{ "category": "Operators", "display_name": "Less than (<)", "entry_kind": "built_in_operator", "eval_api": { "method": "POST", "url": "https://handbook.dnacalc.com/api/eval" }, "function_id": "FUNC.OP_LESS_THAN", "implementation_state": { "answer_bank": null, "detail": "Of 1,618 recorded answers (1,618 workbook cells), 8 do not match: 8 are refused.", "dnacalc_commit": "9e1884369a678158dd82d3d74188daf986995e87", "in_catalogue": true, "state": "differs", "state_label": "Known larger differences", "summary": "Refuses 8 of 1,618 recorded calls; the rest match", "workbook_corpus": { "cells": 1618, "matched": 1610, "refused": 8, "worst_ulp": 0 } }, "implementations": [ { "commit": "9e1884369a678158dd82d3d74188daf986995e87", "flavour": "excel-compatibility-candidate", "language": "Rust", "name": "CalcFunc", "own_code": [ "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/comparison.rs#L58-L58", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/comparison.rs#L128-L133" ], "repository": "https://github.com/DnaCalc/DnaCalc", "shared_code": [ "catalogue/comparison::compare", "catalogue/comparison::Operand::kind", "catalogue/comparison::Operand::blank", "catalogue/comparison::order", "catalogue/comparison::overflow_numbers", "catalogue/comparison::numbers", "catalogue/comparison::in_band", "catalogue/comparison::Rounded::up", "catalogue/comparison::Roundings::of", "catalogue/comparison::Roundings::disjoint", "catalogue/comparison::texts", "catalogue/comparison/collation::compare", "catalogue/comparison/collation::weighed", "catalogue/comparison/collation::measured_iteration_extension", "catalogue/comparison/sort_key::table", "catalogue/comparison/sort_key::decode64", "catalogue/comparison/sort_key::Reader::byte", "catalogue/comparison/sort_key::Reader::varint", "catalogue/comparison/sort_key::Reader::done", "catalogue/comparison/sort_key::in_ranges", "catalogue/comparison/sort_key::build", "catalogue/comparison/sort_key::han_base", "catalogue/comparison/sort_key::derive", "catalogue/comparison/sort_key::shared_jamo_tails", "catalogue/comparison/sort_key::ordinary_jamo_prefix", "catalogue/comparison/sort_key::independent_jamo_suffix", "catalogue/comparison/sort_key::jamo_leading_primary", "catalogue/comparison/sort_key::leading_order", "catalogue/comparison/sort_key::Before::separate_special", "catalogue/comparison/sort_key::Gathered::kana", "catalogue/comparison/sort_key::Gathered::unit", "catalogue/comparison/sort_key::parts", "catalogue/comparison/sort_key::diacritic_order", "catalogue/comparison/sort_key::diacritics", "decimal::low32", "decimal::Natural::from_u64", "decimal::Natural::pow10", "decimal::Natural::normalize", "decimal::Natural::is_zero", "decimal::Natural::mul_add_small", "decimal::Natural::times_pow10", "decimal::Natural::times_pow5", "decimal::Natural::times_pow2", "decimal::ExactDecimal::binary" ], "source": "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/comparison.rs#L58-L58", "state": "differs", "suite": null, "summary": "Refuses 8 of 1,618 recorded calls; the rest match" } ], "json_url": "https://handbook.dnacalc.com/api/functions/FUNC.OP_LESS_THAN.json", "name": "OP_LESS_THAN", "notes": [ { "basis": "32 recorded readings on one collation sheet.", "documentation": null, "evidence": [ { "commit": "eceb809985e244e9d0a20f905e58fe57b8741ed8", "locator": "sheet fn3_collation, rows 290 to 321", "note": null, "path": "crates/calc-func/tests/captures/fn3_questions/oracle.capture.json", "repository": "DnaCalc" } ], "functions": [ "FUNC.OP_EQUAL", "FUNC.OP_LESS_THAN" ], "inferred": null, "kind": "quirk", "note_id": "FN-OP_EQUAL-001", "open": [ "Twelve further comparisons (other leading consonants, a trailing consonant, a compound vowel, compatibility jamo) were read on 2026-11-04. They are not yet in a published capture, so this note does not rest on them." ], "recorded_on": "2026-11-04", "repros": [ { "call": "=\"가\"=\"가\"", "correct": null, "excel": { "bits": null, "display": "FALSE", "kind": "logical" }, "input_route": "formula-literal", "inputs": [], "recorded_in": "Excel 