{ "category": "Engineering functions", "display_name": "IMCSCH", "entry_kind": "built_in_function", "eval_api": { "method": "POST", "url": "https://handbook.dnacalc.com/api/eval" }, "function_id": "FUNC.IMCSCH", "implementation_state": { "answer_bank": { "excel_builds": [ "20430" ], "larger_numeric": 0, "last_bit": 0, "matched": 1201, "other_mismatch": 8, "refused": 0, "rows": 1209, "unread": 0, "worst_ulp": 0 }, "detail": "Of 1,212 recorded answers (1,209 in the answer bank and 3 workbook cells), 8 do not match: 8 differ in kind or value.", "dnacalc_commit": "9e1884369a678158dd82d3d74188daf986995e87", "in_catalogue": true, "state": "differs", "state_label": "Known larger differences", "summary": "Known larger differences on 8 of 1,212 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/engineering.rs#L196-L196" ], "repository": "https://github.com/DnaCalc/DnaCalc", "shared_code": [ "catalogue/engineering::complex_of", "catalogue/engineering::complex_text", "catalogue/engineering::unary_complex", "ported/complex_decimal::nearest_even", "ported/complex_decimal::decimal_pair", "ported/complex_family::parse_ascii_decimal_15", "ported/complex_family::ParsedComplex::new", "ported/complex_family::ParsedComplex::abs", "ported/complex_family::normalize_zero", "ported/complex_family::number_to_excel_text", "ported/complex_family::format_complex_text", "ported/complex_family::parse_real_number", "ported/complex_family::find_real_imag_split", "ported/complex_family::parse_imag_coeff", "ported/complex_family::parse_complex_text", "ported/complex_family::suffix_from_operands" ], "source": "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/engineering.rs#L196-L196", "state": "differs", "suite": null, "summary": "Known larger differences on 8 of 1,212 recorded answers" } ], "json_url": "https://handbook.dnacalc.com/api/functions/FUNC.IMCSCH.json", "name": "IMCSCH", "notes": [], "schema": "efh.function-reference/v1", "section_order": [ "what-it-does", "try-it", "quirks", "how-to-implement", "version-differences", "alternatives" ], "sections": { "alternatives": "\n[IMSINH](FUNC.IMSINH.md) supplies the denominator; [IMDIV](FUNC.IMDIV.md) divides arbitrary complex inputs; [COMPLEX](FUNC.COMPLEX.md) creates a value from coefficients.\n\n\n", "how-to-implement": "\nParse the two coefficients and suffix before doing arithmetic; use the common complex formatter afterward. Retain suffix consistency, suppress a zero component and omit the coefficient one before the imaginary unit. Formatting and parsing have their own fifteen-significant-digit rules, so testing only the algebra misses observable behaviour.\n\nFirst compute the unformatted complex IMSINH pair `(c,d)`. If `abs(c)>=abs(d)`, use `r=d/c`, `v=1/(c+d*r)`, and return `(v,-r*v)`. Otherwise use `r=c/d`, `v=1/(d+c*r)`, and return `(r*v,-v)`. Reject `(0,0)` before division. The current reciprocal forms one reciprocal and multiplies a component by it; calling generic IMDIV with numerator one forms a different rounded graph. Keep this distinction when reproducing recorded results.\n\n\n", "quirks": "\nComplex arguments may be real numbers or text such as `\"2-3i\"`. Use lowercase `i` or `j`; operands in one call must agree on the suffix. The current parser rejects malformed complex text with `#NUM!` and logical values with `#VALUE!`. A complex result is text, so ordinary worksheet arithmetic does not automatically treat it as a pair of numeric components. A zero denominator gives `#NUM!` in the current reciprocal helper. Near a pole, small changes in the input can cause large changes in the result.\n\n\n", "sources": "\n- [Microsoft: IMCSCH function](https://support.microsoft.com/en-us/office/imcsch-function-c0ae4f54-5f09-4fef-8da0-dc33ea2c5ca9), opened 6 November 2026; syntax, documented argument rules and errors.\n- [DnaCalc implementation](https://github.com/DnaCalc/DnaCalc/blob/da3ecc4fb19a3a5529708c311d0e8f05688ac165/crates/calc-func/src/ported/complex_family.rs); implementation steps and the limits identified in the text.