/usr/include/NTL/ZZ.h is in libntl-dev 9.9.1-3.
This file is owned by root:root, with mode 0o644.
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#define NTL_ZZ__H
/********************************************************
LIP INTERFACE
The class ZZ implements signed, arbitrary length integers.
**********************************************************/
#include <NTL/lip.h>
#include <NTL/tools.h>
#include <NTL/vector.h>
#include <NTL/SmartPtr.h>
#include <NTL/sp_arith.h>
NTL_OPEN_NNS
class ZZ_p; // forward declaration
class ZZX;
class ZZ {
public:
typedef ZZ_p residue_type;
typedef ZZX poly_type;
class Deleter {
public:
static void apply(NTL_verylong& p) { NTL_zfree(&p); }
};
WrappedPtr<NTL_verylong_body, Deleter> rep;
// This is currently public for "emergency" situations
// May be private in future versions.
ZZ() { }
explicit ZZ(long a) { *this = a; }
ZZ(INIT_SIZE_TYPE, long k)
// initial value is 0, but space is pre-allocated so that numbers
// x with x.size() <= k can be stored without re-allocation.
// Call with ZZ(INIT_SIZE, k).
// The purpose for the INIT_SIZE argument is to prevent automatic
// type conversion from long to ZZ, which would be tempting, but wrong.
{
NTL_zsetlength(&rep, k);
}
ZZ(const ZZ& a)
// initial value is a.
{
NTL_zcopy(a.rep, &rep);
}
ZZ(INIT_VAL_TYPE, long a) { NTL_zintoz(a, &rep); }
ZZ(INIT_VAL_TYPE, int a) { NTL_zintoz(a, &rep); }
ZZ(INIT_VAL_TYPE, unsigned long a) { NTL_zuintoz(a, &rep); }
ZZ(INIT_VAL_TYPE, unsigned int a) { NTL_zuintoz((unsigned long) a, &rep); }
inline ZZ(INIT_VAL_TYPE, const char *);
inline ZZ(INIT_VAL_TYPE, float);
inline ZZ(INIT_VAL_TYPE, double);
ZZ& operator=(const ZZ& a) { NTL_zcopy(a.rep, &rep); return *this; }
ZZ& operator=(long a) { NTL_zintoz(a, &rep); return *this; }
void kill()
// force the space held by this ZZ to be released.
// The value then becomes 0.
{ rep.kill(); }
void swap(ZZ& x)
{ NTL_zswap(&rep, &x.rep); }
void SetSize(long k)
// pre-allocates space for k-digit numbers (base 2^NTL_ZZ_NBITS);
// does not change the value.
{ NTL_zsetlength(&rep, k); }
long size() const
// returns the number of (NTL_ZZ_NBIT-bit) digits of |a|; the size of 0 is 0.
{ return NTL_zsize(rep); }
long null() const
// test of rep is null
{ return !rep; }
long MaxAlloc() const
// returns max allocation request, possibly rounded up a bit...
{ return NTL_zmaxalloc(rep); }
long SinglePrecision() const
{ return NTL_zsptest(rep); }
// tests if less than NTL_SP_BOUND in absolute value
long WideSinglePrecision() const
{ return NTL_zwsptest(rep); }
// tests if less than NTL_WSP_BOUND in absolute value
static const ZZ& zero();
ZZ(ZZ& x, INIT_TRANS_TYPE) { rep.swap(x.rep); }
// used to cheaply hand off memory management of return value,
// without copying, assuming compiler implements the
// "return value optimization". This is probably obsolete by
// now, as modern compilers can and should optimize
// the copy constructor in the situations where this is used.
// This should only be used for simple, local variables
// that are not be subject to special memory management.
// mainly for internal consumption by ZZWatcher
void KillBig() { if (MaxAlloc() > NTL_RELEASE_THRESH) kill(); }
};
class ZZWatcher {
public:
ZZ& watched;
explicit
ZZWatcher(ZZ& _watched) : watched(_watched) {}
~ZZWatcher() { watched.KillBig(); }
};
#define NTL_ZZRegister(x) NTL_TLS_LOCAL(ZZ, x); ZZWatcher _WATCHER__ ## x(x)
const ZZ& ZZ_expo(long e);
inline void clear(ZZ& x)
// x = 0
{ NTL_zzero(&x.rep); }
inline void set(ZZ& x)
// x = 1
{ NTL_zone(&x.rep); }
inline void swap(ZZ& x, ZZ& y)
// swap the values of x and y (swaps pointers only)
{ x.swap(y); }
inline double log(const ZZ& a)
{ return NTL_zlog(a.rep); }
/**********************************************************
Conversion routines.
