#
# poly_eval.txt, 29 Mar 10

#   Fast cube root by Ken Turkowski
#   http://www.worldserver.com/turk/computergraphics/papers.html

!fuzz 0.00000001

!msgpostfix Turkowski's algorithm to calculate cube root\n

!need all
45.2548339756803022511987494
192.2798368355061050458134625
119.1654824285581628956914143
13.43250139086239872172837314
0.1636161226585754240958355063
14.80884093219134573786480845
151.9714051044435648658557668
168.5254414101568283957668343
33.9905941350215598754191872
# 1.0


# 128-bit accuracy
# Cephes Math Library Release 2.2:  January, 1991
# Range reduction involves determining the power of 2 of
# the argument.  A polynomial of degree 2 applied to the
# mantissa, and multiplication by the cube root of 1, 2, or 4
# approximates the root to within about 0.1%.  Then Newton's
# iteration is used three times to converge to an accurate
# result.

!msgpostfix Calculate cube root, Cephes math library\n

!need all
1.259921049894873164767210607278228350570251
1.587401051968199474751705639272308260391493
0.7937005259840997373758528196361541301957467
0.6299605249474365823836053036391141752851257

 1.3584464340920900529734e-1
-6.3986917220457538402318e-1
 1.2875551670318751538055e0
-1.4897083391357284957891e0
 1.3304961236013647092521e0
 3.7568280825958912391243e-1

 0.3333333333333333333333333333333333333333


!msgpostfix Evaluate the DiLogarithm function\n

!need all
 0.42996693560813697
 0.40975987533077105
-0.01858843665014592
 0.00145751084062268
-0.00014304184442340
 0.00001588415541880
-0.00000190784959387
 0.00000024195180854
-0.00000003193341274
 0.00000000434545063
-0.00000000060578480
 0.00000000008612098
-0.00000000001244332
 0.00000000000182256
-0.00000000000027007
 0.00000000000004042
-0.00000000000000610
 0.00000000000000093
-0.00000000000000014
 0.00000000000000002

!msgpostfix Evaluate the Struve function of order 0\n

!need all
 1.00215845609911981
-1.63969292681309147
 1.50236939618292819
-0.72485115302121872
 0.18955327371093136
-0.03067052022988
 0.00337561447375194
-2.6965014312602e-4
 1.637461692612e-5
-7.8244408508e-7
 3.021593188e-8
-9.6326645e-10
 2.579337e-11
-5.8854e-13
 1.158e-14
#-2e-16

 0.99283727576423943
-0.00696891281138625
 1.8205103787037e-4
-1.063258252844e-5
 9.8198294287e-7
-1.2250645445e-7
 1.894083312e-8
-3.44358226e-9
 7.1119102e-10
-1.6288744e-10
 4.065681e-11
-1.091505e-11
 3.12005e-12
-9.4202e-13
 2.9848e-13
-9.872e-14
 3.394e-14
-1.208e-14
 4.44e-15
-1.68e-15
# 6.5e-16
#-2.6e-16
# 1.1e-16
#-4e-17
# 2e-17
#-1e-17

!msgpostfix Evaluate the Struve function of order 1\n

!need all
 0.5578891446481605
-0.11188325726569816
-0.16337958125200939
 0.32256932072405902
-0.14581632367244242
 0.03292677399374035
-0.00460372142093573
 4.434706163314e-4
-3.142099529341e-5
 1.7123719938e-6
-7.416987005e-8
 2.61837671e-9
-7.685839e-11
 1.9067e-12
-4.052e-14
# 7.5e-16
#-1e-17

 1.00757647293865641
 0.00750316051248257
-7.043933264519e-5
 2.66205393382e-6
-1.8841157753e-7
 1.949014958e-8
-2.6126199e-9
 4.236269e-10
-7.955156e-11
 1.679973e-11
-3.9072e-12
 9.8543e-13
-2.6636e-13
 7.645e-14
-2.313e-14
 7.33e-15
-2.42e-15
# 8.3e-16
#-3e-16
# 1.1e-16
#-4e-17
# 2e-17
#-1e-17


!msgpostfix Legendre polynomial of degree 5\n

!need all
 63.0
-70.0
 15.0
  8.0

!msgpostfix Legendre polynomial of degree 5\n

!need all
 63.0
-70.0
 15.0
  0.125

!msgpostfix Legendre polynomial of degree 6\n

!need all
 231.0
-315.0
 105.0
   5.0
  16.0

!msgpostfix Legendre polynomial of degree 6\n

!need all
 231.0
-315.0
 105.0
   5.0
   0.0625

!msgpostfix Legendre polynomial of degree 7\n

!need all
 429.0
-693.0
 315.0
- 35.0
  16.0

!msgpostfix Legendre polynomial of degree 7\n

!need all
 429.0
-693.0
 315.0
- 35.0
   0.0625

!msgpostfix Legendre polynomial of degree 8\n

!need all
  6435.0
-12012.0
  6930.0
- 1260.0
    35.0
   128.0
!msgpostfix Legendre polynomial of degree 8\n

