Coverage

The characterization checklist, item by item, per engine

The checklist of characterization/areas.json: for each item, the facts that settle it on each engine and the strongest evidence among them, or missing. python -m sverify_dev.facts --coverage <engine> prints the same.

Engine	Items settled	Facts
DuckDB	68 of 69	101
Polars	69 of 69	103
DataFusion	1 of 69	3
Spark	69 of 69	71

integers

Item	Question	DuckDB	Polars	DataFusion	Spark
`overflow`	`+ - ×`, negate, `abs`, `MIN / -1` and integer `sum` past the declared width: raise, wrap or saturate, at which width.	fuzz: duckdb-R6, duckdb-decimal-arith, duckdb-R1, duckdb-R1-min, duckdb-R15-int-arith, duckdb-R15-int-divide, duckdb-R15-int-modulus, duckdb-int-pow	probe: polars-sum-int, polars-decimal-arith, polars-int-abs, polars-int-arith, polars-int-divide, polars-int-mod-overflow	missing	fuzz: spark-sum-int, spark-decimal-arith, spark-decimal-negate, spark-int-abs, spark-int-arith, spark-int-divide, spark-int-modulus, spark-int-pow
`division_type`	Integer `modulus` (and `divide`): truncated or floored.	fuzz: duckdb-R15-double-modulus, duckdb-R15-int-divide, duckdb-R15-int-modulus, duckdb-R2, duckdb-R3, duckdb-int-div-domain	probe: polars-double-modulus, polars-double-scalar-divisor, polars-int-divide, polars-int-modulus	missing	fuzz: spark-double-modulus, spark-int-divide, spark-int-modulus
`on_division_by_zero`	A zero divisor of integers and of doubles: error, NULL, IEEE or a limit.	fuzz: duckdb-R15-double-arith, duckdb-R4, duckdb-R5, duckdb-R15-int-divide, duckdb-R2, duckdb-R3	probe: polars-double-divide, polars-double-modulus, polars-int-divide, polars-int-modulus, polars-int-true-divide	missing	fuzz: spark-double-divide, spark-double-modulus, spark-int-divide, spark-int-modulus
`min_mod_neg_one`	`MIN % -1`: 0 or a raise.	probe: duckdb-R15-int-modulus	probe: polars-int-modulus	missing	probe: spark-int-modulus
`shift_range`	Shifts by a negative count or by the width or more, and bits shifted out.	probe: duckdb-R15-shift-left, duckdb-R15-shift-right	probe: polars-int-shift	missing	fuzz: spark-int-shift

decimals

Item	Question	DuckDB	Polars	DataFusion	Spark
`decimal_rescale`	A result with more digits than its scale: how it rounds.	probe: duckdb-decimal-arith	probe: polars-decimal-arith, polars-decimal-casts	missing	probe: spark-decimal-arith
`decimal_result_type`	The precision and scale of decimal arithmetic and aggregates, and overflow past 38 digits.	probe: duckdb-decimal-arith	probe: polars-decimal-arith	missing	probe: spark-decimal-arith

