kopia lustrzana https://github.com/f4exb/sdrangel
269 wiersze
7.4 KiB
C++
269 wiersze
7.4 KiB
C++
// This file is part of LeanSDR Copyright (C) 2018 <pabr@pabr.org>.
|
|
// See the toplevel README for more information.
|
|
//
|
|
// This program is free software: you can redistribute it and/or modify
|
|
// it under the terms of the GNU General Public License as published by
|
|
// the Free Software Foundation, either version 3 of the License, or
|
|
// (at your option) any later version.
|
|
//
|
|
// This program is distributed in the hope that it will be useful,
|
|
// but WITHOUT ANY WARRANTY; without even the implied warranty of
|
|
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
|
// GNU General Public License for more details.
|
|
//
|
|
// You should have received a copy of the GNU General Public License
|
|
// along with this program. If not, see <http://www.gnu.org/licenses/>.
|
|
|
|
#ifndef LEANSDR_DISCRMATH_H
|
|
#define LEANSDR_DISCRMATH_H
|
|
|
|
#include <cstddef>
|
|
|
|
namespace leansdr
|
|
{
|
|
|
|
// Polynomials with N binary coefficients.
|
|
// This is designed to compile into trivial inline code.
|
|
|
|
// Bits are packed into words of type T.
|
|
// Unused most-significant bits of the last word are 0.
|
|
// T must be an unsigned type.
|
|
|
|
template <typename T, int N>
|
|
struct bitvect
|
|
{
|
|
static const size_t WSIZE = sizeof(T) * 8;
|
|
static const size_t NW = (N + WSIZE - 1) / WSIZE;
|
|
T v[NW];
|
|
|
|
bitvect() {}
|
|
bitvect(T val)
|
|
{
|
|
v[0] = val;
|
|
for (int i = 1; i < NW; ++i)
|
|
v[i] = 0;
|
|
}
|
|
|
|
// Assign from another bitvect, with truncation or padding
|
|
template <int M>
|
|
bitvect<T, N> ©(const bitvect<T, M> &a)
|
|
{
|
|
int nw = (a.NW < NW) ? a.NW : NW;
|
|
for (int i = 0; i < nw; ++i)
|
|
v[i] = a.v[i];
|
|
if (M < N)
|
|
for (int i = a.NW; i < NW; ++i)
|
|
v[i] = 0;
|
|
if (M > N)
|
|
truncate_to_N();
|
|
return *this;
|
|
}
|
|
|
|
bool operator[](unsigned int i) const
|
|
{
|
|
return v[i / WSIZE] & ((T)1 << (i & (WSIZE - 1)));
|
|
}
|
|
|
|
// Add (in GF(2))
|
|
|
|
template <int M>
|
|
bitvect<T, N> &operator+=(const bitvect<T, M> &a)
|
|
{
|
|
int nw = (a.NW < NW) ? a.NW : NW;
|
|
for (int i = 0; i < nw; ++i)
|
|
v[i] ^= a.v[i];
|
|
if (M > N)
|
|
truncate_to_N();
|
|
return *this;
|
|
}
|
|
|
|
// Multiply by X^n
|
|
|
|
bitvect<T, N> &operator<<=(unsigned int n)
|
|
{
|
|
if (n >= WSIZE)
|
|
fail("shift exceeds word width");
|
|
T mask = ~(((T)-1) << n);
|
|
for (int i = NW - 1; i > 0; --i)
|
|
v[i] = (v[i] << n) | ((v[i - 1] >> (WSIZE - n)) & mask);
|
|
v[0] <<= n;
|
|
if (N != NW * WSIZE)
|
|
truncate_to_N();
|
|
return *this;
|
|
}
|
|
|
|
private:
|
|
// Call this whenever bits N .. NW*WSIZE-1 may have been set.
|
|
inline void truncate_to_N()
|
|
{
|
|
v[NW - 1] &= ((T)-1) >> (NW * WSIZE - N);
|
|
}
|
|
|
|
}; // bitvect
|
|
|
|
// Return m modulo (X^N+p).
|
|
// p is typically a generator polynomial of degree N
|
|
// with the highest-coefficient monomial omitted.
|
|
// m is packed into nm words of type Tm.
|
|
// The MSB of m[0] is the highest-order coefficient of m.
|
|
|
|
template <typename T, int N, typename Tm>
|
|
bitvect<T, N> divmod(const Tm *m, size_t nm, const bitvect<T, N> &p)
|
|
{
|
|
bitvect<T, N> res = 0;
|
|
const Tm bitmask = (Tm)1 << (sizeof(Tm) * 8 - 1);
|
|
for (; nm--; ++m)
|
|
{
|
|
Tm mi = *m;
|
|
for (int bit = sizeof(Tm) * 8; bit--; mi <<= 1)
|
|
{
|
|
// Multiply by X, save outgoing coeff of degree N
|
|
bool resN = res[N - 1];
|
|
res <<= 1;
|
|
// Add m[i]
|
|
if (mi & bitmask)
|
|
res.v[0] ^= 1;
|
|
// Modulo X^N+p
|
|
if (resN)
|
|
res += p;
|
|
}
|
|
}
|
|
return res;
|
|
}
|
|
|
|
// Return (m*X^N) modulo (X^N+p).
|
|
// Same as divmod(), slightly faster than appending N zeroes.
