{ "category": "Math and trigonometry functions", "display_name": "ABS", "entry_kind": "built_in_function", "eval_api": { "method": "POST", "url": "https://handbook.dnacalc.com/api/eval" }, "function_id": "FUNC.ABS", "implementation_state": { "answer_bank": { "excel_builds": [ "20430" ], "larger_numeric": 0, "last_bit": 0, "matched": 1225, "other_mismatch": 0, "refused": 2, "rows": 1227, "unread": 0, "worst_ulp": 0 }, "detail": "Of 1,383 recorded answers (1,227 in the answer bank and 156 workbook cells), 2 do not match: 2 are refused.", "dnacalc_commit": "9e1884369a678158dd82d3d74188daf986995e87", "in_catalogue": true, "state": "differs", "state_label": "Known larger differences", "summary": "Refuses 2 of 1,383 recorded calls; the rest match", "workbook_corpus": { "cells": 156, "matched": 156 } }, "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/rounding.rs#L104-L104" ], "repository": "https://github.com/DnaCalc/DnaCalc", "shared_code": [ "catalogue/rounding::call", "catalogue/rounding::numeric", "catalogue/rounding::numbers", "catalogue/rounding::abs" ], "source": "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/rounding.rs#L104-L104", "state": "differs", "suite": null, "summary": "Refuses 2 of 1,383 recorded calls; the rest match" } ], "json_url": "https://handbook.dnacalc.com/api/functions/FUNC.ABS.json", "name": "ABS", "notes": [ { "basis": "About 120 recorded zero-mantissa cases through ABS, and 72 through VALUE. All 72 VALUE readings fit a limit of -308 to 308 on the exponent as counted here.", "documentation": null, "evidence": [ { "commit": "344c1667872a7d62669ca3044decb06c92b1e6f6", "locator": "recorded_zero_percentage_exponents_are_validated", "note": "recorded readings pinned", "path": "apps/dna-onecalc/tests/acceptance.rs", "repository": "DnaCalc" }, { "commit": "2d0eddcac86413014643af81d646581d54ba57bc", "locator": "sheets qt097 to qt168", "note": "72 recorded VALUE readings", "path": "crates/calc-func/tests/captures/fn4_questions/functions-fn4-text-controls.capture.json", "repository": "DnaCalc" } ], "functions": [ "FUNC.ABS", "FUNC.VALUE" ], "inferred": "The exponent formula is inferred, though it fits every reading; that functions other than ABS and VALUE share this conversion is inferred.", "kind": "excel-differs-from-math", "note_id": "FN-ABS-001", "open": [], "recorded_on": "2026-11-04", "repros": [ { "call": "=ABS(\"0e-309\")", "correct": { "bits": "0x0000000000000000", "display": "0", "how": "The text denotes zero: a zero mantissa is 0 at any exponent.", "kind": "number" }, "excel": { "bits": null, "display": "#VALUE!", "kind": "error" }, "input_route": "formula-literal", "inputs": [], "recorded_in": "Excel build not recorded in this run; bulk captures of the same date (2026-09-29) record Excel 16.0 build 20430, Windows 64-bit, workbook compatibility 2", "source": { "commit": "4d5320dfdc385354469b4d506153357bb932ab08", "locator": "w111textbounds-00008-abs-boundary-2-0", "note": null, "path": "runs/w111-numeric-text-percent-bounds-20260929/outcomes/excel.jsonl.gz", "repository": "CalcFunc-Evidence" } }, { "call": "=ABS(\"0e-308\")", "correct": null, "excel": { "bits": "0x0000000000000000", "display": "0", "kind": "number" }, "input_route": "formula-literal", "inputs": [], "recorded_in": "Excel build not recorded in this run; bulk captures of the same date (2026-09-29) record Excel 16.0 build 20430, Windows 64-bit, workbook compatibility 2", "source": { "commit": "4d5320dfdc385354469b4d506153357bb932ab08", "locator": "w111textbounds-00012-abs-boundary-3-0", "note": null, "path": "runs/w111-numeric-text-percent-bounds-20260929/outcomes/excel.jsonl.gz", "repository": "CalcFunc-Evidence" } }, { "call": "=ABS(\"0e-307%\")", "correct": null, "excel": { "bits": null, "display": "#VALUE!", "kind": "error" }, "input_route": "formula-literal", "inputs": [], "recorded_in": "Excel build not recorded in this run; bulk captures of the same date (2026-09-29) record Excel 16.0 build 20430, Windows 