bigunsigned.cc

用C++ 包装了大整数这个类

#include "BigUnsigned.hh"

// Memory management definitions have moved to the bottom of NumberlikeArray.hh.

// The templates used by these constructors and converters are at the bottom of
// BigUnsigned.hh.

BigUnsigned::BigUnsigned(unsigned long  x) { initFromPrimitive      (x); }
BigUnsigned::BigUnsigned(unsigned int   x) { initFromPrimitive      (x); }
BigUnsigned::BigUnsigned(unsigned short x) { initFromPrimitive      (x); }
BigUnsigned::BigUnsigned(         long  x) { initFromSignedPrimitive(x); }
BigUnsigned::BigUnsigned(         int   x) { initFromSignedPrimitive(x); }
BigUnsigned::BigUnsigned(         short x) { initFromSignedPrimitive(x); }

unsigned long  BigUnsigned::toUnsignedLong () const { return convertToPrimitive      <unsigned long >(); }
unsigned int   BigUnsigned::toUnsignedInt  () const { return convertToPrimitive      <unsigned int  >(); }
unsigned short BigUnsigned::toUnsignedShort() const { return convertToPrimitive      <unsigned short>(); }
long           BigUnsigned::toLong         () const { return convertToSignedPrimitive<         long >(); }
int            BigUnsigned::toInt          () const { return convertToSignedPrimitive<         int  >(); }
short          BigUnsigned::toShort        () const { return convertToSignedPrimitive<         short>(); }

// BIT/BLOCK ACCESSORS

void BigUnsigned::setBlock(Index i, Blk newBlock) {
	if (newBlock == 0) {
		if (i < len) {
			blk[i] = 0;
			zapLeadingZeros();
		}
		// If i >= len, no effect.
	} else {
		if (i >= len) {
			// The nonzero block extends the number.
			allocateAndCopy(i+1);
			// Zero any added blocks that we aren't setting.
			for (Index j = len; j < i; j++)
				blk[j] = 0;
			len = i+1;
		}
		blk[i] = newBlock;
	}
}

/* Evidently the compiler wants BigUnsigned:: on the return type because, at
 * that point, it hasn't yet parsed the BigUnsigned:: on the name to get the
 * proper scope. */
BigUnsigned::Index BigUnsigned::bitLength() const {
	if (isZero())
		return 0;
	else {
		Blk leftmostBlock = getBlock(len - 1);
		Index leftmostBlockLen = 0;
		while (leftmostBlock != 0) {
			leftmostBlock >>= 1;
			leftmostBlockLen++;
		}
		return leftmostBlockLen + (len - 1) * N;
	}
}

void BigUnsigned::setBit(Index bi, bool newBit) {
	Index blockI = bi / N;
	Blk block = getBlock(blockI), mask = 1 << (bi % N);
	block = newBit ? (block | mask) : (block & ~mask);
	setBlock(blockI, block);
}

// COMPARISON
BigUnsigned::CmpRes BigUnsigned::compareTo(const BigUnsigned &x) const {
	// A bigger length implies a bigger number.
	if (len < x.len)
		return less;
	else if (len > x.len)
		return greater;
	else {
		// Compare blocks one by one from left to right.
		Index i = len;
		while (i > 0) {
			i--;
			if (blk[i] == x.blk[i])
				continue;
			else if (blk[i] > x.blk[i])
				return greater;
			else
				return less;
		}
		// If no blocks differed, the numbers are equal.
		return equal;
	}
}

// COPY-LESS OPERATIONS

/*
 * On most calls to copy-less operations, it's safe to read the inputs little by
 * little and write the outputs little by little.  However, if one of the
 * inputs is coming from the same variable into which the output is to be
 * stored (an "aliased" call), we risk overwriting the input before we read it.
 * In this case, we first compute the result into a temporary BigUnsigned
 * variable and then copy it into the requested output variable *this.
 * Each put-here operation uses the DTRT_ALIASED macro (Do The Right Thing on
 * aliased calls) to generate code for this check.
 * 
 * I adopted this approach on 2007.02.13 (see Assignment Operators in
 * BigUnsigned.hh).  Before then, put-here operations rejected aliased calls
 * with an exception.  I think doing the right thing is better.
 * 
 * Some of the put-here operations can probably handle aliased calls safely
 * without the extra copy because (for example) they process blocks strictly
 * right-to-left.  At some point I might determine which ones don't need the
 * copy, but my reasoning would need to be verified very carefully.  For now
 * I'll leave in the copy.
 */
#define DTRT_ALIASED(cond, op) \
	if (cond) { \
		BigUnsigned tmpThis; \
		tmpThis.op; \
		*this = tmpThis; \
		return; \
	}



