{ "category": "Math and trigonometry functions", "display_name": "ASINH", "entry_kind": "built_in_function", "eval_api": { "method": "POST", "url": "https://handbook.dnacalc.com/api/eval" }, "function_id": "FUNC.ASINH", "implementation_state": { "answer_bank": { "excel_builds": [ "20430" ], "larger_numeric": 0, "last_bit": 0, "matched": 4534, "other_mismatch": 0, "refused": 0, "rows": 4534, "unread": 0, "worst_ulp": 0 }, "detail": "Recorded: 4,534 in the answer bank and 3 workbook cells.", "dnacalc_commit": "9e1884369a678158dd82d3d74188daf986995e87", "in_catalogue": true, "state": "matches", "state_label": "Matches every recorded Excel answer", "summary": "Matches all 4,537 recorded answers", "workbook_corpus": { "cells": 3, "matched": 3 } }, "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/math.rs#L50-L50", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/ported/asinh.rs#L4-L31" ], "repository": "https://github.com/DnaCalc/DnaCalc", "shared_code": [ "ported/excel_numeric::binary_with", "ported/excel_numeric::excel_x87_add", "ported/excel_numeric::excel_x87_mul", "ported/excel_numeric::excel_sqrt_staged", "ported/excel_numeric/x87::mul", "ported/excel_numeric/x87::add" ], "source": "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/math.rs#L50-L50", "state": "matches", "suite": null, "summary": "Matches all 4,537 recorded answers" } ], "json_url": "https://handbook.dnacalc.com/api/functions/FUNC.ASINH.json", "name": "ASINH", "notes": [ { "basis": "All 4,534 rows of two recorded sets, 3,017 and 1,517 rows, from Excel build 20430. The route was recomputed independently in exact rational arithmetic with a correctly rounded LN, and matched every row. The stored steps matter on 5 of the rows (3 distinct inputs): the same formula in plain binary64 misses exactly those 5.", "documentation": null, "evidence": [ { "commit": "b28be6662097cc6e405878befd8564f90fdbd951", "locator": "asinh_kernel", "note": "the route as implemented", "path": "crates/calc-func/src/ported/asinh.rs", "repository": "DnaCalc" }, { "commit": "b28be6662097cc6e405878befd8564f90fdbd951", "locator": "asinh_stores_each_identity_operation_from_pc64", "note": "the three inputs that need the stored steps", "path": "crates/calc-func/tests/f1_math.rs", "repository": "DnaCalc" }, { "commit": "2d0eddcac86413014643af81d646581d54ba57bc", "locator": "ASINH", "note": "matched rows per function", "path": "crates/calc-func/witness-status.tsv", "repository": "DnaCalc" }, { "commit": "4d5320dfdc385354469b4d506153357bb932ab08", "locator": null, "note": "3,017 recorded rows", "path": "cache/oracle-20430/build-20430/ASINH.jsonl.gz", "repository": "CalcFunc-Evidence" }, { "commit": "4d5320dfdc385354469b4d506153357bb932ab08", "locator": null, "note": "1,517 recorded rows, the same inputs read again", "path": "runs/w111-5-20260924/answers/answers-w1115-asinh.json.gz", "repository": "CalcFunc-Evidence" } ], "functions": [ "FUNC.ASINH" ], "inferred": "That Excel's code is this expression, in this order, is inferred; what is measured is that the route reproduces every recorded row. The overflow boundary at |x| = 2^512, about 1.34E154, is inferred from x*x overflowing there: the recorded rows only bracket it, between 9.23E153 and 2.38E154. Excel reads a subnormal written to a cell back as 0, so the 0 at subnormal inputs may come from that step and not from this route.", "kind": "excel-differs-from-math", "note_id": "FN-ASINH-001", "open": [ "Only one Excel build, 20430, has been read over this range." ], "recorded_on": "2026-11-04", "repros": [ { "call": "ASINH(-1.0126103340069186e-11)", "correct": { "bits": "0xbda6447d498e6f26", "display": "-1.0126103340069186e-11", "how": "mpmath asinh at 2000 bits, rounded to the nearest binary64", "kind": "number" }, "excel": { "bits": "0xbda6447fffff840a", "display": "-1.0126122162949859e-11", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "number", "value": { "bits": "0xbda6447d498e6f26", "display": "-1.0126103340069186e-11", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20430, Windows 64-bit, AMD Ryzen 7 