NxN limb multiplications and squares are done using one of seven algorithms, as the size N increases.
Algorithm Threshold Basecase (none) Karatsuba MUL_TOOM22_THRESHOLDToom-3 MUL_TOOM33_THRESHOLDToom-4 MUL_TOOM44_THRESHOLDToom-6.5 MUL_TOOM6H_THRESHOLDToom-8.5 MUL_TOOM8H_THRESHOLDFFT MUL_FFT_THRESHOLD
Similarly for squaring, with the SQR thresholds.
NxM multiplications of operands with different sizes above
MUL_TOOM22_THRESHOLD are currently done by special Toom-inspired
algorithms or directly with FFT, depending on operand size (see Unbalanced Multiplication).