promote ℝ to an instance of a typeclass

[julialongtin]

No description provided.

[Copilot]

Pull request overview

This PR refactors the codebase to treat ℝ as a dedicated numeric type backed by a new ℚ typeclass, and migrates call sites to use math operations/constants (π, sqrt, cbrt, normalizeℝ2/3, etc.) provided via Graphics.Implicit.Definitions rather than Prelude/vector-space helpers.

Changes:

• Introduces Graphics.Implicit.RationalUtil (defines ℚ and the ℝ newtype) and Graphics.Implicit.RationalFunctions (rational math helpers).
• Updates modeling, export, and OpenSCAD interpreter code to import numeric operations/constants from Graphics.Implicit.Definitions and replaces normalized/magnitude patterns with normalizeℝ*/magnitudeSq + sqrt.
• Updates build configuration to include the new modules and tweaks profiling/dynamic build flags.

Reviewed changes

Copilot reviewed 29 out of 30 changed files in this pull request and generated 7 comments.

Show a summary per file

File	Description
programs/implicitsnap.hs	Switches cube-root usage to cbrt and moves math imports to Definitions.
programs/extopenscad.hs	Same cbrt/math import refactor in CLI executable.
programs/Benchmark.hs	Uses π/cos from Definitions and adds numeric defaulting.
implicit.cabal	Adds new modules to the library; adjusts executable GHC options (dynamic commented).
Makefile	Updates commented profiling flag to library profiling.
Graphics/Implicit/RationalUtil.hs	Adds ℚ typeclass and ℝ newtype + instances (core of the change).
Graphics/Implicit/RationalFunctions.hs	Adds rational trig/sqrt/cbrt/normalize helpers (future precision support).
Graphics/Implicit/ObjectUtil/GetImplicit3.hs	Replaces normalized, pi, and (** (1/3)) usage with normalizeℝ3, π, cbrt.
Graphics/Implicit/ObjectUtil/GetImplicit2.hs	Moves sqrt/sin/cos imports to Definitions.
Graphics/Implicit/ObjectUtil/GetBox3.hs	Uses infty/neginfty from Definitions instead of local 1/0.
Graphics/Implicit/ObjectUtil/GetBox2.hs	Uses infty/neginfty and replaces magnitude with sqrt . magnitudeSq.
Graphics/Implicit/MathUtil.hs	Replaces distance/normalized with distanceSq + sqrt + normalizeℝ2.
Graphics/Implicit/IntegralUtil.hs	Trivial whitespace-only change.
Graphics/Implicit/ExtOpenScad/Util/OVal.hs	Routes numeric-to-ℕ conversion via fromℝtoℕ and enables FlexibleInstances.
Graphics/Implicit/ExtOpenScad/Primitives.hs	Migrates trig/π usage to Definitions.
Graphics/Implicit/ExtOpenScad/Parser/Util.hs	Uses powℝ for exponent parsing instead of (**).
Graphics/Implicit/ExtOpenScad/Parser/Expr.hs	Import list cleanup for refactor.
Graphics/Implicit/ExtOpenScad/Default.hs	Moves constants/functions (π, trig, powℝℝ, etc.) to Definitions.
Graphics/Implicit/Export/Util.hs	Uses normalizeℝ3 and replaces realToFrac-based centroid scaling with ℕ/ℝ conversions.
Graphics/Implicit/Export/TriangleMeshFormats.hs	Uses normalizeℝ3 for normals.
Graphics/Implicit/Export/TextBuilderUtils.hs	Fixes float formatting by converting via fromℝtoFloat.
Graphics/Implicit/Export/SymbolicObj2.hs	Uses π, sqrt, magnitudeSq instead of pi/magnitude.
Graphics/Implicit/Export/SymbolicFormats.hs	Uses π from Definitions and adjusts rad/deg conversion.
Graphics/Implicit/Export/Symbolic/Rebound3.hs	Adds default (ℝ) to avoid ambiguous numeric literals with new ℝ.
Graphics/Implicit/Export/Symbolic/Rebound2.hs	Adds default (ℝ) similarly.
Graphics/Implicit/Export/Render/TesselateLoops.hs	Switches normalization/magnitude to normalizeℝ3 and sqrt . magnitudeSq.
Graphics/Implicit/Export/Render/RefineSegs.hs	Uses normalizeℝ2 and sqrt . magnitudeSq for geometry/refinement logic.
Graphics/Implicit/Export/Render/GetSegs.hs	Moves sqrt import to Definitions.
Graphics/Implicit/Export/RayTrace.hs	Uses normalizeℝ3 and sqrt . magnitudeSq for ray math.
Graphics/Implicit/Definitions.hs	Re-exports the new RationalUtil API via module R and removes the old type ℝ = Double model.