4800H", "source": { "commit": "4d5320dfdc385354469b4d506153357bb932ab08", "locator": "ASINH|0xbda6447d498e6f26", "note": null, "path": "cache/oracle-20430/build-20430/ASINH.jsonl.gz", "repository": "CalcFunc-Evidence" } }, { "call": "ASINH(-1.4901631254755754e-16)", "correct": { "bits": "0xbca579bb4790a498", "display": "-1.4901631254755754e-16", "how": "mpmath asinh at 2000 bits, rounded to the nearest binary64", "kind": "number" }, "excel": { "bits": "0xbcafffffffffffff", "display": "-2.2204460492503128e-16", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "number", "value": { "bits": "0xbca579bb4790a498", "display": "-1.4901631254755754e-16", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20430, Windows 64-bit, AMD Ryzen 7 4800H", "source": { "commit": "4d5320dfdc385354469b4d506153357bb932ab08", "locator": "ASINH|0xbca579bb4790a498", "note": null, "path": "cache/oracle-20430/build-20430/ASINH.jsonl.gz", "repository": "CalcFunc-Evidence" } }, { "call": "ASINH(1.0501151062119094e-16)", "correct": { "bits": "0x3c9e447b5a2fd072", "display": "1.0501151062119094e-16", "how": "mpmath asinh at 2000 bits, rounded to the nearest binary64", "kind": "number" }, "excel": { "bits": "0x0000000000000000", "display": "0", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "number", "value": { "bits": "0x3c9e447b5a2fd072", "display": "1.0501151062119094e-16", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20430, Windows 64-bit, AMD Ryzen 7 4800H", "source": { "commit": "4d5320dfdc385354469b4d506153357bb932ab08", "locator": "ASINH|0x3c9e447b5a2fd072", "note": null, "path": "cache/oracle-20430/build-20430/ASINH.jsonl.gz", "repository": "CalcFunc-Evidence" } }, { "call": "ASINH(5e-324)", "correct": { "bits": "0x0000000000000001", "display": "5e-324", "how": "mpmath asinh at 2000 bits, rounded to the nearest binary64", "kind": "number" }, "excel": { "bits": "0x0000000000000000", "display": "0", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "number", "value": { "bits": "0x0000000000000001", "display": "5e-324", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20430, Windows 64-bit, AMD Ryzen 7 4800H", "source": { "commit": "4d5320dfdc385354469b4d506153357bb932ab08", "locator": "ASINH|0x0000000000000001", "note": null, "path": "cache/oracle-20430/build-20430/ASINH.jsonl.gz", "repository": "CalcFunc-Evidence" } }, { "call": "ASINH(7.193439987815484e-08)", "correct": { "bits": "0x3e734f4b587c8346", "display": "7.193439987815477e-08", "how": "mpmath asinh at 2000 bits, rounded to the nearest binary64", "kind": "number" }, "excel": { "bits": "0x3e734f4b58591206", "display": "7.19343998474134e-08", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "number", "value": { "bits": "0x3e734f4b587c834b", "display": "7.193439987815484e-08", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20430, Windows 64-bit, AMD Ryzen 7 4800H", "source": { "commit": "4d5320dfdc385354469b4d506153357bb932ab08", "locator": "ASINH|0x3e734f4b587c834b", "note": null, "path": "cache/oracle-20430/build-20430/ASINH.jsonl.gz", "repository": "CalcFunc-Evidence" } }, { "call": "ASINH(9.234293629925394e+153)", "correct": null, "excel": { "bits": "0x40763362acc0ad1b", "display": "355.2115905310072", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "number", "value": { "bits": "0x5fe60a092f72d845", "display": "9.234293629925394e+153", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20430, Windows 64-bit, AMD Ryzen 7 4800H", "source": { "commit": "4d5320dfdc385354469b4d506153357bb932ab08", "locator": "ASINH|0x5fe60a092f72d845", "note": null, "path": "cache/oracle-20430/build-20430/ASINH.jsonl.gz", "repository": "CalcFunc-Evidence" } }, { "call": "ASINH(2.3842260672008416e+154)", "correct": { "bits": "0x4076428fe05b79d7", "display": "356.1601260731963", "how": "mpmath asinh at 2000 bits, rounded to the nearest binary64", "kind": "number" }, "excel": { "bits": null, "display": "#NUM!", "kind": "error" }, "input_route": "cell-value2", "inputs": [ { "name": "number", "value": { "bits": "0x5ffc73a8ae6c7c25", "display": "2.3842260672008416e+154", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20430, Windows 64-bit, AMD Ryzen 7 