#=====================================================#

• FILE: rational.hzt #
• COMMENTS: Contains the constants for all the #
• rational approximations required for the #
• RHMC + Hasenbusch #
• ( all the coefficients were obtained #
• using MILC code ) #
• #

#=====================================================#
#-----------------------------------------------------------------------------------

• Coefficients for rational approximations:
• r(x) = r_const + r_num[0]/(r_den[0] + x) + ...
• + r_num[r_order-1]/(r_den[r_order - 1] + x)

#
#-----------------------------------------------------------------------------------

• New rational function
• Approximation bounds are [6.141951e-03,5.000000e+00]
• Precision of arithmetic is 50
• Degree of the approximation is (14,14)
• Approximating the function (x+4*0.000000²⁾(3.000000/8.000000) (x+4*0.078371²⁾(0.000000/8.000000) (x+4*0.000000²⁾(0.000000/8.000000) (x+4*0.000000²⁾(0.000000/8.000000)
• Converged at 676 iterations, error = 2.779623e-13

#-----------------------------------------------------------------------------------

• r_inv_1f

#-----------------------------------------------------------------------------------

• real r_inv_1f_const, r_inv_1f_num[r_high_order_2f], r_inv_1f_den[r_high_order_2f]

r_inv_1f_const = 9.5799902308688729e+00
r_inv_1f_num[0] = -2.3880473787838435e-05
r_inv_1f_num[1] = -1.0671449544258764e-04
r_inv_1f_num[2] = -3.1717723038646850e-04
r_inv_1f_num[3] = -8.4142226353048106e-04
r_inv_1f_num[4] = -2.1452739858442778e-03
r_inv_1f_num[5] = -5.3966009822507960e-03
r_inv_1f_num[6] = -1.3573313299660985e-02
r_inv_1f_num[7] = -3.4525494417373133e-02
r_inv_1f_num[8] = -9.0258923300429186e-02
r_inv_1f_num[9] = -2.4964595146084617e-01
r_inv_1f_num[10] = -7.7374721805354496e-01
r_inv_1f_num[11] = -3.0422670644690353e+00
r_inv_1f_num[12] = -2.0849219100479427e+01
r_inv_1f_num[13] = -9.3490368354455359e+02

r_inv_1f_den[0] = 6.0206770600731280e-04
r_inv_1f_den[1] = 2.8188129874552226e-03
r_inv_1f_den[2] = 7.6423465726770589e-03
r_inv_1f_den[3] = 1.7217394676656957e-02
r_inv_1f_den[4] = 3.5822117273238432e-02
r_inv_1f_den[5] = 7.1849066562576266e-02
r_inv_1f_den[6] = 1.4185070287207752e-01
r_inv_1f_den[7] = 2.7912840318207327e-01
r_inv_1f_den[8] = 5.5339485533928390e-01
r_inv_1f_den[9] = 1.1217154210800853e+00
r_inv_1f_den[10] = 2.3877495289519959e+00
r_inv_1f_den[11] = 5.6605714410429089e+00
r_inv_1f_den[12] = 1.7509595515596569e+01
r_inv_1f_den[13] = 1.4183341331619428e+02

• CHECK: f(6.141951e-03) = 1.481204e-01 = 1.481204e-01?

#-----------------------------------------------------------------------------------

• r_inv_1f

#-----------------------------------------------------------------------------------

• real r_1f_const, r_1f_num[r_high_order_2f], r_1f_den[r_high_order_2f]

r_1f_const = 1.0438424005671490e-01
r_1f_num[0] = 5.2693552520599804e-03
r_1f_num[1] = 7.7105486776882955e-03
r_1f_num[2] = 1.0765259455820657e-02
r_1f_num[3] = 1.5387543078741867e-02
r_1f_num[4] = 2.2496080830430899e-02
r_1f_num[5] = 3.3417013267213067e-02
r_1f_num[6] = 5.0243462588142225e-02
r_1f_num[7] = 7.6484002463905909e-02
r_1f_num[8] = 1.1852931234072184e-01
r_1f_num[9] = 1.8955182977863699e-01
r_1f_num[10] = 3.2183023799828192e-01
r_1f_num[11] = 6.1573843371709258e-01
r_1f_num[12] = 1.5227850521143074e+00
r_1f_num[13] = 7.4696454856828440e+00

r_1f_den[0] = 2.1651988768921224e-04
r_1f_den[1] = 1.7538814471439656e-03
r_1f_den[2] = 5.4252039819043443e-03
r_1f_den[3] = 1.2861380286934360e-02
r_1f_den[4] = 2.7377491781498356e-02
r_1f_den[5] = 5.5493386730116952e-02
r_1f_den[6] = 1.1002017126063761e-01
r_1f_den[7] = 2.1649349703606607e-01
r_1f_den[8] = 4.2742037149576090e-01
r_1f_den[9] = 8.5728474639164576e-01
r_1f_den[10] = 1.7836470208489645e+00
r_1f_den[11] = 4.0183671899405367e+00
r_1f_den[12] = 1.0894569756301662e+01
r_1f_den[13] = 5.1007144903113264e+01

