Multiprecision floating point addition

Authors:
George E. Collins;Werner Krandick
Affiliations:
Dept. Computer and Information Sciences, University of Delaware;Dept. Mathematics and Computer Science, University of Paderborn, Germany
Venue:
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Year:
2000

Citing 5
Cited 3

Polynomial real root isolation using approximate arithmetic

ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
The art of computer programming, volume 3: (2nd ed.) sorting and searching

The art of computer programming, volume 3: (2nd ed.) sorting and searching
LEDA: a platform for combinatorial and geometric computing

LEDA: a platform for combinatorial and geometric computing
Parallel Real Root Isolation Using the Descartes Method

HiPC '99 Proceedings of the 6th International Conference on High Performance Computing
Polynomial real root isolation using Descarte's rule of signs

SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation

Interval arithmetic in cylindrical algebraic decomposition

Journal of Symbolic Computation
MPFR: A multiple-precision binary floating-point library with correct rounding

ACM Transactions on Mathematical Software (TOMS)
In Memoriam: Werner Krandick

ACM Communications in Computer Algebra

Quantified Score

Hi-index	0.00

Visualization

Abstract

An efficient algorithm is presented that returns the exactly rounded sum of two multiprecision floating point numbers. Depending on the input signs and exponents the algorithm distinguishes five cases. In each case, the method minimizes the number of computer words that are subject to de-normalization, addition or subtraction, and normalization. The method achieves further efficiency by trying to combine these three steps into one single pass over the mantissas. To do this, the method guesses the shift amount of the normalizing shift before the sum is known.