Transposition of flat binary coefficient matrices

The input is read as a row-major rows by cols matrix. Transposition writes exactly rows * cols bits in row-major order, reading absent input bits as false and ignoring bits past the requested rectangle. Zero rows or columns give the empty list.

For coefficient packing, take rows = d source coefficients of width cols = b: input position j*b+i becomes output position i*d+j. The runtime evaluator uses pair (pair bits rowsWord) colsWord; dimensions are the lengths of their words, independently of their bit values.

def Complexity.BitPolynomial.transposeBits (rows cols : ℕ) (bits : List Bool) : List Bool

Transpose a row-major binary matrix, supplying false for missing entries.

Equations

• Complexity.BitPolynomial.transposeBits rows cols bits = List.map (fun (k : ℕ) => bits[k % rows * cols + k / rows]?.getD false) (List.range (rows * cols))

def Complexity.BitPolynomial.transposeEval (z : List Bool) : List Bool

Transpose a matrix with both dimensions supplied as runtime word lengths.

Equations

• One or more equations did not get rendered due to their size.