tensor/oracle_test.go

// Copyright (c) 2026 Petr Balvín <opensource@petrbalvin.org> (https://petrbalvin.org)
// SPDX-License-Identifier: MIT

package tensor

import (
	"crypto/sha256"
	"encoding/binary"
	"encoding/hex"
	"fmt"
	"hash"
	"maps"
	"math"
	"os"
	"path/filepath"
	"runtime"
	"runtime/debug"
	"slices"
	"testing"

	"sourcedock.dev/petrbalvin/tensor/internal/core"
	"sourcedock.dev/petrbalvin/tensor/spmd"
)

// The oracle harness. Every domain runs one fixed workload through the
// re-exported facade only, the raw bits of every output are hashed, and
// the per-case digest is pinned in the table below. A silent behaviour
// change, a swapped reduction order, a regression in a kernel: any of
// them moves the digest and fails the test. A deliberate change to an
// algorithm re-records the table in the same commit, so the diff shows
// exactly which case moved.
//
// Inputs are fixed literals or the seeded generator, which is
// bit-stable across Go releases by construction, and the parallel
// kernels promise a fixed reduction order, so the digest is
// deterministic on a given architecture. Run with
// TENSOR_ORACLE_RECORD=1 to print the current digests instead of
// comparing them.

// oracleDigest accumulates the raw bits of the given values. Supported
// carriers: *Array, Scalar, float64, []float64, string, bool and int;
// anything else is a harness bug and panics.
type oracleDigest struct {
	h hash.Hash
}

func newOracleDigest() *oracleDigest { return &oracleDigest{h: sha256.New()} }

func (d *oracleDigest) array(t *testing.T, a *core.Array) {
	d.h.Write([]byte{byte(a.Dtype())})
	for _, s := range a.Shape() {
		var buf [8]byte
		binary.LittleEndian.PutUint64(buf[:], uint64(s))
		d.h.Write(buf[:])
	}
	switch a.Dtype() {
	case core.Int:
		for _, v := range a.RawInts()[:a.Len()] {
			var buf [8]byte
			binary.LittleEndian.PutUint64(buf[:], uint64(v))
			d.h.Write(buf[:])
		}
	case core.Float32:
		for _, v := range a.RawFloat32s()[:a.Len()] {
			var buf [4]byte
			binary.LittleEndian.PutUint32(buf[:], math.Float32bits(v))
			d.h.Write(buf[:])
		}
	case core.Float16:
		for _, v := range a.RawHalves()[:a.Len()] {
			var buf [2]byte
			binary.LittleEndian.PutUint16(buf[:], v)
			d.h.Write(buf[:])
		}
	case core.Float:
		for _, v := range a.RawFloats()[:a.Len()] {
			d.f64(v)
		}
	case core.Complex:
		for _, v := range a.RawComplexes()[:a.Len()] {
			d.f64(real(v))
			d.f64(imag(v))
		}
	case core.Bool:
		// The boolean payload hashes as its own bytes, one 0 or 1 per
		// element, the layout every mask round-trip is read back in.
		for _, v := range a.RawBools()[:a.Len()] {
			if v {
				d.h.Write([]byte{1})
			} else {
				d.h.Write([]byte{0})
			}
		}
	case core.Int8:
		for _, v := range a.RawInt8s()[:a.Len()] {
			d.h.Write([]byte{byte(v)})
		}
	case core.Uint8:
		for _, v := range a.RawUint8s()[:a.Len()] {
			d.h.Write([]byte{byte(v)})
		}
	case core.Int16:
		for _, v := range a.RawInt16s()[:a.Len()] {
			var buf [2]byte
			binary.LittleEndian.PutUint16(buf[:], uint16(v))
			d.h.Write(buf[:])
		}
	case core.Uint16:
		for _, v := range a.RawUint16s()[:a.Len()] {
			var buf [2]byte
			binary.LittleEndian.PutUint16(buf[:], uint16(v))
			d.h.Write(buf[:])
		}
	case core.Int32:
		for _, v := range a.RawInt32s()[:a.Len()] {
			var buf [4]byte
			binary.LittleEndian.PutUint32(buf[:], uint32(v))
			d.h.Write(buf[:])
		}
	case core.Uint32:
		for _, v := range a.RawUint32s()[:a.Len()] {
			var buf [4]byte
			binary.LittleEndian.PutUint32(buf[:], uint32(v))
			d.h.Write(buf[:])
		}
	default:
		// An unhashed payload would pin nothing: fail loudly in the
		// test rather than panicking or hashing the wrong bytes.
		t.Fatalf("oracle harness: array payload of dtype %s (%d) has no hash rule", a.Dtype(), a.Dtype())
	}
}

func (d *oracleDigest) f64(v float64) {
	var buf [8]byte
	binary.LittleEndian.PutUint64(buf[:], math.Float64bits(v))
	d.h.Write(buf[:])
}

func (d *oracleDigest) floats(vals []float64) {
	var n [8]byte
	binary.LittleEndian.PutUint64(n[:], uint64(len(vals)))
	d.h.Write(n[:])
	for _, v := range vals {
		d.f64(v)
	}
}

func (d *oracleDigest) int(v int) {
	var buf [8]byte
	binary.LittleEndian.PutUint64(buf[:], uint64(v))
	d.h.Write(buf[:])
}

// result carries one output of an oracle case into the digest.
func (d *oracleDigest) result(t *testing.T, v any) {
	switch x := v.(type) {
	case *Array:
		d.array(t, x)
	case Scalar:
		d.f64(x.Float())
	case float64:
		d.f64(x)
	case []float64:
		d.floats(x)
	case string:
		d.h.Write([]byte(x))
	case bool:
		// Error paths carry the fact of the refusal, not its wording:
		// the text may be reworded, the refusal must not disappear.
		if x {
			d.h.Write([]byte{1})
		} else {
			d.h.Write([]byte{0})
		}
	case int:
		d.int(x)
	default:
		panic("oracle harness: unsupported carrier type")
	}
}

func (d *oracleDigest) sum() string { return hex.EncodeToString(d.h.Sum(nil)) }

// mustA builds an array from fixed values.
func mustA(t *testing.T, vals []float64, shape ...int) *Array {
	t.Helper()
	a, err := FromFloats(vals, shape...)
	if err != nil {
		t.Fatal(err)
	}
	return a
}

// randA draws n deterministic samples through the seeded generator.
func randA(t *testing.T, seed int64, n int) *Array {
	t.Helper()
	g := NewGenerator(seed)
	a, err := Floats(g, n)
	if err != nil {
		t.Fatal(err)
	}
	return a
}

// wobble is the bounded deterministic wiggle the formula-driven
// workloads use in place of a generator: a fixed function of the
// index, so a case's inputs are its own, not the generator state's.
func wobble(i int) float64 {
	return 0.3*math.Sin(7.3*float64(i)+1.1)*math.Cos(2.1*float64(i)) +
		0.1*math.Sin(0.7*float64(i))
}