|
|
|
|
template <typename T, int N, typename Tm>
|
|
bitvect<T, N> shiftdivmod(const Tm *m, size_t nm, const bitvect<T, N> &p,
|
|
T init = 0)
|
|
{
|
|
bitvect<T, N> res;
|
|
for (int i = 0; i < res.NW; ++i)
|
|
res.v[i] = init;
|
|
const Tm bitmask = (Tm)1 << (sizeof(Tm) * 8 - 1);
|
|
for (; nm--; ++m)
|
|
{
|
|
Tm mi = *m;
|
|
for (int bit = sizeof(Tm) * 8; bit--; mi <<= 1)
|
|
{
|
|
// Multiply by X, save outgoing coeff of degree N
|
|
bool resN = res[N - 1];
|
|
res <<= 1;
|
|
// Add m[i]*X^N
|
|
resN ^= (bool)(mi & bitmask);
|
|
// Modulo X^N+p
|
|
if (resN)
|
|
res += p;
|
|
}
|
|
}
|
|
return res;
|
|
}
|
|
|
|
template <typename T, int N>
|
|
bool operator==(const bitvect<T, N> &a, const bitvect<T, N> &b)
|
|
{
|
|
for (int i = 0; i < a.NW; ++i)
|
|
if (a.v[i] != b.v[i])
|
|
return false;
|
|
return true;
|
|
}
|
|
|
|
// Add (in GF(2))
|
|
|
|
template <typename T, int N>
|
|
bitvect<T, N> operator+(const bitvect<T, N> &a, const bitvect<T, N> &b)
|
|
{
|
|
bitvect<T, N> res;
|
|
for (int i = 0; i < a.NW; ++i)
|
|
res.v[i] = a.v[i] ^ b.v[i];
|
|
return res;
|
|
}
|
|
|
|
// Polynomial multiplication.
|
|
|
|
template <typename T, int N, int NB>
|
|
bitvect<T, N> operator*(bitvect<T, N> a, const bitvect<T, NB> &b)
|
|
{
|
|
bitvect<T, N> res = 0;
|
|
for (int i = 0; i < NB; ++i, a <<= 1)
|
|
if (b[i])
|
|
res += a;
|
|
// TBD If truncation is needed, do it only once at the end.
|
|
return res;
|
|
}
|
|
|
|
// Finite group GF(2^N), for small N.
|
|
|
|
// GF(2) is the ring ({0,1},+,*).
|
|
// GF(2)[X] is the ring of polynomials with coefficients in GF(2).
|
|
// P(X) is an irreducible polynomial of GF(2)[X].
|
|
// N is the degree of P(x).
|
|
// GF(2)[X]/(P) is GF(2)[X] modulo P(X).
|
|
// (GF(2)[X]/(P), +) is a group with 2^N elements.
|
|
// (GF(2)[X]/(P)*, *) is a group with 2^N-1 elements.
|
|
// (GF(2)[X]/(P), +, *) is a field with 2^N elements, noted GF(2^N).
|
|
|
|
// Te is a C++ integer type for encoding elements of GF(2^N).
|
|
// Binary coefficients are packed, with degree 0 at LSB.
|
|
// (Te)0 is 0
|
|
// (Te)1 is 1
|
|
// (Te)2 is X
|
|
// (Te)3 is X+1
|
|
// (Te)4 is X^2
|
|
// TRUNCP is the encoding of the generator, with highest monomial omitted.
|
|
// ALPHA is a primitive element of GF(2^N). Usually "2"=[X] is chosen.
|
|
|
|
template <typename Te, int N, Te ALPHA, Te TRUNCP>
|
|
struct gf2n
|
|
{
|
|
typedef Te element;
|
|
static const Te alpha = ALPHA;
|
|
gf2n()
|
|
{
|
|
if (ALPHA != 2)
|
|
fail("alpha!=2 not implemented");
|
|
// Precompute log and exp tables.
|
|
Te alpha_i = 1; // ALPHA^0
|
|
for (int i = 0; i < (1 << N); ++i)
|
|
{
|
|
lut_exp[i] = alpha_i; // ALPHA^i
|
|
lut_exp[((1 << N) - 1) + i] = alpha_i; // Wrap to avoid modulo 2^N-1
|
|
lut_log[alpha_i] = i;
|
|
bool overflow = alpha_i & (1 << (N - 1));
|
|
alpha_i <<= 1; // Multiply by alpha=[X] i.e. increase degrees
|
|
alpha_i &= ~((~(Te)0) << N); // In case Te is wider than N bits
|
|
if (overflow)
|
|
alpha_i ^= TRUNCP; // Modulo P iteratively
|
|
}
|
|
}
|
|
inline Te add(Te x, Te y) { return x ^ y; } // Addition modulo 2
|
|
inline Te sub(Te x, Te y) { return x ^ y; } // Subtraction modulo 2
|
|
inline Te mul(Te x, Te y)
|
|
{
|
|
if (!x || !y)
|
|
return 0;
|
|
return lut_exp[lut_log[x] + lut_log[y]];
|
|
}
|
|
inline Te div(Te x, Te y)
|
|
{
|
|
if (!x)
|
|
return 0;
|
|
return lut_exp[lut_log[x] + ((1 << N) - 1) - lut_log[y]];
|
|
}
|
|
inline Te inv(Te x)
|
|
{
|
|
return lut_exp[((1 << N) - 1) - lut_log[x]];
|
|
}
|
|
inline Te exp(Te x) { return lut_exp[x]; }
|
|
inline Te log(Te x) { return lut_log[x]; }
|
|
|
|
private:
|
|
Te lut_exp[(1 << N) * 2]; // Extra room for wrapping modulo 2^N-1
|
|
Te lut_log[1 << N];
|
|
}; // gf2n
|
|
|
|
} // namespace leansdr
|
|
|
|
#endif // LEANSDR_DISCRMATH_H
|