diff --git a/lib/node_modules/@stdlib/math/base/special/erfcinv/lib/main.js b/lib/node_modules/@stdlib/math/base/special/erfcinv/lib/main.js index ff743d891c3a..643603c502b7 100644 --- a/lib/node_modules/@stdlib/math/base/special/erfcinv/lib/main.js +++ b/lib/node_modules/@stdlib/math/base/special/erfcinv/lib/main.js @@ -43,6 +43,7 @@ var rationalFcnR2 = require( './rational_p2q2.js' ); var rationalFcnR3 = require( './rational_p3q3.js' ); var rationalFcnR4 = require( './rational_p4q4.js' ); var rationalFcnR5 = require( './rational_p5q5.js' ); +var rationalFcnR6 = require( './rational_p6q6.js' ); // VARIABLES // @@ -52,6 +53,7 @@ var Y2 = 2.249481201171875; var Y3 = 8.07220458984375e-1; var Y4 = 9.3995571136474609375e-1; var Y5 = 9.8362827301025390625e-1; +var Y6 = 9.9714565277099609375e-1; // MAIN // @@ -214,9 +216,15 @@ function erfcinv( x ) { return sign * ( (Y4*q) + (r*q) ); } // q < 18 - qs = q - 6.0; - r = rationalFcnR5( qs ); - return sign * ( (Y5*q) + (r*q) ); + if ( q < 18.0 ) { + qs = q - 6.0; + r = rationalFcnR5( qs ); + return sign * ( (Y5*q) + (r*q) ); + } + // q < 44 (the smallest double gives `q = 27.28...`) + qs = q - 18.0; + r = rationalFcnR6( qs ); + return sign * ( (Y6*q) + (r*q) ); } diff --git a/lib/node_modules/@stdlib/math/base/special/erfcinv/lib/rational_p1q1.js b/lib/node_modules/@stdlib/math/base/special/erfcinv/lib/rational_p1q1.js index b2efa93ed4c5..c463eeb15699 100644 --- a/lib/node_modules/@stdlib/math/base/special/erfcinv/lib/rational_p1q1.js +++ b/lib/node_modules/@stdlib/math/base/special/erfcinv/lib/rational_p1q1.js @@ -1,7 +1,7 @@ /** * @license Apache-2.0 * -* Copyright (c) 2022 The Stdlib Authors. +* Copyright (c) 2026 The Stdlib Authors. * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. diff --git a/lib/node_modules/@stdlib/math/base/special/erfcinv/lib/rational_p2q2.js b/lib/node_modules/@stdlib/math/base/special/erfcinv/lib/rational_p2q2.js index 4a8f2b5fc65a..369a544a0333 100644 --- a/lib/node_modules/@stdlib/math/base/special/erfcinv/lib/rational_p2q2.js +++ b/lib/node_modules/@stdlib/math/base/special/erfcinv/lib/rational_p2q2.js @@ -1,7 +1,7 @@ /** * @license Apache-2.0 * -* Copyright (c) 2022 The Stdlib Authors. +* Copyright (c) 2026 The Stdlib Authors. * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. diff --git a/lib/node_modules/@stdlib/math/base/special/erfcinv/lib/rational_p3q3.js b/lib/node_modules/@stdlib/math/base/special/erfcinv/lib/rational_p3q3.js index d663453bfcee..35052cf0684e 100644 --- a/lib/node_modules/@stdlib/math/base/special/erfcinv/lib/rational_p3q3.js +++ b/lib/node_modules/@stdlib/math/base/special/erfcinv/lib/rational_p3q3.js @@ -1,7 +1,7 @@ /** * @license Apache-2.0 * -* Copyright (c) 2022 The Stdlib Authors. +* Copyright (c) 2026 The Stdlib Authors. * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. diff --git a/lib/node_modules/@stdlib/math/base/special/erfcinv/lib/rational_p4q4.js b/lib/node_modules/@stdlib/math/base/special/erfcinv/lib/rational_p4q4.js index 3cc8919fc59f..ac0ab64c8112 100644 --- a/lib/node_modules/@stdlib/math/base/special/erfcinv/lib/rational_p4q4.js +++ b/lib/node_modules/@stdlib/math/base/special/erfcinv/lib/rational_p4q4.js @@ -1,7 +1,7 @@ /** * @license Apache-2.0 * -* Copyright (c) 2022 The Stdlib Authors. +* Copyright (c) 2026 The Stdlib