// oracleCases is the harness workload: one entry per domain feature,
// every output it produces fed into the digest.
var oracleCases = []struct {
	name string
	run  func(t *testing.T) []any
}{
	{"spmd-shards", func(t *testing.T) []any {
		// The distributed reduction answers the single-array
		// reduction's exact bits at any world size: the digest pins
		// the shards' answers beside the single-array ones they must
		// equal, over a length that cuts the fold's partition into
		// several blocks.
		const gn = 200001
		vals := make([]float64, gn)
		for i := range vals {
			vals[i] = float64((i*6559)%2001-1000) / 7.0
			if i%401 == 3 {
				vals[i] = math.NaN()
			}
		}
		yVals := make([]float64, gn)
		for i := range yVals {
			yVals[i] = float64((i*7919)%901-450) / 5.0
		}
		whole, err := FromFloats(vals, gn)
		if err != nil {
			t.Fatal(err)
		}
		wantSum := Sum(whole)
		wantMax, err := Max(whole)
		if err != nil {
			t.Fatal(err)
		}
		out := []any{wantSum, wantMax}
		for _, size := range []int{1, 3, 5} {
			// Each rank writes its own slots; the digest takes them in
			// rank order after the world has joined up again.
			answers := make([]core.Scalar, size*5)
			err := spmd.Launch(size, func(w *spmd.World) error {
				span, err := spmd.Partition(gn, size, w.Rank())
				if err != nil {
					return err
				}
				local, err := Slice(whole, 0, span.Lo, span.Hi)
				if err != nil {
					return err
				}
				gotSum, err := w.AllReduceShards(local, span, spmd.Sum)
				if err != nil {
					return err
				}
				gotMax, err := w.AllReduceShards(local, span, spmd.Max)
				if err != nil {
					return err
				}
				gotProd, err := w.AllReduceShards(local, span, spmd.Prod)
				if err != nil {
					return err
				}
				gotNorm, err := w.AllReduceNormShards(local, span, 2)
				if err != nil {
					return err
				}
				second, err := FromFloats(yVals, gn)
				if err != nil {
					return err
				}
				secondLocal, err := Slice(second, 0, span.Lo, span.Hi)
				if err != nil {
					return err
				}
				gotDot, err := w.AllReduceDotShards(local, secondLocal, span)
				if err != nil {
					return err
				}
				wantProd, err := Prod(whole, 0, false)
				if err != nil {
					return err
				}
				wantNorm, err := Norm(whole, 2, 0, false)
				if err != nil {
					return err
				}
				wantDot, err := Dot(whole, second)
				if err != nil {
					return err
				}
				if math.Float64bits(gotSum.Float()) != math.Float64bits(wantSum.Float()) ||
					math.Float64bits(gotMax.Float()) != math.Float64bits(wantMax.Float()) ||
					math.Float64bits(gotProd.Float()) != math.Float64bits(wantProd.FloatAt(0)) ||
					math.Float64bits(gotNorm.Float()) != math.Float64bits(wantNorm.FloatAt(0)) ||
					math.Float64bits(gotDot.Float()) != math.Float64bits(wantDot.Float()) {
					t.Fatalf("size %d: the sharded answers moved against the single-array reduction", size)
				}
				answers[w.Rank()*5] = gotSum
				answers[w.Rank()*5+1] = gotMax
				answers[w.Rank()*5+2] = gotProd
				answers[w.Rank()*5+3] = gotNorm
				answers[w.Rank()*5+4] = gotDot
				return nil
			})
			if err != nil {
				t.Fatal(err)
			}
			for _, s := range answers {
				out = append(out, s)
			}
			out = append(out, fmt.Sprintf("size %d agreed", size))
		}
		return out
	}},
	{"core-elementwise", func(t *testing.T) []any {
		a := randA(t, 1, 64)
		b := randA(t, 2, 64)
		sum, _ := Add(a, b)
		prod, _ := Mul(a, b)
		return []any{sum, prod, MulF(a, 1.5)}
	}},
	{"core-matmul-einsum", func(t *testing.T) []any {
		a := randA(t, 3, 64)
		b := randA(t, 4, 64)
		mm, err := MatMul2D(mustA(t, a.RawFloats(), 8, 8), mustA(t, b.RawFloats(), 8, 8))
		if err != nil {
			t.Fatal(err)
		}
		e, err := Einsum("ij,jk->ik", mustA(t, a.RawFloats(), 8, 8), mustA(t, b.RawFloats(), 8, 8))
		if err != nil {
			t.Fatal(err)
		}
		return []any{mm, e}
	}},
	{"core-sort-argsort", func(t *testing.T) []any {
		vals := randA(t, 5, 200).RawFloats()
		vals[3] = math.NaN()
		vals[17] = math.Copysign(0, -1)
		vals[42] = math.Inf(1)
		vals[43] = math.Inf(-1)
		vals[7] = vals[8] // a tie
		src := mustA(t, vals, len(vals))
		s, err := Sort(src)
		if err != nil {
			t.Fatal(err)
		}
		idx, err := ArgSort(src)
		if err != nil {
			t.Fatal(err)
		}
		return []any{s, idx}
	}},
	{"core-reductions", func(t *testing.T) []any {
		a := randA(t, 6, 1000)
		b := randA(t, 7, 1000)
		dot, err := Dot(a, b)
		if err != nil {
			t.Fatal(err)
		}
		mean, err := Mean(a)
		if err != nil {
			t.Fatal(err)
		}
		mn, err := Min(a)
		if err != nil {
			t.Fatal(err)
		}
		mx, err := Max(a)
		if err != nil {
			t.Fatal(err)
		}
		cs, err := CumSum(a, 0)
		if err != nil {
			t.Fatal(err)
		}
		return []any{Sum(a), mean, mn, mx, dot, cs}
	}},
	{"core-shape", func(t *testing.T) []any {
		a := randA(t, 8, 24)
		m := mustA(t, a.RawFloats(), 4, 6)
		tr, err := TransposeAxes(m, 1, 0)
		if err != nil {
			t.Fatal(err)
		}
		r, err := Reshape(m, 3, 8)
		if err != nil {
			t.Fatal(err)
		}
		sl, err := Slice(m, 0, 1, 3)
		if err != nil {
			t.Fatal(err)
		}
		return []any{tr, r, sl}
	}},
	{"core-fft", func(t *testing.T) []any {
		a := randA(t, 9, 256)
		spec, err := FFT(a)
		if err != nil {
			t.Fatal(err)
		}
		back, err := IFFT(spec)
		if err != nil {
			t.Fatal(err)
		}
		return []any{spec, back}
	}},
	{"core-quasirandom", func(t *testing.T) []any {
		sob, err := SobolPoints(64, 4, 0)
		if err != nil {
			t.Fatal(err)
		}
		sob2, err := SobolPoints(32, 4, 1000)
		if err != nil {
			t.Fatal(err)
		}
		hal, err := HaltonPoints(64, 4, 0)
		if err != nil {
			t.Fatal(err)
		}
		return []any{sob, sob2, hal}
	}},
	{"linalg-solve-inv-det", func(t *testing.T) []any {
		a := randA(t, 10, 25)
		// Diagonal dominance keeps the solve well conditioned.
		m := mustA(t, a.RawFloats(), 5, 5)
		md := m.RawFloats()
		for i := range 5 {
			md[i*5+i] += 10
		}
		b := randA(t, 11, 5)
		x, err := Solve(m, b)
		if err != nil {
			t.Fatal(err)
		}
		iv, err := Inv(m)
		if err != nil {
			t.Fatal(err)
		}
		det, err := Det(m)
		if err != nil {
			t.Fatal(err)
		}
		return []any{x, iv, det}
	}},
	{"linalg-factorisations", func(t *testing.T) []any {
		a := randA(t, 12, 36)
		m := mustA(t, a.RawFloats(), 6, 6)
		// Symmetrise, then shift to positive definite.
		sym := make([]float64, 36)
		mm := m.RawFloats()
		for i := range 6 {
			for j := range 6 {
				sym[i*6+j] = (mm[i*6+j] + mm[j*6+i]) / 2
			}
			sym[i*6+i] += 8
		}
		pd := mustA(t, sym, 6, 6)
		q, r, err := QR(pd)
		if err != nil {
			t.Fatal(err)
		}
		chol, err := Cholesky(pd)
		if err != nil {
			t.Fatal(err)
		}
		u, sigma, vt, err := SVD(pd)
		if err != nil {
			t.Fatal(err)
		}
		vals, vecs, err := Eigen(pd)
		if err != nil {
			t.Fatal(err)
		}
		return []any{q, r, chol, u, sigma, vt, vals, vecs}
	}},
	{"linalg-sparse-complex", func(t *testing.T) []any {
		const n = 32
		// Hermitian tridiagonal: real diagonal, imaginary couplings
		// conjugated across the diagonal.
		var hIdx []int64
		var hVal []complex128
		for i := range n {
			hIdx = append(hIdx, int64(i), int64(i))
			hVal = append(hVal, 2+0i)
			if i+1 < n {
				hIdx = append(hIdx, int64(i), int64(i+1))
				hVal = append(hVal, 0.5i)
				hIdx = append(hIdx, int64(i+1), int64(i))
				hVal = append(hVal, -0.5i)
			}
		}
		hIndices, err := FromInts(hIdx, len(hVal), 2)
		if err != nil {
			t.Fatal(err)
		}
		hValues, err := FromComplexes(hVal, len(hVal))
		if err != nil {
			t.Fatal(err)
		}
		h, err := NewSparseCOO(hIndices, hValues, []int{n, n})
		if err != nil {
			t.Fatal(err)
		}
		ones := make([]complex128, n)
		for i := range ones {
			ones[i] = 1
		}
		rhs, err := FromComplexes(ones, n)
		if err != nil {
			t.Fatal(err)
		}
		xCG, err := SpSolveComplexCG(h, rhs, 1e-12, 200)
		if err != nil {
			t.Fatal(err)
		}
		// Genuinely non-Hermitian: different off-diagonal values.
		var gIdx []int64
		var gVal []complex128
		for i := range n {
			gIdx = append(gIdx, int64(i), int64(i))
			gVal = append(gVal, 2+1i)
			if i+1 < n {
				gIdx = append(gIdx, int64(i), int64(i+1))
				gVal = append(gVal, 1)
				gIdx = append(gIdx, int64(i+1), int64(i))
				gVal = append(gVal, 0.25i)
			}
		}
		gIndices, err := FromInts(gIdx, len(gVal), 2)
		if err != nil {
			t.Fatal(err)
		}
		gValues, err := FromComplexes(gVal, len(gVal))
		if err != nil {
			t.Fatal(err)
		}
		g, err := NewSparseCOO(gIndices, gValues, []int{n, n})
		if err != nil {
			t.Fatal(err)
		}
		xBiCG, err := SpSolveComplexBiCGSTAB(g, rhs, 1e-12, 400)
		if err != nil {
			t.Fatal(err)
		}
		vals, vecs, err := SpEigenComplex(h, 4, NewGenerator(11))
		if err != nil {
			t.Fatal(err)
		}
		return []any{xCG, xBiCG, vals, vecs}
	}},
	{"linalg-sparse-cholesky", func(t *testing.T) []any {
		// A shuffled 5-point Laplacian: the ordering does the work,
		// the solve must answer A⁻¹·(A·v) = v for both orderings.
		const n = 100
		g := NewGenerator(31)
		perm := make([]int, n)
		for i := range perm {
			perm[i] = i
		}
		for i := n - 1; i > 0; i-- {
			j := int(g.Next() % uint64(i+1))
			perm[i], perm[j] = perm[j], perm[i]
		}
		label := func(x, y, w int) int { return perm[y*w+x] }
		var idx []int64
		var vals []float64
		add := func(r, c int, v float64) {
			idx = append(idx, int64(r), int64(c))
			vals = append(vals, v)
		}
		const w, h = 10, 10
		for y := range h {
			for x := range w {
				add(label(x, y, w), label(x, y, w), 4)
				if x+1 < w {
					add(label(x, y, w), label(x+1, y, w), -1)
					add(label(x+1, y, w), label(x, y, w), -1)
				}
				if y+1 < h {
					add(label(x, y, w), label(x, y+1, w), -1)
					add(label(x, y+1, w), label(x, y, w), -1)
				}
			}
		}
		indices, err := FromInts(idx, len(vals), 2)
		if err != nil {
			t.Fatal(err)
		}
		valArray, err := FloatsFromArray(vals, len(vals))
		if err != nil {
			t.Fatal(err)
		}
		coo, err := NewSparseCOO(indices, valArray, []int{n, n})
		if err != nil {
			t.Fatal(err)
		}
		csr, err := CSRFromCOO(coo)
		if err != nil {
			t.Fatal(err)
		}
		v := make([]float64, n)
		for i := range v {
			v[i] = float64(i%13) - 6 + 0.5*float64(i%7)
		}
		xTrue := New(Float, n)
		for i := range v {
			xTrue.RawFloats()[i] = v[i]
		}
		b, err := csr.MatVec(xTrue)
		if err != nil {
			t.Fatal(err)
		}
		nat, err := NewSparseCholesky(coo, SparseOrderingNatural)
		if err != nil {
			t.Fatal(err)
		}
		rcm, err := NewSparseCholesky(coo, SparseOrderingReverseCuthillMcKee)
		if err != nil {
			t.Fatal(err)
		}
		xn, err := nat.Solve(b)
		if err != nil {
			t.Fatal(err)
		}
		xr, err := rcm.Solve(b)
		if err != nil {
			t.Fatal(err)
		}
		pn := nat.Permutation()
		pr := rcm.Permutation()
		pnf := make([]float64, len(pn))
		prf := make([]float64, len(pr))
		for i := range pn {
			pnf[i] = float64(pn[i])
			prf[i] = float64(pr[i])
		}
		return []any{pnf, prf, float64(nat.NNZ()), float64(rcm.NNZ()), xn, xr}
	}},
	{"linalg-sparse-lu", func(t *testing.T) []any {
		// A nonsymmetric banded system with real fill: the factor must
		// invert the map the CSR MatVec builds, pivoting included.
		const n = 40
		g := NewGenerator(41)
		var idx []int64
		var vals []float64
		add := func(r, c int, v float64) {
			idx = append(idx, int64(r), int64(c))
			vals = append(vals, v)
		}
		for i := range n {
			add(i, i, 5+2*g.Unit())
			if i+1 < n {
				add(i, i+1, -1-g.Unit())
				add(i+1, i, -1-g.Unit())
			}
			if i+3 < n {
				add(i, i+3, -0.6*g.Unit())
			}
			if i+4 < n {
				add(i+4, i, -0.4*g.Unit())
			}
		}
		indices, err := FromInts(idx, len(vals), 2)
		if err != nil {
			t.Fatal(err)
		}
		valArray, err := FloatsFromArray(vals, len(vals))
		if err != nil {
			t.Fatal(err)
		}
		coo, err := NewSparseCOO(indices, valArray, []int{n, n})
		if err != nil {
			t.Fatal(err)
		}
		csr, err := CSRFromCOO(coo)
		if err != nil {
			t.Fatal(err)
		}
		v := make([]float64, n)
		for i := range v {
			v[i] = float64(i%9) - 4 + 0.25*float64(i%5)
		}
		xTrue := New(Float, n)
		for i := range v {
			xTrue.RawFloats()[i] = v[i]
		}
		b, err := csr.MatVec(xTrue)
		if err != nil {
			t.Fatal(err)
		}
		f, err := NewSparseLU(coo)
		if err != nil {
			t.Fatal(err)
		}
		x, err := f.Solve(b)
		if err != nil {
			t.Fatal(err)
		}
		p := f.Permutation()
		pf := make([]float64, len(p))
		for i := range p {
			pf[i] = float64(p[i])
		}
		return []any{pf, float64(f.NNZ()), x}
	}},
	{"integrate-fem-poisson", func(t *testing.T) []any {
		// The manufactured solution u = sin(πx)·sin(πy) on a 10×10
		// structured mesh of the unit square: assemble, lift the
		// boundary, solve through the sparse Cholesky.
		const m = 10
		n := (m + 1) * (m + 1)
		vertices := make([]float64, 2*n)
		for j := range m + 1 {
			for i := range m + 1 {
				vertices[2*(j*(m+1)+i)] = float64(i) / float64(m)
				vertices[2*(j*(m+1)+i)+1] = float64(j) / float64(m)
			}
		}
		at := func(i, j int) int64 { return int64(j*(m+1) + i) }
		idx := make([]int64, 0, 6*m*m)
		for j := range m {
			for i := range m {
				idx = append(idx, at(i, j), at(i+1, j), at(i+1, j+1), at(i, j), at(i+1, j+1), at(i, j+1))
			}
		}
		vArr, err := FromFloats(vertices, n, 2)
		if err != nil {
			t.Fatal(err)
		}
		tArr, err := FromInts(idx, m*m*2, 3)
		if err != nil {
			t.Fatal(err)
		}
		mesh, err := NewTriangleMesh2D(vArr, tArr)
		if err != nil {
			t.Fatal(err)
		}
		sol := func(x, y float64) float64 { return math.Sin(math.Pi*x) * math.Sin(math.Pi*y) }
		src := func(x, y float64) float64 { return 2 * math.Pi * math.Pi * sol(x, y) }
		var bound []int
		var vals []float64
		for j := range m + 1 {
			for i := range m + 1 {
				if i == 0 || i == m || j == 0 || j == m {
					bound = append(bound, j*(m+1)+i)
					vals = append(vals, sol(float64(i)/float64(m), float64(j)/float64(m)))
				}
			}
		}
		u, err := SolvePoissonFEM2D(mesh, src, FEMPoissonOptions{Kappa: 1, DirichletNodes: bound, DirichletValues: vals, Ordering: SparseOrderingReverseCuthillMcKee})
		if err != nil {
			t.Fatal(err)
		}
		first := make([]float64, 0, 12)
		for i := range 12 {
			first = append(first, u.FloatAt(i))
		}
		return []any{first, u.FloatAt(n / 2), u.FloatAt(n - 1)}
	}},
	{"signal-welch-savgol", func(t *testing.T) []any {
		x := randA(t, 13, 512)
		freqs, psd, err := WelchPSD(x, 1000, 128, 64, "hann")
		if err != nil {
			t.Fatal(err)
		}
		sm, err := SavitzkyGolay(x, 11, 3)
		if err != nil {
			t.Fatal(err)
		}
		return []any{freqs, psd, sm}
	}},
	{"signal-wavelets", func(t *testing.T) []any {
		x := randA(t, 14, 128)
		coef, err := DWT(x, 3)
		if err != nil {
			t.Fatal(err)
		}
		back, err := IDWT(coef, 3)
		if err != nil {
			t.Fatal(err)
		}
		cw, err := CWT(x, Morlet, []float64{1, 2, 4, 8}, 1)
		if err != nil {
			t.Fatal(err)
		}
		return []any{coef, back, cw}
	}},
	{"signal-lombscargle-conv", func(t *testing.T) []any {
		g := NewGenerator(15)
		times, err := Floats(g, 100)
		if err != nil {
			t.Fatal(err)
		}
		acc := 0.0
		for i, v := range times.RawFloats() {
			acc += v + 0.1
			times.RawFloats()[i] = acc // irregular but increasing
		}
		vals := randA(t, 16, 100)
		freqs, power, err := LombScargle(times, vals, 0.1, 5, 32)
		if err != nil {
			t.Fatal(err)
		}
		input := mustA(t, randA(t, 17, 64).RawFloats(), 1, 1, 64)
		kernel := mustA(t, randA(t, 18, 5).RawFloats(), 1, 1, 5)
		conv, err := Conv1D(input, kernel, nil, 1, 0, 1)
		if err != nil {
			t.Fatal(err)
		}
		return []any{freqs, power, conv}
	}},
	{"signal-filters-stencils", func(t *testing.T) []any {
		x := randA(t, 19, 256)
		b, a, err := ButterworthLowPass(4, 1000, 100)
		if err != nil {
			t.Fatal(err)
		}
		filt, err := FilterApply(b, a, x)
		if err != nil {
			t.Fatal(err)
		}
		grad, err := Gradient1D(x, 0.5)
		if err != nil {
			t.Fatal(err)
		}
		m := mustA(t, randA(t, 20, 64).RawFloats(), 8, 8)
		lap, err := Laplacian(m, 1.0, 1.0)
		if err != nil {
			t.Fatal(err)
		}
		return []any{filt, grad, lap}
	}},
	{"stats-moments-quantiles", func(t *testing.T) []any {
		a := randA(t, 21, 1000)
		v, err := Var(a)
		if err != nil {
			t.Fatal(err)
		}
		s, err := Std(a)
		if err != nil {
			t.Fatal(err)
		}
		med, err := Median(a)
		if err != nil {
			t.Fatal(err)
		}
		q, err := Quantile(a, []float64{0.05, 0.25, 0.5, 0.75, 0.95})
		if err != nil {
			t.Fatal(err)
		}
		mean, err := Mean(a)
		if err != nil {
			t.Fatal(err)
		}
		return []any{mean, v, s, med, q}
	}},
	{"stats-correlation-regression", func(t *testing.T) []any {
		x := randA(t, 22, 200)
		ac, err := Autocorrelate(x, 16)
		if err != nil {
			t.Fatal(err)
		}
		pac, err := PartialAutocorrelate(x, 8)
		if err != nil {
			t.Fatal(err)
		}
		// The design carries its own intercept column.
		xd := x.RawFloats()
		design := make([]float64, 400)
		for i := range 200 {
			design[i*2] = 1
			design[i*2+1] = xd[i]
		}
		lr, err := LinearRegression(mustA(t, design, 200, 2), randA(t, 23, 200))
		if err != nil {
			t.Fatal(err)
		}
		return []any{ac, pac, lr.Coefficients, lr.StandardErrors, lr.PValues,
			lr.ResidualVariance, lr.RSquared}
	}},
	{"stats-poisson-regression", func(t *testing.T) []any {
		// Counts from the seeded generator: one draw per row at the
		// mean the true coefficients produce.
		g := NewGenerator(24)
		xv := randA(t, 23, 120)
		design := make([]float64, 240)
		y := make([]float64, 120)
		for i := range 120 {
			design[i*2] = 1
			design[i*2+1] = xv.FloatAt(i)
			counts, err := PoissonDraws(g, 1, math.Exp(0.3+0.7*xv.FloatAt(i)))
			if err != nil {
				t.Fatal(err)
			}
			y[i] = counts.FloatAt(0)
		}
		res, err := PoissonRegression(mustA(t, design, 120, 2), mustA(t, y, 120))
		if err != nil {
			t.Fatal(err)
		}
		return []any{res.Coefficients, res.StandardErrors, res.PValues,
			res.Fitted, res.LogLikelihood, res.Iterations}
	}},
	{"stats-distributions", func(t *testing.T) []any {
		tt, df, p, err := WelchTTest(randA(t, 24, 50), randA(t, 25, 60))
		if err != nil {
			t.Fatal(err)
		}
		gc, err := GammaCDF(2.5, 3, 1.5)
		if err != nil {
			t.Fatal(err)
		}
		ec, err := ExponentialCDF(1.25, 2)
		if err != nil {
			t.Fatal(err)
		}
		sc, err := StudentTCDF(1.5, 7)
		if err != nil {
			t.Fatal(err)
		}
		pc, err := PoissonCDF(3, 2.5)
		if err != nil {
			t.Fatal(err)
		}
		bc, err := BinomialCDF(4, 10, 0.35)
		if err != nil {
			t.Fatal(err)
		}
		nq, err := NormalQuantile(0.975)
		if err != nil {
			t.Fatal(err)
		}
		return []any{NormalCDF(1.96), tt, df, p, gc, ec, sc, pc, bc, nq}
	}},
	{"integrate-quadrature-ode", func(t *testing.T) []any {
		q, qerr, err := IntegrateFunction(func(x float64) (float64, error) {
			return math.Exp(-x * x), nil
		}, 0, 1, QuadratureOptions{})
		if err != nil {
			t.Fatal(err)
		}
		decay := func(t float64, y *Array) (*Array, error) { return MulF(y, -1), nil }
		y0 := mustA(t, []float64{1}, 1)
		end, err := IntegrateODE(decay, 0, 2, y0, ODEOptions{MaxSteps: 10000})
		if err != nil {
			t.Fatal(err)
		}
		nd, err := IntegrateND(func(x []float64) float64 {
			return math.Exp(-x[0] - x[1]*x[1])
		}, []float64{0, 0}, []float64{1, 1}, CubatureOptions{})
		if err != nil {
			t.Fatal(err)
		}
		heat, err := IntegrateHeat1D(mustA(t, []float64{1, 2, 3, 4, 5, 6, 7, 8}, 8),
			0.1, 0.1, 0.05, 0.005, 3, 0, 0)
		if err != nil {
			t.Fatal(err)
		}
		return []any{q, qerr, end, nd, heat}
	}},
	{"optim-roots-minima", func(t *testing.T) []any {
		root, err := FindRoot(func(x float64) float64 { return math.Cos(x) - x }, 0, 1, 1e-12)
		if err != nil {
			t.Fatal(err)
		}
		rosen := func(p *Array) (float64, error) {
			x := p.FloatAt(0)
			y := p.FloatAt(1)
			return (1-x)*(1-x) + 100*(y-x*x)*(y-x*x), nil
		}
		pt, val, err := Minimise(rosen, mustA(t, []float64{-1.2, 1}, 2),
			MinimiseOptions{MaxIterations: 500, Tolerance: 1e-12})
		if err != nil {
			t.Fatal(err)
		}
		return []any{root, pt, val}
	}},
	{"optim-bounded-minima", func(t *testing.T) []any {
		// The bounded solver on the wall case: with x forced past 1.5
		// the Rosenbrock neck at (1, 1) is infeasible and the minimum
		// sits at (1.5, 2.25) with value 0.25, the first coordinate
		// pinned by the projection and released never.
		rosen := func(p *Array) (float64, error) {
			x := p.FloatAt(0)
			y := p.FloatAt(1)
			return (1-x)*(1-x) + 100*(y-x*x)*(y-x*x), nil
		}
		pt, val, err := MinimiseLBFGS(rosen, nil, mustA(t, []float64{-1.2, 1}, 2),
			LBFGSOptions{Tolerance: 1e-10, Lower: []float64{1.5, math.Inf(-1)}})
		if err != nil {
			t.Fatal(err)
		}
		refused := false
		_, _, err = MinimiseLBFGS(rosen, nil, mustA(t, []float64{0, 0}, 2),
			LBFGSOptions{Lower: []float64{2}, Upper: []float64{1}})
		if err != nil {
			refused = true
		}
		return []any{pt, val, refused}
	}},
	{"optim-constrained-minima", func(t *testing.T) []any {
		// The augmented Lagrangian on an active inequality: the bowl
		// around (2, -1) cut by x + y ≤ 0 bottoms out on the wall at
		// (1.5, -1.5) with value 0.5.
		bowl := func(p *Array) (float64, error) {
			dx := p.FloatAt(0) - 2
