#ifndef UTIL_H
#define UTIL_H

#include <algorithm>
#include <vector>
#include <cmath>
#include <iostream>
#include <fstream>

#ifndef M_PI
const double M_PI = 3.1415926535897932384626433832795;
#endif
typedef float		FLOAT32;		// 32 bit floating point
typedef double		FLOAT64;		// 64 bit floating point
typedef long double	FLOAT80;		// 80 bit floating point
typedef unsigned int uint;			// Generic unsigned integer
typedef unsigned char uint8;		// 8 bit unsigned char
typedef unsigned long long uint64;	// 64 bit integer

#ifdef WIN32
#undef min
#undef max
#endif

using std::min;
using std::max;
using std::swap;

template<class T>
inline T sqr(const T& x)
{ return x*x; }

template<class T>
inline T cube(const T& x)
{ return x*x*x; }

template<class T>
inline T min(T a1, T a2, T a3)
{ return min(a1, min(a2, a3)); }

template<class T>
inline T min(T a1, T a2, T a3, T a4)
{ return min(min(a1, a2), min(a3, a4)); }

template<class T>
inline T min(T a1, T a2, T a3, T a4, T a5)
{ return min(min(a1, a2), min(a3, a4), a5); }

template<class T>
inline T min(T a1, T a2, T a3, T a4, T a5, T a6)
{ return min(min(a1, a2), min(a3, a4), min(a5, a6)); }

template<class T>
inline T max(T a1, T a2, T a3)
{ return max(a1, max(a2, a3)); }

template<class T>
inline T max(T a1, T a2, T a3, T a4)
{ return max(max(a1, a2), max(a3, a4)); }

template<class T>
inline T max(T a1, T a2, T a3, T a4, T a5)
{ return max(max(a1, a2), max(a3, a4),  a5); }

template<class T>
inline T max(T a1, T a2, T a3, T a4, T a5, T a6)
{ return max(max(a1, a2), max(a3, a4),  max(a5, a6)); }

template<class T>
inline void minmax(T a1, T a2, T& amin, T& amax)
{
   if(a1<a2){
      amin=a1;
      amax=a2;
   }else{
      amin=a2;
      amax=a1;
   }
}

template<class T>
inline void minmax(T a1, T a2, T a3, T& amin, T& amax)
{
   if(a1<a2){
      if(a1<a3){
         amin=a1;
         if(a2<a3) amax=a3;
         else amax=a2;
      }else{
         amin=a3;
         if(a1<a2) amax=a2;
         else amax=a1;
      }
   }else{
      if(a2<a3){
         amin=a2;
         if(a1<a3) amax=a3;
         else amax=a1;
      }else{
         amin=a3;
         amax=a1;
      }
   }
}

template<class T>
inline void minmax(T a1, T a2, T a3, T a4, T& amin, T& amax)
{
   if(a1<a2){
      if(a3<a4){
         amin=min(a1,a3);
         amax=max(a2,a4);
      }else{
         amin=min(a1,a4);
         amax=max(a2,a3);
      }
   }else{
      if(a3<a4){
         amin=min(a2,a3);
         amax=max(a1,a4);
      }else{
         amin=min(a2,a4);
         amax=max(a1,a3);
      }
   }
}

template<class T>
inline void minmax(T a1, T a2, T a3, T a4, T a5, T& amin, T& amax)
{
   //@@@ the logic could be shortcircuited a lot!
   amin=min(a1,a2,a3,a4,a5);
   amax=max(a1,a2,a3,a4,a5);
}

template<class T>
inline void minmax(T a1, T a2, T a3, T a4, T a5, T a6, T& amin, T& amax)
{
   //@@@ the logic could be shortcircuited a lot!
   amin=min(a1,a2,a3,a4,a5,a6);
   amax=max(a1,a2,a3,a4,a5,a6);
}

template<class T>
inline void update_minmax(T a1, T& amin, T& amax)
{
   if(a1<amin) amin=a1;
   else if(a1>amax) amax=a1;
}

template<class T>
inline void sort(T &a, T &b, T &c)
{
   T temp;
   if(a<b){
      if(a<c){
    if(c<b){ // a<c<b
            temp=c;c=b;b=temp;
    } // else: a<b<c
      }else{ // c<a<b
    temp=c;c=b;b=a;a=temp;
      }
   }else{
      if(b<c){
    if(a<c){ //b<a<c
       temp=b;b=a;a=temp;
    }else{ // b<c<a
       temp=b;b=c;c=a;a=temp;
    }
      }else{ // c<b<a
    temp=c;c=a;a=temp;
      }
   }
}

template<class T>
inline T clamp(T a, T lower, T upper)
{
   if(a<lower) return lower;
   else if(a>upper) return upper;
   else return a;
}

