/usr/include/Lfunction/Lgram.h is in liblfunction-dev 1.23+dfsg-5.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 | /*
Copyright (C) 2001,2002,2003,2004 Michael Rubinstein
This file is part of the L-function package L.
This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License
as published by the Free Software Foundation; either version 2
of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
Check the License for details. You should have received a copy of it, along
with the package; see the file 'COPYING'. If not, write to the Free Software
Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
//returns first gram point >t
template <class ttype>
Double L_function <ttype>::
initialize_gram(Double t)
{
Double N1=N(t)/2,N2;
Double t2=t;
Long n1,n2;
Double incr=1.01/(N(t+1)/2-N1);
Double x,tmp;
Double y;
Long u;
if (incr<0)incr=.1;
n1=(Long)(floor(N1)+.1);
cout <<setprecision(20);
//N(T) behaves funny near the origin. So, if we are
//asking for a small gram point, start at 20, and scan backwards
if(N1<=2.){
//cout << "N1 = " << N1 << endl;
t2=12;
do{
t2=t2-.2;
tmp=N(t2)/2;
//cout<< t2<< " " << tmp << endl;
}while(t2>t&&tmp>0);
if(t2<t) {
t2=t;
//if zeta, dirichlet, cusp form for SL2(Z), or maass L-function,
//we can return 0 as a gram point
if(t==0&&this->what_type_L<4) return 0;
}
else {n1=-1;incr=.2;}
//cout<< n1<<" " << t2 << endl;
}
//cout <<"======="<<endl;
//fudge with the increment until we're sure to capture the next gram point
N2=N(t2+incr)/2;
n2=(Long)(floor(N2)+.1); if(N2<0)n2--;
do{
if((n2-n1)<1){incr=incr*1.4; N2=N(t2+incr)/2;n2=(Long)(floor(N2)+.1);if(N2<0)n2--;}
if((n2-n1)>=2){incr=incr*.9; N2=N(t2+incr)/2;n2=(Long)(floor(N2)+.1);if(N2<0)n2--;}
//cout << t2 << " " << t2+incr << " " << n1 << " " << n2 << endl;
}while((n2-n1)<1||(n2-n1)>=2);
y=t2+incr;
//divide and conquer to compute the next gram point
for(int i=1;i<=20;i++){
x=(t2+y)/2; tmp=N(x)/2;
u=(Long) (floor(tmp)+.1); if(tmp<0) u--;
if(u==n1){ t2=x;}
else{ y=x;}
//cout << t2 << " " << y << endl;
}
return x;
}
//computes the gram point above the current gram point t, i.e.
//assumes that t is itself a gram point.
//I don't want to use initialize_gram(current_gram) because
//the numeric current gram might be slightly smaller than actual current
//gram and we might just get the same point
template <class ttype>
Double L_function <ttype>::
next_gram(Double t)
{
Double N1=(this->N(t))/2,N2;
Double t2=t;
Long n1,n2;
Double incr=1.01/((this->N(t+1))/2-N1);
if (incr<0)incr=.1;
n1=(Long)(rint(N1)+.1); //n1 is the closest int to N(t)/2
cout <<setprecision(20);
//fudge with the increment until we're sure to capture the next gram point
N2=(this->N(t2+incr))/2;
n2=(Long)(floor(N2)+.1);
do{
if((n2-n1)<1){incr=incr*1.4; N2=this->N(t2+incr)/2;n2=(Long)(floor(N2)+.1);}
if((n2-n1)>=2){incr=incr*.9; N2=this->N(t2+incr)/2;n2=(Long)(floor(N2)+.1);}
//cout << N1 << " " << N2 << " " << n1 << " " << n2 << endl;
}while((n2-n1)<1||(n2-n1)>=2);
Double x;
Double y=t2+incr;
//divide and conquer to compute the next gram point
for(int i=1;i<=20;i++){
x=(t2+y)/2;
if(((Long)(floor(this->N(x)/2)+.1))==n1){ t2=x;}
else{ y=x;}
//cout << t2 << " " << y << endl;
}
//cout << x << " " << this->N(x)/2 << endl;
//cout << "========================\n";
return x;
}
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