{ "category": "Math and trigonometry functions", "display_name": "MROUND", "entry_kind": "built_in_function", "eval_api": { "method": "POST", "url": "https://handbook.dnacalc.com/api/eval" }, "function_id": "FUNC.MROUND", "implementation_state": { "answer_bank": { "excel_builds": [ "20430" ], "larger_numeric": 0, "last_bit": 0, "matched": 50782, "other_mismatch": 0, "refused": 0, "rows": 50782, "unread": 0, "worst_ulp": 0 }, "detail": "Recorded: 50,782 in the answer bank and 167 workbook cells.", "dnacalc_commit": "9e1884369a678158dd82d3d74188daf986995e87", "in_catalogue": true, "state": "matches", "state_label": "Matches every recorded Excel answer", "summary": "Matches all 50,949 recorded answers", "workbook_corpus": { "cells": 167, "matched": 167 } }, "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#L111-L111", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/rounding.rs#L472-L488", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/rounding.rs#L490-L513" ], "repository": "https://github.com/DnaCalc/DnaCalc", "shared_code": [ "catalogue/rounding::call", "catalogue/rounding::numeric", "catalogue/rounding::numbers", "catalogue/rounding::quotient", "decimal::truncate", "decimal::floor" ], "source": "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/rounding.rs#L111-L111", "state": "matches", "suite": null, "summary": "Matches all 50,949 recorded answers" } ], "json_url": "https://handbook.dnacalc.com/api/functions/FUNC.MROUND.json", "name": "MROUND", "notes": [ { "basis": "All 50,782 recorded MROUND rows match this rule. The cut-off lies between the adjacent binary64 values 4.996E-15 (rounded up) and 5.0515E-15 (rounded down) from 0.5, measured at floor(q) = 0 over 4,264 rows.", "documentation": { "claim": "MROUND rounds up, away from zero, if the remainder of dividing number by multiple is greater than or equal to half the value of multiple.", "source": "https://support.microsoft.com/en-us/office/mround-function-c299c3b0-15a5-426d-aa4b-d2d5b3baf427" }, "evidence": [ { "commit": "77873410e3b5b659e3ab1c808a7926dd9f36c5ea", "locator": "rounding_family_matches_recorded_bank_rows", "note": "ROUND family rules in the product; failed before the change", "path": "crates/calc-func/tests/f1_math.rs", "repository": "DnaCalc" }, { "commit": "b5d84a80a5a4640eca9ce04f232c0bc115503f34", "locator": null, "note": "research write-up: full-bank result, the rules, what stays open", "path": "content/notes/evidence/2026-11-04/rounding-EVIDENCE.md", "repository": "ExcelFunctionsHandbook" } ], "functions": [ "FUNC.MROUND" ], "inferred": "The window is measured between two neighbouring values; that the constant is the decimal 5E-15 is inferred, as the decimal in that window.", "kind": "excel-differs-from-math", "note_id": "FN-MROUND-001", "open": [], "recorded_on": "2026-11-04", "repros": [ { "call": "MROUND(0.499999999999995, 1)", "correct": { "bits": "0x0000000000000000", "display": "0", "how": "The number is nearer to 0 than to 1.", "kind": "number" }, "excel": { "bits": "0x3ff0000000000000", "display": "1", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "number", "value": { "bits": "0x3fdfffffffffffa6", "display": "0.499999999999995", "kind": "number" } }, { "name": "multiple", "value": { "bits": "0x3ff0000000000000", "display": "1", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20430, Windows 64-bit, CPU not recorded in this capture", "source": { "commit": "4d5320dfdc385354469b4d506153357bb932ab08", "locator": "mround-fraction-cutoff-00181", "note": null, "path": "runs/w111-mround-fraction-cutoff-20260929/answers-mround.json.gz", "repository": "CalcFunc-Evidence" } }, { "call": "MROUND(0.49999999999999495, 