/usr/include/NTL/GF2X.h is in libntl-dev 5.4.2-4.1build1.
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#define NTL_GF2X__H
#include <NTL/vector.h>
#include <NTL/ZZ.h>
#include <NTL/WordVector.h>
#include <NTL/vec_GF2.h>
NTL_OPEN_NNS
class GF2X {
public:
WordVector xrep;
typedef vec_GF2 VectorBaseType;
GF2X() { }
~GF2X() { }
GF2X(INIT_SIZE_TYPE, long n);
GF2X& operator=(const GF2X& a) { xrep = a.xrep; return *this; }
inline GF2X& operator=(GF2 a);
inline GF2X& operator=(long a);
void normalize();
static const GF2X& zero();
void kill() { xrep.kill(); }
void SetMaxLength(long n);
static long HexOutput;
inline GF2X(long i, GF2 c);
inline GF2X(long i, long c);
GF2X(GF2X& x, INIT_TRANS_TYPE) : xrep(x.xrep, INIT_TRANS) { }
};
long IsZero(const GF2X& a);
long IsOne(const GF2X& a);
long IsX(const GF2X& a);
GF2 coeff(const GF2X& a, long i);
GF2 LeadCoeff(const GF2X& a);
GF2 ConstTerm(const GF2X& a);
inline void clear(GF2X& x)
{ x.xrep.ZeroLength(); }
void set(GF2X& x);
void SetX(GF2X& x);
void SetCoeff(GF2X& x, long i);
void SetCoeff(GF2X& x, long i, GF2 a);
void SetCoeff(GF2X& x, long i, long a);
inline GF2X::GF2X(long i, GF2 a)
{ SetCoeff(*this, i, a); }
inline GF2X::GF2X(long i, long a)
{ SetCoeff(*this, i, a); }
void swap(GF2X& a, GF2X& b);
long deg(const GF2X& aa);
long weight(const GF2X& a);
long operator==(const GF2X& a, const GF2X& b);
inline long operator!=(const GF2X& a, const GF2X& b)
{ return !(a == b); }
long operator==(const GF2X& a, GF2 b);
long operator==(const GF2X& a, long b);
inline long operator==(GF2 a, const GF2X& b) { return b == a; }
inline long operator==(long a, const GF2X& b) { return b == a; }
inline long operator!=(const GF2X& a, GF2 b) { return !(a == b); }
inline long operator!=(const GF2X& a, long b) { return !(a == b); }
inline long operator!=(GF2 a, const GF2X& b) { return !(a == b); }
inline long operator!=(long a, const GF2X& b) { return !(a == b); }
NTL_SNS istream & operator>>(NTL_SNS istream& s, GF2X& a);
NTL_SNS ostream& operator<<(NTL_SNS ostream& s, const GF2X& a);
void random(GF2X& x, long n);
inline GF2X random_GF2X(long n)
{ GF2X x; random(x, n); NTL_OPT_RETURN(GF2X, x); }
void add(GF2X& x, const GF2X& a, const GF2X& b);
void add(GF2X& x, const GF2X& a, GF2 b);
void add(GF2X& x, const GF2X& a, long b);
inline void add(GF2X& x, GF2 a, const GF2X& b) { add(x, b, a); }
inline void add(GF2X& x, long a, const GF2X& b) { add(x, b, a); }
inline void sub(GF2X& x, const GF2X& a, const GF2X& b) { add(x, a, b); }
inline void sub(GF2X& x, const GF2X& a, GF2 b) { add(x, a, b); }
inline void sub(GF2X& x, const GF2X& a, long b) { add(x, a, b); }
inline void sub(GF2X& x, GF2 a, const GF2X& b) { add(x, a, b); }
inline void sub(GF2X& x, long a, const GF2X& b) { add(x, a, b); }
inline void negate(GF2X& x, const GF2X& a) { x = a; }
inline GF2X operator+(const GF2X& a, const GF2X& b)
{ GF2X x; add(x, a, b); NTL_OPT_RETURN(GF2X, x); }
inline GF2X operator+(const GF2X& a, GF2 b)
{ GF2X x; add(x, a, b); NTL_OPT_RETURN(GF2X, x); }
