IMSINH

Microsoft publishes '=IMSINH("4+3i")' with the result -27.0168132580039+3.85373803791938i. Derived independently with mpmath at 40 digits: sinh(x+yi) = sinh(x)cos(y) + i*cosh(x)sin(y). At 40 digits sinh(4)cos(3) = -27.01681325800393448814 and cosh(4)sin(3) = 3.853738037919377321623. Cross-check against the sibling published example: batch D asserts IMCOSH("4+3i") = -27.0349456030742+3.85115333481178i, and cosh^2 - sinh^2 = 1 holds for these two complex values to 15 digits.. EXCEL'S COMPLEX-STRING FORMAT, which this corpus derives rather than assumes: a result is rendered as the real part, then the sign, then the imaginary coefficient followed by the suffix, with each part printed to at most 15 significant digits and trailing zeros stripped; a zero real part is omitted entirely, a zero imaginary part reduces the result to a bare real number, and an imaginary coefficient of exactly 1 or -1 prints as "i" / "-i" with no digit. That rule was written as a formatter in Python by batch D and validated against seven independently published Microsoft strings (IMCOS, IMCOSH, IMCOT, IMCSC, IMCSCH, IMEXP, IMLN); batch E re-ran that validation and then extended it, reproducing THIRTEEN MORE published Microsoft strings byte for byte (IMLOG10, IMLOG2, IMPOWER, both IMPRODUCT examples, IMSEC, IMSECH, IMSIN, IMSINH, IMSQRT, IMSUB, IMSUM, IMTAN) before predicting anything -- twenty published strings in all. ONE REFINEMENT BATCH E HAD TO MAKE: batch D fed the formatter the EXACT value computed at 40 digits, which happened to render identically to the IEEE double for all seven of its strings. That is not true here. A spreadsheet engine holds a double, not the exact value, and two of this batch's published strings only come out right if the derivation rounds to the nearest double BEFORE formatting: IMPOWER("2+3i",3) is exactly -46+9i in exact arithmetic but Microsoft publishes -46+9.00000000000001i, which is what exp(3*ln(2+3i)) gives in double precision; and IMSEC("4+3i") has an exact real part of -0.06529402785794704644..., whose 15-digit rounding ends ...47, while the correctly-rounded double -0.065294027857947051 rounds to ...471, which is what Microsoft publishes. So every value in this batch is derived exactly with mpmath at 40 digits, THEN rounded to the double an engine actually holds, THEN formatted. String results are compared exactly, so a formatting-only difference (a trailing zero, "1i" for "i", a different digit count) fails the case and is recorded as its own divergence class, separate from a wrong numeric value. STORAGE-FORM GAP, and NOT a missing capability -- the distinction is the whole point of this case. IMSINH is an Excel 2013 addition, so real Excel does not store it in a .xlsx under its plain name: Microsoft's XLSX-extensions future-function list (the reference this harness has used since batch A, mirrored in XlsxWriter's "Formulas added in Excel 2010 and later" table) gives the storage token as _xlfn.IMSINH, alongside _xlfn.IMCOSH, _xlfn.IMCOT, _xlfn.IMCSC, _xlfn.IMCSCH, _xlfn.IMSEC, _xlfn.IMSECH, _xlfn.IMSINH and _xlfn.IMTAN. harness/xlfn_map.py therefore writes _xlfn.IMSINH here, exactly as Excel would. EXECUTED RESULT: all four LibreOffice builds (24.2.0.3, 24.8.7.2, 25.2.0.3, 25.8.7.3) return #NAME? for that token. A five-spelling probe pins down what this is: _xlfn.IMSINH, COM.MICROSOFT.IMSINH, ORG.OPENOFFICE.IMSINH and _xlfn.ORG.OPENOFFICE.IMSINH are all #NAME? on every build, while the UNPREFIXED IMSINH(...) evaluates on every build and returns exactly the string asserted here, byte for byte. So LibreOffice implements IMSINH, and its OOXML import simply has no mapping for the _xlfn.IMSINH token Excel writes -- meaning a workbook saved by Excel that uses IMSINH arrives in LibreOffice as #NAME? even though LibreOffice could compute it. This is the exact mirror image of batch B's COT/COTH/CSC/CSCH finding, where the _xlfn. token was the ONLY spelling LibreOffice accepted, and it is the same class batch D recorded for IMCOSH, IMCOT, IMCSC and IMCSCH. It is recorded as its own divergence class rather than as an ordinary unsupported-function result.