• CHECK: f(6.141951e-03) = 6.751264e+00 = 6.751264e+00?
• New rational function
• Approximation bounds are [6.141951e-03,5.000000e+00]
• Precision of arithmetic is 50
• Degree of the approximation is (12,12)
• Approximating the function (x+4*0.000000²⁾(3.000000/4.000000) (x+4*0.078371²⁾(0.000000/4.000000) (x+4*0.000000²⁾(0.000000/4.000000) (x+4*0.000000²⁾(0.000000/4.000000)
• Converged at 578 iterations, error = 1.418088e-11

#-----------------------------------------------------------------------------------

• r_bar_1f

#-----------------------------------------------------------------------------------

• real r_bar_1f_const, r_bar_1f_num[r_high_order_2f], r_bar_1f_den[r_high_order_2f]

r_bar_1f_const = 8.9904320728147035e-03
r_bar_1f_num[0] = 1.4667443477677822e-01
r_bar_1f_num[1] = 7.4490391136540310e-02
r_bar_1f_num[2] = 6.7820253879532222e-02
r_bar_1f_num[3] = 7.2068832159019311e-02
r_bar_1f_num[4] = 8.2165265326205564e-02
r_bar_1f_num[5] = 9.7077141706725142e-02
r_bar_1f_num[6] = 1.1726852973156252e-01
r_bar_1f_num[7] = 1.4479710924205830e-01
r_bar_1f_num[8] = 1.8515460701588993e-01
r_bar_1f_num[9] = 2.5402494172511503e-01
r_bar_1f_num[10] = 4.0751068850157962e-01
r_bar_1f_num[11] = 9.8497253325507095e-01
r_bar_1f_num[12] = 0
r_bar_1f_num[13] = 0

r_bar_1f_den[0] = 1.0078407410124585e-04
r_bar_1f_den[1] = 1.7938080148775586e-03
r_bar_1f_den[2] = 6.4392937130325328e-03
r_bar_1f_den[3] = 1.6853627282271529e-02
r_bar_1f_den[4] = 3.9390880203829449e-02
r_bar_1f_den[5] = 8.7964908793317073e-02
r_bar_1f_den[6] = 1.9332522538122635e-01
r_bar_1f_den[7] = 4.2577652318738390e-01
r_bar_1f_den[8] = 9.5824356092852958e-01
r_bar_1f_den[9] = 2.2835230352639240e+00
r_bar_1f_den[10] = 6.2815298721842598e+00
r_bar_1f_den[11] = 2.6554961484951136e+01
r_bar_1f_den[12] = 0
r_bar_1f_den[13] = 0

• CHECK: f(6.141951e-03) = 4.557957e+01 = 4.557957e+01?
• New rational function
• Approximation bounds are [1.535464e-05,5.000000e+00]
• Precision of arithmetic is 160
• Degree of the approximation is (14,14)
• Approximating the function (x+4*0.000000²⁾(2.000000/8.000000) (x+4*0.078273²⁾(-2.000000/8.000000) (x+4*0.000000²⁾(0.000000/8.000000) (x+4*0.000000²⁾(0.000000/8.000000)
• Converged at 1893 iterations, error = 1.814062e-14

#-----------------------------------------------------------------------------------

• r_inv_2f

#-----------------------------------------------------------------------------------

• real r_inv_2f_const, r_inv_2f_num[r_high_order_2f], r_inv_2f_den[r_high_order_2f]

r_inv_2f_const = 9.9999999999997680e-01
r_inv_2f_num[0] = -6.7306087355583814e-08
r_inv_2f_num[1] = -2.5119048121389759e-07
r_inv_2f_num[2] = -6.3574473615695592e-07
r_inv_2f_num[3] = -1.4444416683813671e-06
r_inv_2f_num[4] = -3.1520645760780889e-06
r_inv_2f_num[5] = -6.7449221772861047e-06
r_inv_2f_num[6] = -1.4229150795784731e-05
r_inv_2f_num[7] = -2.9529988004365561e-05
r_inv_2f_num[8] = -5.9763057654019888e-05
r_inv_2f_num[9] = -1.1588451027579001e-04
r_inv_2f_num[10] = -2.0860533311964019e-04
r_inv_2f_num[11] = -3.3033204465383382e-04
r_inv_2f_num[12] = -4.1945288688959709e-04
r_inv_2f_num[13] = -3.4155643438175124e-04

r_inv_2f_den[0] = 1.1228621507033865e-06
r_inv_2f_den[1] = 5.4989686256172966e-06
r_inv_2f_den[2] = 1.4808598806862630e-05
r_inv_2f_den[3] = 3.2518999888912806e-05
r_inv_2f_den[4] = 6.5175560141293577e-05
r_inv_2f_den[5] = 1.2467761184774606e-04
r_inv_2f_den[6] = 2.3214209884346506e-04
r_inv_2f_den[7] = 4.2387036799479741e-04
r_inv_2f_den[8] = 7.5880668627768095e-04
r_inv_2f_den[9] = 1.3223017265206955e-03
r_inv_2f_den[10] = 2.2087251965928851e-03
r_inv_2f_den[11] = 3.4469475924633008e-03
r_inv_2f_den[12] = 4.8481590765212098e-03
r_inv_2f_den[13] = 5.9035679216737644e-03

• CHECK: f(1.535464e-05) = 2.236059e-01 = 2.236059e-01?

