CF

This package implements Gosper's algorithm for arithmetic on (often infinite) continued fractions. This allows us to do arbitrary precision calculations without deciding in advance how much precision we need. Following Vuillemin, our continued fractions may contain zero and negative terms, so that the functions in Floating can be supported.

The type CF has instances for the following typeclasses.

• Eq
• Ord
• Num
• Fractional
• RealFrac
• Floating (currently missing asin, acos, atan)

Because equality of real numbers is not computable, we consider two numbers == if they are closer than epsilon = 1 % 10^10. For the same reason, floor and its cousins may give an incorrect result when the argument is within epsilon of an integer.

References

• Gosper, Ralph W. "Continued fraction arithmetic." HAKMEM Item 101B, MIT Artificial Intelligence Memo 239 (1972). APA
• Vuillemin, Jean E. "Exact real computer arithmetic with continued fractions." Computers, IEEE Transactions on 39.8 (1990): 1087-1105.
• Lester, David R. "Vuillemin’s exact real arithmetic." Functional Programming, Glasgow 1991. Springer London, 1992. 225-238. APA