Excel documents: "If inumber is a logical value, IMSINH returns the #VALUE! error value." A deliberate refusal to coerce -- TRUE becomes 1 in nearly every other numeric context. STORAGE-FORM GAP, and NOT a missing capability -- the distinction is the whole point of this case. IMSINH is an Excel 2013 addition, so real Excel does not store it in a .xlsx under its plain name: Microsoft's XLSX-extensions future-function list (the reference this harness has used since batch A, mirrored in XlsxWriter's "Formulas added in Excel 2010 and later" table) gives the storage token as _xlfn.IMSINH, alongside _xlfn.IMCOSH, _xlfn.IMCOT, _xlfn.IMCSC, _xlfn.IMCSCH, _xlfn.IMSEC, _xlfn.IMSECH, _xlfn.IMSINH and _xlfn.IMTAN. harness/xlfn_map.py therefore writes _xlfn.IMSINH here, exactly as Excel would. EXECUTED RESULT: all four LibreOffice builds (24.2.0.3, 24.8.7.2, 25.2.0.3, 25.8.7.3) return #NAME? for that token. A five-spelling probe pins down what this is: _xlfn.IMSINH, COM.MICROSOFT.IMSINH, ORG.OPENOFFICE.IMSINH and _xlfn.ORG.OPENOFFICE.IMSINH are all #NAME? on every build, while the UNPREFIXED IMSINH(...) evaluates on every build. So LibreOffice implements IMSINH, and its OOXML import simply has no mapping for the _xlfn.IMSINH token Excel writes -- meaning a workbook saved by Excel that uses IMSINH arrives in LibreOffice as #NAME? even though LibreOffice could compute it. This is the exact mirror image of batch B's COT/COTH/CSC/CSCH finding, where the _xlfn. token was the ONLY spelling LibreOffice accepted, and it is the same class batch D recorded for IMCOSH, IMCOT, IMCSC and IMCSCH. It is recorded as its own divergence class rather than as an ordinary unsupported-function result.

Excel documents: "If inumber is a value that is not in the x+yi or x+yj text format, IMSINH returns the #NUM! error value." Note this is #NUM!, not the #VALUE! that the logical-value clause on the same page specifies -- the two malformed-input branches are documented as returning DIFFERENT errors, which is why both are asserted. STORAGE-FORM GAP, and NOT a missing capability -- the distinction is the whole point of this case. IMSINH is an Excel 2013 addition, so real Excel does not store it in a .xlsx under its plain name: Microsoft's XLSX-extensions future-function list (the reference this harness has used since batch A, mirrored in XlsxWriter's "Formulas added in Excel 2010 and later" table) gives the storage token as _xlfn.IMSINH, alongside _xlfn.IMCOSH, _xlfn.IMCOT, _xlfn.IMCSC, _xlfn.IMCSCH, _xlfn.IMSEC, _xlfn.IMSECH, _xlfn.IMSINH and _xlfn.IMTAN. harness/xlfn_map.py therefore writes _xlfn.IMSINH here, exactly as Excel would. EXECUTED RESULT: all four LibreOffice builds (24.2.0.3, 24.8.7.2, 25.2.0.3, 25.8.7.3) return #NAME? for that token. A five-spelling probe pins down what this is: _xlfn.IMSINH, COM.MICROSOFT.IMSINH, ORG.OPENOFFICE.IMSINH and _xlfn.ORG.OPENOFFICE.IMSINH are all #NAME? on every build, while the UNPREFIXED IMSINH(...) evaluates on every build. So LibreOffice implements IMSINH, and its OOXML import simply has no mapping for the _xlfn.IMSINH token Excel writes -- meaning a workbook saved by Excel that uses IMSINH arrives in LibreOffice as #NAME? even though LibreOffice could compute it. This is the exact mirror image of batch B's COT/COTH/CSC/CSCH finding, where the _xlfn. token was the ONLY spelling LibreOffice accepted, and it is the same class batch D recorded for IMCOSH, IMCOT, IMCSC and IMCSCH. It is recorded as its own divergence class rather than as an ordinary unsupported-function result.

