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compact_representations.c
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#include "compact_representations.h"
#include "utility.h"
GEN
expandcr(GEN O, GEN cr)
{
pari_sp ltop = avma, av, av2;
GEN theta, fac;
long i, j, l;
l = lg(cr)-1;
theta = gmael(cr,l,1);
for (i = l-1; i > 0; i--)
{
av2 = avma;
fac = cgetg(3,t_VEC);
av = avma; gel(fac,1) = gerepileupto(av,gdiv(gmael3(cr,i,1,1),gmael(cr,i+1,2)));
av = avma; gel(fac,2) = gerepileupto(av,gdiv(gmael3(cr,i,1,2),gmael(cr,i+1,2)));
for (j = 1; j < l-i; j++) fac = gerepileupto(av2,mulqig(O,fac,fac));
theta = gerepileupto(ltop,mulqig(O,theta,fac));
}
return gerepileupto(ltop,theta);
}
GEN
crmodm (GEN O, GEN cr, GEN m)
{
if (typ(m) != t_INT) pari_err_TYPE("crmodm",m);
pari_sp ltop = avma, av;
GEN D, G, res, tmp, m_;
m_ = mulii(gen_2,m);
ulong l = lg(cr), i, sw = 0;
av = avma;
D = mkintmod(modii(gmael(cr,2,2),m),m);
G = cgetg(3,t_VEC);
if (!cmpii(gel(O,3),gen_1) || Mod2(m)) sw = 1;
if (sw)
{
gel(G,1) = mkintmod(modii(gmael3(cr,1,1,1),m),m);
gel(G,2) = mkintmod(modii(gmael3(cr,1,1,2),m),m);
}
else
{
gel(G,1) = modii(gmael3(cr,1,1,1),m_);
gel(G,2) = modii(gmael3(cr,1,1,2),m_);
}
for (i = 2; i < l-2; i++)
{
D = gmul(gmael(cr,i+1,2),gsqr(D));
if (sw) G = mulqig(O,gmael(cr,i,1),mulqig(O,G,G));
else
{
tmp = mulqig(O,G,G);
gel(tmp,1) = modii(gel(tmp,1),m_);
gel(tmp,2) = modii(gel(tmp,2),m_);
tmp = mulqig(O,tmp,gmael(cr,i,1));
G = cgetg(3,t_VEC);
gel(G,1) = modii(gel(tmp,1),m_);
gel(G,2) = modii(gel(tmp,2),m_);
}
gerepileall(av,2,&D,&G);
}
D = gsqr(D);
if (sw) G = mulqig(O,G,G);
else
{
tmp = mulqig(O,G,G);
G = cgetg(3,t_VEC);
gel(G,1) = modii(gel(tmp,1),m_);
gel(G,2) = modii(gel(tmp,2),m_);
}
tmp = mulqig(O,G,mulqidivn(O,gmael(cr,l-1,1),gmael(cr,l-2,1),gmael(cr,l-1,2)));
if (sw)
{
res = cgetg(3,t_VEC);
av = avma; gel(res,1) = gerepileupto(av,lift(gdiv(gel(tmp,1),D)));
av = avma; gel(res,2) = gerepileupto(av,lift(gdiv(gel(tmp,2),D)));
}
else
{
res = cgetg(3,t_VEC);
av = avma; gel(res,1) = gerepileupto(av,modii(mulii(gel(tmp,1),ginvmod(lift(D),m)),m));
av = avma; gel(res,2) = gerepileupto(av,modii(mulii(gel(tmp,2),ginvmod(lift(D),m)),m));
}
return gerepileupto(ltop,res);
}
GEN
crmodm_alt(GEN O, GEN cr, GEN m) // could be modified to remove the gcd stuff probably
{
pari_sp ltop = avma, av, av2, av3;
GEN D, G, G_, r, r_, d, n, tmp, res;
ulong l = lg(cr), i;
av2 = avma;
D = mulii(powii(gel(O,3),mulis(gen_2,l-2)),mulii(m,gmael(cr,l-1,2)));
for (i = 2; i < l-1; i++) D = gerepileupto(av2,mulii(D,sqri(gmael(cr,i,2))));
G = cgetg(3,t_VEC);
gel(G,1) = modii(gmael3(cr,1,1,1),D);
gel(G,2) = modii(gmael3(cr,1,1,2),D);
r = gen_1;
for (i = 2; i < l-1; i++)
{
tmp = cgetg(3,t_VEC);
av = avma; gel(tmp,1) = gerepileupto(av,addii(sqri(gel(G,1)),mulii(sqri(gel(G,2)),gel(O,1))));
av = avma; gel(tmp,2) = gerepileupto(av,mulii(gen_2,mulii(gel(G,1),gel(G,2))));
G_ = cgetg(3,t_VEC);
av = avma; gel(G_,1) = gerepileupto(av,addii(mulii(gel(tmp,1),gmael3(cr,i,1,1)),mulii(mulii(gel(tmp,2),gmael3(cr,i,1,2)),gel(O,1))));
av = avma; gel(G_,2) = gerepileupto(av,addii(mulii(gel(tmp,1),gmael3(cr,i,1,2)),mulii(gel(tmp,2),gmael3(cr,i,1,1))));
r = sqri(r);
av = avma; tmp = gerepileupto(av,mulii(sqri(gel(O,3)),mulii(sqri(gmael(cr,i,2)),r)));