***********************************************************/
inline void conv(ZZ& x, const ZZ& a) { x = a; }
inline ZZ to_ZZ(const ZZ& a) { return a; }
inline void conv(ZZ& x, long a) { NTL_zintoz(a, &x.rep); }
inline ZZ to_ZZ(long a) { return ZZ(INIT_VAL, a); }
inline void conv(ZZ& x, int a) { NTL_zintoz(long(a), &x.rep); }
inline ZZ to_ZZ(int a) { return ZZ(INIT_VAL, a); }
inline void conv(ZZ& x, unsigned long a) { NTL_zuintoz(a, &x.rep); }
inline ZZ to_ZZ(unsigned long a) { return ZZ(INIT_VAL, a); }
inline void conv(ZZ& x, unsigned int a) { NTL_zuintoz((unsigned long)(a), &x.rep); }
inline ZZ to_ZZ(unsigned int a) { return ZZ(INIT_VAL, a); }
void conv(ZZ& x, const char *s);
inline ZZ::ZZ(INIT_VAL_TYPE, const char *s) { conv(*this, s); }
inline ZZ to_ZZ(const char *s) { return ZZ(INIT_VAL, s); }
inline void conv(ZZ& x, double a) { NTL_zdoubtoz(a, &x.rep); }
inline ZZ::ZZ(INIT_VAL_TYPE, double a) { conv(*this, a); }
inline ZZ to_ZZ(double a) { return ZZ(INIT_VAL, a); }
inline void conv(ZZ& x, float a) { NTL_zdoubtoz(double(a), &x.rep); }
inline ZZ::ZZ(INIT_VAL_TYPE, float a) { conv(*this, a); }
inline ZZ to_ZZ(float a) { return ZZ(INIT_VAL, a); }
inline void conv(long& x, const ZZ& a) { x = NTL_ztoint(a.rep); }
inline long to_long(const ZZ& a) { return NTL_ztoint(a.rep); }
inline void conv(int& x, const ZZ& a)
{ unsigned int res = (unsigned int) NTL_ztouint(a.rep);
x = NTL_UINT_TO_INT(res); }
inline int to_int(const ZZ& a)
{ unsigned int res = (unsigned int) NTL_ztouint(a.rep);
return NTL_UINT_TO_INT(res); }
inline void conv(unsigned long& x, const ZZ& a) { x = NTL_ztouint(a.rep); }
inline unsigned long to_ulong(const ZZ& a) { return NTL_ztouint(a.rep); }
inline void conv(unsigned int& x, const ZZ& a)
{ x = (unsigned int)(NTL_ztouint(a.rep)); }
inline unsigned int to_uint(const ZZ& a)
{ return (unsigned int)(NTL_ztouint(a.rep)); }
inline void conv(double& x, const ZZ& a) { x = NTL_zdoub(a.rep); }
inline double to_double(const ZZ& a) { return NTL_zdoub(a.rep); }
inline void conv(float& x, const ZZ& a) { x = float(NTL_zdoub(a.rep)); }
inline float to_float(const ZZ& a) { return float(NTL_zdoub(a.rep)); }
inline void ZZFromBytes(ZZ& x, const unsigned char *p, long n)
{ NTL_zfrombytes(&x.rep, p, n); }
inline ZZ ZZFromBytes(const unsigned char *p, long n)
{ ZZ x; ZZFromBytes(x, p, n); NTL_OPT_RETURN(ZZ, x); }
inline void BytesFromZZ(unsigned char *p, const ZZ& a, long n)
{ NTL_zbytesfromz(p, a.rep, n); }
// ****** comparisons
inline long sign(const ZZ& a)
// returns the sign of a (-1, 0, or 1).
{ return NTL_zsign(a.rep); }
inline long compare(const ZZ& a, const ZZ& b)
// returns the sign of a-b (-1, 0, or 1).
{
return NTL_zcompare(a.rep, b.rep);
}
inline long IsZero(const ZZ& a)
// zero test
{ return NTL_ziszero(a.rep); }
inline long IsOne(const ZZ& a)
{ return NTL_zisone(a.rep); }
// test for 1
/* the usual comparison operators */
inline long operator==(const ZZ& a, const ZZ& b)
{ return NTL_zcompare(a.rep, b.rep) == 0; }
inline long operator!=(const ZZ& a, const ZZ& b)
{ return NTL_zcompare(a.rep, b.rep) != 0; }
inline long operator<(const ZZ& a, const ZZ& b)
{ return NTL_zcompare(a.rep, b.rep) < 0; }
inline long operator>(const ZZ& a, const ZZ& b)
{ return NTL_zcompare(a.rep, b.rep) > 0; }
inline long operator<=(const ZZ& a, const ZZ& b)
{ return NTL_zcompare(a.rep, b.rep) <= 0; }
inline long operator>=(const ZZ& a, const ZZ& b)
{ return NTL_zcompare(a.rep, b.rep) >= 0; }
/* single-precision versions of the above */
inline long compare(const ZZ& a, long b) { return NTL_zscompare(a.rep, b); }
inline long compare(long a, const ZZ& b) { return -NTL_zscompare(b.rep, a); }
inline long operator==(const ZZ& a, long b) { return NTL_zscompare(a.rep, b) == 0; }
inline long operator!=(const ZZ& a, long b) { return NTL_zscompare(a.rep, b) != 0; }
inline long operator<(const ZZ& a, long b) { return NTL_zscompare(a.rep, b) < 0; }
inline long operator>(const ZZ& a, long b) { return NTL_zscompare(a.rep, b) > 0; }
inline long operator<=(const ZZ& a, long b) { return NTL_zscompare(a.rep, b) <= 0; }
inline long operator>=(const ZZ& a, long b) { return NTL_zscompare(a.rep, b) >= 0; }
inline long operator==(long a, const ZZ& b) { return b == a; }
inline long operator!=(long a, const ZZ& b) { return b != a; }
inline long operator<(long a, const ZZ& b) { return b > a; }
inline long operator>(long a, const ZZ& b) { return b < a; }
inline long operator<=(long a, const ZZ& b) { return b >= a; }
inline long operator>=(long a, const ZZ& b) { return b <= a; }
/**************************************************
Addition
**************************************************/
inline void add(ZZ& x, const ZZ& a, const ZZ& b)
// x = a + b
{ NTL_zadd(a.rep, b.rep, &x.rep); }
inline void sub(ZZ& x, const ZZ& a, const ZZ& b)
// x = a - b
{ NTL_zsub(a.rep, b.rep, &x.rep); }
inline void SubPos(ZZ& x, const ZZ& a, const ZZ& b)
// x = a - b; assumes a >= b >= 0.