64-bit, workbook compatibility 2", "source": { "commit": "4d5320dfdc385354469b4d506153357bb932ab08", "locator": "w111textbounds-00017-abs-boundary-4-1", "note": null, "path": "runs/w111-numeric-text-percent-bounds-20260929/outcomes/excel.jsonl.gz", "repository": "CalcFunc-Evidence" } }, { "call": "=ABS(\"0e309\")", "correct": { "bits": "0x0000000000000000", "display": "0", "how": "The text denotes zero: a zero mantissa is 0 at any exponent.", "kind": "number" }, "excel": { "bits": null, "display": "#VALUE!", "kind": "error" }, "input_route": "formula-literal", "inputs": [], "recorded_in": "Excel build not recorded in this run; bulk captures of the same date (2026-09-29) record Excel 16.0 build 20430, Windows 64-bit, workbook compatibility 2", "source": { "commit": "4d5320dfdc385354469b4d506153357bb932ab08", "locator": "w111textbounds-00028-abs-boundary-7-0", "note": null, "path": "runs/w111-numeric-text-percent-bounds-20260929/outcomes/excel.jsonl.gz", "repository": "CalcFunc-Evidence" } }, { "call": "=ABS(\"0.0e309\")", "correct": null, "excel": { "bits": "0x0000000000000000", "display": "0", "kind": "number" }, "input_route": "formula-literal", "inputs": [], "recorded_in": "Excel build not recorded in this run; bulk captures of the same date (2026-09-29) record Excel 16.0 build 20430, Windows 64-bit, workbook compatibility 2", "source": { "commit": "4d5320dfdc385354469b4d506153357bb932ab08", "locator": "w111textbounds-00108-abs-boundary-27-0", "note": null, "path": "runs/w111-numeric-text-percent-bounds-20260929/outcomes/excel.jsonl.gz", "repository": "CalcFunc-Evidence" } }, { "call": "=VALUE(\"0e-307\")", "correct": null, "excel": { "bits": "0x0000000000000000", "display": "0", "kind": "number" }, "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 qt099, row 20, column 10", "note": null, "path": "crates/calc-func/tests/captures/fn4_questions/functions-fn4-text-controls.capture.json", "repository": "DnaCalc" } }, { "call": "=VALUE(\"0e-307%\")", "correct": null, "excel": { "bits": null, "display": "#VALUE!", "kind": "error" }, "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 qt100, row 20, column 10", "note": null, "path": "crates/calc-func/tests/captures/fn4_questions/functions-fn4-text-controls.capture.json", "repository": "DnaCalc" } }, { "call": "=VALUE(\"0e309\")", "correct": null, "excel": { "bits": null, "display": "#VALUE!", "kind": "error" }, "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 qt107, row 20, column 10", "note": null, "path": "crates/calc-func/tests/captures/fn4_questions/functions-fn4-text-controls.capture.json", "repository": "DnaCalc" } }, { "call": "=VALUE(\"0.0e309\")", "correct": null, "excel": { "bits": "0x0000000000000000", "display": "0", "kind": "number" }, "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 qt143, row 20, column 10", "note": null, "path": "crates/calc-func/tests/captures/fn4_questions/functions-fn4-text-controls.capture.json", "repository": "DnaCalc" } }, { "call": "=VALUE(\"0e309%\")", "correct": null, "excel": { "bits": "0x0000000000000000", "display": "0", "kind": "number" }, "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 qt108, row 20, column 10", "note": null, "path": "crates/calc-func/tests/captures/fn4_questions/functions-fn4-text-controls.capture.json", "repository": "DnaCalc" } }, { "call": "=VALUE(\"0e311%\")", "correct": null, "excel": { "bits": null, "display": "#VALUE!", "kind": "error" }, "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 qt112, row 20, column 10", "note": null, "path": "crates/calc-func/tests/captures/fn4_questions/functions-fn4-text-controls.capture.json", "repository": "DnaCalc" } } ], "schema": "efh.function-note/v1", "statement": "Converting text to a number, measured through ABS and VALUE, rejects a zero mantissa with an out-of-range exponent: ABS(\"0e-309\") is #VALUE! though the text denotes 0, and ABS(\"0e-308\") is 0. The exponent counts as written, less the fraction digits, less 2 for a percent sign, so ABS(\"0.0e309\") is 0, ABS(\"0e309\") is #VALUE!, and ABS(\"0e-307%\") is #VALUE!.", "status": "measured", "title": "Text to number checks the exponent range even when the mantissa is zero" } ], "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- **`SIGN`** — the other half of the polar decomposition of a real number. `SIGN(x) * ABS(x) = x`\n away from the origin.