Initial check in of big integer library, v2010.04.30

R=tsepez@chromium.org

Review URL: https://codereview.chromium.org/773443004

1 files changed, 405 insertions, 0 deletions

diff --git a/third_party/bigint/BigInteger.cc b/third_party/bigint/BigInteger.cc
new file mode 100644
index 0000000000..3b23aa1e7b
--- /dev/null
+++ b/third_party/bigint/BigInteger.cc
@@ -0,0 +1,405 @@
+#include "BigInteger.hh"
+
+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
+	mag = x.mag;
+}
+
+BigInteger::BigInteger(const Blk *b, Index blen, Sign s) : mag(b, blen) {
+	switch (s) {
+	case zero:
+		if (!mag.isZero())
+			throw "BigInteger::BigInteger(const Blk *, Index, Sign): Cannot use a sign of zero with a nonzero magnitude";
+		sign = zero;
+		break;
+	case positive:
+	case negative:
+		// If the magnitude is zero, force the sign to zero.
+		sign = mag.isZero() ? zero : s;
+		break;
+	default:
+		/* g++ seems to be optimizing out this case on the assumption
+		 * that the sign is a valid member of the enumeration.  Oh well. */
+		throw "BigInteger::BigInteger(const Blk *, Index, Sign): Invalid sign";
+	}
+}
+
+BigInteger::BigInteger(const BigUnsigned &x, Sign s) : mag(x) {
+	switch (s) {
+	case zero:
+		if (!mag.isZero())
+			throw "BigInteger::BigInteger(const BigUnsigned &, Sign): Cannot use a sign of zero with a nonzero magnitude";
+		sign = zero;
+		break;
+	case positive:
+	case negative:
+		// If the magnitude is zero, force the sign to zero.
+		sign = mag.isZero() ? zero : s;
+		break;
+	default:
+		/* g++ seems to be optimizing out this case on the assumption
+		 * that the sign is a valid member of the enumeration.  Oh well. */
+		throw "BigInteger::BigInteger(const BigUnsigned &, Sign): Invalid sign";
+	}
+}
+
+/* CONSTRUCTION FROM PRIMITIVE INTEGERS
+ * Same idea as in BigUnsigned.cc, except that negative input results in a
+ * negative BigInteger instead of an exception. */
+
+// Done longhand to let us use initialization.
+BigInteger::BigInteger(unsigned long  x) : mag(x) { sign = mag.isZero() ? zero : positive; }
+BigInteger::BigInteger(unsigned int   x) : mag(x) { sign = mag.isZero() ? zero : positive; }
+BigInteger::BigInteger(unsigned short x) : mag(x) { sign = mag.isZero() ? zero : positive; }
+
+// For signed input, determine the desired magnitude and sign separately.
+
+namespace {
+	template <class X, class UX>
+	BigInteger::Blk magOf(X x) {
+		/* UX(...) cast needed to stop short(-2^15), which negates to
+		 * itself, from sign-extending in the conversion to Blk. */
+		return BigInteger::Blk(x < 0 ? UX(-x) : x);
+	}
+	template <class X>
+	BigInteger::Sign signOf(X x) {
+		return (x == 0) ? BigInteger::zero
+			: (x > 0) ? BigInteger::positive
+			: BigInteger::negative;
+	}
+}
+
+BigInteger::BigInteger(long  x) : sign(signOf(x)), mag(magOf<long , unsigned long >(x)) {}
+BigInteger::BigInteger(int   x) : sign(signOf(x)), mag(magOf<int  , unsigned int  >(x)) {}
+BigInteger::BigInteger(short x) : sign(signOf(x)), mag(magOf<short, unsigned short>(x)) {}
+
+// CONVERSION TO PRIMITIVE INTEGERS
+
+/* Reuse BigUnsigned's conversion to an unsigned primitive integer.
+ * The friend is a separate function rather than
+ * BigInteger::convertToUnsignedPrimitive to avoid requiring BigUnsigned to
+ * declare BigInteger. */
+template <class X>
+inline X convertBigUnsignedToPrimitiveAccess(const BigUnsigned &a) {
+	return a.convertToPrimitive<X>();
+}
+
+template <class X>
+X BigInteger::convertToUnsignedPrimitive() const {
+	if (sign == negative)
+		throw "BigInteger::to<Primitive>: "
+			"Cannot convert a negative integer to an unsigned type";
+	else
+		return convertBigUnsignedToPrimitiveAccess<X>(mag);
+}
+
+/* Similar to BigUnsigned::convertToPrimitive, but split into two cases for
+ * nonnegative and negative numbers. */
+template <class X, class UX>
+X BigInteger::convertToSignedPrimitive() const {
+	if (sign == zero)
+		return 0;
+	else if (mag.getLength() == 1) {
+		// The single block might fit in an X.  Try the conversion.
+		Blk b = mag.getBlock(0);
+		if (sign == positive) {
+			X x = X(b);
