vendor: add kcp-go package

vendor/github.com/klauspost/reedsolomon/matrix.go

@@ -0,0 +1,279 @@
+/**
+ * Matrix Algebra over an 8-bit Galois Field
+ *
+ * Copyright 2015, Klaus Post
+ * Copyright 2015, Backblaze, Inc.
+ */
+
+package reedsolomon
+
+import (
+	"errors"
+	"fmt"
+	"strconv"
+	"strings"
+)
+
+// byte[row][col]
+type matrix [][]byte
+
+// newMatrix returns a matrix of zeros.
+func newMatrix(rows, cols int) (matrix, error) {
+	if rows <= 0 {
+		return nil, errInvalidRowSize
+	}
+	if cols <= 0 {
+		return nil, errInvalidColSize
+	}
+
+	m := matrix(make([][]byte, rows))
+	for i := range m {
+		m[i] = make([]byte, cols)
+	}
+	return m, nil
+}
+
+// NewMatrixData initializes a matrix with the given row-major data.
+// Note that data is not copied from input.
+func newMatrixData(data [][]byte) (matrix, error) {
+	m := matrix(data)
+	err := m.Check()
+	if err != nil {
+		return nil, err
+	}
+	return m, nil
+}
+
+// IdentityMatrix returns an identity matrix of the given size.
+func identityMatrix(size int) (matrix, error) {
+	m, err := newMatrix(size, size)
+	if err != nil {
+		return nil, err
+	}
+	for i := range m {
+		m[i][i] = 1
+	}
+	return m, nil
+}
+
+// errInvalidRowSize will be returned if attempting to create a matrix with negative or zero row number.
+var errInvalidRowSize = errors.New("invalid row size")
+
+// errInvalidColSize will be returned if attempting to create a matrix with negative or zero column number.
+var errInvalidColSize = errors.New("invalid column size")
+
+// errColSizeMismatch is returned if the size of matrix columns mismatch.
+var errColSizeMismatch = errors.New("column size is not the same for all rows")
+
+func (m matrix) Check() error {
+	rows := len(m)
+	if rows <= 0 {
+		return errInvalidRowSize
+	}
+	cols := len(m[0])
+	if cols <= 0 {
+		return errInvalidColSize
+	}
+
+	for _, col := range m {
+		if len(col) != cols {
+			return errColSizeMismatch
+		}
+	}
+	return nil
+}
+
+// String returns a human-readable string of the matrix contents.
+//
+// Example: [[1, 2], [3, 4]]
+func (m matrix) String() string {
+	rowOut := make([]string, 0, len(m))
+	for _, row := range m {
+		colOut := make([]string, 0, len(row))
+		for _, col := range row {
+			colOut = append(colOut, strconv.Itoa(int(col)))
+		}
+		rowOut = append(rowOut, "["+strings.Join(colOut, ", ")+"]")
+	}
+	return "[" + strings.Join(rowOut, ", ") + "]"
+}
+
+// Multiply multiplies this matrix (the one on the left) by another
+// matrix (the one on the right) and returns a new matrix with the result.
+func (m matrix) Multiply(right matrix) (matrix, error) {
+	if len(m[0]) != len(right) {
+		return nil, fmt.Errorf("columns on left (%d) is different than rows on right (%d)", len(m[0]), len(right))
+	}
+	result, _ := newMatrix(len(m), len(right[0]))
+	for r, row := range result {
+		for c := range row {
+			var value byte
+			for i := range m[0] {
+				value ^= galMultiply(m[r][i], right[i][c])
+			}
+			result[r][c] = value
+		}
+	}
+	return result, nil
+}
+
+// Augment returns the concatenation of this matrix and the matrix on the right.
+func (m matrix) Augment(right matrix) (matrix, error) {
+	if len(m) != len(right) {
+		return nil, errMatrixSize
+	}
+
+	result, _ := newMatrix(len(m), len(m[0])+len(right[0]))
+	for r, row := range m {
+		for c := range row {
+			result[r][c] = m[r][c]
+		}
+		cols := len(m[0])
+		for c := range right[0] {
+			result[r][cols+c] = right[r][c]
+		}
+	}
+	return result, nil
+}
+
+// errMatrixSize is returned if matrix dimensions are doesn't match.
