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/********************* */
/*! \file integer_cln_imp.h
** \verbatim
** Top contributors (to current version):
** Tim King, Morgan Deters, Liana Hadarean
** This file is part of the CVC4 project.
** Copyright (c) 2009-2020 by the authors listed in the file AUTHORS
** in the top-level source directory) and their institutional affiliations.
** All rights reserved. See the file COPYING in the top-level source
** directory for licensing information.\endverbatim
**
** \brief A multiprecision integer constant; wraps a CLN multiprecision
** integer.
**
** A multiprecision integer constant; wraps a CLN multiprecision integer.
**/
#include "cvc4_public.h"
#ifndef CVC4__INTEGER_H
#define CVC4__INTEGER_H
#include <cln/input.h>
#include <cln/integer.h>
#include <cln/integer_io.h>
#include <cln/modinteger.h>
#include <iostream>
#include <limits>
#include <sstream>
#include <string>
#include "base/exception.h"
namespace CVC4 {
class Rational;
class CVC4_PUBLIC Integer {
private:
/**
* Stores the value of the rational is stored in a C++ CLN integer class.
*/
cln::cl_I d_value;
/**
* Gets a reference to the cln data that backs up the integer.
* Only accessible to friend classes.
*/
const cln::cl_I& get_cl_I() const { return d_value; }
/**
* Constructs an Integer by copying a CLN C++ primitive.
*/
Integer(const cln::cl_I& val) : d_value(val) {}
// Throws a std::invalid_argument on invalid input `s` for the given base.
void readInt(const cln::cl_read_flags& flags,
const std::string& s,
unsigned base);
// Throws a std::invalid_argument on invalid inputs.
void parseInt(const std::string& s, unsigned base);
// These constants are to help with CLN conversion in 32 bit.
// See http://www.ginac.de/CLN/cln.html#Conversions
static signed int s_fastSignedIntMax; /* 2^29 - 1 */
static signed int s_fastSignedIntMin; /* -2^29 */
static unsigned int s_fastUnsignedIntMax; /* 2^29 - 1 */
static signed long s_slowSignedIntMax; /* std::numeric_limits<signed int>::max() */
static signed long s_slowSignedIntMin; /* std::numeric_limits<signed int>::min() */
static unsigned long s_slowUnsignedIntMax; /* std::numeric_limits<unsigned int>::max() */
static unsigned long s_signedLongMin;
static unsigned long s_signedLongMax;
static unsigned long s_unsignedLongMax;
public:
/** Constructs a rational with the value 0. */
Integer() : d_value(0){}
/**
* Constructs a Integer from a C string.
* Throws std::invalid_argument if the string is not a valid rational.
* For more information about what is a valid rational string,
* see GMP's documentation for mpq_set_str().
*/
explicit Integer(const char* sp, unsigned base = 10)
{
parseInt(std::string(sp), base);
}
explicit Integer(const std::string& s, unsigned base = 10)
{
parseInt(s, base);
}
Integer(const Integer& q) : d_value(q.d_value) {}
Integer( signed int z) : d_value((signed long int)z) {}
Integer(unsigned int z) : d_value((unsigned long int)z) {}
Integer( signed long int z) : d_value(z) {}
Integer(unsigned long int z) : d_value(z) {}
#ifdef CVC4_NEED_INT64_T_OVERLOADS
Integer( int64_t z) : d_value(static_cast<long>(z)) {}
Integer(uint64_t z) : d_value(static_cast<unsigned long>(z)) {}
#endif /* CVC4_NEED_INT64_T_OVERLOADS */
~Integer() {}
/**
* Returns a copy of d_value to enable public access of CLN data.
