void InnerProduct(zz_p& x, const vec_zz_p& a, const vec_zz_p& b,
long offset)
{
if (offset < 0) LogicError("InnerProduct: negative offset");
if (NTL_OVERFLOW(offset, 1, 0)) ResourceError("InnerProduct: offset too big");
long n = min(a.length(), b.length()+offset);
long i;
long accum, t;
long p = zz_p::modulus();
mulmod_t pinv = zz_p::ModulusInverse();
const zz_p *ap = a.elts();
const zz_p *bp = b.elts();
accum = 0;
for (i = offset; i < n; i++) {
t = MulMod(rep(ap[i]), rep(bp[i-offset]), p, pinv);
accum = AddMod(accum, t, p);
}
x.LoopHole() = accum;
}
void sub(vec_zz_p& x, const vec_zz_p& a, const vec_zz_p& b)
{
long n = a.length();
if (b.length() != n) Error("vector sub: dimension mismatch");
x.SetLength(n);
long i;
for (i = 0; i < n; i++)
sub(x[i], a[i], b[i]);
}
void InnerProduct(zz_p& x, const vec_zz_p& a, const vec_zz_p& b)
{
long n = min(a.length(), b.length());
long i;
zz_p accum, t;
clear(accum);
for (i = 0; i < n; i++) {
mul(t, a[i], b[i]);
add(accum, accum, t);
}
x = accum;
}
void clear(vec_zz_p& x)
{
long n = x.length();
long i;
for (i = 0; i < n; i++)
clear(x[i]);
}
void InnerProduct(zz_pX& x, const vec_zz_p& v, long low, long high,
const vec_zz_pX& H, long n, vec_zz_p& t)
{
zz_p s;
long i, j;
zz_p *tp = t.elts();
for (j = 0; j < n; j++)
clear(tp[j]);
long p = zz_p::modulus();
double pinv = zz_p::ModulusInverse();
high = min(high, v.length()-1);
for (i = low; i <= high; i++) {
const vec_zz_p& h = H[i-low].rep;
long m = h.length();
zz_p w = (v[i]);
long W = rep(w);
mulmod_precon_t Wpinv = PrepMulModPrecon(W, p, pinv); // ((double) W)*pinv;
const zz_p *hp = h.elts();
for (j = 0; j < m; j++) {
long S = MulModPrecon(rep(hp[j]), W, p, Wpinv);
S = AddMod(S, rep(tp[j]), p);
tp[j].LoopHole() = S;
}
}
x.rep = t;
x.normalize();
}
void ProjectPowers(vec_zz_p& x, const vec_zz_p& a, long k,
const zz_pXArgument& H, const zz_pXModulus& F)
{
long n = F.n;
if (a.length() > n || k < 0 || NTL_OVERFLOW(k, 1, 0))
Error("ProjectPowers: bad args");
long m = H.H.length()-1;
long l = (k+m-1)/m - 1;
zz_pXMultiplier M;
build(M, H.H[m], F);
vec_zz_p s(INIT_SIZE, n);
s = a;
StripZeroes(s);
x.SetLength(k);
for (long i = 0; i <= l; i++) {
long m1 = min(m, k-i*m);
zz_p* w = &x[i*m];
for (long j = 0; j < m1; j++)
InnerProduct(w[j], H.H[j].rep, s);
if (i < l)
UpdateMap(s, s, M, F);
}
}
void mul(vec_zz_p& x, const vec_zz_p& a, zz_p b)
{
long n = a.length();
x.SetLength(n);
long i;
if (n <= 1) {
for (i = 0; i < n; i++)
mul(x[i], a[i], b);
}
else {
long p = zz_p::modulus();
double pinv = zz_p::ModulusInverse();
long bb = rep(b);
mulmod_precon_t bpinv = PrepMulModPrecon(bb, p, pinv);
const zz_p *ap = a.elts();
zz_p *xp = x.elts();
for (i = 0; i < n; i++)
xp[i].LoopHole() = MulModPrecon(rep(ap[i]), bb, p, bpinv);
