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Harrison Booth
1ce4781d3e
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.