Microsoft publishes '=IMSINH("4+3i")' with the result -27.0168132580039+3.85373803791938i. Derived independently with mpmath at 40 digits: sinh(x+yi) = sinh(x)cos(y) + i*cosh(x)sin(y). At 40 digits sinh(4)cos(3) = -27.01681325800393448814 and cosh(4)sin(3) = 3.853738037919377321623. Cross-check against the sibling published example: batch D asserts IMCOSH("4+3i") = -27.0349456030742+3.85115333481178i, and cosh^2 - sinh^2 = 1 holds for these two complex values to 15 digits.. EXCEL'S COMPLEX-STRING FORMAT, which this corpus derives rather than assumes: a result is rendered as the real part, then the sign, then the imaginary coefficient followed by the suffix, with each part printed to at most 15 significant digits and trailing zeros stripped; a zero real part is omitted entirely, a zero imaginary part reduces the result to a bare real number, and an imaginary coefficient of exactly 1 or -1 prints as "i" / "-i" with no digit. That rule was written as a formatter in Python by batch D and validated against seven independently published Microsoft strings (IMCOS, IMCOSH, IMCOT, IMCSC, IMCSCH, IMEXP, IMLN); batch E re-ran that validation and then extended it, reproducing THIRTEEN MORE published Microsoft strings byte for byte (IMLOG10, IMLOG2, IMPOWER, both IMPRODUCT examples, IMSEC, IMSECH, IMSIN, IMSINH, IMSQRT, IMSUB, IMSUM, IMTAN) before predicting anything -- twenty published strings in all. ONE REFINEMENT BATCH E HAD TO MAKE: batch D fed the formatter the EXACT value computed at 40 digits, which happened to render identically to the IEEE double for all seven of its strings. That is not true here. A spreadsheet engine holds a double, not the exact value, and two of this batch's published strings only come out right if the derivation rounds to the nearest double BEFORE formatting: IMPOWER("2+3i",3) is exactly -46+9i in exact arithmetic but Microsoft publishes -46+9.00000000000001i, which is what exp(3*ln(2+3i)) gives in double precision; and IMSEC("4+3i") has an exact real part of -0.06529402785794704644..., whose 15-digit rounding ends ...47, while the correctly-rounded double -0.065294027857947051 rounds to ...471, which is what Microsoft publishes. So every value in this batch is derived exactly with mpmath at 40 digits, THEN rounded to the double an engine actually holds, THEN formatted. String results are compared exactly, so a formatting-only difference (a trailing zero, "1i" for "i", a different digit count) fails the case and is recorded as its own divergence class, separate from a wrong numeric value. STORAGE-FORM GAP, and NOT a missing capability -- the distinction is the whole point of this case. IMSINH is an Excel 2013 addition, so real Excel does not store it in a .xlsx under its plain name: Microsoft's XLSX-extensions future-function list (the reference this harness has used since batch A, mirrored in XlsxWriter's "Formulas added in Excel 2010 and later" table) gives the storage token as _xlfn.IMSINH, alongside _xlfn.IMCOSH, _xlfn.IMCOT, _xlfn.IMCSC, _xlfn.IMCSCH, _xlfn.IMSEC, _xlfn.IMSECH, _xlfn.IMSINH and _xlfn.IMTAN. harness/xlfn_map.py therefore writes _xlfn.IMSINH here, exactly as Excel would. EXECUTED RESULT: all four LibreOffice builds (24.2.0.3, 24.8.7.2, 25.2.0.3, 25.8.7.3) return #NAME? for that token. A five-spelling probe pins down what this is: _xlfn.IMSINH, COM.MICROSOFT.IMSINH, ORG.OPENOFFICE.IMSINH and _xlfn.ORG.OPENOFFICE.IMSINH are all #NAME? on every build, while the UNPREFIXED IMSINH(...) evaluates on every build and returns exactly the string asserted here, byte for byte. So LibreOffice implements IMSINH, and its OOXML import simply has no mapping for the _xlfn.IMSINH token Excel writes -- meaning a workbook saved by Excel that uses IMSINH arrives in LibreOffice as #NAME? even though LibreOffice could compute it. This is the exact mirror image of batch B's COT/COTH/CSC/CSCH finding, where the _xlfn. token was the ONLY spelling LibreOffice accepted, and it is the same class batch D recorded for IMCOSH, IMCOT, IMCSC and IMCSCH. It is recorded as its own divergence class rather than as an ordinary unsupported-function result.