// only makes sense with T=float or double
template<class T>
inline T smooth_step(T r)
{
   if(r<0) return 0;
   else if(r>1) return 1;
   return r*r*r*(10+r*(-15+r*6));
}

// only makes sense with T=float or double
template<class T>
inline T smooth_step(T r, T r_lower, T r_upper, T value_lower, T value_upper)
{ return value_lower + smooth_step((r-r_lower)/(r_upper-r_lower)) * (value_upper-value_lower); }

// only makes sense with T=float or double
template<class T>
inline T ramp(T r)
{ return smooth_step((r+1)/2)*2-1; }

#ifdef WIN32
//inline int lround(double x)
//{
//   if(x>0)
//      return (x-floor(x)<0.5) ? (int)floor(x) : (int)ceil(x);
//   else
//      return (x-floor(x)<=0.5) ? (int)floor(x) : (int)ceil(x);
//}

inline double remainder(double x, double y)
{
   return x-std::floor(x/y+0.5)*y;
}
#endif

inline unsigned int round_up_to_power_of_two(unsigned int n)
{
   int exponent=0;
   --n;
   while(n){
      ++exponent;
      n>>=1;
   }
   return 1<<exponent;
}

inline unsigned int round_down_to_power_of_two(unsigned int n)
{
   int exponent=0;
   while(n>1){
      ++exponent;
      n>>=1;
   }
   return 1<<exponent;
}

// Transforms even the sequence 0,1,2,3,... into reasonably good random numbers 
// Challenge: improve on this in speed and "randomness"!
// This seems to pass several statistical tests, and is a bijective map (of 32-bit unsigned ints)
inline unsigned int randhash(unsigned int seed)
{
   unsigned int i=(seed^0xA3C59AC3u)*2654435769u;
   i^=(i>>16);
   i*=2654435769u;
   i^=(i>>16);
   i*=2654435769u;
   return i;
}

// the inverse of randhash
inline unsigned int unhash(unsigned int h)
{
   h*=340573321u;
   h^=(h>>16);
   h*=340573321u;
   h^=(h>>16);
   h*=340573321u;
   h^=0xA3C59AC3u;
   return h;
}

// returns repeatable stateless pseudo-random number in [0,1]
inline double randhashd(unsigned int seed)
{ return randhash(seed)/(double)UINT_MAX; }
inline float randhashf(unsigned int seed)
{ return randhash(seed)/(float)UINT_MAX; }

// returns repeatable stateless pseudo-random number in [a,b]
inline double randhashd(unsigned int seed, double a, double b)
{ return (b-a)*randhash(seed)/(double)UINT_MAX + a; }
inline float randhashf(unsigned int seed, float a, float b)
{ return ( (b-a)*randhash(seed)/(float)UINT_MAX + a); }

inline int intlog2(int x)
{
   int exp=-1;
   while(x){
      x>>=1;
      ++exp;
   }
   return exp;
}

template<class T>
inline void get_barycentric(T x, int& i, T& f, int i_low, int i_high)
{
   T s=std::floor(x);
   i=(int)s;
   if(i<i_low){
      i=i_low;
      f=0;
   }else if(i>i_high-2){
      i=i_high-2;
      f=1;
   }else
      f=(T)(x-s);
}

template<class S, class T>
inline S lerp(const S& value0, const S& value1, T f)
{ return (1-f)*value0 + f*value1; }

template<class S, class T>
inline S bilerp(const S& v00, const S& v10, 
                const S& v01, const S& v11, 
                T fx, T fy)
{ 
   return lerp(lerp(v00, v10, fx),
               lerp(v01, v11, fx), 
               fy);
}

template<class S, class T>
inline S trilerp(const S& v000, const S& v100,
                 const S& v010, const S& v110,
                 const S& v001, const S& v101,  
                 const S& v011, const S& v111,
                 T fx, T fy, T fz) 
{
   return lerp(bilerp(v000, v100, v010, v110, fx, fy),
               bilerp(v001, v101, v011, v111, fx, fy),
               fz);
}

template<class S, class T>
inline S quadlerp(const S& v0000, const S& v1000,
                  const S& v0100, const S& v1100,
                  const S& v0010, const S& v1010,  
                  const S& v0110, const S& v1110,
                  const S& v0001, const S& v1001,
                  const S& v0101, const S& v1101,
                  const S& v0011, const S& v1011,  
                  const S& v0111, const S& v1111,
                  T fx, T fy, T fz, T ft) 
{
   return lerp(trilerp(v0000, v1000, v0100, v1100, v0010, v1010, v0110, v1110, fx, fy, fz),
               trilerp(v0001, v1001, v0101, v1101, v0011, v1011, v0111, v1111, fx, fy, fz),
               ft);
}