4800H", "source": { "commit": "4d5320dfdc385354469b4d506153357bb932ab08", "locator": "ASINH|0x5ffc73a8ae6c7c25", "note": null, "path": "cache/oracle-20430/build-20430/ASINH.jsonl.gz", "repository": "CalcFunc-Evidence" } } ], "schema": "efh.function-note/v1", "statement": "ASINH is not the correctly rounded inverse hyperbolic sine. Its answers are those of SIGN(x)*LN(|x|+SQRT(x*x+1)), with x*x, the +1, the SQRT and the |x|+root each rounded to 64 bits and then to 53 bits before the next step, and the LN rounded to binary64. That route loses most of the digits of a small input: once x*x+1 rounds to 1, the answer is LN of |x|+1 after rounding, so it moves in steps of about 2.2E-16. ASINH(-1.4901631254755754E-16) is -2.22E-16, about 1.5 times the true value, and in the recorded rows every |x| up to 1.05E-16, including every subnormal, gives 0 on either sign. At the other end the x*x overflows: answers are finite up to the largest recorded input below it, 9.23E153, and #NUM! from the next recorded input, 2.38E154, although the true value there is about 356. In Excel build 20430 this route reproduces all 4,534 recorded rows (3,017 distinct inputs): 3,427 numbers and 1,107 #NUM!. The correctly rounded asinh matches only 1,224 of the 3,427.", "status": "measured", "title": "ASINH is LN(|x|+SQRT(x*x+1)) with every step stored, so small inputs lose their digits" } ], "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- **`SINH`** — the forward function. `ASINH(SINH(t)) = t` for every real `t`, which is the cleanest\n round trip in the family (no absolute value, no branch), and therefore the best oracle-free test\n on this page.\n- **`ATANH`** — the third inverse hyperbolic primary. `asinh x = atanh(x/sqrt(x^2+1))`.\n- **`ASIN`** — the circular namesake, and a completely different shape: bounded domain, bounded\n range, singular derivative at the endpoints. Sharing a name is the only thing they do.\n- **`LN`** and **`SQRT`** — the substrate, and the source of both the cancellation and the\n overflow.\n- **`LOG1P`** — which Excel does not expose as a worksheet function. Its absence is why a\n worksheet-level workaround for the small-argument hazard is awkward, and why a careful\n implementation of this surface must supply it internally. Excel's recorded answers follow a route\n without it (FN-ASINH-001).\n- **Confused with**: `ASIN`, by name; and with `1/SINH`, which is `CSCH`.\n\n\n", "how-to-implement": "\n### Numerical notes\n\n\nThe closed form is correct and, taken literally, fails at three places. All three are standard, and\nall three have one-line remedies.\n\n**1. Cancellation for negative arguments.** For `x` large and negative, `x + sqrt(x^2 + 1)` is a\ndifference of two nearly equal magnitudes, and the relative accuracy of the sum collapses; the\nlogarithm then magnifies whatever survived. The remedy is oddness: compute on `|x|` and apply the\nsign at the end. This costs nothing and additionally makes `ASINH(-x) = -ASINH(x)` hold to the last bit. Any implementation of an odd function that does not do this has a symmetry defect that is\ntrivially detectable.\n\n**2. Cancellation for small arguments.** For small `x`, `x + sqrt(x^2 + 1)` is near `1`, and `ln`\nof a value near `1` loses exactly the digits that carry the answer. The remedy is `log1p`, applied\nto a rearranged argument:\n\n asinh x = log1p( x + x^2 / (1 + sqrt(1 + x^2)) )\n\nHere nothing near `1` is ever formed and nothing is subtracted. Higham's treatment of `log(1+x)`\nis the standard statement of why this rearrangement is necessary rather than merely tidy. Below a\nthreshold the series `x - x^3/6` — or simply `x` itself — is correctly rounded and cheaper.\n\n**3. Overflow in the intermediate for large arguments.** Described above. The remedy is a branch:\nonce `x` is large enough that `x^2 + 1` would round to `x^2` anyway,\n\n asinh x = ln(x) + ln(2)\n\ncomputed without ever forming `x^2`. This extends the working range from the square root of the\nlargest finite double all the way to the largest finite double itself — a hundred-odd decades\nrecovered for the cost of one comparison.\n\n`fdlibm`'s `s_asinh.c` is the published implementation of exactly this three-branch structure, and\nit is what \"a careful implementation\" means for this function.