{ NTL_zsubpos(a.rep, b.rep, &x.rep); }
inline void negate(ZZ& x, const ZZ& a)
// x = -a
{ NTL_zcopy(a.rep, &x.rep); NTL_znegate(&x.rep); }
inline void abs(ZZ& x, const ZZ& a)
// x = |a|
{ NTL_zcopy(a.rep, &x.rep); NTL_zabs(&x.rep); }
/* single-precision versions of the above */
inline void add(ZZ& x, const ZZ& a, long b)
{ NTL_zsadd(a.rep, b, &x.rep); }
inline void add(ZZ& x, long a, const ZZ& b) { add(x, b, a); }
void sub(ZZ& x, const ZZ& a, long b);
void sub(ZZ& x, long a, const ZZ& b);
/* operator/function notation */
inline ZZ operator+(const ZZ& a, const ZZ& b)
{ ZZ x; add(x, a, b); NTL_OPT_RETURN(ZZ, x); }
inline ZZ operator+(const ZZ& a, long b)
{ ZZ x; add(x, a, b); NTL_OPT_RETURN(ZZ, x); }
inline ZZ operator+(long a, const ZZ& b)
{ ZZ x; add(x, a, b); NTL_OPT_RETURN(ZZ, x); }
inline ZZ operator-(const ZZ& a, const ZZ& b)
{ ZZ x; sub(x, a, b); NTL_OPT_RETURN(ZZ, x); }
inline ZZ operator-(const ZZ& a, long b)
{ ZZ x; sub(x, a, b); NTL_OPT_RETURN(ZZ, x); }
inline ZZ operator-(long a, const ZZ& b)
{ ZZ x; sub(x, a, b); NTL_OPT_RETURN(ZZ, x); }
inline ZZ operator-(const ZZ& a)
{ ZZ x; negate(x, a); NTL_OPT_RETURN(ZZ, x); }
inline ZZ abs(const ZZ& a)
{ ZZ x; abs(x, a); NTL_OPT_RETURN(ZZ, x); }
/* op= notation */
inline ZZ& operator+=(ZZ& x, const ZZ& a)
{ add(x, x, a); return x; }
inline ZZ& operator+=(ZZ& x, long a)
{ add(x, x, a); return x; }
inline ZZ& operator-=(ZZ& x, const ZZ& a)
{ sub(x, x, a); return x; }
inline ZZ& operator-=(ZZ& x, long a)
{ sub(x, x, a); return x; }
/* inc/dec */
inline ZZ& operator++(ZZ& x) { add(x, x, 1); return x; }
inline void operator++(ZZ& x, int) { add(x, x, 1); }
inline ZZ& operator--(ZZ& x) { add(x, x, -1); return x; }
inline void operator--(ZZ& x, int) { add(x, x, -1); }
/*******************************************************
Multiplication.
********************************************************/
inline void mul(ZZ& x, const ZZ& a, const ZZ& b)
// x = a * b
{ NTL_zmul(a.rep, b.rep, &x.rep); }
inline void sqr(ZZ& x, const ZZ& a)
// x = a*a
{ NTL_zsq(a.rep, &x.rep); }
inline ZZ sqr(const ZZ& a)
{ ZZ x; sqr(x, a); NTL_OPT_RETURN(ZZ, x); }
/* single-precision versions */
inline void mul(ZZ& x, const ZZ& a, long b)
{ NTL_zsmul(a.rep, b, &x.rep); }
inline void mul(ZZ& x, long a, const ZZ& b)
{ mul(x, b, a); }
/* operator notation */
inline ZZ operator*(const ZZ& a, const ZZ& b)
{ ZZ x; mul(x, a, b); NTL_OPT_RETURN(ZZ, x); }
inline ZZ operator*(const ZZ& a, long b)
{ ZZ x; mul(x, a, b); NTL_OPT_RETURN(ZZ, x); }
inline ZZ operator*(long a, const ZZ& b)
{ ZZ x; mul(x, a, b); NTL_OPT_RETURN(ZZ, x); }
/* op= notation */
inline ZZ& operator*=(ZZ& x, const ZZ& a)
{ mul(x, x, a); return x; }
inline ZZ& operator*=(ZZ& x, long a)
{ mul(x, x, a); return x; }
// x += a*b
inline void
MulAddTo(ZZ& x, const ZZ& a, long b)
{
NTL_zsaddmul(a.rep, b, &x.rep);
}
inline void
MulAddTo(ZZ& x, const ZZ& a, const ZZ& b)
{
NTL_zaddmul(a.rep, b.rep, &x.rep);
}
// x -= a*b
inline void
MulSubFrom(ZZ& x, const ZZ& a, long b)
{
NTL_zssubmul(a.rep, b, &x.rep);
}
inline void
MulSubFrom(ZZ& x, const ZZ& a, const ZZ& b)
{
NTL_zsubmul(a.rep, b.rep, &x.rep);
}
// Special routines for implementing CRT in ZZ_pX arithmetic
// These are verbose, but fairly boilerplate
class ZZ_CRTStructAdapter;
class ZZ_RemStructAdapter;
class ZZ_TmpVecAdapter {
public:
UniquePtr<_ntl_tmp_vec> rep;
inline void fetch(const ZZ_CRTStructAdapter&);
inline void fetch(ZZ_CRTStructAdapter&);
inline void fetch(const ZZ_RemStructAdapter&);
};
class ZZ_CRTStructAdapter {
public:
UniquePtr<_ntl_crt_struct> rep;
void init(long n, const ZZ& p, long (*primes)(long))
{
rep.reset(_ntl_crt_struct_build(n, p.rep, primes));
}
void insert(long i, const ZZ& m)
{
rep->insert(i, m.rep);
}
void eval(ZZ& t, const long *a, ZZ_TmpVecAdapter& tmp_vec) const
{
rep->eval(&t.rep, a, tmp_vec.rep.get());
}
bool special() const
{
return rep->special();
}
};
class ZZ_RemStructAdapter {
public:
UniquePtr<_ntl_rem_struct> rep;
void init(long n, const ZZ& p, long (*primes)(long))
{
rep.reset(_ntl_rem_struct_build(n, p.rep, primes));
}
void eval(long *x, const ZZ& a, ZZ_TmpVecAdapter& tmp_vec) const
{
rep->eval(x, a.rep, tmp_vec.rep.get());
}
};
inline void ZZ_TmpVecAdapter::fetch(const ZZ_CRTStructAdapter& crt_struct)
{
rep.reset(crt_struct.rep->fetch());
}
inline void ZZ_TmpVecAdapter::fetch(ZZ_CRTStructAdapter& crt_struct)
{
rep.reset(crt_struct.rep->extract()); // EXTRACT!!
