A Parallel Algorithm for Multiple-Precision Division by a Single-Precision Integer
Large-Scale Scientific Computing
Computation of high-precision mathematical constants in a combined cluster and grid environment
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
| Hi-index | 0.00 |
We present efficient parallel algorithms for multiple-precision division and square root operation of more than sever al million decimal digits on distributed-memory parallel computers. It is well known that multiple-precision division and square root operation 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-base d multiplication is used. We also parallelized an operation of releasing propagate d 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.