inline GF2X operator+(const GF2X& a, long b)
{ GF2X x; add(x, a, b); NTL_OPT_RETURN(GF2X, x); }
inline GF2X operator+(GF2 a, const GF2X& b)
{ GF2X x; add(x, a, b); NTL_OPT_RETURN(GF2X, x); }
inline GF2X operator+(long a, const GF2X& b)
{ GF2X x; add(x, a, b); NTL_OPT_RETURN(GF2X, x); }
inline GF2X operator-(const GF2X& a, const GF2X& b)
{ GF2X x; sub(x, a, b); NTL_OPT_RETURN(GF2X, x); }
inline GF2X operator-(const GF2X& a, GF2 b)
{ GF2X x; sub(x, a, b); NTL_OPT_RETURN(GF2X, x); }
inline GF2X operator-(const GF2X& a, long b)
{ GF2X x; sub(x, a, b); NTL_OPT_RETURN(GF2X, x); }
inline GF2X operator-(GF2 a, const GF2X& b)
{ GF2X x; sub(x, a, b); NTL_OPT_RETURN(GF2X, x); }
inline GF2X operator-(long a, const GF2X& b)
{ GF2X x; sub(x, a, b); NTL_OPT_RETURN(GF2X, x); }
inline GF2X& operator+=(GF2X& x, const GF2X& b)
{ add(x, x, b); return x; }
inline GF2X& operator+=(GF2X& x, GF2 b)
{ add(x, x, b); return x; }
inline GF2X& operator+=(GF2X& x, long b)
{ add(x, x, b); return x; }
inline GF2X& operator-=(GF2X& x, const GF2X& b)
{ sub(x, x, b); return x; }
inline GF2X& operator-=(GF2X& x, GF2 b)
{ sub(x, x, b); return x; }
inline GF2X& operator-=(GF2X& x, long b)
{ sub(x, x, b); return x; }
inline GF2X operator-(const GF2X& a)
{ GF2X x; negate(x, a); NTL_OPT_RETURN(GF2X, x); }
inline GF2X& operator++(GF2X& x) { add(x, x, 1); return x; }
inline void operator++(GF2X& x, int) { add(x, x, 1); }
inline GF2X& operator--(GF2X& x) { sub(x, x, 1); return x; }
inline void operator--(GF2X& x, int) { sub(x, x, 1); }
void mul(GF2X& c, const GF2X& a, const GF2X& b);
void mul(GF2X& x, const GF2X& a, GF2 b);
void mul(GF2X& x, const GF2X& a, long b);
inline void mul(GF2X& x, GF2 a, const GF2X& b) { mul(x, b, a); }
inline void mul(GF2X& x, long a, const GF2X& b) { mul(x, b, a); }
void MulByX(GF2X& x, const GF2X& a);
inline GF2X MulByX(const GF2X& a)
{ GF2X x; MulByX(x, a); NTL_OPT_RETURN(GF2X, x); }
void sqr(GF2X& c, const GF2X& a);
inline GF2X sqr(const GF2X& a)
{ GF2X x; sqr(x, a); NTL_OPT_RETURN(GF2X, x); }
void trunc(GF2X& x, const GF2X& a, long m);
inline GF2X trunc(const GF2X& a, long m)
{ GF2X x; trunc(x, a, m); NTL_OPT_RETURN(GF2X, x); }
inline GF2X operator*(const GF2X& a, const GF2X& b)
{ GF2X x; mul(x, a, b); NTL_OPT_RETURN(GF2X, x); }
inline GF2X operator*(const GF2X& a, GF2 b)
{ GF2X x; mul(x, a, b); NTL_OPT_RETURN(GF2X, x); }
inline GF2X operator*(const GF2X& a, long b)
{ GF2X x; mul(x, a, b); NTL_OPT_RETURN(GF2X, x); }
inline GF2X operator*(GF2 a, const GF2X& b)
{ GF2X x; mul(x, a, b); NTL_OPT_RETURN(GF2X, x); }
inline GF2X operator*(long a, const GF2X& b)
{ GF2X x; mul(x, a, b); NTL_OPT_RETURN(GF2X, x); }
inline GF2X& operator*=(GF2X& x, const GF2X& b)
{ mul(x, x, b); return x; }
inline GF2X& operator*=(GF2X& x, GF2 b)
{ mul(x, x, b); return x; }
inline GF2X& operator*=(GF2X& x, long b)
{ mul(x, x, b); return x; }
void power(GF2X& x, const GF2X& a, long e); // x = a^e (e >= 0)
inline GF2X power(const GF2X& a, long e)
{ GF2X x; power(x, a, e); NTL_OPT_RETURN(GF2X, x); }
