// matematica.c
# include "alfa.h"

double tabcos[3600],tabsin[3600];
///////////////////////////////////////
double Bin (int n, int k)
{double num,den,i,j;
for (num=den=j=1,i=n;j<=k;i--,j++)
{num*=i; den*=j;}
return num/den;}

// Creazione delle tabelle
// per seno e coseno.
void Creatabtrig ()
{int k; double x; Double C,S;
for (k=0,C=tabcos,S=tabsin;k<3600;
  k++,C++,S++)
{x=k*CMPid180/10;
*C=cos(x); *S=sin(x);}}

// Quoziente intero di due numeri reali.
int FaDiv (double a, double b)
{int q=floor(a/b); double r=a-b*q;
if ((b<0)&&(r<0)) q++; return q;}

// Divisione e resto simultaneamente.
void FaDivResto (double a, double b,
  Int Q, Double R)
{int q=floor(a/b); double r=a-b*q;
if ((b<0)&&(r<0)) {q++; r-=b;}
*Q=q; *R=r;}

// Resto nella divisione
// di numeri reali.
double FaResto (double a, double b)
{int q=floor(a/b); double r=a-b*q;
if ((b<0)&&(r<0)) r-=b; return r;}

double Fatt (int n)
{if (n==0) return 1; return Fatt(n-1)*n;}

// Coseno per argomenti espressi in gradi.
double FtCosg (double x)
{return cos(x*CMPid180);}

// Seno per argomenti espressi in gradi.
double FtSing (double x)
{return sin(x*CMPid180);}

double Gamma (double x)
{return exp(lgamma(x));}

Double Hadamard (Double A, Double B, int m)
{int k; Double P,U;
P=calloc(m,sizeof(double));
for (k=0,U=P;k<m;k++,A++,B++,U++) *U=*A**B;
return P;}

double Horner (double alfa, Double A, int n)
{double b; int k;
for (b=*(A++),k=1;k<=n;k++,A++) b=b*alfa+*A;
return b;}

double Max (double a, double b) {return a<=b ? b : a;}

double Max3 (double a, double b, double c) {return Max(a,Max(b,c));}

double Min (double a, double b) {return a<=b ? a : b;}

double Min3 (double a, double b, double c) {return Min(a,Min(b,c));}

double Potenza (double x, int n)
{if (!n) return 1;
if (n%2) return x*Potenza(x,n-1);
return Potenza(x*x,n/2);}

// Calcola x alla n modulo m.
int Potenzamodulare (int x, int n, int m)
{if (!n) return 1;
if (n%2) return (x*Potenzamodulare(x,n-1,m))%m;
return Potenzamodulare((x*x)%m,n/2,m);}

double Prodottoscalare (Double X, int m, Double Y)
{int k; double s;
for (s=k=0;k<m;k++,X++,Y++) s+=(*X**Y);
return s;}

void Rapp2 (int n, Char A)
{if (n==1) {A[0]='1'; A[1]=0;}
else if (n%2) {Rapp2((n-1)/2,A);
A=strchr(A,0); A[0]='1'; A[1]=0;}
else {Rapp2(n/2,A);
A=strchr(A,0); A[0]='0'; A[1]=0;}}

int S (int n)
{if (n==0) return 0; return S(n-1)+n;}

int Segno (double x)
{return x>0 ? 1 : x==0 ? 0 : -1;}

double Somma (double *A)
{double s,v;
for (s=0;(v=*A)>=0;A++) s+=v;
return s;}

int T (int x)
{if (x%2==0) return x/2; return 3*x+1;}

double Trigdatabella (double x, Double Tabella)
{x=FaResto(x,360)*10; return Tabella[lrint(x)];}