/* return a bound for T_2(P), P | polbase in C[X]
* NB: Mignotte bound: A | S ==>
* |a_i| <= binom(d-1, i-1) || S ||_2 + binom(d-1, i) lc(S)
*
* Apply to sigma(S) for all embeddings sigma, then take the L_2 norm over
* sigma, then take the sup over i.
**/
static GEN
nf_Mignotte_bound(GEN nf, GEN polbase)
{
GEN G = gmael(nf,5,2), lS = leading_term(polbase); /* t_INT */
GEN p1, C, N2, matGS, binlS, bin;
long prec, i, j, d = degpol(polbase), n = degpol(nf[1]), r1 = nf_get_r1(nf);
binlS = bin = vecbinome(d-1);
if (!gcmp1(lS)) binlS = gmul(lS, bin);
N2 = cgetg(n+1, t_VEC);
prec = gprecision(G);
for (;;)
{
nffp_t F;
matGS = cgetg(d+2, t_MAT);
for (j=0; j<=d; j++) gel(matGS,j+1) = arch_for_T2(G, gel(polbase,j+2));
matGS = shallowtrans(matGS);
for (j=1; j <= r1; j++) /* N2[j] = || sigma_j(S) ||_2 */
{
gel(N2,j) = gsqrt( QuickNormL2(gel(matGS,j), DEFAULTPREC), DEFAULTPREC );
if (lg(N2[j]) < DEFAULTPREC) goto PRECPB;
}
for ( ; j <= n; j+=2)
{
GEN q1 = QuickNormL2(gel(matGS,j ), DEFAULTPREC);
GEN q2 = QuickNormL2(gel(matGS,j+1), DEFAULTPREC);
p1 = gmul2n(mpadd(q1, q2), -1);
gel(N2,j) = gel(N2,j+1) = gsqrt( p1, DEFAULTPREC );
if (lg(N2[j]) < DEFAULTPREC) goto PRECPB;
}
if (j > n) break; /* done */
PRECPB:
prec = (prec<<1)-2;
remake_GM(nf, &F, prec); G = F.G;
if (DEBUGLEVEL>1) pari_warn(warnprec, "nf_factor_bound", prec);
}
/* Take sup over 0 <= i <= d of
* sum_sigma | binom(d-1, i-1) ||sigma(S)||_2 + binom(d-1,i) lc(S) |^2 */
/* i = 0: n lc(S)^2 */
C = mulsi(n, sqri(lS));
/* i = d: sum_sigma ||sigma(S)||_2^2 */
p1 = gnorml2(N2); if (gcmp(C, p1) < 0) C = p1;
for (i = 1; i < d; i++)
{
GEN s = gen_0;
for (j = 1; j <= n; j++)
{
p1 = mpadd( mpmul(gel(bin,i), gel(N2,j)), gel(binlS,i+1) );
s = mpadd(s, gsqr(p1));
}
if (gcmp(C, s) < 0) C = s;
}
return C;
}
static void
bestlift_init(long a, GEN nf, GEN pr, GEN C, nflift_t *L)
{
const long D = 100;
const double alpha = ((double)D-1) / D; /* LLL parameter */
const long d = degpol(nf[1]);
pari_sp av = avma;
GEN prk, PRK, B, GSmin, pk;
pari_timer ti;
TIMERstart(&ti);
if (!a) a = (long)bestlift_bound(C, d, alpha, pr_norm(pr));
for (;; avma = av, a<<=1)
{
if (DEBUGLEVEL>2) fprintferr("exponent: %ld\n",a);
PRK = prk = idealpows(nf, pr, a);
pk = gcoeff(prk,1,1);
/* reduce size first, "scramble" matrix */
PRK = lllintpartial_ip(PRK);
/* now floating point reduction is fast */
PRK = lllint_fp_ip(PRK, 4);
PRK = lllint_i(PRK, D, 0, NULL, NULL, &B);
if (!PRK) { PRK = prk; GSmin = pk; } /* nf = Q */
else
{
pari_sp av2 = avma;
GEN S = invmat( get_R(PRK) ), BB = GS_norms(B, DEFAULTPREC);
GEN smax = gen_0;
long i, j;
for (i=1; i<=d; i++)
{
GEN s = gen_0;
for (j=1; j<=d; j++)
s = gadd(s, gdiv( gsqr(gcoeff(S,i,j)), gel(BB,j)));
if (gcmp(s, smax) > 0) smax = s;
}
GSmin = gerepileupto(av2, ginv(gmul2n(smax, 2)));
}
if (gcmp(GSmin, C) >= 0) break;
}
if (DEBUGLEVEL>2)
fprintferr("for this exponent, GSmin = %Z\nTime reduction: %ld\n",
