void sampleGaussian(ZZX &poly, long n, double stdev)
{
static double const Pi=4.0*atan(1.0); // Pi=3.1415..
static long const bignum = 0xfffffff;
// THREADS: C++11 guarantees these are initialized only once
if (n<=0) n=deg(poly)+1; if (n<=0) return;
poly.SetMaxLength(n); // allocate space for degree-(n-1) polynomial
for (long i=0; i<n; i++) SetCoeff(poly, i, ZZ::zero());
// Uses the Box-Muller method to get two Normal(0,stdev^2) variables
for (long i=0; i<n; i+=2) {
double r1 = (1+RandomBnd(bignum))/((double)bignum+1);
double r2 = (1+RandomBnd(bignum))/((double)bignum+1);
double theta=2*Pi*r1;
double rr= sqrt(-2.0*log(r2))*stdev;
assert(rr < 8*stdev); // sanity-check, no more than 8 standard deviations
// Generate two Gaussians RV's, rounded to integers
long x = (long) floor(rr*cos(theta) +0.5);
SetCoeff(poly, i, x);
if (i+1 < n) {
x = (long) floor(rr*sin(theta) +0.5);
SetCoeff(poly, i+1, x);
}
}
poly.normalize(); // need to call this after we work on the coeffs
}
ZZX RandPoly(long n,const ZZ& p)
{
ZZX F; F.SetMaxLength(n);
ZZ p2; p2=p>>1;
for (long i=0; i<n; i++)
{ SetCoeff(F,i,RandomBnd(p)-p2); }
return F;
}
// multiply the polynomial f by the integer a modulo q
void MulMod(ZZX& out, const ZZX& f, long a, long q, bool abs/*default=true*/)
{
// ensure that out has the same degree as f
out.SetMaxLength(deg(f)+1); // allocate space if needed
if (deg(out)>deg(f)) trunc(out,out,deg(f)+1); // remove high degrees
for (int i=0; i<=deg(f); i++) {
int c = rem(coeff(f,i), q);
c = MulMod(c, a, q); // returns c \in [0,q-1]
if (!abs && c >= q/2)
c -= q;
SetCoeff(out,i,c);
}
}
void sampleSmall(ZZX &poly, long n)
{
if (n<=0) n=deg(poly)+1; if (n<=0) return;
poly.SetMaxLength(n); // allocate space for degree-(n-1) polynomial
for (long i=0; i<n; i++) { // Chosse coefficients, one by one
long u = lrand48();
if (u&1) { // with prob. 1/2 choose between -1 and +1
u = (u & 2) -1;
SetCoeff(poly, i, u);
}
else SetCoeff(poly, i, 0); // with ptob. 1/2 set to 0
}
poly.normalize(); // need to call this after we work on the coeffs
}
void sampleHWt(ZZX &poly, long Hwt, long n)
{
if (n<=0) n=deg(poly)+1; if (n<=0) return;
clear(poly); // initialize to zero
poly.SetMaxLength(n); // allocate space for degree-(n-1) polynomial
long b,u,i=0;
if (Hwt>n) Hwt=n;
while (i<Hwt) { // continue until exactly Hwt nonzero coefficients
u=lrand48()%n; // The next coefficient to choose
if (IsZero(coeff(poly,u))) { // if we didn't choose it already
b = lrand48()&2; // b random in {0,2}
b--; // random in {-1,1}
SetCoeff(poly,u,b);
i++; // count another nonzero coefficient
}
}
poly.normalize(); // need to call this after we work on the coeffs
}
void PolyRed(ZZX& out, const ZZX& in, long q, bool abs)
{
// ensure that out has the same degree as in
out.SetMaxLength(deg(in)+1); // allocate space if needed
if (deg(out)>deg(in)) trunc(out,out,deg(in)+1); // remove high degrees
long q2; q2=q>>1;
for (long i=0; i<=deg(in); i++)
{ long c=coeff(in,i)%q;
if (abs)
{ if (c<0) { c=c+q; } }
else if (q==2)
{ if (coeff(in,i)<0) { c=-c; } }
else
{ if (c>=q2) { c=c-q; }
else if (c<-q2) { c=c+q; }
}
SetCoeff(out,i,c);
}
}
void sampleUniform(ZZX& poly, const ZZ& B, long n)
{
if (n<=0) n=deg(poly)+1; if (n<=0) return;
if (B <= 0) {
clear(poly);
return;
}
poly.SetMaxLength(n); // allocate space for degree-(n-1) polynomial
ZZ UB, tmp;
UB = 2*B + 1;
for (long i = 0; i < n; i++) {
RandomBnd(tmp, UB);
tmp -= B;
poly.rep[i] = tmp;
}
poly.normalize();
}
/* When q=2 maintains the same sign as the input */
void PolyRed(ZZX& out, const ZZX& in, const ZZ& q, bool abs)
{
// ensure that out has the same degree as in
out.SetMaxLength(deg(in)+1); // allocate space if needed
if (deg(out)>deg(in)) trunc(out,out,deg(in)+1); // remove high degrees
ZZ q2; q2=q>>1;
for (long i=0; i<=deg(in); i++)
{ ZZ c=coeff(in,i);
c %= q;
if (abs) {
if (c<0) c += q;
}
else if (q!=2) {
if (c>q2) { c=c-q; }
else if (c<-q2) { c=c+q; }
}
else // q=2
{ if (sign(coeff(in,i))!=sign(c))
{ c=-c; }
}
SetCoeff(out,i,c);
}
}