feat(spreadsheet): read the formula of every cell of a shared group

[andiwand]

🤖 Generated with Claude Code

Step 3.1 of docs/design/spreadsheet-editing.md, finishing what the parser was for.

The problem

[ECMA-376] 18.3.1.40 spells a shared formula on the group's master alone:

<c r="C1"><f t="shared" ref="C1:C3" si="0">A1+$B$1</f><v>3</v></c>
<c r="C2"><f t="shared" si="0"/><v>7</v></c>
<c r="C3"><f t="shared" si="0"/><v>9</v></c>

Excel writes this whenever you fill a column down, so most formula cells in a real workbook are members. A member reported an empty formula, which leaves a formula bar with nothing to show and the dependency graph (next PR) with nothing to read.

What it does

The parser collects the masters per sheet, and sheet_cell_value reads a member through the one its si names: parse the master's expression, move every relative reference by the offset between the two cells, write it again. So C2 above answers A2+$B$1 and C3 A3+$B$1 — the $B$1 does not move, because a $ axis never does.

That needs two pieces beside the parser, both in internal/formula:

• shift over the tree. A reference moved off the grid becomes #REF!, as a sheet makes it.
• a writer, to_string(node, syntax), which spells a tree back in either syntax. It drops a parenthesis the precedence already states, so 1+(2*3) comes back as 1+2*3 while 1-(2-3) keeps its own.

One fix fell out of having a writer: the parser accepted 1e999 as infinity, which the writer would then spell inf. It refuses the number instead, so the master's own text is what a member gets.

Two cells that keep what they had

• a master the parser cannot read is handed out as it stands rather than dropped;
• a member whose si names no master stays set and empty — it computes, and nothing here can spell what.

An array formula (t="array") writes no <f> at all on its members, so those still report none. Noted in the module's AGENTS.md.

Test

test/src/internal/formula/formula_writer_test.cpp round-trips both syntaxes and pins the shift; the shared-formula cases are in ooxml_spreadsheet_value_test.cpp, from inline fixtures. test/data/input/odr-public/xlsx/sample.xlsx is a real file of the shape — 32 members of one RAND() group.