}
}
static void StripZeroes(vec_zz_p& x)
{
long n = x.length();
while (n > 0 && IsZero(x[n-1]))
n--;
x.SetLength(n);
}
long CRT(vec_ZZ& gg, ZZ& a, const vec_zz_p& G)
{
long n = gg.length();
if (G.length() != n) Error("CRT: vector length mismatch");
long p = zz_p::modulus();
ZZ new_a;
mul(new_a, a, p);
long a_inv;
a_inv = rem(a, p);
a_inv = InvMod(a_inv, p);
long p1;
p1 = p >> 1;
ZZ a1;
RightShift(a1, a, 1);
long p_odd = (p & 1);
long modified = 0;
long h;
ZZ g;
long i;
for (i = 0; i < n; i++) {
if (!CRTInRange(gg[i], a)) {
modified = 1;
rem(g, gg[i], a);
if (g > a1) sub(g, g, a);
}
else
g = gg[i];
h = rem(g, p);
h = SubMod(rep(G[i]), h, p);
h = MulMod(h, a_inv, p);
if (h > p1)
h = h - p;
if (h != 0) {
modified = 1;
if (!p_odd && g > 0 && (h == p1))
MulSubFrom(g, a, h);
else
MulAddTo(g, a, h);
}
gg[i] = g;
}
a = new_a;
return modified;
}
void conv(vec_ZZ& x, const vec_zz_p& a)
{
long n = a.length();
x.SetLength(n);
long i;
for (i = 0; i < n; i++)
x[i] = rep(a[i]);
}
void negate(vec_zz_p& x, const vec_zz_p& a)
{
long n = a.length();
x.SetLength(n);
long i;
for (i = 0; i < n; i++)
negate(x[i], a[i]);
}
void add(vec_zz_p& x, const vec_zz_p& a, const vec_zz_p& b)
{
long n = a.length();
if (b.length() != n) LogicError("vector add: dimension mismatch");
long p = zz_p::modulus();
x.SetLength(n);
const zz_p *ap = a.elts();
const zz_p *bp = b.elts();
zz_p *xp = x.elts();
long i;
for (i = 0; i < n; i++)
xp[i].LoopHole() = AddMod(rep(ap[i]), rep(bp[i]), p);
}
void InnerProduct(zz_p& x, const vec_zz_p& a, const vec_zz_p& b,
long offset)
{
if (offset < 0) Error("InnerProduct: negative offset");
if (NTL_OVERFLOW(offset, 1, 0)) Error("InnerProduct: offset too big");
long n = min(a.length(), b.length()+offset);
long i;
zz_p accum, t;
clear(accum);
for (i = offset; i < n; i++) {
mul(t, a[i], b[i-offset]);
add(accum, accum, t);
}
x = accum;
}
void mul_aux(vec_zz_p& x, const mat_zz_p& A, const vec_zz_p& b)
{
long n = A.NumRows();
long l = A.NumCols();
if (l != b.length())
LogicError("matrix mul: dimension mismatch");
x.SetLength(n);
zz_p* xp = x.elts();
long p = zz_p::modulus();
mulmod_t pinv = zz_p::ModulusInverse();
long i, k;
long acc, tmp;
const zz_p* bp = b.elts();
if (n <= 1) {
for (i = 0; i < n; i++) {
acc = 0;
const zz_p* ap = A[i].elts();
for (k = 0; k < l; k++) {
tmp = MulMod(rep(ap[k]), rep(bp[k]), p, pinv);
acc = AddMod(acc, tmp, p);
}
xp[i].LoopHole() = acc;
}
}
else {
Vec<mulmod_precon_t>::Watcher watch_precon_vec(precon_vec);
precon_vec.SetLength(l);
mulmod_precon_t *bpinv = precon_vec.elts();
for (k = 0; k < l; k++)
bpinv[k] = PrepMulModPrecon(rep(bp[k]), p, pinv);
for (i = 0; i < n; i++) {
acc = 0;
const zz_p* ap = A[i].elts();
for (k = 0; k < l; k++) {