1)", "correct": null, "excel": { "bits": "0x0000000000000000", "display": "0", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "number", "value": { "bits": "0x3fdfffffffffffa5", "display": "0.49999999999999495", "kind": "number" } }, { "name": "multiple", "value": { "bits": "0x3ff0000000000000", "display": "1", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20430, Windows 64-bit, CPU not recorded in this capture", "source": { "commit": "4d5320dfdc385354469b4d506153357bb932ab08", "locator": "mround-fraction-cutoff-00183", "note": null, "path": "runs/w111-mround-fraction-cutoff-20260929/answers-mround.json.gz", "repository": "CalcFunc-Evidence" } }, { "call": "MROUND(0.49999999999999994, 1)", "correct": { "bits": "0x0000000000000000", "display": "0", "how": "The number is nearer to 0 than to 1.", "kind": "number" }, "excel": { "bits": "0x3ff0000000000000", "display": "1", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "number", "value": { "bits": "0x3fdfffffffffffff", "display": "0.49999999999999994", "kind": "number" } }, { "name": "multiple", "value": { "bits": "0x3ff0000000000000", "display": "1", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20430, Windows 64-bit, CPU not recorded in this capture", "source": { "commit": "4d5320dfdc385354469b4d506153357bb932ab08", "locator": "mround-fraction-cutoff-00003", "note": null, "path": "runs/w111-mround-fraction-cutoff-20260929/answers-mround.json.gz", "repository": "CalcFunc-Evidence" } } ], "schema": "efh.function-note/v1", "statement": "MROUND(n,m) forms q = n/m on the x87 unit and stores it to binary64, counts floor(q), adds 1 when 0.5 - frac(q) <= 5E-15, and returns count*m from the x87 unit. A number just below a half therefore rounds up though it is nearer the lower multiple: 0.499999999999995 with multiple 1 gives 1, and the next binary64 below it gives 0. MROUND(6.05,0.1) stays 6, because its quotient 60.49999999999999 lies 7.1E-15 below the half.", "status": "measured", "title": "MROUND counts a quotient within 5E-15 below a half up" } ], "schema": "efh.function-reference/v1", "section_order": [ "what-it-does", "try-it", "quirks", "how-to-implement", "version-differences", "alternatives" ], "sections": { "alternatives": "\n[ROUND](FUNC.ROUND.md) chooses decimal places; [CEILING.MATH](FUNC.CEILING.MATH.md) and [FLOOR.MATH](FUNC.FLOOR.MATH.md) choose a directional multiple.\n\n\n\n\n", "how-to-implement": "\nAfter coercion and sign checks, compute `q=R(number/multiple)`, where `R` is the stored 64-bit-significand operation described for variance. Let `c=floor(q)` and `f=q-c`. Increment `c` when `0.5-f<=5e-15`. Return `R(c*multiple)`.\n\nWorked: `14/4=3.5`; `c=3`, `f=0.5`, so increment to four and multiply by four to obtain sixteen. The same positive quotient with two negative arguments produces a negative multiple. Preserve the division store and final product store, and use the binary64 constant `5e-15` rather than a decimal-string comparison. The adjacent-half probes distinguish the tolerance on the measured inputs. The cited bank contains 50,782 matching rows; no Handbook suite has been published.\n\n\n", "quirks": "\nOpposite signs give `#NUM!`; the current implementation returns zero for a zero multiple. A decimal multiple is already a binary64 approximation before rounding begins. The recorded decision admits a small tolerance below one half, rather than comparing exact decimal distances.\n\n\n", "sources": "\n- [Microsoft: MROUND function](https://support.microsoft.com/en-us/excel/functions/mround-function), opened 6 November 2026; syntax, documented argument rules and errors.\n- [DnaCalc implementation](https://github.com/DnaCalc/DnaCalc/blob/da3ecc4fb19a3a5529708c311d0e8f05688ac165/crates/calc-func/src/catalogue/rounding.rs); implementation steps and the limits identified in the text.