GSmin, TIMER(&ti));
L->k = a;
L->den = L->pk = pk;
L->prk = PRK;
L->iprk = ZM_inv(PRK, pk);
L->GSmin= GSmin;
L->prkHNF = prk;
init_proj(L, gel(nf,1), gel(pr,1));
}
static GEN
bound_for_coeff(long m, GEN rr, GEN *maxroot)
{
long i,r1, lrr=lg(rr);
GEN p1,b1,b2,B,M, C = matpascal(m-1);
for (r1=1; r1 < lrr; r1++)
if (typ(rr[r1]) != t_REAL) break;
r1--;
rr = gabs(rr,0); *maxroot = vecmax(rr);
for (i=1; i<lrr; i++)
if (gcmp(gel(rr,i), gen_1) < 0) gel(rr,i) = gen_1;
for (b1=gen_1,i=1; i<=r1; i++) b1 = gmul(b1, gel(rr,i));
for (b2=gen_1 ; i<lrr; i++) b2 = gmul(b2, gel(rr,i));
B = gmul(b1, gsqr(b2)); /* Mahler measure */
M = cgetg(m+2, t_VEC); gel(M,1) = gel(M,2) = gen_0; /* unused */
for (i=1; i<m; i++)
{
p1 = gadd(gmul(gcoeff(C, m, i+1), B),/* binom(m-1, i) */
gcoeff(C, m, i)); /* binom(m-1, i-1) */
gel(M,i+2) = ceil_safe(p1);
}
return M;
}
/* return a minimal lift of elt modulo id */
static GEN
nf_bestlift(GEN elt, GEN bound, nflift_t *L)
{
GEN u;
long i,l = lg(L->prk), t = typ(elt);
if (t != t_INT)
{
if (t == t_POL) elt = mulmat_pol(L->tozk, elt);
u = gmul(L->iprk,elt);
for (i=1; i<l; i++) gel(u,i) = diviiround(gel(u,i), L->den);
}
else
{
u = gmul(elt, gel(L->iprk,1));
for (i=1; i<l; i++) gel(u,i) = diviiround(gel(u,i), L->den);
elt = gscalcol(elt, l-1);
}
u = gsub(elt, gmul(L->prk, u));
if (bound && gcmp(QuickNormL2(u,DEFAULTPREC), bound) > 0) u = NULL;
return u;
}
static GEN
nf_LLL_cmbf(nfcmbf_t *T, GEN p, long k, long rec)
{
nflift_t *L = T->L;
GEN pk = L->pk, PRK = L->prk, PRKinv = L->iprk, GSmin = L->GSmin;
GEN Tpk = L->Tpk;
GEN famod = T->fact, nf = T->nf, ZC = T->ZC, Br = T->Br;
GEN Pbase = T->polbase, P = T->pol, dn = T->dn;
GEN nfT = gel(nf,1);
GEN Btra;
long dnf = degpol(nfT), dP = degpol(P);
double BitPerFactor = 0.5; /* nb bits / modular factor */
long i, C, tmax, n0;
GEN lP, Bnorm, Tra, T2, TT, CM_L, m, list, ZERO;
double Bhigh;
pari_sp av, av2, lim;
long ti_LLL = 0, ti_CF = 0;
pari_timer ti2, TI;
lP = absi(leading_term(P));
if (is_pm1(lP)) lP = NULL;
n0 = lg(famod) - 1;
/* Lattice: (S PRK), small vector (vS vP). To find k bound for the image,
* write S = S1 q + S0, P = P1 q + P0
* |S1 vS + P1 vP|^2 <= Bhigh for all (vS,vP) assoc. to true factors */
Btra = mulrr(ZC, mulsr(dP*dP, normlp(Br, 2, dnf)));
Bhigh = get_Bhigh(n0, dnf);
C = (long)ceil(sqrt(Bhigh/n0)) + 1; /* C^2 n0 ~ Bhigh */
Bnorm = dbltor( n0 * C * C + Bhigh );
ZERO = zeromat(n0, dnf);
av = avma; lim = stack_lim(av, 1);
TT = cgetg(n0+1, t_VEC);
Tra = cgetg(n0+1, t_MAT);
for (i=1; i<=n0; i++) TT[i] = 0;
CM_L = gscalsmat(C, n0);
/* tmax = current number of traces used (and computed so far) */
for(tmax = 0;; tmax++)
{
long a, b, bmin, bgood, delta, tnew = tmax + 1, r = lg(CM_L)-1;
GEN oldCM_L, M_L, q, S1, P1, VV;
int first = 1;
/* bound for f . S_k(genuine factor) = ZC * bound for T_2(S_tnew) */
