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#if ! defined Already_Included_Util
#define Already_Included_Util
#include <stdio.h>
#include <stdlib.h>
#include <assert.h>
#include <string>
#include <sstream>
#include <stdexcept>
namespace omega {
#define LONG_LONG_COEF 1
#if LONG_LONG_COEF
#if defined BOGUS_LONG_DOUBLE_COEF
typedef long double coef_t; // type of coefficients
#define coef_fmt "%llf"
#define posInfinity (1e+24)
#define negInfinity (-1e+24)
#else
#ifdef WIN32
typedef _int64 coef_t; // type of coefficients
#else
typedef long long coef_t;
#endif
#define coef_fmt "%lld"
#define posInfinity (0x7ffffffffffffffLL)
#define negInfinity (-0x7ffffffffffffffLL)
#endif
#else
typedef int coef_t; // type of coefficients
#define coef_fmt "%d"
#define posInfinity (0x7ffffff)
#define negInfinity (-0x7ffffff)
#endif
template<typename T> inline const T& max(const T &x, const T &y) {
if (x >= y) return x; else return y;
}
template<typename T> inline const T& max(const T &x, const T &y, const T &z) {
return max(x, max(y, z));
}
template<typename T> inline const T& min(const T &x, const T &y) {
if (x <= y) return x; else return y;
}
template<typename T> inline const T& min(const T &x, const T &y, const T &z) {
return min(x, min(y, z));
}
template<class T> inline void set_max(T &m, const T &x) {
if (m < x) m = x;
}
template<class T> inline void set_min(T &m, const T &x) {
if (m > x) m = x;
}
/* template<class T> inline void swap(T &i, T &j) { */
/* T tmp; */
/* tmp = i; */
/* i = j; */
/* j = tmp; */
/* } */
/* template<class T> inline T copy(const T &t) { return t; } */
/* inline coef_t check_pos_mul(coef_t x, coef_t y) { */
/* if (y >= 48051280 && y < posInfinity) */
/* fprintf(stderr, "%d %d\n", x, y); */
/* /\* #if !defined NDEBUG *\/ */
/* /\* if (x != 0) *\/ */
/* /\* assert(((MAXINT)/4) / x > y); *\/ */
/* /\* #elif defined STILL_CHECK_MULT *\/ */
/* /\* if (x != 0 && !(((MAXINT)/4) / x > y)) { *\/ */
/* /\* assert(0&&"Integer overflow during multiplication (util.h)"); *\/ */
/* /\* } *\/ */
/* /\* #endif *\/ */
/* #if !defined NDEBUG */
/* if (x != 0 && y != 0) */
/* assert(x*y > 0); */
/* #elif defined STILL_CHECK_MULT */
/* if (x != 0 && y != 0 && x*y < 0) */
/* assert(0&&"Integer overflow during multiplication (util.h)"); */
/* #endif */
/* return x * y; */
/* } */
/* inline int */
/* check_pos_mul(int x, int y) { */
/* #if !defined NDEBUG */
/* if (x != 0) */
/* assert(((posInfinity)/4) / x > y); */
/* #elif defined STILL_CHECK_MULT */
/* if (x != 0 && !(((posInfinity)/4) / x > y)) { */
/* assert(0&&"Integer overflow during multiplication (util.h)"); */
/* } */
/* #endif */
/* return x * y; */
/* } */
/* inline LONGLONG */
/* check_pos_mul(LONGLONG x, LONGLONG y) { */
/* #if !defined NDEBUG */
/* if (x != 0) */
/* assert(((posInfinity)/4) / x > y); */
/* #elif defined STILL_CHECK_MULT */
/* if (x != 0 && !(((posInfinity)/4) / x > y)) { */
/* assert(0&&"Integer overflow during multiplication (util.h)"); */
/* } */
/* #endif */
/* return x * y; */
/* } */
/* inline LONGLONG abs(LONGLONG c) { return (c>=0?c:(-c)); } */
template<typename T> inline T check_mul(const T &x, const T &y) {
#if defined NDEBUG && ! defined STILL_CHECK_MULT
return x*y;
#else
if (x == 0 || y == 0)
return 0;
T z = x*y;
int sign_x = (x>0)?1:-1;
int sign_y = (y>0)?1:-1;
int sign_z = (z>0)?1:-1;
if (sign_x * sign_y != sign_z)
throw std::overflow_error("coefficient multiply overflow");
return z;
/* if (x > 0) { */
/* if (y > 0) { */
/* assert(x*y > 0); */
/* } */
/* else */
/* assert(x*y < 0); */
/* } */
/* else { */
/* if (y > 0) */
/* assert(x*y < 0); */
/* else */
/* assert(x*y > 0); */
/* } */
/* return x*y; */
#endif
}
template<typename T> inline T abs(const T &v) {
return (v >= static_cast<T>(0))?v:-v;
}
template<class T> inline T int_div(const T &a, const T &b) {
T result;
assert(b > 0);
if (a>0) result = a/b;
else result = -((-a+b-1)/b);
return result;
}
template<class T> inline T int_mod(const T &a, const T &b) {
return a-b*int_div(a,b);
}
template<class T> inline T int_mod_hat(const T &a, const T &b) {
T r;
assert(b > 0);
r = a-b*int_div(a,b);
if (r > -(r-b)) r -= b;
return r;
}
template<typename T> inline T gcd(T b, T a) {/* First argument is non-negative */
assert(a >= 0);
assert(b >= 0);
if (b == 1)
return (1);
while (b != 0) {
T t = b;
b = a % b;
a = t;
}
return (a);
}
template<typename T> inline T lcm(T b, T a) { /* First argument is non-negative */
assert(a >= 0);
assert(b >= 0);
return check_mul(a/gcd(a,b), b);
}
template<typename T> T square_root(const T &n, T precision = 1) {
T guess = 1;
while (true) {
T next_guess = 0.5*(guess+n/guess);
if (abs(next_guess-guess) <= precision)
return next_guess;
else
guess = next_guess;
}
}
template<typename T> T factor(const T &n) {
assert(n >= 0);
if (n == 1) return 1;
static int prime[30] = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113};
if (n <= 113*113) {
for (int i = 0; i < 30; i++)
if (n % static_cast<T>(prime[i]) == 0)
return static_cast<T>(prime[i]);
return n;
}
T i = 1;
T k = 2;
T x = static_cast<T>(rand())%n;
T y = x;
while(i < square_root<float>(n, 1)) {
i++;
x = (x*x-1) % n;
T d = gcd(abs(y-x), n);
if(d != 1 && d != n)
return factor(d);
if(i == k) {
y = x;
k *= 2;
}
}
return n;
}
/* #define implies(A,B) (A==(A&B)) */
template<typename T> std::string to_string(const T &t) {
std::ostringstream ss;
ss << t;
return ss.str();
}
template<typename T> T from_string(const std::string &s) {
std::istringstream ss(s);
ss.exceptions(std::ios::failbit);
T t;
ss >> t;
return t;
}
} // namespace
#endif
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