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[Copilot]

Typo in comment: “arithmatic” → “arithmetic”.

Suggested change

	-- for the type arithmatic in the types of normalizedℝ(2,3).
	-- for the type arithmetic in the types of normalizedℝ(2,3).

[Copilot]

Typo in comment: “acurate” → “accurate”.

Suggested change

	-- FIXME: since the taylor series for asin is acurate only in a certain range, rollover in that range.
	-- FIXME: since the taylor series for asin is accurate only in a certain range, rollover in that range.

[Copilot]

Data.VectorSpace.InnerSpace requires (<.>) :: ℝ -> ℝ -> Scalar ℝ (i.e., ℝ), but this implementation uses P.* (Double multiplication), which won’t typecheck with the ℝ newtype. Use (*) on ℝ (or pattern-match and rewrap) instead of P.* here.

Suggested change

	(*^) (ℝ a) (ℝ b) = ℝ $ (P.*) a b
	{-# INLINABLE (*^) #-}
	instance InnerSpace ℝ where
	(<.>) = (P.*)
	(*^) = (*)
	{-# INLINABLE (*^) #-}
	instance InnerSpace ℝ where
	(<.>) = (*)

[Copilot]

AffineSpace operations here are defined using P.+/P.- (Double operations), which won’t typecheck for the ℝ newtype and will fail the build under -Werror. Define (.-.)/(.+^) using the ℝ numeric instances (or unwrap/rewrap explicitly) instead.

Suggested change

	(.-.) = (P.-)
	{-# INLINABLE (.-.) #-}
	(.+^) = (P.+)
	(ℝ a) .-. (ℝ b) = ℝ $ (P.-) a b
	{-# INLINABLE (.-.) #-}
	(ℝ a) .+^ (ℝ b) = ℝ $ (P.+) a b

[Copilot]

The explicit Prelude import list includes floor twice (once via RealFrac(..., floor, ...) and again as a standalone import). With this repo’s -Wall -Werror, this will be promoted to an error (-Wduplicate-imports). Remove the duplicate import item.

Suggested change

	import Prelude (RealFrac(properFraction, ceiling, floor, round, truncate), Fractional(fromRational, (/)), Ord, Double, Show(show), Eq, Num((+), (*), abs, negate, signum, fromInteger), Real(toRational), Read(readsPrec), ($), seq, (==), floor, Float, map)
	import Prelude (RealFrac(properFraction, ceiling, floor, round, truncate), Fractional(fromRational, (/)), Ord, Double, Show(show), Eq, Num((+), (*), abs, negate, signum, fromInteger), Real(toRational), Read(readsPrec), ($), seq, (==), Float, map)

[Copilot]

cbrt implemented as x ** (1/3) returns NaN for negative inputs with Doubles (e.g. (-8) ** (1/3)). Since cbrt is now part of the public numeric API, it should be sign-preserving (e.g. signum x * abs x ** (1/3)) to behave as a real cube root.

Suggested change

	cbrt (ℝ x) = ℝ $ (P.**(1/3)) x
	cbrt (ℝ x) = ℝ $ P.signum x P.* (P.abs x P.** (1 P./ 3))

[Copilot]

This import list includes powℝ twice. With -Wall -Werror enabled in this repo, the duplicate import item will fail the build (-Wduplicate-imports). Remove the duplicated powℝ entry.

Suggested change

	import Graphics.Implicit.RationalUtil as R (ℚ(minℝ, π, sqrt, cbrt, powℝ, powℝℝ, exp, log, cos, sin, tan, asin, acos, atan, sinh, cosh, tanh, atan2, fromℝ, toℝ, normalizeℝ2, normalizeℝ3, powℝ, (%), infty, neginfty), ℝ, fromFastℕtoℝ, fromℕtoℝ, fromℝtoℕ, fromℝtoFloat)
	import Graphics.Implicit.RationalUtil as R (ℚ(minℝ, π, sqrt, cbrt, powℝ, powℝℝ, exp, log, cos, sin, tan, asin, acos, atan, sinh, cosh, tanh, atan2, fromℝ, toℝ, normalizeℝ2, normalizeℝ3, (%), infty, neginfty), ℝ, fromFastℕtoℝ, fromℕtoℝ, fromℝtoℕ, fromℝtoFloat)