diff --git a/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/README.md b/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/README.md new file mode 100644 index 000000000000..f06c78d02d36 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/README.md @@ -0,0 +1,160 @@ + + +# Legendre Polynomial + +> Evaluate a [Legendre polynomial][legendre-polynomial]. + +
+ +The [Legendre polynomials][legendre-polynomial] $P_n(x)$ are classical orthogonal polynomials which are solutions to the Legendre differential equation + + + +```math +(1 - x^2) P_n''(x) - 2x P_n'(x) + n(n+1) P_n(x) = 0 +``` + + + + + +For **integer** non-negative $n$, they satisfy the three-term recurrence relation + + + +```math +(n+1) P_{n+1}(x) = (2n+1)\, x\, P_n(x) - n\, P_{n-1}(x) +``` + + + + + +with $P_0(x) = 1$ and $P_1(x) = x$. For **non-integer** $n$, the polynomial is generalized via the relation to the Gauss hypergeometric function + + + +```math +P_n(x) = {}_2F_1 \left( -n,\, n+1;\, 1;\, \tfrac{1-x}{2} \right) +``` + + + + + +
+ + + +
+ +## Usage + +```javascript +var legendrepoly = require( '@stdlib/math/base/special/legendre-polynomial' ); +``` + +#### legendrepoly( n, x ) + +Evaluates a [Legendre polynomial][legendre-polynomial] of degree `n` at a point `x`. + +```javascript +var v = legendrepoly( 1.0, 0.5 ); +// returns 0.5 + +v = legendrepoly( 2.0, 0.5 ); +// returns -0.125 +``` + +If `n` is not an integer, the polynomial is evaluated using the Gauss hypergeometric function. + +```javascript +var v = legendrepoly( 1.5, 0.5 ); +// returns ~0.172 +``` + +If provided `NaN` for any argument, the function returns `NaN`. + +```javascript +var v = legendrepoly( NaN, 0.5 ); +// returns NaN + +v = legendrepoly( 1.0, NaN ); +// returns NaN +``` + +
+ + + +
+ +## Examples + + + +```javascript +var uniform = require( '@stdlib/random/base/uniform' ); +var legendrepoly = require( '@stdlib/math/base/special/legendre-polynomial' ); + +var x; +var n; +var v; +var i; + +for ( i = 0; i < 100; i++ ) { + n = uniform( -50.0, 50.0 ); + x = uniform( -1.0, 1.0 ); + v = legendrepoly( n, x ); + console.log( 'P_%d(%d) = %d', n, x, v ); +} +``` + +
+ + + + + +
+ +
+ + + + + +
+ +[legendre-polynomial]: https://en.wikipedia.org/wiki/Legendre_polynomials + +
+ + diff --git a/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/benchmark/benchmark.js b/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/benchmark/benchmark.js new file mode 100644 index 000000000000..d97a810f2f09 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/benchmark/benchmark.js @@ -0,0 +1,54 @@ +/** +* @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. +*/ + +'use strict'; + +// MODULES // + +var bench = require( '@stdlib/bench' ); +var uniform = require( '@stdlib/random/array/uniform' ); +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var pkg = require( './../package.json' ).name; +var legendrepoly = require( './../lib' ); + + +// MAIN // + +bench( pkg, function benchmark( b ) { + var n; + var x; + var y; + var i; + + n = uniform( 100, -50.0, 50.0 ); + x = uniform( 100, -1.0, 1.0 ); + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + y = legendrepoly( n[ i%n.length ], x[ i%x.length ] ); + if ( isnan( y ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnan( y ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); +}); diff --git a/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/docs/types/index.d.ts b/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/docs/types/index.d.ts new file mode 100644 index 000000000000..dc46649085f8 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/docs/types/index.d.ts @@ -0,0 +1,45 @@ +/* +* @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. +*/ + +// TypeScript Version: 4.1 + +/** +* Evaluates a Legendre polynomial. +* +* @param n - degree of the polynomial +* @param x - evaluation point +* @returns polynomial value +* +* @example +* var v = legendrepoly( 1.0, 0.5 ); +* // returns 0.5 +* +* @example +* var v = legendrepoly( 2.0, 0.5 ); +* // returns -0.125 +* +* @example +* var v = legendrepoly( 1.5, 0.5 ); +* // returns ~0.172 +*/ +declare function legendrepoly( n: number, x: number ): number; + + +// EXPORTS // + +export = legendrepoly; diff --git a/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/docs/types/test.ts b/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/docs/types/test.ts new file mode 100644 index 000000000000..c6b68fd1bc08 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/docs/types/test.ts @@ -0,0 +1,52 @@ +/* +* @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. +*/ + +import legendrepoly = require( './index' ); + + +// TESTS // + +// The function returns a number... +{ + legendrepoly( 1.0, 0.5 ); // $ExpectType number + legendrepoly( 2.0, 0.5 ); // $ExpectType number + legendrepoly( 1.5, 0.5 ); // $ExpectType number +} + +// The compiler throws an error if the function is provided values other than two numbers... +{ + legendrepoly( true, 0.5 ); // $ExpectError + legendrepoly( false, 0.5 ); // $ExpectError + legendrepoly( '5', 0.5 ); // $ExpectError + legendrepoly( [], 0.5 ); // $ExpectError + legendrepoly( {}, 0.5 ); // $ExpectError + legendrepoly( ( x: number ): number => x, 0.5 ); // $ExpectError + + legendrepoly( 1.0, true ); // $ExpectError + legendrepoly( 1.0, false ); // $ExpectError + legendrepoly( 1.0, '5' ); // $ExpectError + legendrepoly( 1.0, [] ); // $ExpectError + legendrepoly( 1.0, {} ); // $ExpectError + legendrepoly( 1.0, ( x: number ): number => x ); // $ExpectError +} + +// The compiler throws an error if the function is provided insufficient arguments... +{ + legendrepoly(); // $ExpectError + legendrepoly( 1.0 ); // $ExpectError +} diff --git a/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/examples/index.js b/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/examples/index.js new file mode 100644 index 000000000000..936e26623425 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/examples/index.js @@ -0,0 +1,34 @@ +/** +* @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. +*/ + +'use strict'; + +var uniform = require( '@stdlib/random/base/uniform' ); +var legendrepoly = require( './../lib' ); + +var x; +var n; +var v; +var i; + +for ( i = 0; i < 100; i++ ) { + n = uniform( -50.0, 50.0 ); + x = uniform( -1.0, 1.0 ); + v = legendrepoly( n, x ); + console.log( 'P_%d(%d) = %d', n, x, v ); +} diff --git a/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/lib/index.js b/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/lib/index.js new file mode 100644 index 000000000000..cfc604a5377b --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/lib/index.js @@ -0,0 +1,46 @@ +/** +* @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. +*/ + +'use strict'; + +/** +* Evaluate a Legendre polynomial. +* +* @module @stdlib/math/base/special/legendre-polynomial +* +* @example +* var legendrepoly = require( '@stdlib/math/base/special/legendre-polynomial' ); +* +* var v = legendrepoly( 1.0, 0.5 ); +* // returns 0.5 +* +* v = legendrepoly( 0.0, 0.5 ); +* // returns 1.0 +* +* v = legendrepoly( 2.0, 0.5 ); +* // returns -0.125 +*/ + +// MODULES // + +var main = require( './main.js' ); + + +// EXPORTS // + +module.exports = main; diff --git a/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/lib/main.js