Elamur Groupantsalgorithm-alias-method-tests
The groupant beside algorithms/src/alias_method/tests.rs in the Mova repository: what the code computes, what it never does, how to go back from its outputs, its invariants, cost and checks.
Facts
Implementation material. A Mova code model describes this code at one source revision: partial models, finite checks and their stated scope. It is not a reviewed general exposition, and its labels are shown as written, never raised.
Components
| component | label | where |
|---|---|---|
| approximant | partial | approximant |
| ast | partial | syntax.json |
| descriptant | present | descriptant |
| invariant | partial | model |
| tests | existing checks referenced | tests |
Obernants
The typed relations around the forward model: the behaviour complement (what the code never does), the reverse reconstruction (every input compatible with an output) and specialised views.
| id | type | label | where |
|---|---|---|---|
behavior_complement | behavior_complement | partial source derived model | behavior_complement |
reverse_reconstruction | reverse_reconstruction | partial source derived model | reverse_reconstruction |
independent_oracle | independent_oracle | partial source derived model | independent_oracle |
boundary_partition | boundary_partition | partial source derived model | boundary_partition |
compiled_mutation | compiled_mutation | partial source derived model | compiled_mutation |
Model text
descriptant
alias_method checks
Original std-only implementation and fixtures; source citations appear in module documentation.
Independent finite oracle and boundary tests for alias_method. Production: n1..4096; finite nonnegative weights, positive maximum. Normalize by maximum and total. Match a small column with a large column, transfer its deficit, finish residual columns at probability one. Explicit column and coin in [0,1). Dimension precedes weight validation; weights precede empty-mass failure. No RNG.
Epoch 2026-10-30: independent tiny-domain oracle, repeated debug/release and compiled production mutation. No timing or end-to-end Mova claims.
model
Invariants and state
Independent finite oracle and boundary tests for alias_method. Production: n1..4096; finite nonnegative weights, positive maximum. Normalize by maximum and total. Match a small column with a large column, transfer its deficit, finish residual columns at probability one. Explicit column and coin in [0,1). Dimension precedes weight validation; weights precede empty-mass failure. No RNG.
All-pass excludes represented oracle mismatches and rejected boundary violations in these finite fixtures only. Production excluded-output relation: Outputs outside 0..n and selecting an exact zero-mass column are excluded in exact arithmetic. Invalid coordinates exclude any successful draw; no generated random state exists. Floating underflow can erase tiny positive probabilities.
O(n) build and storage; O(1) draw; bounded standard allocations.
All allocations follow standard Rust process policy, not fallible allocation APIs. No callbacks or external effects. f64 roundoff and underflow remain explicit limitations.
approximant
Forward and cost approximant
Independent finite oracle and boundary tests for alias_method. Production: n1..4096; finite nonnegative weights, positive maximum. Normalize by maximum and total. Match a small column with a large column, transfer its deficit, finish residual columns at probability one. Explicit column and coin in [0,1). Dimension precedes weight validation; weights precede empty-mass failure. No RNG.
O(n) build and storage; O(1) draw; bounded standard allocations.
No executable cheaper surrogate or supported generic 1/2/5/10% profile is claimed. Residuals and floating estimates are not solution-error certificates.
models
behavior_complement
All-pass excludes represented oracle mismatches and rejected boundary violations in these finite fixtures only. Production excluded-output relation: Outputs outside 0..n and selecting an exact zero-mass column are excluded in exact arithmetic. Invalid coordinates exclude any successful draw; no generated random state exists. Floating underflow can erase tiny positive probabilities.
reverse_reconstruction
All-pass observations admit implementations differing on unsampled inputs. This finite test fiber does not uniquely identify source or prove universality. Production fiber: Multiplying all weights by a positive finite factor preserving representability retains ideal distribution. A single returned category admits many coordinate pairs; its preimage is the union of direct threshold intervals and alias intervals. Neither weights nor draw coordinates are uniquely reconstructed.
independent_oracle
Tiny path enumeration, analytical rank-one matrices or independent weighted moments reconstruct expectations without calling the production recurrence; scope is finite.
boundary_partition
Shape, zero/empty, invalid finite values, ties or budget boundaries are explicitly asserted. Numeric tolerance is fixture-specific.
compiled_mutation
A compiled changed production recurrence must fail the named oracle assertion. Restoration plus positive rerun checks that the gate can distinguish this wrong behavior.
