constants.py

import numpy as np

alphas_cumprod = np.array([
    0.9991, 0.9983, 0.9974, 0.9966, 0.9957, 0.9948, 0.9940, 0.9931, 0.9922,
    0.9913, 0.9904, 0.9895, 0.9886, 0.9877, 0.9868, 0.9859, 0.9850, 0.9841,
    0.9832, 0.9822, 0.9813, 0.9804, 0.9794, 0.9785, 0.9776, 0.9766, 0.9757,
    0.9747, 0.9737, 0.9728, 0.9718, 0.9708, 0.9698, 0.9689, 0.9679, 0.9669,
    0.9659, 0.9649, 0.9639, 0.9629, 0.9619, 0.9609, 0.9599, 0.9588, 0.9578,
    0.9568, 0.9557, 0.9547, 0.9537, 0.9526, 0.9516, 0.9505, 0.9495, 0.9484,
    0.9473, 0.9463, 0.9452, 0.9441, 0.9430, 0.9420, 0.9409, 0.9398, 0.9387,
    0.9376, 0.9365, 0.9354, 0.9343, 0.9332, 0.9320, 0.9309, 0.9298, 0.9287,
    0.9275, 0.9264, 0.9252, 0.9241, 0.9229, 0.9218, 0.9206, 0.9195, 0.9183,
    0.9171, 0.9160, 0.9148, 0.9136, 0.9124, 0.9112, 0.9100, 0.9089, 0.9077,
    0.9065, 0.9052, 0.9040, 0.9028, 0.9016, 0.9004, 0.8992, 0.8979, 0.8967,
    0.8955, 0.8942, 0.8930, 0.8917, 0.8905, 0.8892, 0.8880, 0.8867, 0.8854,
    0.8842, 0.8829, 0.8816, 0.8804, 0.8791, 0.8778, 0.8765, 0.8752, 0.8739,
    0.8726, 0.8713, 0.8700, 0.8687, 0.8674, 0.8661, 0.8647, 0.8634, 0.8621,
    0.8607, 0.8594, 0.8581, 0.8567, 0.8554, 0.8540, 0.8527, 0.8513, 0.8500,
    0.8486, 0.8473, 0.8459, 0.8445, 0.8431, 0.8418, 0.8404, 0.8390, 0.8376,
    0.8362, 0.8348, 0.8334, 0.8320, 0.8306, 0.8292, 0.8278, 0.8264, 0.8250,
    0.8236, 0.8221, 0.8207, 0.8193, 0.8179, 0.8164, 0.8150, 0.8136, 0.8121,
    0.8107, 0.8092, 0.8078, 0.8063, 0.8049, 0.8034, 0.8019, 0.8005, 0.7990,
    0.7975, 0.7960, 0.7946, 0.7931, 0.7916, 0.7901, 0.7886, 0.7871, 0.7856,
    0.7842, 0.7827, 0.7812, 0.7796, 0.7781, 0.7766, 0.7751, 0.7736, 0.7721,
    0.7706, 0.7690, 0.7675, 0.7660, 0.7645, 0.7629, 0.7614, 0.7599, 0.7583,
    0.7568, 0.7552, 0.7537, 0.7521, 0.7506, 0.7490, 0.7475, 0.7459, 0.7444,
    0.7428, 0.7412, 0.7397, 0.7381, 0.7365, 0.7350, 0.7334, 0.7318, 0.7302,
    0.7286, 0.7271, 0.7255, 0.7239, 0.7223, 0.7207, 0.7191, 0.7175, 0.7159,
    0.7143, 0.7127, 0.7111, 0.7095, 0.7079, 0.7063, 0.7047, 0.7031, 0.7015,
    0.6999, 0.6982, 0.6966, 0.6950, 0.6934, 0.6918, 0.6901, 0.6885, 0.6869,
    0.6852, 0.6836, 0.6820, 0.6803, 0.6787, 0.6771, 0.6754, 0.6738, 0.6722,
    0.6705, 0.6689, 0.6672, 0.6656, 0.6639, 0.6623, 0.6606, 0.6590, 0.6573,
    0.6557, 0.6540, 0.6524, 0.6507, 0.6490, 0.6474, 0.6457, 0.6441, 0.6424,
    0.6407, 0.6391, 0.6374, 0.6357, 0.6341, 0.6324, 0.6307, 0.6291, 0.6274,
    0.6257, 0.6241, 0.6224, 0.6207, 0.6190, 0.6174, 0.6157, 0.6140, 0.6123,
    0.6107, 0.6090, 0.6073, 0.6056, 0.6039, 0.6023, 0.6006, 0.5989, 0.5972,
    0.5955, 0.5939, 0.5922, 0.5905, 0.5888, 0.5871, 0.5855, 0.5838, 0.5821,