Authors. * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. diff --git a/lib/node_modules/@stdlib/math/base/special/erfcinv/lib/rational_p5q5.js b/lib/node_modules/@stdlib/math/base/special/erfcinv/lib/rational_p5q5.js index 00e5c1dd3d2b..26aab9baf352 100644 --- a/lib/node_modules/@stdlib/math/base/special/erfcinv/lib/rational_p5q5.js +++ b/lib/node_modules/@stdlib/math/base/special/erfcinv/lib/rational_p5q5.js @@ -1,7 +1,7 @@ /** * @license Apache-2.0 * -* Copyright (c) 2022 The Stdlib Authors. +* Copyright (c) 2026 The Stdlib Authors. * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. diff --git a/lib/node_modules/@stdlib/math/base/special/erfcinv/lib/rational_p6q6.js b/lib/node_modules/@stdlib/math/base/special/erfcinv/lib/rational_p6q6.js new file mode 100644 index 000000000000..7031e18ad85a --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/erfcinv/lib/rational_p6q6.js @@ -0,0 +1,64 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +/* This is a generated file. Do not edit directly. */ +'use strict'; + +// MAIN // + +/** +* Evaluates a rational function (i.e., the ratio of two polynomials described by the coefficients stored in \\(P\\) and \\(Q\\)). +* +* ## Notes +* +* - Coefficients should be sorted in ascending degree. +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @private +* @param {number} x - value at which to evaluate the rational function +* @returns {number} evaluated rational function +*/ +function evalrational( x ) { + var ax; + var s1; + var s2; + if ( x === 0.0 ) { + return -0.002497821279189813; + } + if ( x < 0.0 ) { + ax = -x; + } else { + ax = x; + } + if ( ax <= 1.0 ) { + s1 = -0.002497821279189813 + (x * (-0.00000779190719229054 + (x * (0.000025472303741302746 + (x * (0.0000016239777734251093 + (x * (3.963410113048012e-8 + (x * (4.116328311909442e-10 + (x * (1.4559628671867504e-12 + (x * -1.1676501239718427e-18))))))))))))); // eslint-disable-line max-len + s2 = 1.0 + (x * (0.2071231122144225 + (x * (0.01694108381209759 + (x * (0.0006905382656226846 + (x * (0.000014500735981823264 + (x * (1.4443775662814415e-7 + (x * (5.097612765997785e-10 + (x * 0.0))))))))))))); // eslint-disable-line max-len + } else { + x = 1.0 / x; + s1 = -1.1676501239718427e-18 + (x * (1.4559628671867504e-12 + (x * (4.116328311909442e-10 + (x * (3.963410113048012e-8 + (x * (0.0000016239777734251093 + (x * (0.000025472303741302746 + (x * (-0.00000779190719229054 + (x * -0.002497821279189813))))))))))))); // eslint-disable-line max-len + s2 = 0.0 + (x * (5.097612765997785e-10 + (x * (1.4443775662814415e-7 + (x * (0.000014500735981823264 + (x * (0.0006905382656226846 + (x * (0.01694108381209759 + (x * (0.2071231122144225 + (x * 1.0))))))))))))); // eslint-disable-line max-len + } + return s1 / s2; +} + + +// EXPORTS // + +module.exports = evalrational; diff --git a/lib/node_modules/@stdlib/math/base/special/erfcinv/scripts/evalrational.js b/lib/node_modules/@stdlib/math/base/special/erfcinv/scripts/evalrational.js index f9a0b4b228ce..0bb33e9ff5ac 100644 --- a/lib/node_modules/@stdlib/math/base/special/erfcinv/scripts/evalrational.js +++ b/lib/node_modules/@stdlib/math/base/special/erfcinv/scripts/evalrational.js @@ -163,6 +163,27 @@ var Q5 = [ 0.0 ]; +var P6 = [ + -2.4978212791898131227e-3, + -7.79190719229053954292e-6, + 2.54723037413027451751e-5, + 1.62397777342510920873e-6, + 