*/
cln::cl_I getValue() const
{
return d_value;
}
Integer& operator=(const Integer& x){
if(this == &x) return *this;
d_value = x.d_value;
return *this;
}
bool operator==(const Integer& y) const {
return d_value == y.d_value;
}
Integer operator-() const{
return Integer(-(d_value));
}
bool operator!=(const Integer& y) const {
return d_value != y.d_value;
}
bool operator< (const Integer& y) const {
return d_value < y.d_value;
}
bool operator<=(const Integer& y) const {
return d_value <= y.d_value;
}
bool operator> (const Integer& y) const {
return d_value > y.d_value;
}
bool operator>=(const Integer& y) const {
return d_value >= y.d_value;
}
Integer operator+(const Integer& y) const {
return Integer( d_value + y.d_value );
}
Integer& operator+=(const Integer& y) {
d_value += y.d_value;
return *this;
}
Integer operator-(const Integer& y) const {
return Integer( d_value - y.d_value );
}
Integer& operator-=(const Integer& y) {
d_value -= y.d_value;
return *this;
}
Integer operator*(const Integer& y) const {
return Integer( d_value * y.d_value );
}
Integer& operator*=(const Integer& y) {
d_value *= y.d_value;
return *this;
}
Integer bitwiseOr(const Integer& y) const {
return Integer(cln::logior(d_value, y.d_value));
}
Integer bitwiseAnd(const Integer& y) const {
return Integer(cln::logand(d_value, y.d_value));
}
Integer bitwiseXor(const Integer& y) const {
return Integer(cln::logxor(d_value, y.d_value));
}
Integer bitwiseNot() const {
return Integer(cln::lognot(d_value));
}
/**
* Return this*(2^pow).
*/
Integer multiplyByPow2(uint32_t pow) const {
cln::cl_I ipow(pow);
return Integer( d_value << ipow);
}
bool isBitSet(uint32_t i) const {
return !extractBitRange(1, i).isZero();
}
Integer setBit(uint32_t i) const {
cln::cl_I mask(1);
mask = mask << i;
return Integer(cln::logior(d_value, mask));
}
Integer oneExtend(uint32_t size, uint32_t amount) const;
uint32_t toUnsignedInt() const {
return cln::cl_I_to_uint(d_value);
}
/** See CLN Documentation. */
Integer extractBitRange(uint32_t bitCount, uint32_t low) const {
cln::cl_byte range(bitCount, low);
return Integer(cln::ldb(d_value, range));
}
/**
* Returns the floor(this / y)
*/
Integer floorDivideQuotient(const Integer& y) const {
return Integer( cln::floor1(d_value, y.d_value) );
}
/**
* Returns r == this - floor(this/y)*y
*/
Integer floorDivideRemainder(const Integer& y) const {
return Integer( cln::floor2(d_value, y.d_value).remainder );
}
/**
* Computes a floor quoient and remainder for x divided by y.
*/
static void floorQR(Integer& q, Integer& r, const Integer& x, const Integer& y) {
cln::cl_I_div_t res = cln::floor2(x.d_value, y.d_value);
q.d_value = res.quotient;
r.d_value = res.remainder;
}
/**
* Returns the ceil(this / y)
*/
Integer ceilingDivideQuotient(const Integer& y) const {
return Integer( cln::ceiling1(d_value, y.d_value) );
}
/**
* Returns the ceil(this / y)
*/
Integer ceilingDivideRemainder(const Integer& y) const {
return Integer( cln::ceiling2(d_value, y.d_value).remainder );
}
/**
* Computes a quoitent and remainder according to Boute's Euclidean definition.
* euclidianDivideQuotient, euclidianDivideRemainder.
*
* Boute, Raymond T. (April 1992).
* The Euclidean definition of the functions div and mod.
* ACM Transactions on Programming Languages and Systems (TOPLAS)
* ACM Press. 14 (2): 127 - 144. doi:10.1145/128861.128862.