    0.5804, 0.5787, 0.5770, 0.5754, 0.5737, 0.5720, 0.5703, 0.5686, 0.5669,
    0.5652, 0.5636, 0.5619, 0.5602, 0.5585, 0.5568, 0.5551, 0.5535, 0.5518,
    0.5501, 0.5484, 0.5467, 0.5450, 0.5434, 0.5417, 0.5400, 0.5383, 0.5366,
    0.5350, 0.5333, 0.5316, 0.5299, 0.5282, 0.5266, 0.5249, 0.5232, 0.5215,
    0.5199, 0.5182, 0.5165, 0.5148, 0.5132, 0.5115, 0.5098, 0.5082, 0.5065,
    0.5048, 0.5032, 0.5015, 0.4998, 0.4982, 0.4965, 0.4948, 0.4932, 0.4915,
    0.4898, 0.4882, 0.4865, 0.4849, 0.4832, 0.4816, 0.4799, 0.4782, 0.4766,
    0.4749, 0.4733, 0.4716, 0.4700, 0.4684, 0.4667, 0.4651, 0.4634, 0.4618,
    0.4601, 0.4585, 0.4569, 0.4552, 0.4536, 0.4520, 0.4503, 0.4487, 0.4471,
    0.4455, 0.4438, 0.4422, 0.4406, 0.4390, 0.4374, 0.4357, 0.4341, 0.4325,
    0.4309, 0.4293, 0.4277, 0.4261, 0.4245, 0.4229, 0.4213, 0.4197, 0.4181,
    0.4165, 0.4149, 0.4133, 0.4117, 0.4101, 0.4086, 0.4070, 0.4054, 0.4038,
    0.4022, 0.4007, 0.3991, 0.3975, 0.3960, 0.3944, 0.3928, 0.3913, 0.3897,
    0.3882, 0.3866, 0.3850, 0.3835, 0.3819, 0.3804, 0.3789, 0.3773, 0.3758,
    0.3742, 0.3727, 0.3712, 0.3697, 0.3681, 0.3666, 0.3651, 0.3636, 0.3621,
    0.3605, 0.3590, 0.3575, 0.3560, 0.3545, 0.3530, 0.3515, 0.3500, 0.3485,
    0.3470, 0.3456, 0.3441, 0.3426, 0.3411, 0.3396, 0.3382, 0.3367, 0.3352,
    0.3338, 0.3323, 0.3308, 0.3294, 0.3279, 0.3265, 0.3250, 0.3236, 0.3222,
    0.3207, 0.3193, 0.3178, 0.3164, 0.3150, 0.3136, 0.3122, 0.3107, 0.3093,
    0.3079, 0.3065, 0.3051, 0.3037, 0.3023, 0.3009, 0.2995, 0.2981, 0.2967,
    0.2954, 0.2940, 0.2926, 0.2912, 0.2899, 0.2885, 0.2871, 0.2858, 0.2844,
    0.2831, 0.2817, 0.2804, 0.2790, 0.2777, 0.2763, 0.2750, 0.2737, 0.2723,
    0.2710, 0.2697, 0.2684, 0.2671, 0.2658, 0.2645, 0.2631, 0.2618, 0.2606,
    0.2593, 0.2580, 0.2567, 0.2554, 0.2541, 0.2528, 0.2516, 0.2503, 0.2490,
    0.2478, 0.2465, 0.2453, 0.2440, 0.2428, 0.2415, 0.2403, 0.2391, 0.2378,
    0.2366, 0.2354, 0.2341, 0.2329, 0.2317, 0.2305, 0.2293, 0.2281, 0.2269,
    0.2257, 0.2245, 0.2233, 0.2221, 0.2209, 0.2198, 0.2186, 0.2174, 0.2163,
    0.2151, 0.2139, 0.2128, 0.2116, 0.2105, 0.2093, 0.2082, 0.2071, 0.2059,
    0.2048, 0.2037, 0.2026, 0.2014, 0.2003, 0.1992, 0.1981, 0.1970, 0.1959,
    0.1948, 0.1937, 0.1926, 0.1915, 0.1905, 0.1894, 0.1883, 0.1872, 0.1862,
    0.1851, 0.1841, 0.1830, 0.1820, 0.1809, 0.1799, 0.1788, 0.1778, 0.1768,
    0.1757, 0.1747, 0.1737, 0.1727, 0.1717, 0.1707, 0.1696, 0.1686, 0.1677,
    0.1667, 0.1657, 0.1647, 0.1637, 0.1627, 0.1618, 0.1608, 0.1598, 0.1589,
    0.1579, 0.1569, 0.1560, 0.1550, 0.1541, 0.1532, 0.1522, 0.1513, 0.1504,