Btra = mulrr(ZC, mulsr(dP*dP, normlp(Br, 2*tnew, dnf)));
bmin = logint(ceil_safe(sqrtr(Btra)), gen_2, NULL);
if (DEBUGLEVEL>2)
fprintferr("\nLLL_cmbf: %ld potential factors (tmax = %ld, bmin = %ld)\n",
r, tmax, bmin);
/* compute Newton sums (possibly relifting first) */
if (gcmp(GSmin, Btra) < 0)
{
nflift_t L1;
GEN polred;
bestlift_init(k<<1, nf, T->pr, Btra, &L1);
polred = ZqX_normalize(Pbase, lP, &L1);
k = L1.k;
pk = L1.pk;
PRK = L1.prk;
PRKinv = L1.iprk;
GSmin = L1.GSmin;
Tpk = L1.Tpk;
famod = hensel_lift_fact(polred, famod, Tpk, p, pk, k);
for (i=1; i<=n0; i++) TT[i] = 0;
}
for (i=1; i<=n0; i++)
{
GEN h, lPpow = lP? gpowgs(lP, tnew): NULL;
GEN z = polsym_gen(gel(famod,i), gel(TT,i), tnew, Tpk, pk);
gel(TT,i) = z;
h = gel(z,tnew+1);
/* make Newton sums integral */
lPpow = mul_content(lPpow, dn);
if (lPpow) h = FpX_red(gmul(h,lPpow), pk);
gel(Tra,i) = nf_bestlift(h, NULL, L); /* S_tnew(famod) */
}
/* compute truncation parameter */
if (DEBUGLEVEL>2) { TIMERstart(&ti2); TIMERstart(&TI); }
oldCM_L = CM_L;
av2 = avma;
b = delta = 0; /* -Wall */
AGAIN:
M_L = Q_div_to_int(CM_L, utoipos(C));
VV = get_V(Tra, M_L, PRK, PRKinv, pk, &a);
if (first)
{ /* initialize lattice, using few p-adic digits for traces */
bgood = (long)(a - max(32, BitPerFactor * r));
b = max(bmin, bgood);
delta = a - b;
}
else
{ /* add more p-adic digits and continue reduction */
if (a < b) b = a;
b = max(b-delta, bmin);
if (b - delta/2 < bmin) b = bmin; /* near there. Go all the way */
}
/* restart with truncated entries */
q = int2n(b);
P1 = gdivround(PRK, q);
S1 = gdivround(Tra, q);
T2 = gsub(gmul(S1, M_L), gmul(P1, VV));
m = vconcat( CM_L, T2 );
if (first)
{
first = 0;
m = shallowconcat( m, vconcat(ZERO, P1) );
/* [ C M_L 0 ]
* m = [ ] square matrix
* [ T2' PRK ] T2' = Tra * M_L truncated
*/
}
CM_L = LLL_check_progress(Bnorm, n0, m, b == bmin, /*dbg:*/ &ti_LLL);
if (DEBUGLEVEL>2)
fprintferr("LLL_cmbf: (a,b) =%4ld,%4ld; r =%3ld -->%3ld, time = %ld\n",
a,b, lg(m)-1, CM_L? lg(CM_L)-1: 1, TIMER(&TI));
if (!CM_L) { list = mkcol(QXQX_normalize(P,nfT)); break; }
if (b > bmin)
{
CM_L = gerepilecopy(av2, CM_L);
goto AGAIN;
}
if (DEBUGLEVEL>2) msgTIMER(&ti2, "for this trace");
i = lg(CM_L) - 1;
if (i == r && gequal(CM_L, oldCM_L))
{
CM_L = oldCM_L;
avma = av2; continue;
}
if (i <= r && i*rec < n0)
{
pari_timer ti;
if (DEBUGLEVEL>2) TIMERstart(&ti);
list = nf_chk_factors(T, P, Q_div_to_int(CM_L,utoipos(C)), famod, pk);
if (DEBUGLEVEL>2) ti_CF += TIMER(&ti);
if (list) break;
CM_L = gerepilecopy(av2, CM_L);
}
if (low_stack(lim, stack_lim(av,1)))
{
if(DEBUGMEM>1) pari_warn(warnmem,"nf_LLL_cmbf");
gerepileall(av, Tpk? 9: 8,
&CM_L,&TT,&Tra,&famod,&pk,&GSmin,&PRK,&PRKinv,&Tpk);
}
}
if (DEBUGLEVEL>2)
fprintferr("* Time LLL: %ld\n* Time Check Factor: %ld\n",ti_LLL,ti_CF);
return list;
}
/*
* generate comparison of nl, nr, both 64-bit.
* nl is memory; nr is constant or memory.
