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liancheng / rose

ROSE is an Obscure Scheme Evaluator

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Refactor the number tower

liancheng opened this issue · comments

commented

Current situation

Current number tower implementation is too lame and cumbersome, which makes arithmetic procedures actually a mess.

Currently, there are only three kinds of numbers:

  • Small integer: 30-bit (or 62-bit on x64) immediate signed integer value.
  • Fixnum: boxed exact complex number, represented by two mpq_t. Fixnum is used to represent all exact numbers that cannot fit in a small integer, i.e., exact big integers, exact rationals, and exact complexes.
  • Flonum: boxed inexact complex number, represented by two double. Flonum is used to represent all inexact numbers. Yes, there's no immediate version of inexact number.

The plan

The plan is to add two new number types:

  • Fixreal: boxed exact rational number, represented by a mpq_t, used to represent exact big integers and exact rationals.
  • Floreal: boxed inexact rational number, represented by a double, used to represent inexact rationals.

Correspondingly, Fixnum and Flonum will be merged into 1 Complex type, which is represented by two rational numbers real and imag under the coat of rsexp.

Invariables

  1. The real part and the imaginary part of a Complex number must be both exact numbers or inexact numbers. For exact Complex, real and imag must be small integer or Fixreal; for inexact Complex, real and imag must be Floreal.
  2. r_exact_p should return TRUE for small integers, Fixreals and exact Complex
  3. r_inexact_p should return TRUE for Floreal and inexact Complex

Normalization

When creating Fixreals, input will be checked to see whether it can fit into a small integer, if yes, a small integer will be returned. This process is called Fixnum normalization.

On the other hand, Flonums won't be normalized automatically. But normalization do happens when r_inexact_to_exact is called with a Flonum. For example, when evaluating (inexact->exact 1.0), resulted exact integer 1 is represented by a small integer, rather than a Fixreal.

commented

Added a new branch finer-number-tower to fix this issue.

commented

The number tower has been fixed commit 5ccd831. Arithmetic procedures hasn't been updated yet.

commented

I think this issue can be closed now. The number tower is fully refactored, and all the previously implemented arithmetic procedures have been re-implemented with the new number tower (see 2180d9b).