16.0.20527.20088 Current Channel, Windows 64-bit (NT 10.0.26200), x86-64, AMD Ryzen 7 4800H, en-ZA", "source": { "commit": "eceb809985e244e9d0a20f905e58fe57b8741ed8", "locator": "sheet fn3_collation, row 290, column 4", "note": null, "path": "crates/calc-func/tests/captures/fn3_questions/oracle.capture.json", "repository": "DnaCalc" } }, { "call": "=\"가\"<\"가\"", "correct": null, "excel": { "bits": null, "display": "TRUE", "kind": "logical" }, "input_route": "formula-literal", "inputs": [], "recorded_in": "Excel 16.0.20527.20088 Current Channel, Windows 64-bit (NT 10.0.26200), x86-64, AMD Ryzen 7 4800H, en-ZA", "source": { "commit": "eceb809985e244e9d0a20f905e58fe57b8741ed8", "locator": "sheet fn3_collation, row 291, column 4", "note": null, "path": "crates/calc-func/tests/captures/fn3_questions/oracle.capture.json", "repository": "DnaCalc" } }, { "call": "=\"각\"=\"각\"", "correct": null, "excel": { "bits": null, "display": "FALSE", "kind": "logical" }, "input_route": "formula-literal", "inputs": [], "recorded_in": "Excel 16.0.20527.20088 Current Channel, Windows 64-bit (NT 10.0.26200), x86-64, AMD Ryzen 7 4800H, en-ZA", "source": { "commit": "eceb809985e244e9d0a20f905e58fe57b8741ed8", "locator": "sheet fn3_collation, row 296, column 4", "note": null, "path": "crates/calc-func/tests/captures/fn3_questions/oracle.capture.json", "repository": "DnaCalc" } } ], "schema": "efh.function-note/v1", "statement": "U+1100 U+1161 is canonically equivalent to the syllable U+AC00 in Unicode, but Excel's comparison says they are not equal, and the jamo sequence sorts first. The same holds with a final consonant, U+1100 U+1161 U+11A8 against U+AC01.", "status": "measured", "title": "Conjoining Hangul jamo do not compare equal to the precomposed syllable" }, { "basis": "66 recorded readings of =, < and > on 22 pairs of strings, 11 pairs after 時 and 11 after a.", "documentation": null, "evidence": [ { "commit": "2d0eddcac86413014643af81d646581d54ba57bc", "locator": "sheets q001 to q066", "note": "66 recorded readings", "path": "crates/calc-func/tests/captures/fn4_questions/functions-fn4.capture.json", "repository": "DnaCalc" } ], "functions": [ "FUNC.OP_GREATER_THAN", "FUNC.OP_LESS_THAN" ], "inferred": null, "kind": "quirk", "note_id": "FN-OP_LESS_THAN-001", "open": [ "The collation rule behind this is not identified, and none is claimed here." ], "recorded_on": "2026-11-04", "repros": [ { "call": "=\"a-ゝx\"<\"aゝx\"", "correct": null, "excel": { "bits": null, "display": "TRUE", "kind": "logical" }, "input_route": "formula-literal", "inputs": [], "recorded_in": "Excel 16.0.20527.20088 Current Channel, Windows 64-bit (NT 10.0.26200), x86-64, AMD Ryzen 7 4800H, en-ZA", "source": { "commit": "2d0eddcac86413014643af81d646581d54ba57bc", "locator": "sheet q059, row 20, column 10", "note": null, "path": "crates/calc-func/tests/captures/fn4_questions/functions-fn4.capture.json", "repository": "DnaCalc" } }, { "call": "=\"a-ゝx\">\"aゝx\"", "correct": null, "excel": { "bits": null, "display": "FALSE", "kind": "logical" }, "input_route": "formula-literal", "inputs": [], "recorded_in": "Excel 16.0.20527.20088 Current Channel, Windows 64-bit (NT 10.0.26200), x86-64, AMD Ryzen 7 4800H, en-ZA", "source": { "commit": "2d0eddcac86413014643af81d646581d54ba57bc", "locator": "sheet q060, row 20, column 10", "note": null, "path": "crates/calc-func/tests/captures/fn4_questions/functions-fn4.capture.json", "repository": "DnaCalc" } }, { "call": "=\"時-ゝx\"<\"時ゝx\"", "correct": null, "excel": { "bits": null, "display": "FALSE", "kind": "logical" }, "input_route": "formula-literal", "inputs": [], "recorded_in": "Excel 16.0.20527.20088 Current Channel, Windows 64-bit (NT 10.0.26200), x86-64, AMD Ryzen 7 4800H, en-ZA", "source": { "commit": "2d0eddcac86413014643af81d646581d54ba57bc", "locator": "sheet q050, row 20, column 