GEN
addui_sign(ulong x, GEN y, long sy)
{
long ly;
GEN z;
if (!x) return icopy_sign(y, sy);
if (!sy) return utoipos(x);
if (sy == 1) return adduispec(x,y+2, lgefint(y)-2);
ly=lgefint(y);
if (ly==3)
{
const ulong t = y[2];
if (x == t) return gen_0;
z=cgeti(3);
if (x < t) {
z[1] = evalsigne(-1) | evallgefint(3);
z[2] = t - x;
}
else {
z[1] = evalsigne(1) | evallgefint(3);
z[2] = x - t;
}
return z;
}
z = subiuspec(y+2,x, ly-2);
setsigne(z,-1); return z;
}
GEN
addsi_sign(long x, GEN y, long sy)
{
long sx,ly;
GEN z;
if (!x) return icopy_sign(y, sy);
if (!sy) return stoi(x);
if (x<0) { sx=-1; x=-x; } else sx=1;
if (sx==sy)
{
z = adduispec(x,y+2, lgefint(y)-2);
setsigne(z,sy); return z;
}
ly=lgefint(y);
if (ly==3)
{
const long d = (long)(uel(y,2) - (ulong)x);
if (!d) return gen_0;
z=cgeti(3);
if (y[2] < 0 || d > 0) {
z[1] = evalsigne(sy) | evallgefint(3);
z[2] = d;
}
else {
z[1] = evalsigne(-sy) | evallgefint(3);
z[2] =-d;
}
return z;
}
z = subiuspec(y+2,x, ly-2);
setsigne(z,sy); return z;
}
static GEN
makepoldeg1(GEN c, GEN d)
{
GEN z;
if (signe(c)) {
z = cgetg(4,t_POL); z[1] = evalsigne(1);
gel(z,2) = d; gel(z,3) = c;
} else if (signe(d)) {
z = cgetg(3,t_POL); z[1] = evalsigne(1);
gel(z,2) = d;
} else {
z = cgetg(2,t_POL); z[1] = evalsigne(0);
}
return z;
}
/* x a non-zero VECSMALL */
static GEN
smallpolrev(GEN x)
{
long i,j, lx = lg(x);
GEN y;
while (lx-- && x[lx]==0) /* empty */;
i = lx+2; y = cgetg(i,t_POL);
y[1] = evalsigne(1);
for (j=2; j<i; j++) gel(y,j) = stoi(x[j-1]);
return y;
}
GEN
gcdii(GEN a, GEN b)
{
long v, w;
pari_sp av;
GEN t;
switch (absi_cmp(a,b))
{
case 0: return absi(a);
case -1: swap(a,b);
}
if (!signe(b)) return absi(a);
/* here |a|>|b|>0. Try single precision first */
if (lgefint(a)==3)
return igcduu((ulong)a[2], (ulong)b[2]);
if (lgefint(b)==3)
{
ulong u = resiu(a,(ulong)b[2]);
if (!u) return absi(b);
return igcduu((ulong)b[2], u);
}
/* larger than gcd: "avma=av" gerepile (erasing t) is valid */
av = avma; (void)new_chunk(lgefint(b)+1); /* HACK */
t = remii(a,b);
if (!signe(t)) { avma=av; return absi(b); }
a = b; b = t;
v = vali(a); a = shifti(a,-v); setabssign(a);
w = vali(b); b = shifti(b,-w); setabssign(b);
if (w < v) v = w;
switch(absi_cmp(a,b))
{
case 0: avma=av; a=shifti(a,v); return a;
case -1: swap(a,b);
}
if (is_pm1(b)) { avma=av; return int2n(v); }
{
/* general case */
/*This serve two purposes: 1) mpn_gcd destroy its input and need an extra
* limb 2) this allows us to use icopy instead of gerepile later. NOTE: we
* must put u before d else the final icopy could fail.
