ntt: rename canonical/ to subring/ - clearer naming for ring quotient

ntt/purego.go

@@ -7,22 +7,22 @@ import (
 	"fmt"
 	"sync"
 
-	"github.com/luxfi/math/ntt/canonical"
+	"github.com/luxfi/math/ntt/subring"
 	"github.com/luxfi/math/params"
 )
 
-// pureGoBackend is the canonical pure-Go NTT realization. It owns the
-// Lattigo-derived Montgomery NTT body via the internal canonical
-// package; lattice/v7/ring re-exports the same body for downstream
-// consumers, so callers see no behavior change vs the v0.1.x lattice
-// path.
+// pureGoBackend is the pure-Go NTT realization. It owns the
+// Lattigo-derived Montgomery NTT body via the subring package;
+// lattice/v7/ring re-exports the same body for downstream
+// consumers, so callers see no behavior change vs the v0.1.x
+// lattice path.
 //
-// LP-107 Phase 3 (this file): the canonical kernel body now lives in
-// luxfi/math/ntt/internal/canonical. luxfi/lattice/ring is a thin shim
+// LP-107 Phase 3 (this file): the kernel body lives in
+// luxfi/math/ntt/subring. luxfi/lattice/ring is a thin shim
 // that delegates to it.
 type pureGoBackend struct {
 	mu       sync.RWMutex
-	subRings map[params.NTTParamID]*canonical.SubRing
+	subRings map[params.NTTParamID]*subring.SubRing
 }
 
 // PureGoBackend returns the singleton pure-Go NTT backend. Always
@@ -32,7 +32,7 @@ func PureGoBackend() Backend {
 }
 
 var thePureGo = pureGoBackend{
-	subRings: make(map[params.NTTParamID]*canonical.SubRing),
+	subRings: make(map[params.NTTParamID]*subring.SubRing),
 }
 
 func init() {
@@ -49,8 +49,8 @@ func (b *pureGoBackend) Supports(p *Params) bool {
 	return p != nil && p.Validate() == nil
 }
 
-// resolveSubRing returns or builds the cached *canonical.SubRing for p.
-func (b *pureGoBackend) resolveSubRing(p *Params) (*canonical.SubRing, error) {
+// resolveSubRing returns or builds the cached *subring.SubRing for p.
+func (b *pureGoBackend) resolveSubRing(p *Params) (*subring.SubRing, error) {
 	b.mu.RLock()
 	sr, ok := b.subRings[p.ID]
 	b.mu.RUnlock()
@@ -62,9 +62,9 @@ func (b *pureGoBackend) resolveSubRing(p *Params) (*canonical.SubRing, error) {
 	if sr, ok := b.subRings[p.ID]; ok {
 		return sr, nil
 	}
-	sr, err := canonical.NewSubRing(int(p.N), p.Q)
+	sr, err := subring.NewSubRing(int(p.N), p.Q)
 	if err != nil {
-		return nil, fmt.Errorf("ntt(pure-go): canonical.NewSubRing(N=%d, Q=%d): %w",
+		return nil, fmt.Errorf("ntt(pure-go): subring.NewSubRing(N=%d, Q=%d): %w",
 			p.N, p.Q, err)
 	}
 	if err := sr.GenerateNTTConstants(); err != nil {

ntt/subring/doc.go

@@ -1,8 +1,8 @@
 // Copyright (c) 2026 Lux Industries Inc.
 // SPDX-License-Identifier: BSD-3-Clause
 
-// Package canonical owns the canonical Lattigo-derived Montgomery NTT
-// body — SubRing layout, root-table generator, scalar primitives
+// Package subring owns the Lattigo-derived Montgomery NTT body —
+// SubRing layout, root-table generator, scalar primitives
 // (MRed/MRedLazy/MForm/BRed/CRed/...), the loop-unrolled-by-16 NTT
 // kernel, and the SIMD AVX2 dispatch hooks.
 //
@@ -12,12 +12,12 @@
 // luxfi/threshold, ...) compile unchanged. Application callers should
 // route through one of:
 //
-//   - github.com/luxfi/math/ntt           — the canonical Service /
-//     Backend interface (recommended for new code).
+//   - github.com/luxfi/math/ntt           — the Service / Backend
+//     interface (recommended for new code).
 //   - github.com/luxfi/lattice/v7/ring    — the historical SubRing API
 //     for FHE-flavoured callers.
 //
 // This package is NOT a general-purpose import target: its surface is
 // optimized for the two consumers above and is not part of the public
 // luxfi/math semver contract for downstream code.
-package canonical
+package subring

ntt/subring/factorization.go

@@ -1,12 +1,12 @@
 // Body migrated from luxfi/lattice/v7/utils/factorization/factorization.go.
-// LP-107 Phase 3 — moved into the canonical NTT package so the
+// LP-107 Phase 3 — moved into the NTT package so the
 // SubRing constructor can factor q-1 to find a primitive root without
 // importing lattice.
 //
 // Renamed: IsPrime -> isPrimeBig (avoids collision with utils.IsPrime
 // which takes uint64; both stay package-internal here).
 
