{ "category": "Statistical functions", "display_name": "GAMMALN", "entry_kind": "built_in_function", "eval_api": { "method": "POST", "url": "https://handbook.dnacalc.com/api/eval" }, "function_id": "FUNC.GAMMALN", "implementation_state": { "answer_bank": { "excel_builds": [ "20131", "20228", "?" ], "larger_numeric": 0, "last_bit": 2403, "matched": 2135, "other_mismatch": 0, "refused": 0, "rows": 4538, "unread": 0, "worst_ulp": 7 }, "detail": "Everything else matches (4,538 in the answer bank and 3 workbook cells). Last-bit means a finite number within 16 ULP of Excel's.", "dnacalc_commit": "9e1884369a678158dd82d3d74188daf986995e87", "in_catalogue": true, "state": "close", "state_label": "Close: last-bit deviations remain", "summary": "Close: 2,403 of 4,541 recorded answers differ in the last bits, worst 7 ULP", "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/distributions.rs#L240-L240" ], "repository": "https://github.com/DnaCalc/DnaCalc", "shared_code": [ "ported/special_dist_family::gammaln_kernel" ], "source": "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/distributions.rs#L240-L240", "state": "close", "suite": null, "summary": "Close: 2,403 of 4,541 recorded answers differ in the last bits, worst 7 ULP" } ], "json_url": "https://handbook.dnacalc.com/api/functions/FUNC.GAMMALN.json", "name": "GAMMALN", "notes": [ { "basis": "6,000 of 6,000 fractions at each n from 3 to 7, 30,000 answers, from Excel's own GAMMALN(2+y) (build 20527). The descending product fits 5,430 to 5,527 of 6,000. Replayed for this note in exact rational arithmetic with a correctly rounded logarithm on 300 of those fractions: 300 of 300 at n = 3 to 6, and 299 of 300 at n = 7. Recorded rows match GAMMALN 2,106 of 4,538 and GAMMALN.PRECISE 10,627 of 14,278, with stand-ins for the bands below 3.", "documentation": null, "evidence": [ { "commit": "b5d84a80a5a4640eca9ce04f232c0bc115503f34", "locator": null, "note": "research write-up: how the stored stages were read", "path": "content/notes/evidence/2026-11-04/gamma-EVIDENCE.md", "repository": "ExcelFunctionsHandbook" }, { "commit": "1c7a4ab86b12b53d80947f06b6d381e8e5dd5f3f", "locator": null, "note": "the routes in the product, with stand-ins where the code says so; the commit message carries the row counts", "path": "crates/calc-func/src/ported/excel_numeric/gammaln.rs", "repository": "DnaCalc" }, { "commit": "af74247e1ed54f0b535143f1305261b98d80d18e", "locator": null, "note": "rows matched per function", "path": "crates/calc-func/witness-status.tsv", "repository": "DnaCalc" } ], "functions": [ "FUNC.GAMMALN", "FUNC.GAMMALN.PRECISE" ], "inferred": "That GAMMALN.PRECISE takes the same route is inferred: the 30,000 answers are GAMMALN, and the two functions agree at every shared recorded input tried, including 3.", "kind": "bit-matching-detail", "note_id": "FN-GAMMALN-001", "open": [ "The rationals below 3. They are rationals in x itself, [1.5,2) and [2,3] are separate bands, and their tables are not identified: no rescaled Cody-Hillstrom table and no fresh minimax table tried reproduces the steps of their mean error." ], "recorded_on": "2026-11-04", "repros": [ { "call": "GAMMALN(3)", "correct": { "bits": "0x3fe62e42fefa39ef", "display": "0.6931471805599453", "how": "ln 2, correctly rounded.", "kind": "number" }, "excel": { "bits": "0x3fe62e42fefa39f0", "display": "0.6931471805599454", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "x", "value": { "bits": "0x4008000000000000", "display": "3", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20131, platform and bitness not recorded, AMD Ryzen 7 4800H", "source": { "commit": "4d5320dfdc385354469b4d506153357bb932ab08", "locator": "line 273, key GAMMALN|0x4008000000000000", "note": null, "path": "cache/oracle/build-20131/GAMMALN.jsonl.gz", "repository": "CalcFunc-Evidence" } }, { "call": "GAMMALN.PRECISE(3)", "correct": { "bits": "0x3fe62e42fefa39ef", "display": "0.6931471805599453", "how": "ln 2, correctly rounded.", "kind": "number" }, "excel": { "bits": "0x3fe62e42fefa39f0", "display": "0.6931471805599454", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "x", "value": { "bits": "0x4008000000000000", "display": "3", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20131, platform