\n- **`IMABS`** — the complex modulus, which is the same idea one dimension up and *not* the same\n computation: it is `hypot(a, b)`, an operation with real overflow and cancellation questions,\n where the real `ABS` has none.\n- **Unary minus** — `ABS` is not \"negate if negative\" implemented as a comparison plus a\n negation; it is a single sign-bit clear. The distinction is invisible in results and visible in\n performance.\n- **`SUMSQ`, `SUMXMY2`, `DEVSQ`** — squaring is the other standard way to discard a sign, and it\n is the one that overflows. Where a formula can use either, `ABS` has the wider range.\n- **`AVEDEV`** — the mean absolute deviation, which is `ABS` under an aggregate, and the reason\n the function exists in the statistical category at all.\n- **Confused with**: `INT` and `TRUNC`, which also \"simplify\" a number but change its magnitude;\n `ABS` never does.\n\n\n", "how-to-implement": "\n### Numerical notes\n\n\n`ABS` is the rare function whose numerical note is that it has no numerical error. Everything\ninteresting happens on either side of it.\n\n**The comparison idiom.** `ABS(a - b) < tol` is the standard floating-point equality test, and the\nerror in it belongs entirely to the subtraction. Sterbenz's lemma gives the good case: if `a` and\n`b` are within a factor of two of each other, `a - b` is computed exactly, so `ABS(a - b)` is the\nexact distance. Outside that band the subtraction rounds, and for widely separated magnitudes it\ncan round to something with no correct digits at all. `ABS` faithfully reports whatever the\nsubtraction produced; readers who see a surprising result from this idiom are looking at the wrong\nfunction.\n\n**Absolute versus relative tolerance.** A fixed `tol` in the idiom above is an *absolute*\ntolerance, and it is meaningful only over a narrow range of magnitudes. The relative form\n`ABS(a - b) <= tol * ABS(b)` scales correctly but fails when `b` is zero. The mixed form\n`ABS(a - b) <= tol * MAX(ABS(a), ABS(b), 1)` is the usual compromise, and it is worth writing out\nrather than reaching for, because the choice is a modelling decision and not a numerical one.\n\n**Why implementations should not branch.** The obvious implementation — compare against zero,\nnegate if negative — is correct but has two defects: it is a branch on data, and it maps `-0` to\n`-0` rather than to `+0` unless the comparison is written carefully. Clearing the sign bit has\nneither problem. Any implementation claiming `ABS` should be checked at `-0` for exactly this\nreason.\n\n**`ABS` as a guard.** A common pattern wraps a domain-restricted function in `ABS` to keep its\nargument admissible — `SQRT(ABS(x))`, `LN(ABS(x))`. This silently changes the function being\ncomputed. The Handbook notes it because it turns a `#NUM!` into a plausible wrong answer, which is\nthe worse of the two failures.\n\n\n", "quirks": "\n### Result and edge cases\n\n\nReturns `Number`.\n\n- **Zero.** `|0| = 0`. The interesting sub-case is negative zero: IEEE 754 distinguishes `-0`\n from `+0`, and absolute value maps `-0` to `+0`. Whether a negative zero can reach an Excel\n worksheet function at all, and what it displays as if it does, is not settled on this page.\n- **Subnormals.** Pass through with their magnitude unchanged; there is no underflow, because no\n arithmetic happens.\n- **The largest finite double.** Passes through unchanged; there is no overflow, for the same\n reason.\n- **Logicals.** Convert by the shared rule (`TRUE` to 1, `FALSE` to 0) before the kernel sees\n them.\n- **Text that reads as a number.