*/
void
cmp64(Node *nl, Node *nr, int op, Prog *to)
{
Node lo1, hi1, lo2, hi2, r1, r2;
Prog *br;
Type *t;
split64(nl, &lo1, &hi1);
split64(nr, &lo2, &hi2);
// compare most significant word;
// if they differ, we're done.
t = hi1.type;
regalloc(&r1, types[TINT32], N);
regalloc(&r2, types[TINT32], N);
gins(AMOVW, &hi1, &r1);
gins(AMOVW, &hi2, &r2);
gcmp(ACMP, &r1, &r2);
regfree(&r1);
regfree(&r2);
br = P;
switch(op) {
default:
fatal("cmp64 %O %T", op, t);
case OEQ:
// cmp hi
// bne L
// cmp lo
// beq to
// L:
br = gbranch(ABNE, T);
break;
case ONE:
// cmp hi
// bne to
// cmp lo
// bne to
patch(gbranch(ABNE, T), to);
break;
case OGE:
case OGT:
// cmp hi
// bgt to
// blt L
// cmp lo
// bge to (or bgt to)
// L:
patch(gbranch(optoas(OGT, t), T), to);
br = gbranch(optoas(OLT, t), T);
break;
case OLE:
case OLT:
// cmp hi
// blt to
// bgt L
// cmp lo
// ble to (or jlt to)
// L:
patch(gbranch(optoas(OLT, t), T), to);
br = gbranch(optoas(OGT, t), T);
break;
}
// compare least significant word
t = lo1.type;
regalloc(&r1, types[TINT32], N);
regalloc(&r2, types[TINT32], N);
gins(AMOVW, &lo1, &r1);
gins(AMOVW, &lo2, &r2);
gcmp(ACMP, &r1, &r2);
regfree(&r1);
regfree(&r2);
// jump again
patch(gbranch(optoas(op, t), T), to);
// point first branch down here if appropriate
if(br != P)
patch(br, pc);
splitclean();
splitclean();
}
/*
* attempt to generate 64-bit
* res = n
* return 1 on success, 0 if op not handled.
*/
void
cgen64(Node *n, Node *res)
{
Node t1, t2, *l, *r;
Node lo1, lo2, hi1, hi2;
Node al, ah, bl, bh, cl, ch, s, n1, creg;
Prog *p1, *p2, *p3, *p4, *p5, *p6;
uint64 v;
if(res->op != OINDREG && res->op != ONAME) {
dump("n", n);
dump("res", res);
fatal("cgen64 %O of %O", n->op, res->op);
}
l = n->left;
if(!l->addable) {
tempname(&t1, l->type);
cgen(l, &t1);
l = &t1;
}
split64(l, &lo1, &hi1);
switch(n->op) {
default:
fatal("cgen64 %O", n->op);
case OMINUS:
split64(res, &lo2, &hi2);
regalloc(&t1, lo1.type, N);
regalloc(&al, lo1.type, N);
regalloc(&ah, hi1.type, N);
gins(AMOVW, &lo1, &al);
gins(AMOVW, &hi1, &ah);
gmove(ncon(0), &t1);
p1 = gins(ASUB, &al, &t1);
p1->scond |= C_SBIT;
gins(AMOVW, &t1, &lo2);
gmove(ncon(0), &t1);
gins(ASBC, &ah, &t1);
gins(AMOVW, &t1, &hi2);
regfree(&t1);
regfree(&al);
regfree(&ah);
splitclean();
splitclean();
return;
case OCOM:
split64(res, &lo2, &hi2);
regalloc(&n1, lo1.type, N);
gins(AMOVW, &lo1, &n1);
gins(AMVN, &n1, &n1);
gins(AMOVW, &n1, &lo2);
gins(AMOVW, &hi1, &n1);
gins(AMVN, &n1, &n1);
gins(AMOVW, &n1, &hi2);
regfree(&n1);
splitclean();
splitclean();
return;
case OADD:
case OSUB:
case OMUL:
case OLSH:
case ORSH:
case OAND:
case OOR:
case OXOR:
// binary operators.
// common setup below.
break;
}
// setup for binary operators
r = n->right;
if(r != N && !r->addable) {
tempname(&t2, r->type);
cgen(r, &t2);
r = &t2;
}
if(is64(r->type))
split64(r, &lo2, &hi2);
regalloc(&al, lo1.type, N);
regalloc(&ah, hi1.type, N);
// Do op. Leave result in ah:al.
switch(n->op) {
default:
fatal("cgen64: not implemented: %N\n", n);
case OADD:
// TODO: Constants
regalloc(&bl, types[TPTR32], N);
regalloc(&bh, types[TPTR32], N);
gins(AMOVW, &hi1, &ah);
gins(AMOVW, &lo1, &al);
gins(AMOVW, &hi2, &bh);
gins(AMOVW, &lo2, &bl);
p1 = gins(AADD, &bl, &al);
p1->scond |= C_SBIT;
gins(AADC, &bh, &ah);
regfree(&bl);
regfree(&bh);
break;
case OSUB:
// TODO: Constants.