\n- [Rounding research](../notes/evidence/2026-11-04/rounding-EVIDENCE.md).\n\n", "try-it": "\n`=MROUND(14,4)` returns `16`. `=MROUND(-14,-4)` returns `-16`. For decimal multiples, Microsoft documents differing midpoint directions: `MROUND(6.05,0.1)` gives `6`, while `MROUND(7.05,0.1)` gives `7.1`.\n\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 | 108 |\n| 20430 | Windows, 64-bit, AMD Ryzen 7 4800H with Radeon Graphics | 1,999 |\n| 20430 | Windows, 64-bit, CPU not recorded | 48,783 |\n\n- XC-MROUND-001: build 19929 versus build 20430; 3 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.MROUND.json).\n\nRetained controls from the indexed captures:\n\n| Build and recorded CPU | Captured call or arguments | Excel result |\n|---|---|---|\n| 19929, CPU not recorded | [`=MROUND(0,0.25000000000000000)`](https://github.com/DnaCalc/CalcFunc-Evidence/blob/4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2/runs/W097-R-B-validation-cellref-module/comparisons/excel_sample_comparisons.jsonl.gz) | `0.0` (`0x0000000000000000`) |\n| 20430, AMD Ryzen 7 4800H with Radeon Graphics | [`MROUND(45.5,7)`](https://github.com/DnaCalc/CalcFunc-Evidence/blob/4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2/cache/oracle-20430/build-20430/MROUND.jsonl.gz) | `49` (`0x4048800000000000`) |\n| 20430, CPU not recorded | [`MROUND(0.5,1)`](https://github.com/DnaCalc/CalcFunc-Evidence/blob/4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2/cache/w111-extended-regenerated-20260929/answers-mround.json.gz) | `1` (`0x3ff0000000000000`) |\n\nThese are earlier recorded answers, not new Excel runs or an additional cross-build comparison. The function JSON retains each source locator, exact argument bits where available, and input-route status. Call notation does not imply that captured binary64 values were entered as decimal formula literals.", "what-it-does": "\n`MROUND(number, multiple)` selects a nearest multiple, with mathematical halves away from zero. Both nonzero inputs must have the same sign.\n\n\n" }, "signature": { "display": "MROUND(number, multiple)", "parameters": [ { "description": null, "name": "number", "optional": false, "repeats": false }, { "description": null, "name": "multiple", "optional": false, "repeats": false } ], "trailing_repeats": false }, "sources": { "metadata": { "admission": { "label": "implemented", "reason": null }, "arity": { "max": 2, "min": 2 }, "category": "Math and trigonometry functions", "classification": { "arg_preparation_profile": "ValuesOnlyPreAdapter", "coercion_lift_profile": "UnaryNumericScalarOnly", "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": "Number rounded to the nearest multiple of another", "short_source": "dna-calc-own" }, "docs": { "english_description": "Returns a number rounded to the desired multiple", "microsoft_url": "https://support.microsoft.com/en-us/office/mround-function-c299c3b0-15a5-426d-aa4b-d2d5b3baf427" }, "entry_kind": "built_in_function", "localized_family_names": null, "localized_names": [ { "locale": "ar-SA", "name": "MROUND" }, { "locale": "bg-BG", "name": "MROUND" }, { "locale": "cs-CZ", "name": "MROUND" }, { "locale": "da-DK", "name": "MAFRUND" }, { "locale": "de-DE", "name": "MROUND" }, { "locale": "el-GR", "name": "MROUND" }, { "locale": "en-AU", "name": "MROUND" }, { "locale": "en-GB", "name": "MROUND" }, { "locale": "en-US", "name": "MROUND" }, { "locale": "es-ES", "name": "REDOND.MULT" }, { "locale": "et-EE", "name": "MROUND" }, { "locale": "fi-FI", "name": "PYÖRISTÄ.KERR" }, { "locale": "fr-FR", "name": "ARRONDI.AU.MULTIPLE*" }, { "locale": "he-IL", "name": "MROUND" }, { "locale": "hr-HR", "name": "MROUND" }, { "locale": "hu-HU", "name": "TÖBBSZ.KEREKÍT" }, { "locale": "id-ID", "name": "MROUND" }, { "locale": "it-IT", "name": "MROUND" }, { "locale": "ja-JP", "name": "MROUND" }, { "locale": "ko-KR", "name": "MROUND" }, { "locale": "lt-LT", "name": "MROUND" }, { "locale": "lv-LV", "name": "MROUND" }, { "locale": "nb-NO", "name": "MRUND" }, { "locale": "nl-NL", "name": "AFRONDEN.N.VEELVOUD" }, { "locale": "pl-PL", "name": "ZAOKR.DO.WIELOKR" }, { "locale": "pt-BR", "name": "MROUND" }, { "locale": "pt-PT", "name": "MARRED" }, { "locale": "ro-RO", "name": "MROUND" }, { "locale": "ru-RU", "name": "ОКРУГЛТ" }, { "locale": "sk-SK", "name": "MROUND" }, { "locale": "sl-SI", "name": "MROUND" }, { "locale": "sr-Latn-RS", "name": "MROUND" }, { "locale": "sv-SE", "name": "MAVRUNDA" }, { "locale": "th-TH", "name": "MROUND" }, { "locale": "tr-TR", "name": "KYUVARLA işlevi" }, { "locale": "uk-UA", "name": "MROUND" }, { "locale": "vi-VN", "name": "MROUND" }, { "locale": "zh-CN", "name": "MROUND" }, { "locale": "zh-HK", "name": "MROUND" }, { "locale": "zh-TW", "name": "MROUND" } ], "signature": { "display": "MROUND(number, multiple)", "parameters": [ { "description": null, "name": "number", "optional": false, "repeats": false }, { "description": null, "name": "multiple", "optional": false, "repeats": false } ], "trailing_repeats": false }, "surface_name": "MROUND", "version_marker": null, "xlcall": { "code": "422", "symbol": "xlfMround" } }, "microsoft": "https://support.microsoft.com/en-us/office/mround-function-c299c3b0-15a5-426d-aa4b-d2d5b3baf427" }, "try_it": { "formula": "=MROUND(14,4)" }, "url": "https://handbook.dnacalc.com/functions/MROUND.html", "variants": [], "versions": [ { "behaviour": "MROUND(0.499999999999995, 1) returned 1 (0x3ff0000000000000). MROUND(0.49999999999999495, 1) returned 0 (0x0000000000000000). 1 further recorded control is attached. Inputs were supplied through cells using Value2. These are controls from this environment, not a same-input comparison with another build.", "excel_build": "16.0 build 20430", "observations": [ { "call": "MROUND(0.499999999999995, 1)", "excel": { "bits": "0x3ff0000000000000", "display": "1", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "number", "value": { "bits": "0x3fdfffffffffffa6", "display": "0.499999999999995", "kind": "number" } }, { "name": "multiple", "value": { "bits": "0x3ff0000000000000", "display": "1", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20430, Windows 64-bit, CPU not recorded in this capture" }, { "call": "MROUND(0.49999999999999495, 1)", "excel": { "bits": "0x0000000000000000", "display": "0", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "number", "value": { "bits": "0x3fdfffffffffffa5", "display": "0.49999999999999495", "kind": "number" } }, { "name": "multiple", "value": { "bits": "0x3ff0000000000000", "display": "1", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20430, Windows 64-bit, CPU not recorded in this capture" }, { "call": "MROUND(0.49999999999999994, 1)", "excel": { "bits": "0x3ff0000000000000", "display": "1", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "number", "value": { "bits": "0x3fdfffffffffffff", "display": "0.49999999999999994", "kind": "number" } }, { "name": "multiple", "value": { "bits": "0x3ff0000000000000", "display": "1", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20430, Windows 64-bit, CPU not recorded in this capture" } ], "platform": "Windows 64-bit, CPU not recorded in this capture", "sources": [ "https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/3345a87/content/notes/FN-MROUND-001.json" ] }, { "behaviour": "108 captured inputs are indexed for this environment. Capture dates are not recorded. This is a reading count, not