*/
static void euclidianQR(Integer& q, Integer& r, const Integer& x, const Integer& y) {
// compute the floor and then fix the value up if needed.
floorQR(q,r,x,y);
if(r.strictlyNegative()){
// if r < 0
// abs(r) < abs(y)
// - abs(y) < r < 0, then 0 < r + abs(y) < abs(y)
// n = y * q + r
// n = y * q - abs(y) + r + abs(y)
if(r.sgn() >= 0){
// y = abs(y)
// n = y * q - y + r + y
// n = y * (q-1) + (r+y)
q -= 1;
r += y;
}else{
// y = -abs(y)
// n = y * q + y + r - y
// n = y * (q+1) + (r-y)
q += 1;
r -= y;
}
}
}
/**
* Returns the quoitent according to Boute's Euclidean definition.
* See the documentation for euclidianQR.
*/
Integer euclidianDivideQuotient(const Integer& y) const {
Integer q,r;
euclidianQR(q,r, *this, y);
return q;
}
/**
* Returns the remainfing according to Boute's Euclidean definition.
* See the documentation for euclidianQR.
*/
Integer euclidianDivideRemainder(const Integer& y) const {
Integer q,r;
euclidianQR(q,r, *this, y);
return r;
}
/**
* If y divides *this, then exactQuotient returns (this/y)
*/
Integer exactQuotient(const Integer& y) const;
Integer modByPow2(uint32_t exp) const {
cln::cl_byte range(exp, 0);
return Integer(cln::ldb(d_value, range));
}
Integer divByPow2(uint32_t exp) const {
return d_value >> exp;
}
/**
* Raise this Integer to the power <code>exp</code>.
*
* @param exp the exponent
*/
Integer pow(unsigned long int exp) const;
/**
* Return the greatest common divisor of this integer with another.
*/
Integer gcd(const Integer& y) const {
cln::cl_I result = cln::gcd(d_value, y.d_value);
return Integer(result);
}
/**
* Return the least common multiple of this integer with another.
*/
Integer lcm(const Integer& y) const {
cln::cl_I result = cln::lcm(d_value, y.d_value);
return Integer(result);
}
/**
* Compute addition of this Integer x + y modulo m.
*/
Integer modAdd(const Integer& y, const Integer& m) const;
/**
* Compute multiplication of this Integer x * y modulo m.
*/
Integer modMultiply(const Integer& y, const Integer& m) const;
/**
* Compute modular inverse x^-1 of this Integer x modulo m with m > 0.
* Returns a value x^-1 with 0 <= x^-1 < m such that x * x^-1 = 1 modulo m
* if such an inverse exists, and -1 otherwise.
*
* Such an inverse only exists if
* - x is non-zero
* - x and m are coprime, i.e., if gcd (x, m) = 1
*
* Note that if x and m are coprime, then x^-1 > 0 if m > 1 and x^-1 = 0
* if m = 1 (the zero ring).
*/
Integer modInverse(const Integer& m) const;
/**
* Return true if *this exactly divides y.
*/
bool divides(const Integer& y) const {
cln::cl_I result = cln::rem(y.d_value, d_value);
return cln::zerop(result);
}
/**
* Return the absolute value of this integer.