\n\n**Why the naive form survives in the wild.** It is one line, it is correct on the range people\nactually use, and its failure mode at the top of the range is an error rather than a wrong number;\nat small inputs it does give wrong numbers (FN-ASINH-001). That is a defensible engineering position\nand it is very likely how the behaviour on record came to exist. The Handbook\nrecords it as a departure from the mathematics without implying carelessness.\n\n", "quirks": "\n### Result and edge cases\n\n\nReturns `Number`.\n\n- **Zero** returns zero, and an odd implementation preserves the sign of zero.\n- **Subnormals and very small arguments** do not pass through. In the recorded rows every `|x|` up\n to 1.05E-16, including every subnormal, gives 0, and slightly larger inputs move in steps of about\n 2.2E-16 (FN-ASINH-001).\n- **Negative arguments** are the case the closed form handles badly and the oddness handles for\n free.\n- **Very large arguments** are the interesting case, and the reason this page carries an evidence\n record.\n\n### The overflow boundary — the substantive finding on this page\n\nMathematically, `asinh` of the largest finite double is a modest number just above 710: finite,\nrepresentable, and nowhere near any limit. But the closed form\n`ln(x + sqrt(x^2 + 1))` forms `x^2` first, and `x^2` overflows binary64 as soon as `|x|` exceeds\nthe square root of the largest finite double — approximately `1.34e154`. Above that point the\nintermediate is infinite while the answer is small.\n\n**`EV-MATH-0009` is an `excel-math-deviation` record whose subject is `FUNC.ASINH`**, and what it\nidentifies is exactly this: the substrate is the literal `ln(x + sqrt(x^2+1))`, the `x^2`\nintermediate overflows, and an error is published well below where the mathematical result would\nrequire one. The record states the mechanism and, in its own words, publishes **no count**; its\nreader warning says that an exactness claim without a denominator is not a count and that this\nrecord publishes none. The Handbook repeats the shape and not the figures, which are rendered\nmechanically beside this page.\n\n**The documentation-versus-record divergence, stated plainly.** Microsoft's Learn reference\ndocuments the argument as \"any real number\" and lists no error condition. The identified substrate\nmakes an entire band of real numbers — more than a hundred decades of the double range, from about\n`1.34e154` to the largest finite double — fail. Documentation and behaviour disagree, and the\nHandbook publishes both.\n\n- **Arrays** lift elementwise.\n\n\n\n### Errors\n\nThere is **no mathematical domain error for `ASINH`**. The `#NUM!` above is an artefact of an\nevaluation form, not a statement about the function.\n\n\n", "sources": "- Microsoft Learn, \"WorksheetFunction.Asinh method (Excel)\" —\n (retrieved: the\n description, the **\"any real number\"** argument statement, and the round trip; **no error\n condition is stated there**).\n- Abramowitz & Stegun, *Handbook of Mathematical Functions*, chapter 4 section 4.6 — the closed\n form and series.\n- `fdlibm` `s_asinh.c` — the published three-branch reference implementation.\n- Higham, *Accuracy and Stability of Numerical Algorithms*, chapter 1 — the `log(1+x)` problem.\n- Muller, *Elementary Functions: Algorithms and Implementation* — spurious intermediate overflow\n and its avoidance.\n- Handbook evidence record `EV-MATH-0009` (subject `FUNC.ASINH`) — the identified substrate and\n overflow boundary, with its own statement that **no count is published**.\n- Handbook projections `data/functions/FUNC.ASINH.json` and `data/presence/FUNC.ASINH.json`.\n- Handbook [About implementation options](../model/07-implementation-options.md) — why an\n Excel-compatible and a mathematically-best implementation must disagree on the overflow band —\n and [Coercion and lifting](../model/02-coercion-and-lifting.md).\n- Sibling page [ACOSH](FUNC.ACOSH.md) — the same hazard, treated differently.\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 | 41 |\n| 20430 | Windows, 64-bit, AMD Ryzen 7 4800H with Radeon Graphics | 3,017 |\n\n- XC-ASINH-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.ASINH.json).", "what-it-does": "\n`ASINH(number)` is the inverse hyperbolic sine.