tmp = MulModPrecon(rep(ap[k]), rep(bp[k]), p, bpinv[k]);
acc = AddMod(acc, tmp, p);
}
xp[i].LoopHole() = acc;
}
}
}
void MinPolySeq(zz_pX& h, const vec_zz_p& a, long m)
{
if (m < 0 || NTL_OVERFLOW(m, 1, 0)) Error("MinPoly: bad args");
if (a.length() < 2*m) Error("MinPoly: sequence too short");
if (m > NTL_zz_pX_BERMASS_CROSSOVER)
GCDMinPolySeq(h, a, m);
else
BerlekampMassey(h, a, m);
}
void clear(vec_zz_p& x)
{
long n = x.length();
zz_p *xp = x.elts();
long i;
for (i = 0; i < n; i++)
clear(xp[i]);
}
void InnerProduct(zz_p& x, const vec_zz_p& a, const vec_zz_p& b)
{
long n = min(a.length(), b.length());
long i;
long accum, t;
long p = zz_p::modulus();
mulmod_t pinv = zz_p::ModulusInverse();
const zz_p *ap = a.elts();
const zz_p *bp = b.elts();
accum = 0;
for (i = 0; i < n; i++) {
t = MulMod(rep(ap[i]), rep(bp[i]), p, pinv);
accum = AddMod(accum, t, p);
}
x.LoopHole() = accum;
}
void cvt(vec_GF2& x, const vec_zz_p& a)
{
long n = a.length();
x.SetLength(n);
long i;
for (i = 0; i < n; i++)
x.put(i, rep(a[i]));
}
long IsZero(const vec_zz_p& a)
{
long n = a.length();
long i;
for (i = 0; i < n; i++)
if (!IsZero(a[i]))
return 0;
return 1;
}
static
void MulAdd(vec_ZZ& x, const ZZ& prod, const vec_zz_p& h)
{
long n = x.length();
if (h.length() != n) Error("MulAdd: dimension mismatch");
ZZ t;
long i;
for (i = 0; i < n; i++) {
mul(t, prod, rep(h[i]));
add(x[i], x[i], t);
}
}
void negate(vec_zz_p& x, const vec_zz_p& a)
{
long n = a.length();
long p = zz_p::modulus();
x.SetLength(n);
const zz_p *ap = a.elts();
zz_p *xp = x.elts();
long i;
for (i = 0; i < n; i++)
xp[i].LoopHole() = NegateMod(rep(ap[i]), p);
}
void eval(vec_zz_p& b, const zz_pX& f, const vec_zz_p& a)
// naive algorithm: repeats Horner
{
if (&b == &f.rep) {
vec_zz_p bb;
eval(bb, f, a);
b = bb;
return;
}
long m = a.length();
b.SetLength(m);
long i;
for (i = 0; i < m; i++)
eval(b[i], f, a[i]);
}
void VectorCopy(vec_zz_p& x, const vec_zz_p& a, long n)
{
if (n < 0) Error("VectorCopy: negative length");
if (NTL_OVERFLOW(n, 1, 0)) Error("overflow in VectorCopy");
long m = min(n, a.length());
x.SetLength(n);
long i;
for (i = 0; i < m; i++)
x[i] = a[i];
for (i = m; i < n; i++)
clear(x[i]);
}
void ProjectPowers(vec_zz_p& x, const vec_zz_p& a, long k,
const zz_pX& h, const zz_pXModulus& F)
{
if (a.length() > F.n || k < 0) Error("ProjectPowers: bad args");
if (k == 0) {
x.SetLength(0);
return;
}
long m = SqrRoot(k);
zz_pXArgument H;
build(H, h, F, m);
ProjectPowers(x, a, k, H, F);
}
void VectorCopy(vec_zz_p& x, const vec_zz_p& a, long n)
{
if (n < 0) LogicError("VectorCopy: negative length");
if (NTL_OVERFLOW(n, 1, 0)) ResourceError("overflow in VectorCopy");
long m = min(n, a.length());
x.SetLength(n);
const zz_p *ap = a.elts();