}
inline void ZZ_TmpVecAdapter::fetch(const ZZ_RemStructAdapter& rem_struct)
{
rep.reset(rem_struct.rep->fetch());
}
// montgomery
class ZZ_ReduceStructAdapter {
public:
UniquePtr<_ntl_reduce_struct> rep;
void init(const ZZ& p, const ZZ& excess)
{
rep.reset(_ntl_reduce_struct_build(p.rep, excess.rep));
}
void eval(ZZ& x, ZZ& a) const
{
rep->eval(&x.rep, &a.rep);
}
void adjust(ZZ& x) const
{
rep->adjust(&x.rep);
}
};
/*******************************************************
Division
*******************************************************/
inline void DivRem(ZZ& q, ZZ& r, const ZZ& a, const ZZ& b)
// q = [a/b], r = a - b*q
// |r| < |b|, and if r != 0, sign(r) = sign(b)
{ NTL_zdiv(a.rep, b.rep, &q.rep, &r.rep); }
inline void div(ZZ& q, const ZZ& a, const ZZ& b)
// q = a/b
{ NTL_zdiv(a.rep, b.rep, &q.rep, 0); }
inline void rem(ZZ& r, const ZZ& a, const ZZ& b)
// r = a%b
{ NTL_zmod(a.rep, b.rep, &r.rep); }
inline void QuickRem(ZZ& r, const ZZ& b)
// r = r%b
// assumes b > 0 and r >=0
// division is performed in place and may cause r to be re-allocated.
{ NTL_zquickmod(&r.rep, b.rep); }
long divide(ZZ& q, const ZZ& a, const ZZ& b);
// if b | a, sets q = a/b and returns 1; otherwise returns 0.
long divide(const ZZ& a, const ZZ& b);
// if b | a, returns 1; otherwise returns 0.
/* non-standard single-precision versions */
inline long DivRem(ZZ& q, const ZZ& a, long b)
{ return NTL_zsdiv(a.rep, b, &q.rep); }
inline long rem(const ZZ& a, long b)
{ return NTL_zsmod(a.rep, b); }
/* single precision versions */
inline void div(ZZ& q, const ZZ& a, long b)
{ (void) NTL_zsdiv(a.rep, b, &q.rep); }
long divide(ZZ& q, const ZZ& a, long b);
// if b | a, sets q = a/b and returns 1; otherwise returns 0.
long divide(const ZZ& a, long b);
// if b | a, returns 1; otherwise returns 0.
inline ZZ operator/(const ZZ& a, const ZZ& b)
{ ZZ x; div(x, a, b); NTL_OPT_RETURN(ZZ, x); }
inline ZZ operator/(const ZZ& a, long b)
{ ZZ x; div(x, a, b); NTL_OPT_RETURN(ZZ, x); }
inline ZZ operator%(const ZZ& a, const ZZ& b)
{ ZZ x; rem(x, a, b); NTL_OPT_RETURN(ZZ, x); }
inline long operator%(const ZZ& a, long b)
{ return rem(a, b); }
inline ZZ& operator/=(ZZ& x, const ZZ& b)
{ div(x, x, b); return x; }
inline ZZ& operator/=(ZZ& x, long b)
{ div(x, x, b); return x; }
inline ZZ& operator%=(ZZ& x, const ZZ& b)
{ rem(x, x, b); return x; }
// preconditioned single-precision variant
// not documented for now...
class PreconditionedRemainder {
private:
long p;
UniquePtr<_ntl_general_rem_one_struct> pinfo;
public:
PreconditionedRemainder(long _p, long sz) : p(_p)
{
pinfo.reset(_ntl_general_rem_one_struct_build(p, sz));
}
long operator()(const ZZ& a)
{
return _ntl_general_rem_one_struct_apply(a.rep, p, pinfo.get());
}
};
/**********************************************************
GCD's
***********************************************************/
inline void GCD(ZZ& d, const ZZ& a, const ZZ& b)
// d = gcd(a, b)
{ NTL_zgcd(a.rep, b.rep, &d.rep); }
inline ZZ GCD(const ZZ& a, const ZZ& b)
{ ZZ x; GCD(x, a, b); NTL_OPT_RETURN(ZZ, x); }
inline void XGCD(ZZ& d, ZZ& s, ZZ& t, const ZZ& a, const ZZ& b)
// d = gcd(a, b) = a*s + b*t;
{ NTL_zexteucl(a.rep, &s.rep, b.rep, &t.rep, &d.rep); }
// single-precision versions
long GCD(long a, long b);
void XGCD(long& d, long& s, long& t, long a, long b);
/************************************************************
Bit Operations
*************************************************************/
inline void LeftShift(ZZ& x, const ZZ& a, long k)
// x = (a << k), k < 0 => RightShift
{ NTL_zlshift(a.rep, k, &x.rep); }
inline ZZ LeftShift(const ZZ& a, long k)
{ ZZ x; LeftShift(x, a, k); NTL_OPT_RETURN(ZZ, x); }
inline void RightShift(ZZ& x, const ZZ& a, long k)
// x = (a >> k), k < 0 => LeftShift
{ NTL_zrshift(a.rep, k, &x.rep); }
inline ZZ RightShift(const ZZ& a, long k)
{ ZZ x; RightShift(x, a, k); NTL_OPT_RETURN(ZZ, x); }
#ifndef NTL_TRANSITION
inline ZZ operator>>(const ZZ& a, long n)
{ ZZ x; RightShift(x, a, n); NTL_OPT_RETURN(ZZ, x); }
inline ZZ operator<<(const ZZ& a, long n)
{ ZZ x; LeftShift(x, a, n); NTL_OPT_RETURN(ZZ, x); }
inline ZZ& operator<<=(ZZ& x, long n)
{ LeftShift(x, x, n); return x; }
inline ZZ& operator>>=(ZZ& x, long n)
{ RightShift(x, x, n); return x; }
#endif
inline long MakeOdd(ZZ& x)
// removes factors of 2 from x, returns the number of 2's removed
// returns 0 if x == 0
{ return NTL_zmakeodd(&x.rep); }
inline long NumTwos(const ZZ& x)
// returns max e such that 2^e divides x if x != 0, and returns 0 if x == 0.
