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* -3 -2 3 0 2 -1 0
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* -4 -3 3 1 0 -2 2
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* -5 -4 3 1 1 -2 1
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* -6 -5 3 1 2 -2 0
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*
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* It appears that we need a total of 3 corrections:
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* Decrease the magnitude of a to get A. Increase the
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* magnitude of Q to get q (and make it negative).
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* Find r = (b - 1) - R and give it the desired sign.
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*/
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}
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// Divide the magnitudes.
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mag.divideWithRemainder(b.mag, q.mag);
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if (sign != b.sign) {
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// More for the harder case (as described):
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// Increase the magnitude of the quotient by one.
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q.mag++;
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// Modify the remainder.
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mag.subtract(b.mag, mag);
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mag--;
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}
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// Sign of the remainder is always the sign of the divisor b.
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sign = b.sign;
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// Set signs to zero as necessary. (Thanks David Allen!)
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if (mag.isZero())
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sign = zero;
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if (q.mag.isZero())
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q.sign = zero;
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// WHEW!!!
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}
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// Negation
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void BigInteger::negate(const BigInteger &a) {
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DTRT_ALIASED(this == &a, negate(a));
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// Copy a's magnitude
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mag = a.mag;
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// Copy the opposite of a.sign
|
||
|
|
sign = Sign(-a.sign);
|
||
|
|
}
|
||
|
|
|
||
|
|
// INCREMENT/DECREMENT OPERATORS
|
||
|
|
|
||
|
|
// Prefix increment
|
||
|
|
void BigInteger::operator ++() {
|
||
|
|
if (sign == negative) {
|
||
|
|
mag--;
|
||
|
|
if (mag == 0)
|
||
|
|
sign = zero;
|
||
|
|
} else {
|
||
|
|
mag++;
|
||
|
|
sign = positive; // if not already
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// Postfix increment: same as prefix
|
||
|
|
void BigInteger::operator ++(int) {
|
||
|
|
operator ++();
|
||
|
|
}
|
||
|
|
|
||
|
|
// Prefix decrement
|
||
|
|
void BigInteger::operator --() {
|
||
|
|
if (sign == positive) {
|
||
|
|
mag--;
|
||
|
|
if (mag == 0)
|
||
|
|
sign = zero;
|
||
|
|
} else {
|
||
|
|
mag++;
|
||
|
|
sign = negative;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// Postfix decrement: same as prefix
|
||
|
|
void BigInteger::operator --(int) {
|
||
|
|
operator --();
|
||
|
|
}
|
||
|
|
|