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authorClifford Wolf <clifford@clifford.at>2013-02-27 09:32:19 +0100
committerClifford Wolf <clifford@clifford.at>2013-02-27 09:32:19 +0100
commita321a5c412090d04dfaea4b4876c4901c42cfe44 (patch)
treeb08d286e0aea76be9aab7a543df0b51e76b6ede4 /libs/bigint/BigInteger.cc
parent4f0c2862a0d7e1ca247e0a4d54301c7f8cc92fd8 (diff)
Moved stand-alone libs to libs/ directory and added libs/subcircuit
Diffstat (limited to 'libs/bigint/BigInteger.cc')
-rw-r--r--libs/bigint/BigInteger.cc405
1 files changed, 405 insertions, 0 deletions
diff --git a/libs/bigint/BigInteger.cc b/libs/bigint/BigInteger.cc
new file mode 100644
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+++ b/libs/bigint/BigInteger.cc
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+#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 --();
+}
+