begin
global tab_diff, tab_diffv

diff_tab = [
[1],
[-1/60,3/20,-3/4,0,3/4,-3/20,1/60],
[1/90,-3/20,3/2,-49/18,3/2,-3/20,1/90],
[-7/240,3/10,-169/120,61/30,0,-61/30,169/120,-3/10,7/240],
[7/240,-2/5,169/60,-122/15,91/8,-122/15,169/60,-2/5,7/240],

[139/12096,-121/756,3125/3024,-3011/756,33853/4032,-1039/126,0,
1039/126,-33853/4032,3011/756,-3125/3024,121/756,-139/12096],
[-139/12096,121/630,-3125/2016,3011/378,-33853/1344,1039/21,
-44473/720,1039/21,-33853/1344,3011/378,-3125/2016,121/630,
-139/12096],
[-2473/518400, 2747/32400, -1363/1920, 4787/1296, -678739/51840,
37517/1200, -12312353/259200, 251539/6480, 0, -251539/6480,
12312353/259200, -37517/1200, 678739/51840, -4787/1296, 1363/1920,
-2747/32400, 2473/518400],
[2473/518400, -2747/28350, 1363/1440, -4787/810, 678739/25920,
-37517/450, 12312353/64800, -251539/810, 4913051/13440, -251539/810,
12312353/64800, -37517/450, 678739/25920, -4787/810, 1363/1440,
-2747/28350, 2473/518400],
[-2021/268800, 7403/50400, -156031/115200, 65377/8400, -248167/8064,
309691/3600, -1618681/9600, 5586823/25200, -66976673/403200, 0,
66976673/403200, -5586823/25200, 1618681/9600, -309691/3600,
248167/8064, -65377/8400, 156031/115200, -7403/50400, 2021/268800],

[-21713/10644480, 32699/665280, -3039931/5322240, 44989/10560,
-81091903/3548160, 5165621/55440, -130451323/443520, 39926233/55440,
-269158459/197120, 666523661/332640, -78685061/34560,
666523661/332640, -269158459/197120, 39926233/55440,
-130451323/443520, 5165621/55440, -81091903/3548160, 44989/10560,
-3039931/5322240, 32699/665280, -21713/10644480],
[2677/829440, -55057/725760, 109819/129024, -548749/90720,
25219187/829440, -9186451/80640, 628607179/1935360,
-10656949/15120, 368867591/322560, -478917077/362880,
916.2723252177028, 0, -916.2723252177028, 478917077/362880,
-368867591/322560, 10656949/15120, -628607179/1935360,
9186451/80640, -25219187/829440, 548749/90720, -109819/129024,
55057/725760, -2677/829440],
[-2677/760320, 55057/604800, -109819/96768, 548749/60480,
-3602741/69120, 9186451/40320, -628607179/806400, 10656949/5040,
-368867591/80640, 478917077/60480, -10995.267902612433,
12264.447302188551, -10995.267902612433, 478917077/60480,
-368867591/80640, 10656949/5040, -628607179/806400,
9186451/40320, -3602741/69120, 548749/60480, -109819/96768,
55057/604800, -2677/760320],
[392251/79833600, -301141/2419200, 803105/532224,
-28111729/2419200, 38447137/604800, -90273149/345600,
828.9862464175485, -66270565/32256, 3968.854857390873,
-5875.183389274692, 548397449/86400, -4234.884892300986,
0, 4234.884892300986, -548397449/86400, 5875.183389274692,
-3968.854857390873, 66270565/32256, -828.9862464175485,
90273149/345600, -38447137/604800, 28111729/2419200,
-803105/532224, 301141/2419200, -392251/79833600],
[-392251/68428800, 301141/1900800, -160621/76032,
28111729/1555200, -38447137/345600, 90273149/172800,
-1934.3012416409465, 13254113/2304, -13890.992000868055,
27417.522483281893, -44430.34887731481, 59288.3884922138,
-65260.40946063646, 59288.3884922138, -44430.34887731481,
27417.522483281893, -13890.992000868055, 13254113/2304,
-1934.3012416409465, 90273149/172800, -38447137/345600,
28111729/1555200, -160621/76032, 301141/1900800,
-392251/68428800],