doubles

Item	Question	DuckDB	Polars	DataFusion	Spark
`rounding`	Rounding of arithmetic and of `round` (to `d` digits too).	probe: duckdb-avg-double, duckdb-float-sum-order, duckdb-stat-arg-types, duckdb-sum-double, duckdb-R15-elementary, duckdb-R15-round, duckdb-float-ieee, duckdb-float-math-double, duckdb-round-digits-2, duckdb-ulp-arith, duckdb-ulp-libm, duckdb-ulp-round, duckdb-window-sum-order	probe: polars-mean-float-streaming, polars-sum-float-streaming, polars-var-std-streaming, polars-double-scalar-divisor, polars-elem-rounding, polars-fp-ieee, polars-log-base, polars-round, polars-round-digits, polars-scalar-divisor, polars-ulp-arith, polars-ulp-libm, polars-ulp-round	missing	fuzz: spark-sum-double, spark-var-stddev, spark-double-arith, spark-double-divide, spark-elem-rounding, spark-round
`on_domain_error`	`sqrt`, logs, `asin`, `acos`, `atan2`, `power` outside their domain: NaN, NULL or a raise.	fuzz: duckdb-R15-atan2, duckdb-R15-double-arith, duckdb-R15-math-domain, duckdb-float-math-double, duckdb-int-div-domain, duckdb-int-pow	probe: polars-atan2, polars-double-divide, polars-math-domain, polars-int-div-domain, polars-int-pow-exponent	missing	fuzz: spark-double-divide, spark-math-domain, spark-int-divide, spark-int-pow
`on_log_zero`	A logarithm of zero: -inf, NaN or a raise.	probe: duckdb-R15-math-domain, duckdb-float-math-double	probe: polars-math-domain	missing	fuzz: spark-math-domain
`nan_creation`	`inf - inf`, `0 · inf`, `inf / inf`, `fmod(inf, y)`, a sum of both infinities: NaN or a raise.	fuzz: duckdb-float-sum-order, duckdb-nonfinite-aggregates, duckdb-R15-double-arith, duckdb-R15-double-modulus, duckdb-R4	probe: polars-nonfinite-aggregates, polars-double-arith, polars-double-divide, polars-double-modulus, polars-double-scalar-divisor, polars-scalar-divisor	missing	fuzz: spark-nonfinite-aggregates, spark-double-arith, spark-double-divide, spark-double-modulus
`float_overflow`	A finite double operation whose result overflows: `±∞`, or a raise (#575).	probe: duckdb-double-overflow	probe: polars-nonfinite-aggregates, polars-double-arith, polars-double-divide	missing	fuzz: spark-nonfinite-aggregates, spark-double-arith, spark-double-divide
`nan_equality`	Is NaN equal to NaN in `=`, grouping, `DISTINCT` and joins.	probe: duckdb-nan-equality	probe: polars-nan-equality	missing	probe: spark-nan-equality
`nan_order`	Where NaN sorts, and how `MIN`, `MAX`, `<`, greatest treat it.	fuzz: duckdb-arg-min-nulls, duckdb-quantile-disc, duckdb-nan-order	probe: polars-min-max-nan, polars-nan-order	missing	probe: spark-nan-order
`nan_kind`	Does a NaN’s sign (or payload) survive and show.	probe: duckdb-float-signs, duckdb-signbit	probe: polars-nan-sign	missing	fuzz: spark-nan-sign
`zero_sign`	`-0.0` in arithmetic, comparison, sorting and grouping.	probe: duckdb-minmax-zero-sign, duckdb-R14, duckdb-float-signs, duckdb-signbit	probe: polars-min-max-zero, polars-double-modulus, polars-zero-add, polars-zero-order, polars-zero-sign-streaming	missing	fuzz: spark-double-modulus, spark-zero-order, spark-zero-sign
`fp32`	Single-precision arithmetic and its conversions.	probe: duckdb-ulp-casts, duckdb-R12, duckdb-ulp-arith, duckdb-ulp-libm, duckdb-ulp-round	probe: polars-cast-to-double, polars-ulp-casts, polars-fp32, polars-ulp-arith, polars-ulp-libm, polars-ulp-round	missing	fuzz: spark-fp32

strings

Item	Question	DuckDB	Polars	DataFusion	Spark
`char_set`	`upper`, `lower`: Unicode or ASCII mappings.	probe: duckdb-case-mapping	probe: polars-case, polars-length, polars-reverse	missing	probe: spark-case, spark-string-plain
`case_sensitivity`	like, `contains`, `starts_with`, `strpos`, regexes: case-sensitive or not.	probe: duckdb-F4, duckdb-string-match-case	probe: polars-match-functions, polars-regex	missing	fuzz: spark-match-functions, spark-regex
`substring_range`	substring offsets and lengths outside 32 bits.	probe: duckdb-substring-range	probe: polars-substring-range	missing	fuzz: spark-substring-range
`negative_start`	substring with a negative or zero start; its indexing (characters or bytes, 0- or 1-based).	engine_test: duckdb-R13	probe: polars-strpos, polars-substring	missing	fuzz: spark-strpos, spark-substring
`string_positions`	What substring and `strpos` positions count: characters or bytes, from 0 or 1; `strpos` without a match.	probe: duckdb-R13, duckdb-string-match-case	probe: polars-strpos, polars-substring	missing	fuzz: spark-strpos, spark-substring
`regex_dialect`	The regex engine and syntax, classes on non-ASCII text, a match that fails, replacement references.	probe: duckdb-R15-regexp	probe: polars-regex	missing	fuzz: spark-regex
digests	`md5`, `sha256` and other digests: present, and on which bytes.	probe: duckdb-R15-digests	probe: polars-string-functions-missing	missing	probe: spark-digests

