{ "category": "Compatibility", "display_name": "GAMMADIST", "entry_kind": "built_in_function", "eval_api": { "method": "POST", "url": "https://handbook.dnacalc.com/api/eval" }, "function_id": "FUNC.GAMMADIST", "implementation_state": { "answer_bank": { "excel_builds": [ "20131", "?" ], "larger_numeric": 0, "last_bit": 2, "matched": 4, "other_mismatch": 0, "refused": 0, "rows": 6, "unread": 0, "worst_ulp": 3 }, "detail": "Everything else matches (6 in the answer bank and 6 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: 4 of 12 recorded answers differ in the last bits, worst 13 ULP", "workbook_corpus": { "cells": 6, "last_bit": 2, "matched": 4, "worst_ulp": 13 } }, "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#L227-L230" ], "repository": "https://github.com/DnaCalc/DnaCalc", "shared_code": [ "catalogue/distributions::nums", "ported/beta_gamma_stats_family::validate_gamma_shape", "ported/beta_gamma_stats_family::gamma_dist_kernel", "ported/discrete_dist::finite", "ported/discrete_dist::expon_dist_kernel", "ported/excel_numeric::binary_with", "ported/excel_numeric::excel_expm1_internal", "ported/excel_numeric::excel_expm1_spilled", "ported/excel_numeric::expm1_internal_graph", "ported/excel_numeric::excel_x87_add", "ported/excel_numeric::excel_x87_sub", "ported/excel_numeric::excel_x87_mul", "ported/excel_numeric::excel_x87_temme_finish", "ported/excel_numeric::excel_x87_div", "ported/excel_numeric/x87::mul", "ported/excel_numeric/x87::add", "ported/excel_numeric/x87::sub", "ported/excel_numeric/x87::div", "ported/excel_numeric/x87_chains::pow2_positive", "ported/excel_numeric/x87_chains::pow2", "ported/excel_numeric/x87_chains::exp_ext", "ported/excel_numeric/x87_chains::exp_with", "ported/excel_numeric/x87_chains::excel_exp", "ported/excel_numeric/x87_chains::log_with", "ported/excel_numeric/x87_chains::excel_log", "ported/normal_dist_common::stored_horner", "ported/normal_dist_common::erf_approx", "ported/normal_dist_common::erfc_upper", "ported/special_dist_family::erf_precise_kernel", "ported/special_math_common::ln_gamma", "ported/special_math_common::gratio_norm_gamma", "ported/special_math_common::gratio_rexp", "ported/special_math_common::gratio_rlog", "ported/special_math_common::gratio_gam1", "ported/special_math_common::gratio", "ported/special_math_common::series_prefactor", "ported/special_math_common::gratio_after40", "ported/special_math_common::gratio_cf", "ported/special_math_common::gratio_temme_270", "ported/special_math_common::gratio_temme_340", "ported/special_math_common::gratio_temme_330", "ported/special_math_common::gratio_temme_finish", "ported/special_math_common::regularized_gamma_p" ], "source": "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/distributions.rs#L227-L230", "state": "close", "suite": null, "summary": "Close: 4 of 12 recorded answers differ in the last bits, worst 13 ULP" } ], "json_url": "https://handbook.dnacalc.com/api/functions/FUNC.GAMMADIST.json", "name": "GAMMADIST", "notes": [], "schema": "efh.function-reference/v1", "section_order": [ "what-it-does", "try-it", "quirks", "how-to-implement", "version-differences", "alternatives" ], "sections": { "alternatives": "\n[GAMMA.DIST](FUNC.GAMMA.DIST.md) is the current spelling; [EXPON.DIST](FUNC.EXPON.DIST.md) handles the shape-one waiting time; [CHISQ.DIST](FUNC.CHISQ.DIST.md) is a shape/scale specialization.\n\n\n", "how-to-implement": "\nThe current shared CDF route first forms the binary64 scale ratio `y=x/beta`:\n\n1. At shape `alpha=0.5`, it calls the ERF.PRECISE body at the current binary64 `sqrt(y)`.\n2. At shape one, it calls the exponential CDF with arguments `(y,1)`. Computing `EXPON.DIST(x,1/beta,TRUE)` instead forms a different rounded ratio/product.\n3. Other shapes call the regularized lower gamma ratio `P(alpha,y)`.\n\nThe source retains modern-spelling composition controls for the first two branches, including non-dyadic scales. They do not identify every general-shape branch, and the shape-one **density** is not established by the CDF identity.\n\nFor positive `x` with shape other than one, the current density candidate forms stored `y=R(x/beta)` and `t=R(alpha*LN(y))`, then obtains an exponential prefix corresponding to `exp(t-y-logGamma(alpha+1))`. It finally multiplies that prefix by the separately stored ratio `R(alpha/x)`, with another stored multiplication. The outer ratio/product consumer has discriminating controls; the prefix producer and its return stage remain open. Shape one and zero input have separate fallback code.\n\nFor the example `x=2,alpha=1,beta=2`, `y=1`, so the mathematical CDF is `1-exp(-1)`, about `0.632120558828558`. That reduction explains the probability; substituting an integer-shape finite sum, a host gamma library or a reciprocal scale is another numerical candidate. The problem report retains general distribution mismatches, and no whole-function Handbook suite is published.\n\n\n", "quirks": "\nNegative `x` or nonpositive shape or scale gives `#NUM!`; nonnumeric numeric arguments give `#VALUE!`. A scale of two is not an exponential rate of two: for shape one it corresponds to rate one half.\n\nThe zero-input density needs a separate boundary decision. Mathematically its right-hand limit is zero for `alpha>1`, `1/beta` for `alpha=1`, and unbounded for `0