*/
GEN res= cgeti(lgefint(a)+1);
GEN ca = icopy_ef(a,lgefint(a)+1);
GEN cb = icopy_ef(b,lgefint(b)+1);
long l = mpn_gcd(LIMBS(res), LIMBS(ca), NLIMBS(ca), LIMBS(cb), NLIMBS(cb));
res[1] = evalsigne(1)|evallgefint(l+2);
avma=av;
return shifti(res,v);
}
}
/* x t_VECSMALL, as red_cyclo2n_ip */
static GEN
u_red_cyclo2n_ip(GEN x, long n)
{
long i, pow2 = 1L<<(n-1);
GEN z;
for (i = lg(x)-1; i>pow2; i--) x[i-pow2] -= x[i];
for (; i>0; i--)
if (x[i]) break;
i += 2;
z = cgetg(i, t_POL); z[1] = evalsigne(1);
for (i--; i>=2; i--) gel(z,i) = stoi(x[i-1]);
return z;
}
long
pari_var_create(entree *ep)
{
GEN p = (GEN)initial_value(ep);
long v;
if (*p) return varn(p);
if (nvar == max_avail) pari_err(e_MISC,"no more variables available");
v = nvar++;
/* set p = pol_x(v) */
p[0] = evaltyp(t_POL) | _evallg(4);
p[1] = evalsigne(1) | evalvarn(v);
gel(p,2) = gen_0;
gel(p,3) = gen_1;
varentries_set(v, ep);
varpriority[v]= min_priority--;
return v;
}
static GEN
nf_DDF_roots(GEN pol, GEN polred, GEN nfpol, GEN lt, GEN init_fa, long nbf,
long fl, nflift_t *L)
{
long Cltx_r[] = { evaltyp(t_POL)|_evallg(4), 0,0,0 };
long i, m;
GEN C2ltpol, C = L->topowden;
GEN Clt = mul_content(C, lt);
GEN C2lt = mul_content(C,Clt);
GEN z;
if (L->Tpk)
{
int cof = (degpol(pol) > nbf); /* non trivial cofactor ? */
z = FqX_split_roots(init_fa, L->Tp, L->p, cof? polred: NULL);
z = hensel_lift_fact(polred, z, L->Tpk, L->p, L->pk, L->k);
if (cof) setlg(z, lg(z)-1); /* remove cofactor */
z = roots_from_deg1(z);
}
else
z = rootpadicfast(polred, L->p, L->k);
Cltx_r[1] = evalsigne(1) | evalvarn(varn(pol));
gel(Cltx_r,3) = Clt? Clt: gen_1;
C2ltpol = C2lt? gmul(C2lt, pol): pol;
for (m=1,i=1; i<lg(z); i++)
{
GEN q, r = gel(z,i);
r = nf_bestlift_to_pol(lt? gmul(lt,r): r, NULL, L);
gel(Cltx_r,2) = gneg(r); /* check P(r) == 0 */
q = RgXQX_divrem(C2ltpol, Cltx_r, nfpol, ONLY_DIVIDES); /* integral */
if (q) {
C2ltpol = C2lt? gmul(Clt,q): q;
if (Clt) r = gdiv(r, Clt);
gel(z,m++) = r;
}
else if (fl == 2) return cgetg(1, t_VEC);
}
z[0] = evaltyp(t_VEC) | evallg(m);
return z;
}
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);
}
GEN
addrr_sign(GEN x, long sx, GEN y, long sy)
{
long lx, ex = expo(x);
long ly, ey = expo(y), e = ey - ex;
long i, j, lz, ez, m;
int extend, f2;
GEN z;
LOCAL_OVERFLOW;
if (!sy)
{
if (!sx)
{
if (e > 0) ex = ey;
return real_0_bit(ex);
}
if (e >= 0) return real_0_bit(ey);
lz = nbits2prec(-e);
lx = lg(x); if (lz > lx) lz = lx;
z = cgetr(lz); while(--lz) z[lz] = x[lz];
setsigne(z,sx); return z;
}
if (!sx)
{
if (e <= 0) return real_0_bit(ex);
lz = nbits2prec(e);
ly = lg(y); if (lz > ly) lz = ly;
z = cgetr(lz); while (--lz) z[lz] = y[lz];
setsigne(z,sy); return z;
}
if (e < 0) { swap(x,y); lswap(sx,sy); ey=ex; e=-e; }
/* now ey >= ex */
lx = lg(x);
ly = lg(y);
/* If exponents differ, need to shift one argument, here x. If
