-/*
-* 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)
// Copy sign
sign = x.sign;
// Copy the rest
- BigUnsigned::operator =(x);
+ mag = x.mag;
}
-// Constructor from an array of blocks and a sign
-BigInteger::BigInteger(const Blk *b, Index l, Sign s) : BigUnsigned(b, l) {
+BigInteger::BigInteger(const Blk *b, Index blen, Sign s) : mag(b, blen) {
switch (s) {
- case zero:
- case positive:
- case negative:
- sign = (len == 0) ? zero : 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;
- 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;
+ case positive:
+ case negative:
+ // If the magnitude is zero, force the sign to zero.
+ sign = mag.isZero() ? zero : s;
break;
- default:
- throw "BigInteger::BigInteger(Blk *, Index, Sign): Invalid sign";
+ 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";
}
}
-/*
-* 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)
+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;
- else {
- cap = 1;
- blk = new Blk[1];
- sign = positive;
- len = 1;
- blk[0] = Blk(x);
+ 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";
}
}
-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;
-}
+/* CONSTRUCTION FROM PRIMITIVE INTEGERS
+ * Same idea as in BigUnsigned.cc, except that negative input results in a
+ * negative BigInteger instead of an exception. */
-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;
-}
+// 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; }
-// 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.
-*/
+// For signed input, determine the desired magnitude and sign separately.
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";
+ 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);
}
-}
-
-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";
+ template <class X>
+ BigInteger::Sign signOf(X x) {
+ return (x == 0) ? BigInteger::zero
+ : (x > 0) ? BigInteger::positive
+ : BigInteger::negative;
}
}
-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::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)) {}
-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";
- }
+// 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>();
}
-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";
- }
+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);
}
-BigInteger::operator short() const {
- switch (sign) {
- case zero:
+/* 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;
- 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";
+ 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
return greater;
else switch (sign) {
// If the signs are the same...
- case zero:
+ case zero:
return equal; // Two zeros are equal
- case positive:
+ case positive:
// Compare the magnitudes
- return BigUnsigned::compareTo(x);
- case negative:
+ return mag.compareTo(x.mag);
+ case negative:
// Compare the magnitudes, but return the opposite result
- return CmpRes(-BigUnsigned::compareTo(x));
- default:
- throw "BigInteger: Internal error";
+ return CmpRes(-mag.compareTo(x.mag));
+ 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.
+/* 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) \
return; \
}
-// Addition
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.
// common sign and add their magnitudes.
else if (a.sign == b.sign) {
sign = a.sign;
- BigUnsigned::add(a, b);
+ mag.add(a.mag, b.mag);
} else {
// Otherwise, their magnitudes must be compared.
- switch (a.BigUnsigned::compareTo(b)) {
+ switch (a.mag.compareTo(b.mag)) {
+ case equal:
// If their magnitudes are the same, copy zero.
- case equal:
- len = 0;
+ mag = 0;
sign = zero;
break;
// Otherwise, take the sign of the greater, and subtract
// the lesser magnitude from the greater magnitude.
- case greater:
+ case greater:
sign = a.sign;
- BigUnsigned::subtract(a, b);
+ mag.subtract(a.mag, b.mag);
break;
- case less:
+ case less:
sign = b.sign;
- BigUnsigned::subtract(b, a);
+ mag.subtract(b.mag, a.mag);
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.
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) {
- BigUnsigned::operator =(b);
+ 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);
// If their signs differ, take a.sign and add the magnitudes.
else if (a.sign != b.sign) {
sign = a.sign;
- BigUnsigned::add(a, b);
+ mag.add(a.mag, b.mag);
} else {
// Otherwise, their magnitudes must be compared.
- switch (a.BigUnsigned::compareTo(b)) {
+ switch (a.mag.compareTo(b.mag)) {
// If their magnitudes are the same, copy zero.
- case equal:
- len = 0;
+ case equal:
+ mag = 0;
sign = zero;
break;
// If a's magnitude is greater, take a.sign and
// subtract a from b.
- case greater:
+ case greater:
sign = a.sign;
- BigUnsigned::subtract(a, b);
+ 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:
+ case less:
sign = Sign(-b.sign);
- BigUnsigned::subtract(b, a);
+ mag.subtract(b.mag, a.mag);
break;
}
}
}
-// Multiplication
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;
- len = 0;
+ 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.
- BigUnsigned::multiply(a, b);
+ 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
-*/
+ * 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 .
// Division by zero gives quotient 0 and remainder *this
if (b.sign == zero) {
- q.len = 0;
+ q.mag = 0;
q.sign = zero;
return;
}
// 0 / b gives quotient 0 and remainder 0
if (sign == zero) {
- q.len = 0;
+ q.mag = 0;
q.sign = zero;
return;
}
// No: harder case. Quotient is negative.
q.sign = negative;
// Decrease the magnitude of the dividend by one.
- BigUnsigned::operator --();
+ 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.
- */
+ * 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);
+ 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.BigUnsigned::operator ++();
+ q.mag++;
// Modify the remainder.
- BigUnsigned temp(*this);
- BigUnsigned::subtract(b, temp);
- BigUnsigned::operator --();
+ 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 (len == 0)
+ if (mag.isZero())
sign = zero;
- if (q.len == 0)
+ if (q.mag.isZero())
q.sign = zero;
// WHEW!!!
void BigInteger::negate(const BigInteger &a) {
DTRT_ALIASED(this == &a, negate(a));
// Copy a's magnitude
- BigUnsigned::operator =(a);
+ mag = a.mag;
// Copy the opposite of a.sign
sign = Sign(-a.sign);
}
// 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)
+ if (sign == negative) {
+ mag--;
+ if (mag == 0)
sign = zero;
- break;
+ } else {
+ mag++;
+ sign = positive; // if not already
}
}
// 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)
+ if (sign == positive) {
+ mag--;
+ if (mag == 0)
sign = zero;
- break;
+ } else {
+ mag++;
+ sign = negative;
}
}
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