Initial check in of big integer library

third_party/bigint/BigInteger.cc

+#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 --();
+}
+