\n\n", "try-it": "\n`=IMCSCH(\"1\")` gives real text about `\"0.850918128239322\"`, the reciprocal of `sinh(1)`. At zero the denominator is zero and the current reciprocal helper returns `#NUM!`.\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| 20430 | Windows, 64-bit, CPU not recorded | 1,209 |\n\nThe record contains no same-input comparison between these environments. Reading different inputs on different builds does not establish either a version change or cross-build agreement.\n\n[Recorded environments and comparison details](https://github.com/DnaCalc/ExcelFunctionsHandbook/blob/5dc75391aa5125ccc5abdb095da85950980d6fd8/content/evidence/environments/FUNC.IMCSCH.json).", "what-it-does": "\n`IMCSCH(inumber)` returns the complex hyperbolic cosecant, mathematically the reciprocal of IMSINH. It returns complex text, including when the answer has only a real component.\n\n\n" }, "signature": { "display": "IMCSCH(inumber)", "parameters": [ { "description": null, "name": "inumber", "optional": false, "repeats": false } ], "trailing_repeats": false }, "sources": { "metadata": { "admission": { "label": "implemented", "reason": null }, "arity": { "max": 1, "min": 1 }, "category": "Engineering 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": "None", "thread_safety_class": "SafePure", "volatility_class": "NonVolatile" }, "descriptions": { "long": null, "short": "Hyperbolic cosecant of a complex number", "short_source": "dna-calc-own" }, "docs": { "english_description": "Returns the hyperbolic cosecant of a complex number", "microsoft_url": "https://support.microsoft.com/en-us/office/imcsch-function-c0ae4f54-5f09-4fef-8da0-dc33ea2c5ca9" }, "entry_kind": "built_in_function", "localized_family_names": null, "localized_names": [ { "locale": "ar-SA", "name": "IMCSCH" }, { "locale": "bg-BG", "name": "IMCSCH" }, { "locale": "cs-CZ", "name": "IMCSCH" }, { "locale": "da-DK", "name": "IMAGCSCH" }, { "locale": "de-DE", "name": "IMCSCH" }, { "locale": "el-GR", "name": "IMCSCH" }, { "locale": "en-AU", "name": "IMCSCH" }, { "locale": "en-GB", "name": "IMCSCH" }, { "locale": "en-US", "name": "IMCSCH" }, { "locale": "es-ES", "name": "IM.CSCH" }, { "locale": "et-EE", "name": "IMCSCH" }, { "locale": "fi-FI", "name": "KOMPLEKSI.KOSEKH" }, { "locale": "fr-FR", "name": "COMPLEXE.CSCH*" }, { "locale": "he-IL", "name": "IMCSCH" }, { "locale": "hr-HR", "name": "IMCSCH" }, { "locale": "hu-HU", "name": "KÉPZ.CSCH" }, { "locale": "id-ID", "name": "IMCSCH" }, { "locale": "it-IT", "name": "IMCSCH" }, { "locale": "ja-JP", "name": "IMCSCH" }, { "locale": "ko-KR", "name": "IMCSCH" }, { "locale": "lt-LT", "name": "IMCSCH" }, { "locale": "lv-LV", "name": "IMCSCH" }, { "locale": "nb-NO", "name": "IMCSCH" }, { "locale": "nl-NL", "name": "C.COSECH" }, { "locale": "pl-PL", "name": "CSCH.LICZBY.ZESP" }, { "locale": "pt-BR", "name": "IMCSCH" }, { "locale": "pt-PT", "name": "IMCSCH" }, { "locale": "ro-RO", "name": "IMCSCH" }, { "locale": "ru-RU", "name": "МНИМ.CSCH" }, { "locale": "sk-SK", "name": "IMCSCH" }, { "locale": "sl-SI", "name": "IMCSCH" }, { "locale": "sr-Latn-RS", "name": "IMCSCH" }, { "locale": "sv-SE", "name": "IMCSCH" }, { "locale": "th-TH", "name": "IMCSCH" }, { "locale": "tr-TR", "name": "SANCSCH" }, { "locale": "uk-UA", "name": "IMCSCH" }, { "locale": "vi-VN", "name": "IMCSCH" }, { "locale": "zh-CN", "name": "IMCSCH" }, { "locale": "zh-HK", "name": "IMCSCH" }, { "locale": "zh-TW", "name": "IMCSCH" } ], "signature": { "display": "IMCSCH(inumber)", "parameters": [ { "description": null, "name": "inumber", "optional": false, "repeats": false } ], "trailing_repeats": false }, "surface_name": "IMCSCH", "version_marker": null, "xlcall": { "code": "559", "symbol": "xlfImcsch" } }, "microsoft": "https://support.microsoft.com/en-us/office/imcsch-function-c0ae4f54-5f09-4fef-8da0-dc33ea2c5ca9" }, "try_it": { "formula": "=IMCSCH(\"1\")" }, "url": "https://handbook.dnacalc.com/functions/IMCSCH.html", "variants": [], "versions": [ { "behaviour": "1,209 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.IMCSCH.json" ] } ] }