3.96341011304801168516e-8, + 4.11632831190944208473e-10, + 1.45596286718675035587e-12, + -1.16765012397184275695e-18 +]; +var Q6 = [ + 1.0, + 2.07123112214422517181e-1, + 1.69410838120975906478e-2, + 6.90538265622684595676e-4, + 1.45007359818232637924e-5, + 1.44437756628144157666e-7, + 5.09761276599778486139e-10, + 0.0 +]; + // Header to add to output files: var header = licenseHeader( 'Apache-2.0', 'js', { 'year': currentYear(), @@ -236,6 +257,10 @@ function main() { str = header + compile( P5, Q5 ); writeFileSync( fpath, str, opts ); + fpath = resolve( __dirname, '..', 'lib', 'rational_p6q6.js' ); + str = header + compile( P6, Q6 ); + writeFileSync( fpath, str, opts ); + copts = { 'dtype': 'double', 'name': '' @@ -264,6 +289,10 @@ function main() { str = compileC( P5, Q5, copts ); file = insert( file, copts.name, str ); + copts.name = 'rational_p6q6'; + str = compileC( P6, Q6, copts ); + file = insert( file, copts.name, str ); + writeFileSync( fpath, file, opts ); } diff --git a/lib/node_modules/@stdlib/math/base/special/erfcinv/src/main.c b/lib/node_modules/@stdlib/math/base/special/erfcinv/src/main.c index ee0660485870..3896b90a97b2 100644 --- a/lib/node_modules/@stdlib/math/base/special/erfcinv/src/main.c +++ b/lib/node_modules/@stdlib/math/base/special/erfcinv/src/main.c @@ -43,6 +43,7 @@ static const double Y2 = 2.249481201171875; static const double Y3 = 8.07220458984375e-1; static const double Y4 = 9.3995571136474609375e-1; static const double Y5 = 9.8362827301025390625e-1; +static const double Y6 = 9.9714565277099609375e-1; /* Begin auto-generated functions. The following functions are auto-generated. Do not edit directly. */ @@ -251,6 +252,47 @@ static double rational_p5q5( const double x ) { // END: rational_p5q5 +// BEGIN: rational_p6q6 + +/** +* Evaluates a rational function (i.e., the ratio of two polynomials described by the coefficients stored in \\(P\\) and \\(Q\\)). +* +* ## Notes +* +* - Coefficients should be sorted in ascending degree. +* - The implementation uses [Horner's rule][horners-method] for efficient computation. +* +* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method +* +* @param x value at which to evaluate the rational function +* @return evaluated rational function +*/ +static double rational_p6q6( const double x ) { + double ax; + double ix; + double s1; + double s2; + if ( x == 0.0 ) { + return -0.002497821279189813; + } + if ( x < 0.0 ) { + ax = -x; + } else { + ax = x; + } + if ( ax <= 1.0 ) { + s1 = -0.002497821279189813 + (x * (-0.00000779190719229054 + (x * (0.000025472303741302746 + (x * (0.0000016239777734251093 + (x * (3.963410113048012e-8 + (x * (4.116328311909442e-10 + (x * (1.4559628671867504e-12 + (x * -1.1676501239718427e-18))))))))))))); + s2 = 1.0 + (x * (0.2071231122144225 + (x * (0.01694108381209759 + (x * (0.0006905382656226846 + (x * (0.000014500735981823264 + (x * (1.4443775662814415e-7 + (x * (5.097612765997785e-10 + (x * 0.0))))))))))))); + } else { + ix = 1.0 / x; + s1 = -1.1676501239718427e-18 + (ix * (1.4559628671867504e-12 + (ix * (4.116328311909442e-10 + (ix * (3.963410113048012e-8 + (ix * (0.0000016239777734251093 + (ix * (0.000025472303741302746 + (ix * (-0.00000779190719229054 + (ix * -0.002497821279189813))))))))))))); + s2 = 0.0 + (ix * (5.097612765997785e-10 + (ix * (1.4443775662814415e-7 + (ix * (0.000014500735981823264 + (ix * (0.0006905382656226846 + (ix * (0.01694108381209759 + (ix * (0.2071231122144225 + (ix * 1.0))))))))))))); + } + return s1 / s2; +} + +// END: rational_p6q6 + /* End auto-generated functions. */ /** @@ -396,7 +438,13 @@ double stdlib_base_erfcinv( const double x ) { return sign * ( ( Y4 * q ) + ( r * q ) ); } // q < 18 - qs = q - 6.0; - r = rational_p5q5( qs ); - return sign * ( ( Y5 * q ) + ( r * q ) ); + if ( q < 18.0 ) { + qs = q - 6.0; + r = rational_p5q5( qs ); + return sign * ( ( Y5 * q ) + ( r * q ) ); + } + // q < 44 (the smallest double gives `q = 27.28...`) + qs = q - 18.0; + r = rational_p6q6( qs ); + return sign * ( ( Y6 * q ) + ( r * q ) ); } diff --git a/lib/node_modules/@stdlib/math/base/special/erfcinv/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/math/base/special/erfcinv/test/fixtures/julia/runner.jl index e071c5a890b7..d75e66ab5aa8 100644 --- a/lib/node_modules/@stdlib/math/base/special/erfcinv/test/fixtures/julia/runner.jl +++ b/lib/node_modules/@stdlib/math/base/special/erfcinv/test/fixtures/julia/runner.jl @@ -20,7 +20,7 @@ import JSON using SpecialFunctions """ - gen( x, filepath ) + gen( x, filepath ) Generate fixture data and write to file. @@ -53,6 +53,35 @@ function gen( x, filepath ) close( outfile ); end +""" + gen_tiny( x, filepath ) + +Generate fixture data for tiny `x` in extended precision and write to file. + +# Arguments + +* `x`: domain +* `filepath::AbstractString`: filepath of the output file +""" +function gen_tiny( x, filepath ) + y = Array{Float64}( undef, length(x) ); + setprecision( BigFloat, 2048 ) do + for i in eachindex(x) + y[i] = Float64( erfcinv( BigFloat( x[i] ) ) ); + end + end + + data = Dict([ + ("x", x), + ("expected", y) + ]); + + outfile = open( filepath, "w" ); + write( outfile, JSON.json(data) ); + write( outfile, "\n" ); + close( outfile ); +end + # Get the filename: file = @__FILE__; @@ -93,3 +122,8 @@ gen( x, out ); x = range( 1.9999999999999998, stop = 2, length = 500 ); out = joinpath( dir, "x_1.9999..8_2.json" ); gen( x, out ); + +# Tiny values, `sqrt(-ln(x)) >= 6` (log-spaced down to the smallest subnormal): +x = vcat( exp10.( range( -15.0, stop = -323.0, length = 1000 ) ), [ 5.0e-324 ] ); +out = joinpath( dir, "x_tiny.json" ); +gen_tiny( x, out ); diff --git a/lib/node_modules/@stdlib/math/base/special/erfcinv/test/fixtures/julia/x_tiny.json b/lib/node_modules/@stdlib/math/base/special/erfcinv/test/fixtures/julia/x_tiny.json new file mode 100644 index 000000000000..6aff932ca49c --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/erfcinv/test/fixtures/julia/x_tiny.json @@ -0,0 +1 @@ +{"expected":[5.675846347467647,5.737133851564973,5.797791678865005,5.8578386841568495,5.917292804061603,5.976171118239097,6.0344899054585674,6.092264695049486,6.149510314188598,6.206240931427069,6.262470096816168,6.318210778950291,6.373475399211453,6.428275863468978,6.4826235914613894,6.536529544064012,6.590004248625021,6.643057822534304,6.6956999951732845,6.747940128379383,6.7997872355459625,6.851249999467182,6.902336789026957,6.953055674822107,7.003414443801612,7.053420612996541,7.1030814424086675,7.152403947119838,7.201394908678843,7.250060885817703,7.29840822454497,7.346443067659666,7.3941713637259525,7.4415988755453775,7.488731188160599,7.535573716421844,7.582131712144