+			if (x >= 0 && Blk(x) == b)
+				return x;
+		} else {
+			X x = -X(b);
+			/* UX(...) needed to avoid rejecting conversion of
+			 * -2^15 to a short. */
+			if (x < 0 && Blk(UX(-x)) == b)
+				return x;
+		}
+		// Otherwise fall through.
+	}
+	throw "BigInteger::to<Primitive>: "
+		"Value is too big to fit in the requested type";
+}
+
+unsigned long  BigInteger::toUnsignedLong () const { return convertToUnsignedPrimitive<unsigned long >       (); }
+unsigned int   BigInteger::toUnsignedInt  () const { return convertToUnsignedPrimitive<unsigned int  >       (); }
+unsigned short BigInteger::toUnsignedShort() const { return convertToUnsignedPrimitive<unsigned short>       (); }
+long           BigInteger::toLong         () const { return convertToSignedPrimitive  <long , unsigned long> (); }
+int            BigInteger::toInt          () const { return convertToSignedPrimitive  <int  , unsigned int>  (); }
+short          BigInteger::toShort        () const { return convertToSignedPrimitive  <short, unsigned short>(); }
+
+// 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 mag.compareTo(x.mag);
+	case negative:
+		// Compare the magnitudes, but return the opposite result
+		return CmpRes(-mag.compareTo(x.mag));
+	default:
+		throw "BigInteger internal error";
+	}
+}
+
+/* COPY-LESS OPERATIONS
+ * These do some messing around to determine the sign of the result,
+ * then call one of BigUnsigned's copy-less operations. */
+
+// See remarks about aliased calls in BigUnsigned.cc .
+#define DTRT_ALIASED(cond, op) \
+	if (cond) { \
+		BigInteger tmpThis; \
+		tmpThis.op; \
+		*this = tmpThis; \
+		return; \
+	}
+
+void BigInteger::add(const BigInteger &a, const BigInteger &b) {
+	DTRT_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;
+		mag.add(a.mag, b.mag);
+	} else {
+		// Otherwise, their magnitudes must be compared.
+		switch (a.mag.compareTo(b.mag)) {
+		case equal:
+			// If their magnitudes are the same, copy zero.
+			mag = 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;
+			mag.subtract(a.mag, b.mag);
+			break;
+		case less:
+			sign = b.sign;
+			mag.subtract(b.mag, a.mag);
+			break;
+		}
+	}
+}
+
+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.
+	DTRT_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) {
+		mag = b.mag;
+		// 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;
+		mag.add(a.mag, b.mag);
+	} else {
+		// Otherwise, their magnitudes must be compared.
+		switch (a.mag.compareTo(b.mag)) {
+			// If their magnitudes are the same, copy zero.
+		case equal:
+			mag = 0;
+			sign = zero;
+			break;
+			// If a's magnitude is greater, take a.sign and
+			// subtract a from b.
+		case greater:
+			sign = a.sign;
+			mag.subtract(a.mag, b.mag);
+			break;
+			// If b's magnitude is greater, take the opposite
+			// of b.sign and subtract b from a.
+		case less:
+			sign = Sign(-b.sign);
+			mag.subtract(b.mag, a.mag);
+			break;
+		}
+	}
+}
+
+void BigInteger::multiply(const BigInteger &a, const BigInteger &b) {
+	DTRT_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;
+		mag = 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.
+	mag.multiply(a.mag, b.mag);
+}
+
+/*
+ * 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.mag = 0;
+		q.sign = zero;
+		return;
+	}
+	// 0 / b gives quotient 0 and remainder 0
+	if (sign == zero) {
+		q.mag = 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.
+		mag--;
+		/*
+		 * 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.
+	mag.divideWithRemainder(b.mag, q.mag);
+
+	if (sign != b.sign) {
+		// More for the harder case (as described):
+		// Increase the magnitude of the quotient by one.
+		q.mag++;
+		// Modify the remainder.
+		mag.subtract(b.mag, mag);
+		mag--;
+	}
+
+	// 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 (mag.isZero())
+		sign = zero;
+	if (q.mag.isZero())
+		q.sign = zero;
+
+	// WHEW!!!
+}
+
+// Negation
+void BigInteger::negate(const BigInteger &a) {
+	DTRT_ALIASED(this == &a, negate(a));
+	// Copy a's magnitude
+	mag = a.mag;
+	// 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 --();
+}
+