Efficient Exact Arithmetic over Constructive Reals
We describe a computing method of the computable (or constructive) real numbers based on analysis of expressions. This method take precision estimate into account in order to get a better algorithm than Ménissier-Morain’s method, which is also based on the representation of constructive reals. We solve two problems which appear in exact real arithmetic based on the representation of constructive reals. First, by balancing every item’s precision in the expression, we can avoid unnecessary precision growth. Second, by distributing different weights to different operations, we can make sure that complex operations do not waste much time when to compute the whole expression. In these ways, we finally get a more efficient and proper method than prior implementations.
KeywordsReal Number Cauchy Sequence Error Range Original Algorithm Linear Fractional Transformation
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