\n\n asinh x = ln( x + sqrt(x^2 + 1) )\n\n- **Domain**: all real numbers. `sinh` is a strictly increasing bijection from `R` onto `R`, so\n its inverse needs no branch choice and has no domain restriction. Microsoft's Learn reference\n says exactly this: the argument is \"any real number\".\n- **Range**: all real numbers.\n- **Parity**: odd, exactly. `asinh(-x) = -asinh(x)`. Because the square root is always at least\n `|x|`, the closed form above never cancels for positive `x` — but it cancels badly for negative\n `x`, which is why every implementation folds the sign. See the numerical notes.\n- **Monotonicity**: strictly increasing everywhere.\n- **Derivative**: `d/dx asinh x = 1 / sqrt(x^2 + 1)` — bounded by 1, positive, and smooth on the\n whole line. There are no singularities of any kind. `ASINH` is the best-conditioned function in\n its family and its difficulties are entirely about representation.\n- **Series about zero**: `asinh x = x - x^3/6 + 3x^5/40 - ...`, so `asinh x -> x` for small `x` and\n subnormals pass through unchanged in the mathematics. Excel's do not: see *Result and edge cases*.\n- **Asymptotics**: `asinh x = ln(2x) + 1/(4x^2) - ...` as `x -> +infinity`. Growth is logarithmic:\n every argument in the upper half of the double range maps into a narrow band of results, and at\n the top of binary64 the answer is a little over 710.\n- **Relations**: `asinh x = sign(x) * acosh(sqrt(x^2 + 1))` and\n `asinh x = atanh( x / sqrt(x^2 + 1) )`; also `asinh(sinh t) = t` for every real `t`, which is\n the round trip Microsoft's Learn reference states.\n- **Complex continuation**: branch cuts along the imaginary axis outside `[-i, i]`. Nothing on the\n real line is cut, which is the precise reason the real domain is unrestricted.\n\nAbramowitz & Stegun give the logarithmic closed form in chapter 4 section 4.6.\n\n\n\n### Arguments\n\n\n| Argument | Meaning | Default |\n|---|---|---|\n| `number` | Any real number. Required. | — |\n\nThat is Microsoft's own wording from the Learn reference. **The Handbook flags it as the most\nconsequential documented statement on this page**, because what is on record upstream about the\nimplementation contradicts it — see *Result and edge cases* below.\n\nThere are no units here. `ASINH` takes a number, not an angle; the `RADIANS`/`DEGREES` apparatus\nthat attaches to the circular inverses is meaningless for it.\n\n\n" }, "signature": { "display": "ASINH(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": "Inverse of the hyperbolic sine", "short_source": "dna-calc-own" }, "docs": { "english_description": "Returns the inverse hyperbolic sine of a number", "microsoft_url": "https://support.microsoft.com/en-us/office/asinh-function-4e00475a-067a-43cf-926a-765b0249717c" }, "entry_kind": "built_in_function", "localized_family_names": null, "localized_names": [ { "locale": "ar-SA", "name": "ASINH" }, { "locale": "bg-BG", "name": "ASINH" }, { "locale": "cs-CZ", "name": "ARCSINH" }, { "locale": "da-DK", "name": "ARCSINH" }, { "locale": "de-DE", "name": "ASINH" }, { "locale": "el-GR", "name": "ASINH" }, { "locale": "en-AU", "name": "ASINH" }, { "locale": "en-GB", "name": "ASINH" }, { "locale": "en-US", "name": "ASINH" }, { "locale": "es-ES", "name": "ASENOH" }, { "locale": "et-EE", "name": "ASINH" }, { "locale": "fi-FI", "name": "ASINH" }, { "locale": "fr-FR", "name": "ASINH*" }, { "locale": "he-IL", "name": "ASINH" }, { "locale": "hr-HR", "name": "ASINH" }, { "locale": "hu-HU", "name": "ASINH" }, { "locale": "id-ID", "name": "ASINH" }, { "locale": "it-IT", "name": "ASINH" }, { "locale": "ja-JP", "name": "ASINH" }, { "locale": "ko-KR", "name": "ASINH" }, { "locale": "lt-LT", "name": "ASINH" }, { "locale": "lv-LV", "name": "ASINH" }, { "locale": "nb-NO", "name": "ARCSINH" }, { "locale": "nl-NL", "name": "ASINH" }, { "locale": "pl-PL", "name": "ASINH" }, { "locale": "pt-BR", "name": "ASINH" }, { "locale": "pt-PT", "name": "ASENH" }, { "locale": "ro-RO", "name": "ASINH" }, { "locale": "ru-RU", "name": "ASINH" }, { "locale": "sk-SK", "name": "ASINH" }, { "locale": "sl-SI", "name": "ASINH" }, { "locale": "sr-Latn-RS", "name": "ASINH" }, { "locale": "sv-SE", "name": "ARCSINH" }, { "locale": "th-TH", "name": "ASINH" }, { "locale": "tr-TR", "name": "ASİNH