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separation-bounds

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Constructive separation bounds: exact zero and sign proofs for arithmetic expressions.

Roadmap

  • BFMSS bound with expressions represented as trees
  • ability to encode expressions as DAGs to get better bounds
  • automatic transformation into DAG
  • simpler expression construction using operators or macros
  • power node, instead of multiple multiplications
  • dyadic rational node, instead of division for better handling of float constants
  • BFMSS[k] optimization
  • Li-Yap bound
  • heuristics for picking bound type
  • RootOf / diamond operator, to represent every real algebraic number
  • DAG rewrite rules to get better bounds
  • return negative / zero / positive, instead of the bit count
  • optimize evaluation of easy cases
  • ...

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at your option.

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Exact zero and sign tests for arithmetic expressions via constructive separation bounds

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