{ return NTL_znumtwos(x.rep); }
inline long IsOdd(const ZZ& a)
// returns 1 if a is odd, otherwise 0
{ return NTL_zodd(a.rep); }
inline long NumBits(const ZZ& a)
// returns the number of bits in |a|; NumBits(0) = 0
{ return NTL_z2log(a.rep); }
inline long bit(const ZZ& a, long k)
// returns bit k of a, 0 being the low-order bit
{ return NTL_zbit(a.rep, k); }
#ifndef NTL_GMP_LIP
// only defined for the "classic" long integer package, for backward
// compatability.
inline long digit(const ZZ& a, long k)
{ return NTL_zdigit(a.rep, k); }
#endif
// returns k-th digit of |a|, 0 being the low-order digit.
inline void trunc(ZZ& x, const ZZ& a, long k)
// puts k low order bits of |a| into x
{ NTL_zlowbits(a.rep, k, &x.rep); }
inline ZZ trunc_ZZ(const ZZ& a, long k)
{ ZZ x; trunc(x, a, k); NTL_OPT_RETURN(ZZ, x); }
inline long trunc_long(const ZZ& a, long k)
// returns k low order bits of |a|
{ return NTL_zslowbits(a.rep, k); }
inline long SetBit(ZZ& x, long p)
// returns original value of p-th bit of |a|, and replaces
// p-th bit of a by 1 if it was zero;
// error if p < 0
{ return NTL_zsetbit(&x.rep, p); }
inline long SwitchBit(ZZ& x, long p)
// returns original value of p-th bit of |a|, and switches
// the value of p-th bit of a;
// p starts counting at 0;
// error if p < 0
{ return NTL_zswitchbit(&x.rep, p); }
inline long weight(long a)
// returns Hamming weight of |a|
{ return NTL_zweights(a); }
inline long weight(const ZZ& a)
// returns Hamming weight of |a|
{ return NTL_zweight(a.rep); }
inline void bit_and(ZZ& x, const ZZ& a, const ZZ& b)
// x = |a| AND |b|
{ NTL_zand(a.rep, b.rep, &x.rep); }
void bit_and(ZZ& x, const ZZ& a, long b);
inline void bit_and(ZZ& x, long a, const ZZ& b)
{ bit_and(x, b, a); }
inline void bit_or(ZZ& x, const ZZ& a, const ZZ& b)
// x = |a| OR |b|
{ NTL_zor(a.rep, b.rep, &x.rep); }
void bit_or(ZZ& x, const ZZ& a, long b);
inline void bit_or(ZZ& x, long a, const ZZ& b)
{ bit_or(x, b, a); }
inline void bit_xor(ZZ& x, const ZZ& a, const ZZ& b)
// x = |a| XOR |b|
{ NTL_zxor(a.rep, b.rep, &x.rep); }
void bit_xor(ZZ& x, const ZZ& a, long b);
inline void bit_xor(ZZ& x, long a, const ZZ& b)
{ bit_xor(x, b, a); }
inline ZZ operator&(const ZZ& a, const ZZ& b)
{ ZZ x; bit_and(x, a, b); NTL_OPT_RETURN(ZZ, x); }
inline ZZ operator&(const ZZ& a, long b)
{ ZZ x; bit_and(x, a, b); NTL_OPT_RETURN(ZZ, x); }
inline ZZ operator&(long a, const ZZ& b)
{ ZZ x; bit_and(x, a, b); NTL_OPT_RETURN(ZZ, x); }
inline ZZ operator|(const ZZ& a, const ZZ& b)
{ ZZ x; bit_or(x, a, b); NTL_OPT_RETURN(ZZ, x); }
inline ZZ operator|(const ZZ& a, long b)
{ ZZ x; bit_or(x, a, b); NTL_OPT_RETURN(ZZ, x); }
inline ZZ operator|(long a, const ZZ& b)
{ ZZ x; bit_or(x, a, b); NTL_OPT_RETURN(ZZ, x); }
inline ZZ operator^(const ZZ& a, const ZZ& b)
{ ZZ x; bit_xor(x, a, b); NTL_OPT_RETURN(ZZ, x); }
inline ZZ operator^(const ZZ& a, long b)
{ ZZ x; bit_xor(x, a, b); NTL_OPT_RETURN(ZZ, x); }
inline ZZ operator^(long a, const ZZ& b)
{ ZZ x; bit_xor(x, a, b); NTL_OPT_RETURN(ZZ, x); }
inline ZZ& operator&=(ZZ& x, const ZZ& b)
{ bit_and(x, x, b); return x; }
inline ZZ& operator&=(ZZ& x, long b)
{ bit_and(x, x, b); return x; }
inline ZZ& operator|=(ZZ& x, const ZZ& b)
{ bit_or(x, x, b); return x; }
inline ZZ& operator|=(ZZ& x, long b)
{ bit_or(x, x, b); return x; }
inline ZZ& operator^=(ZZ& x, const ZZ& b)
{ bit_xor(x, x, b); return x; }
inline ZZ& operator^=(ZZ& x, long b)
{ bit_xor(x, x, b); return x; }
long NumBits(long a);
long bit(long a, long k);
long NextPowerOfTwo(long m);
// returns least nonnegative k such that 2^k >= m
inline
long NumBytes(const ZZ& a)
{ return (NumBits(a)+7)/8; }
inline
long NumBytes(long a)
{ return (NumBits(a)+7)/8; }
/***********************************************************
Some specialized routines
************************************************************/
inline long ZZ_BlockConstructAlloc(ZZ& x, long d, long n)
{ return NTL_zblock_construct_alloc(&x.rep, d, n); }
inline void ZZ_BlockConstructSet(ZZ& x, ZZ& y, long i)
{ NTL_zblock_construct_set(x.rep, &y.rep, i); }
inline long ZZ_BlockDestroy(ZZ& x)
{ return NTL_zblock_destroy(x.rep); }
inline long ZZ_storage(long d)
{ return NTL_zblock_storage(d); }
inline long ZZ_RoundCorrection(const ZZ& a, long k, long residual)
{ return NTL_zround_correction(a.rep, k, residual); }
/***********************************************************
Psuedo-random Numbers
************************************************************/
// ================ NEW PRG STUFF =================
