{ "category": "Operators", "display_name": "Subtraction (-)", "entry_kind": "built_in_operator", "eval_api": { "method": "POST", "url": "https://handbook.dnacalc.com/api/eval" }, "function_id": "FUNC.OP_SUBTRACT", "implementation_state": { "answer_bank": null, "detail": "Of 514 recorded answers (514 workbook cells), 1 do not match: 1 differ in kind or value.", "dnacalc_commit": "9e1884369a678158dd82d3d74188daf986995e87", "in_catalogue": true, "state": "differs", "state_label": "Known larger differences", "summary": "Known larger differences on 1 of 514 recorded answers", "workbook_corpus": { "cells": 517, "matched": 513, "other_mismatch": 1, "pending": 3, "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/arithmetic.rs#L39-L39", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/arithmetic.rs#L56-L61" ], "repository": "https://github.com/DnaCalc/DnaCalc", "shared_code": [ "catalogue/arithmetic::binary", "catalogue/arithmetic::operands" ], "source": "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/arithmetic.rs#L39-L39", "state": "differs", "suite": null, "summary": "Known larger differences on 1 of 514 recorded answers" } ], "json_url": "https://handbook.dnacalc.com/api/functions/FUNC.OP_SUBTRACT.json", "name": "OP_SUBTRACT", "notes": [], "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_ADD`](FUNC.OP_ADD.md) — the additive sibling; same coercion, same broadcast\n shapes.\n- [`FUNC.OP_NEGATE`](FUNC.OP_NEGATE.md) — prefix `-`. Same character, one operand.\n- `IMSUB` — complex subtraction over text-encoded complex numbers.\n- `DAYS`, `DATEDIF`, `YEARFRAC` — the calendar-aware alternatives to subtracting two date\n serials. They answer different questions; `-` answers only \"difference of two numbers\".\n\n\n", "how-to-implement": "\n### Notes for implementers\n\n\n- Do not \"optimize\" `A - B` into `A + (-B)` or vice versa in a compatibility implementation.\n The finite results agree, but the call shape, the operand count, and the zero-sign story do\n not, and a compatibility target should preserve the shape it was given.\n- Cancellation is a modelling problem, not an operator problem. If a workbook loses\n significance in a subtraction, the fix belongs in the expression that produced the\n operands, not in a \"better\" subtraction — there is no better subtraction; the IEEE\n difference is already exact when it matters.\n- Broadcast and coercion are shared machinery. Implementing `-` as a distinct code path from\n `+` invites the two to drift; the reference implementation keeps them in one family module\n for exactly that reason.\n\n\n", "quirks": "\n### Result and edge cases\n\n- **Text and logical operands.** Governed by the shared to-number rules, exactly as for\n [`+`](FUNC.OP_ADD.md). Nothing about `-` changes them.\n- **Dates.** Date arithmetic is subtraction: a date is a number wearing a format, so\n `date2 - date1` is an ordinary difference of serial numbers and the \"number of days\" reading\n is a presentation fact, not a semantic one. The published result carries no date format of\n its own; how the host formats the difference cell is host-side adaptation, outside the\n function's semantics (chapter 03).\n- **Empty and omitted operands.** Per-family policy under chapter 02, and unrecorded here.\n- **Overflow.** The recorded real-result policy is `non_finite=allow`, and\n `data/functions/FUNC.OP_SUBTRACT.json` marks that axis `default-unexamined`. A difference\n of two large opposite-signed operands can overflow; what Excel publishes there is not\n settled on this page.\n\n\n", "sources": "- `data/presence/FUNC.OP_SUBTRACT.json` — implementing module\n `earlier-implementation/operator_arithmetic_family.rs`, the family slug for this\n page.\n- Handbook `content/model/01-value-universe.md`, `02-coercion-and-lifting.md`,\n `03-call-pipeline.md`.\n- Sterbenz's lemma is standard floating-point theory (Sterbenz, *Floating-Point Computation*,\n 1974); it is a property of IEEE-754 arithmetic, not a claim about Excel.\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` converts each operand to a number and returns the IEEE-754 binary64 difference,\nrounded once to nearest with ties to even.\n\nSubtraction is where floating-point arithmetic stops being invisible. Two properties are\nworth stating precisely, because they generate most of the questions readers arrive with:\n\n1. **The subtraction itself is exact when the operands are close.** By Sterbenz's lemma, if\n `B/2 ≤ A ≤ 2B` then `A - B` is representable exactly and the operation introduces no error\n at all. The damage was done earlier: catastrophic cancellation is the *revelation* of\n error already present in `A` and `B`, not error created by `-`.\n2. **`A - B` is not `A + (-B)` in every observable respect.** They agree on the finite\n arithmetic, but they are different call shapes with different operand counts, and the\n sign of a zero result differs: `x - x` is a positive zero under round-to-nearest, while\n `x + (-x)` is too, but `0 - 0` and `0 + -0` are not the same expression. If anything in a\n workbook can observe the sign of a zero, the rewrite is not neutral.\n\nAs with every operator in this family, the operand conversion is the part that varies: `-`\nnever sees a cell, only values already resolved and coerced by the shared rules of\n[coercion and lifting](../model/02-coercion-and-lifting.md).\n\n\n\n### Arguments\n\n\n| Position | Name | Meaning |\n|---|---|---|\n| 0 | `A` | Minuend. Required. |\n| 1 | `B` | Subtrahend. Required. |\n\nArity is exactly 2; no optional arguments, no defaults. Order is load-bearing —\n`A - B` and `B - A` differ in sign — which distinguishes this row from `+` and `*`.\n\nThe same `-` character in prefix position is [`FUNC.OP_NEGATE`](FUNC.OP_NEGATE.md), a\none-argument operator. Which one a given `-` is depends on the formula grammar, and formula\ngrammar is explicitly out of this Handbook's scope (`CHARTER.md` section 4).\n\n\n" }, "signature": { "display": "number1 - number2", "parameters": [ { "description": null, "name": "number1", "optional": false, "repeats": false }, { "description": null, "name": "number2", "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": "NumsToNum", "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": "number1 - number2", "parameters": [ { "description": null, "name": "number1", "optional": false, "repeats": false }, { "description": null, "name": "number2", "optional": false, "repeats": false } ], "trailing_repeats": false }, "surface_name": "OP_SUBTRACT", "version_marker": null, "xlcall": null }, "microsoft": null }, "try_it": { "formula": "=5-2" }, "url": "https://handbook.dnacalc.com/functions/OP_SUBTRACT.html", "variants": [], "versions": [] }