zz_p *xp = x.elts();
long i;
for (i = 0; i < m; i++)
xp[i] = ap[i];
for (i = m; i < n; i++)
clear(xp[i]);
}
static
void MixedMul(vec_ZZ& x, const vec_zz_p& a, const mat_ZZ& B)
{
long n = B.NumRows();
long l = B.NumCols();
if (n != a.length())
Error("matrix mul: dimension mismatch");
x.SetLength(l);
long i, k;
ZZ acc, tmp;
for (i = 1; i <= l; i++) {
clear(acc);
for (k = 1; k <= n; k++) {
mul(tmp, B(k, i), rep(a(k)));
add(acc, acc, tmp);
}
x(i) = acc;
}
}
void mul(vec_zz_p& x, const vec_zz_p& a, const mat_zz_p& B)
{
long l = a.length();
long m = B.NumCols();
if (l != B.NumRows())
LogicError("matrix mul: dimension mismatch");
if (m == 0) {
x.SetLength(0);
}
else if (m == 1) {
long p = zz_p::modulus();
mulmod_t pinv = zz_p::ModulusInverse();
long acc, tmp;
long k;
acc = 0;
for(k = 1; k <= l; k++) {
tmp = MulMod(rep(a(k)), rep(B(k,1)), p, pinv);
acc = AddMod(acc, tmp, p);
}
x.SetLength(1);
x(1).LoopHole() = acc;
}
else { // m > 1. precondition
long p = zz_p::modulus();
mulmod_t pinv = zz_p::ModulusInverse();
vec_long::Watcher watch_mul_aux_vec(mul_aux_vec);
mul_aux_vec.SetLength(m);
long *acc = mul_aux_vec.elts();
long j, k;
const zz_p* ap = a.elts();
for (j = 0; j < m; j++) acc[j] = 0;
for (k = 0; k < l; k++) {
long aa = rep(ap[k]);
if (aa != 0) {
const zz_p* bp = B[k].elts();
long T1;
mulmod_precon_t aapinv = PrepMulModPrecon(aa, p, pinv);
for (j = 0; j < m; j++) {
T1 = MulModPrecon(rep(bp[j]), aa, p, aapinv);
acc[j] = AddMod(acc[j], T1, p);
}
}
}
x.SetLength(m);
zz_p *xp = x.elts();
for (j = 0; j < m; j++)
xp[j].LoopHole() = acc[j];
}
}
void interpolate(zz_pX& f, const vec_zz_p& a, const vec_zz_p& b)
{
long m = a.length();
if (b.length() != m) Error("interpolate: vector length mismatch");
if (m == 0) {
clear(f);
return;
}
vec_zz_p prod;
prod = a;
zz_p t1, t2;
long k, i;
vec_zz_p res;
res.SetLength(m);
for (k = 0; k < m; k++) {
const zz_p& aa = a[k];
set(t1);
for (i = k-1; i >= 0; i--) {
mul(t1, t1, aa);
add(t1, t1, prod[i]);
}
clear(t2);
for (i = k-1; i >= 0; i--) {
mul(t2, t2, aa);
add(t2, t2, res[i]);
}
inv(t1, t1);
sub(t2, b[k], t2);
mul(t1, t1, t2);
for (i = 0; i < k; i++) {
mul(t2, prod[i], t1);
add(res[i], res[i], t2);
}
res[k] = t1;
if (k < m-1) {
if (k == 0)
negate(prod[0], prod[0]);
else {
negate(t1, a[k]);
add(prod[k], t1, prod[k-1]);
for (i = k-1; i >= 1; i--) {
mul(t2, prod[i], t1);
add(prod[i], t2, prod[i-1]);
}
mul(prod[0], prod[0], t1);
}
}
}
while (m > 0 && IsZero(res[m-1])) m--;
res.SetLength(m);
f.rep = res;
}
void solve(zz_p& d, vec_zz_p& X,
const mat_zz_p& A, const vec_zz_p& b)
{
long n = A.NumRows();
if (A.NumCols() != n)
LogicError("solve: nonsquare matrix");
if (b.length() != n)
LogicError("solve: dimension mismatch");
if (n == 0) {
set(d);