and bitness not recorded, AMD Ryzen 7 4800H", "source": { "commit": "4d5320dfdc385354469b4d506153357bb932ab08", "locator": "line 22, key GAMMALN.PRECISE|0x4008000000000000", "note": null, "path": "cache/oracle/build-20131/GAMMALN.PRECISE.jsonl.gz", "repository": "CalcFunc-Evidence" } }, { "call": "GAMMALN(2.020222407046596)", "correct": null, "excel": { "bits": "0x3f81c75cc69b54fc", "display": "0.008681034861562235", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "x", "value": { "bits": "0x4000296a5d874ad0", "display": "2.020222407046596", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20527, Windows; bitness and CPU not recorded in this reading", "source": { "commit": "b5d84a80a5a4640eca9ce04f232c0bc115503f34", "locator": "GAMMALN 4000296a5d874ad0", "note": null, "path": "content/notes/evidence/2026-11-04/gamma-readings.tsv", "repository": "ExcelFunctionsHandbook" } }, { "call": "GAMMALN(6.020222407046596)", "correct": { "bits": "0x401349c26258ddb8", "display": "4.822030579256015", "how": "mpmath loggamma at 800 bits from the binary64 input, correctly rounded.", "kind": "number" }, "excel": { "bits": "0x401349c26258ddb7", "display": "4.8220305792560145", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "x", "value": { "bits": "0x401814b52ec3a568", "display": "6.020222407046596", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20527, Windows; bitness and CPU not recorded in this reading", "source": { "commit": "b5d84a80a5a4640eca9ce04f232c0bc115503f34", "locator": "GAMMALN 401814b52ec3a568", "note": null, "path": "content/notes/evidence/2026-11-04/gamma-readings.tsv", "repository": "ExcelFunctionsHandbook" } } ], "schema": "efh.function-note/v1", "statement": "With RN(v) meaning v rounded to 64 bits on the x87 unit and then stored to binary64, write x = n + y with n the integer part. For 3 < x < 8, Excel forms z = (y+2)(y+3)...(y+n-1) from the left with every product RN, and GAMMALN(x) is RN(RN(ln z) + GAMMALN(2+y)). So answers on this range carry the rounding of a value on [2,3]. x = 3 itself belongs to the band on [2,3], not to this route, and returns 0x3fe62e42fefa39f0, one unit above the stored ln 2, although GAMMALN(3) is exactly ln 2.", "status": "measured", "title": "GAMMALN from 3 to 8 is a stored recurrence, and GAMMALN(3) is one unit above ln 2" } ], "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- **[GAMMA](FUNC.GAMMA.md)** — the value rather than its logarithm. The two share a module and\n **not** a numeric path: upstream's landed log-gamma kernel is wired only to the two `GAMMALN`\n surfaces, and the source says so in as many words. `LN(GAMMA(x))` and `GAMMALN(x)` are\n therefore different computations with different accuracy and different domains, and the\n first overflows where the second does not.\n- **`FACT`, `COMBIN`, `MULTINOMIAL`** — combinatorial quantities better computed through this\n function than through `GAMMA` or `FACT` when the intermediate factorials would overflow.\n `COMBIN(n,k)` as `EXP(GAMMALN(n+1) − GAMMALN(k+1) − GAMMALN(n−k+1))` is the standard rewrite,\n and it is *less* accurate for small n than an exact integer route — a real trade, not a free\n improvement.\n- **[GAMMA.DIST](FUNC.GAMMA.DIST.md), `BETA.DIST`, `POISSON.DIST`** — consumers: their\n normalising constants are log-gammas.\n- **Module siblings**: `ERF`, `ERF.PRECISE`, `ERFC`, `ERFC.PRECISE`, `GAMMA`, `WEIBULL`,\n `WEIBULL.DIST`.\n\n\n", "how-to-implement": "\n### Numerical notes\n\n\n**The classical design is a three-region split.** Every serious implementation of ln Γ does the\nsame three things, and their boundaries are the implementation's fingerprint:\n\n1. **Small x** — use the recurrence to lift x into the well-behaved region:\n ln Γ(x) = ln Γ(x + 1) − ln x. This is essential because the Lanczos and rational forms both\n degrade as x → 0, and the reciprocal singularity is best handled by an explicit `ln x` term.\n2. **The middle**, roughly [1, 8] — a minimax rational or Chebyshev approximation. Cody &\n Hillstrom's 1967 Chebyshev approximations are the classical answer and the ancestor of\n SPECFUN's `ALGAMA`/`DLGAMA`, of fdlibm's `lgamma`, and of most libm implementations. Excel\n differs here: from 3 to 8 it uses a stored recurrence (FN-GAMMALN-001).