/* jac^floor(N/pk) mod (N, polcyclo(pk)), flexible window */ static GEN _powpolmod(Cache *C, GEN jac, Red *R, GEN (*_sqr)(GEN, Red *)) { const GEN taba = C->aall; const GEN tabt = C->tall; const long efin = lg(taba)-1, lv = R->lv; GEN L, res = jac, pol2 = _sqr(res, R); long f; pari_sp av0 = avma, av; L = cgetg(lv+1, t_VEC); gel(L,1) = res; for (f=2; f<=lv; f++) gel(L,f) = _mul(gel(L,f-1), pol2, R); av = avma; for (f = efin; f >= 1; f--) { GEN t = gel(L, taba[f]); long tf = tabt[f]; res = (f==efin)? t: _mul(t, res, R); while (tf--) { res = _sqr(res, R); if (gc_needed(av,1)) { res = gerepilecopy(av, res); if(DEBUGMEM>1) pari_warn(warnmem,"powpolmod: f = %ld",f); } } } return gerepilecopy(av0, res); }
GEN shallowconcat1(GEN x) { pari_sp av = avma; long lx, t, i; GEN z; switch(typ(x)) { case t_VEC: lx = lg(x); if (lx==1) pari_err_DOMAIN("concat","vector","=",x,x); break; case t_LIST: if (list_typ(x)!=t_LIST_RAW) pari_err_TYPE("concat",x); if (!list_data(x)) pari_err_DOMAIN("concat","vector","=",x,x); x = list_data(x); lx = lg(x); break; default: pari_err_TYPE("concat",x); return NULL; /* not reached */ } if (lx==2) return gel(x,1); z = gel(x,1); t = typ(z); i = 2; if (is_matvec_t(t) || t == t_VECSMALL || t == t_STR) { /* detect a "homogeneous" object: catmany is faster */ for (; i<lx; i++) if (typ(gel(x,i)) != t) break; z = catmany(x + 1, x + i-1, t); } for (; i<lx; i++) { z = shallowconcat(z, gel(x,i)); if (gc_needed(av,3)) { if (DEBUGMEM>1) pari_warn(warnmem,"concat: i = %ld", i); z = gerepilecopy(av, z); } } return z; }
GEN vecsum(GEN v) { pari_sp av = avma; long i, l; GEN p; if (!is_vec_t(typ(v))) pari_err_TYPE("vecsum", v); l = lg(v); if (l == 1) return gen_0; p = gel(v,1); if (l == 2) return gcopy(p); for (i=2; i<l; i++) { p = gadd(p, gel(v,i)); if (gc_needed(av, 2)) { if (DEBUGMEM>1) pari_warn(warnmem,"sum"); p = gerepileupto(av, p); } } return gerepileupto(av, p); }
GEN bezout(GEN a, GEN b, GEN *pu, GEN *pv) { GEN t,u,u1,v,v1,d,d1,q,r; GEN *pt; pari_sp av, av1; long s, sa, sb; ulong g; ulong xu,xu1,xv,xv1; /* Lehmer stage recurrence matrix */ int lhmres; /* Lehmer stage return value */ s = abscmpii(a,b); if (s < 0) { t=b; b=a; a=t; pt=pu; pu=pv; pv=pt; } /* now |a| >= |b| */ sa = signe(a); sb = signe(b); if (!sb) { if (pv) *pv = gen_0; switch(sa) { case 0: if (pu) *pu = gen_0; return gen_0; case 1: if (pu) *pu = gen_1; return icopy(a); case -1: if (pu) *pu = gen_m1; return(negi(a)); } } if (s == 0) /* |a| == |b| != 0 */ { if (pu) *pu = gen_0; if (sb > 0) { if (pv) *pv = gen_1; return icopy(b); } else { if (pv) *pv = gen_m1; return(negi(b)); } } /* now |a| > |b| > 0 */ if (lgefint(a) == 3) /* single-word affair */ { g = xxgcduu(uel(a,2), uel(b,2), 0, &xu, &xu1, &xv, &xv1, &s); sa = s > 0 ? sa : -sa; sb = s > 0 ? -sb : sb; if (pu) { if (xu == 0) *pu = gen_0; /* can happen when b divides a */ else if (xu == 1) *pu = sa < 0 ? gen_m1 : gen_1; else if (xu == 