b/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/lib/main.js new file mode 100644 index 000000000000..b205c43e78fa --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/lib/main.js @@ -0,0 +1,166 @@ +/** +* @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. +* +* +* ## Notice +* +* The following copyright, license, and long description were part of the original implementation available as part of [SciPy]{@link https://github.com/scipy/scipy/blob/fe5fd89f1d13791f8bee620e424fe8f91fbecb02/scipy/special/orthogonal_eval.pxd#L365}. The implementation has been modified for JavaScript. +* +* ```text +* Copyright (c) 2001-2002 Enthought, Inc. 2003-2025, SciPy Developers. +* All rights reserved. +* +* Redistribution and use in source and binary forms, with or without +* modification, are permitted provided that the following conditions +* are met: +* +* 1. Redistributions of source code must retain the above copyright +* notice, this list of conditions and the following disclaimer. +* +* 2. Redistributions in binary form must reproduce the above +* copyright notice, this list of conditions and the following +* disclaimer in the documentation and/or other materials provided +* with the distribution. +* +* 3. Neither the name of the copyright holder nor the names of its +* contributors may be used to endorse or promote products derived +* from this software without specific prior written permission. +* +* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR +* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT +* OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, +* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT +* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, +* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY +* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT +* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE +* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. +* ``` +*/ + +'use strict'; + +// MODULES // + +var isnan = require( '@stdlib/assert/is-nan' ); +var hyp2f1 = require( '@stdlib/math/base/special/hyp2f1' ); +var gamma = require( '@stdlib/math/base/special/gamma' ); +var abs = require( '@stdlib/math/base/special/abs' ); +var floor = require( '@stdlib/math/base/special/floor' ); + + +// MAIN // + +/** +* Evaluates a Legendre polynomial. +* +* @param {number} n - degree of the polynomial +* @param {number} x - evaluation point +* @returns {number} polynomial value +* +* @example +* var v = legendrepoly( 1.0, 0.5 ); +* // returns 0.5 +* +* @example +* var v = legendrepoly( 2.0, 0.5 ); +* // returns -0.125 +* +* @example +* var v = legendrepoly( -1.0, 0.5 ); +* // returns 1.0 +* +* @example +* var v = legendrepoly( NaN, 0.5 ); +* // returns NaN +*/ +function legendrepoly( n, x ) { + var nFloor; + var isInt; + var kk; + var d; + var g; + var a; + var b; + var c; + var p; + var k; + + if ( isnan( n ) || isnan( x ) ) { + return NaN; + } + + nFloor = floor( n ); + isInt = ( n === nFloor ); + + if ( !isInt ) { + a = -n; + b = n + 1.0; + c = 1.0; + g = 0.5 * ( 1.0 - x ); + return hyp2f1( a, b, c, g ); + } + + // For integer n, we use the recurrence relation... + if ( n < 0.0 ) { + n = -n - 1.0; + } + + if ( n === 0.0 ) { + return 1.0; + } + if ( n === 1.0 ) { + return x; + } + + if ( abs( x ) < 1e-5 ) { + // Power series rather than recurrence due to loss of precision + // http://functions.wolfram.com/Polynomials/LegendreP/02/ + a = floor( n / 2.0 ); + d = ( a % 2 === 0 ) ? 