			dy := p.FloatAt(1) + 1
			return dx*dx + dy*dy, nil
		}
		A := mustA(t, []float64{1, 1}, 1, 2)
		pt, val, err := MinimiseConstrained(bowl, nil, mustA(t, []float64{4, 4}, 2),
			LinearConstraints{A: A, Lower: []float64{math.Inf(-1)}, Upper: []float64{0}},
			LBFGSOptions{Tolerance: 1e-10})
		if err != nil {
			t.Fatal(err)
		}
		refused := false
		_, _, err = MinimiseConstrained(bowl, nil, mustA(t, []float64{0, 0}, 2),
			LinearConstraints{Lower: []float64{0}, Upper: []float64{1}}, LBFGSOptions{})
		if err != nil {
			refused = true
		}
		return []any{pt, val, refused}
	}},
	{"grad-backward", func(t *testing.T) []any {
		x := FromArray(mustA(t, []float64{1.5, -2, 3}, 3), true)
		loss, err := x.Mul(x)
		if err != nil {
			t.Fatal(err)
		}
		l, err := loss.Sum()
		if err != nil {
			t.Fatal(err)
		}
		if err := l.Backward(); err != nil {
			t.Fatal(err)
		}
		return []any{x.Grad()}
	}},
	{"io-roundtrips", func(t *testing.T) []any {
		dir := t.TempDir()
		a := randA(t, 26, 24)
		m := mustA(t, a.RawFloats(), 4, 6)
		fitsPath := filepath.Join(dir, "o.fits")
		if err := SaveFITS(fitsPath, m, map[string]string{"OBJECT": "oracle"}); err != nil {
			t.Fatal(err)
		}
		backFits, hdr, err := LoadFITS(fitsPath)
		if err != nil {
			t.Fatal(err)
		}
		ncPath := filepath.Join(dir, "o.nc")
		dims := []NetCDFDim{{Name: "row", Length: 4}, {Name: "col", Length: 6}}
		vars := []NetCDFVar{{Name: "field", Dims: []string{"row", "col"}, Values: m}}
		if err := SaveNetCDF(ncPath, dims, vars, map[string]string{"title": "oracle"}); err != nil {
			t.Fatal(err)
		}
		_, backNc, ncAttrs, err := LoadNetCDF(ncPath)
		if err != nil {
			t.Fatal(err)
		}
		return []any{backFits, hdr["OBJECT"], backNc[0].Values, ncAttrs["title"]}
	}},
	{"core-views-and-int-precision", func(t *testing.T) []any {
		// Views, the integer range above 2^53 and a widened query
		// array: the 2026-09 review found defects in all three.
		x := randA(t, 41, 12)
		view, err := Slice(x, 0, 3, 9)
		if err != nil {
			t.Fatal(err)
		}
		pow, err := PowI(view, 3)
		if err != nil {
			t.Fatal(err)
		}
		big, err := FromInts([]int64{1 << 53, 1<<53 + 1, -(1 << 53)}, 3)
		if err != nil {
			t.Fatal(err)
		}
		hi, err := ArgMax(big)
		if err != nil {
			t.Fatal(err)
		}
		lo, err := ArgMin(big)
		if err != nil {
			t.Fatal(err)
		}
		// A float32 view whose payload is longer than its extent: the
		// widening inside Interpolate2D used to walk the payload.
		xs, err := FromFloat32s(make([]float32, x.Len()), x.Len())
		if err != nil {
			t.Fatal(err)
		}
		for i := range xs.Len() {
			// Stay inside the (3, 4) grid's closed domain.
			xs.SetFloatAt(i, float64(i%4))
		}
		viewXs, err := Slice(xs, 0, 0, view.Len())
		if err != nil {
			t.Fatal(err)
		}
		grid, err := FromFloats(make([]float64, 12), 3, 4)
		if err != nil {
			t.Fatal(err)
		}
		// The y queries need their own range: the grid's y domain is
		// [0, rows−1], narrower than x's.
		ys, err := FromFloat32s(make([]float32, viewXs.Len()), viewXs.Len())
		if err != nil {
			t.Fatal(err)
		}
		for i := range ys.Len() {
			ys.SetFloatAt(i, float64(i%3))
		}
		interp, err := Interpolate2D(grid, viewXs, ys, 0, 0, 1, 1)
		if err != nil {
			t.Fatal(err)
		}
		return []any{pow, hi, lo, interp}
	}},
	{"io-hdf5-fixture", func(t *testing.T) []any {
		// The HDF5 reference-library fixture: contiguous ints, a chunked
		// deflate+shuffle float vector, a float32 matrix in a group,
		// and attributes inherited from the groups.
		sets, err := LoadHDF5(filepath.Join("io", "testdata", "h5", "fixture.h5"))
		if err != nil {
			t.Fatal(err)
		}
		out := []any{}
		for _, d := range sets {
			out = append(out, d.Path, d.Values)
			for _, k := range slices.Sorted(maps.Keys(d.Attrs)) {
				out = append(out, k, d.Attrs[k])
			}
		}
		return out
	}},
	{"io-hostile-inputs", func(t *testing.T) []any {
		// A header that lies about its sizes must be refused, never
		// allocated and never panicked over: both files here are a few
		// dozen bytes and claim data no file could hold.
		dir := t.TempDir()
		ncPath := filepath.Join(dir, "hostile.nc")
		if err := os.WriteFile(ncPath, hostileOracleHeader(), 0o644); err != nil {
			t.Fatal(err)
		}
		_, _, _, ncErr := LoadNetCDF(ncPath)
		fitsPath := filepath.Join(dir, "hostile.fits")
		if err := os.WriteFile(fitsPath, hostileOracleTable(), 0o644); err != nil {
			t.Fatal(err)
		}
		_, fitsErr := LoadFITSTable(fitsPath)
		return []any{ncErr != nil, fitsErr != nil}
	}},
	{"core-float16", func(t *testing.T) []any {
		// The half dtype end to end: narrowing of values that straddle
		// the format's corners, arithmetic through the promotion
		// ladder, ordering that must widen before it compares.
		vals := []float64{1, -2.5, 0.25, 65504, -65504, 1.0 / 16384, 1.0 / 16777216, 0.1, 2048.5}
		h, err := FromFloat16s(vals, len(vals))
		if err != nil {
			t.Fatal(err)
		}
		s := Sum(h)
		sorted, err := Sort(h)
		if err != nil {
			t.Fatal(err)
		}
		prod := MulF(h, 2)
		widened, err := Add(h, mustA(t, make([]float64, len(vals)), len(vals)))
		if err != nil {
			t.Fatal(err)
		}
		ints, err := Astype(h, Int)
		if err != nil {
			t.Fatal(err)
		}
		return []any{h, s, sorted, prod, widened, ints,
			HalfToFloat64(HalfFromFloat64(0.1)), HalfToFloat64(0x7BFF),
			HalfToFloat64(0x0001), HalfFromFloat64(65520) == 0x7C00,
			HalfFromFloat64(-1.0/33554432.0) == 0x8000}
	}},
	{"signal-kalman-arma", func(t *testing.T) []any {
		// The linear filter on a scalar random walk with noisy
		// measurements from the seeded generator, the unscented filter
		// over the same exactly linear model, and the AR fit with its
		// theoretical spectrum.
		g := NewGenerator(50)
		z, err := Floats(g, 40)
		if err != nil {
			t.Fatal(err)
		}
		one := mustA(t, []float64{1}, 1, 1)
		qv := mustA(t, []float64{0.01}, 1, 1)
		rv := mustA(t, []float64{1}, 1, 1)
		zero := mustA(t, []float64{0}, 1)
		pv := mustA(t, []float64{1}, 1, 1)
		res, err := KalmanFilter(z, one, one, KalmanOptions{
			InitialState: zero, InitialCovariance: pv,
			ProcessNoise: qv, MeasurementNoise: rv})
		if err != nil {
			t.Fatal(err)
		}
		uk, err := UnscentedKalmanFilter(z,
			func(x *Array) (*Array, error) { return MulF(x, 1), nil },
			func(x *Array) (*Array, error) { return MulF(x, 1), nil },
			KalmanOptions{
				InitialState: zero, InitialCovariance: pv,
				ProcessNoise: qv, MeasurementNoise: rv})
		if err != nil {
			t.Fatal(err)
		}
		x, err := Floats(NewGenerator(51), 300)
		if err != nil {
			t.Fatal(err)
		}
		ar, err := EstimateAR(x, 2)
		if err != nil {
			t.Fatal(err)
		}
		freqs, psd, err := ARMASpectrum(ar, 32)
		if err != nil {
			t.Fatal(err)
		}
		return []any{res.States, res.Covariances, res.Innovations, res.LogLikelihood,
			uk.LogLikelihood, uk.States, ar.AR, ar.InnovationVariance, ar.AIC, freqs, psd}
	}},
	{"signal-windows-filtfilt-dwt", func(t *testing.T) []any {
		// The window catalogue, the zero-phase filter, the 2-D median
		// and the Daubechies transform over seeded inputs.
		hann, err := WindowHann(16, false)
		if err != nil {
			t.Fatal(err)
		}
		kaiser, err := WindowKaiser(16, 4.5, true)
		if err != nil {
			t.Fatal(err)
		}
		x := randA(t, 52, 128)
		b, a, err := ButterworthLowPass(3, 100, 20)
		if err != nil {
			t.Fatal(err)
		}
		ff, err := Filtfilt(b, a, x)
		if err != nil {
			t.Fatal(err)
		}
		img := mustA(t, randA(t, 53, 64).RawFloats(), 8, 8)
		med, err := MedianFilter2D(img, 3)
		if err != nil {
			t.Fatal(err)
		}
		coef, err := DaubechiesDWT(x, DB4, 2, DWTPeriodic)
		if err != nil {
			t.Fatal(err)
		}
		back, err := DaubechiesIDWT(coef, DB4, 2, DWTPeriodic)
		if err != nil {
			t.Fatal(err)
		}
		return []any{hann, kaiser, ff, med, coef, back}
	}},
	{"stats-distributions2-multipletest", func(t *testing.T) []any {
		// The second-league distributions and the corrections, on
		// fixed parameters and the classic Benjamini-Hochberg vector.
		wc, err := WeibullCDF(1.5, 2, 3)
		if err != nil {
			t.Fatal(err)
		}
		wq, err := WeibullQuantile(0.4, 2, 3)
		if err != nil {
			t.Fatal(err)
		}
		lc, err := LognormalCDF(1, 0, 0.5)
		if err != nil {
			t.Fatal(err)
		}
		pq, err := ParetoQuantile(0.5, 1, 3)
		if err != nil {
			t.Fatal(err)
		}
		nb, err := NegativeBinomialCDF(5, 3, 0.4)
		if err != nil {
			t.Fatal(err)
		}
		ncx, err := NoncentralChiSquareCDF(9, 4, 2.5)
		if err != nil {
			t.Fatal(err)
		}
		nct, err := NoncentralTCDF(2, 8, 3)
		if err != nil {
			t.Fatal(err)
		}
		ncf, err := NoncentralFQuantile(0.5, 4, 10, 2)
		if err != nil {
			t.Fatal(err)
		}
		draws, err := DirichletDraws(NewGenerator(54), 12, []float64{2, 3, 4})
		if err != nil {
			t.Fatal(err)
		}
		px := randA(t, 55, 100)
		py := randA(t, 56, 100)
		rho, err := SpearmanRho(px, py)
		if err != nil {
			t.Fatal(err)
		}
		tau, err := KendallTau(px, py)
		if err != nil {
			t.Fatal(err)
		}
		p := []float64{0.001, 0.008, 0.039, 0.041, 0.042, 0.06, 0.074, 0.205,
			0.212, 0.216, 0.222, 0.251, 0.269, 0.275, 0.34, 0.341, 0.384,
			0.456, 0.657, 0.876}
		bonf, err := Bonferroni(p)
		if err != nil {
			t.Fatal(err)
		}
		holm, err := Holm(p)
		if err != nil {
			t.Fatal(err)
		}
		bh, err := BenjaminiHochberg(p)
		if err != nil {
			t.Fatal(err)
		}
		return []any{wc, wq, lc, pq, nb, ncx, nct, ncf, draws, rho, tau, bonf, holm, bh}
	}},
	{"stats-regression2", func(t *testing.T) []any {
		// The regularised, robust and quantile fits on one seeded
		// design, with one gross outlier the robust fit must survive.
		g := NewGenerator(57)
		xv, err := Floats(g, 60)
		if err != nil {
			t.Fatal(err)
		}
		n := xv.Len()
		design := make([]float64, 0, 2*n)
		y := make([]float64, n)
		for i := range n {
			design = append(design, 1, xv.FloatAt(i))
			y[i] = 1 + 2*xv.FloatAt(i) + 0.3*(float64(i%7)-3)
		}
		y[7] += 100
		dArr := mustA(t, design, n, 2)
		yArr := mustA(t, y, n)
		xOnly := make([]float64, n)
		for i := range n {
			xOnly[i] = xv.FloatAt(i)
		}
		xArr := mustA(t, xOnly, n, 1)
		lasso, err := Lasso(xArr, yArr, 0.05)
		if err != nil {
			t.Fatal(err)
		}
		en, err := ElasticNet(xArr, yArr, 0.05, 0.5)
		if err != nil {
			t.Fatal(err)
		}
		huber, err := HuberRegression(dArr, yArr)
		if err != nil {
			t.Fatal(err)
		}
		si, sl, err := TheilSenRegression(xv, yArr)
		if err != nil {
			t.Fatal(err)
		}
		qr, err := QuantileRegression(dArr, yArr, 0.75)
		if err != nil {
			t.Fatal(err)
		}
		return []any{lasso.Intercept, lasso.Coefficients, lasso.Iterations,
			en.Coefficients, huber.Coefficients, huber.Scale, huber.Iterations,
			si, sl, qr.Coefficients, qr.Objective}
	}},
	{"stats-unsupervised", func(t *testing.T) []any {
		// PCA over a seeded cloud, k-means over two blobs, the mixture
		// over a univariate draw and the Gaussian-process posterior.
		g := NewGenerator(58)
		a1, err := Normal(g, 48, 0, 1)
		if err != nil {
			t.Fatal(err)
		}
		a2, err := Normal(g, 48, 0, 1)
		if err != nil {
			t.Fatal(err)
		}
		a3, err := Normal(g, 48, 0, 1)
		if err != nil {
			t.Fatal(err)
		}
		cloud := make([]float64, 144)
		for i := range 48 {
			cloud[3*i] = 3 * a1.FloatAt(i)
			cloud[3*i+1] = a2.FloatAt(i)
			cloud[3*i+2] = 0.1 * a3.FloatAt(i)
		}
		pca, err := PCA(mustA(t, cloud, 48, 3))
		if err != nil {
			t.Fatal(err)
		}
		bg := NewGenerator(59)
		b1, err := Normal(bg, 40, 0, 1)
		if err != nil {
			t.Fatal(err)
		}
		b2, err := Normal(bg, 40, 0, 1)
		if err != nil {
			t.Fatal(err)
		}
		b3, err := Normal(bg, 40, 8, 1)
		if err != nil {
			t.Fatal(err)
		}
		b4, err := Normal(bg, 40, 8, 1)
		if err != nil {
			t.Fatal(err)
		}
		blobs := make([]float64, 160)
		for i := range 40 {
			blobs[2*i] = b1.FloatAt(i)
			blobs[2*i+1] = b2.FloatAt(i)
			blobs[40+2*i] = b3.FloatAt(i)
			blobs[40+2*i+1] = b4.FloatAt(i)
		}
		km, err := KMeans(NewGenerator(60), mustA(t, blobs, 80, 2), 2)
		if err != nil {
			t.Fatal(err)
		}
		centres := make([]float64, 0, 4)
		for _, c := range km.Centres {
			centres = append(centres, c...)
		}
		mg := NewGenerator(61)
		hi, err := Normal(mg, 40, 6, 1)
		if err != nil {
			t.Fatal(err)
		}
		lo, err := Normal(mg, 40, 0, 1)
		if err != nil {
			t.Fatal(err)
		}
		mix := make([]float64, 80)
		for i := range 40 {
			mix[2*i] = hi.FloatAt(i)
			mix[2*i+1] = lo.FloatAt(i)
		}
		gmm, err := GaussianMixture(NewGenerator(62), mustA(t, mix, 80, 1), 2)
		if err != nil {
			t.Fatal(err)
		}
		means := make([]float64, 0, len(gmm.Means))
		for _, m := range gmm.Means {
			means = append(means, m...)
		}
		trainX := mustA(t, randA(t, 63, 16).RawFloats(), 16, 1)
		sinVals, err := Sin(trainX)
		if err != nil {
			t.Fatal(err)
		}
		trainY, err := Reshape(sinVals, 16)
		if err != nil {
			t.Fatal(err)
		}
		testX := mustA(t, randA(t, 64, 8).RawFloats(), 8, 1)
		kern, err := SquaredExponentialKernel(1)
		if err != nil {
			t.Fatal(err)
		}
		gp, err := GaussianProcessRegression(kern, trainX, trainY, 0.05, testX)
		if err != nil {
			t.Fatal(err)
		}
		mll, err := MarginalLogLikelihood(kern, trainX, trainY, 0.05)
		if err != nil {
			t.Fatal(err)
		}
		return []any{pca.Loadings, pca.ExplainedVarianceRatio, float64(km.Iterations),
			centres, km.Inertia, gmm.Weights, means, gmm.BIC, gp.Mean, gp.Variance, mll}
	}},
	{"stats-contingency", func(t *testing.T) []any {
		// The exact and the asymptotic table tests over fixed tables,
		// every alternative, and the effect sizes beside them.
		out := []any{}
		tables := [][]float64{
			{12, 5, 7, 10},
			{8, 2, 1, 5},
			{17, 0, 0, 23},
			{21, 8, 3, 9, 15, 11, 4, 12, 30},
		}
		for ti, tab := range tables[:3] {
			a, _, err := FisherExactTest(mustA(t, tab, 2, 2), TwoSided)
			if err != nil {
				t.Fatal(err)
			}
			less, _, err := FisherExactTest(mustA(t, tab, 2, 2), Less)
			if err != nil {
				t.Fatal(err)
			}
			greater, or, err := FisherExactTest(mustA(t, tab, 2, 2), Greater)
			if err != nil {
				t.Fatal(err)
			}
			out = append(out, a, less, greater, or)
			p, err := McNemarTest(mustA(t, tab, 2, 2))
			if err != nil {
				t.Fatal(err)
			}
			out = append(out, p)
			if ti < 2 {
				v, err := CramersV(mustA(t, tab, 2, 2))
				if err != nil {
					t.Fatal(err)
				}
				out = append(out, v)
			}
		}
		chi2, df, p, err := ChiSquareIndependence(mustA(t, tables[3], 3, 3))
		if err != nil {
			t.Fatal(err)
		}
		v, err := CramersV(mustA(t, tables[3], 3, 3))
		if err != nil {
			t.Fatal(err)
		}
		out = append(out, chi2, df, p, v)
		return out
	}},
	{"stats-mixedmodel", func(t *testing.T) []any {
		// A balanced random-intercept fit and a random-slope fit, over
		// formula-driven data no generator touches.
		const groups8 = 8
		const per = 6
		y := make([]float64, 0, groups8*per)
		labels := make([]int, 0, groups8*per)
		for g := range groups8 {
			effect := 2 * math.Sin(1.7*float64(g)+0.4)
			for i := range per {
				y = append(y, 5+effect+wobble(g*per+i))
				labels = append(labels, g)
			}
		}
		ones := make([]float64, len(y))
		for i := range ones {
			ones[i] = 1
		}
		res, err := LinearMixedModel(mustA(t, y, len(y)), mustA(t, ones, len(y), 1),
			mustA(t, ones, len(y), 1), labels)
		if err != nil {
			t.Fatal(err)
		}
		out := []any{res.Coefficients, res.StandardErrors,
			res.RandomEffects[0], res.RandomEffects[7], res.RandomCovariance,
			res.ResidualVariance, res.LogLikelihood, res.Converged,
			fmt.Sprintf("%v", res.GroupLabels)}
		// The slope fit: the random design carries the covariate
		// alone, the identified configuration.
		slopes := []float64{0.9, -1.1, 1.9, -0.3, -1.8, 0.4}
		sy := make([]float64, 0, len(slopes)*per)
		sx := make([]float64, 0, 2*len(slopes)*per)
		sz := make([]float64, 0, len(slopes)*per)
		slabels := make([]int, 0, len(slopes)*per)
		jitter := make([]float64, 0, len(slopes)*per)
		for g := range slopes {
			for _, x := range []float64{-1, -0.6, -0.2, 0.2, 0.6, 1} {
				jitter = append(jitter, wobble(len(jitter)+13)*0.1)
				slabels = append(slabels, g)
				sz = append(sz, x)
			}
		}
		mean := 0.0
		for _, j := range jitter {
			mean += j
		}
		mean /= float64(len(jitter))
		for g, s := range slopes {
			for k := range per {
				i := g*per + k
				x := sz[i]
				sy = append(sy, 1+2*x+0.5*s*x+0.1*(jitter[i]-mean))
				sx = append(sx, 1, x)
			}
		}
		slope, err := LinearMixedModel(mustA(t, sy, len(sy)), mustA(t, sx, len(sy), 2),
			mustA(t, sz, len(sz), 1), slabels)
		if err != nil {
			t.Fatal(err)
		}
		return append(out, slope.Coefficients, slope.RandomCovariance,
			slope.ResidualVariance, slope.Converged)
	}},
	{"stats-hmm", func(t *testing.T) []any {
		// The scaled recursions, the decode and the Baum-Welch fit on
		// a fixed sequence under a fixed model.
		model, err := NewHiddenMarkovModel([]float64{0.6, 0.4},
			[]float64{0.7, 0.3, 0.2, 0.8}, []float64{0.9, 0.1, 0.25, 0.75})
		if err != nil {
			t.Fatal(err)
		}
		observations := []int{0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0}
		filtered, ll, err := model.Forward(observations)
		if err != nil {
			t.Fatal(err)
		}
		smoothed, sll, err := model.Smooth(observations)
		if err != nil {
			t.Fatal(err)
		}
		path, pathProb, err := model.Viterbi(observations)
		if err != nil {
			t.Fatal(err)
		}
		out := []any{filtered[len(observations)-1], smoothed[0], ll, sll,
			fmt.Sprintf("%v", path), pathProb}
		seq := make([]int, 240)
		for i := range seq {
			// The wiggle stays inside ±0.4, so the shifted scale is
			// positive and the modulo lands inside the symbol set.
			seq[i] = int(wobble(i)*100+200) % 3
		}
		fit, err := FitHiddenMarkovModel(NewGenerator(77), seq, 2, 3)
		if err != nil {
			t.Fatal(err)
		}
		return append(out, fit.Model.Initial, fit.Model.Transition, fit.Model.Emission,
			fit.LogLikelihood, fit.Converged)
	}},
	{"stats-hierarchy", func(t *testing.T) []any {
		// The five linkages over one fixed two-column sample, with the
		// cuts the dendrogram answers.
		sample := make([]float64, 24)
		for i := range 12 {
			sample[2*i] = wobble(2*i+5)*3 + float64(i%4)
			sample[2*i+1] = wobble(2*i+31) * 2
		}
		out := []any{}
		for _, method := range []Linkage{SingleLinkage, CompleteLinkage, AverageLinkage, CentroidLinkage, WardLinkage} {
			d, err := HierarchicalClustering(mustA(t, sample, 12, 2), method)
			if err != nil {
				t.Fatal(err)
			}
			labels, err := d.Cut(3)
			if err != nil {
				t.Fatal(err)
			}
			out = append(out, d.Heights, fmt.Sprintf("%v", labels), d.Sizes[10])
		}
		first, err := HierarchicalClustering(mustA(t, sample, 12, 2), WardLinkage)
		if err != nil {
			t.Fatal(err)
		}
		byHeight, err := first.CutHeight(first.Heights[8])
		if err != nil {
			t.Fatal(err)
		}
		return append(out, fmt.Sprintf("%v", byHeight))
	}},
	{"integrate-stiff-solvers", func(t *testing.T) []any {
		// The stiff batch on one decay problem, the index-1 DAE on its
		// circuit, the collocation on a linear two-point problem, the
		// symplectic pair and the advection pair.
		decay := func(t float64, y *Array) (*Array, error) { return MulF(y, -1), nil }
		y0 := mustA(t, []float64{1}, 1)
		stats := &BDFVarStats{}
		bdf, err := IntegrateBDFVar(decay, 0, 2, y0, BDFVarOptions{MaxSteps: 10000, Stats: stats})
		if err != nil {
			t.Fatal(err)
		}
		ros, err := IntegrateROS4(decay, 0, 2, y0, ODEOptions{MaxSteps: 10000})
		if err != nil {
			t.Fatal(err)
		}
		daeRHS := func(t float64, y *Array) (*Array, error) {
			out, err := Zeros(Float, 2)
			if err != nil {
				return nil, err
			}
			out.SetFloatAt(0, 1-y.FloatAt(0))
			out.SetFloatAt(1, y.FloatAt(1)-y.FloatAt(0))
			return out, nil
		}
		mass, err := FromFloats([]float64{1, 0, 0, 0}, 2, 2)
		if err != nil {
			t.Fatal(err)
		}
		dae, err := IntegrateDAE(daeRHS, mass, 0, 1, mustA(t, []float64{0, 0}, 2), 50, DAEOptions{})
		if err != nil {
			t.Fatal(err)
		}
		colRHS := func(t float64, y *Array) (*Array, error) {
			out, err := Zeros(Float, 2)
			if err != nil {
				return nil, err
			}
			out.SetFloatAt(0, y.FloatAt(1))
			return out, nil
		}
		col, err := SolveBoundaryCollocation(colRHS, 0, 1, mustA(t, []float64{0, 0}, 2),
			BoundaryConditions{Start: []int{0}, End: []int{0}, EndValues: []float64{1}},
			CollocationOptions{})
		if err != nil {
			t.Fatal(err)
		}
		accel := func(q *Array) (*Array, error) { return MulF(q, -1), nil }
		positions, momenta, err := IntegrateYoshida4(accel, 0, 6.283185307179586,
			mustA(t, []float64{1}, 1), mustA(t, []float64{0}, 1), 200)
		if err != nil {
			t.Fatal(err)
		}
		gradH := func(z *Array) (*Array, error) {
			out, err := Zeros(Float, 2)
			if err != nil {
				return nil, err
			}
			out.SetFloatAt(0, z.FloatAt(1))
			out.SetFloatAt(1, z.FloatAt(0))
			return out, nil
		}
		mids, _, err := IntegrateMidpoint(gradH, 0, 1, mustA(t, []float64{1}, 1),
			mustA(t, []float64{1}, 1), 32, MidpointOptions{})
		if err != nil {
			t.Fatal(err)
		}
		n := 64
		dx := 1.0 / 65