void BigUnsigned::add(const BigUnsigned &a, const BigUnsigned &b) {
	DTRT_ALIASED(this == &a || this == &b, add(a, b));
	// If one argument is zero, copy the other.
	if (a.len == 0) {
		operator =(b);
		return;
	} else if (b.len == 0) {
		operator =(a);
		return;
	}
	// Some variables...
	// Carries in and out of an addition stage
	bool carryIn, carryOut;
	Blk temp;
	Index i;
	// a2 points to the longer input, b2 points to the shorter
	const BigUnsigned *a2, *b2;
	if (a.len >= b.len) {
		a2 = &a;
		b2 = &b;
	} else {
		a2 = &b;
		b2 = &a;
	}
	// Set prelimiary length and make room in this BigUnsigned
	len = a2->len + 1;
	allocate(len);
	// For each block index that is present in both inputs...
	for (i = 0, carryIn = false; i < b2->len; i++) {
		// Add input blocks
		temp = a2->blk[i] + b2->blk[i];
		// If a rollover occurred, the result is less than either input.
		// This test is used many times in the BigUnsigned code.
		carryOut = (temp < a2->blk[i]);
		// If a carry was input, handle it
		if (carryIn) {
			temp++;
			carryOut |= (temp == 0);
		}
		blk[i] = temp; // Save the addition result
		carryIn = carryOut; // Pass the carry along
	}
	// If there is a carry left over, increase blocks until
	// one does not roll over.
	for (; i < a2->len && carryIn; i++) {
		temp = a2->blk[i] + 1;
		carryIn = (temp == 0);
		blk[i] = temp;
	}
	// If the carry was resolved but the larger number
	// still has blocks, copy them over.
	for (; i < a2->len; i++)
		blk[i] = a2->blk[i];
	// Set the extra block if there's still a carry, decrease length otherwise
	if (carryIn)
		blk[i] = 1;
	else
		len--;
}

void BigUnsigned::subtract(const BigUnsigned &a, const BigUnsigned &b) {
	DTRT_ALIASED(this == &a || this == &b, subtract(a, b));
	if (b.len == 0) {
		// If b is zero, copy a.
		operator =(a);
		return;
	} else if (a.len < b.len)
		// If a is shorter than b, the result is negative.
		throw "BigUnsigned::subtract: "
			"Negative result in unsigned calculation";
	// Some variables...
	bool borrowIn, borrowOut;
	Blk temp;
	Index i;
	// Set preliminary length and make room
	len = a.len;
	allocate(len);
	// For each block index that is present in both inputs...
	for (i = 0, borrowIn = false; i < b.len; i++) {
		temp = a.blk[i] - b.blk[i];
		// If a reverse rollover occurred,
		// the result is greater than the block from a.
		borrowOut = (temp > a.blk[i]);
		// Handle an incoming borrow
		if (borrowIn) {
			borrowOut |= (temp == 0);
			temp--;
		}
		blk[i] = temp; // Save the subtraction result
		borrowIn = borrowOut; // Pass the borrow along
	}
	// If there is a borrow left over, decrease blocks until
	// one does not reverse rollover.
	for (; i < a.len && borrowIn; i++) {
		borrowIn = (a.blk[i] == 0);
		blk[i] = a.blk[i] - 1;
	}
	/* If there's still a borrow, the result is negative.
	 * Throw an exception, but zero out this object so as to leave it in a
	 * predictable state. */
	if (borrowIn) {
		len = 0;
		throw "BigUnsigned::subtract: Negative result in unsigned calculation";
	} else
		// Copy over the rest of the blocks
		for (; i < a.len; i++)
			blk[i] = a.blk[i];
	// Zap leading zeros
	zapLeadingZeros();
}

