| // Copyright 2014 PDFium Authors. All rights reserved. |
| // Use of this source code is governed by a BSD-style license that can be |
| // found in the LICENSE file. |
| |
| // Original code by Matt McCutchen, see the LICENSE file. |
| |
| #include "BigInteger.hh" |
| |
| BigInteger& BigInteger::operator =(const BigInteger &x) { |
| // Calls like a = a have no effect |
| if (this == &x) |
| return *this; |
| // Copy sign |
| sign = x.sign; |
| // Copy the rest |
| mag = x.mag; |
| return *this; |
| } |
| |
| BigInteger::BigInteger(const Blk *b, Index blen, Sign s) : mag(b, blen) { |
| switch (s) { |
| case zero: |
| if (!mag.isZero()) |
| abort(); |
| 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. */ |
| abort(); |
| } |
| } |
| |
| BigInteger::BigInteger(const BigUnsigned &x, Sign s) : mag(x) { |
| switch (s) { |
| case zero: |
| if (!mag.isZero()) |
| abort(); |
| 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. */ |
| abort(); |
| } |
| } |
| |
| /* 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) |
| abort(); |
| 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. |
| } |
| abort(); |
| } |
| |
| 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: |
| abort(); |
| } |
| } |
| |
| /* 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) |
| abort(); |
| 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 |
| BigInteger& BigInteger::operator ++() { |
| if (sign == negative) { |
| mag--; |
| if (mag == 0) |
| sign = zero; |
| } else { |
| mag++; |
| sign = positive; // if not already |
| } |
| return *this; |
| } |
| |
| // Postfix increment |
| BigInteger BigInteger::operator ++(int) { |
| BigInteger temp(*this); |
| operator ++(); |
| return temp; |
| } |
| |
| // Prefix decrement |
| BigInteger& BigInteger::operator --() { |
| if (sign == positive) { |
| mag--; |
| if (mag == 0) |
| sign = zero; |
| } else { |
| mag++; |
| sign = negative; |
| } |
| return *this; |
| } |
| |
| // Postfix decrement |
| BigInteger BigInteger::operator --(int) { |
| BigInteger temp(*this); |
| operator --(); |
| return temp; |
| } |
| |