		pulse := make([]float64, n)
		for i := range n {
			c := (float64(i) + 0.5) * dx
			if c >= 0.3 && c <= 0.6 {
				pulse[i] = 1
			}
		}
		upwind, err := IntegrateUpwindAdvection1D(mustA(t, pulse, n), 1, dx, 0.2, 0.9*dx, 2, 0, 0)
		if err != nil {
			t.Fatal(err)
		}
		koren, err := IntegrateAdvection1D(mustA(t, pulse, n), 1, dx, 0.2, 0.9*dx, 2, 0, 0)
		if err != nil {
			t.Fatal(err)
		}
		return []any{bdf, float64(stats.MaxOrder), ros, dae,
			col.Values[len(col.Values)-1], float64(len(col.Mesh)),
			positions[len(positions)-1], momenta[len(momenta)-1], mids[len(mids)-1],
			upwind, koren}
	}},
	{"integrate-fem3d", func(t *testing.T) []any {
		// The tetrahedral Poisson assembly on the unit box with the
		// manufactured sin(πx)·sin(πy)·sin(πz) solution.
		mesh, err := BoxTetraMesh3D(0, 0, 0, 1, 1, 1, 4, 4, 4)
		if err != nil {
			t.Fatal(err)
		}
		src := func(x, y, z float64) float64 {
			return 3 * math.Pi * math.Pi * math.Sin(math.Pi*x) * math.Sin(math.Pi*y) * math.Sin(math.Pi*z)
		}
		var bound []int
		var vals []float64
		for i := range mesh.Vertices3() {
			x, y, z := mesh.Vertices[3*i], mesh.Vertices[3*i+1], mesh.Vertices[3*i+2]
			if x == 0 || x == 1 || y == 0 || y == 1 || z == 0 || z == 1 {
				bound = append(bound, i)
				vals = append(vals, 0)
			}
		}
		u, err := SolvePoissonFEM3D(mesh, src, FEMPoisson3DOptions{
			Kappa: 1, DirichletNodes: bound, DirichletValues: vals,
			Ordering: SparseOrderingReverseCuthillMcKee})
		if err != nil {
			t.Fatal(err)
		}
		return []any{u.FloatAt(u.Len() / 2), u.FloatAt(u.Len() - 1), u.FloatAt(7)}
	}},
	{"linalg-sparse-lsqr-rrqr-update", func(t *testing.T) []any {
		// Sparse least squares against a consistent right-hand side,
		// the pivoted QR on a seeded matrix and the sparse rank-one
		// round trip on a banded factor.
		g := NewGenerator(65)
		const m, n = 12, 8
		var idx []int64
		var vals []float64
		for i := range m {
			idx = append(idx, int64(i), int64(i%(n)))
			vals = append(vals, 2+g.Unit())
			if i+1 < m && i%(n)+1 < n {
				idx = append(idx, int64(i), int64(i%n+1))
				vals = append(vals, -0.5-0.5*g.Unit())
			}
		}
		indices, err := FromInts(idx, len(vals), 2)
		if err != nil {
			t.Fatal(err)
		}
		valArr, err := FloatsFromArray(vals, len(vals))
		if err != nil {
			t.Fatal(err)
		}
		coo, err := NewSparseCOO(indices, valArr, []int{m, n})
		if err != nil {
			t.Fatal(err)
		}
		csr, err := CSRFromCOO(coo)
		if err != nil {
			t.Fatal(err)
		}
		xTrue := New(Float, n)
		for i := range n {
			xTrue.RawFloats()[i] = float64(i%5) - 2 + 0.25*float64(i%3)
		}
		b, err := csr.MatVec(xTrue)
		if err != nil {
			t.Fatal(err)
		}
		xl, infoL, err := SpLSQR(coo, b, 1e-12, 300, 0)
		if err != nil {
			t.Fatal(err)
		}
		xm, infoM, err := SpLSMR(coo, b, 1e-12, 300, 0)
		if err != nil {
			t.Fatal(err)
		}
		dm := mustA(t, randA(t, 66, 60).RawFloats(), 10, 6)
		q, r, perm, rank, err := RRQR(dm)
		if err != nil {
			t.Fatal(err)
		}
		permF := make([]float64, len(perm))
		for i, p := range perm {
			permF[i] = float64(p)
		}
		b6 := randA(t, 67, 10)
		xr, err := SolveRRQR(dm, b6)
		if err != nil {
			t.Fatal(err)
		}
		const bn = 30
		var bIdx []int64
		var bVals []float64
		for i := range bn {
			bIdx = append(bIdx, int64(i), int64(i))
			bVals = append(bVals, 4)
			if i+1 < bn {
				bIdx = append(bIdx, int64(i), int64(i+1))
				bVals = append(bVals, -1)
				bIdx = append(bIdx, int64(i+1), int64(i))
				bVals = append(bVals, -1)
			}
		}
		bIndices, err := FromInts(bIdx, len(bVals), 2)
		if err != nil {
			t.Fatal(err)
		}
		bValArr, err := FloatsFromArray(bVals, len(bVals))
		if err != nil {
			t.Fatal(err)
		}
		bCoo, err := NewSparseCOO(bIndices, bValArr, []int{bn, bn})
		if err != nil {
			t.Fatal(err)
		}
		factor, err := NewSparseCholesky(bCoo, SparseOrderingNatural)
		if err != nil {
			t.Fatal(err)
		}
		bv := New(Float, bn)
		for i := range bn {
			bv.RawFloats()[i] = float64(i%7) - 3
		}
		before, err := factor.Solve(bv)
		if err != nil {
			t.Fatal(err)
		}
		upd := New(Float, bn)
		upd.RawFloats()[7] = 2
		if err := factor.Update(upd); err != nil {
			t.Fatal(err)
		}
		after, err := factor.Solve(bv)
		if err != nil {
			t.Fatal(err)
		}
		if err := factor.Downdate(upd); err != nil {
			t.Fatal(err)
		}
		restored, err := factor.Solve(bv)
		if err != nil {
			t.Fatal(err)
		}
		return []any{xl, infoL.Criterion, infoL.ResidualNorm, float64(infoL.Iterations),
			xm, infoM.Criterion, q, r, permF, float64(rank), xr,
			before, after, restored}
	}},
	{"optim-lp-qp-global2", func(t *testing.T) []any {
		// The simplex through the two-sided rows, the active-set QP on
		// an active wall, the seeded global pair on one rotated bowl,
		// the nonlinear equality and the scalar bracket.
		a := mustA(t, []float64{1, 1, 1, 0}, 2, 2)
		xLP, vLP, err := MinimiseLinearRows(mustA(t, []float64{1, 1}, 2),
			LinearConstraints{A: a, Lower: []float64{2, math.Inf(-1)}, Upper: []float64{math.Inf(1), 3}},
			LinearProgramOptions{})
		if err != nil {
			t.Fatal(err)
		}
		h := mustA(t, []float64{2, 0, 0, 2}, 2, 2)
		xQP, vQP, multQP, err := MinimiseQP(h, mustA(t, []float64{-2, -4}, 2),
			LinearConstraints{A: mustA(t, []float64{1, 0}, 1, 2),
				Lower: []float64{math.Inf(-1)}, Upper: []float64{1}},
			nil, QPOptions{})
		if err != nil {
			t.Fatal(err)
		}
		cmaF := func(p *Array) (float64, error) {
			var s float64
			w := []float64{4, 3, 2, 1}
			for i := range 4 {
				di := p.FloatAt(i) - float64(i+1)
				s += w[i] * di * di
				if i+1 < 4 {
					s += 0.5 * di * (p.FloatAt(i+1) - float64(i+2))
				}
			}
			return s, nil
		}
		xCMA, vCMA, err := MinimiseCMAES(cmaF, mustA(t, []float64{2, -2, 1, -1}, 4),
			CMAESOptions{Sigma0: 0.5, Generations: 300, Tolerance: 1e-10, Seed: 7})
		if err != nil {
			t.Fatal(err)
		}
		xSA, vSA, err := MinimiseSimulatedAnnealing(cmaF, mustA(t, []float64{2, -2, 1, -1}, 4),
			SimulatedAnnealingOptions{Steps: 20000, Tolerance: 1e-6, Seed: 42, AllowBudgetExit: true})
		if err != nil {
			t.Fatal(err)
		}
		xNL, vNL, multNL, err := MinimiseNonlinearConstrained(
			func(p *Array) (float64, error) { return p.FloatAt(0), nil },
			nil, mustA(t, []float64{0.5, 0.5}, 2),
			NonlinearConstraints{Equalities: []func(*Array) (float64, error){
				func(p *Array) (float64, error) {
					x, y := p.FloatAt(0), p.FloatAt(1)
					return x*x + y*y - 1, nil
				},
			}}, LBFGSOptions{})
		if err != nil {
			t.Fatal(err)
		}
		root, err := FindRootBrent(func(x float64) float64 { return math.Cos(x) - x }, -10, 10, BrentOptions{})
		if err != nil {
			t.Fatal(err)
		}
		broydenRHS := func(x *Array) (*Array, error) {
			out, err := Zeros(Float, 2)
			if err != nil {
				return nil, err
			}
			xf, yf := x.FloatAt(0), x.FloatAt(1)
			out.SetFloatAt(0, xf*xf+yf*yf-1)
			out.SetFloatAt(1, xf-yf)
			return out, nil
		}
		xBr, resBr, err := FindRootSystem(broydenRHS, mustA(t, []float64{2, 0.5}, 2),
			RootSystemOptions{UseBroyden: true})
		if err != nil {
			t.Fatal(err)
		}
		return []any{xLP, vLP, xQP, vQP, multQP, xCMA, vCMA, xSA, vSA,
			xNL, vNL, multNL, root, xBr, resBr}
	}},
	{"io-hdf5-write", func(t *testing.T) []any {
		// The writer round trip: chunked, shuffled, deflated floats, a
		// float32 matrix, wide integers, a nested group and attributes,
		// read back through the unchanged reader in both superblocks.
		dir := t.TempDir()
		f64 := randA(t, 68, 32)
		f32, err := FromFloat32s([]float32{1.5, -2.5, 3.25, 4, 5, 6}, 2, 3)
		if err != nil {
			t.Fatal(err)
		}
		wide, err := FromInts([]int64{5, -3, 1 << 40}, 3)
		if err != nil {
			t.Fatal(err)
		}
		nested, err := FromFloats([]float64{1, 2, 3, 4}, 2, 2)
		if err != nil {
			t.Fatal(err)
		}
		sets := []HDF5Dataset{
			{Path: "/signals/main", Shape: f64.Shape(), Values: f64, Attrs: map[string]string{"units": "m"}},
			{Path: "/image", Shape: f32.Shape(), Values: f32},
			{Path: "/wide", Shape: wide.Shape(), Values: wide},
			{Path: "/g/sub/deep", Shape: nested.Shape(), Values: nested},
		}
		attrs := map[string]map[string]string{"/": {"title": "oracle"}, "/g": {"note": "middle"}}
		classic := filepath.Join(dir, "classic.h5")
		if err := SaveHDF5(classic, sets, attrs, HDF5WriteOptions{Gzip: 6, Shuffle: true}); err != nil {
			t.Fatal(err)
		}
		back, err := LoadHDF5(classic)
		if err != nil {
			t.Fatal(err)
		}
		out := []any{}
		for _, d := range back {
			out = append(out, d.Path, d.Values)
			for _, k := range slices.Sorted(maps.Keys(d.Attrs)) {
				out = append(out, k, d.Attrs[k])
			}
		}
		latest := filepath.Join(dir, "latest.h5")
		if err := SaveHDF5(latest, sets, attrs, HDF5WriteOptions{Latest: true}); err != nil {
			t.Fatal(err)
		}
		backLatest, err := LoadHDF5(latest)
		if err != nil {
			t.Fatal(err)
		}
		out = append(out, len(backLatest) == len(back))
		for _, d := range backLatest {
			if d.Path == "/signals/main" {
				out = append(out, d.Values)
			}
		}
		return out
	}},
	{"io-hdf5-narrow-write-roundtrip", func(t *testing.T) []any {
		// The seven narrow dtypes through the writer and back, the
		// values at each dtype's extremes: bool through the boolean
		// enumeration convention, every integer at its stored width and
		// signedness. The same sets are written contiguous, in the
		// latest layout and chunked with shuffle and deflate, and every
		// read-back must land the written dtype and values.
		dir := t.TempDir()
		sets := []HDF5Dataset{}
		must := func(values *Array, err error) *Array {
			if err != nil {
				t.Fatal(err)
			}
			return values
		}
		put := func(path string, values *Array) {
			sets = append(sets, HDF5Dataset{Path: path, Shape: values.Shape(), Values: values})
		}
		put("/bool", must(FromBools([]bool{false, true, true, false}, 2, 2)))
		put("/i8", must(FromInt8s([]int8{-128, 127, 0, -1}, 2, 2)))
		put("/u8", must(FromUint8s([]uint8{0, 255, 7, 128}, 2, 2)))
		put("/i16", must(FromInt16s([]int16{-32768, 32767, 0, -2}, 2, 2)))
		put("/u16", must(FromUint16s([]uint16{0, 65535, 5, 32768}, 2, 2)))
		put("/i32", must(FromInt32s([]int32{-2147483648, 2147483647, 0, -3}, 2, 2)))
		put("/u32", must(FromUint32s([]uint32{0, 4294967295, 9, 2147483648}, 2, 2)))
		out := []any{}
		for _, c := range []struct {
			file string
			opts HDF5WriteOptions
		}{
			{"contiguous.h5", HDF5WriteOptions{}},
			{"latest.h5", HDF5WriteOptions{Latest: true}},
			{"chunked.h5", HDF5WriteOptions{Gzip: 1, Shuffle: true, ChunkBytes: 8}},
		} {
			path := filepath.Join(dir, c.file)
			if err := SaveHDF5(path, sets, nil, c.opts); err != nil {
				t.Fatal(err)
			}
			back, err := LoadHDF5(path)
			if err != nil {
				t.Fatal(err)
			}
			out = append(out, c.file)
			for _, d := range back {
				out = append(out, d.Path, d.Values)
			}
		}
		return out
	}},
	{"io-hdf5-uint8-roundtrip", func(t *testing.T) []any {
		// A uint8 dataset through the HDF5 read path: the fixture pins
		// the reader's decode directly, hand-built in the classic
		// layout, and must land uint8 on the values below. The writer
		// path is covered by io-hdf5-narrow-write-roundtrip above,
		// which writes every narrow dtype and reads it back.
		path := filepath.Join(t.TempDir(), "u8.h5")
		file := oracleHDF5Narrow(oracleHDF5Fixed(1, false), []uint64{5},
			[]byte{0, 1, 200, 255, 42})
		if err := os.WriteFile(path, file, 0o644); err != nil {
			t.Fatal(err)
		}
		sets, err := LoadHDF5(path)
		if err != nil {
			t.Fatal(err)
		}
		return []any{len(sets), sets[0].Path, sets[0].Values}
	}},
	{"io-hdf5-int16-roundtrip", func(t *testing.T) []any {
		// An int16 dataset through the same hand-built fixture path:
		// the read-back must land int16 on the extremes below.
		path := filepath.Join(t.TempDir(), "i16.h5")
		file := oracleHDF5Narrow(oracleHDF5Fixed(2, true), []uint64{4},
			[]byte{0xfd, 0xff, 0x00, 0x80, 0xff, 0x7f, 0x07, 0x00})
		if err := os.WriteFile(path, file, 0o644); err != nil {
			t.Fatal(err)
		}
		sets, err := LoadHDF5(path)
		if err != nil {
			t.Fatal(err)
		}
		return []any{len(sets), sets[0].Path, sets[0].Values}
	}},
	{"io-hdf5-bool-roundtrip", func(t *testing.T) []any {
		// A boolean enumeration dataset, the convention HDF5 writers
		// carry booleans in: the read-back must land core.Bool.
		path := filepath.Join(t.TempDir(), "bool.h5")
		file := oracleHDF5Narrow(oracleHDF5EnumBool(), []uint64{3}, []byte{1, 0, 1})
		if err := os.WriteFile(path, file, 0o644); err != nil {
			t.Fatal(err)
		}
		sets, err := LoadHDF5(path)
		if err != nil {
			t.Fatal(err)
		}
		return []any{len(sets), sets[0].Path, sets[0].Values}
	}},
	{"io-netcdf-classic-natives", func(t *testing.T) []any {
		// A NetCDF classic file carrying byte, short, int, char, float
		// and double values, read natively. The NetCDF writer stores
		// float64, float32 and int64 only, so the fixture is written
		// here as classic-format bytes and the oracle pins the landings.
		path := filepath.Join(t.TempDir(), "natives.nc")
		if err := os.WriteFile(path, oracleNetCDFNatives(), 0o644); err != nil {
			t.Fatal(err)
		}
		_, vars, _, err := LoadNetCDF(path)
		if err != nil {
			t.Fatal(err)
		}
		out := []any{len(vars)}
		for _, v := range vars {
			out = append(out, v.Name, v.Values)
		}
		return out
	}},
	{"optim-lm-fit", func(t *testing.T) []any {
		// The Levenberg-Marquardt fit through the Fit surface: an
		// exact exponential decay with a requested covariance, then a
		// diagonal-Sigma run whose first observation carries a quarter
		// of the variance, so the whitening moves the answer. The
		// digest pins the parameters, both chi2 values, the statuses
		// and the covariance.
		xs := []float64{0, 1, 2, 3, 4, 5, 6, 7}
		ys := make([]float64, len(xs))
		for i, x := range xs {
			ys[i] = 2.5*math.Exp(-0.7*float64(x)) + 0.3
		}
		residual := func(p *Array) (*Array, error) {
			out := New(Float, len(xs))
			for i := range len(xs) {
				out.RawFloats()[i] = ys[i] - (p.FloatAt(0)*math.Exp(-p.FloatAt(1)*float64(xs[i])) + p.FloatAt(2))
			}
			return out, nil
		}
		p0, err := FromFloats([]float64{2, 0.5, 0.1}, 3)
		if err != nil {
			t.Fatal(err)
		}
		res, err := LevenbergMarquardtFit(residual, p0, LMOptions{RequestCovariance: true})
		if err != nil {
			t.Fatal(err)
		}
		if res.Status != FitConverged {
			t.Fatalf("status %d, want FitConverged", res.Status)
		}
		out := []any{res.Parameters, res.Chi2, int(res.Status), res.Covariance}
		sigma, err := FromFloats([]float64{0.25, 1, 1, 1, 1, 1, 1, 1}, 8)
		if err != nil {
			t.Fatal(err)
		}
		wres, err := LevenbergMarquardtFit(residual, p0, LMOptions{Sigma: sigma})
		if err != nil {
			t.Fatal(err)
		}
		if wres.Status != FitConverged {
			t.Fatalf("weighted status %d, want FitConverged", wres.Status)
		}
		return append(out, wres.Parameters, wres.Chi2, int(wres.Status))
	}},
	{"core-cosm1", func(t *testing.T) []any {
		// The small-argument cosine deficit across its regimes: the
		// digest pins the factored series from the underflowed end to
		// the crossover and the direct subtraction above it.
		a, err := FromFloats([]float64{
			1e-300, 1e-12, 1e-9, 1e-8, 1e-4, 0.01, 0.5,
			math.Pi / 4, 0.79, 1, 2, -0.3, -2.5, 1e6,
		}, 14)
		if err != nil {
			t.Fatal(err)
		}
		v, err := Cosm1(a)
		if err != nil {
			t.Fatal(err)
		}
		return []any{v}
	}},
	{"core-substream", func(t *testing.T) []any {
		// The substream family and the scalar splitmix64 chain: the
		// digest pins the first draws of three members of one seed's
		// family beside the chain of states the scalar surface hands
		// out, so a change to the seeding moves loudly.
		out := []any{}
		for _, i := range []int{0, 1, 7} {
			g, err := Substream(42, i)
			if err != nil {
				t.Fatal(err)
			}
			a, err := Floats(g, 8)
			if err != nil {
				t.Fatal(err)
			}
			out = append(out, a)
		}
		state, v := Splitmix64(0)
		for range 3 {
			out = append(out, fmt.Sprintf("%#016x", state), fmt.Sprintf("%#016x", v))
			state, v = Splitmix64(state)
		}
		return out
	}},
	{"signal-chirp", func(t *testing.T) []any {
		// The chirp synthesiser: the digest pins a rising sweep, a
		// falling one and the constant tone that must be the plain
		// sine.
		rise, err := Chirp(64, 5, 60, 128)
		if err != nil {
			t.Fatal(err)
		}
		fall, err := Chirp(16, 900, 100, 8000)
		if err != nil {
			t.Fatal(err)
		}
		tone, err := Chirp(32, 11, 11, 256)
		if err != nil {
			t.Fatal(err)
		}
		return []any{rise, fall, tone}
	}},
	{"core-besseljreal", func(t *testing.T) []any {
		// The real-order Bessel J across its regimes: the series at a
		// small argument, the climb seeded from the expansion, the
		// fractional Miller walk past the argument, and the integer
		// delegation, pinned beside the points themselves.
		type point struct {
			nu, x float64
		}
		pts := []point{
			{0.5, 2}, {2.5, 0.05}, {1.5, 12.1}, {2.3, 15},
			{7.7, 40}, {20.5, 15}, {1.7, 1000}, {3, 20},
		}
		out := []any{len(pts)}
		for _, p := range pts {
			v, err := BesselJRealOrder(p.nu, p.x)
			if err != nil {
				t.Fatal(err)
			}
			out = append(out, v)
		}
		return out
	}},
	{"integrate-filon", func(t *testing.T) []any {
		// The Filon quadrature across its regimes: polynomial
		// amplitudes, where the construction is exact whatever the
		// carrier does, an exponential amplitude under a carrier of
		// five hundred, and the zero-frequency degeneration beside
		// them.
		poly := func(x float64) (float64, error) { return x, nil }
		c1, s1, err := IntegrateFilon(poly, 2, 7, 500, FilonOptions{})
		if err != nil {
			t.Fatal(err)
		}
		exp := func(x float64) (float64, error) { return math.Exp(0.5 * x), nil }
		c2, s2, err := IntegrateFilon(exp, 2, 7, 500, FilonOptions{})
		if err != nil {
			t.Fatal(err)
		}
		c3, s3, err := IntegrateFilon(exp, 0, 3, 0, FilonOptions{})
		if err != nil {
			t.Fatal(err)
		}
		return []any{c1, s1, c2, s2, c3, s3}
	}},
	{"core-narrow", func(t *testing.T) []any {
		// The narrow integer dtypes end to end: every width over the
		// corners of its own range, promotion across widths and across
		// the class boundary, the exact int64 folds, the bool masks the
		// comparisons answer and the selection and logic they feed.
		i8, err := Int8sFromArray([]int8{-128, -1, 0, 1, 127, -128, 127, 0, 3, -7}, 10)
		if err != nil {
			t.Fatal(err)
		}
		u8, err := Uint8sFromArray([]uint8{0, 1, 127, 128, 255, 254, 3, 0, 9, 200}, 10)
		if err != nil {
			t.Fatal(err)
		}
		i16, err := Int16sFromArray([]int16{-32768, -1, 0, 1, 32767, -32768, 32767, 0, 500, -900}, 10)
		if err != nil {
			t.Fatal(err)
		}
		u16, err := Uint16sFromArray([]uint16{0, 1, 32767, 32768, 65535, 65534, 7, 0, 40, 60000}, 10)
		if err != nil {
			t.Fatal(err)
		}
		i32, err := Int32sFromArray([]int32{-2147483648, -1, 0, 1, 2147483647, -2147483648, 2147483647, 0, 70000, -300}, 10)
		if err != nil {
			t.Fatal(err)
		}
		u32, err := Uint32sFromArray([]uint32{0, 1, 2147483647, 2147483648, 4294967295, 4294967294, 11, 0, 5, 4000000000}, 10)
		if err != nil {
			t.Fatal(err)
		}
		cross1, err := Add(i8, u16)
		if err != nil {
			t.Fatal(err)
		}
		cross2, err := Sub(i32, u8)
		if err != nil {
			t.Fatal(err)
		}
		cross3, err := Mul(i16, u8)
		if err != nil {
			t.Fatal(err)
		}
		cross4, err := Add(u32, i16)
		if err != nil {
			t.Fatal(err)
		}
		ltMask, err := Lt(i8, u16)
		if err != nil {
			t.Fatal(err)
		}
		eqMask, err := EqI(u8, 1)
		if err != nil {
			t.Fatal(err)
		}
		leMask, err := LeI(i32, -1)
		if err != nil {
			t.Fatal(err)
		}
		geMask, err := GeF(i8, 0.5)
		if err != nil {
			t.Fatal(err)
		}
		ltfMask, err := LtF(i16, -0.5)
		if err != nil {
			t.Fatal(err)
		}
		joined, err := And(ltMask, eqMask)
		if err != nil {
			t.Fatal(err)
		}
		flipped, err := Not(eqMask)
		if err != nil {
			t.Fatal(err)
		}
		picked, err := Select(i8, joined)
		if err != nil {
			t.Fatal(err)
		}
		chosen, err := Where(eqMask, u8, i8)
		if err != nil {
			t.Fatal(err)
		}
		widened, err := Astype(u32, Float)
		if err != nil {
			t.Fatal(err)
		}
		wide, err := FromInts([]int64{2147483648, -2147483649, -1}, 3)
		if err != nil {
			t.Fatal(err)
		}
		_, narrowErr := Astype(wide, Int32)
		if narrowErr == nil {
			t.Fatal("Astype narrowed 2^31 into int32")
		}
		inRange, err := FromInts([]int64{2147483647, -2147483648, -1}, 3)
		if err != nil {
			t.Fatal(err)
		}
		narrowed, err := Astype(inRange, Int32)
		if err != nil {
			t.Fatal(err)
		}
		count, err := CountNonzero(leMask)
		if err != nil {
			t.Fatal(err)
		}
		minU8, err := Min(u8)
		if err != nil {
			t.Fatal(err)
		}
		maxI32, err := Max(i32)
		if err != nil {
			t.Fatal(err)
		}
		return []any{i8, u8, i16, u16, i32, u32,
			cross1, cross2, cross3, cross4,
			Sum(i8), Sum(i16), Sum(u32), minU8, maxI32,
			ltMask, eqMask, leMask, geMask, ltfMask, joined, flipped,
			picked, chosen, widened, narrowed, narrowErr != nil, count}
	}},
}