+var errMatrixSize = errors.New("matrix sizes does not match")
+
+func (m matrix) SameSize(n matrix) error {
+	if len(m) != len(n) {
+		return errMatrixSize
+	}
+	for i := range m {
+		if len(m[i]) != len(n[i]) {
+			return errMatrixSize
+		}
+	}
+	return nil
+}
+
+// Returns a part of this matrix. Data is copied.
+func (m matrix) SubMatrix(rmin, cmin, rmax, cmax int) (matrix, error) {
+	result, err := newMatrix(rmax-rmin, cmax-cmin)
+	if err != nil {
+		return nil, err
+	}
+	// OPTME: If used heavily, use copy function to copy slice
+	for r := rmin; r < rmax; r++ {
+		for c := cmin; c < cmax; c++ {
+			result[r-rmin][c-cmin] = m[r][c]
+		}
+	}
+	return result, nil
+}
+
+// SwapRows Exchanges two rows in the matrix.
+func (m matrix) SwapRows(r1, r2 int) error {
+	if r1 < 0 || len(m) <= r1 || r2 < 0 || len(m) <= r2 {
+		return errInvalidRowSize
+	}
+	m[r2], m[r1] = m[r1], m[r2]
+	return nil
+}
+
+// IsSquare will return true if the matrix is square
+// and nil if the matrix is square
+func (m matrix) IsSquare() bool {
+	return len(m) == len(m[0])
+}
+
+// errSingular is returned if the matrix is singular and cannot be inversed
+var errSingular = errors.New("matrix is singular")
+
+// errNotSquare is returned if attempting to inverse a non-square matrix.
+var errNotSquare = errors.New("only square matrices can be inverted")
+
+// Invert returns the inverse of this matrix.
+// Returns ErrSingular when the matrix is singular and doesn't have an inverse.
+// The matrix must be square, otherwise ErrNotSquare is returned.
+func (m matrix) Invert() (matrix, error) {
+	if !m.IsSquare() {
+		return nil, errNotSquare
+	}
+
+	size := len(m)
+	work, _ := identityMatrix(size)
+	work, _ = m.Augment(work)
+
+	err := work.gaussianElimination()
+	if err != nil {
+		return nil, err
+	}
+
+	return work.SubMatrix(0, size, size, size*2)
+}
+
+func (m matrix) gaussianElimination() error {
+	rows := len(m)
+	columns := len(m[0])
+	// Clear out the part below the main diagonal and scale the main
+	// diagonal to be 1.
+	for r := 0; r < rows; r++ {
+		// If the element on the diagonal is 0, find a row below
+		// that has a non-zero and swap them.
+		if m[r][r] == 0 {
+			for rowBelow := r + 1; rowBelow < rows; rowBelow++ {
+				if m[rowBelow][r] != 0 {
+					m.SwapRows(r, rowBelow)
+					break
+				}
+			}
+		}
+		// If we couldn't find one, the matrix is singular.
+		if m[r][r] == 0 {
+			return errSingular
+		}
+		// Scale to 1.
+		if m[r][r] != 1 {
+			scale := galDivide(1, m[r][r])
+			for c := 0; c < columns; c++ {
+				m[r][c] = galMultiply(m[r][c], scale)
+			}
+		}
+		// Make everything below the 1 be a 0 by subtracting
+		// a multiple of it.  (Subtraction and addition are
+		// both exclusive or in the Galois field.)
+		for rowBelow := r + 1; rowBelow < rows; rowBelow++ {
+			if m[rowBelow][r] != 0 {
+				scale := m[rowBelow][r]
+				for c := 0; c < columns; c++ {
+					m[rowBelow][c] ^= galMultiply(scale, m[r][c])
+				}
+			}
+		}
+	}
+
+	// Now clear the part above the main diagonal.
+	for d := 0; d < rows; d++ {
+		for rowAbove := 0; rowAbove < d; rowAbove++ {
+			if m[rowAbove][d] != 0 {
+				scale := m[rowAbove][d]
+				for c := 0; c < columns; c++ {
+					m[rowAbove][c] ^= galMultiply(scale, m[d][c])
+				}
+
+			}
+		}
+	}
+	return nil
+}
+
+// Create a Vandermonde matrix, which is guaranteed to have the
+// property that any subset of rows that forms a square matrix
+// is invertible.
+func vandermonde(rows, cols int) (matrix, error) {
+	result, err := newMatrix(rows, cols)
+	if err != nil {
+		return nil, err
+	}
+	for r, row := range result {
+		for c := range row {
+			result[r][c] = galExp(byte(r), c)
+		}
+	}
+	return result, nil
+}