// 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"
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())
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
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 --();
}