temporal

Item	Question	DuckDB	Polars	DataFusion	Spark
`date_range`	Date and timestamp arithmetic past 0001-01-01 … 9999-12-31.	probe: duckdb-date-range	probe: polars-date-range, polars-month-arith	missing	fuzz: spark-date-range
`time_interval_months`	`TIME ± INTERVAL` with months, and time arithmetic past midnight.	probe: duckdb-time-plus-interval	probe: polars-temporal-errors	missing	probe: spark-time-type
`timestamp_precision`	The timestamp unit (s, ms, µs, ns) and its range.	engine_test: duckdb-R10	probe: polars-timestamp-unit	missing	probe: spark-timestamp-precision
`time_zones`	Time zones: DST gaps and overlaps, conversions.	probe: duckdb-time-zones	probe: polars-temporal-errors	missing	probe: spark-time-zones
`week_numbering`	Week numbers, weekdays, ISO years, date_trunc to a week, parts before 1970.	probe: duckdb-yearweek	probe: polars-date-parts	missing	probe: spark-week-parts

casts

Item	Question	DuckDB	Polars	DataFusion	Spark
float_to_int	A double or decimal cast to an integer: truncate or round.	probe: duckdb-R9	probe: polars-cast-double-to-int, polars-decimal-casts	missing	probe: spark-cast-double-to-int
`cast_failure`	A cast that does not fit or parse: raise or NULL.	engine_test: duckdb-R8	probe: polars-cast-double-to-int, polars-cast-int, polars-cast-string, polars-decimal-casts	missing	fuzz: spark-cast-double-to-int, spark-cast-string
`cast_parsing`	Text to numbers, booleans and dates: what is accepted (spaces, signs, `nan`, `inf`, exponents).	engine_test: duckdb-R10	probe: polars-cast-string, polars-temporal-errors	missing	fuzz: spark-cast-string
`cast_formatting`	Numbers, booleans and dates to text: the format.	probe: duckdb-printf	probe: polars-cast-string, polars-strftime	missing	fuzz: spark-cast-string

nulls

Item	Question	DuckDB	Polars	DataFusion	Spark
`null_handling`	`concat` and other functions given a NULL: NULL or skip.	probe: duckdb-null-concat	probe: polars-concat	missing	probe: spark-concat
`three_valued_logic`	`and`, `or`, `not` with NULLs; `bool_and`, `bool_or` over NULLs.	probe: duckdb-kleene	probe: polars-kleene	missing	probe: spark-kleene
`null_join_keys`	Do NULL keys match in joins, and how `IS NOT DISTINCT FROM` is spelled.	probe: duckdb-null-keys, duckdb-set-operations	probe: polars-null-keys, polars-set-operations	missing	probe: spark-null-keys, spark-set-operations

nested

Item	Question	DuckDB	Polars	DataFusion	Spark
`list_null_order`	A NULL element deciding `<` of lists, in comparisons and in `ORDER BY`.	engine_test: duckdb-R11	probe: polars-list-order	missing	fuzz: spark-list-order
`list_indexing`	List indexing: base, negative and out-of-range indexes.	probe: duckdb-list-index	probe: polars-list-index	missing	fuzz: spark-list-index
`struct_equality`	Equality and order of structs with NULL fields.	probe: duckdb-struct-equality	probe: polars-nested-equality	missing	probe: spark-nested-equality
`unnest_null_empty`	UNNEST of a NULL list and of an empty one.	probe: duckdb-unnest	probe: polars-explode	missing	probe: spark-explode