regalloc(&bl, types[TPTR32], N);
regalloc(&bh, types[TPTR32], N);
gins(AMOVW, &lo1, &al);
gins(AMOVW, &hi1, &ah);
gins(AMOVW, &lo2, &bl);
gins(AMOVW, &hi2, &bh);
p1 = gins(ASUB, &bl, &al);
p1->scond |= C_SBIT;
gins(ASBC, &bh, &ah);
regfree(&bl);
regfree(&bh);
break;
case OMUL:
// TODO(kaib): this can be done with 4 regs and does not need 6
regalloc(&bl, types[TPTR32], N);
regalloc(&bh, types[TPTR32], N);
regalloc(&cl, types[TPTR32], N);
regalloc(&ch, types[TPTR32], N);
// load args into bh:bl and bh:bl.
gins(AMOVW, &hi1, &bh);
gins(AMOVW, &lo1, &bl);
gins(AMOVW, &hi2, &ch);
gins(AMOVW, &lo2, &cl);
// bl * cl
p1 = gins(AMULLU, N, N);
p1->from.type = D_REG;
p1->from.reg = bl.val.u.reg;
p1->reg = cl.val.u.reg;
p1->to.type = D_REGREG;
p1->to.reg = ah.val.u.reg;
p1->to.offset = al.val.u.reg;
//print("%P\n", p1);
// bl * ch
p1 = gins(AMULA, N, N);
p1->from.type = D_REG;
p1->from.reg = bl.val.u.reg;
p1->reg = ch.val.u.reg;
p1->to.type = D_REGREG;
p1->to.reg = ah.val.u.reg;
p1->to.offset = ah.val.u.reg;
//print("%P\n", p1);
// bh * cl
p1 = gins(AMULA, N, N);
p1->from.type = D_REG;
p1->from.reg = bh.val.u.reg;
p1->reg = cl.val.u.reg;
p1->to.type = D_REGREG;
p1->to.reg = ah.val.u.reg;
p1->to.offset = ah.val.u.reg;
//print("%P\n", p1);
regfree(&bh);
regfree(&bl);
regfree(&ch);
regfree(&cl);
break;
case OLSH:
regalloc(&bl, lo1.type, N);
regalloc(&bh, hi1.type, N);
gins(AMOVW, &hi1, &bh);
gins(AMOVW, &lo1, &bl);
if(r->op == OLITERAL) {
v = mpgetfix(r->val.u.xval);
if(v >= 64) {
// TODO(kaib): replace with gins(AMOVW, nodintconst(0), &al)
// here and below (verify it optimizes to EOR)
gins(AEOR, &al, &al);
gins(AEOR, &ah, &ah);
} else if(v > 32) {
gins(AEOR, &al, &al);
// MOVW bl<<(v-32), ah
gshift(AMOVW, &bl, SHIFT_LL, (v-32), &ah);
} else if(v == 32) {
gins(AEOR, &al, &al);
gins(AMOVW, &bl, &ah);
} else if(v > 0) {
// MOVW bl<<v, al
gshift(AMOVW, &bl, SHIFT_LL, v, &al);
// MOVW bh<<v, ah
gshift(AMOVW, &bh, SHIFT_LL, v, &ah);
// OR bl>>(32-v), ah
gshift(AORR, &bl, SHIFT_LR, 32-v, &ah);
} else {
gins(AMOVW, &bl, &al);
gins(AMOVW, &bh, &ah);
}
goto olsh_break;
}
regalloc(&s, types[TUINT32], N);
regalloc(&creg, types[TUINT32], N);
if (is64(r->type)) {
// shift is >= 1<<32
split64(r, &cl, &ch);
gmove(&ch, &s);
p1 = gins(AMOVW, &s, &s);
p1->scond |= C_SBIT;
p6 = gbranch(ABNE, T);
gmove(&cl, &s);
splitclean();
} else {
gmove(r, &s);
p6 = P;
}
p1 = gins(AMOVW, &s, &s);
p1->scond |= C_SBIT;
// shift == 0
p1 = gins(AMOVW, &bl, &al);
p1->scond = C_SCOND_EQ;
p1 = gins(AMOVW, &bh, &ah);
p1->scond = C_SCOND_EQ;