Excel documents: "If inumber is a logical value, IMSINH returns the #VALUE! error value." A deliberate refusal to coerce -- TRUE becomes 1 in nearly every other numeric context. STORAGE-FORM GAP, and NOT a missing capability -- the distinction is the whole point of this case. IMSINH is an Excel 2013 addition, so real Excel does not store it in a .xlsx under its plain name: Microsoft's XLSX-extensions future-function list (the reference this harness has used since batch A, mirrored in XlsxWriter's "Formulas added in Excel 2010 and later" table) gives the storage token as _xlfn.IMSINH, alongside _xlfn.IMCOSH, _xlfn.IMCOT, _xlfn.IMCSC, _xlfn.IMCSCH, _xlfn.IMSEC, _xlfn.IMSECH, _xlfn.IMSINH and _xlfn.IMTAN. harness/xlfn_map.py therefore writes _xlfn.IMSINH here, exactly as Excel would. EXECUTED RESULT: all four LibreOffice builds (24.2.0.3, 24.8.7.2, 25.2.0.3, 25.8.7.3) return #NAME? for that token. A five-spelling probe pins down what this is: _xlfn.IMSINH, COM.MICROSOFT.IMSINH, ORG.OPENOFFICE.IMSINH and _xlfn.ORG.OPENOFFICE.IMSINH are all #NAME? on every build, while the UNPREFIXED IMSINH(...) evaluates on every build. So LibreOffice implements IMSINH, and its OOXML import simply has no mapping for the _xlfn.IMSINH token Excel writes -- meaning a workbook saved by Excel that uses IMSINH arrives in LibreOffice as #NAME? even though LibreOffice could compute it. This is the exact mirror image of batch B's COT/COTH/CSC/CSCH finding, where the _xlfn. token was the ONLY spelling LibreOffice accepted, and it is the same class batch D recorded for IMCOSH, IMCOT, IMCSC and IMCSCH. It is recorded as its own divergence class rather than as an ordinary unsupported-function result.

Excel documents: "If inumber is a value that is not in the x+yi or x+yj text format, IMSINH returns the #NUM! error value." Note this is #NUM!, not the #VALUE! that the logical-value clause on the same page specifies -- the two malformed-input branches are documented as returning DIFFERENT errors, which is why both are asserted. STORAGE-FORM GAP, and NOT a missing capability -- the distinction is the whole point of this case. IMSINH is an Excel 2013 addition, so real Excel does not store it in a .xlsx under its plain name: Microsoft's XLSX-extensions future-function list (the reference this harness has used since batch A, mirrored in XlsxWriter's "Formulas added in Excel 2010 and later" table) gives the storage token as _xlfn.IMSINH, alongside _xlfn.IMCOSH, _xlfn.IMCOT, _xlfn.IMCSC, _xlfn.IMCSCH, _xlfn.IMSEC, _xlfn.IMSECH, _xlfn.IMSINH and _xlfn.IMTAN. harness/xlfn_map.py therefore writes _xlfn.IMSINH here, exactly as Excel would. EXECUTED RESULT: all four LibreOffice builds (24.2.0.3, 24.8.7.2, 25.2.0.3, 25.8.7.3) return #NAME? for that token. A five-spelling probe pins down what this is: _xlfn.IMSINH, COM.MICROSOFT.IMSINH, ORG.OPENOFFICE.IMSINH and _xlfn.ORG.OPENOFFICE.IMSINH are all #NAME? on every build, while the UNPREFIXED IMSINH(...) evaluates on every build. So LibreOffice implements IMSINH, and its OOXML import simply has no mapping for the _xlfn.IMSINH token Excel writes -- meaning a workbook saved by Excel that uses IMSINH arrives in LibreOffice as #NAME? even though LibreOffice could compute it. This is the exact mirror image of batch B's COT/COTH/CSC/CSCH finding, where the _xlfn. token was the ONLY spelling LibreOffice accepted, and it is the same class batch D recorded for IMCOSH, IMCOT, IMCSC and IMCSCH. It is recorded as its own divergence class rather than as an ordinary unsupported-function result.