// hostileNetCDF builds a CDF-1 file whose single variable spans three
// dimensions of 2^21, 2^20 and 2^20 elements: their product times the
// 8-byte element width wraps to zero in 64-bit arithmetic, so a reader
// that multiplies before it bounds would allocate what the header
// claims. The file is 112 bytes.
func hostileOracleHeader() []byte {
	u32 := func(v uint32) []byte {
		var b [4]byte
		binary.BigEndian.PutUint32(b[:], v)
		return b[:]
	}
	name := func(s string) []byte {
		b := u32(uint32(len(s)))
		b = append(b, s...)
		for len(s)%4 != 0 {
			b = append(b, 0)
			s += " "
		}
		return b
	}
	var b []byte
	b = append(b, 'C', 'D', 'F', 1)
	b = append(b, u32(0)...)  // numrecs
	b = append(b, u32(10)...) // NC_DIMENSION
	b = append(b, u32(3)...)
	for i, l := range []uint32{1 << 21, 1 << 20, 1 << 20} {
		b = append(b, name(string(rune('a'+i)))...)
		b = append(b, u32(l)...)
	}
	b = append(b, u32(0)...) // absent attribute list
	b = append(b, u32(0)...)
	b = append(b, u32(11)...) // NC_VARIABLE
	b = append(b, u32(1)...)
	b = append(b, name("v")...)
	b = append(b, u32(3)...)
	b = append(b, u32(0)...)
	b = append(b, u32(1)...)
	b = append(b, u32(2)...)
	b = append(b, u32(0)...) // absent variable attributes
	b = append(b, u32(0)...)
	b = append(b, u32(6)...) // NC_DOUBLE
	b = append(b, u32(0)...) // vsize
	b = append(b, u32(0)...) // begin
	return b
}

