Typed entry, VALUE and arithmetic now read $(1,234), $ (5) and (5)% as
negative numbers, as Excel 365 does. Parentheses no longer nest: (-5),
((5)), $5% and dates in parentheses stay text. This changes main's
((100)) from 100 to text; the no-recursion guard from #2180 is kept and
its test now asserts the new result.
PMT computed (1 + rate)^nper with powf, which rounds 1 + rate first and
drops the low bits of a small rate. Over 400 synthetic probes that left
PMT up to about 1000 ULPs from Excel (59 bit-exact); the ln_1p/exp_m1 form
is within 4 ULPs (244 bit-exact). A loan schedule guarded by
IF(p - SUM(principal) > 0, ...) turns on those bits: in 3000 synthetic
schedules main disagreed with Excel on the number of live periods in 1382,
the fix in 823.
Also follows Excel at the edges: a rate of -1 or less is #NUM!, a huge
nper gives -pv*rate instead of #NUM!, a tiny rate no longer collapses, and
a small negative rate keeps its payment. IPMT, PPMT, CUMIPMT and CUMPRINC
pick this up through pmt_calc. FV and PV are unchanged: Excel's own FV/PV
sit further from the exact value than the current powf form does.
The tests allow the one-ULP libm difference between platforms.
Harrison Booth