Elamur Groupantsmath-calc-evaluation-mixed-zero
The groupant beside math/src/calc.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 | Forward |
| ast | partial | ../../syntax.json |
| cost | partial | Cost |
| descriptant | present | Epoch |
| invariant | partial | Invariant |
| tests | bounded actual helper checks | 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 |
signed_zero_divisor | signed_zero_divisor | partial source derived model | signed_zero_divisor |
nonfinite_operand_exclusion | nonfinite_operand_exclusion | partial source derived model | nonfinite_operand_exclusion |
sticky_approximation | sticky_approximation | partial source derived model | sticky_approximation |
tick_avoidance | tick_avoidance | partial source derived model | tick_avoidance |
Model text
Scope
Source-derived bounded relation for the manifest byte interval. All relations observe one invocation and its stated state effects. Valid caller structures and finite values where specified are premises. No universal proof, percentage-error surrogate or production replacement is claimed.
Forward
Before scalar fallback and tick, finite R times exact Q(0), in either operand order, returns Q(0). Q(0)/R(x) returns Q(0) only for finite nonzero x. All other pairs continue through arith; this fragment is a conditional short-circuit with identity Env effects.
Invariant
The shortcut never modifies Env.steps or approx. A previously set approx flag is not cleared. Q0/R0 falls through and eventually rejects nonfinite division result.
Cost
Constant tag/finite/zero checks; cloning or evaluation of operands occurs outside this scope. Successful shortcut avoids tick and mixed arithmetic.
behavior_complement
An admitted finite mixed multiplication with exact zero excludes R(0) output and a newly incremented step count. Zero divided by approximate zero is excluded from this shortcut's successful transition.
reverse_reconstruction
Observing Q0 with unchanged Env admits either operand order for multiplication and any finite nonzero divisor for division. Observing only Q0 cannot distinguish these cases or the incoming approx flag.
signed_zero_divisor
Both +0.0 and -0.0 compare equal to0 and block the division shortcut; neither sign grants an exact quotient.
nonfinite_operand_exclusion
NaN and infinities fail is_finite and therefore bypass the exact-zero shortcut. If the later tick and conversions succeed, exact zero multiplied by NaN/infinity and exact zero divided by NaN produce nonfinite results rejected by real(). Exact zero divided by positive or negative infinity instead produces finite signed floating zero, returned as R with approx=true after a tick. Shortcut exclusion is not universal rejection of nonfinite operands.
sticky_approximation
Env.approx may already be true because eval computed an R operand. Returning exact Q0 preserves that historical flag, so value exactness and trace approximation are distinct observations.
tick_avoidance
Direct arith(Q0,R2.5,Mul) succeeds at unchanged steps. Non-shortcut Q0/R0 ticks before real() fails, so failure effects differ from early exact return.
Tests
Actual helper fixture: calc::wave34::syntax_zero_and_binding_boundaries. See file-root wave34-evidence.md for named profile/control receipts. Complement relations above are exclusions, not merely test lists; inverse relations retain compatible antecedents. Unexecuted paths remain source-derived.
Epoch
2026-10-31 wave34: new descendant refining the existing parent; prior parent descriptions and evidence retained as historical snapshots. Production code is unchanged; inline synthetic tests add bounded observations.
This page in Markdown → https://md.groupants.elamur.ai/free/en/mova/math/src/calc.rs.groupant/evaluation.groupant/mixed-zero.groupant/