901,7.628410270887251,7.674414338366911,7.720148716546719,7.7656180694051065,7.810826928412852,7.855779697733899,7.900480659167033,7.944933976843981,7.989143701698467,8.033113775719682,8.076848036002737,8.120350218607816,8.163623962238931,8.206672811752469,8.249500221505059,8.29210955854965,8.334504105688094,8.376687064388065,8.418661557571568,8.46043063228188,8.501997262235358,8.543364350264069,8.584534730654964,8.625511171390826,8.666296376298043,8.706892987105833,8.747303585421395,8.787530694625096,8.827576781689634,8.867444258926875,8.907135485665805,8.946652769864931,8.985998369662214,9.02517449486545,9.064183308385887,9.103026927617691,9.14170742576573,9.180226833124042,9.21858713830717,9.256790289436506,9.294838195283615,9.332732726372427,9.370475716042101,9.408068961472248,9.445514224672147,9.482813233435461,9.519967682261939,9.556979233247455,9.593849516943736,9.630580133189017,9.667172651910784,9.703628613901813,9.739949531570495,9.776136889666565,9.812192145983134,9.848116732036024,9.88391205372126,9.919579491951593,9.955120403272833,9.990536120460813,10.025827953099682,10.06099718814226,10.096045090453115,10.130972903335026,10.165781849039423,10.200473129261418,10.235047925619991,10.269507400123842,10.303852695623474,10.338084936249956,10.372205227840874,10.406214658353912,10.440114298268492,10.473905200975912,10.507588403158346,10.541164925157142,10.574635771330737,10.60800193040257,10.641264375799334,10.67442406597987,10.70748194475505,10.740438941598917,10.773295971951397,10.806053937512841,10.83871372653068,10.87127621407844,10.903742262327366,10.936112720810895,10.968388426682205,11.000570204965058,11.032658868798162,11.064655219673226,11.096560047666943,11.128374131667055,11.16009823959272,11.191733128609307,11.223279545337842,11.254738226059223,11.286109896913398,11.317395274093633,11.348595064036026,11.3797099636044,11.41074066027074,11.441687832291258,11.472552148878261,11.503334270367906,11.534034848383998,11.564654525997902,11.595193937884723,11.625653710475833,11.656034462107854,11.686336803168208,11.716561336237312,11.746708656227527,11.77677935051895,11.806773999092115,11.836693174657738,11.86653744278351,11.896307362018108,11.926003484012416,11.95562635363809,11.985176509103518,12.014654482067236,12.04406079774887,12.073395975037698,12.10266052659885,12.13185495897723,12.160979772699244,12.190035462372334,12.219022516782422,12.24794141898931,12.276792646420065,12.305576670960466,12.334293959044553,12.362944971742316,12.391530164845593,12.420049988952192,12.448504889548325,12.476895307089334,12.505221677078813,12.533484430146128,12.561683992122388,12.589820784114895,12.617895222580122,12.645907719395252,12.673858681928296,12.701748513106855,12.729577611485524,12.757346371312003,12.785055182591913,12.812704431152373,12.840294498704365,12.867825762903891,12.89529859741198,12.922713371953556,12.950070452375193,12.977370200701788,13.004612975192178,13.031799130393713,13.058929017195824,13.086002982882599,13.11302137118439,13.139984522328481,13.166892773088822,13.193746456834871,13.220545903579541,13.247291440026292,13.27398338961536,13.300622072569197,13.32720780593705,13.353740903638794,13.380221676507965,13.406650432334045,13.433027475904,13.459353109043098,13.48562763065502,13.51185133676126,13.538024520539858,13.564147472363471,13.590220479836775