FN-LINEST-001: LINEST's Householder reflector stores each step from the x87 unit
Detail for matching Excel's bits · measured · recorded 2026-11-04
In Excel's QR route the reflector arithmetic behaves as stored precision-64 steps: v0 = x0 - alpha, v'v, each dot-product term, f = 2t/v'v, and a - f*v. With this change the row below gets Excel's last bits, where a plain binary64 reflector does not.
| Call and input route | Inputs | Excel | Correct value | Recorded in |
|---|---|---|---|---|
=INDEX(LINEST({-17.979;-0.126;8;-5;1.7;37;12.4;14.46;-8;24.2},{20.8,50;34,23.41;38.875,-17.7;4.863,36.9;42.1,6;-14.55,44.41;-4.57,-12.96;-9.909,2.589;47.549,42;54.9,-17.63},TRUE,TRUE),2,1)formula-literal | As typed | 0.190541445313446440x3fc863a97e13b089 | — | Excel 16.0.20527.20088 Current Channel, Windows 64-bit (NT 10.0.26200), x86-64, AMD Ryzen 7 4800H, en-ZA |
Basis: Gains 11 recorded answers and loses none over the 3,944 regression rows of the corpus; 35 selections from two fits were checked directly.
Open: Norm, rank, mean, pivot and back-substitution policies are not identified. 48 fixed rank policies and 240 rounded Gram/LDL rank labels are contradicted by the 241 recorded degrees-of-freedom observations.
Evidence and capture sources
- DnaCalc · crates/calc-func/tests/f1_stats.rs 3f3b1622003f4f349a08ee8b054163e58f8dba67 · line 680 recorded selections pinned
- DnaCalc-Research · round22-result.json 130ec21b3da03276c01fb27dce70463f08f90d9a · reflector_study research round 22 result
- DnaCalc-Research · evidence/round22/householder-all-hard.json 130ec21b3da03276c01fb27dce70463f08f90d9a · reflector study
- DnaCalc · crates/calc-func/tests/captures/catalogue/sections/dcj9k_linest_stats.capture.json c9f9d354165d2c20b9455c32582ea50baac7ba73 · sheet dcj9k_linest_stats, row 1094, column 4