[462397/63866880, -116357/591360, 14891341/5806080,
-34012985/1596672, 49759967/394240, -205141127/362880,
819550333/414720, -147381799/26880, 12150.355132034007,
-21429.566915371473, 29559.504599144344, -30366.093272256294,
19658.44724708644, 0, -19658.44724708644, 30366.093272256294,
-29559.504599144344, 21429.566915371473, -12150.355132034007,
147381799/26880, -819550333/414720, 205141127/362880,
-49759967/394240, 34012985/1596672, -14891341/5806080,
116357/591360, -462397/63866880],
[-35569/3991680, 116357/443520, -14891341/3991680,
6802597/199584, -49759967/221760, 205141127/181440,
-117078619/25920, 147381799/10080, -38881.13642250882,
85718.2676614859, -157650.69119543652, 242928.74617805035,
-314535.155953383, 1085856289/3168, -314535.155953383,
242928.74617805035, -157650.69119543652, 85718.2676614859,
-38881.13642250882, 147381799/10080, -117078619/25920,
205141127/181440, -49759967/221760, 6802597/199584,
-14891341/3991680, 116357/443520, -35569/3991680],
[354971/34214400, -18033847/59875200, 3107353/739200,
-68025869/1814400, 764658775/3193344, -28638419/24640,
4437.5358114878945, -70496837/5184, 1817870687/53760,
-551961925/8064, 112225.73000716491, -146344.3397389069,
144464.45257679725, -91323.99824535033, 0, 91323.99824535033,
-144464.45257679725, 146344.3397389069, -112225.73000716491,
551961925/8064, -1817870687/53760, 70496837/5184,
-4437.5358114878945, 28638419/24640, -764658775/3193344,
68025869/1814400, -3107353/739200, 18033847/59875200,
-354971/34214400],
[-354971/26611200, 1387219/3326400, -3107353/492800,
68025869/1108800, -152931755/354816, 28638419/12320,
-9984.455575847764, 70496837/2016, -1817870687/17920,
110392385/448, -505015.78503224207, 878066.0384334415,
-1300180.0731911752, 1643831.968416306, -1777206.4762581168,
1643831.968416306, -1300180.0731911752, 878066.0384334415,
-505015.78503224207, 110392385/448, -1817870687/17920,
70496837/2016, -9984.455575847764, 28638419/12320,
-152931755/354816, 68025869/1108800, -3107353/492800,
1387219/3326400, -354971/26611200],
[154477/10644480, -26633/59400, 355238273/53222400,
-26472629/415800, 703770169/1612800, -63290987/27720,
9454.461361099839, -219560281/6930, 87099.3596216067,
-498555697/2520, 371712.25739397324, -574075.5604256854,
715038.4507268557, -683314.7463564214, 423682.9584378946,
0, -423682.9584378946, 683314.7463564214, -715038.4507268557,
574075.5604256854, -371712.25739397324, 498555697/2520,
-87099.3596216067, 219560281/6930, -9454.461361099839,
63290987/27720, -703770169/1612800, 26472629/415800,
-355238273/53222400, 26633/59400, -154477/10644480],