p2 = gbranch(ABEQ, T);
// shift is < 32
nodconst(&n1, types[TUINT32], 32);
gmove(&n1, &creg);
gcmp(ACMP, &s, &creg);
// MOVW.LO bl<<s, al
p1 = gregshift(AMOVW, &bl, SHIFT_LL, &s, &al);
p1->scond = C_SCOND_LO;
// MOVW.LO bh<<s, ah
p1 = gregshift(AMOVW, &bh, SHIFT_LL, &s, &ah);
p1->scond = C_SCOND_LO;
// SUB.LO s, creg
p1 = gins(ASUB, &s, &creg);
p1->scond = C_SCOND_LO;
// OR.LO bl>>creg, ah
p1 = gregshift(AORR, &bl, SHIFT_LR, &creg, &ah);
p1->scond = C_SCOND_LO;
// BLO end
p3 = gbranch(ABLO, T);
// shift == 32
p1 = gins(AEOR, &al, &al);
p1->scond = C_SCOND_EQ;
p1 = gins(AMOVW, &bl, &ah);
p1->scond = C_SCOND_EQ;
p4 = gbranch(ABEQ, T);
// shift is < 64
nodconst(&n1, types[TUINT32], 64);
gmove(&n1, &creg);
gcmp(ACMP, &s, &creg);
// EOR.LO al, al
p1 = gins(AEOR, &al, &al);
p1->scond = C_SCOND_LO;
// MOVW.LO creg>>1, creg
p1 = gshift(AMOVW, &creg, SHIFT_LR, 1, &creg);
p1->scond = C_SCOND_LO;
// SUB.LO creg, s
p1 = gins(ASUB, &creg, &s);
p1->scond = C_SCOND_LO;
// MOVW bl<<s, ah
p1 = gregshift(AMOVW, &bl, SHIFT_LL, &s, &ah);
p1->scond = C_SCOND_LO;
p5 = gbranch(ABLO, T);
// shift >= 64
if (p6 != P) patch(p6, pc);
gins(AEOR, &al, &al);
gins(AEOR, &ah, &ah);
patch(p2, pc);
patch(p3, pc);
patch(p4, pc);
patch(p5, pc);
regfree(&s);
regfree(&creg);
olsh_break:
regfree(&bl);
regfree(&bh);
break;
case ORSH:
regalloc(&bl, lo1.type, N);
regalloc(&bh, hi1.type, N);
gins(AMOVW, &hi1, &bh);
gins(AMOVW, &lo1, &bl);
if(r->op == OLITERAL) {
v = mpgetfix(r->val.u.xval);
if(v >= 64) {
if(bh.type->etype == TINT32) {
// MOVW bh->31, al
gshift(AMOVW, &bh, SHIFT_AR, 31, &al);
// MOVW bh->31, ah
gshift(AMOVW, &bh, SHIFT_AR, 31, &ah);
} else {
gins(AEOR, &al, &al);
gins(AEOR, &ah, &ah);
}
} else if(v > 32) {
if(bh.type->etype == TINT32) {
// MOVW bh->(v-32), al
gshift(AMOVW, &bh, SHIFT_AR, v-32, &al);
// MOVW bh->31, ah
gshift(AMOVW, &bh, SHIFT_AR, 31, &ah);
} else {
// MOVW bh>>(v-32), al
gshift(AMOVW, &bh, SHIFT_LR, v-32, &al);
gins(AEOR, &ah, &ah);
}
} else if(v == 32) {
gins(AMOVW, &bh, &al);
if(bh.type->etype == TINT32) {
// MOVW bh->31, ah
gshift(AMOVW, &bh, SHIFT_AR, 31, &ah);
} else {
gins(AEOR, &ah, &ah);
}
} else if( v > 0) {
// MOVW bl>>v, al
gshift(AMOVW, &bl, SHIFT_LR, v, &al);
// OR bh<<(32-v), al
gshift(AORR, &bh, SHIFT_LL, 32-v, &al);
if(bh.type->etype == TINT32) {
// MOVW bh->v, ah
gshift(AMOVW, &bh, SHIFT_AR, v, &ah);
} else {
// MOVW bh>>v, ah
gshift(AMOVW, &bh, SHIFT_LR, v, &ah);
}
} else {
gins(AMOVW, &bl, &al);
gins(AMOVW, &bh, &ah);
}
goto orsh_break;
}
regalloc(&s, types[TUINT32], N);
regalloc(&creg, types[TUINT32], N);