// Low-level key-derivation
void DeriveKey(unsigned char *key, long klen,
const unsigned char *data, long dlen);
// Low-level chacha stuff
#define NTL_PRG_KEYLEN (32)
class RandomStream {
private:
_ntl_uint32 state[16];
unsigned char buf[64];
long pos;
void do_get(unsigned char *res, long n);
public:
explicit
RandomStream(const unsigned char *key);
// No default constructor
// default copy and assignment
void get(unsigned char *res, long n)
{
// optimize short reads
if (n >= 0 && n <= 64-pos) {
long i;
for (i = 0; i < n; i++) {
res[i] = buf[pos+i];
}
pos += n;
}
else {
do_get(res, n);
}
}
};
RandomStream& GetCurrentRandomStream();
// get reference to the current random by stream --
// if SetSeed has not been called, it is called with
// a default value (which should be unique to each
// process/thread
void SetSeed(const ZZ& s);
void SetSeed(const unsigned char *data, long dlen);
void SetSeed(const RandomStream& s);
// initialize random number generator
// in the first two version, a PRG key is derived from
// the data using DeriveKey.
// RAII for saving/restoring current state of PRG
class RandomStreamPush {
private:
RandomStream saved;
RandomStreamPush(const RandomStreamPush&); // disable
void operator=(const RandomStreamPush&); // disable
public:
RandomStreamPush() : saved(GetCurrentRandomStream()) { }
~RandomStreamPush() { SetSeed(saved); }
};
void RandomBnd(ZZ& x, const ZZ& n);
// x = "random number" in the range 0..n-1, or 0 if n <= 0
inline ZZ RandomBnd(const ZZ& n)
{ ZZ x; RandomBnd(x, n); NTL_OPT_RETURN(ZZ, x); }
void RandomLen(ZZ& x, long NumBits);
// x = "random number" with precisely NumBits bits.
inline ZZ RandomLen_ZZ(long NumBits)
{ ZZ x; RandomLen(x, NumBits); NTL_OPT_RETURN(ZZ, x); }
void RandomBits(ZZ& x, long NumBits);
// x = "random number", 0 <= x < 2^NumBits
inline ZZ RandomBits_ZZ(long NumBits)
{ ZZ x; RandomBits(x, NumBits); NTL_OPT_RETURN(ZZ, x); }
// single-precision version of the above
long RandomBnd(long n);
inline void RandomBnd(long& x, long n) { x = RandomBnd(n); }
long RandomLen_long(long l);
inline void RandomLen(long& x, long l) { x = RandomLen_long(l); }
long RandomBits_long(long l);
inline void RandomBits(long& x, long l) { x = RandomBits_long(l); }
// specialty routines
unsigned long RandomWord();
unsigned long RandomBits_ulong(long l);
/**********************************************************
Incremental Chinese Remaindering
***********************************************************/
long CRT(ZZ& a, ZZ& p, const ZZ& A, const ZZ& P);
long CRT(ZZ& a, ZZ& p, long A, long P);
// 0 <= A < P, (p, P) = 1;
// computes b such that b = a mod p, b = A mod p,
// and -p*P/2 < b <= p*P/2;
// sets a = b, p = p*P, and returns 1 if a's value
// has changed, otherwise 0
inline long CRTInRange(const ZZ& gg, const ZZ& aa)
{ return NTL_zcrtinrange(gg.rep, aa.rep); }
// an auxilliary routine used by newer CRT routines to maintain
// backward compatability.
// test if a > 0 and -a/2 < g <= a/2
// this is "hand crafted" so as not too waste too much time
// in the CRT routines.
/**********************************************************
Rational Reconstruction
***********************************************************/
inline
long ReconstructRational(ZZ& a, ZZ& b, const ZZ& u, const ZZ& m,
const ZZ& a_bound, const ZZ& b_bound)
{
return NTL_zxxratrecon(u.rep, m.rep, a_bound.rep, b_bound.rep, &a.rep, &b.rep);
}
/************************************************************
Primality Testing
*************************************************************/
void GenPrime(ZZ& n, long l, long err = 80);
inline ZZ GenPrime_ZZ(long l, long err = 80)
{ ZZ x; GenPrime(x, l, err); NTL_OPT_RETURN(ZZ, x); }
long GenPrime_long(long l, long err = 80);
// This generates a random prime n of length l so that the
// probability of erroneously returning a composite is bounded by 2^(-err).
void GenGermainPrime(ZZ& n, long l, long err = 80);
inline ZZ GenGermainPrime_ZZ(long l, long err = 80)
{ ZZ x; GenGermainPrime(x, l, err); NTL_OPT_RETURN(ZZ, x); }
long GenGermainPrime_long(long l, long err = 80);
// This generates a random prime n of length l so that the
long ProbPrime(const ZZ& n, long NumTrials = 10);
// tests if n is prime; performs a little trial division,
// followed by a single-precision MillerWitness test, followed by
// up to NumTrials general MillerWitness tests.
long MillerWitness(const ZZ& n, const ZZ& w);
// Tests if w is a witness to primality a la Miller.
