Level-index arithmetic operations

@article{Clenshaw1987LevelindexAO,
  title={Level-index arithmetic operations},
  author={C. W. Clenshaw and Frank W. J. Olver},
  journal={SIAM Journal on Numerical Analysis},
  year={1987},
  volume={24},
  pages={470-485}
}
In a recent paper the authors described a system for the internal representation of numbers in a computer, based on repeated exponentiations. The main objective in introducing this system is to eradicate the problems of overflow and underflow. The present paper supplies algorithms for performing the four basic arithmetical operations in the new system. The algorithms are accompanied by error analyses, which show that the algorithms can be executed with fixed-point arithmetic. Illustrative… Expand
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