pow-ops.hpp
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/* -*- mode: C++; c-basic-offset: 2; indent-tabs-mode: nil -*- */
/*
* Main authors:
* Christian Schulte <schulte@gecode.org>
*
* Copyright:
* Christian Schulte, 2012
*
* This file is part of Gecode, the generic constraint
* development environment:
* http://www.gecode.org
*
* Permission is hereby granted, free of charge, to any person obtaining
* a copy of this software and associated documentation files (the
* "Software"), to deal in the Software without restriction, including
* without limitation the rights to use, copy, modify, merge, publish,
* distribute, sublicense, and/or sell copies of the Software, and to
* permit persons to whom the Software is furnished to do so, subject to
* the following conditions:
*
* The above copyright notice and this permission notice shall be
* included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
* LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
* OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
* WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*
*/
namespace Gecode { namespace Int { namespace Arithmetic {
forceinline
PowOps::PowOps(int n0) : n(n0) {}
forceinline bool
PowOps::even(int m) {
return (m & 1) == 0;
}
forceinline bool
PowOps::even(void) const {
return even(n);
}
forceinline int
PowOps::exp(void) const {
return n;
}
forceinline void
PowOps::exp(int m) {
n=m;
}
template<class IntType>
inline IntType
PowOps::pow(IntType x) const {
int m = n;
IntType p = 1;
do {
if (even(m)) {
x *= x; m >>= 1;
} else {
p *= x; m--;
}
} while (m > 0);
return p;
}
inline int
PowOps::tpow(int _x) const {
int m = n;
long long int p = 1;
long long int x = _x;
do {
if (even(m)) {
x *= x; m >>= 1;
} else {
p *= x; m--;
}
if (p > Limits::max)
return Limits::max+1;
if (p < Limits::min)
return Limits::min-1;
} while (m > 0);
return static_cast<int>(p);
}
forceinline bool
PowOps::powgr(long long int r, int x) const {
assert(r >= 0);
int m = n;
long long int y = r;
long long int p = 1;
do {
if (even(m)) {
y *= y; m >>= 1;
if (y > x)
return true;
} else {
p *= y; m--;
if (p > x)
return true;
}
} while (m > 0);
assert(y <= x);
return false;
}
inline int
PowOps::fnroot(int x) const {
if (x < 2)
return x;
/*
* We look for l such that: l^n <= x < (l+1)^n
*/
long long int l = 1;
long long int u = x;
do {
long long int m = (l + u) >> 1;
if (powgr(m,x)) u=m; else l=m;
} while (l+1 < u);
assert((pow(l) <= x) && (x < pow(l+1)));
return static_cast<int>(l);
}
forceinline bool
PowOps::powle(long long int r, int x) const {
assert(r >= 0);
int m = n;
long long int y = r;
long long int p = 1;
do {
if (even(m)) {
y *= y; m >>= 1;
if (y >= x)
return false;
} else {
p *= y; m--;
if (p >= x)
return false;
}
} while (m > 0);
assert(y < x);
return true;
}
inline int
PowOps::cnroot(int x) const {
if (x < 2)
return x;
/*
* We look for u such that: (u-1)^n < x <= u^n
*/
long long int l = 1;
long long int u = x;
do {
long long int m = (l + u) >> 1;
if (powle(m,x)) l=m; else u=m;
} while (l+1 < u);
assert((pow(u-1) < x) && (x <= pow(u)));
return static_cast<int>(u);
}
forceinline bool
SqrOps::even(void) const {
return true;
}
forceinline int
SqrOps::exp(void) const {
return 2;
}
forceinline void
SqrOps::exp(int) {
GECODE_NEVER;
}
template<class IntType>
inline IntType
SqrOps::pow(IntType x) const {
return x * x;
}
inline int
SqrOps::tpow(int _x) const {
long long int x = _x;
if (x*x > Limits::max)
return Limits::max+1;
if (x*x < Limits::min)
return Limits::min-1;
return static_cast<int>(x*x);
}
inline int
SqrOps::fnroot(int x) const {
if (x < 2)
return x;
/*
* We look for l such that: l^2 <= x < (l+1)^2
*/
long long int l = 1;
long long int u = x;
do {
long long int m = (l + u) >> 1;
if (m*m > x) u=m; else l=m;
} while (l+1 < u);
assert((pow(l) <= x) && (x < pow(l+1)));
return static_cast<int>(l);
}
inline int
SqrOps::cnroot(int x) const {
if (x < 2)
return x;
/*
* We look for u such that: (u-1)^n < x <= u^n
*/
long long int l = 1;
long long int u = x;
do {
long long int m = (l + u) >> 1;
if (m*m < x) l=m; else u=m;
} while (l+1 < u);
assert((pow(u-1) < x) && (x <= pow(u)));
return static_cast<int>(u);
}
}}}
// STATISTICS: int-other
Gecode::Int::Arithmetic::PowOps::cnroot
int cnroot(int x) const
Return where x must be non-negative and .