-package canonical
+package subring
 
 import (
 	"math"

ntt/subring/modular_reduction.go

@@ -3,10 +3,10 @@
 //
 // Body migrated from github.com/luxfi/lattice/v7/ring/modular_reduction.go
 // (Lattigo-derived). LP-107 Phase 3 establishes luxfi/math as the
-// canonical owner of the Montgomery / Barrett scalar primitives; the
+// owner of the Montgomery / Barrett scalar primitives; the
 // lattice copy now delegates to this package.
 
-package canonical
+package subring
 
 import (
 	"math/big"

ntt/subring/ntt.go

@@ -2,10 +2,10 @@
 // SPDX-License-Identifier: BSD-3-Clause
 //
 // Body migrated verbatim from luxfi/lattice/v7/ring/ntt.go.
-// LP-107 Phase 3 — luxfi/math is the canonical owner of the
+// LP-107 Phase 3 — luxfi/math is the owner of the
 // Lattigo-derived Montgomery NTT body.
 
-package canonical
+package subring
 
 import (
 	"fmt"

ntt/subring/ntt_simd.go

@@ -3,7 +3,7 @@
 // SIMD-accelerated NTT body for AVX2 amd64 with GOEXPERIMENT=simd.
 // LP-107 Phase 3 — verbatim from luxfi/lattice/v7/ring/ntt_simd.go.
 
-package canonical
+package subring
 
 import (
 	"math/bits"

ntt/subring/ntt_simd_stub.go

@@ -3,7 +3,7 @@
 // SIMD stub for non-AVX2 / non-experimental-simd builds.
 // LP-107 Phase 3 — verbatim from luxfi/lattice/v7/ring/ntt_simd_stub.go.
 
-package canonical
+package subring
 
 // nttCoreLazyAccel is the stub for non-SIMD builds.
 // Returns false to indicate no acceleration was applied.

ntt/subring/subring.go

@@ -2,7 +2,7 @@
 // SPDX-License-Identifier: BSD-3-Clause
 //
 // Body migrated from luxfi/lattice/v7/ring/subring.go.
-// LP-107 Phase 3 — luxfi/math is the canonical owner of the Lattigo-derived
+// LP-107 Phase 3 — luxfi/math is the owner of the Lattigo-derived
 // Montgomery NTT body and SubRing layout. luxfi/lattice/ring re-exports.
 //
 // Changes from upstream:
@@ -10,7 +10,7 @@
 //   - utils.BitReverse64       -> BitReverse64 (same package)
 //   - bignum.NewInt(uint64)    -> new(big.Int).SetUint64(...)
 
-package canonical
+package subring
 
 import (
 	"fmt"

ntt/subring/subring_test.go

@@ -1,7 +1,7 @@
 // Copyright (c) 2026 Lux Industries Inc.
 // SPDX-License-Identifier: BSD-3-Clause
 
-package canonical
+package subring
 
 import (
 	"math/rand/v2"
@@ -14,7 +14,7 @@ const (
 	pulsarQ  = uint64(0x1000000004A01)
 )
 
-// TestSubRing_RoundTrip exercises the full canonical path:
+// TestSubRing_RoundTrip exercises the full path:
 // constructor + GenerateNTTConstants + forward NTT + inverse NTT.
 func TestSubRing_RoundTrip(t *testing.T) {
 	sr, err := NewSubRing(pulsarN, pulsarQ)

ntt/subring/utils.go

@@ -4,7 +4,7 @@
 // Helpers migrated from luxfi/lattice/v7/ring (utils.go, primes.go) and
 // luxfi/lattice/v7/utils (BitReverse64). LP-107 Phase 3.
 
-package canonical
+package subring
 
 import (
 	"math/big"

ntt/subring/vec_ops.go

@@ -5,7 +5,7 @@
 // LP-107 Phase 3 — only the helpers required by the NTT body
 // (reducevec, mulscalarmontgomeryvec, mulscalarmontgomerylazyvec).
 
-package canonical
+package subring
 
 import "unsafe"
 

ntt/subring/weierstrass.go

@@ -2,7 +2,7 @@
 // LP-107 Phase 3 — randInt inlined to drop the lattice/v7/utils/sampling
 // import so this package has zero lattice dependencies.
 
-package canonical
+package subring
 
 import (
 	"crypto/rand"