/*
    Copyright (C) 2019 Alessandro Languasco
*/

/****************   	A. LANGUASCO  		******************** 
************* COMPUTATION OF THE EULER KRONECKER CONSTANTS MOD q(PRIME) *******/

 /* Here we compute the values of -T(a/q) */


/*****************   Precomputations for the external C program   ****************/
 \\ \p needed to decide the precision  default (format, f)  for the floating point 
 
{precT(x,y)=  local(vec, aoverq, q, g, a, minutes, millisec, seconds, elaptimeprecomp, Tfile, tab,name, namefile);

default(format , f);  \\ print numbers with floating point notation (not E notation)

vec = readvec("./primroot.res"); \\getting q and g from primroot.res
q=vec[1];
g=vec[2];
\\ print(q);print(g);

print("Precomputation T-values for q = ",q, " and saving on file");
 
tab=sumnuminit();  \\ needed for the sumnum function

if (x<0, x=0); \\ needed to avoid problem with the first interval
if (x>=y, error("first exponent should be less than the second"));
if (y>q-2, y=q-2); \\ needed to avoid problem with the last interval


name="./precomp_T-";
namefile = Strprintf("%s-%012d-%012d.res", name, x, y); 

Tfile = fileopen(namefile, "w");  
if (x==0,filewrite(Tfile,q)); 
 
gettime();

	a=g^x%q;		
	for(k=x, y, 
				aoverq = a/q; \\ already sorted for the final summation in external program 
				filewrite(Tfile,sumnum(m=0, (log(aoverq+m)/(aoverq+m))-(log(1+m)/(1+m)),tab)); 		
				a=(a*g)%q;   \\a=g^k%q; 
		);
elaptimeprecomp=gettime();
fileclose(Tfile); 

/* print computation time */
seconds=floor(elaptimeprecomp/1000)%60;
minutes=floor(elaptimeprecomp/60000);
millisec=elaptimeprecomp- minutes*60000 - seconds*1000;
\\print(elaptimeprecomp); 
print("Precomputation time (I/O included): ", minutes, " min, ", seconds, " sec, ", millisec, " millisec");	
 
 
}

 

 
 
 
/************************************  
  
 DA FARE SU OGNI MACCHINA (le librerie create da gp2c dipendono dalla macchina che si usa)
 air:Desktop languasc$ gp2c-run -pmy_ -g -W precT.gp 
 
per creare le librerie .so e il file .gp2c

*******/