// hostileFITSTable builds a BINTABLE header with a zero-width TFORM and
// no data block: the row arithmetic must not be able to divide by the
// row size, and the truncated file must be refused.
func hostileOracleTable() []byte {
	var b []byte
	for _, body := range []string{
		"XTENSION= 'BINTABLE'", "BITPIX  =                    8", "NAXIS   =                    2",
		"NAXIS1  =                    4", "NAXIS2  =                    2", "TFIELDS =                    1",
		"TFORM1  = 'X       '", "END",
	} {
		b = append(b, []byte(body)...)
		for len(b)%80 != 0 {
			b = append(b, ' ')
		}
	}
	return b
}

// oracleHDF5Fixed renders a version 1 fixed-point datatype message of
// the given element width and signedness, with the bit offset and bit
// precision the HDF5 file format specification's fixed-point property
// table defines behind the header.
func oracleHDF5Fixed(size uint32, signed bool) []byte {
	m := []byte{0x10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0} // version 1, class 0
	if signed {
		m[1] = 0x08 // class bit field: bit 3 marks two's complement
	}
	binary.LittleEndian.PutUint32(m[4:], size)
	binary.LittleEndian.PutUint16(m[10:], uint16(8*size)) // bit precision
	return m
}

// oracleHDF5EnumBool renders the boolean enumeration datatype message:
// class 8 over a one-byte unsigned base, the member names padded in
// their own fields to multiples of eight bytes, the member values
// packed behind them, exactly as the HDF5 file format specification's
// enumeration class defines.
func oracleHDF5EnumBool() []byte {
	m := []byte{0x18, 2, 0, 0, 1, 0, 0, 0}      // class 8, two members, size 1
	m = append(m, oracleHDF5Fixed(1, false)...) // the base type
	for _, name := range []string{"TRUE", "FALSE"} {
		start := len(m)
		m = append(m, name...)
		m = append(m, 0)
		for (len(m)-start)%8 != 0 {
			m = append(m, 0)
		}
	}
	return append(m, 1, 0) // TRUE = 1, FALSE = 0
}

