Functions |
static mzd_slice_t * | mzd_slice_init (const gf2e *ff, const rci_t m, const rci_t n) |
| Create a new matrix of dimension \( m \times n\) over ff.
|
void | mzd_slice_set_ui (mzd_slice_t *A, word value) |
| Return diagonal matrix with value on the diagonal.
|
static mzd_slice_t * | _mzd_slice_adapt_depth (mzd_slice_t *A, const unsigned int new_depth) |
| Extend or truncate the depth of A to depth new_depth.
|
static void | mzd_slice_free (mzd_slice_t *A) |
| Free a matrix created with mzd_slice_init().
|
static mzd_slice_t * | mzd_slice_concat (mzd_slice_t *C, const mzd_slice_t *A, const mzd_slice_t *B) |
| Concatenate B to A and write the result to C.
|
static mzd_slice_t * | mzd_slice_stack (mzd_slice_t *C, const mzd_slice_t *A, const mzd_slice_t *B) |
| Stack A on top of B and write the result to C.
|
static mzd_slice_t * | mzd_slice_submatrix (mzd_slice_t *S, const mzd_slice_t *A, const size_t lowr, const size_t lowc, const size_t highr, const size_t highc) |
| Copy a submatrix.
|
static mzd_slice_t * | mzd_slice_init_window (const mzd_slice_t *A, const size_t lowr, const size_t lowc, const size_t highr, const size_t highc) |
| Create a window/view into the matrix M.
|
static void | mzd_slice_free_window (mzd_slice_t *A) |
| Free a matrix window created with mzd_slice_init_window().
|
static mzd_slice_t * | _mzd_slice_add (mzd_slice_t *C, const mzd_slice_t *A, const mzd_slice_t *B) |
| \( C = A + B\).
|
static mzd_slice_t * | mzd_slice_add (mzd_slice_t *C, const mzd_slice_t *A, const mzd_slice_t *B) |
| \( C = A + B\).
|
mzd_slice_t * | _mzd_slice_mul_naive (mzd_slice_t *C, const mzd_slice_t *A, const mzd_slice_t *B) |
| \( C = A \cdot B \) using quadratic polynomial multiplication with matrix coefficients.
|
mzd_slice_t * | _mzd_slice_mul_karatsuba2 (mzd_slice_t *C, const mzd_slice_t *A, const mzd_slice_t *B) |
| \( C = A \cdot B \) over \(\mathbb{F}_{2^2}\) using 3 multiplications over \(\mathbb{F}_2\) and 2 temporary \(\mathbb{F}_2\) matrices..
|
mzd_slice_t * | _mzd_slice_mul_karatsuba3 (mzd_slice_t *C, const mzd_slice_t *A, const mzd_slice_t *B) |
| \( C = A \cdot B \) over \(\mathbb{F}_{2^3}\) using 6 multiplications over \(\mathbb{F}_2\) and 3 temporary \(\mathbb{F}_2\) matrices..
|
mzd_slice_t * | _mzd_slice_mul_karatsuba4 (mzd_slice_t *C, const mzd_slice_t *A, const mzd_slice_t *B) |
| \( C = A \cdot B \) over \(\mathbb{F}_{2^4}\) using 9 multiplications over \(\mathbb{F}_2\) and 3 temporary \(\mathbb{F}_2\) matrices..
|
mzd_slice_t * | _mzd_slice_mul_karatsuba5 (mzd_slice_t *C, const mzd_slice_t *A, const mzd_slice_t *B) |
| \( C = A \cdot B \) over \(\mathbb{F}_{2^5}\) using 13 multiplications over \(\mathbb{F}_2\) and 3 temporary \(\mathbb{F}_2\) matrices..
|
mzd_slice_t * | _mzd_slice_mul_karatsuba6 (mzd_slice_t *C, const mzd_slice_t *A, const mzd_slice_t *B) |
| \( C = A \cdot B \) over \(\mathbb{F}_{2^6}\) using 17 multiplications over \(\mathbb{F}_2\) and 3 temporary \(\mathbb{F}_2\) matrices.
|
mzd_slice_t * | _mzd_slice_mul_karatsuba7 (mzd_slice_t *C, const mzd_slice_t *A, const mzd_slice_t *B) |
| \( C = A \cdot B \) over \(\mathbb{F}_{2^7}\) using 22 multiplications over \(\mathbb{F}_2\) and 3 temporary \(\mathbb{F}_2\) matrices.
|
mzd_slice_t * | _mzd_slice_mul_karatsuba8 (mzd_slice_t *C, const mzd_slice_t *A, const mzd_slice_t *B) |
| \( C = A \cdot B \) over \(\mathbb{F}_{2^8}\) using 27 multiplications over \(\mathbb{F}_2\) and 15 temporary \(\mathbb{F}_2\) matrices.