aggregates

Item	Question	DuckDB	Polars	DataFusion	Spark
`avg_int_result`	`avg` of integers: its type and how it is computed.	probe: duckdb-R6, duckdb-avg-int	probe: polars-avg-int	missing	fuzz: spark-avg-int
`sum_order`	The order and grouping of a double `SUM`, `AVG`.	probe: duckdb-R7, duckdb-avg-double, duckdb-float-sum-order, duckdb-kahan-sum, duckdb-sum-double, duckdb-window-sum-order	probe: polars-mean-float-streaming, polars-sum-float-streaming	missing	fuzz: spark-avg-double, spark-sum-double
`stat_algo`	The algorithm of `VAR_`, `STDDEV_`, `COVAR_*`, `CORR`.	probe: duckdb-corr, duckdb-covar, duckdb-stat-arg-types, duckdb-var-stddev	probe: polars-corr, polars-cov, polars-var-std-streaming	missing	fuzz: spark-corr, spark-covar, spark-var-stddev
`stat_degenerate`	`CORR` of one pair or a constant side; a statistical aggregate of a single value.	probe: duckdb-corr, duckdb-nonfinite-aggregates, duckdb-stat-arg-types	probe: polars-corr, polars-var-std-streaming	missing	fuzz: spark-corr, spark-nonfinite-aggregates, spark-var-stddev
`quantile_interp`	`QUANTILE_CONT`, `QUANTILE_DISC`, `MEDIAN`: the position and interpolation.	probe: duckdb-quantile-cont-interpolation, duckdb-quantile-disc	probe: polars-quantile	missing	fuzz: spark-quantile
`tie_pick`	Which row `FIRST`, `LAST`, `ARG_MIN`, `ARG_MAX`, `any_value`, `MODE` take among ties.	probe: duckdb-arg-min-nulls, duckdb-mode-ties	probe: polars-arg-min-max, polars-first-last, polars-mode	missing	probe: spark-first-last
`empty_group_aggregates`	Aggregates of no rows or of NULLs only (`SUM`, `COUNT`, `MIN`, `AVG`).	probe: duckdb-avg-int, duckdb-statistical-aggregates, duckdb-sum-double, duckdb-list-sum	probe: polars-avg-int, polars-count-empty, polars-mean-float-streaming, polars-sum-float-streaming, polars-sum-int	missing	fuzz: spark-avg-int, spark-sum-double, spark-sum-int
`nonfinite_aggregates`	Aggregates of ±inf and NaN inputs.	probe: duckdb-R7, duckdb-kahan-sum, duckdb-moments, duckdb-nonfinite-aggregates	probe: polars-nonfinite-aggregates	missing	fuzz: spark-nonfinite-aggregates

windows

Item	Question	DuckDB	Polars	DataFusion	Spark
`ntile_spread`	How `NTILE` spreads the remainder.	probe: duckdb-ntile	probe: polars-rank	missing	probe: spark-rank
`default_window_frame`	The frame when none is given, with and without an order; rank functions over ties and NULLs.	probe: duckdb-window-frame	probe: polars-rank, polars-window-values	missing	probe: spark-rank, spark-window-values

relations

Item	Question	DuckDB	Polars	DataFusion	Spark
`tie_order`	The order of ties in a sort, `STRING_AGG`, collect, a window: stable or not.	probe: duckdb-mode-ties, duckdb-sort-ties	probe: polars-first-last, polars-sort-stability-streaming, polars-rank, polars-window-values	missing	probe: spark-first-last, spark-sort-stability, spark-rank, spark-window-values
`null_order`	Where NULLs sort by default, ascending and descending.	probe: duckdb-F2, duckdb-window-frame	probe: polars-null-order	missing	probe: spark-null-order
`clustered`	A sort that only clusters equal keys.	probe: duckdb-clustered	probe: polars-clustered	missing	probe: spark-clustered
`set_operations`	`UNION`, `INTERSECT`, `EXCEPT`, with and without `ALL`: duplicates, NULLs, order.	probe: duckdb-set-operations	probe: polars-set-operations	missing	probe: spark-set-operations
`nan_zero_grouping`	Grouping, `DISTINCT` and join keys with NaN and `-0.0`: one group, and which value represents it.	probe: duckdb-R14, duckdb-nan-equality	probe: polars-nan-equality, polars-zero-order	missing	fuzz: spark-nan-equality, spark-zero-order