    0.1494, 0.1485, 0.1476, 0.1467, 0.1458, 0.1449, 0.1440, 0.1431, 0.1422,
    0.1413, 0.1404, 0.1395, 0.1386, 0.1378, 0.1369, 0.1360, 0.1352, 0.1343,
    0.1334, 0.1326, 0.1317, 0.1309, 0.1301, 0.1292, 0.1284, 0.1276, 0.1267,
    0.1259, 0.1251, 0.1243, 0.1235, 0.1227, 0.1219, 0.1211, 0.1203, 0.1195,
    0.1187, 0.1179, 0.1171, 0.1163, 0.1155, 0.1148, 0.1140, 0.1132, 0.1125,
    0.1117, 0.1110, 0.1102, 0.1095, 0.1087, 0.1080, 0.1073, 0.1065, 0.1058,
    0.1051, 0.1044, 0.1036, 0.1029, 0.1022, 0.1015, 0.1008, 0.1001, 0.0994,
    0.0987, 0.0980, 0.0973, 0.0967, 0.0960, 0.0953, 0.0946, 0.0940, 0.0933,
    0.0926, 0.0920, 0.0913, 0.0907, 0.0900, 0.0894, 0.0887, 0.0881, 0.0875,
    0.0868, 0.0862, 0.0856, 0.0850, 0.0844, 0.0837, 0.0831, 0.0825, 0.0819,
    0.0813, 0.0807, 0.0801, 0.0795, 0.0789, 0.0784, 0.0778, 0.0772, 0.0766,
    0.0761, 0.0755, 0.0749, 0.0744, 0.0738, 0.0732, 0.0727, 0.0721, 0.0716,
    0.0711, 0.0705, 0.0700, 0.0694, 0.0689, 0.0684, 0.0679, 0.0673, 0.0668,
    0.0663, 0.0658, 0.0653, 0.0648, 0.0643, 0.0638, 0.0633, 0.0628, 0.0623,
    0.0618, 0.0613, 0.0608, 0.0604, 0.0599, 0.0594, 0.0589, 0.0585, 0.0580,
    0.0575, 0.0571, 0.0566, 0.0562, 0.0557, 0.0553, 0.0548, 0.0544, 0.0539,
    0.0535, 0.0531, 0.0526, 0.0522, 0.0518, 0.0514, 0.0509, 0.0505, 0.0501,
    0.0497, 0.0493, 0.0489, 0.0485, 0.0481, 0.0477, 0.0473, 0.0469, 0.0465,
    0.0461, 0.0457, 0.0453, 0.0450, 0.0446, 0.0442, 0.0438, 0.0435, 0.0431,
    0.0427, 0.0424, 0.0420, 0.0416, 0.0413, 0.0409, 0.0406, 0.0402, 0.0399,
    0.0395, 0.0392, 0.0389, 0.0385, 0.0382, 0.0379, 0.0375, 0.0372, 0.0369,
    0.0365, 0.0362, 0.0359, 0.0356, 0.0353, 0.0350, 0.0347, 0.0343, 0.0340,
    0.0337, 0.0334, 0.0331, 0.0328, 0.0325, 0.0323, 0.0320, 0.0317, 0.0314,
    0.0311, 0.0308, 0.0305, 0.0303, 0.0300, 0.0297, 0.0295, 0.0292, 0.0289,
    0.0286, 0.0284, 0.0281, 0.0279, 0.0276, 0.0274, 0.0271, 0.0268, 0.0266,
    0.0264, 0.0261, 0.0259, 0.0256, 0.0254, 0.0251, 0.0249, 0.0247, 0.0244,
    0.0242, 0.0240, 0.0237, 0.0235, 0.0233, 0.0231, 0.0229, 0.0226, 0.0224,
    0.0222, 0.0220, 0.0218, 0.0216, 0.0214, 0.0212, 0.0210, 0.0207, 0.0205,
    0.0203, 0.0201, 0.0200, 0.0198, 0.0196, 0.0194, 0.0192, 0.0190, 0.0188,
    0.0186, 0.0184, 0.0182, 0.0181, 0.0179, 0.0177, 0.0175, 0.0174, 0.0172,
    0.0170, 0.0168, 0.0167, 0.0165, 0.0163, 0.0162, 0.0160, 0.0158, 0.0157,
    0.0155, 0.0154, 0.0152, 0.0151, 0.0149, 0.0147, 0.0146, 0.0144, 0.0143,
    0.0142, 0.0140, 0.0139, 0.0137, 0.0136, 0.0134, 0.0133, 0.0132, 0.0130,
    0.0129, 0.0127, 0.0126, 0.0125, 0.0123, 0.0122, 0.0121, 0.0120, 0.0118,