*/
Integer abs() const {
return d_value >= 0 ? *this : -*this;
}
std::string toString(int base = 10) const{
std::stringstream ss;
switch(base){
case 2:
fprintbinary(ss,d_value);
break;
case 8:
fprintoctal(ss,d_value);
break;
case 10:
fprintdecimal(ss,d_value);
break;
case 16:
fprinthexadecimal(ss,d_value);
break;
default:
throw Exception("Unhandled base in Integer::toString()");
}
std::string output = ss.str();
for( unsigned i = 0; i <= output.length(); ++i){
if(isalpha(output[i])){
output.replace(i, 1, 1, tolower(output[i]));
}
}
return output;
}
int sgn() const {
cln::cl_I sgn = cln::signum(d_value);
return cln::cl_I_to_int(sgn);
}
inline bool strictlyPositive() const {
return sgn() > 0;
}
inline bool strictlyNegative() const {
return sgn() < 0;
}
inline bool isZero() const {
return sgn() == 0;
}
inline bool isOne() const {
return d_value == 1;
}
inline bool isNegativeOne() const {
return d_value == -1;
}
/** fits the C "signed int" primitive */
bool fitsSignedInt() const;
/** fits the C "unsigned int" primitive */
bool fitsUnsignedInt() const;
int getSignedInt() const;
unsigned int getUnsignedInt() const;
bool fitsSignedLong() const;
bool fitsUnsignedLong() const;
long getLong() const {
// ensure there isn't overflow
CheckArgument(d_value <= std::numeric_limits<long>::max(), this,
"Overflow detected in Integer::getLong()");
CheckArgument(d_value >= std::numeric_limits<long>::min(), this,
"Overflow detected in Integer::getLong()");
return cln::cl_I_to_long(d_value);
}
unsigned long getUnsignedLong() const {
// ensure there isn't overflow
CheckArgument(d_value <= std::numeric_limits<unsigned long>::max(), this,
"Overflow detected in Integer::getUnsignedLong()");
CheckArgument(d_value >= std::numeric_limits<unsigned long>::min(), this,
"Overflow detected in Integer::getUnsignedLong()");
return cln::cl_I_to_ulong(d_value);
}
/**
* Computes the hash of the node from the first word of the
* numerator, the denominator.
*/
size_t hash() const {
return equal_hashcode(d_value);
}
/**
* Returns true iff bit n is set.
*
* @param n the bit to test (0 == least significant bit)
* @return true if bit n is set in this integer; false otherwise
*/
bool testBit(unsigned n) const {
return cln::logbitp(n, d_value);
}
/**
* Returns k if the integer is equal to 2^(k-1)
* @return k if the integer is equal to 2^(k-1) and 0 otherwise
*/
unsigned isPow2() const {
if (d_value <= 0) return 0;
// power2p returns n such that d_value = 2^(n-1)
return cln::power2p(d_value);
}
/**
* If x != 0, returns the unique n s.t. 2^{n-1} <= abs(x) < 2^{n}.
* If x == 0, returns 1.
*/
size_t length() const {
int s = sgn();
if(s == 0){
return 1;
}else if(s < 0){
size_t len = cln::integer_length(d_value);
/*If this is -2^n, return len+1 not len to stay consistent with the definition above!
* From CLN's documentation of integer_length:
* This is the smallest n >= 0 such that -2^n <= x < 2^n.
* If x > 0, this is the unique n > 0 such that 2^(n-1) <= x < 2^n.
*/
size_t ord2 = cln::ord2(d_value);
return (len == ord2) ? (len + 1) : len;
}else{
return cln::integer_length(d_value);
}
}
/* cl_I xgcd (const cl_I& a, const cl_I& b, cl_I* u, cl_I* v) */
/* This function ("extended gcd") returns the greatest common divisor g of a and b and at the same time the representation of g as an integral linear combination of a and b: u and v with u*a+v*b = g, g >= 0. u and v will be normalized to be of smallest possible absolute value, in the following sense: If a and b are non-zero, and abs(a) != abs(b), u and v will satisfy the inequalities abs(u) <= abs(b)/(2*g), abs(v) <= abs(a)/(2*g). */
static void extendedGcd(Integer& g, Integer& s, Integer& t, const Integer& a, const Integer& b){
g.d_value = cln::xgcd(a.d_value, b.d_value, &s.d_value, &t.d_value);
}
/** Returns a reference to the minimum of two integers. */
static const Integer& min(const Integer& a, const Integer& b){
return (a <=b ) ? a : b;
}
/** Returns a reference to the maximum of two integers. */
static const Integer& max(const Integer& a, const Integer& b){
return (a >= b ) ? a : b;
}
friend class CVC4::Rational;
};/* class Integer */
struct IntegerHashFunction {
inline size_t operator()(const CVC4::Integer& i) const {
return i.hash();
}
};/* struct IntegerHashFunction */
inline std::ostream& operator<<(std::ostream& os, const Integer& n) {
return os << n.toString();
}
}/* CVC4 namespace */
#endif /* CVC4__INTEGER_H */
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