* extend = 1: extension of x,z by m < BIL bits (round to 1 word) */
/* in this case, lz = lx + d + 1, otherwise lx + d */
extend = 0;
if (e)
{
long d = dvmdsBIL(e, &m), l = ly-d;
if (l <= 2) return rcopy_sign(y, sy);
if (l > lx) { lz = lx + d + 1; extend = 1; }
else { lz = ly; lx = l; }
if (m)
{ /* shift x right m bits */
const pari_sp av = avma;
const ulong sh = BITS_IN_LONG-m;
GEN p1 = x; x = new_chunk(lx + lz + 1);
shift_right(x,p1,2,lx, 0,m);
if (extend) uel(x,lx) = uel(p1,lx-1) << sh;
avma = av; /* HACK: cgetr(lz) will not overwrite x */
}
}
else
{ /* d = 0 */
m = 0;
if (lx > ly) lx = ly;
lz = lx;
}
if (sx == sy)
{ /* addition */
i = lz-1;
j = lx-1;
if (extend) {
ulong garde = addll(x[lx], y[i]);
if (m < 4) /* don't extend for few correct bits */
z = cgetr(--lz);
else
{
z = cgetr(lz);
z[i] = garde;
}
}
else
{
z = cgetr(lz);
z[i] = addll(x[j], y[i]); j--;
}
i--;
for (; j>=2; i--,j--) z[i] = addllx(x[j],y[i]);
if (overflow)
{
z[1] = 1; /* stops since z[1] != 0 */
for (;;) { z[i] = uel(y,i)+1; if (z[i--]) break; }
if (i <= 0)
{
shift_right(z,z, 2,lz, 1,1);
z[1] = evalsigne(sx) | evalexpo(ey+1); return z;
}
}
for (; i>=2; i--) z[i] = y[i];
z[1] = evalsigne(sx) | evalexpo(ey); return z;
}
/* subtraction */
if (e) f2 = 1;
else
{
i = 2; while (i < lx && x[i] == y[i]) i++;
if (i==lx) return real_0_bit(ey+1 - prec2nbits(lx));
f2 = (uel(y,i) > uel(x,i));
}
/* result is non-zero. f2 = (y > x) */
i = lz-1; z = cgetr(lz);
if (f2)
{
j = lx-1;
if (extend) z[i] = subll(y[i], x[lx]);
else z[i] = subll(y[i], x[j--]);
for (i--; j>=2; i--) z[i] = subllx(y[i], x[j--]);
if (overflow) /* stops since y[1] != 0 */
for (;;) { z[i] = uel(y,i)-1; if (y[i--]) break; }
for (; i>=2; i--) z[i] = y[i];
sx = sy;
}
else
{
if (extend) z[i] = subll(x[lx], y[i]);
else z[i] = subll(x[i], y[i]);
for (i--; i>=2; i--) z[i] = subllx(x[i], y[i]);
}
x = z+2; i = 0; while (!x[i]) i++;
lz -= i; z += i;
j = bfffo(z[2]); /* need to shift left by j bits to normalize mantissa */
ez = ey - (j | (i * BITS_IN_LONG));
if (extend)
{ /* z was extended by d+1 words [should be e bits = d words + m bits] */
/* not worth keeping extra word if less than 5 significant bits in there */
if (m - j < 5 && lz > 3)
{ /* shorten z */
ulong last = (ulong)z[--lz]; /* cancelled word */
/* if we need to shift anyway, shorten from left
* If not, shorten from right, neutralizing last word of z */
if (j == 0)
/* stackdummy((pari_sp)(z + lz+1), (pari_sp)(z + lz)); */
z[lz] = evaltyp(t_VECSMALL) | _evallg(1);
else
{
GEN t = z;
z++; shift_left(z,t,2,lz-1, last,j);
}
if ((last<<j) & HIGHBIT)
{ /* round up */
i = lz-1;
while (++((ulong*)z)[i] == 0 && i > 1) i--;
if (i == 1) { ez++; z[2] = (long)HIGHBIT; }
}
}
else if (j) shift_left(z,z,2,lz-1, 0,j);
}
else if (j) shift_left(z,z,2,lz-1, 0,j);
z[1] = evalsigne(sx) | evalexpo(ez);
z[0] = evaltyp(t_REAL) | evallg(lz);
avma = (pari_sp)z; return z;
}