/*****
 * runmath.in
 *
 * Runtime functions for math operations.
 *
 *****/

pair     => primPair()
realarray* => realArray()
pairarray* => pairArray()

#include <inttypes.h>
#include "mathop.h"
#include "path.h"

using namespace camp;

typedef array realarray;
typedef array pairarray;

using types::realArray;
using types::pairArray;

using run::integeroverflow;
using vm::frame;

const char *invalidargument="invalid argument";

extern uint32_t CLZ(uint32_t a);

// Return the factorial of a non-negative integer using a lookup table.
Int factorial(Int n)
{
  static Int *table;
  static Int size=0;
  if(size == 0) {
    Int f=1;
    size=2;
    while(f <= Int_MAX/size)
      f *= (size++);
    table=new Int[size];
    table[0]=f=1;
    for(Int i=1; i < size; ++i) {
      f *= i;
      table[i]=f;
    }
  }
  if(n >= size) integeroverflow(0);
  return table[n];
}

static inline Int Round(double x) 
{
  return Int(x+((x >= 0) ? 0.5 : -0.5));
}

inline Int sgn(double x) 
{
  return (x > 0.0 ? 1 : (x < 0.0 ? -1 : 0));
}

static bool initializeRandom=true;

void Srand(Int seed)
{ 
  initializeRandom=false;
  const int n=256;
  static char state[n];
  initstate(intcast(seed),state,n);
}  

// Autogenerated routines:


real ^(real x, Int y)
{
  return pow(x,y);
}

pair ^(pair z, Int y)
{
  return pow(z,y);
}

Int quotient(Int x, Int y)
{ 
  if(y == 0) dividebyzero();
  if(y == -1) return Negate(x);
// Implementation-independent definition of integer division: round down
  return (x-portableMod(x,y))/y;
}  

Int abs(Int x)
{ 
  return Abs(x);
}  

Int sgn(real x)
{ 
  return sgn(x);
}  

Int rand()
{ 
  if(initializeRandom)
    Srand(1);
  return random();
}  

void srand(Int seed)
{ 
  Srand(seed);
}  

// a random number uniformly distributed in the interval [0,1]
real unitrand()
{                         
  return ((real) random())/RAND_MAX;
}

Int ceil(real x)
{ 
  return Intcast(ceil(x));
}

Int floor(real x)
{ 
  return Intcast(floor(x));
}

Int round(real x)
{ 
  if(validInt(x)) return Round(x);
  integeroverflow(0);
}

Int Ceil(real x)
{ 
  return Ceil(x);
}

Int Floor(real x)
{ 
  return Floor(x);
}

Int Round(real x)
{ 
  return Round(Intcap(x));
}

real fmod(real x, real y)
{
  if (y == 0.0) dividebyzero();
  return fmod(x,y);
}

real atan2(real y, real x)
{ 
  return atan2(y,x);
}  

real hypot(real x, real y)
{ 
  return hypot(x,y);
}  

real remainder(real x, real y)
{ 
  return remainder(x,y);
}  

real Jn(Int n, real x)
{
  return jn(n,x);
}

real Yn(Int n, real x)
{
  return yn(n,x);
}

real erf(real x)
{
  return erf(x);
}

real erfc(real x)
{
  return erfc(x);
}

Int factorial(Int n) {
  if(n < 0) error(invalidargument);
  return factorial(n);
}

Int choose(Int n, Int k) {
  if(n < 0 || k < 0 || k > n) error(invalidargument);
  Int f=1;
  Int r=n-k;
  for(Int i=n; i > r; --i) {
    if(f > Int_MAX/i) integeroverflow(0);
    f=(f*i)/(n-i+1);
  }
  return f;
}

real gamma(real x)
{
#ifdef HAVE_TGAMMA
  return tgamma(x);
#else
  real lg = lgamma(x);
  return signgam*exp(lg);
#endif
}

realarray *quadraticroots(real a, real b, real c)
{
  quadraticroots q(a,b,c);
  array *roots=new array(q.roots);
  if(q.roots >= 1) (*roots)[0]=q.t1;
  if(q.roots == 2) (*roots)[1]=q.t2;
  return roots;
}

pairarray *quadraticroots(explicit pair a, explicit pair b, explicit pair c)
{
  Quadraticroots q(a,b,c);
  array *roots=new array(q.roots);
  if(q.roots >= 1) (*roots)[0]=q.z1;
  if(q.roots == 2) (*roots)[1]=q.z2;
  return roots;
}

realarray *cubicroots(real a, real b, real c, real d)
{
  cubicroots q(a,b,c,d);
  array *roots=new array(q.roots);
  if(q.roots >= 1) (*roots)[0]=q.t1;
  if(q.roots >= 2) (*roots)[1]=q.t2;
  if(q.roots == 3) (*roots)[2]=q.t3;
  return roots;
}


// Logical operations

bool !(bool b)
{
  return !b;
}

bool :boolMemEq(frame *a, frame *b)
{
  return a == b;
}

bool :boolMemNeq(frame *a, frame *b)
{
  return a != b;
}

bool :boolFuncEq(callable *a, callable *b)
{
  return a->compare(b);
}

bool :boolFuncNeq(callable *a, callable *b)
{
  return !(a->compare(b));
}


// Bit operations

Int AND(Int a, Int b) 
{
  return a & b;
}

Int OR(Int a, Int b) 
{
  return a | b;
}

Int XOR(Int a, Int b) 
{
  return a ^ b;
}

Int NOT(Int a)
{
  return ~a;
}

Int CLZ(Int a) 
{
  if((uint32_t) a > 0xFFFFFFFF) return -1;
  return CLZ((uint32_t) a);
}

Int CTZ(Int a) 
{
  if((uint32_t) a > 0xFFFFFFFF) return -1;
#if __GNUC_PREREQ(3,4)
  return __builtin_ctz(a);
#else
  // find the number of trailing zeros in a 32-bit number
  static const int MultiplyDeBruijnBitPosition[32] = {
    0, 1, 28, 2, 29, 14, 24, 3, 30, 22, 20, 15, 25, 17, 4, 8, 
    31, 27, 13, 23, 21, 19, 16, 7, 26, 12, 18, 6, 11, 5, 10, 9
  };
  return MultiplyDeBruijnBitPosition[((uint32_t)((a & -a) * 0x077CB531U))
                                     >> 27];
#endif
}