Microsoft publishes '=IMSINH("4+3i")' with the result -27.0168132580039+3.85373803791938i. Derived independently with mpmath at 40 digits: sinh(x+yi) = sinh(x)cos(y) + i*cosh(x)sin(y). At 40 digits sinh(4)cos(3) = -27.01681325800393448814 and cosh(4)sin(3) = 3.853738037919377321623. Cross-check against the sibling published example: batch D asserts IMCOSH("4+3i") = -27.0349456030742+3.85115333481178i, and cosh^2 - sinh^2 = 1 holds for these two complex values to 15 digits.. EXCEL'S COMPLEX-STRING FORMAT, which this corpus derives rather than assumes: a result is rendered as the real part, then the sign, then the imaginary coefficient followed by the suffix, with each part printed to at most 15 significant digits and trailing zeros stripped; a zero real part is omitted entirely, a zero imaginary part reduces the result to a bare real number, and an imaginary coefficient of exactly 1 or -1 prints as "i" / "-i" with no digit. That rule was written as a formatter in Python by batch D and validated against seven independently published Microsoft strings (IMCOS, IMCOSH, IMCOT, IMCSC, IMCSCH, IMEXP, IMLN); batch E re-ran that validation and then extended it, reproducing THIRTEEN MORE published Microsoft strings byte for byte (IMLOG10, IMLOG2, IMPOWER, both IMPRODUCT examples, IMSEC, IMSECH, IMSIN, IMSINH, IMSQRT, IMSUB, IMSUM, IMTAN) before predicting anything -- twenty published strings in all. ONE REFINEMENT BATCH E HAD TO MAKE: batch D fed the formatter the EXACT value computed at 40 digits, which happened to render identically to the IEEE double for all seven of its strings. That is not true here. A spreadsheet engine holds a double, not the exact value, and two of this batch's published strings only come out right if the derivation rounds to the nearest double BEFORE formatting: IMPOWER("2+3i",3) is exactly -46+9i in exact arithmetic but Microsoft publishes -46+9.00000000000001i, which is what exp(3*ln(2+3i)) gives in double precision; and IMSEC("4+3i") has an exact real part of -0.06529402785794704644..., whose 15-digit rounding ends ...47, while the correctly-rounded double -0.065294027857947051 rounds to ...471, which is what Microsoft publishes. So every value in this batch is derived exactly with mpmath at 40 digits, THEN rounded to the double an engine actually holds, THEN formatted. String results are compared exactly, so a formatting-only difference (a trailing zero, "1i" for "i", a different digit count) fails the case and is recorded as its own divergence class, separate from a wrong numeric value. STORAGE-FORM GAP, and NOT a missing capability -- the distinction is the whole point of this case. IMSINH is an Excel 2013 addition, so real Excel does not store it in a .xlsx under its plain name: Microsoft's XLSX-extensions future-function list (the reference this harness has used since batch A, mirrored in XlsxWriter's "Formulas added in Excel 2010 and later" table) gives the storage token as _xlfn.IMSINH, alongside _xlfn.IMCOSH, _xlfn.IMCOT, _xlfn.IMCSC, _xlfn.IMCSCH, _xlfn.IMSEC, _xlfn.IMSECH, _xlfn.IMSINH and _xlfn.IMTAN. harness/xlfn_map.py therefore writes _xlfn.IMSINH here, exactly as Excel would. EXECUTED RESULT: all four LibreOffice builds (24.2.0.3, 24.8.7.2, 25.2.0.3, 25.8.7.3) return #NAME? for that token. A five-spelling probe pins down what this is: _xlfn.IMSINH, COM.MICROSOFT.IMSINH, ORG.OPENOFFICE.IMSINH and _xlfn.ORG.OPENOFFICE.IMSINH are all #NAME? on every build, while the UNPREFIXED IMSINH(...) evaluates on every build and returns exactly the string asserted here, byte for byte. So LibreOffice implements IMSINH, and its OOXML import simply has no mapping for the _xlfn.IMSINH token Excel writes -- meaning a workbook saved by Excel that uses IMSINH arrives in LibreOffice as #NAME? even though LibreOffice could compute it. This is the exact mirror image of batch B's COT/COTH/CSC/CSCH finding, where the _xlfn. token was the ONLY spelling LibreOffice accepted, and it is the same class batch D recorded for IMCOSH, IMCOT, IMCSC and IMCSCH. It is recorded as its own divergence class rather than as an ordinary unsupported-function result.