X.SetLength(0);
return;
}
long i, j, k, pos;
zz_p t1, t2, t3;
zz_p *x, *y;
mat_zz_p M;
M.SetDims(n, n+1);
for (i = 0; i < n; i++) {
for (j = 0; j < n; j++)
M[i][j] = A[j][i];
M[i][n] = b[i];
}
zz_p det;
set(det);
long p = zz_p::modulus();
mulmod_t pinv = zz_p::ModulusInverse();
for (k = 0; k < n; k++) {
pos = -1;
for (i = k; i < n; i++) {
if (!IsZero(M[i][k])) {
pos = i;
break;
}
}
if (pos != -1) {
if (k != pos) {
swap(M[pos], M[k]);
negate(det, det);
}
mul(det, det, M[k][k]);
inv(t3, M[k][k]);
M[k][k] = t3;
for (i = k+1; i < n; i++) {
// M[i] = M[i] - M[k]*M[i,k]*t3
mul(t1, M[i][k], t3);
negate(t1, t1);
x = M[i].elts() + (k+1);
y = M[k].elts() + (k+1);
long T1 = rep(t1);
mulmod_precon_t t1pinv = PrepMulModPrecon(T1, p, pinv); // T1*pinv;
long T2;
for (j = k+1; j <= n; j++, x++, y++) {
// *x = *x + (*y)*t1
T2 = MulModPrecon(rep(*y), T1, p, t1pinv);
x->LoopHole() = AddMod(rep(*x), T2, p);
}
}
}
else {
clear(d);
return;
}
}
X.SetLength(n);
for (i = n-1; i >= 0; i--) {
clear(t1);
for (j = i+1; j < n; j++) {
mul(t2, X[j], M[i][j]);
add(t1, t1, t2);
}
sub(t1, M[i][n], t1);
mul(X[i], t1, M[i][i]);
}
d = det;
}
void BuildFromRoots(zz_pX& x, const vec_zz_p& a)
{
long n = a.length();
if (n == 0) {
set(x);
return;
}
long k0 = NextPowerOfTwo(NTL_zz_pX_MUL_CROSSOVER)-1;
long crossover = 1L << k0;
if (n <= NTL_zz_pX_MUL_CROSSOVER) {
x.rep.SetMaxLength(n+1);
x.rep = a;
IterBuild(&x.rep[0], n);
x.rep.SetLength(n+1);
SetCoeff(x, n);
return;
}
long k = NextPowerOfTwo(n);
long m = 1L << k;
long i, j;
long l, width;
zz_pX b(INIT_SIZE, m+1);
b.rep = a;
b.rep.SetLength(m+1);
for (i = n; i < m; i++)
clear(b.rep[i]);
set(b.rep[m]);
fftRep R1(INIT_SIZE, k), R2(INIT_SIZE, k);
zz_p t1, one;
set(one);
vec_zz_p G(INIT_SIZE, crossover), H(INIT_SIZE, crossover);
zz_p *g = G.elts();
zz_p *h = H.elts();
zz_p *tmp;
for (i = 0; i < m; i+= crossover) {
for (j = 0; j < crossover; j++)
negate(g[j], b.rep[i+j]);
if (k0 > 0) {
for (j = 0; j < crossover; j+=2) {
mul(t1, g[j], g[j+1]);
add(g[j+1], g[j], g[j+1]);
g[j] = t1;
}
}
for (l = 1; l < k0; l++) {
width = 1L << l;
for (j = 0; j < crossover; j += 2*width)
mul(&h[j], &g[j], &g[j+width], width);
tmp = g; g = h; h = tmp;
}
for (j = 0; j < crossover; j++)
b.rep[i+j] = g[j];
}
for (l = k0; l < k; l++) {
width = 1L << l;
for (i = 0; i < m; i += 2*width) {
t1 = b.rep[i+width];
set(b.rep[i+width]);
TofftRep(R1, b, l+1, i, i+width);
b.rep[i+width] = t1;
t1 = b.rep[i+2*width];
set(b.rep[i+2*width]);
TofftRep(R2, b, l+1, i+width, i+2*width);
b.rep[i+2*width] = t1;
mul(R1, R1, R2);
FromfftRep(&b.rep[i], R1, 0, 2*width-1);
sub(b.rep[i], b.rep[i], one);
}
}
x.rep.SetLength(n+1);
long delta = m-n;
for (i = 0; i <= n; i++)
x.rep[i] = b.rep[i+delta];
// no need to normalize
}