,13.616243827833241,13.64221779853128,13.668142671449793,13.694018723483076,13.719846228935198,13.745625459553755,13.771356684563086,13.797040170696928,13.822676182230522,13.848264981012218,13.873806826494521,13.899301975764653,13.924750683574619,13.95015320237076,13.975509782322854,14.00082067135273,14.02608611516243,14.051306357261907,14.076481638996297,14.101612199572747,14.12669827608682,14.151740103548475,14.17673791490765,14.201691941079435,14.226602410968855,14.25146955149526,14.276293587616347,14.301074742351796,14.325813236806557,14.350509290193763,14.375163119857303,14.399774941294048,14.42434496817573,14.448873412370506,14.473360483964175,14.497806391281093,14.522211340904768,14.546575537698136,14.570899184823551,14.59518248376247,14.619425634334846,14.643628834718232,14.667792281466607,14.691916169528929,14.71600069226741,14.740046041475523,14.764052407395761,14.788019978737116,14.81194894269233,14.835839484954878,14.859691789735717,14.883506039779796,14.9072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diff --git a/lib/node_modules/@stdlib/math/base/special/erfcinv/test/test.js b/lib/node_modules/@stdlib/math/base/special/erfcinv/test/test.js index 4fbb3c761ec8..9ded76144af0 100644 --- a/lib/node_modules/@stdlib/math/base/special/erfcinv/test/test.js +++ b/lib/node_modules/@stdlib/math/base/special/erfcinv/test/test.js @@ -38,6 +38,7 @@ var x4 = require( './fixtures/julia/x_1.75_1.9998.json' ); var x5 = require( './fixtures/julia/x_0.0002_0.25.json' ); var x6 = require( './fixtures/julia/x_1.9998_1.9999..8.json' ); var x7 = require( './fixtures/julia/x_1.9999..8_2.json' ); +var x8 = require( './fixtures/julia/x_tiny.json' ); // TESTS // @@ -200,3 +201,18 @@ tape( 'the function evaluates the inverse complementary error function for `x` o } t.end(); }); + +tape( 'the function evaluates the inverse complementary error function for tiny `x`', function test( t ) { + var expected; + var x; + var y; + var i; + + expected = x8.expected; + x = x8.x; + for ( i = 0; i < x.length; i++ ) { + y = erfcinv( x[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'x: '+x[i]+'. y: '+y+'. E: '+expected[i] ); + } + t.end(); +}); diff --git a/lib/node_modules/@stdlib/math/base/special/erfcinv/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/erfcinv/test/test.native.js index 698e0dc5c65d..34c1337fd246 100644 --- a/lib/node_modules/@stdlib/math/base/special/erfcinv/test/test.native.js +++ b/lib/node_modules/@stdlib/math/base/special/erfcinv/test/test.native.js @@ -39,6 +39,7 @@ var x4 = require( './fixtures/julia/x_1.75_1.9998.json' ); var x5 = require( './fixtures/julia/x_0.0002_0.25.json' ); var x6 = require( './fixtures/julia/x_1.9998_1.9999..8.json' ); var x7 = require( './fixtures/julia/x_1.9999..8_2.json' ); +var x8 = require( './fixtures/julia/x_tiny.json' ); // VARIABLES // @@ -209,3 +210,18 @@ tape( 'the function evaluates the inverse complementary error function for `x` o } t.end(); }); + +tape( 'the function evaluates the inverse complementary error function for tiny `x`', opts, function test( t ) { + var expected; + var x; + var y; + var i; + + expected = x8.expected; + x = x8.x; + for ( i = 0; i < x.length; i++ ) { + y = erfcinv( x[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 2 ), true, 'x: '+x[i]+'. y: '+y+'. E: '+expected[i] ); + } + t.end(); +});