** Converts as a direct argument under the shared to-number rule;\n text in a *scanned range* is a different question and does not arise for a unary kernel. A zero\n mantissa with an out-of-range exponent, such as `\"0e-309\"`, does not convert: `#VALUE!`\n (FN-ABS-001).\n\n\n\n### Errors\n\n\n| Error | Condition | Source |\n|---|---|---|\n| `#VALUE!` | The argument does not convert to a number | Shared coercion rules, not an `ABS`-specific condition |\n| propagated | An error value in the argument is returned unchanged | Shared coercion rules |\n\n", "sources": "- IEEE Std 754-2019, clause 5.5.1 — absolute value as a sign-bit operation: exact, quiet, and\n total.\n- Higham, *Accuracy and Stability of Numerical Algorithms*, chapter 2 — Sterbenz's lemma and the\n conditioning of subtraction, which is where the error in the `ABS(a - b)` idiom actually lives.\n- Handbook projections `data/functions/FUNC.ABS.json` (arity, `NumToNum` kernel signature,\n `UnaryNumericScalarOrArrayElementwise` lift profile, `real_result_policy` with\n `non_finite=allow`) and `data/presence/FUNC.ABS.json` (implementing modules and the\n `BUG-FUNC-022` array-lift defect stream).\n- Handbook [The value universe](../model/01-value-universe.md) and\n [Coercion and lifting](../model/02-coercion-and-lifting.md).\n\n", "version-differences": "The recorded environments below distinguish a reading from a same-input comparison. Counts describe captured inputs in each environment; overlapping captures and comparisons are not totals of unique worksheet calls.\n\n| Excel 16.0 build | Platform and CPU | Captured inputs |\n|---|---|---:|\n| 19929 | Windows, bitness not recorded, CPU not recorded | 40 |\n| 20430 | Windows, 64-bit, CPU not recorded | 1,227 |\n\n- XC-ABS-001: build 19929 versus build 20430; 2 same-input pairs, 0 differing answers. Compared axes: excel-build. Numeric answers were compared by their recorded binary64 bits; other answers by typed value.\n\nAgreement on these compared inputs does not establish agreement on unmeasured inputs.\n\n[Recorded environments and comparison details](https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.ABS.json).", "what-it-does": "\n`ABS(number)` is the absolute value — the distance of *number* from zero on the real line:\n\n |x| = x if x >= 0\n -x if x < 0\n\n- **Domain**: all real numbers.\n- **Range**: the non-negative reals, `[0, +infinity)`.\n- **Parity**: even. `|-x| = |x|`, and this is the defining symmetry.\n- **Smoothness**: continuous everywhere, differentiable everywhere *except* at zero, where the\n left and right derivatives are `-1` and `+1`. The corner at the origin is the whole reason\n `ABS` shows up in optimisation problems as the awkward term.\n- **Algebra**: `|xy| = |x||y|`, `|x/y| = |x|/|y|`, and the triangle inequality\n `|x + y| <= |x| + |y|` with equality exactly when `x` and `y` have the same sign. Absolute\n value is the standard norm on `R`; that is what makes `ABS(a - b)` the natural distance.\n\nThe identity that ties it to its sibling is `x = SIGN(x) * ABS(x)`, exact for every `x` except\nthat `SIGN(0)` is `0` and so contributes nothing at the origin.\n\nIn binary64 terms `ABS` is not an approximation of anything. The magnitude of a representable\nnumber is representable, so the correctly rounded result *is* the exact result: `ABS` clears the\nsign bit and leaves every other bit alone. Under IEEE 754 that makes it one of a very small set\nof operations — sign-bit operations — that are exact, cannot overflow, cannot underflow, and\nraise no exception on any input.\n\n\n\n### Arguments\n\n\n| Argument | Meaning | Default |\n|---|---|---|\n| `number` | The real number whose magnitude you want. Required. | — |\n\nThere is no commonly misunderstood position here, because there is only one. The misunderstanding\nthat does occur is upstream of the call: readers reach for `ABS` to make a *result* positive when\nwhat they wanted was to make an *argument* positive, and the two differ whenever anything\nnon-monotonic sits in between.