1.0 : -1.0; + if ( n === ( 2.0 * a ) ) { + d *= -2.0 / ( ( gamma( a + 1.0 ) * gamma( -0.5 ) ) / gamma( a + 0.5 ) ); + } else { + d *= ( 2.0 * x ) / ( ( gamma( a + 1.0 ) * gamma( 0.5 ) ) / gamma( a + 1.5 ) ); + } + p = 0.0; + for ( kk = 0; kk <= a; kk++ ) { + p += d; + d *= -2.0 * x * x * ( a - kk ) * ( ( 2.0 * n ) + 1.0 - ( 2.0 * a ) + ( 2.0 * kk ) ) / ( ( n + 1.0 - ( 2.0 * a ) + ( 2.0 * kk ) ) * ( n + 2.0 - ( 2.0 * a ) + ( 2.0 * kk ) ) ); + if ( abs( d ) === 1e-20 * abs( p ) ) { + break; + } + } + return p; + } + + d = x - 1.0; + p = x; + for ( kk = 0; kk < n - 1; kk++ ) { + k = kk + 1.0; + d = ( ( ( ( 2.0 * k ) + 1.0 ) / ( k + 1.0 ) ) * ( x - 1.0 ) * p ) + ( ( k / ( k + 1.0 ) ) * d ); + p += d; + } + return p; +} + + +// EXPORTS // + +module.exports = legendrepoly; diff --git a/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/package.json b/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/package.json new file mode 100644 index 000000000000..71093955388a --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/package.json @@ -0,0 +1,63 @@ +{ + "name": "@stdlib/math/base/special/legendre-polynomial", + "version": "0.0.0", + "description": "Evaluate a Legendre polynomial.", + "license": "Apache-2.0", + "author": { + "name": "The Stdlib Authors", + "url": "https://github.com/stdlib-js/stdlib/graphs/contributors" + }, + "contributors": [ + { + "name": "The Stdlib Authors", + "url": "https://github.com/stdlib-js/stdlib/graphs/contributors" + } + ], + "main": "./lib", + "directories": { + "benchmark": "./benchmark", + "doc": "./docs", + "example": "./examples", + "lib": "./lib", + "test": "./test" + }, + "types": "./docs/types", + "scripts": {}, + "homepage": "https://github.com/stdlib-js/stdlib", + "repository": { + "type": "git", + "url": "git://github.com/stdlib-js/stdlib.git" + }, + "bugs": { + "url": "https://github.com/stdlib-js/stdlib/issues" + }, + "dependencies": {}, + "devDependencies": {}, + "engines": { + "node": ">=0.10.0", + "npm": ">2.7.0" + }, + "os": [ + "aix", + "darwin", + "freebsd", + "linux", + "macos", + "openbsd", + "sunos", + "win32", + "windows" + ], + "keywords": [ + "stdlib", + "stdmath", + "math", + "mathematics", + "special function", + "special", + "function", + "legendre", + "polynomial", + "evaluate" + ] +} diff --git a/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/test/fixtures/python/decimals.json b/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/test/fixtures/python/decimals.json new file mode 100644 index 000000000000..22b95af97d6d --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/test/fixtures/python/decimals.json @@ -0,0 +1 @@ +{"n": [-20.0, -19.95995995995996, -19.91991991991992, -19.87987987987988, -19.83983983983984, -19.7997997997998, -19.75975975975976, -19.71971971971972, -19.67967967967968, -19.63963963963964, -19.5995995995996, -19.55955955955956, -19.51951951951952, -19.47947947947948, -19.43943943943944, -19.3993993993994, -19.35935935935936, -19.31931931931932, -19.27927927927928, -19.23923923923924, -19.1991991991992, -19.15915915915916, -19.11911911911912, -19.07907907907908, -19.03903903903904, -18.998998998999, -18.95895895895896, -18.91891891891892, -18.87887887887888, -18.83883883883884, -18.7987987987988, -18.75875875875876, -18.71871871871872, -18.67867867867868, -18.63863863863864, -18.5985985985986, -18.55855855855856, -18.51851851851852, -18.47847847847848, -18.43843843843844, -18.3983983983984, -18.35835835835836, -18.31831831831832, -18.27827827827828, -18.23823823823824, -18.1981981981982, -18.15815815815816, -18.11811811811812, -18.07807807807808, -18.03803803803804, -17.997997997998, -17.95795795795796, -17.91791791791792, -17.87787787787788, -17.83783783783784, -17.7977977977978, -17.75775775775776, -17.71771771771772, -17.67767767