NTL_vector_decl(GF2X,vec_GF2X)
NTL_io_vector_decl(GF2X,vec_GF2X)
NTL_eq_vector_decl(GF2X,vec_GF2X)
void LeftShift(GF2X& c, const GF2X& a, long n);
inline GF2X LeftShift(const GF2X& a, long n)
{ GF2X x; LeftShift(x, a, n); NTL_OPT_RETURN(GF2X, x); }
void ShiftAdd(GF2X& c, const GF2X& a, long n);
void RightShift(GF2X& c, const GF2X& a, long n);
inline GF2X RightShift(const GF2X& a, long n)
{ GF2X x; RightShift(x, a, n); NTL_OPT_RETURN(GF2X, x); }
#ifndef NTL_TRANSITION
inline GF2X operator>>(const GF2X& a, long n)
{ GF2X x; RightShift(x, a, n); NTL_OPT_RETURN(GF2X, x); }
inline GF2X operator<<(const GF2X& a, long n)
{ GF2X x; LeftShift(x, a, n); NTL_OPT_RETURN(GF2X, x); }
inline GF2X& operator<<=(GF2X& x, long n)
{ LeftShift(x, x, n); return x; }
inline GF2X& operator>>=(GF2X& x, long n)
{ RightShift(x, x, n); return x; }
#endif
void CopyReverse(GF2X& c, const GF2X& a, long hi);
// c[0..hi] = reverse(a[0..hi]), with zero fill as necessary
inline void reverse(GF2X& c, const GF2X& a, long hi)
{ CopyReverse(c, a, hi); }
inline GF2X reverse(const GF2X& a, long hi)
{ GF2X x; reverse(x, a, hi); NTL_OPT_RETURN(GF2X, x); }
inline void reverse(GF2X& c, const GF2X& a)
{ CopyReverse(c, a, deg(a)); }
inline GF2X reverse(const GF2X& a)
{ GF2X x; reverse(x, a); NTL_OPT_RETURN(GF2X, x); }
void InvTrunc(GF2X& c, const GF2X& a, long e);
inline GF2X InvTrunc(const GF2X& a, long e)
{ GF2X x; InvTrunc(x, a, e); NTL_OPT_RETURN(GF2X, x); }
class GF2XModulus {
public:
GF2XModulus();
~GF2XModulus();
GF2XModulus(const GF2XModulus&);
GF2XModulus& operator=(const GF2XModulus&);
GF2XModulus(const GF2X& ff);
GF2X f; // the modulus
operator const GF2X& () const { return f; }
const GF2X& val() const { return f; }
long n; // deg(f)
long sn; // f.xrep.length()
long posn; // n - NTL_BITS_PER_LONG*(sn-1);
long k3; // used for trinomials and pentanomials
long k2;
long k1;
long size; // word length of residues
long WordLength() const { return size; }
_ntl_ulong msk; // mask of high bits of residues
long method;
vec_GF2X stab;
_ntl_ulong **stab_ptr;
long *stab_cnt;
_ntl_ulong *stab1;
GF2X h0, f0;
vec_GF2 tracevec;
};
inline long deg(const GF2XModulus& F) { return F.n; }
void build(GF2XModulus& F, const GF2X& f);
void rem(GF2X& r, const GF2X& a, const GF2XModulus& F);
void DivRem(GF2X& q, GF2X& r, const GF2X& a, const GF2XModulus& F);
void div(GF2X& q, const GF2X& a, const GF2XModulus& F);
void PlainDivRem(GF2X& q, GF2X& r, const GF2X& a, const GF2X& b);
void PlainDiv(GF2X& q, const GF2X& a, const GF2X& b);
void PlainRem(GF2X& r, const GF2X& a, const GF2X& b);
void MulMod(GF2X& c, const GF2X& a, const GF2X& b, const GF2XModulus& F);
inline GF2X MulMod(const GF2X& a, const GF2X& b, const GF2XModulus& F)
{ GF2X x; MulMod(x, a, b, F); NTL_OPT_RETURN(GF2X, x); }
void SqrMod(GF2X& c, const GF2X& a, const GF2XModulus& F);
inline GF2X SqrMod(const GF2X& a, const GF2XModulus& F)
{ GF2X x; SqrMod(x, a, F); NTL_OPT_RETURN(GF2X, x); }
void MulByXMod(GF2X& c, const GF2X& a, const GF2XModulus& F);