if (is64(r->type)) {
// shift is >= 1<<32
split64(r, &cl, &ch);
gmove(&ch, &s);
p1 = gins(AMOVW, &s, &s);
p1->scond |= C_SBIT;
p6 = gbranch(ABNE, T);
gmove(&cl, &s);
splitclean();
} else {
gmove(r, &s);
p6 = P;
}
p1 = gins(AMOVW, &s, &s);
p1->scond |= C_SBIT;
// shift == 0
p1 = gins(AMOVW, &bl, &al);
p1->scond = C_SCOND_EQ;
p1 = gins(AMOVW, &bh, &ah);
p1->scond = C_SCOND_EQ;
p2 = gbranch(ABEQ, T);
// check if shift is < 32
nodconst(&n1, types[TUINT32], 32);
gmove(&n1, &creg);
gcmp(ACMP, &s, &creg);
// MOVW.LO bl>>s, al
p1 = gregshift(AMOVW, &bl, SHIFT_LR, &s, &al);
p1->scond = C_SCOND_LO;
// SUB.LO s,creg
p1 = gins(ASUB, &s, &creg);
p1->scond = C_SCOND_LO;
// OR.LO bh<<(32-s), al
p1 = gregshift(AORR, &bh, SHIFT_LL, &creg, &al);
p1->scond = C_SCOND_LO;
if(bh.type->etype == TINT32) {
// MOVW bh->s, ah
p1 = gregshift(AMOVW, &bh, SHIFT_AR, &s, &ah);
} else {
// MOVW bh>>s, ah
p1 = gregshift(AMOVW, &bh, SHIFT_LR, &s, &ah);
}
p1->scond = C_SCOND_LO;
// BLO end
p3 = gbranch(ABLO, T);
// shift == 32
if(bh.type->etype == TINT32)
p1 = gshift(AMOVW, &bh, SHIFT_AR, 31, &ah);
else
p1 = gins(AEOR, &al, &al);
p1->scond = C_SCOND_EQ;
p1 = gins(AMOVW, &bh, &al);
p1->scond = C_SCOND_EQ;
p4 = gbranch(ABEQ, T);
// check if shift is < 64
nodconst(&n1, types[TUINT32], 64);
gmove(&n1, &creg);
gcmp(ACMP, &s, &creg);
// MOVW.LO creg>>1, creg
p1 = gshift(AMOVW, &creg, SHIFT_LR, 1, &creg);
p1->scond = C_SCOND_LO;
// SUB.LO creg, s
p1 = gins(ASUB, &creg, &s);
p1->scond = C_SCOND_LO;
if(bh.type->etype == TINT32) {
// MOVW bh->(s-32), al
p1 = gregshift(AMOVW, &bh, SHIFT_AR, &s, &al);
p1->scond = C_SCOND_LO;
// MOVW bh->31, ah
p1 = gshift(AMOVW, &bh, SHIFT_AR, 31, &ah);
p1->scond = C_SCOND_LO;
} else {
// MOVW bh>>(v-32), al
p1 = gregshift(AMOVW, &bh, SHIFT_LR, &s, &al);
p1->scond = C_SCOND_LO;
p1 = gins(AEOR, &ah, &ah);
p1->scond = C_SCOND_LO;
}
// BLO end
p5 = gbranch(ABLO, T);
// s >= 64
if (p6 != P) patch(p6, pc);
if(bh.type->etype == TINT32) {
// MOVW bh->31, al
gshift(AMOVW, &bh, SHIFT_AR, 31, &al);
// MOVW bh->31, ah
gshift(AMOVW, &bh, SHIFT_AR, 31, &ah);
} else {
gins(AEOR, &al, &al);
gins(AEOR, &ah, &ah);
}
patch(p2, pc);
patch(p3, pc);
patch(p4, pc);
patch(p5, pc);
regfree(&s);
regfree(&creg);
orsh_break:
regfree(&bl);
regfree(&bh);
break;
case OXOR:
case OAND:
case OOR:
// TODO(kaib): literal optimizations
// make constant the right side (it usually is anyway).
// if(lo1.op == OLITERAL) {
// nswap(&lo1, &lo2);
// nswap(&hi1, &hi2);
// }
// if(lo2.op == OLITERAL) {
// // special cases for constants.