767768, -17.63763763763764, -17.5975975975976, -17.55755755755756, -17.51751751751752, -17.47747747747748, -17.43743743743744, -17.3973973973974, -17.35735735735736, -17.31731731731732, -17.27727727727728, -17.237237237237238, -17.197197197197198, -17.157157157157158, -17.117117117117118, -17.077077077077078, -17.037037037037038, -16.996996996996998, -16.956956956956958, -16.916916916916918, -16.876876876876878, -16.836836836836838, -16.796796796796798, -16.756756756756758, -16.716716716716718, -16.676676676676678, -16.636636636636638, -16.596596596596598, -16.556556556556558, -16.516516516516518, -16.476476476476478, -16.436436436436438, -16.396396396396398, -16.356356356356358, -16.316316316316318, -16.276276276276278, -16.236236236236238, -16.196196196196198, -16.156156156156158, -16.116116116116117, -16.076076076076077, -16.036036036036037, -15.995995995995996, -15.955955955955956, -15.915915915915916, -15.875875875875876, -15.835835835835836, -15.795795795795796, -15.755755755755755, -15.715715715715715, -15.675675675675675, -15.635635635635635, -15.595595595595595, -15.555555555555555, -15.515515515515515, -15.475475475475475, -15.435435435435435, -15.395395395395395, -15.355355355355355, -15.315315315315315, -15.275275275275275, -15.235235235235235, -15.195195195195195, -15.155155155155155, -15.115115115115115, -15.075075075075075, -15.035035035035035, -14.994994994994995, -14.954954954954955, -14.914914914914915, -14.874874874874875, -14.834834834834835, -14.794794794794795, -14.754754754754755, -14.714714714714715, -14.674674674674675, -14.634634634634635, -14.594594594594595, -14.554554554554555, -14.514514514514515, -14.474474474474475, -14.434434434434435, -14.394394394394395, -14.354354354354355, -14.314314314314315, -14.274274274274275, -14.234234234234235, -14.194194194194194, -14.154154154154154, -14.114114114114114, -14.074074074074074, -14.034034034034034, -13.993993993993994, -13.953953953953954, -13.913913913913914, -13.873873873873874, -13.833833833833834, -13.793793793793794, -13.753753753753754, -13.713713713713714, -13.673673673673674, -13.633633633633634, -13.593593593593594, -13.553553553553552, -13.513513513513512, -13.473473473473472, -13.433433433433432, -13.393393393393392, -13.353353353353352, -13.313313313313312, -13.273273273273272, -13.233233233233232, -13.193193193193192, -13.153153153153152, -13.113113113113112, -13.073073073073072, -13.033033033033032, -12.992992992992992, -12.952952952952952, -12.912912912912912, -12.872872872872872, -12.832832832832832, -12.792792792792792, -12.752752752752752, -12.712712712712712, -12.672672672672672, -12.632632632632632, -12.592592592592592, -12.552552552552552, -12.512512512512512, -12.472472472472472, -12.432432432432432, -12.392392392392392, -12.352352352352352, -12.312312312312311, -12.272272272272271, -12.232232232232231, -12.192192192192191, -12.152152152152151, -12.112112112112111, -12.072072072072071, -12.032032032032031, -11.991991991991991, -11.951951951951951, -11.911911911911911, -11.871871871871871, -11.831831831831831, -11.791791791791791, -11.751751751751751, -11.711711711711711, -11.671671671671671, -11.631631631631631, -11.591591591591591, -11.551551551551551, -11.511511511511511, -11.471471471471471, -11.431431431431431, -11.391391391391391, -11.35135135135135, -11.31131131131131, -11.27127127127127, -11.23123123123123, -11.19119119119119, -11.15115115115115, -11.11111111111111, -11.07107107107107, -11.03103103103103, -10.99099099099099, -10.95095095095095, -10.91091091091091, -10.87087087087087, -10.83083083083083, -10.79079079079079, -10.75075075075075, -10.71071071071071, -10.67067067