We present efficient parallel algorithms for multiple-precision division and square root operation of more than several million decimal digits on distributed-memory parallel computers. It is well known that multiple-precision division and square root operations can be reduced to multiple-precision addition, subtraction, and multiplication by using Newton iteration. Because a key operation in fast multiple-precision arithmetic is multiplication, a parallel implementation of floating-point real FFT-based multiplication is used. We also parallelized an operation of releasing propagated carries and borrows in multiple-precision addition, subtraction and multiplication. In parallel implementation of Newton iteration based multiple-precision division and square root operation, there is a tradeoff between load balance and communication overhead on distributed-memory parallel computers. An efficient data distribution for multiple-precision division and square root operation by using Newton iteration is given with confirmation of the theoretical analysis. We achieved high performance multiple-precision calculation of division and square root operation on distributed-memory parallel computers.
['Daisuke Takahashi']
Implementation of multiple-precision parallel division and square root on distributed-memory parallel computers