|
static mzd_slice_t * | _mzd_slice_mul_karatsuba (mzd_slice_t *C, const mzd_slice_t *A, const mzd_slice_t *B) |
| \( C = C + A \cdot B \) using Karatsuba multiplication of polynomials over matrices over \(\mathbb{F}_2\).
|
static mzd_slice_t * | mzd_slice_mul_karatsuba (mzd_slice_t *C, const mzd_slice_t *A, const mzd_slice_t *B) |
| \( C = A \cdot B \) using Karatsuba multiplication of polynomials over matrices over \(\mathbb{F}_2\).
|
static mzd_slice_t * | mzd_slice_addmul_karatsuba (mzd_slice_t *C, const mzd_slice_t *A, const mzd_slice_t *B) |
| \( C = C + A \cdot B\) using Karatsuba multiplication of polynomials over matrices over \(\mathbb{F}_2\).
|
mzd_slice_t * | mzd_slice_mul_scalar (mzd_slice_t *C, const word a, const mzd_slice_t *B) |
| \( C = a \cdot B \).
|
mzd_slice_t * | mzd_slice_addmul_scalar (mzd_slice_t *C, const word a, const mzd_slice_t *B) |
| \( C += a \cdot B \).
|
static mzd_slice_t * | mzd_slice_mul (mzd_slice_t *C, const mzd_slice_t *A, const mzd_slice_t *B) |
| \( C = A \cdot B \).
|
static mzd_slice_t * | mzd_slice_addmul (mzd_slice_t *C, const mzd_slice_t *A, const mzd_slice_t *B) |
| \( C = C + A \cdot B \).
|
static void | mzd_slice_randomize (mzd_slice_t *A) |
| Fill matrix A with random elements.
|
static mzd_slice_t * | mzd_slice_copy (mzd_slice_t *B, const mzd_slice_t *A) |
| Copy matrix A to B.
|
static word | mzd_slice_read_elem (const mzd_slice_t *A, const rci_t row, const rci_t col) |
| Get the element at position (row,col) from the matrix A.
|
static void | mzd_slice_add_elem (mzd_slice_t *A, const rci_t row, const rci_t col, word elem) |
| At the element elem to the element at position (row,col) in the matrix A.
|
static void | mzd_slice_write_elem (mzd_slice_t *A, const rci_t row, const rci_t col, word elem) |
| Write the element elem to the position (row,col) in the matrix A.
|
static int | mzd_slice_cmp (mzd_slice_t *A, mzd_slice_t *B) |
| Return -1,0,1 if if A < B, A == B or A > B respectively.
|
static int | mzd_slice_is_zero (const mzd_slice_t *A) |
| Zero test for matrix.
|
static void | mzd_slice_row_swap (mzd_slice_t *A, const rci_t rowa, const rci_t rowb) |
| Swap the two rows rowa and rowb.
|
static void | mzd_slice_copy_row (mzd_slice_t *B, size_t i, const mzd_slice_t *A, size_t j) |
| copy row j from A to row i from B.
|
static void | mzd_slice_col_swap (mzd_slice_t *A, const rci_t cola, const rci_t colb) |
| Swap the two columns cola and colb.
|
static void | mzd_slice_col_swap_in_rows (mzd_slice_t *A, const rci_t cola, const rci_t colb, const rci_t start_row, rci_t stop_row) |
| Swap the two columns cola and colb but only between start_row and stop_row.
|
static void | mzd_slice_row_add (mzd_slice_t *A, const rci_t sourcerow, const rci_t destrow) |
| Add the rows sourcerow and destrow and stores the total in the row destrow.
|
static void | mzd_slice_row_clear_offset (mzd_slice_t *A, const rci_t row, const rci_t coloffset) |
| Clear the given row, but only begins at the column coloffset.
|
void | mzd_slice_print (const mzd_slice_t *A) |
| Print a matrix to stdout.
|
static void | _mzd_slice_compress_l (mzd_slice_t *A, const rci_t r1, const rci_t n1, const rci_t r2) |
| Move the submatrix L of rank r2 starting at column n1 to the left to column r1.
|
Matrices using a bitsliced representation.
Matrices over \(\mathbb{F}_{2^e}\) can be represented as polynomials with matrix coefficients where the matrices are in \(\mathbb{F}_2\).
In this file, matrices over \(\mathbb{F}_{2^e}\) are implemented as \(e\) slices of matrices over \(\mathbb{F}_2\) where each slice holds the coefficients of one degree when viewing elements of \(\mathbb{F}_{2^e}\) as polynomials over \(\mathbb{F}_2\).
- Author
- Martin Albrecht marti.nosp@m.nral.nosp@m.brech.nosp@m.t@go.nosp@m.oglem.nosp@m.ail..nosp@m.com