    0.0117, 0.0116, 0.0115, 0.0113, 0.0112, 0.0111, 0.0110, 0.0109, 0.0107,
    0.0106, 0.0105, 0.0104, 0.0103, 0.0102, 0.0101, 0.0100, 0.0098, 0.0097,
    0.0096, 0.0095, 0.0094, 0.0093, 0.0092, 0.0091, 0.0090, 0.0089, 0.0088,
    0.0087, 0.0086, 0.0085, 0.0084, 0.0083, 0.0082, 0.0082, 0.0081, 0.0080,
    0.0079, 0.0078, 0.0077, 0.0076, 0.0075, 0.0074, 0.0074, 0.0073, 0.0072,
    0.0071, 0.0070, 0.0070, 0.0069, 0.0068, 0.0067, 0.0066, 0.0066, 0.0065,
    0.0064, 0.0063, 0.0063, 0.0062, 0.0061, 0.0061, 0.0060, 0.0059, 0.0058,
    0.0058, 0.0057, 0.0056, 0.0056, 0.0055, 0.0054, 0.0054, 0.0053, 0.0053,
    0.0052, 0.0051, 0.0051, 0.0050, 0.0049, 0.0049, 0.0048, 0.0048, 0.0047,
    0.0047
])

log_sigmas = np.array([
    -3.465247869e+00, -3.262352705e+00, -3.006420135e+00, -2.837683201e+00,
    -2.711531878e+00, -2.610528946e+00, -2.566935062e+00, -2.489443779e+00,
    -2.422124147e+00, -2.362802029e+00, -2.309390783e+00, -2.284866810e+00,
    -2.238821030e+00, -2.196660280e+00, -2.157779932e+00, -2.121440172e+00,
    -2.087811947e+00, -2.056070566e+00, -2.040925026e+00, -2.011517525e+00,
    -1.984147549e+00, -1.958198309e+00, -1.933165073e+00, -1.909325600e+00,
    -1.886571169e+00, -1.864807487e+00, -1.843951702e+00, -1.823931098e+00,
    -1.804399610e+00, -1.785873890e+00, -1.767748117e+00, -1.750256658e+00,
    -1.733356476e+00, -1.717008829e+00, -1.701178789e+00, -1.685834646e+00,
    -1.670516253e+00, -1.656071663e+00, -1.642032743e+00, -1.627981305e+00,
    -1.614699244e+00, -1.601385355e+00, -1.588416934e+00, -1.576133013e+00,
    -1.563795447e+00, -1.545673847e+00, -1.534057021e+00, -1.522703886e+00,
    -1.511602998e+00, -1.500743032e+00, -1.490114093e+00, -1.479412079e+00,
    -1.469222426e+00, -1.453897834e+00, -1.444210291e+00, -1.434437990e+00,
    -1.424853086e+00, -1.415448427e+00, -1.401916742e+00, -1.392930031e+00,
    -1.383858919e+00, -1.375188112e+00, -1.362457633e+00, -1.354147196e+00,
    -1.345972657e+00, -1.337486506e+00, -1.325669765e+00, -1.317518473e+00,
    -1.309916973e+00, -1.302429318e+00, -1.291000366e+00, -1.283390999e+00,
    -1.276287556e+00, -1.265434384e+00, -1.258201718e+00, -1.251072049e+00,
    -1.240747213e+00, -1.234220743e+00, -1.223881721e+00, -1.217221856e+00,
    -1.210649729e+00, -1.201119065e+00, -1.194753885e+00, -1.185192108e+00,
    -1.179025173e+00, -1.172933459e+00, -1.163776278e+00, -1.157866359e+00,
    -1.148978591e+00, -1.142939925e+00, -1.134311318e+00, -1.128737688e+00,
    -1.120061994e+00, -1.114644170e+00, -1.106207609e+00, -1.100661159e+00,
    -1.092726707e+00, -1.087327003e+00, -1.079335332e+00, -1.074077725e+00,