\n3. **Large x** — Stirling's asymptotic series (A&S 6.1.40), typically with terms through 1/x⁷ or\n so, above a seam around x = 8 to 12.\n\n**The two zeros are the trap.** Because ln Γ vanishes at x = 1 and x = 2, the *relative* error\nnear those points is unbounded for any implementation that computes the value directly: the\nanswer is a small number obtained by cancelling large terms, and the surviving digits are few.\nfdlibm handles this by evaluating a polynomial in (x − 1) or (x − 2) directly near each zero,\nso that the small quantity is the *argument* rather than a difference. An implementation that\nskips that step will produce residuals that spike sharply in two narrow bands and look fine\neverywhere else — which is exactly the pattern that makes a coarse accuracy sweep miss the\nproblem.\n\n**Argument reduction is the other half.** The recurrence multiplies by x, so lifting a small\nargument requires computing `ln x` accurately and subtracting; near x = 1 that subtraction is\nitself a cancellation. The interaction of the reduction seam with the zero at x = 1 is the\nsubtlest part of the whole function.\n\n**What upstream identified.** The evidence records describe an identification campaign that\npinned a structural form for Excel's surface — a threshold near 0.7, a seam at 8.0, and a\nStirling form beyond it — and then fitted coefficients, with two held-out tests plus one fresh\nnever-probed corpus used to decide which candidate landed. Two properties of that campaign\nmatter to a reader and are stated in the records themselves. First, the held-out tests were held\nout from the **coefficient fits**, not from the structural identification: the threshold, the\nseam and the form were pinned on batteries surrounding those very rows. Second, the arguments in\nboth held-out tests are `GAMMALN.PRECISE` captures, so the inheritance runs from `.PRECISE` to\n`GAMMALN` and not the other way — the surface with the fresh corpus of its own is this one, and\nthe record says so explicitly.\n\n**Recommended practice.** Prefer `GAMMALN` over `LN(GAMMA(x))` unconditionally: it is defined on\na larger useful range, it does not overflow where `GAMMA` does, and it avoids the\nexp-then-log round trip. Where a *ratio* of gammas is wanted, keep it in log space to the last\nstep. Where an exact small factorial is wanted, use the integer route, not this one.\n\n\n", "quirks": "\n### Result and edge cases\n\n\nReturns `Number`.\n\n- **Small positive x** behaves like −ln x: ln Γ(x) = −ln x − γx + O(x²). At the bottom of the\n double range the value is large and finite, which is the good news `GAMMALN` exists to\n deliver — where `GAMMA` overflows, `GAMMALN` still answers.\n- **x ≤ 0** is documented `#NUM!`, including the poles and the whole negative axis where the\n real logarithm of Γ does not exist.\n- **Array arguments** lift elementwise through the module's broadcast helper.\n\n\n\n### Errors\n\n\nAs documented by Microsoft:\n\n| Error | Condition |\n|---|---|\n| `#VALUE!` | `x` is nonnumeric |\n| `#NUM!` | `x` ≤ 0 |\n\n", "sources": "- Abramowitz & Stegun, *Handbook of Mathematical Functions*, §6.1 — the recurrence, the two\n zeros, the location of the minimum, and Stirling's asymptotic series at 6.1.40.\n- W. J. Cody & K. E. Hillstrom, \"Chebyshev approximations for the natural logarithm of the gamma\n function\", *Math. Comp.* 21 (1967); SPECFUN `ALGAMA`/`DLGAMA`; fdlibm `e_lgamma_r.c` — the\n three-region design and the special handling near the zeros.\n- Handbook evidence records `EV-MATH-0012` (the fresh per-surface test), `EV-MATH-0013` (the two\n held-out tests, their scope caveats, and the upstream self-contradiction on one figure) and\n `EV-MATH-0014` (the Excel-versus-Excel alias identity on one named build).\n- Handbook, [GAMMA](FUNC.GAMMA.md) — the value form, and the record that the landed kernel does\n not touch it.\n- Handbook, [Coercion and lifting](../model/02-coercion-and-lifting.md).