evalpoly.js (7580B)
1 /** 2 * @license Apache-2.0 3 * 4 * Copyright (c) 2019 The Stdlib Authors. 5 * 6 * Licensed under the Apache License, Version 2.0 (the "License"); 7 * you may not use this file except in compliance with the License. 8 * You may obtain a copy of the License at 9 * 10 * http://www.apache.org/licenses/LICENSE-2.0 11 * 12 * Unless required by applicable law or agreed to in writing, software 13 * distributed under the License is distributed on an "AS IS" BASIS, 14 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 15 * See the License for the specific language governing permissions and 16 * limitations under the License. 17 */ 18 19 /* 20 * This script compiles modules for evaluating polynomial functions. If any polynomial coefficients change, this script should be rerun to update the compiled files. 21 */ 22 'use strict'; 23 24 // MODULES // 25 26 var resolve = require( 'path' ).resolve; 27 var writeFileSync = require( '@stdlib/fs/write-file' ).sync; 28 var licenseHeader = require( '@stdlib/_tools/licenses/header' ); 29 var compile = require( './../../../../base/tools/evalpoly-compile' ); 30 31 32 // VARIABLES // 33 34 // The tables below are from Fukushima, Toshio. 2009. "Fast computation of complete elliptic integrals and Jacobian elliptic functions." _Celestial Mechanics and Dynamical Astronomy_ 105 (4): 305. doi:[10.1007/s10569-009-9228-z](https://doi.org/10.1007/s10569-009-9228-z). 35 36 // Table 2 for expansion about x = 0.05: 37 var P1 = [ 38 1.550973351780472328, 39 -0.400301020103198524, 40 -0.078498619442941939, 41 -0.034318853117591992, 42 -0.019718043317365499, 43 -0.013059507731993309, 44 -0.009442372874146547, 45 -0.007246728512402157, 46 -0.005807424012956090, 47 -0.004809187786009338 48 ]; 49 50 // Table 3 for expansion about 0.15: 51 var P2 = [ 52 1.510121832092819728, 53 -0.417116333905867549, 54 -0.090123820404774569, 55 -0.043729944019084312, 56 -0.027965493064761785, 57 -0.020644781177568105, 58 -0.016650786739707238, 59 -0.014261960828842520, 60 -0.012759847429264803, 61 -0.011799303775587354, 62 -0.011197445703074968 63 ]; 64 65 // Table 4 for expansion about 0.25: 66 var P3 = [ 67 1.467462209339427155, 68 -0.436576290946337775, 69 -0.105155557666942554, 70 -0.057371843593241730, 71 -0.041391627727340220, 72 -0.034527728505280841, 73 -0.031495443512532783, 74 -0.030527000890325277, 75 -0.030916984019238900, 76 -0.032371395314758122, 77 -0.034789960386404158 78 ]; 79 80 // Table 5 for expansion about 0.35: 81 var P4 = [ 82 1.422691133490879171, 83 -0.459513519621048674, 84 -0.125250539822061878, 85 -0.078138545094409477, 86 -0.064714278472050002, 87 -0.062084339131730311, 88 -0.065197032815572477, 89 -0.072793895362578779, 90 -0.084959075171781003, 91 -0.102539850131045997, 92 -0.127053585157696036, 93 -0.160791120691274606 94 ]; 95 96 // Table 6 for expansion about 0.45: 97 var P5 = [ 98 1.375401971871116291, 99 -0.487202183273184837, 100 -0.153311701348540228, 101 -0.111849444917027833, 102 -0.108840952523135768, 103 -0.122954223120269076, 104 -0.152217163962035047, 105 -0.200495323642697339, 106 -0.276174333067751758, 107 -0.393513114304375851, 108 -0.575754406027879147, 109 -0.860523235727239756, 110 -1.308833205758540162 111 ]; 112 113 // Table 7 for expansion about 0.55: 114 var P6 = [ 115 1.325024497958230082, 116 -0.521727647557566767, 117 -0.194906430482126213, 118 -0.171623726822011264, 119 -0.202754652926419141, 120 -0.278798953118534762, 121 -0.420698457281005762, 122 -0.675948400853106021, 123 -1.136343121839229244, 124 -1.976721143954398261, 125 -3.531696773095722506, 126 -6.446753640156048150, 127 -11.97703130208884026 128 ]; 129 130 // Table 8 for expansion about 0.65: 131 var P7 = [ 132 1.270707479650149744, 133 -0.566839168287866583, 134 -0.262160793432492598, 135 -0.292244173533077419, 136 -0.440397840850423189, 137 -0.774947641381397458, 138 -1.498870837987561088, 139 -3.089708310445186667, 140 -6.667595903381001064, 141 -14.89436036517319078, 142 -34.18120574251449024, 143 -80.15895841905397306, 144 -191.3489480762984920, 145 -463.5938853480342030, 146 -1137.380822169360061 147 ]; 148 149 // Table 9 for expansion about 0.75: 150 var P8 = [ 151 1.211056027568459525, 152 -0.630306413287455807, 153 -0.387166409520669145, 154 -0.592278235311934603, 155 -1.237555584513049844, 156 -3.032056661745247199, 157 -8.181688221573590762, 158 -23.55507217389693250, 159 -71.04099935893064956, 160 -221.8796853192349888, 161 -712.1364793277635425, 162 -2336.125331440396407, 163 -7801.945954775964673, 164 -26448.19586059191933, 165 -90799.48341621365251, 166 -315126.0406449163424, 167 -1104011.344311591159 168 ]; 169 170 // Table 10 for expansion about 0.825: 171 var P9 = [ 172 1.161307152196282836, 173 -0.701100284555289548, 174 -0.580551474465437362, 175 -1.243693061077786614, 176 -3.679383613496634879, 177 -12.81590924337895775, 178 -49.25672530759985272, 179 -202.1818735434090269, 180 -869.8602699308701437, 181 -3877.005847313289571, 182 -17761.70710170939814, 183 -83182.69029154232061, 184 -396650.4505013548170, 185 -1920033.413682634405 186 ]; 187 188 // Table 11 for expansion about 0.875: 189 var P10 = [ 190 1.124617325119752213, 191 -0.770845056360909542, 192 -0.844794053644911362, 193 -2.490097309450394453, 194 -10.23971741154384360, 195 -49.74900546551479866, 196 -267.0986675195705196, 197 -1532.665883825229947, 198 -9222.313478526091951, 199 -57502.51612140314030, 200 -368596.1167416106063, 201 -2415611.088701091428, 202 -16120097.81581656797, 203 -109209938.5203089915, 204 -749380758.1942496220, 205 -5198725846.725541393, 206 -36409256888.12139973 207 ]; 208 209 // Table 2 for the expansion of K(m) around 0.05 210 var P11 = [ 211 1.591003453790792180, 212 0.416000743991786912, 213 0.245791514264103415, 214 0.179481482914906162, 215 0.144556057087555150, 216 0.123200993312427711, 217 0.108938811574293531, 218 0.098853409871592910, 219 0.091439629201749751, 220 0.085842591595413900, 221 0.081541118718303215 222 ]; 223 224 // Table 2 for the expansion of E(m) around 0.05 225 var P12 = [ 226 1.550973351780472328, 227 -0.400301020103198524, 228 -0.078498619442941939, 229 -0.034318853117591992, 230 -0.019718043317365499, 231 -0.013059507731993309, 232 -0.009442372874146547, 233 -0.007246728512402157, 234 -0.005807424012956090, 235 -0.004809187786009338 236 ]; 237 238 // Header to add to output files: 239 var header = licenseHeader( 'Apache-2.0', 'js', { 240 'year': ( new Date() ).getFullYear(), 241 'copyright': 'The Stdlib Authors' 242 }); 243 header += '\n/* This is a generated file. Do not edit directly. */\n'; 244 245 246 // MAIN // 247 248 /** 249 * Main execution sequence. 250 * 251 * @private 252 */ 253 function main() { 254 var fpath; 255 var opts; 256 var str; 257 258 opts = { 259 'encoding': 'utf8' 260 }; 261 262 fpath = resolve( __dirname, '..', 'lib', 'poly_p1.js' ); 263 str = header + compile( P1 ); 264 writeFileSync( fpath, str, opts ); 265 266 fpath = resolve( __dirname, '..', 'lib', 'poly_p2.js' ); 267 str = header + compile( P2 ); 268 writeFileSync( fpath, str, opts ); 269 270 fpath = resolve( __dirname, '..', 'lib', 'poly_p3.js' ); 271 str = header + compile( P3 ); 272 writeFileSync( fpath, str, opts ); 273 274 fpath = resolve( __dirname, '..', 'lib', 'poly_p4.js' ); 275 str = header + compile( P4 ); 276 writeFileSync( fpath, str, opts ); 277 278 fpath = resolve( __dirname, '..', 'lib', 'poly_p5.js' ); 279 str = header + compile( P5 ); 280 writeFileSync( fpath, str, opts ); 281 282 fpath = resolve( __dirname, '..', 'lib', 'poly_p6.js' ); 283 str = header + compile( P6 ); 284 writeFileSync( fpath, str, opts ); 285 286 fpath = resolve( __dirname, '..', 'lib', 'poly_p7.js' ); 287 str = header + compile( P7 ); 288 writeFileSync( fpath, str, opts ); 289 290 fpath = resolve( __dirname, '..', 'lib', 'poly_p8.js' ); 291 str = header + compile( P8 ); 292 writeFileSync( fpath, str, opts ); 293 294 fpath = resolve( __dirname, '..', 'lib', 'poly_p9.js' ); 295 str = header + compile( P9 ); 296 writeFileSync( fpath, str, opts ); 297 298 fpath = resolve( __dirname, '..', 'lib', 'poly_p10.js' ); 299 str = header + compile( P10 ); 300 writeFileSync( fpath, str, opts ); 301 302 fpath = resolve( __dirname, '..', 'lib', 'poly_p11.js' ); 303 str = header + compile( P11 ); 304 writeFileSync( fpath, str, opts ); 305 306 fpath = resolve( __dirname, '..', 'lib', 'poly_p12.js' ); 307 str = header + compile( P12 ); 308 writeFileSync( fpath, str, opts ); 309 } 310 311 main();