inline GF2X MulByXMod(const GF2X& a, const GF2XModulus& F)
{ GF2X x; MulByXMod(x, a, F); NTL_OPT_RETURN(GF2X, x); }
void MulMod(GF2X& c, const GF2X& a, const GF2X& b, const GF2X& f);
inline GF2X MulMod(const GF2X& a, const GF2X& b, const GF2X& f)
{ GF2X x; MulMod(x, a, b, f); NTL_OPT_RETURN(GF2X, x); }
void SqrMod(GF2X& c, const GF2X& a, const GF2X& f);
inline GF2X SqrMod(const GF2X& a, const GF2X& f)
{ GF2X x; SqrMod(x, a, f); NTL_OPT_RETURN(GF2X, x); }
void MulByXMod(GF2X& c, const GF2X& a, const GF2X& f);
inline GF2X MulByXMod(const GF2X& a, const GF2X& f)
{ GF2X x; MulByXMod(x, a, f); NTL_OPT_RETURN(GF2X, x); }
void InvMod(GF2X& c, const GF2X& a, const GF2X& f);
inline GF2X InvMod(const GF2X& a, const GF2X& f)
{ GF2X x; InvMod(x, a, f); NTL_OPT_RETURN(GF2X, x); }
long InvModStatus(GF2X& c, const GF2X& a, const GF2X& f);
inline long InvModStatus(GF2X& c, const GF2X& a, const GF2XModulus& F)
{ return InvModStatus(c, a, F.f); }
void PowerMod(GF2X& h, const GF2X& g, const ZZ& e, const GF2XModulus& F);
inline void PowerMod(GF2X& x, const GF2X& g, long e, const GF2XModulus& F)
{ PowerMod(x, g, ZZ_expo(e), F); }
void PowerXMod(GF2X& hh, const ZZ& e, const GF2XModulus& F);
inline void PowerXMod(GF2X& x, long e, const GF2XModulus& F)
{ PowerXMod(x, ZZ_expo(e), F); }
inline GF2X PowerMod(const GF2X& g, const ZZ& e, const GF2XModulus& F)
{ GF2X x; PowerMod(x, g, e, F); NTL_OPT_RETURN(GF2X, x); }
inline GF2X PowerMod(const GF2X& g, long e, const GF2XModulus& F)
{ GF2X x; PowerMod(x, g, e, F); NTL_OPT_RETURN(GF2X, x); }
inline GF2X PowerXMod(const ZZ& e, const GF2XModulus& F)
{ GF2X x; PowerXMod(x, e, F); NTL_OPT_RETURN(GF2X, x); }
inline GF2X PowerXMod(long e, const GF2XModulus& F)
{ GF2X x; PowerXMod(x, e, F); NTL_OPT_RETURN(GF2X, x); }
inline GF2X operator%(const GF2X& a, const GF2XModulus& F)
{ GF2X x; rem(x, a, F); NTL_OPT_RETURN(GF2X, x); }
inline GF2X& operator%=(GF2X& x, const GF2XModulus& F)
{ rem(x, x, F); return x; }
inline GF2X operator/(const GF2X& a, const GF2XModulus& F)
{ GF2X x; div(x, a, F); NTL_OPT_RETURN(GF2X, x); }
inline GF2X& operator/=(GF2X& x, const GF2XModulus& F)
{ div(x, x, F); return x; }
void DivRem(GF2X& q, GF2X& r, const GF2X& a, const GF2X& b);
void div(GF2X& q, const GF2X& a, const GF2X& b);
void div(GF2X& q, const GF2X& a, GF2 b);
void div(GF2X& q, const GF2X& a, long b);
void rem(GF2X& r, const GF2X& a, const GF2X& b);
inline GF2X operator/(const GF2X& a, const GF2X& b)
{ GF2X x; div(x, a, b); NTL_OPT_RETURN(GF2X, x); }
inline GF2X operator/(const GF2X& a, GF2 b)
{ GF2X x; div(x, a, b); NTL_OPT_RETURN(GF2X, x); }
inline GF2X operator/(const GF2X& a, long b)
{ GF2X x; div(x, a, b); NTL_OPT_RETURN(GF2X, x); }
inline GF2X& operator/=(GF2X& x, GF2 b)
{ div(x, x, b); return x; }
inline GF2X& operator/=(GF2X& x, long b)
{ div(x, x, b); return x; }
inline GF2X& operator/=(GF2X& x, const GF2X& b)
{ div(x, x, b); return x; }
inline GF2X operator%(const GF2X& a, const GF2X& b)
{ GF2X x; rem(x, a, b); NTL_OPT_RETURN(GF2X, x); }