av = avma; d = gerepileupto(av,gcdii(tmp,gcdii(gel(G_,1),gel(G_,2))));
r = diviiexact(tmp,d);
av = avma; D = gerepileupto(av,diviiexact(D,gcdii(D,d)));
G = cgetg(3,t_VEC);
gel(G,1) = modii(diviiexact(gel(G_,1),d),D);
gel(G,2) = modii(diviiexact(gel(G_,2),d),D);
av3 = avma;
av = avma; r_ = gerepileupto(av,diviiexact(r,gcdii(r,D)));
while (cmpii(gcdii(r_,D),gen_1) > 1) r_ = gerepileupto(av3,diviiexact(r_,gcdii(r_,D)));
if (cmpii(r_,gen_1) > 1)
{
n = ginvmod(r_,D);
r = diviiexact(r,r_);
G_ = cgetg(3,t_VEC);
av = avma; gel(G_,1) = gerepileupto(av,modii(mulii(gel(G,1),n),D));
av = avma; gel(G_,1) = gerepileupto(av,modii(mulii(gel(G,1),n),D));
G = G_;
}
gerepileall(av2,3,&G,&r,&D);
}
av = avma; D = gerepileupto(av,diviiexact(D,gcdii(D,mulii(sqri(gel(O,3)),gmael(cr,l-1,2)))));
if (cmpii(D,m)) pari_err_BUG("crmodm_alt"); //crmodm_alt(O,cr,mulii(m,diviiexact(m,D)));
G = mulqig(O,G,gmael(cr,l-1,1));
res = cgetg(3,t_VEC);
av = avma; gel(res,1) = gerepileupto(av,modii(diviiexact(gel(G,1),gmael(cr,l-1,2)),D));
av = avma; gel(res,2) = gerepileupto(av,modii(diviiexact(gel(G,2),gmael(cr,l-1,2)),D));
return gerepileupto(ltop,res);
}
ulong
crpval(GEN O, GEN cr, ulong p, ulong c)
{
pari_sp ltop = avma;
ulong k = 16, k_ = 0, m; //starting value of 16 good?
GEN tmp;
tmp = gel(crmodm(O,cr,powuu(p,k)),c);
while (!cmpii(tmp,gen_0))
{
tmp = gel(crmodm(O,cr,powuu(p,k)),c);
k_ = k;
k *= 2;
set_avma(ltop);
}
while (1) // v_p is now in [k_,k); do a binary search
{
m = k_ + (k-k_)/2;
tmp = gel(crmodm(O,cr,powuu(p,m)),c);
if (!cmpii(tmp,gen_0)) k_ = m;
else k = m;
set_avma(ltop);
if (k_+1 == k) break;
}
return gc_long(ltop,k_);
}
ulong
crpval_alt(GEN O, GEN cr, ulong p, ulong c)
{ //code duplication...
pari_sp ltop = avma;
ulong k = 16, k_ = 0, m; //starting value of 16 good?
GEN tmp;
tmp = gel(crmodm_alt(O,cr,powuu(p,k)),c);
while (!cmpii(tmp,gen_0))
{
tmp = gel(crmodm(O,cr,powuu(p,k)),c);
k_ = k;
k *= 2;
set_avma(ltop);
}
while (1) // v_p is now in [k_,k); do a binary search
{
m = k_ + (k-k_)/2;
tmp = gel(crmodm_alt(O,cr,powuu(p,m)),c);
if (!cmpii(tmp,gen_0)) k_ = m;
else k = m;
set_avma(ltop);
if (k_+1 == k) break;
}
return gc_long(ltop,k_);
}
GEN
crsmoothpart(GEN O, GEN cr, GEN S, ulong c)
{
pari_sp ltop = avma;
GEN res = gen_1;
ulong i;
for (i = 1; i < lg(S); i++) res = gerepileupto(ltop,mulii(res,powuu((ulong)gel(S,i),crpval(O,cr,(ulong)gel(S,i),c))));
return gerepileupto(ltop,res);
}
GEN
crsmoothpart2(GEN O, GEN b, GEN y, GEN q, GEN S, ulong c)
{
pari_sp ltop = avma;
GEN res = gen_1;
ulong i;
for (i = 1; i < lg(S); i++) res = gerepileupto(ltop,mulii(res,powuu((ulong)gel(S,i),crpval(O,gel(cr(O,b,y,q,stoi((ulong)gel(S,i))),2),(ulong)gel(S,i),c))));
return gerepileupto(ltop,res);
}
GEN
crsmoothpart_alt(GEN O, GEN cr, GEN S, ulong c)
{ //code duplication...
pari_sp ltop = avma;
GEN res = gen_1;
ulong i;
for (i = 1; i < lg(S); i++) res = gerepileupto(ltop,mulii(res,powuu((ulong)gel(S,i),crpval_alt(O,cr,(ulong)gel(S,i),c))));
return gerepileupto(ltop,res);
}
long
crnorm_sign(GEN O, GEN cr)
{
pari_sp ltop = avma;
return gc_long(ltop,signe(subii(sqri(gmael3(cr,lg(cr)-2,1,1)),mulii(gel(O,1),sqri(gmael3(cr,lg(cr)-2,1,2)))))*signe(gmael(cr,lg(cr)-1,2))*signe(subii(sqri(gmael3(cr,lg(cr)-1,1,1)),mulii(gel(O,1),sqri(gmael3(cr,lg(cr)-1,1,2))))));
}