Some math/flonum functions have much larger error than expected

[samth]

Random testing (see #35) discovered a number of cases where functions such as fl2+ and fl2- have substantial error (32 ulps) and functions such as fl2exp, flexp/error, and fl2expm1 have very large error (4e15 ulps, for example).

The documentation says (quoting a few different places):

For arithmetic, error is less than 8 ulps. For fl2exp and fl2expm1, error is less than 3 ulps. For flexp/error and flexpm1/error, the largest observed error is 3 ulps.

Here are some examples:

(fl2+ -6.999886226206346e+45 5.792628225761353e+29 6.9274150349997e+45 5.2105937810748895e+29)                 => -7.247119120664389267701608263587e+43
(bf+ (bf -6999886226206345021638066463653546405883019264) (bf 6927415034999701128961050381017604717751042048)) => -7.247119120664389267701608263594e+43
(fl+ -6.999886226206346e+45 6.9274150349997e+45)                                                               => -7.247119120664499299921676626019e+43
error is 32.0 ulps (relative 9.70989202827024208564e-31, absolute 7.0368744177664e+13) with precision 500                                                   
error when just using floats is 111.10414941005564 ulps (relative 1.5182891054545697262e-14, absolute 1.10032220068362431535e+30) with precision 500        
                                                                                                                                                                                                                                                                                                                      
(fl2- -6.307625868783824e-189 -7.650829856531877e-206 -6.221347182541859e-189 3.486864837367133e-205)               => -8.627868624196532783073584510346e-191
(bf- (bf "-6.307625868783823708767532620142220868851e-189") (bf "-6.221347182541858380936796775038726932571e-189")) => -8.627868624196532783073584510349e-191                                                                                                                                                           
(fl- -6.307625868783824e-189 -6.221347182541859e-189)                                                               => -8.627868624196490263595354307142e-191                                                                                                                                                           
error is 12.0 ulps (relative 3.84769743523996817173e-31, absolute 3.3197427976908391985e-221) with precision 128                                    
error when just using floats is 34.12753813992254 ulps (relative 4.92815550192302754348e-15, absolute 4.25194782302032044546e-205) with precision 128
 
(flexp/error -247.29245235328085)                         => 4.001773708963990941924920379399e-108
(bfexp (bf #e-247.2924523532808507297886535525321960449)) => 4.001773708963991419271664949602e-108
(flexp -247.29245235328085)                               => 4.001773708963991129369240222464e-108
error is 2842247977943596.5 ulps (relative 1.19283792459564869331e-16, absolute 4.77346744570203899599e-124) with precision 128
error when just using floats is 0.383283456465281 ulps (relative 7.24434827680924324972e-17, absolute 2.8990242472713825709e-124) with precision 128

(fl2exp 249.9020736185187 6.819710735232684e-15)         => 3.39696903982644185464484379844e+108
(bfexp (bf #e249.9020736185187058693838948394391650218)) => 3.396969039826441449441493860216e+108
(flexp 249.9020736185187)                                => 3.396969039826418533426604116558e+108
error is 3499404429155425.5 ulps (relative 1.19283792459564860048e-16, absolute 4.05203349938224559331e+92) with precision 128
error when just using floats is 43.944085525744526 ulps (relative 6.7460181771084045627e-15, absolute 2.29160148897436568801e+94) with precision 128

(fl2expm1 253.6199382443308 1.0330029387260226e-14)      => 1.398748649286222641619642494376e+110
(bfexpm1 (bf #e253.61993824433080713605470606162883303)) => 1.398748649286222474771598909821e+110
(flexpm1 253.6199382443308)                              => 1.39874864928620803800496605084e+110
error is 4502899460887364.0 ulps (relative 1.19283792459564859339e-16, absolute 1.66848043584554436406e+94) with precision 128
error when just using floats is 86.51298429857945 ulps (relative 1.03212014826438060794e-14, absolute 1.44367666328589814078e+96) with precision 128

These examples are taken from the samth/fltest program, which can reproduce them with the above output.

[samth]

In #37 I propose changing the random testing to allow these errors in random testing, with error up to 32 in double-double arithmetic, and error up to 1e20 in the exponential functions that return double-doubles.

[samth]

Here is an example where fl2+ has much much worse error (2048 ulps):

(fl2+ 5.754365118051034e+54 2.8307141643929314e+38 -5.753780528274009e+54 1.6423048070836051e+38)              => 5.845897770256615269301622678206e+50
(bf+ (bf #e5.754365118051034256255201488574884919768e54) (bf #e-5.753780528274008594728271326307026578003e54)) => 5.845897770256615269301622678583e+50
(fl+ 5.754365118051034e+54 -5.753780528274009e+54)                                                             => 5.845897770252142250330146142053e+50
error is 2048.0 ulps (relative 6.46246878540587163601e-29, absolute 3.77789318629571617096e+22) with precision 128
error when just using floats is 5384.200736861785 ulps (relative 7.65155181849884757515e-13, absolute 4.47301897147653615284e+38) with precision 128