    -1.066293478e+00, -1.061170459e+00, -1.053583026e+00, -1.048588037e+00,
    -1.041187763e+00, -1.036314487e+00, -1.028614521e+00, -1.021502018e+00,
    -1.016816020e+00, -1.009868264e+00, -1.004833817e+00, -9.980494976e-01,
    -9.909129143e-01, -9.865037203e-01, -9.795289040e-01, -9.730771780e-01,
    -9.683983326e-01, -9.620876908e-01, -9.554430842e-01, -9.509256482e-01,
    -9.444267154e-01, -9.380112886e-01, -9.340429306e-01, -9.277585149e-01,
    -9.215520620e-01, -9.173294306e-01, -9.112502933e-01, -9.048712254e-01,
    -8.989408016e-01, -8.949041367e-01, -8.890901208e-01, -8.833428621e-01,
    -8.773080707e-01, -8.734416366e-01, -8.675243855e-01, -8.620184660e-01,
    -8.562340736e-01, -8.505159020e-01, -8.468504548e-01, -8.412380219e-01,
    -8.356878161e-01, -8.301985860e-01, -8.247689605e-01, -8.193976879e-01,
    -8.159526587e-01, -8.106746674e-01, -8.054519296e-01, -7.999807000e-01,
    -7.948679328e-01, -7.895107269e-01, -7.845033407e-01, -7.792554498e-01,
    -7.760753036e-01, -7.709147334e-01, -7.658068538e-01, -7.610301971e-01,
    -7.560217977e-01, -7.510631084e-01, -7.461530566e-01, -7.412908077e-01,
    -7.364753485e-01, -7.314421535e-01, -7.267202139e-01, -7.220424414e-01,
    -7.174080014e-01, -7.125622630e-01, -7.080144882e-01, -7.032585144e-01,
    -6.985473037e-01, -6.941246986e-01, -6.892561316e-01, -6.849145889e-01,
    -6.806104183e-01, -6.758710146e-01, -6.716436744e-01, -6.669880748e-01,
    -6.623755097e-01, -6.582603455e-01, -6.537271738e-01, -6.492347121e-01,
    -6.452258825e-01, -6.408088803e-01, -6.364305019e-01, -6.320902705e-01,
    -6.277872920e-01, -6.235210299e-01, -6.180288196e-01, -6.138446331e-01,
    -6.096953154e-01, -6.055800319e-01, -6.014983058e-01, -5.974497199e-01,
    -5.934336782e-01, -5.890529156e-01, -5.839246511e-01, -5.796260834e-01,
    -5.757501125e-01, -5.715209246e-01, -5.677070618e-01, -5.635449886e-01,
    -5.597913265e-01, -5.545829535e-01, -5.505282879e-01, -5.468706489e-01,
    -5.428779125e-01, -5.389168262e-01, -5.339202881e-01, -5.300292373e-01,
    -5.261682272e-01, -5.223367810e-01, -5.185344815e-01, -5.133956671e-01,
    -5.096604824e-01, -5.059530735e-01, -5.022729635e-01, -4.986196458e-01,
    -4.936805069e-01, -4.897640347e-01, -4.862006307e-01, -4.823421836e-01,
    -4.775604010e-01, -4.740827084e-01, -4.703162014e-01, -4.656476974e-01,
    -4.619439840e-01, -4.582674205e-01, -4.546177685e-01, -4.500928521e-01,
    -4.465022087e-01, -4.429371059e-01, -4.393972456e-01, -4.347161353e-01,
    -4.312338531e-01, -4.274884760e-01, -4.229170978e-01, -4.195156395e-01,
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])