// Assumption: n is odd and positive, 0 <= w < n.
void RandomPrime(ZZ& n, long l, long NumTrials=10);
// n = random l-bit prime
inline ZZ RandomPrime_ZZ(long l, long NumTrials=10)
{ ZZ x; RandomPrime(x, l, NumTrials); NTL_OPT_RETURN(ZZ, x); }
void NextPrime(ZZ& n, const ZZ& m, long NumTrials=10);
// n = smallest prime >= m.
inline ZZ NextPrime(const ZZ& m, long NumTrials=10)
{ ZZ x; NextPrime(x, m, NumTrials); NTL_OPT_RETURN(ZZ, x); }
// single-precision versions
long ProbPrime(long n, long NumTrials = 10);
long RandomPrime_long(long l, long NumTrials=10);
long NextPrime(long l, long NumTrials=10);
/************************************************************
Exponentiation
*************************************************************/
inline void power(ZZ& x, const ZZ& a, long e)
{ NTL_zexp(a.rep, e, &x.rep); }
inline ZZ power(const ZZ& a, long e)
{ ZZ x; power(x, a, e); NTL_OPT_RETURN(ZZ, x); }
inline void power(ZZ& x, long a, long e)
{ NTL_zexps(a, e, &x.rep); }
inline ZZ power_ZZ(long a, long e)
{ ZZ x; power(x, a, e); NTL_OPT_RETURN(ZZ, x); }
long power_long(long a, long e);
void power2(ZZ& x, long e);
inline ZZ power2_ZZ(long e)
{ ZZ x; power2(x, e); NTL_OPT_RETURN(ZZ, x); }
/*************************************************************
Square Roots
**************************************************************/
inline void SqrRoot(ZZ& x, const ZZ& a)
// x = [a^{1/2}], a >= 0
{
NTL_zsqrt(a.rep, &x.rep);
}
inline ZZ SqrRoot(const ZZ& a)
{ ZZ x; SqrRoot(x, a); NTL_OPT_RETURN(ZZ, x); }
inline long SqrRoot(long a) { return NTL_zsqrts(a); }
// single-precision version
/***************************************************************
Modular Arithmetic
***************************************************************/
// The following routines perform arithmetic mod n, n positive.
// All args (other than exponents) are assumed to be in the range 0..n-1.
inline void AddMod(ZZ& x, const ZZ& a, const ZZ& b, const ZZ& n)
// x = (a+b)%n
{ NTL_zaddmod(a.rep, b.rep, n.rep, &x.rep); }
inline ZZ AddMod(const ZZ& a, const ZZ& b, const ZZ& n)
{ ZZ x; AddMod(x, a, b, n); NTL_OPT_RETURN(ZZ, x); }
inline void SubMod(ZZ& x, const ZZ& a, const ZZ& b, const ZZ& n)
// x = (a-b)%n
{ NTL_zsubmod(a.rep, b.rep, n.rep, &x.rep); }
inline ZZ SubMod(const ZZ& a, const ZZ& b, const ZZ& n)
{ ZZ x; SubMod(x, a, b, n); NTL_OPT_RETURN(ZZ, x); }
inline void NegateMod(ZZ& x, const ZZ& a, const ZZ& n)
// x = -a % n
{ NTL_zsubmod(0, a.rep, n.rep, &x.rep); }
inline ZZ NegateMod(const ZZ& a, const ZZ& n)
{ ZZ x; NegateMod(x, a, n); NTL_OPT_RETURN(ZZ, x); }
void AddMod(ZZ& x, const ZZ& a, long b, const ZZ& n);
inline ZZ AddMod(const ZZ& a, long b, const ZZ& n)
{ ZZ x; AddMod(x, a, b, n); NTL_OPT_RETURN(ZZ, x); }
inline void AddMod(ZZ& x, long a, const ZZ& b, const ZZ& n)
{ AddMod(x, b, a, n); }
inline ZZ AddMod(long a, const ZZ& b, const ZZ& n)
{ ZZ x; AddMod(x, a, b, n); NTL_OPT_RETURN(ZZ, x); }
void SubMod(ZZ& x, const ZZ& a, long b, const ZZ& n);
inline ZZ SubMod(const ZZ& a, long b, const ZZ& n)
{ ZZ x; SubMod(x, a, b, n); NTL_OPT_RETURN(ZZ, x); }
void SubMod(ZZ& x, long a, const ZZ& b, const ZZ& n);
inline ZZ SubMod(long a, const ZZ& b, const ZZ& n)
{ ZZ x; SubMod(x, a, b, n); NTL_OPT_RETURN(ZZ, x); }
inline void MulMod(ZZ& x, const ZZ& a, const ZZ& b, const ZZ& n)
// x = (a*b)%n
{ NTL_zmulmod(a.rep, b.rep, n.rep, &x.rep); }
inline ZZ MulMod(const ZZ& a, const ZZ& b, const ZZ& n)
{ ZZ x; MulMod(x, a, b, n); NTL_OPT_RETURN(ZZ, x); }
inline void MulMod(ZZ& x, const ZZ& a, long b, const ZZ& n)
// x = (a*b)%n
{ NTL_zsmulmod(a.rep, b, n.rep, &x.rep); }
inline ZZ MulMod(const ZZ& a, long b, const ZZ& n)
{ ZZ x; MulMod(x, a, b, n); NTL_OPT_RETURN(ZZ, x); }
inline void MulMod(ZZ& x, long a, const ZZ& b, const ZZ& n)
{ MulMod(x, b, a, n); }
inline ZZ MulMod(long a, const ZZ& b, const ZZ& n)
{ ZZ x; MulMod(x, a, b, n); NTL_OPT_RETURN(ZZ, x); }
inline void SqrMod(ZZ& x, const ZZ& a, const ZZ& n)
// x = a^2 % n
{ NTL_zsqmod(a.rep, n.rep, &x.rep); }
