Changelog for posit-2022.2.0.0

Changelog for Posit Numbers

Updated divide (/) to have one less round operation, previous default was a * recip b, divide two rational numbers then round viaRational2 (/) a b, it sort of fuses the old default, reducing error
New flag for Fused Operations applied automatically via rewrite rules --flag posit:do-rewrite
Test for Fused Operations stack test posit:test-posit-fusedRewrite, with no fusing
Test for Fused Operations stack test posit:test-posit-fusedRewrite --flag posit:do-rewrite, to execute with the rewrite rules for fusing
Added several fms or fma functions to asin, acos, asinh, acosh. No apparent change in the elementary functions.
User defined rewrite rules seem to work before but break in ghc-9.6.3. I really hope it gets fixed. See: (How Cool is Rulz!)[https://discourse.haskell.org/t/how-cool-is-rulz/7738/9]
Added new approxEq function to the AltFloating class
Implemented approxEq by converting to the next lower ES and then using the normal (==) function, using a new Prev es type family
Added new Prev es type family to the PositF es Constraint Synonym
Changed naming in AltFloating to free up the name space and not use greek letters, eps is now machEps, psi is now goldenRatio
Removed gamma, sinc, expm1 from AltFloating making way for updates to the Posit Standard in the future for special functions

Optimized the Show instance to properly handle the tapered precision
Changes to round better
Improved accuracy of exp
Changed titles of accuracy charts to be more consistant
Added test to confirm read.show == id to perhaps optimise the textual representation, and verify that the implementation is sufficent
Test round trip with command to run: stack test posit:test-posit-readShowId
Added catagory to .cabal file

atan 1 :: Posit256 is very slow, added a few precice constants to speed it up
Improved accuracy of sin and cos at the extreme positive and negative values

Much thanks to @svlc sugesting to link to a raw image rather than an html, and that finaly made the images display on Hackage

Added Random and Uniform Instances
Uniform provides a uniform distribution over all possible posits, sampling the entire projective real line
Random provides a uniform distribution between 0 and 1, sampling the real numbers in that range
Example: take 10 (randomRs (1,100) (mkStdGen 2023)) :: [Posit64]
Added hypot2, hypot3, hypot4, to the AltFloating class

Added PositF constraint synonym to simplify the usage of (PositC es, PositC (Next es)), as is needed for Floating instances
More coverage in the test suite for multiple types

Added Types (P8, P16, P32, P64, P128, P256) for the Posit Standard 2022 encoding, exponent size = 2, and with nBytes = 2^es
Refactored Floating to step up in resolution and then calculate a function, and then round it down to the the lower resolution
Added polymorphic Posit es approximations for the Floating class
Moved functions used in the test suite to the Test.Algorithms module, to eliminate the do-test flag
Since the test flag has been removed the test can be run by: stack test
Please forgive the lack of camelCase in some of the Floating functions... I think it reads better this time
The Weigh test can be run as a benchmark: stack bench

Bug fix for mkIntRep to resolve an overflow issue with the fractional part when it rounds up, in anticipation of the 2022 Standard release

No more Orphan Instances for Storable!
Figured out how to resolve the orphan instances problem with newtype, DerivingVia and UndecidableInstances.
Added a "weigh" based test to verify the proper size of each Posit type
Added a WeighPosit test; command to run: stack test posit:test-posit-weigh
Added NFData instance.
New GitHub Snapshot of Liquid Haskell makes it work with GHC 9.0.2!

Made the following changes in anticipation of adding the 2022 Posit Standard:
- Made the IntN type family non-Injective, and added more visable type applications to help the compiler select the proper types
- Corrected some bad uses of nBytes @es, with 2^(exponentSize @es), in order to be more general
- Chagned maxPosRat to match the more general form as described in "Posit Arithmetic" (John L Gustafson, 10 October 2017)
- Changed lnOf2 to be a long decimal value, in order to be more general
Changed Borwein's algorithm, with quintic convergence, to check for a fixed point of both a and s
Added Borwein's Quadradic 1985
Added Borewein's Cubic

Added FlexableContexts back in to Posit.hs, a build error occured on GHC-9.2 that didn't occur with GHC-9.0 or GHC-8.10

Refactored IntN Type Family to be a closed type family instead of an associated type family
Refactored IntN constraints to use ConstraintKinds and made that to be a Super Class of PositC to improve the encapsulation the Constraints of the internal implementation
Refactored PositC to make use of ConstrainedClassMethods vastly reducing code duplication
Eliminated the FlexableContexts Language Extension from Posit.hs Interface, since the InN constraints no longer bleed into that file
Added test of Heegner numbers (almost integers)
Added test of various Gamma Function approximations
Improved function names in the Orphan Instance for Storable ( Word128 )
Improved documentation

Posit Standard 3.2 [Posit Standard] (https://posithub.org/docs/posit_standard.pdf)
LiquidHaskell support: stack build --flag posit:do-liquid
To run the test suite: stack test --flag posit:do-test
To play around: stack repl --flag posit:do-test