// oracleHDF5Narrow builds a minimal classic-layout HDF5 file carrying
// one dataset: a version 0 superblock of eight-byte addresses and
// lengths, a version 1 object header with the given datatype message,
// contiguous storage and the payload bytes. The io tests build their
// hostile fixtures the same way; these bytes are fixed, so the digest
// of what the reader lands is stable across runs.
func oracleHDF5Narrow(dtypeMsg []byte, dims []uint64, payload []byte) []byte {
	const headerAt, dataAt = 96, 448
	align8 := func(n int) int { return (n + 7) / 8 * 8 }
	n := dataAt + len(payload)
	f := make([]byte, n)
	copy(f, []byte{0x89, 'H', 'D', 'F', '\r', '\n', 0x1a, '\n'})
	f[8] = 0            // superblock version 0, the classic layout
	f[13], f[14] = 8, 8 // address and length sizes
	put := func(at int, v uint64) { binary.LittleEndian.PutUint64(f[at:], v) }
	put(32, math.MaxUint64) // free space undefined
	put(40, uint64(n))      // end of file
	put(48, math.MaxUint64) // driver information undefined
	put(64, headerAt)       // the root object header
	space := make([]byte, 8+8*len(dims))
	space[0] = 1 // dataspace version 1
	space[1] = byte(len(dims))
	for i, d := range dims {
		binary.LittleEndian.PutUint64(space[8+8*i:], d)
	}
	lay := make([]byte, 18)
	lay[0], lay[1] = 3, 1 // layout version 3, contiguous
	binary.LittleEndian.PutUint64(lay[2:], dataAt)
	binary.LittleEndian.PutUint64(lay[10:], uint64(len(payload)))
	msgs := []struct {
		typ  uint16
		body []byte
	}{
		{1, space}, // dataspace
		{3, dtypeMsg},
		{8, lay}, // data layout
	}
	off := headerAt
	f[off] = 1 // object header version 1
	binary.LittleEndian.PutUint16(f[off+2:], uint16(len(msgs)))
	binary.LittleEndian.PutUint32(f[off+4:], 1) // reference count
	region := off + 16
	size := 0
	for _, m := range msgs {
		size = align8(size + 8 + len(m.body))
	}
	binary.LittleEndian.PutUint32(f[off+8:], uint32(size))
	for _, m := range msgs {
		binary.LittleEndian.PutUint16(f[region:], m.typ)
		binary.LittleEndian.PutUint16(f[region+2:], uint16(len(m.body)))
		copy(f[region+8:], m.body)
		region += align8(8 + len(m.body))
	}
	copy(f[dataAt:], payload)
	return f
}

// oracleNetCDFNatives builds a CDF-1 file by hand carrying one
// variable per classic type code: NC_BYTE, NC_SHORT, NC_INT, NC_CHAR,
// NC_FLOAT and NC_DOUBLE over one shared four-element dimension, the
// integers at the extremes of every width and the floats at
// recognisable values. The NetCDF writer stores float64, float32 and
// int64 only, so the fixture bytes live here exactly as the foreign
// fixtures the io package carries.
func oracleNetCDFNatives() []byte {
	u32 := func(v uint32) []byte {
		var b [4]byte
		binary.BigEndian.PutUint32(b[:], v)
		return b[:]
	}
	name := func(s string) []byte {
		b := u32(uint32(len(s)))
		b = append(b, s...)
		for len(b)%4 != 0 {
			b = append(b, 0)
		}
		return b
	}
	type classicVar struct {
		name string
		code uint32
		data []byte
	}
	vars := []classicVar{
		{"b", 1, []byte{0x80, 0xff, 0x00, 0x7f}},                                                    // NC_BYTE: -128, -1, 0, 127
		{"s", 3, []byte{0x80, 0x00, 0xff, 0xff, 0x00, 0x01, 0x7f, 0xff}},                            // NC_SHORT extremes
		{"i", 4, []byte{0x80, 0, 0, 0, 0xff, 0xff, 0xff, 0xff, 0, 0, 0, 1, 0x7f, 0xff, 0xff, 0xff}}, // NC_INT
		{"c", 2, []byte{0x00, 0x41, 0xc8, 0xff}},                                                    // NC_CHAR: raw bytes
		{"f", 5, []byte{ // NC_FLOAT: 1.5, -2.5, 0, 3.25
			0x3f, 0xc0, 0x00, 0x00, 0xc0, 0x20, 0x00, 0x00,
			0x00, 0x00, 0x00, 0x00, 0x40, 0x50, 0x00, 0x00}},
		{"d", 6, []byte{ // NC_DOUBLE: 1.5, -2.5, 0, 4
			0x3f, 0xf8, 0, 0, 0, 0, 0, 0, 0xc0, 0x04, 0, 0, 0, 0, 0, 0,
			0, 0, 0, 0, 0, 0, 0, 0, 0x40, 0x10, 0, 0, 0, 0, 0, 0}},
	}
	var b []byte
	b = append(b, 'C', 'D', 'F', 1)
	b = append(b, u32(0)...)  // numrecs
	b = append(b, u32(10)...) // NC_DIMENSION
	b = append(b, u32(1)...)  // one dimension
	b = append(b, name("n")...)
	b = append(b, u32(4)...)                 // length 4
	b = append(b, u32(0)...)                 // gatt_list ABSENT
	b = append(b, u32(0)...)                 // gatt_list ABSENT
	b = append(b, u32(11)...)                // NC_VARIABLE
	b = append(b, u32(uint32(len(vars)))...) // six variables
	// The header ends where the first payload begins: one 36-byte
	// variable record per variable behind the fixed prefix.
	begin := len(b) + len(vars)*36
	off := begin
	for _, v := range vars {
		b = append(b, name(v.name)...)
		b = append(b, u32(1)...) // rank 1
		b = append(b, u32(0)...) // dimid 0
		b = append(b, u32(0)...) // variable attributes ABSENT
		b = append(b, u32(0)...) // variable attributes ABSENT
		b = append(b, u32(v.code)...)
		b = append(b, u32(uint32(len(v.data)))...) // vsize
		b = append(b, u32(uint32(off))...)
		off += len(v.data)
	}
	for _, v := range vars {
		b = append(b, v.data...)
	}
	return b
}