// lv = mpgetfix(lo2.val.u.xval);
// hv = mpgetfix(hi2.val.u.xval);
// splitclean(); // right side
// split64(res, &lo2, &hi2);
// switch(n->op) {
// case OXOR:
// gmove(&lo1, &lo2);
// gmove(&hi1, &hi2);
// switch(lv) {
// case 0:
// break;
// case 0xffffffffu:
// gins(ANOTL, N, &lo2);
// break;
// default:
// gins(AXORL, ncon(lv), &lo2);
// break;
// }
// switch(hv) {
// case 0:
// break;
// case 0xffffffffu:
// gins(ANOTL, N, &hi2);
// break;
// default:
// gins(AXORL, ncon(hv), &hi2);
// break;
// }
// break;
// case OAND:
// switch(lv) {
// case 0:
// gins(AMOVL, ncon(0), &lo2);
// break;
// default:
// gmove(&lo1, &lo2);
// if(lv != 0xffffffffu)
// gins(AANDL, ncon(lv), &lo2);
// break;
// }
// switch(hv) {
// case 0:
// gins(AMOVL, ncon(0), &hi2);
// break;
// default:
// gmove(&hi1, &hi2);
// if(hv != 0xffffffffu)
// gins(AANDL, ncon(hv), &hi2);
// break;
// }
// break;
// case OOR:
// switch(lv) {
// case 0:
// gmove(&lo1, &lo2);
// break;
// case 0xffffffffu:
// gins(AMOVL, ncon(0xffffffffu), &lo2);
// break;
// default:
// gmove(&lo1, &lo2);
// gins(AORL, ncon(lv), &lo2);
// break;
// }
// switch(hv) {
// case 0:
// gmove(&hi1, &hi2);
// break;
// case 0xffffffffu:
// gins(AMOVL, ncon(0xffffffffu), &hi2);
// break;
// default:
// gmove(&hi1, &hi2);
// gins(AORL, ncon(hv), &hi2);
// break;
// }
// break;
// }
// splitclean();
// splitclean();
// goto out;
// }
regalloc(&n1, lo1.type, N);
gins(AMOVW, &lo1, &al);
gins(AMOVW, &hi1, &ah);
gins(AMOVW, &lo2, &n1);
gins(optoas(n->op, lo1.type), &n1, &al);
gins(AMOVW, &hi2, &n1);
gins(optoas(n->op, lo1.type), &n1, &ah);
regfree(&n1);
break;
}
if(is64(r->type))
splitclean();
splitclean();
split64(res, &lo1, &hi1);
gins(AMOVW, &al, &lo1);
gins(AMOVW, &ah, &hi1);
splitclean();
//out:
regfree(&al);
regfree(&ah);
}
void
pariplot(GEN a, GEN b, GEN code, GEN ysmlu,GEN ybigu, long prec)
{
const char BLANK = ' ', YY = '|', XX_UPPER = '\'', XX_LOWER = '.';
long jz, j, i, sig;
pari_sp av = avma;
int jnew, jpre = 0; /* for lint */
GEN x, dx;
double diff, dyj, ysml, ybig, y[ISCR+1];
screen scr;
char buf[80], z;
sig=gcmp(b,a); if (!sig) return;
if (sig<0) { x=a; a=b; b=x; }
x = gtofp(a, prec); push_lex(x, code);
dx = divru(gtofp(gsub(b,a),prec), ISCR-1);
for (j=1; j<=JSCR; j++) scr[1][j]=scr[ISCR][j]=YY;
for (i=2; i<ISCR; i++)
{
scr[i][1] = XX_LOWER;
scr[i][JSCR]= XX_UPPER;
for (j=2; j<JSCR; j++) scr[i][j] = BLANK;
}
ysml = ybig = 0.; /* -Wall */
for (i=1; i<=ISCR; i++)
{
pari_sp av2 = avma;
y[i] = gtodouble( READ_EXPR(code,x) );
avma = av2;
if (i == 1)
ysml = ybig = y[1];
else
{
if (y[i] < ysml) ysml = y[i];
if (y[i] > ybig) ybig = y[i];
}
x = addrr(x,dx);
}
avma = av;
if (ysmlu) ysml = gtodouble(ysmlu);
if (ybigu) ybig = gtodouble(ybigu);
diff = ybig - ysml;
if (!diff) { ybig += 1; diff= 1.; }
dyj = ((JSCR-1)*3+2) / diff;
/* work around bug in gcc-4.8 (32bit): plot(x=-5,5,sin(x)))) */
jz = 3 - (long)(ysml*dyj + 0.5); /* 3 - DTOL(ysml*dyj) */
z = PICTZERO(jz); jz /= 3;
for (i=1; i<=ISCR; i++)
{
if (0<=jz && jz<=JSCR) scr[i][jz]=z;
j = 3 + DTOL((y[i]-ysml)*dyj);
jnew = j/3;
if (i > 1) fill_gap(scr, i, jnew, jpre);
if (0<=jnew && jnew<=JSCR) scr[i][jnew] = PICT(j);
jpre = jnew;
}
pari_putc('\n');
pari_printf("%s ", dsprintf9(ybig, buf));
for (i=1; i<=ISCR; i++) pari_putc(scr[i][JSCR]);
pari_putc('\n');
for (j=(JSCR-1); j>=2; j--)
{
pari_puts(" ");
for (i=1; i<=ISCR; i++) pari_putc(scr[i][j]);
pari_putc('\n');
}
pari_printf("%s ", dsprintf9(ysml, buf));
for (i=1; i<=ISCR; i++) pari_putc(scr[i][1]);
pari_putc('\n');
{
char line[10 + 32 + 32 + ISCR - 9];
sprintf(line, "%10s%-9.7g%*.7g\n"," ",todbl(a),ISCR-9,todbl(b));
pari_printf(line);
}
pop_lex(1);
}