Excel documents: "If inumber is a logical value, IMSINH returns the #VALUE! error value." A deliberate refusal to coerce -- TRUE becomes 1 in nearly every other numeric context. STORAGE-FORM GAP, and NOT a missing capability -- the distinction is the whole point of this case. IMSINH is an Excel 2013 addition, so real Excel does not store it in a .xlsx under its plain name: Microsoft's XLSX-extensions future-function list (the reference this harness has used since batch A, mirrored in XlsxWriter's "Formulas added in Excel 2010 and later" table) gives the storage token as _xlfn.IMSINH, alongside _xlfn.IMCOSH, _xlfn.IMCOT, _xlfn.IMCSC, _xlfn.IMCSCH, _xlfn.IMSEC, _xlfn.IMSECH, _xlfn.IMSINH and _xlfn.IMTAN. harness/xlfn_map.py therefore writes _xlfn.IMSINH here, exactly as Excel would. EXECUTED RESULT: all four LibreOffice builds (24.2.0.3, 24.8.7.2, 25.2.0.3, 25.8.7.3) return #NAME? for that token. A five-spelling probe pins down what this is: _xlfn.IMSINH, COM.MICROSOFT.IMSINH, ORG.OPENOFFICE.IMSINH and _xlfn.ORG.OPENOFFICE.IMSINH are all #NAME? on every build, while the UNPREFIXED IMSINH(...) evaluates on every build. So LibreOffice implements IMSINH, and its OOXML import simply has no mapping for the _xlfn.IMSINH token Excel writes -- meaning a workbook saved by Excel that uses IMSINH arrives in LibreOffice as #NAME? even though LibreOffice could compute it. This is the exact mirror image of batch B's COT/COTH/CSC/CSCH finding, where the _xlfn. token was the ONLY spelling LibreOffice accepted, and it is the same class batch D recorded for IMCOSH, IMCOT, IMCSC and IMCSCH. It is recorded as its own divergence class rather than as an ordinary unsupported-function result.

Excel documents: "If inumber is a value that is not in the x+yi or x+yj text format, IMSINH returns the #NUM! error value." Note this is #NUM!, not the #VALUE! that the logical-value clause on the same page specifies -- the two malformed-input branches are documented as returning DIFFERENT errors, which is why both are asserted. STORAGE-FORM GAP, and NOT a missing capability -- the distinction is the whole point of this case. IMSINH is an Excel 2013 addition, so real Excel does not store it in a .xlsx under its plain name: Microsoft's XLSX-extensions future-function list (the reference this harness has used since batch A, mirrored in XlsxWriter's "Formulas added in Excel 2010 and later" table) gives the storage token as _xlfn.IMSINH, alongside _xlfn.IMCOSH, _xlfn.IMCOT, _xlfn.IMCSC, _xlfn.IMCSCH, _xlfn.IMSEC, _xlfn.IMSECH, _xlfn.IMSINH and _xlfn.IMTAN. harness/xlfn_map.py therefore writes _xlfn.IMSINH here, exactly as Excel would. EXECUTED RESULT: all four LibreOffice builds (24.2.0.3, 24.8.7.2, 25.2.0.3, 25.8.7.3) return #NAME? for that token. A five-spelling probe pins down what this is: _xlfn.IMSINH, COM.MICROSOFT.IMSINH, ORG.OPENOFFICE.IMSINH and _xlfn.ORG.OPENOFFICE.IMSINH are all #NAME? on every build, while the UNPREFIXED IMSINH(...) evaluates on every build. So LibreOffice implements IMSINH, and its OOXML import simply has no mapping for the _xlfn.IMSINH token Excel writes -- meaning a workbook saved by Excel that uses IMSINH arrives in LibreOffice as #NAME? even though LibreOffice could compute it. This is the exact mirror image of batch B's COT/COTH/CSC/CSCH finding, where the _xlfn. token was the ONLY spelling LibreOffice accepted, and it is the same class batch D recorded for IMCOSH, IMCOT, IMCSC and IMCSCH. It is recorded as its own divergence class rather than as an ordinary unsupported-function result.