Definition pow-ops.hpp:153
Gecode::Int::Arithmetic::PowOps::tpow
int tpow(int x) const
Return where truncated to integer limits.
Definition pow-ops.hpp:75
Gecode::Int::Arithmetic::PowOps::powgr
bool powgr(long long int r, int x) const
Test whether .
Definition pow-ops.hpp:94
Gecode::Int::Arithmetic::PowOps::pow
IntType pow(IntType x) const
Return where .
Definition pow-ops.hpp:61
Gecode::Int::Arithmetic::PowOps::exp
int exp(void) const
Return exponent.
Definition pow-ops.hpp:50
Gecode::Int::Arithmetic::PowOps::powle
bool powle(long long int r, int x) const
Test whether .
Definition pow-ops.hpp:132
Gecode::Int::Arithmetic::PowOps::n
int n
The exponent and root index.
Definition arithmetic.hh:330
Gecode::Int::Arithmetic::PowOps::PowOps
PowOps(int n)
Initialize with exponent n.
Definition pow-ops.hpp:37
Gecode::Int::Arithmetic::PowOps::fnroot
int fnroot(int x) const
Return where x must be non-negative and .
Definition pow-ops.hpp:115
Gecode::Int::Arithmetic::PowOps::even
bool even(void) const
Return whether exponent is even.
Definition pow-ops.hpp:45
Gecode::Int::Arithmetic::SqrOps::tpow
int tpow(int x) const
Return truncated to integer limits.
Definition pow-ops.hpp:193
Gecode::Int::Arithmetic::SqrOps::fnroot
int fnroot(int x) const
Return where x must be non-negative and .
Definition pow-ops.hpp:203
Gecode::Int::Arithmetic::SqrOps::even
bool even(void) const
Return whether exponent is even.
Definition pow-ops.hpp:172
Gecode::Int::Arithmetic::SqrOps::pow
IntType pow(IntType x) const
Return .
Definition pow-ops.hpp:188
Gecode::Int::Arithmetic::SqrOps::cnroot
int cnroot(int x) const
Return where x must be non-negative and .
Definition pow-ops.hpp:220
Gecode::Int::Arithmetic::SqrOps::exp
int exp(void) const
Return exponent.
Definition pow-ops.hpp:177
Gecode::Int::Arithmetic
Numerical (arithmetic) propagators.
Gecode::Int::Limits::min
const int min
Smallest allowed integer value.
Definition int.hh:118
Gecode::Int::Limits::max
const int max
Largest allowed integer value.
Definition int.hh:116
Gecode::Int
Finite domain integers.
Gecode
Gecode toplevel namespace
forceinline
#define forceinline
Definition config.hpp:187
GECODE_NEVER
#define GECODE_NEVER
Assert that this command is never executed.
Definition macros.hpp:56