!need all
  6435.0
-12012.0
  6930.0
- 1260.0
    35.0
     0.0078125

!msgpostfix Legendre polynomial of degree 9\n

!need all
 0.24609375e+1
-0.3609375e+2
 0.140765625e+3
-0.20109375e+3
 0.949609375e+2

!msgpostfix Legendre polynomial of degree 10\n

!need all
-0.24609375e+0
 0.1353515625e+2
-0.1173046875e+3
 0.3519140625e+3
-0.42732421875e+3
 0.18042578125e+3

!msgpostfix Legendre polynomial of degree 11\n

!need all
-0.270703125e+1
 0.5865234375e+2
-0.3519140625e+3
 0.8546484375e+3
-0.90212890625e+3
 0.34444921875e+3

!msgpostfix Legendre polynomial of degree 12\n

!need all
 0.2255859375e+0
-0.17595703125e+2
 0.2199462890625e+3
-0.99708984375e+3
 0.20297900390625e+4
-0.1894470703125e+4
 0.6601943359375e+3

!msgpostfix Legendre polynomial of degree 13\n

!need all
 0.29326171875e+1
-0.87978515625e+2
 0.7478173828125e+3
-0.270638671875e+4
 0.47361767578125e+4
-0.3961166015625e+4
 0.12696044921875e+4

!msgpostfix Legendre polynomial of degree 14\n

!need all
-0.20947265625e+0
 0.2199462890625e+2
-0.37390869140625e+3
 0.236808837890625e+4
-0.710426513671875e+4
 0.1089320654296875e+5
-0.825242919921875e+4
 0.244852294921875e+4

!msgpostfix Legendre polynomial of degree 15\n

!need all
-0.314208984375e+1
 0.12463623046875e+3
-0.142085302734375e+4
 0.710426513671875e+4
-0.1815534423828125e+5
 0.2475728759765625e+5
-0.1713966064453125e+5
 0.473381103515625e+4

!msgpostfix Legendre polynomial of degree 16\n

!need all
 0.196380615234375e+0
-0.26707763671875e+2
 0.5920220947265625e+3
-0.4972985595703125e+4
 0.2042476226806641e+5
-0.4538836059570312e+5
 0.5570389709472656e+5
-0.3550358276367188e+5
 0.9171758880615234e+4

!msgpostfix Legendre polynomial of degree 17\n

!need all
 0.3338470458984375e+1
-0.169149169921875e+3
 0.2486492797851562e+4
-0.1633980981445312e+5
 0.5673545074462891e+5
-0.1114077941894531e+6
 0.1242625396728516e+6
-0.7337407104492188e+5
 0.1780400253295898e+5

!msgpostfix Legendre polynomial of degree 18\n

!need all
-0.1854705810546875e+0
 0.3171546936035156e+2
-0.8880331420898438e+3
 0.9531555725097656e+4
-0.5106190567016602e+5
 0.153185717010498e+6
-0.2692355026245117e+6
 0.275152766418457e+6
-0.1513340215301514e+6
 0.3461889381408691e+5
 
!msgpostfix Legendre polynomial of degree 19\n

!need all
-0.3523941040039062e+1
 0.2220082855224609e+3
-0.4084952453613281e+4
 0.3404127044677734e+5
-0.153185717010498e+6
 0.4038532539367676e+6
-0.6420231216430664e+6
 0.6053360861206055e+6
-0.3115700443267822e+6
 0.6741574058532715e+5
 
!msgpostfix Legendre polynomial of degree 20\n

!need all
 0.1761970520019531e+0
-0.3700138092041016e+2
 0.127654764175415e+4
-0.1702063522338867e+5
 0.1148892877578735e+6
-0.4442385793304443e+6
 0.1043287572669983e+7
-0.1513340215301514e+7
 0.1324172688388824e+7
-0.6404495355606079e+6
 0.1314606941413879e+6


!msgpostfix Gegenbauer polynomials of degree 6\n

!need all
 0.0625
-0.9375
 2.1875
-1.3125


!msgpostfix Gegenbauer polynomials of degree 7\n
!need all
 0.3125
-2.1875
 3.9375
-2.0625


!msgpostfix Gegenbauer polynomials of degree 8\n
!need all
-0.0390625
 1.09375
-4.921875
 7.21875
-3.3515625


!msgpostfix Gegenbauer polynomials of degree 9\n
!need all
- 0.2734375
  3.28125
-10.828125
 13.40625
- 5.5859375

#    Armido DiDinato, Alfred Morris,
#    Algorithm 708:
#    Significant Digit Computation of the Incomplete Beta Function Ratios,
#    ACM Transactions on Mathematical Software,
#    Volume 18, 1993, pages 360-373.

!msgpostfix Compute ln(1 + x)\n

!need all
-0.129418923021993D+01
 0.405303492862024D+00
-0.178874546012214D-01
-0.162752256355323D+01
 0.747811014037616D+00
-0.845104217945565D-01


!msgpostfix Laguerre's method for finding roots of polynomial\n

!need all
0.5
0.25
0.75
0.13
0.38
0.62
0.88
1.0

