RPN-PRGM: New Windows console application emulating HP calculators

[Albert Chan]

RPN.exe users manual Wrote:The result of [forensic test] is affected by the multiple (6) conversions of the angular mode between the FPU native Radians to the requested Degrees. If the mode is keep in Radians and just two conversions are performed at beginning and end of the expression (RPN FPUPC:0 9 D->R Rad Sin Cos Tan ATan ACos ASin R->D FIX:16), then the precision of the results improves: 9.0000047683715820, 9.0000000000000071 and 9.0000000000000000.

This is not the main reason for round-trip accuracy improvement.
Errors mostly comes from cosine of tiny number (in radian), giving result close to 1
(similarly, for arc-cosine of number close to 1, to recover tiny angle)

Even without unit conversion errors, we still hit with it.

lua> u = pi/180     -- 180 u = pi radian. In other words u = degree.
lua> asin(acos(atan(tan(cos(sin(9*u)*u)*u))/u)/u)/u
8.999999999832568

lua> u = 1/64        -- 64 u = 1 radian. Conversion, u ⇄ radian, is exact
lua> asin(acos(atan(tan(cos(sin(9*u)*u)*u))/u)/u)/u
9.000000000229626