/*
 * About the multiplication and division algorithms:
 *
 * I searched unsucessfully for fast C++ built-in operations like the `b_0'
 * and `c_0' Knuth describes in Section 4.3.1 of ``The Art of Computer
 * Programming'' (replace `place' by `Blk'):
 *
 *    ``b_0[:] multiplication of a one-place integer by another one-place
 *      integer, giving a two-place answer;
 *
 *    ``c_0[:] division of a two-place integer by a one-place integer,
 *      provided that the quotient is a one-place integer, and yielding
 *      also a one-place remainder.''
 *
 * I also missed his note that ``[b]y adjusting the word size, if
 * necessary, nearly all computers will have these three operations
 * available'', so I gave up on trying to use algorithms similar to his.
 * A future version of the library might include such algorithms; I
 * would welcome contributions from others for this.
 *
 * I eventually decided to use bit-shifting algorithms.  To multiply `a'
 * and `b', we zero out the result.  Then, for each `1' bit in `a', we
 * shift `b' left the appropriate amount and add it to the result.
 * Similarly, to divide `a' by `b', we shift `b' left varying amounts,
 * repeatedly trying to subtract it from `a'.  When we succeed, we note
 * the fact by setting a bit in the quotient.  While these algorithms
 * have the same O(n^2) time complexity as Knuth's, the ``constant factor''
 * is likely to be larger.
 *
 * Because I used these algorithms, which require single-block addition
 * and subtraction rather than single-block multiplication and division,
 * the innermost loops of all four routines are very similar.  Study one
 * of them and all will become clear.
 */

/*
 * This is a little inline function used by both the multiplication
 * routine and the division routine.
 *
 * `getShiftedBlock' returns the `x'th block of `num << y'.
 * `y' may be anything from 0 to N - 1, and `x' may be anything from
 * 0 to `num.len'.
 *
 * Two things contribute to this block:
 *
 * (1) The `N - y' low bits of `num.blk[x]', shifted `y' bits left.
 *
 * (2) The `y' high bits of `num.blk[x-1]', shifted `N - y' bits right.
 *
 * But we must be careful if `x == 0' or `x == num.len', in
 * which case we should use 0 instead of (2) or (1), respectively.
 *
 * If `y == 0', then (2) contributes 0, as it should.  However,
 * in some computer environments, for a reason I cannot understand,
 * `a >> b' means `a >> (b % N)'.  This means `num.blk[x-1] >> (N - y)'
 * will return `num.blk[x-1]' instead of the desired 0 when `y == 0';
 * the test `y == 0' handles this case specially.
 */
inline BigUnsigned::Blk getShiftedBlock(const BigUnsigned &num,
	BigUnsigned::Index x, unsigned int y) {
	BigUnsigned::Blk part1 = (x == 0 || y == 0) ? 0 : (num.blk[x - 1] >> (BigUnsigned::N - y));
	BigUnsigned::Blk part2 = (x == num.len) ? 0 : (num.blk[x] << y);
	return part1 | part2;
}

void BigUnsigned::multiply(const BigUnsigned &a, const BigUnsigned &b) {
	DTRT_ALIASED(this == &a || this == &b, multiply(a, b));
	// If either a or b is zero, set to zero.
	if (a.len == 0 || b.len == 0) {
		len = 0;
		return;
	}
	/*
	 * Overall method:
	 *
	 * Set this = 0.
	 * For each 1-bit of `a' (say the `i2'th bit of block `i'):
	 *    Add `b << (i blocks and i2 bits)' to *this.
	 */
	// Variables for the calculation
	Index i, j, k;
	unsigned int i2;
	Blk temp;
	bool carryIn, carryOut;
	// Set preliminary length and make room
	len = a.len + b.len;
	allocate(len);
	// Zero out this object
	for (i = 0; i < len; i++)
		blk[i] = 0;
	// For each block of the first number...
	for (i = 0; i < a.len; i++) {
		// For each 1-bit of that block...
		for (i2 = 0; i2 < N; i2++) {
			if ((a.blk[i] & (Blk(1) << i2)) == 0)
				continue;
			/*
			 * Add b to this, shifted left i blocks and i2 bits.
			 * j is the index in b, and k = i + j is the index in this.
			 *
			 * `getShiftedBlock', a short inline function defined above,
			 * is now used for the bit handling.  It replaces the more
			 * complex `bHigh' code, in which each run of the loop dealt
			 * immediately with the low bits and saved the high bits to
			 * be picked up next time.  The last run of the loop used to
			 * leave leftover high bits, which were handled separately.
			 * Instead, this loop runs an additional time with j == b.len.
			 * These changes were made on 2005.01.11.
			 */
			for (j = 0, k = i, carryIn = false; j <= b.len; j++, k++) {
				/*
				 * The body of this loop is very similar to the body of the first loop
				 * in `add', except that this loop does a `+=' instead of a `+'.
				 */
				temp = blk[k] + getShiftedBlock(b, j, i2);