other

Binomial distribution with `trials` (n ≥ 0, ≤ 1e6) and success `probability` (0..1). `function` selects the mass (pmf), cumulative distribution (cdf) or quantile / inverse-CDF.

Compute the RFC 6902 JSON Patch that transforms `source` into `target`. The patch is a minimal array of add/remove/replace operations.

List every physical constant in the dataset, or only those in a given category (universal, adopted, electromagnetic, atomic, physico-chemical). Returns the constants, the total count and the set of available categories.

Compute (base ^ exponent) mod modulus efficiently for arbitrary-precision integers. The modulus must be positive.

Normal distribution with optional mean (default 0) and standard deviation sd (default 1). `function` selects the density (pdf), cumulative distribution (cdf) or quantile / inverse-CDF.

Validate an IBAN (mod-97 checksum, length, country format) and decompose it into country, bank, branch and account parts.

Validate a JSON value against a JSON Schema (draft-07, with the standard string formats enabled). An invalid schema is rejected as a clean 400 before payment; a valid schema that the data simply fails to satisfy is a successful result with valid=false and a list of errors (path, keyword, message).

Area (Heron's formula), perimeter and interior angles of a triangle from its three side lengths. Sides that violate the triangle inequality are rejected as a clean 400.

Evaluate an SPF record against an IPv4/IPv6 address using only its literal ip4/ip6/all mechanisms. DNS-dependent mechanisms (include, a, mx, exists, redirect) reached before a match yield an honest `indeterminate` result rather than a guess.

Split the input into parts on each match of a RE2 pattern. An optional limit caps the number of parts (0 = unlimited). Returns the parts array and its count.

Internal rate of return (per period) of a series of cash flows, solved with a bounded bisection. Requires at least one positive and one negative flow; flows with no sign change or no bracketable root are rejected as a clean 400.

Infer a JSON Schema (draft-07) from a sample document in any supported format. Types are inferred, present keys are marked required, and heterogeneous array item schemas are merged. The result validates out of the box with /v1/validate.

Find the first match (or all matches with all=true) of a RE2 pattern, returning each match's text, start/end offsets, and numbered and named capture groups. No match is a successful 200 with an empty match list.

Prime-factorize a positive integer (≤ 10^15 so the computation is always fast). Returns the prime factors with exponents, the divisor count, and whether n is prime.

Euler's totient φ(n) — the count of integers in [1, n] coprime to n — for a positive integer ≤ 10^15 (it is computed from the prime factorization).

Infer a JSON Schema (draft-07) from an example value, walking objects and arrays recursively. Set detectFormat=true to tag strings that look like date-time/date/email/uri/uuid, requireAll=false to leave object properties optional, and additionalProperties=true to allow extra keys.

Euclidean, Manhattan and Chebyshev distance between two 2-D points.

Number of ordered arrangements of r items from n, nPr = n!/(n-r)!. Requires r ≤ n and r ≤ 10000.

Grow a principal by simple or compound interest over a number of years. Compound interest uses compoundsPerYear compounding periods (default 12, monthly).

Deep-merge an ordered list of JSON documents, left to right. Objects are merged key-by-key; arrays, scalars and null in a later document replace the earlier value (last-wins, no array concatenation).

Parse a document (json, json5, jsonc, yaml, xml, csv, tsv, toml, ndjson, ini, env, properties, plist or querystring) and validate it against a JSON Schema. Returns whether it is valid and a list of precise, path-tagged errors. Malformed input or an invalid schema is rejected before payment.

Apply an RFC 6902 JSON Patch to a JSON document and return the result. An invalid or unresolvable patch (e.g. a failed `test`, or a path that does not exist) is rejected before payment.

Poisson distribution with rate `lambda` (> 0, ≤ 1e9). `function` selects the mass (pmf), cumulative distribution (cdf) or quantile / inverse-CDF.

Parse a document (in any format) and re-emit it in the RFC 8785 JSON Canonicalization Scheme form — sorted keys, canonical number/string formatting — plus the SHA-256 of the canonical bytes for stable hashing, signing and dedup.