errors

Item	Question	DuckDB	Polars	DataFusion	Spark
`raise_set`	Where the engine raises beyond the reference (D2): extra raises, and raises that are planning errors or panics.	probe: duckdb-moments, duckdb-decimal-arith, duckdb-R15-int-modulus, duckdb-R15-shift-left, duckdb-list-vectors, duckdb-printf, duckdb-date-range, duckdb-ntile	probe: polars-decimal-arith, polars-list-index, polars-date-range	missing	fuzz: spark-decimal-negate, spark-raise-set, spark-list-index, spark-regex, spark-substring-range, spark-date-range

execution

Item	Question	DuckDB	Polars	DataFusion	Spark
`evaluation_order`	Short-circuit in `CASE`, `AND`, `OR`, `COALESCE`: does the engine evaluate an expression on rows a filter or a branch removes, and raise there (division by zero, a failing cast)? This can break the reference’s no-error guarantee.	fuzz: duckdb-exec-filter-pushdown, duckdb-exec-short-circuit	probe: polars-exec-cse-hoist, polars-exec-predicate-pushdown, polars-exec-when-eager	missing	probe: spark-exec-evaluation-order
`settings`	Which session settings change results: DuckDB’s `default_null_order`, `integer_division`, `threads`, …; Polars’s `Config` and environment variables.	probe: duckdb-exec-settings	engine_test: polars-exec-engine	missing	fuzz: spark-exec-parser-cache, spark-exec-settings, spark-list-index, spark-case, spark-time-zones
`parallel_nondeterminism`	Results that change with the thread count or from run to run: the order of a double `SUM`, row order without `ORDER BY`, ties.	probe: duckdb-exec-row-order	probe: polars-exec-row-order	missing	fuzz: spark-first-last, spark-sum-double, spark-sum-int, spark-exec-parallel, spark-sort-stability, spark-window-values
`platform`	Results that depend on the platform: libm (`sin`, `pow`, `exp`), NaN signs, SIMD paths; probes ran on macOS arm64, CI on Linux x86_64.	probe: duckdb-exec-platform	probe: polars-exec-platform	missing	fuzz: spark-elem-rounding, spark-nan-sign, spark-exec-platform
`size_limits`	Limits on string, blob and list lengths, decimal precision, nesting depth, and what happens past them.	engine_test: duckdb-exec-size-limits	engine_test: polars-exec-size-limits	missing	fuzz: spark-exec-parser-cache, spark-exec-size-limits
`streaming_fallback`	Operations a streaming engine cannot run itself and hands to its in-memory engine (Polars’s streaming engine, which sverify targets): which, and whether results differ.	missing	engine_test: polars-exec-streaming-fallback	missing	source: spark-exec-streaming-fallback
`try_variants`	`TRY_CAST`, `TRY(…)` and other non-raising forms: which errors become NULL and which still raise.	engine_test: duckdb-exec-try	engine_test: polars-exec-strict-false	missing	fuzz: spark-try-variants

frontend

Item	Question	DuckDB	Polars	DataFusion	Spark
`type_names`	The engine’s names of the types.	probe: duckdb-typeof-names, duckdb-F4	probe: polars-type-names	missing	probe: spark-type-names
`implicit_casts`	Implicit casts and type promotion in arithmetic and comparisons.	engine_test: duckdb-F1	probe: polars-fp32, polars-int-float-compare, polars-implicit-casts, polars-int-true-divide	missing	fuzz: spark-fp32, spark-implicit-casts
`literal_types`	The types of literals.	engine_test: duckdb-F3	probe: polars-literal-types	engine_test: datafusion-S4	probe: spark-literal-types

io

Item	Question	DuckDB	Polars	DataFusion	Spark
`io_formats`	File formats read and written, and their type mappings.	probe: duckdb-IO3	probe: polars-io	missing	engine_test: spark-io
`object_stores`	Object stores and their credentials.	probe: duckdb-IO1, duckdb-IO2, duckdb-IO3	probe: polars-io	missing	engine_test: spark-io
`catalogs`	Catalogs (Unity, Iceberg, …) and how the engine attaches them.	probe: duckdb-IO1, duckdb-IO2	probe: polars-io	missing	engine_test: spark-io