inline ZZ SqrMod(const ZZ& a, const ZZ& n)
{ ZZ x; SqrMod(x, a, n); NTL_OPT_RETURN(ZZ, x); }
void InvMod(ZZ& x, const ZZ& a, const ZZ& n);
// defined in ZZ.c in terms of InvModStatus
inline ZZ InvMod(const ZZ& a, const ZZ& n)
{ ZZ x; InvMod(x, a, n); NTL_OPT_RETURN(ZZ, x); }
inline long InvModStatus(ZZ& x, const ZZ& a, const ZZ& n)
// if gcd(a,n) = 1, then ReturnValue = 0, x = a^{-1} mod n
// otherwise, ReturnValue = 1, x = gcd(a, n)
{ return NTL_zinv(a.rep, n.rep, &x.rep); }
void PowerMod(ZZ& x, const ZZ& a, const ZZ& e, const ZZ& n);
// defined in ZZ.c in terms of LowLevelPowerMod
inline void LowLevelPowerMod(ZZ& x, const ZZ& a, const ZZ& e, const ZZ& n)
{ NTL_zpowermod(a.rep, e.rep, n.rep, &x.rep); }
inline ZZ PowerMod(const ZZ& a, const ZZ& e, const ZZ& n)
{ ZZ x; PowerMod(x, a, e, n); NTL_OPT_RETURN(ZZ, x); }
inline void PowerMod(ZZ& x, const ZZ& a, long e, const ZZ& n)
{ PowerMod(x, a, ZZ_expo(e), n); }
inline ZZ PowerMod(const ZZ& a, long e, const ZZ& n)
{ ZZ x; PowerMod(x, a, e, n); NTL_OPT_RETURN(ZZ, x); }
/*************************************************************
Jacobi symbol and modular squre roots
**************************************************************/
long Jacobi(const ZZ& a, const ZZ& n);
// compute Jacobi symbol of a and n;
// assumes 0 <= a < n, n odd
void SqrRootMod(ZZ& x, const ZZ& a, const ZZ& n);
// computes square root of a mod n;
// assumes n is an odd prime, and that a is a square mod n
inline ZZ SqrRootMod(const ZZ& a, const ZZ& n)
{ ZZ x; SqrRootMod(x, a, n); NTL_OPT_RETURN(ZZ, x); }
/*************************************************************
Small Prime Generation
*************************************************************/
// primes are generated in sequence, starting at 2,
// and up until (2*NTL_PRIME_BND+1)^2, which is less than NTL_SP_BOUND.
#if (NTL_SP_NBITS > 30)
#define NTL_PRIME_BND ((1L << 14) - 1)
#else
#define NTL_PRIME_BND ((1L << (NTL_SP_NBITS/2-1)) - 1)
#endif
class PrimeSeq {
const char *movesieve;
Vec<char> movesieve_mem;
long pindex;
long pshift;
long exhausted;
public:
PrimeSeq();
long next();
// returns next prime in the sequence.
// returns 0 if list of small primes is exhausted.
void reset(long b);
// resets generator so that the next prime in the sequence
// is the smallest prime >= b.
private:
PrimeSeq(const PrimeSeq&); // disabled
void operator=(const PrimeSeq&); // disabled
// auxilliary routines
void start();
void shift(long);
};
/**************************************************************
Input/Output
***************************************************************/
NTL_SNS istream& operator>>(NTL_SNS istream& s, ZZ& x);
NTL_SNS ostream& operator<<(NTL_SNS ostream& s, const ZZ& a);
// Some additional SP arithmetic routines, not defined in sp_arith.h
long InvMod(long a, long n);
// computes a^{-1} mod n. Error is raised if undefined.
long InvModStatus(long& x, long a, long n);
// if gcd(a,n) = 1, then ReturnValue = 0, x = a^{-1} mod n
// otherwise, ReturnValue = 1, x = gcd(a, n)
long PowerMod(long a, long e, long n);
// computes a^e mod n, e >= 0
// Error handling
#ifdef NTL_EXCEPTIONS
class InvModErrorObject : public ArithmeticErrorObject {
private:
SmartPtr<ZZ> a_ptr;
SmartPtr<ZZ> n_ptr;
public:
InvModErrorObject(const char *s, const ZZ& a, const ZZ& n)
: ArithmeticErrorObject(s) , a_ptr(MakeSmart<ZZ>(a)),
n_ptr(MakeSmart<ZZ>(n)) { }
const ZZ& get_a() const { return *a_ptr; }
const ZZ& get_n() const { return *n_ptr; }
};
#else
// We need this alt definition to keep pre-C++11
// compilers happy (NTL_EXCEPTIONS should only be used
// with C++11 compilers).
class InvModErrorObject : public ArithmeticErrorObject {
public:
InvModErrorObject(const char *s, const ZZ& a, const ZZ& n)
: ArithmeticErrorObject(s) { }
const ZZ& get_a() const { return ZZ::zero(); }
const ZZ& get_n() const { return ZZ::zero(); }
};
#endif
void InvModError(const char *s, const ZZ& a, const ZZ& n);
NTL_CLOSE_NNS
#endif
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