#-----------------------------------------------------------------------------------

• r_inv_2f

#-----------------------------------------------------------------------------------

• real r_2f_const, r_2f_num[r_high_order_2f], r_2f_den[r_high_order_2f]

r_2f_const = 1.0000000000000231e+00
r_2f_num[0] = 4.1081008191569664e-06
r_2f_num[1] = 7.4721819021838214e-06
r_2f_num[2] = 1.1611455269516283e-05
r_2f_num[3] = 1.7770235852122681e-05
r_2f_num[4] = 2.7290385666846997e-05
r_2f_num[5] = 4.2019625070741930e-05
r_2f_num[6] = 6.4504138001444396e-05
r_2f_num[7] = 9.7896530879487654e-05
r_2f_num[8] = 1.4497690223761557e-04
r_2f_num[9] = 2.0489997770136638e-04
r_2f_num[10] = 2.6577253725552311e-04
r_2f_num[11] = 2.9480210559988603e-04
r_2f_num[12] = 2.4382982428816232e-04
r_2f_num[13] = 1.0469507495727132e-04

r_2f_den[0] = 5.7786368301505536e-07
r_2f_den[1] = 4.0312292026215251e-06
r_2f_den[2] = 1.1869209543158398e-05
r_2f_den[3] = 2.7015312512693615e-05
r_2f_den[4] = 5.5080481676469050e-05
r_2f_den[5] = 1.0633619774630016e-04
r_2f_den[6] = 1.9912262671075548e-04
r_2f_den[7] = 3.6526975843470175e-04
r_2f_den[8] = 6.5739591852995551e-04
r_2f_den[9] = 1.1545793684653736e-03
r_2f_den[10] = 1.9529402913489034e-03
r_2f_den[11] = 3.1093393557870587e-03
r_2f_den[12] = 4.5055422727565938e-03
r_2f_den[13] = 5.7075743064500441e-03

• CHECK: f(1.535464e-05) = 4.472153e+00 = 4.472153e+00?
• New rational function
• Approximation bounds are [1.535464e-05,5.000000e+00]
• Precision of arithmetic is 160
• Degree of the approximation is (12,12)
• Approximating the function (x+4*0.000000²⁾(2.000000/4.000000) (x+4*0.078273²⁾(-2.000000/4.000000) (x+4*0.000000²⁾(0.000000/4.000000) (x+4*0.000000²⁾(0.000000/4.000000)
• Converged at 1639 iterations, error = 2.353143e-12

#-----------------------------------------------------------------------------------

• r_bar_2f

#-----------------------------------------------------------------------------------

• real r_bar_2f_const, r_bar_2f_num[r_high_order_2f], r_bar_2f_den[r_high_order_2f]

r_bar_2f_const = 1.0000000000028322e+00
r_bar_2f_num[0] = 6.9434115109567141e-05
r_bar_2f_num[1] = 7.7983713610091675e-05
r_bar_2f_num[2] = 9.6063854669967629e-05
r_bar_2f_num[3] = 1.2566256997493963e-04
r_bar_2f_num[4] = 1.6971961993037757e-04
r_bar_2f_num[5] = 2.3164533455583800e-04
r_bar_2f_num[6] = 3.1348723749748955e-04
r_bar_2f_num[7] = 4.1062799120068224e-04
r_bar_2f_num[8] = 4.9980464988231773e-04
r_bar_2f_num[9] = 5.2276934739441941e-04
r_bar_2f_num[10] = 3.9959970512076207e-04
r_bar_2f_num[11] = 1.4650000964304107e-04
r_bar_2f_num[12] = 0
r_bar_2f_num[13] = 0

r_bar_2f_den[0] = 4.7571462970011230e-07
r_bar_2f_den[1] = 4.6413603153149898e-06
r_bar_2f_den[2] = 1.5091934786403394e-05
r_bar_2f_den[3] = 3.7121880375535716e-05
r_bar_2f_den[4] = 8.1787546836386687e-05
r_bar_2f_den[5] = 1.7107213561193624e-04
r_bar_2f_den[6] = 3.4718775481307467e-04
r_bar_2f_den[7] = 6.8670287789194726e-04
r_bar_2f_den[8] = 1.3126535940222099e-03
r_bar_2f_den[9] = 2.3702357001896750e-03
r_bar_2f_den[10] = 3.8798822940055945e-03
r_bar_2f_den[11] = 5.4300587437934814e-03
r_bar_2f_den[12] = 0
r_bar_2f_den[13] = 0

• CHECK: f(1.535464e-05) = 2.000015e+01 = 2.000015e+01?

#=================== End of File =====================#