// f should be between 0 and 1, with f=0.5 corresponding to balanced weighting between w0 and w2
template<class T>
inline void quadratic_bspline_weights(T f, T& w0, T& w1, T& w2)
{
   w0=T(0.5)*sqr(f-1);
   w1=T(0.75)-sqr(f-T(0.5));;
   w2=T(0.5)*sqr(f);
}

// f should be between 0 and 1
template<class T>
inline void cubic_interp_weights(T f, T& wneg1, T& w0, T& w1, T& w2)
{
   T f2(f*f), f3(f2*f);
   wneg1=-T(1./3)*f+T(1./2)*f2-T(1./6)*f3;
   w0=1-f2+T(1./2)*(f3-f);
   w1=f+T(1./2)*(f2-f3);
   w2=T(1./6)*(f3-f);
}

template<class S, class T>
inline S cubic_interp(const S& value_neg1, const S& value0, const S& value1, const S& value2, T f)
{
   T wneg1, w0, w1, w2;
   cubic_interp_weights(f, wneg1, w0, w1, w2);
   return wneg1*value_neg1 + w0*value0 + w1*value1 + w2*value2;
}

template<class T>
void zero(std::vector<T>& v)
{ for(int i=(int)v.size()-1; i>=0; --i) v[i]=0; }

template<class T>
T abs_max(const std::vector<T>& v)
{
   T m=0;
   for(int i=(int)v.size()-1; i>=0; --i){
      if(std::fabs(v[i])>m)
         m=std::fabs(v[i]);
   }
   return m;
}

template<class T>
bool contains(const std::vector<T>& a, T e)
{
   for(unsigned int i=0; i<a.size(); ++i)
      if(a[i]==e) return true;
   return false;
}

template<class T>
void add_unique(std::vector<T>& a, T e)
{
   for(unsigned int i=0; i<a.size(); ++i)
      if(a[i]==e) return;
   a.push_back(e);
}

template<class T>
void insert(std::vector<T>& a, unsigned int index, T e)
{
   a.push_back(a.back());
   for(unsigned int i=(unsigned int)a.size()-1; i>index; --i)
      a[i]=a[i-1];
   a[index]=e;
}

template<class T>
void erase(std::vector<T>& a, unsigned int index)
{
   for(unsigned int i=index; i<a.size()-1; ++i)
      a[i]=a[i+1];
   a.pop_back();
}

template<class T>
void erase_swap(std::vector<T>& a, unsigned int index)
{
   for(unsigned int i=index; i<a.size()-1; ++i)
      swap(a[i], a[i+1]);
   a.pop_back();
}

template<class T>
void erase_unordered(std::vector<T>& a, unsigned int index)
{
   a[index]=a.back();
   a.pop_back();
}

template<class T>
void erase_unordered_swap(std::vector<T>& a, unsigned int index)
{
   swap(a[index], a.back());
   a.pop_back();
}

template<class T>
void find_and_erase_unordered(std::vector<T>& a, const T& doomed_element)
{
   for(unsigned int i=0; i<a.size(); ++i)
      if(a[i]==doomed_element){
         erase_unordered(a, i);
         return;
      }
}

template<class T>
void replace_once(std::vector<T>& a, const T& old_element, const T& new_element)
{
   for(unsigned int i=0; i<a.size(); ++i)
      if(a[i]==old_element){
         a[i]=new_element;
         return;
      }
}

template<class T>
void write_matlab(std::ostream& output, const std::vector<T>& a, const char *variable_name, bool column_vector=true, int significant_digits=18)
{
   output<<variable_name<<"=[";
   std::streamsize old_precision=output.precision();
   output.precision(significant_digits);
   for(unsigned int i=0; i<a.size(); ++i){
      output<<a[i]<<" ";
   }
   output<<"]";
   if(column_vector)
      output<<"'";
   output<<";"<<std::endl;
   output.precision(old_precision);
}

#endif
