Comparision: 4 different methods of interpolation

[sheldonison]

A plot of the differences (absolute difference between the evaluations of the two methods) shows two surprising *spikes*. Possibly there is a method- or an implementation-specific anomaly/bug?

I see no evidence of any jumps in any of the first 25 derivatives of sexp(z), centered at z=I, which corresponds to the observed jump at exp(Pi*I/2). I generated these derivatives via Cauchy/Fourier integral, using a sample circle of radius=0.1 about sexp(z=I).
- Sheldon

Code:

0.576484729284574635281197 + 0.961366385497526303664192*I
0.467090029275013068362180 + 0.569916587535513312268876*I
-0.114761722576321231281567 + 0.465827218266975054414939*I
-0.161232170099668615555009 + 0.169045593187154316250322*I
-0.126613456383497199239067 + 0.0568918998688819763780698*I
-0.0762199970552966637382709 - 0.00833069158238119062194641*I
-0.0327098687746058093598951 - 0.0199959613710679405091179*I
-0.0114125765107396462800570 - 0.0167958355490362372839906*I
-0.00129636291030330078307152 - 0.0101328625577288779178557*I
0.00143930066431348953343801 - 0.00476584137840711770103100*I
0.00163769580449573434820048 - 0.00186185520615716786409671*I
0.00109070849328481275176054 - 0.000471938920586012785461553*I
0.000564655613106594209769527 + 0.00000181946046575202049960332*I
0.000245597595059366084519137 + 0.000111877991428776009534293*I
0.0000826274897755178426743768 + 0.0000942697925037007220291984*I
0.0000179529687173593648409477 + 0.0000554432825612102322217693*I
-0.00000285496852089677910122697 + 0.0000268624135777202968381695*I
-0.00000607171248036292730890827 + 0.0000106620295670742196028191*I
-0.00000445871359894296793470106 + 0.00000338692819941567600965410*I
-0.00000246334653238799809994874 + 0.000000592525326678551839351098*I
-0.00000111582497849715807791042 - 0.000000188196751582523640944798*I
-0.000000428067241111207786093519 - 0.000000273619144710082058056908*I
-0.000000126112874499856506266031 - 0.000000186858413233270239477061*I
-0.0000000196315391530546026715320 - 0.0000000976905679317030189981616*I
0.00000000815096620645684871922301 - 0.0000000425620288040458215752126*I