a comparison with another build. Retained control =MROUND(0,0.25000000000000000) returned 0.0 (0x0000000000000000). The selected archive row does not record its input plumbing; no input route is inferred.", "excel_build": "16.0 build 19929", "observations": [ { "call": "=MROUND(0,0.25000000000000000)", "excel": { "bits": "0x0000000000000000", "display": "0.0", "kind": "number" }, "input_route": "not-recorded", "inputs": [], "recorded_in": "Excel 16.0 build 19929, Windows, bitness not recorded, CPU not recorded.", "source": { "commit": "4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2", "locator": "BSE-000000359", "path": "runs/W097-R-B-validation-cellref-module/comparisons/excel_sample_comparisons.jsonl.gz", "repository": "CalcFunc-Evidence" } } ], "platform": "Windows, bitness not recorded, CPU not recorded", "sources": [ "https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.MROUND.json", "https://github.com/DnaCalc/CalcFunc-Evidence/blob/4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2/runs/W097-R-B-validation-cellref-module/comparisons/excel_sample_comparisons.jsonl.gz" ] }, { "behaviour": "1,999 captured inputs are indexed for this environment. Capture dates: 2026-09-25 to 2026-09-25. This is a reading count, not a comparison with another build. Retained control MROUND(45.5,7) returned 49 (0x4048800000000000). The selected archive row does not record its input plumbing; no input route is inferred.", "excel_build": "16.0 build 20430", "observations": [ { "call": "MROUND(45.5,7)", "excel": { "bits": "0x4048800000000000", "display": "49", "kind": "number" }, "input_route": "not-recorded", "inputs": [ { "name": "argument1", "value": { "bits": "0x4046c00000000000", "display": "45.5", "kind": "number" } }, { "name": "argument2", "value": { "bits": "0x401c000000000000", "display": "7", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20430, Windows, 64-bit, AMD Ryzen 7 4800H with Radeon Graphics.", "source": { "commit": "4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2", "locator": "MROUND|0x4046c00000000000|0x401c000000000000", "path": "cache/oracle-20430/build-20430/MROUND.jsonl.gz", "repository": "CalcFunc-Evidence" } } ], "platform": "Windows, 64-bit, AMD Ryzen 7 4800H with Radeon Graphics", "sources": [ "https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.MROUND.json", "https://github.com/DnaCalc/CalcFunc-Evidence/blob/4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2/cache/oracle-20430/build-20430/MROUND.jsonl.gz" ] }, { "behaviour": "48,783 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. Retained control MROUND(0.5,1) returned 1 (0x3ff0000000000000). The capture specifies exact-double bulk Value2 cell input.", "excel_build": "16.0 build 20430", "observations": [ { "call": "MROUND(0.5,1)", "excel": { "bits": "0x3ff0000000000000", "display": "1", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "argument1", "value": { "bits": "0x3fe0000000000000", "display": "0.5", "kind": "number" } }, { "name": "argument2", "value": { "bits": "0x3ff0000000000000", "display": "1", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20430, Windows, 64-bit, CPU not recorded.", "source": { "commit": "4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2", "locator": "w111extended-2026092903-MROUND-00022", "path": "cache/w111-extended-regenerated-20260929/answers-mround.json.gz", "repository": "CalcFunc-Evidence" } } ], "platform": "Windows, 64-bit, CPU not recorded", "sources": [ "https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.MROUND.json", "https://github.com/DnaCalc/CalcFunc-Evidence/blob/4287ba192d2e3a7fd54671ea1cee1c34cb2e84e2/cache/w111-extended-regenerated-20260929/answers-mround.json.gz" ] } ] }