Draw-observation fiber, 2026-11-01
The mass oracle computes each category's mass from private thresholds and aliases; it does not call draw. The remaining fixtures call draw at a finite set of coordinates. Let T be these three tests' pass/fail observation, F the current implementation, and G the same implementation except that, for a two-column table at column 0 and coin 0.123456, G returns the other category. A separately compiled source mutation passes all three tests, while for weights [1,3] F returns 0 and G returns 1 at that coordinate. Thus T(F) = T(G) but F and G differ on a valid input. This is a converse fiber of the test observation, not a production behavior complement or an error bound. It does not establish that arbitrary mutations survive, nor that the mass oracle covers the floating-point distribution outside its four-weight integer fixtures.
tests
Validation
Run cargo test -p mova-algorithms alias_method::tests. Evidence in $MOVA_DATA/runs/octopus-wave26-probability-2026-10-30: repeated profiles, mutation logs and restored positive runs. Three named tests per module. See receipt.json for evidence hashes. No allocator fault injection, timing or full-school measurement.
2026-11-01: the three actual tests passed; an external compiled mutation of draw at an unsampled valid coordinate also passed them. An actual-API probe distinguished the mutation rule at [1,3], column 0, coin 0.123456. This is a negative control for the stronger claim that all-pass uniquely determines draw behavior, not a failure of the finite mass oracle.
prospective
Probability batch prospective math
Written before implementation. All code original, std-only. Bounded allocations use standard Vec; allocator failure follows Rust process policy, no callbacks or RNG.
Alias: Walker (1977), An efficient method for generating discrete random variables with general distributions; Vose (1991), A linear algorithm for generating random numbers with a given distribution. n 1..4096, finite nonnegative weights, positive maximum. Scale by maximum then total to avoid overflow. Small/large work lists conserve total scaled mass. Column uniform and coin uniform [0,1) produce the specified categorical distribution in real arithmetic; caller explicitly supplies coordinates. O(n) build/storage, O(1) draw. No probabilistic draw generation or numeric percentage guarantee.
HMM: Rabiner (1989), A tutorial on hidden Markov models and selected applications in speech recognition; Viterbi (1967), Error bounds for convolutional codes and an asymptotically optimum decoding algorithm. n1..64, T0..4096; finite probabilities in [0,1], initial/transition rows sum to one within 1e-10. Emissions time-major likelihoods in [0,1], need not sum across states. Validate structure then numeric values before empty sequence. Empty log likelihood0/path empty. Viterbi log max-plus recurrence, predecessor ties lowest index and terminal ties lowest index (not global lexicographic). No positive path =>None. Forward/backward log-sum-exp, posterior proportional exp(alpha+beta-logZ); per-row normalization corrects rounding. O(Tn²) time/O(Tn) space. Tiny exhaustive state-sequence enumeration is independent oracle. Log scales avoid direct-product underflow; no general floating error bound.
Sinkhorn: Sinkhorn and Knopp (1967), Concerning nonnegative matrices and doubly stochastic matrices. Positive matrix entries and marginals restricted [1e-100,1e100], dims1..64, equal marginal totals within tolerance1e-12 relative. Alternate row and column multiplication to target marginals; residual max absolute marginal discrepancy. Budget0..10000, finite tolerance>0. Stop on residual<=tolerance or budget; overflow/underflow to zero explicit arithmetic error. O(iterationsrc) time/O(rc) space. Residual is feasibility evidence, not solution distance/optimality guarantee. Scale-invariant input fibers and budget status explicit.
Weighted covariance: West (1979), Updating mean and variance estimates: an improved method; Chan, Golub, LeVeque (1983), Algorithms for computing the sample variance. dimension1..64; finite coordinates |x|<=1e100, weights[0,1e100]. Population covariance M2/W, not unbiased sample covariance. Zero weight validates coordinates then does nothing. Merge dimensions must match, empty neutral. Merge W=A+B; delta=muB-muA; mu=muA+deltaB/W; M2=M2A+M2B+delta outer deltaA*(B/W). Atomic error updates, finite intermediates required. O(d²) push/merge/storage. Independent batch weighted centered moments oracle, partition merge equivalence within tolerance. No order-bitwise identity or universal covariance error certificate.
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