inline GF2X& operator%=(GF2X& x, const GF2X& b)
{ rem(x, x, b); return x; }
void GCD(GF2X& d, const GF2X& a, const GF2X& b);
inline GF2X GCD(const GF2X& a, const GF2X& b)
{ GF2X x; GCD(x, a, b); NTL_OPT_RETURN(GF2X, x); }
void XGCD(GF2X& d, GF2X& s, GF2X& t, const GF2X& a, const GF2X& b);
void diff(GF2X& c, const GF2X& a);
inline GF2X diff(const GF2X& a)
{ GF2X x; diff(x, a); NTL_OPT_RETURN(GF2X, x); }
void conv(GF2X& c, long a);
void conv(GF2X& c, GF2 a);
void conv(GF2X& x, const vec_GF2& a);
inline void conv(GF2X& x, const ZZ& a)
{ conv(x, to_GF2(a)); }
void conv(vec_GF2& x, const GF2X& a);
inline GF2X to_GF2X(long a)
{ GF2X x; conv(x, a); NTL_OPT_RETURN(GF2X, x); }
inline GF2X to_GF2X(GF2 a)
{ GF2X x; conv(x, a); NTL_OPT_RETURN(GF2X, x); }
inline GF2X to_GF2X(const vec_GF2& a)
{ GF2X x; conv(x, a); NTL_OPT_RETURN(GF2X, x); }
inline GF2X to_GF2X(const ZZ& a)
{ GF2X x; conv(x, a); NTL_OPT_RETURN(GF2X, x); }
inline vec_GF2 to_vec_GF2(const GF2X& a)
{ vec_GF2 x; conv(x, a); NTL_OPT_RETURN(vec_GF2, x); }
inline GF2X& GF2X::operator=(long a)
{ conv(*this, a); return *this; }
inline GF2X& GF2X::operator=(GF2 a)
{ conv(*this, a); return *this; }
void VectorCopy(vec_GF2& x, const GF2X& a, long n);
inline vec_GF2 VectorCopy(const GF2X& a, long n)
{ vec_GF2 x; VectorCopy(x, a, n); NTL_OPT_RETURN(vec_GF2, x); }
void MulTrunc(GF2X& c, const GF2X& a, const GF2X& b, long n);
inline GF2X MulTrunc(const GF2X& a, const GF2X& b, long n)
{ GF2X x; MulTrunc(x, a, b, n); NTL_OPT_RETURN(GF2X, x); }
void SqrTrunc(GF2X& c, const GF2X& a, long n);
inline GF2X SqrTrunc(const GF2X& a, long n)
{ GF2X x; SqrTrunc(x, a, n); NTL_OPT_RETURN(GF2X, x); }
long divide(GF2X& q, const GF2X& a, const GF2X& b);
long divide(const GF2X& a, const GF2X& b);
/*** modular composition routines and data structures ***/
struct GF2XArgument {
vec_GF2X H;
};
void CompMod(GF2X& x, const GF2X& g,
const GF2XArgument& A, const GF2XModulus& F);
inline GF2X CompMod(const GF2X& g,
const GF2XArgument& A, const GF2XModulus& F)
{ GF2X x; CompMod(x, g, A, F); NTL_OPT_RETURN(GF2X, x); }
void build(GF2XArgument& A, const GF2X& h, const GF2XModulus& F, long m);
void CompMod(GF2X& x, const GF2X& g, const GF2X& h, const GF2XModulus& F);
inline GF2X CompMod(const GF2X& g, const GF2X& h, const GF2XModulus& F)
{ GF2X x; CompMod(x, g, h, F); NTL_OPT_RETURN(GF2X, x); }
void Comp2Mod(GF2X& x1, GF2X& x2, const GF2X& g1, const GF2X& g2,
const GF2X& h, const GF2XModulus& F);
void Comp3Mod(GF2X& x1, GF2X& x2, GF2X& x3,
const GF2X& g1, const GF2X& g2, const GF2X& g3,
const GF2X& h, const GF2XModulus& F);
void MinPolySeq(GF2X& h, const vec_GF2& a, long m);
inline GF2X MinPolySeq(const vec_GF2& a, long m)
{ GF2X x; MinPolySeq(x, a, m); NTL_OPT_RETURN(GF2X, x); }
void ProbMinPolyMod(GF2X& hh, const GF2X& g, const GF2XModulus& F);
inline GF2X ProbMinPolyMod(const GF2X& g, const GF2XModulus& F)
{ GF2X x; ProbMinPolyMod(x, g, F); NTL_OPT_RETURN(GF2X, x); }
void ProbMinPolyMod(GF2X& hh, const GF2X& g, const GF2XModulus& F, long m);