\n- Handbook projections `data/functions/FUNC.GAMMALN.json` (arity, category **Statistical\n functions**) and `data/presence/FUNC.GAMMALN.json` (the `special_dist_family` module).\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 | 43 |\n| 20131 | Windows, bitness not recorded, AMD Ryzen 7 4800H with Radeon Graphics | 4,450 |\n| 20228 | Windows, 64-bit, CPU not recorded | 88 |\n\n- XC-GAMMALN-001: build 19929 versus build 20228; 1 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- XC-GAMMALN-002: build 20131 versus build 20228; 13 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.GAMMALN.json).", "what-it-does": "\n`GAMMALN(x)` returns the natural logarithm of the gamma function:\n\n GAMMALN(x) = ln Γ(x) = ln ∫₀^∞ t^{x−1} e^{−t} dt for x > 0\n\n**Domain:** the positive reals. Excel does not expose the negative-argument branch (where Γ\nalternates sign and its logarithm is complex), so the documented domain is x > 0 with `#NUM!`\noutside it. Note this makes `GAMMALN` a *restriction* of `LN(GAMMA(x))`, not an equivalent: the\nlatter is defined on more of the line and overflows on far less of it.\n\n**Range and shape.** ln Γ is strictly convex on (0, ∞) — this is the Bohr–Mollerup\ncharacterisation, and it is the property that makes ln Γ the natural object rather than Γ. It\nfalls from +∞ at x → 0⁺ to a single minimum near x ≈ 1.4616 (value ≈ −0.1214) and rises\nthereafter without bound. It has **exactly two zeros**, at x = 1 and x = 2, because Γ(1) =\nΓ(2) = 1. Those two zeros are the source of the function's only real accuracy trap; see\n**Numerical notes**.\n\n**The identities.**\n\n ln Γ(x + 1) = ln x + ln Γ(x) (recurrence)\n ln Γ(n) = ln (n − 1)! for positive integers n\n ln Γ(x) ~ (x − ½) ln x − x + ½ ln(2π) + 1/(12x) − 1/(360x³) + … (Stirling, A&S 6.1.40)\n\nMicrosoft states the integer relation from the other side: \"The number e raised to the\nGAMMALN(i) power, where i is an integer, returns the same result as (i − 1)!\" That is exact as\nmathematics and, as with `GAMMA`, is a floating-point *claim about the round trip* rather than a\nguarantee — exp(lnΓ(i)) need not land on the integer.\n\n**Why this function exists at all.** Γ overflows binary64 a little above x ≈ 171.6; ln Γ stays\ncomfortably finite until x is astronomically large. Every ratio of gamma functions — binomial\ncoefficients, beta functions, distribution normalising constants, multinomials — should be\ncomputed as a difference of log-gammas and exponentiated once at the end, if at all. That is\nthe entire practical argument for the function, and it is why `GAMMALN` appears far more often\nthan `GAMMA` in careful spreadsheet work.\n\n\n\n### Arguments\n\n\n| Argument | Meaning | Default |\n|---|---|---|\n| `x` | The value at which to evaluate ln Γ. Required. | — |\n\n" }, "signature": { "display": "GAMMALN(x)", "parameters": [ { "description": null, "name": "x", "optional": false, "repeats": false } ], "trailing_repeats": false }, "sources": { "metadata": { "admission": { "label": "implemented", "reason": null }, "arity": { "max": 1, "min": 1 }, "category": "Statistical functions", "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": "Natural logarithm of the gamma function", "short_source": "dna-calc-own" }, "docs": { "english_description": "Returns the natural logarithm of the gamma function, ?(x)", "microsoft_url": "https://support.microsoft.com/en-us/office/gammaln-function-b838c48b-c65f-484f-9e1d-141c55470eb9" }, "entry_kind": "built_in_function", "localized_family_names": null, "localized_names": [ { "locale": "ar-SA", "name": "GAMMALN" }, { "locale": "bg-BG", "name": "GAMMALN" }, { "locale": "cs-CZ", "name": "GAMMALN" }, { "locale": "da-DK", "name": "GAMMALN" }, { "locale": "de-DE", "name": "GAMMALN" }, { "locale": "el-GR", "name": "GAMMALN" }, { "locale": "en-AU", "name": "GAMMALN" }, { "locale": "en-GB", "name": "GAMMALN" }, { "locale": "en-US", "name": "GAMMALN" }, { "locale": "es-ES", "name": "GAMMA.LN" }, { "locale": "et-EE", "name": "GAMMALN" }, { "locale": "fi-FI", "name": "GAMMALN" }, { "locale": "fr-FR", "name": "LNGAMMA*" }, { "locale": "he-IL", "name": "GAMMALN" }, { "locale": "hr-HR", "name": "GAMMALN" }, { "locale": "hu-HU", "name": "GAMMALN" }, { "locale": "id-ID", "name": "GAMMALN" }, { "locale": "it-IT", "name": "GAMMALN" }, { "locale": "ja-JP", "name": "GAMMALN" }, { "locale": "ko-KR", "name": "GAMMALN" }, { "locale": "lt-LT", "name": "GAMMALN" }, { "locale": "lv-LV", "name": "GAMMALN" }, { "locale": "nb-NO", "name": "GAMMALN" }, { "locale": "nl-NL", "name": "GAMMA.LN" }, { "locale": "pl-PL", "name": "ROZKŁAD.LIN.GAMMA" }, { "locale": "pt-BR", "name": "GAMMALN" }, { "locale": "pt-PT", "name": "LNGAMA" }, { "locale": "ro-RO", "name": "GAMMALN" }, { "locale": "ru-RU", "name": "ГАММАНЛОГ" }, { "locale": "sk-SK", "name": "GAMMALN" }, { "locale": "sl-SI", "name": "GAMMALN" }, { "locale": "sr-Latn-RS", "name": "GAMMALN" }, { "locale": "sv-SE", "name": "GAMMALN" }, { "locale": "th-TH", "name": "GAMMALN" }, { "locale": "tr-TR", "name": "GAMALN işlevi" }, { "locale": "uk-UA", "name": "GAMMALN" }, { "locale": "vi-VN", "name": "GAMMALN" }, { "locale": "zh-CN", "name": "GAMMALN" }, { "locale": "zh-HK", "name": "GAMMALN" }, { "locale": "zh-TW", "name": "GAMMALN" } ], "signature": { "display": "GAMMALN(x)", "parameters": [ { "description": null, "name": "x", "optional": false, "repeats": false } ], "trailing_repeats": false }, "surface_name": "GAMMALN", "version_marker": null, "xlcall": { "code": "271", "symbol": "xlfGammaln" } }, "microsoft": "https://support.microsoft.com/en-us/office/gammaln-function-b838c48b-c65f-484f-9e1d-141c55470eb9" }, "try_it": { "formula": "=GAMMALN(1)" }, "url": "https://handbook.dnacalc.com/functions/GAMMALN.html", "variants": [], "versions": [ { "behaviour": "GAMMALN(3) returned 0.6931471805599454 (0x3fe62e42fefa39f0). 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 20131", "observations": [ { "call": "GAMMALN(3)", "excel": { "bits": "0x3fe62e42fefa39f0", "display": "0.6931471805599454", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "x", "value": { "bits": "0x4008000000000000", "display": "3", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20131, platform and bitness not recorded, AMD Ryzen 7 4800H" } ], "platform": null, "sources": [ "https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/3345a87/content/notes/FN-GAMMALN-001.json" ] }, { "behaviour": "GAMMALN(2.020222407046596) returned 0.008681034861562235 (0x3f81c75cc69b54fc). GAMMALN(6.020222407046596) returned 4.8220305792560145 (0x401349c26258ddb7). 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 20527", "observations": [ { "call": "GAMMALN(2.020222407046596)", "excel": { "bits": "0x3f81c75cc69b54fc", "display": "0.008681034861562235", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "x", "value": { "bits": "0x4000296a5d874ad0", "display": "2.020222407046596", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20527, Windows; bitness and CPU not recorded in this reading" }, { "call": "GAMMALN(6.020222407046596)", "excel": { "bits": "0x401349c26258ddb7", "display": "4.8220305792560145", "kind": "number" }, "input_route": "cell-value2", "inputs": [ { "name": "x", "value": { "bits": "0x401814b52ec3a568", "display": "6.020222407046596", "kind": "number" } } ], "recorded_in": "Excel 16.0 build 20527, Windows; bitness and CPU not recorded in this reading" } ], "platform": "Windows; bitness and CPU not recorded in this reading", "sources": [ "https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/3345a87/content/notes/FN-GAMMALN-001.json" ] }, { "behaviour": "43 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.GAMMALN.json" ] }, { "behaviour": "4,450 captured inputs are indexed for this environment. Capture dates: 2026-07-11 to 2026-07-18. This is a reading count, not a comparison with another build.", "excel_build": "16.0 build 20131", "platform": "Windows, bitness not recorded, AMD Ryzen 7 4800H with Radeon Graphics", "sources": [ "https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.GAMMALN.json" ] }, { "behaviour": "88 captured inputs are indexed for this environment. Capture dates: 2026-08-09 to 2026-08-09. This is a reading count, not a comparison with another build.", "excel_build": "16.0 build 20228", "platform": "Windows, 64-bit, CPU not recorded", "sources": [ "https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.GAMMALN.json" ] } ] }