10", "note": null, "path": "crates/calc-func/tests/captures/fn4_questions/functions-fn4.capture.json", "repository": "DnaCalc" } }, { "call": "=\"時-ゝx\">\"時ゝx\"", "correct": null, "excel": { "bits": null, "display": "TRUE", "kind": "logical" }, "input_route": "formula-literal", "inputs": [], "recorded_in": "Excel 16.0.20527.20088 Current Channel, Windows 64-bit (NT 10.0.26200), x86-64, AMD Ryzen 7 4800H, en-ZA", "source": { "commit": "2d0eddcac86413014643af81d646581d54ba57bc", "locator": "sheet q051, row 20, column 10", "note": null, "path": "crates/calc-func/tests/captures/fn4_questions/functions-fn4.capture.json", "repository": "DnaCalc" } }, { "call": "=\"a−ゝ\"<\"aゝ\"", "correct": null, "excel": { "bits": null, "display": "TRUE", "kind": "logical" }, "input_route": "formula-literal", "inputs": [], "recorded_in": "Excel 16.0.20527.20088 Current Channel, Windows 64-bit (NT 10.0.26200), x86-64, AMD Ryzen 7 4800H, en-ZA", "source": { "commit": "2d0eddcac86413014643af81d646581d54ba57bc", "locator": "sheet q029, row 20, column 10", "note": null, "path": "crates/calc-func/tests/captures/fn4_questions/functions-fn4.capture.json", "repository": "DnaCalc" } }, { "call": "=\"時−ゝ\">\"時ゝ\"", "correct": null, "excel": { "bits": null, "display": "TRUE", "kind": "logical" }, "input_route": "formula-literal", "inputs": [], "recorded_in": "Excel 16.0.20527.20088 Current Channel, Windows 64-bit (NT 10.0.26200), x86-64, AMD Ryzen 7 4800H, en-ZA", "source": { "commit": "2d0eddcac86413014643af81d646581d54ba57bc", "locator": "sheet q006, row 20, column 10", "note": null, "path": "crates/calc-func/tests/captures/fn4_questions/functions-fn4.capture.json", "repository": "DnaCalc" } }, { "call": "=\"a−ゝ\">\"a−\"", "correct": null, "excel": { "bits": null, "display": "TRUE", "kind": "logical" }, "input_route": "formula-literal", "inputs": [], "recorded_in": "Excel 16.0.20527.20088 Current Channel, Windows 64-bit (NT 10.0.26200), x86-64, AMD Ryzen 7 4800H, en-ZA", "source": { "commit": "2d0eddcac86413014643af81d646581d54ba57bc", "locator": "sheet q027, row 20, column 10", "note": null, "path": "crates/calc-func/tests/captures/fn4_questions/functions-fn4.capture.json", "repository": "DnaCalc" } }, { "call": "=\"時−ゝ\">\"時−\"", "correct": null, "excel": { "bits": null, "display": "TRUE", "kind": "logical" }, "input_route": "formula-literal", "inputs": [], "recorded_in": "Excel 16.0.20527.20088 Current Channel, Windows 64-bit (NT 10.0.26200), x86-64, AMD Ryzen 7 4800H, en-ZA", "source": { "commit": "2d0eddcac86413014643af81d646581d54ba57bc", "locator": "sheet q003, row 20, column 10", "note": null, "path": "crates/calc-func/tests/captures/fn4_questions/functions-fn4.capture.json", "repository": "DnaCalc" } } ], "schema": "efh.function-note/v1", "statement": "Comparing a string with punctuation before a repeat or prolonged-sound mark against the same string without the punctuation, the order depends on the character at the start. After a Latin letter the punctuated string is smaller: \"a-ゝx\" < \"aゝx\". After a Han character it is larger: \"時-ゝx\" > \"時ゝx\". This held for every pair read, with the marks ゝ, 々 and ー and with hyphen-minus, U+2212 and U+2019 as the punctuation. In all 66 readings the two strings are never equal, and a string with the mark added sorts after the string without it, after Latin and after Han alike: \"a−ゝ\" > \"a−\".", "status": "measured", "title": "Punctuation before a Japanese repeat mark sorts one way after a Latin letter, the other after Han" }, { "basis": "77 recorded controls over three bases (時, 人, 漢).", "documentation": null, "evidence": [ { "commit": "44db028d72d692e94557b3657748d25643cd199d", "locator": "fn1_han_iteration_comparison_and_lookup_order", "note": "recorded order pinned", "path": "crates/calc-fml/tests/acceptance/f3.rs", "repository": "DnaCalc" } ], "functions": [ "FUNC.OP_LESS_THAN", "FUNC.SORT" ], "inferred": null, "kind": "quirk", "note_id": "FN-SORT-001", "open": [], "recorded_on": "2026-11-04", "repros": [ { "call": "=\"時々\"<\"時時\"", "correct": null, "excel": { "bits": null, "display": "TRUE", "kind": "logical" }, "input_route": "formula-literal", "inputs": [], "recorded_in": "Excel 