inline GF2X ProbMinPolyMod(const GF2X& g, const GF2XModulus& F, long m)
{ GF2X x; ProbMinPolyMod(x, g, F, m); NTL_OPT_RETURN(GF2X, x); }
void MinPolyMod(GF2X& hh, const GF2X& g, const GF2XModulus& F);
inline GF2X MinPolyMod(const GF2X& g, const GF2XModulus& F)
{ GF2X x; MinPolyMod(x, g, F); NTL_OPT_RETURN(GF2X, x); }
void MinPolyMod(GF2X& hh, const GF2X& g, const GF2XModulus& F, long m);
inline GF2X MinPolyMod(const GF2X& g, const GF2XModulus& F, long m)
{ GF2X x; MinPolyMod(x, g, F, m); NTL_OPT_RETURN(GF2X, x); }
void IrredPolyMod(GF2X& h, const GF2X& g, const GF2XModulus& F);
inline GF2X IrredPolyMod(const GF2X& g, const GF2XModulus& F)
{ GF2X x; IrredPolyMod(x, g, F); NTL_OPT_RETURN(GF2X, x); }
void IrredPolyMod(GF2X& h, const GF2X& g, const GF2XModulus& F, long m);
inline GF2X IrredPolyMod(const GF2X& g, const GF2XModulus& F, long m)
{ GF2X x; IrredPolyMod(x, g, F, m); NTL_OPT_RETURN(GF2X, x); }
// undocumented stuff:
void MinPolyInternal(GF2X& h, const GF2X& x, long m);
struct GF2XTransMultiplier {
GF2X f0, fbi, b;
long shamt, shamt_fbi, shamt_b;
};
void build(GF2XTransMultiplier& B, const GF2X& b, const GF2XModulus& F);
void UpdateMap(vec_GF2& x, const vec_GF2& a, const GF2XTransMultiplier& B,
const GF2XModulus& F);
inline vec_GF2 UpdateMap(const vec_GF2& a,
const GF2XTransMultiplier& B, const GF2XModulus& F)
{ vec_GF2 x; UpdateMap(x, a, B, F); NTL_OPT_RETURN(vec_GF2, x); }
inline void project(GF2& x, const vec_GF2& a, const GF2X& b)
{ x = to_GF2(InnerProduct(a.rep, b.xrep)); }
inline GF2 project(const vec_GF2& a, const GF2X& b)
{ return to_GF2(InnerProduct(a.rep, b.xrep)); }
void ProjectPowers(vec_GF2& x, const vec_GF2& a, long k,
const GF2XArgument& H, const GF2XModulus& F);
inline vec_GF2 ProjectPowers(const vec_GF2& a, long k,
const GF2XArgument& H, const GF2XModulus& F)
{ vec_GF2 x; ProjectPowers(x, a, k, H, F);
NTL_OPT_RETURN(vec_GF2, x); }
void ProjectPowers(vec_GF2& x, const vec_GF2& a, long k, const GF2X& h,
const GF2XModulus& F);
inline vec_GF2 ProjectPowers(const vec_GF2& a, long k,
const GF2X& H, const GF2XModulus& F)
{ vec_GF2 x; ProjectPowers(x, a, k, H, F);
NTL_OPT_RETURN(vec_GF2, x); }
void TraceVec(vec_GF2& S, const GF2X& f);
inline vec_GF2 TraceVec(const GF2X& f)
{ vec_GF2 x; TraceVec(x, f); NTL_OPT_RETURN(vec_GF2, x); }
void TraceMod(GF2& x, const GF2X& a, const GF2XModulus& F);
inline GF2 TraceMod(const GF2X& a, const GF2XModulus& F)
{ GF2 x; TraceMod(x, a, F); return x; }
void TraceMod(GF2& x, const GF2X& a, const GF2X& f);
inline GF2 TraceMod(const GF2X& a, const GF2X& f)
{ GF2 x; TraceMod(x, a, f); return x; }
void GF2XFromBytes(GF2X& x, const unsigned char *p, long n);
inline GF2X GF2XFromBytes(const unsigned char *p, long n)
{ GF2X x; GF2XFromBytes(x, p, n); NTL_OPT_RETURN(GF2X, x); }
void BytesFromGF2X(unsigned char *p, const GF2X& a, long n);
inline long NumBits(const GF2X& a)
{ return deg(a) + 1; }
inline long NumBytes(const GF2X& a)
{ return (NumBits(a) + 7)/8; }
NTL_CLOSE_NNS
#endif
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