[0.005873343259565978, -0.2072968570414007, 3.5537025472690154,
-39.400399164970096, 317.3166509668866, -1976.1420670886469,
9888.825953571892, -40778.74178604712, 140984.0369842934,
-413595.54362350475, 1038367.7376354603, -2244654.089502898,
4196536.657000686, -6807167.396956872, 9602050.567143656,
-11796342.893053222, 12632811.42748226, -11796342.893053222,
9602050.567143656, -6807167.396956872, 4196536.657000686,
-2244654.089502898, 1038367.7376354603, -413595.54362350475,
140984.0369842934, -40778.74178604712, 9888.825953571892,
-1976.1420670886469, 317.3166509668866, -39.400399164970096,
3.5537025472690154, -0.2072968570414007, 0.005873343259565978],
[-0.006687176916126569, 182035669/778377600, -3.9614914834153114,
43.260384273648164, -341.90064621496043, 2080.7542524373775,
-10126.582118695027, 40390.02018330178, -134186.6825709837,
375262.41314945085, -888771.9697958316, 1786407.53815386,
-3040050.4498071615, 4341946.758998833, -5097356.637806768,
4673525.878001358, -2827559.224280478, 0, 2827559.224280478,
-4673525.878001358, 5097356.637806768, -4341946.758998833,
3040050.4498071615, -1786407.53815386, 888771.9697958316,
-375262.41314945085, 134186.6825709837, -40390.02018330178,
10126.582118695027, -2080.7542524373775, 341.90064621496043,
-43.260384273648164, 3.9614914834153114, -182035669/778377600,
0.006687176916126569],
[9797927/1132185600, -182035669/566092800, 5.810187509009124,
-67.98060385858997, 578.6010935945485, -3814.716129468525,
20253.164237390054, -88858.04440326392, 328011.8907290713,
-1031971.6361609899, 2793283.3336440423, -6550160.97323082,
13376221.97915151, -23880707.17449358, 37380615.3439163,
-51408784.65801494, 62206302.93417052, -66281815.12236388,
62206302.93417052, -51408784.65801494, 37380615.3439163,
-23880707.17449358, 13376221.97915151, -6550160.97323082,
2793283.3336440423, -1031971.6361609899, 328011.8907290713,
-88858.04440326392, 20253.164237390054, -3814.716129468525,
578.6010935945485, -67.98060385858997, 5.810187509009124,
-182035669/566092800, 9797927/1132185600],
[-0.009332470275581635, 0.34402346379324306, -6.15213852441283,
71.05165114070279, -595.1122156963487, 3847.767250900206,
-19955.02716637555, 85132.52554556729, -303953.20031468215,
918926.1148505581, -2370511.92168014, 5240062.788594784,
-9934784.39219035, 16104729.814346485, -22115672.239893954,
25188993.19451772, -22603469.63177157, 13500898.864533069, 0,
-13500898.864533069, 22603469.63177157, -25188993.19451772,
22115672.239893954, -16104729.814346485, 9934784.39219035,
-5240062.788594784, 2370511.92168014, -918926.1148505581,
303953.20031468215, -85132.52554556729, 19955.02716637555,
-3847.767250900206, 595.1122156963487, -71.05165114070279,
6.15213852441283, -0.34402346379324306, 0.009332470275581635],
[0.012443293700775513, -0.4856801841786961, 9.228207786619246,
-113.68264182512446, 1020.1923697651692, -7103.570309354226,
39910.0543327511, -185743.69209941954, 729487.6807552371,
-2450469.639601488, 7111535.76504042, -17965929.560896404,
39739137.5687614, -77302703.10886313, 132694033.43936373,
-201511945.55614176, 271241635.58125883, -324021572.7487936,
343777625.044988, -324021572.7487936, 271241635.58125883,
-201511945.55614176, 132694033.43936373, -77302703.10886313,
39739137.5687614, -17965929.560896404, 7111535.76504042,
-2450469.639601488, 729487.6807552371, -185743.69209941954,
39910.0543327511, -7103.570309354226, 1020.1923697651692,
-113.68264182512446, 9.228207786619246, -0.4856801841786961,
0.012443293700775513],
]

function tab_diff(h)
   return fn diff|f,x,n|
      if n==0
         return f(x)
      else
         a = diff_tab[n]
         m = len(a)//2
         d = h^(1/n)
         return (-m..m).sum(|k| a[m+k]*f(x+k*d))/h
      end
   end
end

function tab_diffv(h)
   return fn diffv|v,f,x,n|
     if n==0
        return f(x)
     else
        a = diff_tab[n]
        m = len(a)//2
        dv = h^(1/n)*v
        return (-m..m).sum(|k| a[m+k]*f(x+k*dv))/h
     end
   end
end

end