2) *pu = sa < 0 ? gen_m2 : gen_2; else { *pu = cgeti(3); (*pu)[1] = evalsigne(sa)|evallgefint(3); (*pu)[2] = xu; } } if (pv) { if (xv == 1) *pv = sb < 0 ? gen_m1 : gen_1; else if (xv == 2) *pv = sb < 0 ? gen_m2 : gen_2; else { *pv = cgeti(3); (*pv)[1] = evalsigne(sb)|evallgefint(3); (*pv)[2] = xv; } } if (g == 1) return gen_1; else if (g == 2) return gen_2; else return utoipos(g); } /* general case */ av = avma; (void)new_chunk(lgefint(b) + (lgefint(a)<<1)); /* room for u,v,gcd */ /* if a is significantly larger than b, calling lgcdii() is not the best * way to start -- reduce a mod b first */ if (lgefint(a) > lgefint(b)) { d = absi(b), q = dvmdii(absi(a), d, &d1); if (!signe(d1)) /* a == qb */ { avma = av; if (pu) *pu = gen_0; if (pv) *pv = sb < 0 ? gen_m1 : gen_1; return (icopy(d)); } else { u = gen_0; u1 = v = gen_1; v1 = negi(q); } /* if this results in lgefint(d) == 3, will fall past main loop */ } else { d = absi(a); d1 = absi(b); u = v1 = gen_1; u1 = v = gen_0; } av1 = avma; /* main loop is almost identical to that of invmod() */ while (lgefint(d) > 3 && signe(d1)) { lhmres = lgcdii((ulong *)d, (ulong *)d1, &xu, &xu1, &xv, &xv1, ULONG_MAX); if (lhmres != 0) /* check progress */ { /* apply matrix */ if ((lhmres == 1) || (lhmres == -1)) { if (xv1 == 1) { r = subii(d,d1); d=d1; d1=r; a = subii(u,u1); u=u1; u1=a; a = subii(v,v1); v=v1; v1=a; } else { r = subii(d, mului(xv1,d1)); d=d1; d1=r; a = subii(u, mului(xv1,u1)); u=u1; u1=a; a = subii(v, mului(xv1,v1)); v=v1; v1=a; } } else { r = subii(muliu(d,xu), muliu(d1,xv)); d1 = subii(muliu(d,xu1), muliu(d1,xv1)); d = r; a = subii(muliu(u,xu), muliu(u1,xv)); u1 = subii(muliu(u,xu1), muliu(u1,xv1)); u = a; a = subii(muliu(v,xu), muliu(v1,xv)); v1 = subii(muliu(v,xu1), muliu(v1,xv1)); v = a; if (lhmres&1) { togglesign(d); togglesign(u); togglesign(v); } else { togglesign(d1); togglesign(u1); togglesign(v1); } } } if (lhmres <= 0 && signe(d1)) { q = dvmdii(d,d1,&r); a = subii(u,mulii(q,u1)); u=u1; u1=a; a = subii(v,mulii(q,v1)); v=v1; v1=a; d=d1; d1=r; } if (gc_needed(av,1)) { if(DEBUGMEM>1) pari_warn(warnmem,"bezout"); gerepileall(av1,6, &d,&d1,&u,&u1,&v,&v1); } } /* end while */ /* Postprocessing - final sprint */ if (signe(d1)) { /* Assertions: lgefint(d)==lgefint(d1)==3, and * gcd(d,d1) is nonzero and fits into one word */ g = xxgcduu(uel(d,2), uel(d1,2), 0, &xu, &xu1, &xv, &xv1, &s); u = subii(muliu(u,xu), muliu(u1, xv)); v = subii(muliu(v,xu), muliu(v1, xv)); if (s < 0) { sa = -sa; sb = -sb; } avma = av; if (pu) *pu = sa < 0 ? negi(u) : icopy(u); if (pv) *pv = sb < 0 ? negi(v) : icopy(v); if (g == 1) return gen_1; else if (g == 2) return gen_2; else return utoipos(g); } /* get here when the final sprint was skipped (d1 was zero already). * Now the matrix is final, and d contains the gcd. */ avma = av; if (pu) *pu = sa < 0 ? negi(u) : icopy(u); if (pv) *pv = sb < 0 ? negi(v) : icopy(v); return icopy(d); }