işlevi" }, { "locale": "uk-UA", "name": "ASINH" }, { "locale": "vi-VN", "name": "ASINH" }, { "locale": "zh-CN", "name": "ASINH" }, { "locale": "zh-HK", "name": "ASINH" }, { "locale": "zh-TW", "name": "ASINH" } ], "signature": { "display": "ASINH(number)", "parameters": [ { "description": null, "name": "number", "optional": false, "repeats": false } ], "trailing_repeats": false }, "surface_name": "ASINH", "version_marker": null, "xlcall": { "code": "232", "symbol": "xlfAsinh" } }, "microsoft": "https://support.microsoft.com/en-us/office/asinh-function-4e00475a-067a-43cf-926a-765b0249717c" }, "try_it": { "formula": "=ASINH(1)" }, "url": "https://handbook.dnacalc.com/functions/ASINH.html", "variants": [], "versions": [ { "behaviour": "ASINH(-1.0126103340069186e-11) returned -1.0126122162949859e-11 (0xbda6447fffff840a). ASINH(-1.4901631254755754e-16) returned -2.2204460492503128e-16 (0xbcafffffffffffff). 5 further recorded controls are 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": "ASINH(-1.0126103340069186e-11)", "excel": { "bits": "0xbda6447fffff840a", "display": "-1.0126122162949859e-11", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "number", "value": { "bits": "0xbda6447d498e6f26", "display": "-1.0126103340069186e-11", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20430, Windows 64-bit, AMD Ryzen 7 4800H" }, { "call": "ASINH(-1.4901631254755754e-16)", "excel": { "bits": "0xbcafffffffffffff", "display": "-2.2204460492503128e-16", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "number", "value": { "bits": "0xbca579bb4790a498", "display": "-1.4901631254755754e-16", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20430, Windows 64-bit, AMD Ryzen 7 4800H" }, { "call": "ASINH(1.0501151062119094e-16)", "excel": { "bits": "0x0000000000000000", "display": "0", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "number", "value": { "bits": "0x3c9e447b5a2fd072", "display": "1.0501151062119094e-16", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20430, Windows 64-bit, AMD Ryzen 7 4800H" }, { "call": "ASINH(5e-324)", "excel": { "bits": "0x0000000000000000", "display": "0", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "number", "value": { "bits": "0x0000000000000001", "display": "5e-324", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20430, Windows 64-bit, AMD Ryzen 7 4800H" }, { "call": "ASINH(7.193439987815484e-08)", "excel": { "bits": "0x3e734f4b58591206", "display": "7.19343998474134e-08", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "number", "value": { "bits": "0x3e734f4b587c834b", "display": "7.193439987815484e-08", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20430, Windows 64-bit, AMD Ryzen 7 4800H" }, { "call": "ASINH(9.234293629925394e+153)", "excel": { "bits": "0x40763362acc0ad1b", "display": "355.2115905310072", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "number", "value": { "bits": "0x5fe60a092f72d845", "display": "9.234293629925394e+153", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20430, Windows 64-bit, AMD Ryzen 7 4800H" }, { "call": "ASINH(2.3842260672008416e+154)", "excel": { "bits": null, "display": "#NUM!", "kind": "error" }, "input_route": "cell-value2", "inputs": [ { "name": "number", "value": { "bits": "0x5ffc73a8ae6c7c25", "display": "2.3842260672008416e+154", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20430, Windows 64-bit, AMD Ryzen 7 4800H" } ], "platform": "Windows 64-bit, AMD Ryzen 7 4800H", "sources": [ "https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/3345a87/content/notes/FN-ASINH-001.json" ] }, { "behaviour": "41 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.ASINH.json" ] }, { "behaviour": "3,017 captured inputs are indexed for this environment. Capture dates: 2026-09-24 to 2026-09-25. This is a reading count, not a comparison with another build.", "excel_build": "16.0 build 20430", "platform": "Windows, 64-bit, AMD Ryzen 7 4800H with Radeon Graphics", "sources": [ "https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.ASINH.json" ] } ] }