16.0.20527.20088 Current Channel, Windows 64-bit (NT 10.0.26200), x86-64, AMD Ryzen 7 4800H, en-ZA", "source": { "commit": "f3275d997ae0706471e7b2c52b36fafad6966a03", "locator": "sheet fn1_collation, row 2, column 4", "note": null, "path": "crates/calc-func/tests/captures/catalogue/sections/fn1_collation.capture.json", "repository": "DnaCalc" } }, { "call": "=\"時々\"<\"時a\"", "correct": null, "excel": { "bits": null, "display": "TRUE", "kind": "logical" }, "input_route": "formula-literal", "inputs": [], "recorded_in": "Excel 16.0.20527.20088 Current Channel, Windows 64-bit (NT 10.0.26200), x86-64, AMD Ryzen 7 4800H, en-ZA", "source": { "commit": "f3275d997ae0706471e7b2c52b36fafad6966a03", "locator": "sheet fn1_collation, row 3, column 4", "note": null, "path": "crates/calc-func/tests/captures/catalogue/sections/fn1_collation.capture.json", "repository": "DnaCalc" } }, { "call": "=TEXTJOIN(\"|\",FALSE,SORT({\"時々\";\"時時\";\"時\";\"時a\";\"時b\"}))", "correct": null, "excel": { "bits": null, "display": "時|時々|時a|時b|時時", "kind": "text" }, "input_route": "formula-literal", "inputs": [], "recorded_in": "Excel 16.0.20527.20088 Current Channel, Windows 64-bit (NT 10.0.26200), x86-64, AMD Ryzen 7 4800H, en-ZA", "source": { "commit": "f3275d997ae0706471e7b2c52b36fafad6966a03", "locator": "sheet fn1_collation, row 229, column 4", "note": null, "path": "crates/calc-func/tests/captures/catalogue/sections/fn1_collation.capture.json", "repository": "DnaCalc" } } ], "schema": "efh.function-note/v1", "statement": "In text comparison and SORT, after a Han character the iteration mark 々 sorts before Latin letters and before the doubled character: 時 < 時々 < 時a < 時b < 時時. Latin letters sort before Han here, and 時々 is not treated as 時時.", "status": "measured", "title": "A Han iteration mark is not read as a repeat of the character" } ], "schema": "efh.function-reference/v1", "section_order": [ "what-it-does", "try-it", "quirks", "how-to-implement", "version-differences", "alternatives" ], "sections": { "alternatives": "\n### Relationships\n\n\n- [`FUNC.OP_LESS_EQUAL`](FUNC.OP_LESS_EQUAL.md) — the non-strict form.\n- [`FUNC.OP_GREATER_THAN`](FUNC.OP_GREATER_THAN.md) — the mirror. `AA` should\n agree; that they do is an assumption worth testing rather than a theorem.\n- [`FUNC.OP_EQUAL`](FUNC.OP_EQUAL.md) — the rules; also the third leg of trichotomy.\n- `MIN`, `SMALL`, `SORT`, `RANK` — functions that order values. They do not necessarily use\n this operator's rules; `MIN` over a range ignores text entirely, where `<` ranks it above\n every number. Do not reason from one to the other.\n- `MATCH` with match type `1` or `-1`, and `VLOOKUP`/`HLOOKUP` in approximate mode, depend on\n a data ordering that must agree with the comparison ordering. Mixed-kind columns are where\n that assumption breaks.\n- `COUNTIF(range,\"<5\")` — criteria strings again: parsed by the consuming function, not this\n operator.\n\n\n", "how-to-implement": "\n### Notes for implementers\n\n\n- Implement one comparison core returning a three-way result (less, equal, greater, plus an\n error lane), and derive all six operators from it. Six independent implementations will\n disagree somewhere, and the disagreement will be invisible until a user finds it.\n- The kind ordering must be applied before any within-kind comparison, and must be total.\n- Case-insensitive text comparison and locale collation are not the same problem. Record\n which one you implemented; the contract's own slice stops at the installed baseline.\n- Do not reduce `A=B)` in the presence of errors — the error must reach the\n result, not become a logical.\n\n\n", "quirks": "\n### Result and edge cases\n\n- **Equal operands** give `FALSE`; `<` is strict.\n- **Different kinds** give the kind ordering, always, with no numeric interpretation of text.\n- **Blank operands.