// pinnedOracleDigests is the recorded behaviour of the harness, keyed
// by runtime.GOOS/GOARCH plus the code generation the binary was built
// with: floating-point kernels may differ between architectures (FMA
// availability, libm corners), and GOAMD64 decides whether the compiler
// may contract a multiply and an add into one fused operation, which
// changes the last bits without changing the algorithm. A deliberate
// algorithm change re-records the affected entries on the configuration
// it was made on; an accidental one fails the test there. A build whose
// combination has no block skips loudly until it is recorded, so
// determinism is measured per configuration, never claimed in general.
//
// The portable build is the product and the only build, and its
// digests are recorded at the toolchain default level (v1): the
// compiler has no auto-vectoriser, so a pinned higher level would buy
// only scalar FMA contraction, which the bit-pinned kernels already
// suppress by spelling. A build pinned to another GOAMD64 level has no
// block and skips with the recording instructions rather than failing.
//
// A re-recorded digest is sometimes the point itself: an old digest
// can have pinned a bug, and three entries exist because their
// predecessors did. signal-welch-savgol's magnitude goes through
// math.Hypot, so it no longer rounds through a squared sum.
// optim-roots-minima and optim-constrained-minima carry the L-BFGS
// line search that no longer returns its start point when a stiff
// objective rejects every trial step, the Nelder-Mead that no longer
// stops on a simplex lying on one level set, and MinimiseConstrained
// returning f at the answer instead of the augmented Lagrangian value.
var pinnedOracleDigests = map[string]map[string]string{
	"linux/amd64+v1": {
		"spmd-shards":                       "0bec5217a9a79b182241ac0937f32e9d20c89a5b392fc797ab3787a03fc8c9ed",
		"io-hdf5-narrow-write-roundtrip":    "f2e87eaadcbab846e4acf5473b3023faca3015cd3b3f0919c4c3792114589ee9",
		"io-hdf5-uint8-roundtrip":           "54550518525945c92d970a38d2d81a5005fb8a899b597819c6060610ae77dd54",
		"io-hdf5-int16-roundtrip":           "b4163c6e9ed7a04ddb4a2328d394afe074237533738d19aa5ecaa68bff9e2685",
		"io-hdf5-bool-roundtrip":            "fa56fd9a421d2e78f17711e717f851c4b19dc1f6946d5c4e1dddad85cc42d347",
		"io-netcdf-classic-natives":         "c0219b60aa963176ce509f5633c22b96bc070529db1035d53a643b67d614d01b",
		"core-elementwise":                  "0812ac01c62b084326d0e590941a46327136e9022a101fad68998781b68f7014",
		"core-matmul-einsum":                "a62b07d724f06603fe4c5ebf3d448b61d7638b93d1b58df605d94096d30ba4b4",
		"core-sort-argsort":                 "24fc532b4140bc6633b5fabb8a19c708c1919932c75ae8fce048c413c94aff0f",
		"core-reductions":                   "764eac75a3bcc1a38f7975ed4de1e5df39d70889dfb845507ef1cfe1ff456eac",
		"core-shape":                        "c84940b2aff4e4a25e7a4292fa6d76c2a0306f328ba334e3a6085843d94fcc3b",
		"core-fft":                          "1848e23763a0a72f282eff45c1cc54a3d2486f4ff53b12b4a8f462bcdc773061",
		"core-quasirandom":                  "000620721b8ce6fff07287da6301b89dbcdaa7293d68a0783aae60fa4370aa6d",
		"linalg-solve-inv-det":              "5b73c4a57a6221f2b5abd3b6769d6aa13723db0ada0373e870d551f795c61bf3",
		"linalg-factorisations":             "f70c03b3759703a6fcd1ff1ef3cbab024acd000781e2065331c18f95c45b4d15",
		"linalg-sparse-cholesky":            "da49d6554341ffbf40500a99f241e0133528c2e6fadfc385cfa6d7d59685da28",
		"linalg-sparse-lu":                  "3ccf6e7064b410c3c6df0a6b2697b4c66f3722aec99491ed9298db6212d65fbb",
		"integrate-fem-poisson":             "065cb65bb7fba9838ed6f84b703d7ffb69d877564bfbe006905e81fdea6b9175",
		"linalg-sparse-complex":             "d81a8dd242a23ce7026ded53c44a4fea3a58d9b20c8be4ed2c03147c740e2130",
		"signal-welch-savgol":               "36d6581ac2b06191b2d6eb743e042283d8cd0cbc187c54b6d40f490eef5984a4",
		"signal-wavelets":                   "f324710c1f67c8e5bb099731c8647c944744a62e9219ef8fdbb070412df434ab",
		"signal-lombscargle-conv":           "4c3f3eb0f292b978d701dcea384ccbfc26be06acff348756ec0bda19c4cca20e",
		"signal-filters-stencils":           "00bccd2f3b5d61f07c3383280dc8111897e1eaf57a6e16a0d70081a703a8b158",
		"stats-moments-quantiles":           "61d196193641395bbb855685f2727cfe29521848bba111d89de9f480ef7264cc",
		"stats-correlation-regression":      "f398fea69ae522ffaafdf0d307edd02d657aaf7a452c6c75d174307becbf7218",
		"stats-poisson-regression":          "e385d9fda18acef4669ac1d1f1e8b12a5abeb682eff37a06f6ec140dd7b9f91a",
		"stats-distributions":               "8986f622708f3f1f28c1c00fed9225014c17a90a8e0714e2ce6e2f181ee03321",
		"integrate-quadrature-ode":          "66dd47bbc30de692902937078808da5322c76e6de1facaf5099fd72344f248a5",
		"optim-roots-minima":                "9af044a7e71416f0ab1f8dcbd4073f199163791ad28779b59c7faabdf982e6f4",
		"optim-bounded-minima":              "368dbb82d31c5e53c7dad9f944921e741ccccedafa7fda8d8b180f9daa58628e",
		"optim-constrained-minima":          "884020c56542ac84e5460f0cbd171f64904f86254ebbae6479e3bd6662cc6662",
		"grad-backward":                     "0f3a1be94160019b796b457aa42531817685b7bc478ed041cc6c73ec5810b744",
		"io-roundtrips":                     "de1a36e2b2e9235a40af37b4ee5823e526f6a46583c34af6245dbbd322e3f1e3",
		"core-views-and-int-precision":      "ca3c789ead2894ed2c53416f128b8aa665aed9dc3d4d67e38ae9d540a1ac5ccd",
		"io-hdf5-fixture":                   "01e96137069f7d9dd7d4cd2e236de8f5fbcf4ba6121a1f121f21c041197cf117",
		"io-hostile-inputs":                 "9dcf97a184f32623d11a73124ceb99a5709b083721e878a16d78f596718ba7b2",
		"core-float16":                      "6af37847cc6187b64f2bb20b7fefdd3b28a039e42988708d942c41bf62576949",
		"signal-kalman-arma":                "874b9c7bfd3dae3111cb49576a51913972ad572963a2ab7ad1eaa3187f15196b",
		"signal-windows-filtfilt-dwt":       "b435d694350e7a7f06303ded85c2b63e0e562795cf69686f2ae854f2c6dc81c5",
		"stats-distributions2-multipletest": "6d2f2661fa3a2bdaefbdf16f3d26b41ef69b29c93347e16e6df8542f30b14078",
		"stats-regression2":                 "cabb52d66ccb5d92b8d0885f5a5a166c1814d364dc75a4e8cac89819820edba3",
		"stats-unsupervised":                "c8a17031b7133d58a6b6b6ec21a5624281d8f291717749869e41251b3e8ef68f",
		"integrate-stiff-solvers":           "48276e65576eeefa8d7c3da8da42ee782441462ce34cf6bb814e494c0e00668f",
		"integrate-fem3d":                   "8323b5c89ac9187441cfac694193ef6394aff0508e71b53052d1b76fd59a535b",
		"linalg-sparse-lsqr-rrqr-update":    "806455d7e53765a272afca8cfef90aa233ab78e62e4ad682c085ff7e117231fc",
		"optim-lp-qp-global2":               "510ce65940755a164784ed4577502db2b60604aa9cbe184f22b2ab2a4c03bd57",
		"io-hdf5-write":                     "21482614860f885f277b05666924ab3b63a2c55b8b24734cbadc4577f2c7ac90",
		"optim-lm-fit":                      "cdbf15c3a4c5615e1a364a9fe4e5ec431d0cb65d9744cab52cbca66af51c58cf",
		"core-cosm1":                        "f995296d5c1f285ec6f2e719ee62f8eaf7c9a8e751cea8702cbe16b3df66ddb2",
		"core-substream":                    "ce49fae36f5e15b37aacc25d62b97c9f800d51aa08dee553cee1a5b6e1c01798",
		"signal-chirp":                      "ff9af5783d32eed88bf2658bde5660c247a0bd30a699c403f1755da290830a4b",
		"core-besseljreal":                  "49698a21228f091079cd65ae94cda134b16c3b0bec58a47642f6ad3fec7461d7",
		"integrate-filon":                   "4d5242520a5c144e4bdf111df83c2f2faf4fadce0859f87738acab91e3ed93e0",
		"core-narrow":                       "80913507636c4aabcdc57e5f90a75cd18499c86e244d84006650de3e1273da92",
		"stats-contingency":                 "9ac61a7a29227ddae02861076c85a669fd467f466a8c1118c52965ad4ac20a1b",
		"stats-mixedmodel":                  "6db27ea7908863a1f2d0725325d8a72a93a5ec83ad3882bca28a5d3d2b614227",
		"stats-hmm":                         "779e2c9cb8ee1e1871b17a04a42b2d574ff3de6132430bae8c58be502d450b75",
		"stats-hierarchy":                   "c4171ae9c61b76c676d016356ae319c5e3c15c0e32f7d0c26f0b1b38700cb96e",
	},
	"linux/amd64+v1+race": {
		"spmd-shards":                       "0bec5217a9a79b182241ac0937f32e9d20c89a5b392fc797ab3787a03fc8c9ed",
		"io-hdf5-narrow-write-roundtrip":    "f2e87eaadcbab846e4acf5473b3023faca3015cd3b3f0919c4c3792114589ee9",
		"io-hdf5-uint8-roundtrip":           "54550518525945c92d970a38d2d81a5005fb8a899b597819c6060610ae77dd54",
		"io-hdf5-int16-roundtrip":           "b4163c6e9ed7a04ddb4a2328d394afe074237533738d19aa5ecaa68bff9e2685",
		"io-hdf5-bool-roundtrip":            "fa56fd9a421d2e78f17711e717f851c4b19dc1f6946d5c4e1dddad85cc42d347",
		"io-netcdf-classic-natives":         "c0219b60aa963176ce509f5633c22b96bc070529db1035d53a643b67d614d01b",
		"core-elementwise":                  "0812ac01c62b084326d0e590941a46327136e9022a101fad68998781b68f7014",
		"core-matmul-einsum":                "a62b07d724f06603fe4c5ebf3d448b61d7638b93d1b58df605d94096d30ba4b4",
		"core-sort-argsort":                 "24fc532b4140bc6633b5fabb8a19c708c1919932c75ae8fce048c413c94aff0f",
		"core-reductions":                   "764eac75a3bcc1a38f7975ed4de1e5df39d70889dfb845507ef1cfe1ff456eac",
		"core-shape":                        "c84940b2aff4e4a25e7a4292fa6d76c2a0306f328ba334e3a6085843d94fcc3b",
		"core-fft":                          "1848e23763a0a72f282eff45c1cc54a3d2486f4ff53b12b4a8f462bcdc773061",
		"core-quasirandom":                  "000620721b8ce6fff07287da6301b89dbcdaa7293d68a0783aae60fa4370aa6d",
		"linalg-solve-inv-det":              "5b73c4a57a6221f2b5abd3b6769d6aa13723db0ada0373e870d551f795c61bf3",
		"linalg-factorisations":             "f70c03b3759703a6fcd1ff1ef3cbab024acd000781e2065331c18f95c45b4d15",
		"linalg-sparse-cholesky":            "da49d6554341ffbf40500a99f241e0133528c2e6fadfc385cfa6d7d59685da28",
		"linalg-sparse-lu":                  "3ccf6e7064b410c3c6df0a6b2697b4c66f3722aec99491ed9298db6212d65fbb",
		"integrate-fem-poisson":             "065cb65bb7fba9838ed6f84b703d7ffb69d877564bfbe006905e81fdea6b9175",
		"linalg-sparse-complex":             "d81a8dd242a23ce7026ded53c44a4fea3a58d9b20c8be4ed2c03147c740e2130",
		"signal-welch-savgol":               "36d6581ac2b06191b2d6eb743e042283d8cd0cbc187c54b6d40f490eef5984a4",
		"signal-wavelets":                   "f324710c1f67c8e5bb099731c8647c944744a62e9219ef8fdbb070412df434ab",
		"signal-lombscargle-conv":           "4c3f3eb0f292b978d701dcea384ccbfc26be06acff348756ec0bda19c4cca20e",
		"signal-filters-stencils":           "00bccd2f3b5d61f07c3383280dc8111897e1eaf57a6e16a0d70081a703a8b158",
		"stats-moments-quantiles":           "61d196193641395bbb855685f2727cfe29521848bba111d89de9f480ef7264cc",
		"stats-correlation-regression":      "f398fea69ae522ffaafdf0d307edd02d657aaf7a452c6c75d174307becbf7218",
		"stats-poisson-regression":          "e385d9fda18acef4669ac1d1f1e8b12a5abeb682eff37a06f6ec140dd7b9f91a",
		"stats-distributions":               "8986f622708f3f1f28c1c00fed9225014c17a90a8e0714e2ce6e2f181ee03321",
		"integrate-quadrature-ode":          "66dd47bbc30de692902937078808da5322c76e6de1facaf5099fd72344f248a5",
		"optim-roots-minima":                "9af044a7e71416f0ab1f8dcbd4073f199163791ad28779b59c7faabdf982e6f4",
		"optim-bounded-minima":              "368dbb82d31c5e53c7dad9f944921e741ccccedafa7fda8d8b180f9daa58628e",
		"optim-constrained-minima":          "884020c56542ac84e5460f0cbd171f64904f86254ebbae6479e3bd6662cc6662",
		"grad-backward":                     "0f3a1be94160019b796b457aa42531817685b7bc478ed041cc6c73ec5810b744",
		"io-roundtrips":                     "de1a36e2b2e9235a40af37b4ee5823e526f6a46583c34af6245dbbd322e3f1e3",
		"core-views-and-int-precision":      "ca3c789ead2894ed2c53416f128b8aa665aed9dc3d4d67e38ae9d540a1ac5ccd",
		"io-hdf5-fixture":                   "01e96137069f7d9dd7d4cd2e236de8f5fbcf4ba6121a1f121f21c041197cf117",
		"io-hostile-inputs":                 "9dcf97a184f32623d11a73124ceb99a5709b083721e878a16d78f596718ba7b2",
		"core-float16":                      "6af37847cc6187b64f2bb20b7fefdd3b28a039e42988708d942c41bf62576949",
		"signal-kalman-arma":                "874b9c7bfd3dae3111cb49576a51913972ad572963a2ab7ad1eaa3187f15196b",
		"signal-windows-filtfilt-dwt":       "b435d694350e7a7f06303ded85c2b63e0e562795cf69686f2ae854f2c6dc81c5",
		"stats-distributions2-multipletest": "6d2f2661fa3a2bdaefbdf16f3d26b41ef69b29c93347e16e6df8542f30b14078",
		"stats-regression2":                 "cabb52d66ccb5d92b8d0885f5a5a166c1814d364dc75a4e8cac89819820edba3",
		"stats-unsupervised":                "c8a17031b7133d58a6b6b6ec21a5624281d8f291717749869e41251b3e8ef68f",
		"integrate-stiff-solvers":           "48276e65576eeefa8d7c3da8da42ee782441462ce34cf6bb814e494c0e00668f",
		"integrate-fem3d":                   "8323b5c89ac9187441cfac694193ef6394aff0508e71b53052d1b76fd59a535b",
		"linalg-sparse-lsqr-rrqr-update":    "806455d7e53765a272afca8cfef90aa233ab78e62e4ad682c085ff7e117231fc",
		"optim-lp-qp-global2":               "510ce65940755a164784ed4577502db2b60604aa9cbe184f22b2ab2a4c03bd57",
		"io-hdf5-write":                     "21482614860f885f277b05666924ab3b63a2c55b8b24734cbadc4577f2c7ac90",
		"optim-lm-fit":                      "cdbf15c3a4c5615e1a364a9fe4e5ec431d0cb65d9744cab52cbca66af51c58cf",
		"core-cosm1":                        "f995296d5c1f285ec6f2e719ee62f8eaf7c9a8e751cea8702cbe16b3df66ddb2",
		"core-substream":                    "ce49fae36f5e15b37aacc25d62b97c9f800d51aa08dee553cee1a5b6e1c01798",
		"signal-chirp":                      "ff9af5783d32eed88bf2658bde5660c247a0bd30a699c403f1755da290830a4b",
		"core-besseljreal":                  "49698a21228f091079cd65ae94cda134b16c3b0bec58a47642f6ad3fec7461d7",
		"integrate-filon":                   "4d5242520a5c144e4bdf111df83c2f2faf4fadce0859f87738acab91e3ed93e0",
		"core-narrow":                       "80913507636c4aabcdc57e5f90a75cd18499c86e244d84006650de3e1273da92",
		"stats-contingency":                 "9ac61a7a29227ddae02861076c85a669fd467f466a8c1118c52965ad4ac20a1b",
		"stats-mixedmodel":                  "6db27ea7908863a1f2d0725325d8a72a93a5ec83ad3882bca28a5d3d2b614227",
		"stats-hmm":                         "779e2c9cb8ee1e1871b17a04a42b2d574ff3de6132430bae8c58be502d450b75",
		"stats-hierarchy":                   "c4171ae9c61b76c676d016356ae319c5e3c15c0e32f7d0c26f0b1b38700cb96e",
	},
}

// oracleBuild names the code generation this binary was built with: the
// GOAMD64 level decides whether the compiler may contract a multiply and
// an add into one fused operation, and the race detector's
// instrumentation changes which loops the compiler still contracts.
// Each changes the last bits of ordinary arithmetic without changing
// the algorithm, so the digests are keyed by both alongside the
// architecture: a build whose combination has no recorded block skips
// loudly instead of failing, exactly as an unseen architecture does.
func oracleBuild() string {
	level := "v1"
	if bi, ok := debug.ReadBuildInfo(); ok {
		for _, s := range bi.Settings {
			if s.Key == "GOAMD64" && s.Value != "" {
				level = s.Value
			}
		}
	}
	return "+" + level + oracleRaceSuffix
}

// oracleKey names this architecture and code-generation block.
func oracleKey() string {
	return runtime.GOOS + "/" + runtime.GOARCH + oracleBuild()
}

func TestOracle(t *testing.T) {
	record := os.Getenv("TENSOR_ORACLE_RECORD") == "1"
	current := make(map[string]string, len(oracleCases))
	for _, c := range oracleCases {
		d := newOracleDigest()
		for _, v := range c.run(t) {
			d.result(t, v)
		}
		current[c.name] = d.sum()
	}
	if record {
		for _, c := range oracleCases {
			t.Logf("oracle %s %s", c.name, current[c.name])
		}
		t.Logf("record these into pinnedOracleDigests[%q] and commit", oracleKey())
		return
	}
	pinned, known := pinnedOracleDigests[oracleKey()]
	if !known {
		t.Skipf("no oracle digests recorded for %s; run TENSOR_ORACLE_RECORD=1 go test -run TestOracle -v . on it, "+
			"then commit the pinnedOracleDigests[%q] block", oracleKey(), oracleKey())
	}
	if len(pinned) != len(oracleCases) {
		t.Fatalf("pinnedOracleDigests[%q] holds %d entries, the harness runs %d; record with TENSOR_ORACLE_RECORD=1",
			oracleKey(), len(pinned), len(oracleCases))
	}
	for _, c := range oracleCases {
		want, ok := pinned[c.name]
		if !ok {
			t.Errorf("oracle case %q is not pinned", c.name)
			continue
		}
		if current[c.name] != want {
			t.Errorf("oracle case %q moved:\n got %s\nwant %s\n"+
				"If the change is deliberate, re-record with TENSOR_ORACLE_RECORD=1 in the same commit.",
				c.name, current[c.name], want)
		}
	}
}