mirror of
https://github.com/vale981/arb
synced 2025-03-06 01:41:39 -05:00
77 lines
2.9 KiB
Text
77 lines
2.9 KiB
Text
* Make sure that excessive shifts in add/sub are detected
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with exact precision. Write tests for correctness of overlaps/contains
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in huge-exponent cases.
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* Work out semantics for comparisons/overlap/containment checks
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when NaNs are involved, and write test code.
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* Fix missing/wrong error bounds currently used in the code (see TODO/XXX).
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* Add missing polynomial functionality (conversions, arithmetic, etc.)
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* More transcendental functions.
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* Add adjustment code for balls (when the mantissa is much more precise than
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the error bound, it can be truncated). Also, try to work out more consistent
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semantics for ball arithmetic (with regard to extra working precision, etc.)
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* Do a low-level rewrite of the fmpr type.
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The mantissa should probably be changed to an unsigned, top-aligned fraction
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(i.e. the exponent will point to the top rather than the bottom, and
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the top bit of the ).
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This requires a separate sign field, increasing the struct size from
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2 to 3 words, but ought to lead to simpler code and slightly less overhead.
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The unsigned fraction can be stored directly in a ulong when it has
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most 64 bits. A zero top bit can be used to tag the field as a pointer.
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The pointer could either be to an mpz struct or directly to a limb array
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where the first two limbs encode the allocation and used size.
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There should probably be a recycling mechanism as for fmpz.
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Required work:
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memory allocation code
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conversions to/from various integer types
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rounding/normalization
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addition
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subtraction
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comparison
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multiplication
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fix any code accessing the exponent and mantissa directly as integers
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Lower priority:
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low-level division, square root (these are not as critical for
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performance -- it is ok to do them by converting to integers and back)
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direct low-level code for addmul, mul_ui etc
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* Native string conversion code instead of relying on mpfr (so we can have
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big exponents, etc.).
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* Add functions for sloppy arithmetic (non-exact rounding). This could be
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used to speed up some ball operations with inexact output, where we don't
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need the best possible result, just a correct error bound.
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* Write functions that ignore the possibility that exponents might be
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large, and use where appropriate (e.g. polynomial and matrix multiplication
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where one bounds magnitudes in an initial pass).
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* Write a faster logarithmic rising factorial (with correct branch
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cuts) for reducing the complex log gamma function. Also implement
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the logarithmic reflection formula.
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* Rewrite fmprb_div (similar to fmprb_mul)
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* Faster elementary functions at low precision (especially log/arctan).
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* Document fmpz_extras
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* Move zeta functions to own module and cleanup.
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* Use the complex Newton iteration for cos(pi p/q) when appropriate.
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Double check the proof of correctness of the complex Newton iteration
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and make it work when the polynomial is not exact.
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* Write a cleanup function that frees all cached data.
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