** The context-sensitive blank rule applies: blank behaves as `0` against\n a number, `\"\"` against text, `FALSE` against a logical. So a blank cell is not less than\n zero, and is not less than `\"\"` — but it *is* less than any positive number and less than\n `TRUE`.\n- **Text ordering of numeric strings.** `\"10\" < \"9\"` is `TRUE` under text ordering while\n `10 < 9` is `FALSE`; the difference is entirely in whether the operands are text. Sorted\n columns of numbers stored as text are the standard way this reaches a real workbook.\n- **Arrays.** Ordinary broadcast with `#N/A` for unsupplied coordinates.\n\n\n\n### Errors\n\n`data/functions/FUNC.OP_LESS_THAN.json` records no Microsoft documentation URL (`docs` is\n`null`).\n\n\n", "sources": "- `data/presence/FUNC.OP_LESS_THAN.json` — implementing module\n `earlier-implementation/operator_compare_concat_family.rs`.\n- Handbook `content/model/01-value-universe.md`, `02-coercion-and-lifting.md`,\n `03-call-pipeline.md`, and [`FUNC.OP_EQUAL`](FUNC.OP_EQUAL.md) for the three rules.\n\n", "version-differences": "No comparison between specific Excel builds is recorded here yet. This does not establish that all builds behave alike.", "what-it-does": "\n`A < B` returns `TRUE` when `A` precedes `B` in Excel's comparison order, and `FALSE`\notherwise.\n\nThe three shared comparison rules are stated in full on\n[`FUNC.OP_EQUAL`](FUNC.OP_EQUAL.md). This operator is where the first of them stops being an\nabstraction, because ordering across kinds is only observable through the strict\ninequalities:\n\n```\n any Number < any Text < any Logical\n```\n\nWithin a kind:\n\n- **Numbers** order numerically, but through the family's normalization lane rather than\n exact IEEE comparison — the contract records `=0.1+0.2<0.3` as `FALSE`, which exact\n arithmetic would make `TRUE`. See [`FUNC.OP_EQUAL`](FUNC.OP_EQUAL.md) rule 3.\n- **Text** orders by a case-insensitive comparison. The collation beyond that — accents,\n non-Latin scripts, locale-specific sequences — is explicitly out of the contract's slice,\n and the Handbook has measured only the cases in FN-OP_EQUAL-001, FN-OP_LESS_THAN-001 and\n FN-SORT-001.\n- **Logicals** order `FALSE` before `TRUE`.\n\n\n\n### Arguments\n\n\n| Position | Name | Meaning |\n|---|---|---|\n| 0 | `A` | Left operand: the candidate lesser value. Required. |\n| 1 | `B` | Right operand: the candidate greater value. Required. |\n\nArity is exactly 2; no optional arguments, no defaults. Order is load-bearing — this is the\nfirst comparison page where swapping operands changes the answer.\n\n\n" }, "signature": { "display": "value1 < value2", "parameters": [ { "description": null, "name": "value1", "optional": false, "repeats": false }, { "description": null, "name": "value2", "optional": false, "repeats": false } ], "trailing_repeats": false }, "sources": { "metadata": { "admission": { "label": "implemented", "reason": null }, "arity": { "max": 2, "min": 2 }, "category": "Operators", "classification": { "arg_preparation_profile": "ValuesOnlyPreAdapter", "coercion_lift_profile": "Custom", "determinism_class": "Deterministic", "error_collapse_profile": "None", "fec_dependency_profile": "None", "host_interaction_class": "None", "kernel_signature_class": "Custom", "rich_value_usage": "RichBlind", "surface_fec_dependency_profile": "RefOnly", "thread_safety_class": "SafePure", "volatility_class": "NonVolatile" }, "descriptions": { "long": null, "short": null, "short_source": "no-short-description" }, "docs": null, "entry_kind": "built_in_operator", "localized_family_names": null, "localized_names": [], "signature": { "display": "value1 < value2", "parameters": [ { "description": null, "name": "value1", "optional": false, "repeats": false }, { "description": null, "name": "value2", "optional": false, "repeats": false } ], "trailing_repeats": false }, "surface_name": "OP_LESS_THAN", "version_marker": null, "xlcall": null }, "microsoft": null }, "try_it": { "formula": "=1<2" }, "url": "https://handbook.dnacalc.com/functions/OP_LESS_THAN.html", "variants": [], "versions": [] }