\n\n\n" }, "signature": { "display": "ABS(number)", "parameters": [ { "description": null, "name": "number", "optional": false, "repeats": false } ], "trailing_repeats": false }, "sources": { "metadata": { "admission": { "label": "implemented", "reason": null }, "arity": { "max": 1, "min": 1 }, "category": "Math and trigonometry functions", "classification": { "arg_preparation_profile": "ValuesOnlyPreAdapter", "coercion_lift_profile": "UnaryNumericScalarOrArrayElementwise", "determinism_class": "Deterministic", "error_collapse_profile": "None", "fec_dependency_profile": "None", "host_interaction_class": "None", "kernel_signature_class": "NumToNum", "rich_value_usage": "RichBlind", "surface_fec_dependency_profile": "RefOnly", "thread_safety_class": "SafePure", "volatility_class": "NonVolatile" }, "descriptions": { "long": null, "short": "Absolute value: the number without its sign, its distance from zero", "short_source": "dna-calc-own" }, "docs": { "english_description": "Returns the absolute value of a number", "microsoft_url": "https://support.microsoft.com/en-us/office/abs-function-3420200f-5628-4e8c-99da-c99d7c87713c" }, "entry_kind": "built_in_function", "localized_family_names": null, "localized_names": [ { "locale": "ar-SA", "name": "ABS" }, { "locale": "bg-BG", "name": "ABS" }, { "locale": "cs-CZ", "name": "ABS" }, { "locale": "da-DK", "name": "ABS" }, { "locale": "de-DE", "name": "ABS" }, { "locale": "el-GR", "name": "ABS" }, { "locale": "en-AU", "name": "ABS" }, { "locale": "en-GB", "name": "ABS" }, { "locale": "en-US", "name": "ABS" }, { "locale": "es-ES", "name": "ABS" }, { "locale": "et-EE", "name": "ABS" }, { "locale": "fi-FI", "name": "ITSEISARVO" }, { "locale": "fr-FR", "name": "ABS" }, { "locale": "he-IL", "name": "ABS" }, { "locale": "hr-HR", "name": "ABS" }, { "locale": "hu-HU", "name": "ABS" }, { "locale": "id-ID", "name": "ABS" }, { "locale": "it-IT", "name": "ASS" }, { "locale": "ja-JP", "name": "ABS" }, { "locale": "ko-KR", "name": "ABS" }, { "locale": "lt-LT", "name": "ABS" }, { "locale": "lv-LV", "name": "ABS" }, { "locale": "nb-NO", "name": "ABS" }, { "locale": "nl-NL", "name": "ABS" }, { "locale": "pl-PL", "name": "ABS" }, { "locale": "pt-BR", "name": "ABS" }, { "locale": "pt-PT", "name": "ABS" }, { "locale": "ro-RO", "name": "ABS" }, { "locale": "ru-RU", "name": "ABS" }, { "locale": "sk-SK", "name": "ABS" }, { "locale": "sl-SI", "name": "ABS" }, { "locale": "sr-Latn-RS", "name": "ABS" }, { "locale": "sv-SE", "name": "ABS" }, { "locale": "th-TH", "name": "ABS" }, { "locale": "tr-TR", "name": "MUTLAK" }, { "locale": "uk-UA", "name": "ABS" }, { "locale": "vi-VN", "name": "ABS" }, { "locale": "zh-CN", "name": "ABS" }, { "locale": "zh-HK", "name": "ABS" }, { "locale": "zh-TW", "name": "ABS" } ], "signature": { "display": "ABS(number)", "parameters": [ { "description": null, "name": "number", "optional": false, "repeats": false } ], "trailing_repeats": false }, "surface_name": "ABS", "version_marker": null, "xlcall": { "code": "24", "symbol": "xlfAbs" } }, "microsoft": "https://support.microsoft.com/en-us/office/abs-function-3420200f-5628-4e8c-99da-c99d7c87713c" }, "try_it": { "formula": "=ABS(-0)" }, "url": "https://handbook.dnacalc.com/functions/ABS.html", "variants": [], "versions": [ { "behaviour": "40 captured inputs are indexed for this environment. Capture dates are not recorded. This is a reading count, not a comparison with another build.", "excel_build": "16.0 build 19929", "platform": "Windows, bitness not recorded, CPU not recorded", "sources": [ "https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.ABS.json" ] }, { "behaviour": "1,227 captured inputs are indexed for this environment. Capture dates: 2026-09-29 to 2026-09-29. This is a reading count, not a comparison with another build.", "excel_build": "16.0 build 20430", "platform": "Windows, 64-bit, CPU not recorded", "sources": [ "https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.ABS.json" ] } ] }