067067, -10.63063063063063, -10.59059059059059, -10.55055055055055, -10.51051051051051, -10.47047047047047, -10.43043043043043, -10.39039039039039, -10.35035035035035, -10.31031031031031, -10.27027027027027, -10.23023023023023, -10.19019019019019, -10.15015015015015, -10.11011011011011, -10.07007007007007, -10.03003003003003, -9.98998998998999, -9.94994994994995, -9.90990990990991, -9.86986986986987, -9.82982982982983, -9.78978978978979, -9.74974974974975, -9.70970970970971, -9.66966966966967, -9.62962962962963, -9.58958958958959, -9.54954954954955, -9.50950950950951, -9.46946946946947, -9.42942942942943, -9.38938938938939, -9.34934934934935, -9.30930930930931, -9.26926926926927, -9.22922922922923, -9.18918918918919, -9.14914914914915, -9.10910910910911, -9.06906906906907, -9.02902902902903, -8.98898898898899, -8.94894894894895, -8.90890890890891, -8.86886886886887, -8.82882882882883, -8.78878878878879, -8.74874874874875, -8.70870870870871, -8.66866866866867, -8.62862862862863, -8.588588588588589, -8.548548548548549, -8.508508508508509, -8.468468468468469, -8.428428428428429, -8.388388388388389, -8.348348348348349, -8.308308308308309, -8.268268268268269, -8.228228228228229, -8.188188188188189, -8.148148148148149, -8.108108108108109, -8.068068068068069, -8.028028028028029, -7.987987987987989, -7.947947947947949, -7.907907907907909, -7.867867867867869, -7.827827827827829, -7.787787787787789, -7.7477477477477485, -7.7077077077077085, -7.6676676676676685, -7.6276276276276285, -7.5875875875875884, -7.547547547547548, -7.507507507507508, -7.467467467467468, -7.427427427427428, -7.387387387387388, -7.347347347347348, -7.307307307307308, -7.267267267267268, -7.227227227227228, -7.187187187187188, -7.147147147147146, -7.107107107107106, -7.067067067067066, -7.027027027027026, -6.986986986986986, -6.946946946946946, -6.906906906906906, -6.866866866866866, -6.826826826826826, -6.786786786786786, -6.746746746746746, -6.706706706706706, -6.666666666666666, -6.626626626626626, -6.586586586586586, -6.546546546546546, -6.506506506506506, -6.466466466466466, -6.426426426426426, -6.386386386386386, -6.346346346346346, -6.306306306306306, -6.266266266266266, -6.226226226226226, -6.186186186186186, -6.146146146146146, -6.106106106106106, -6.066066066066066, -6.026026026026026, -5.985985985985986, -5.945945945945946, -5.905905905905906, -5.865865865865866, -5.8258258258258255, -5.7857857857857855, -5.7457457457457455, -5.7057057057057055, -5.665665665665665, -5.625625625625625, -5.585585585585585, -5.545545545545545, -5.505505505505505, -5.465465465465465, -5.425425425425425, -5.385385385385385, -5.345345345345345, -5.305305305305305, -5.265265265265265, -5.225225225225225, -5.185185185185185, -5.145145145145145, -5.105105105105105, -5.065065065065065, -5.025025025025025, -4.984984984984985, -4.944944944944945, -4.904904904904905, -4.864864864864865, -4.824824824824825, -4.784784784784785, -4.744744744744745, -4.704704704704705, -4.664664664664665, -4.624624624624625, -4.584584584584585, -4.544544544544545, -4.504504504504505, -4.464464464464465, -4.424424424424425, -4.384384384384385, -4.344344344344345, -4.3043043043043046, -4.2642642642642645, -4.2242242242242245, -4.1841841841841845, -4.1441441441441444, -4.104104104104104, -4.064064064064064, -4.024024024024024, -3.9839839839839826, -3.9439439439439425, -3.9039039039039025, -3.8638638638638625, -3.8238238238238225, -3.7837837837837824, -3.7437437437437424, -3.7037037037037024, -3.6636636636636624, -3.6236236236236223, -3.5835835835835823, -3.5435435435435423, -3.5035035035035023, -3.4634634634634622, -3.423423423423422, -3.383383383383382, -3.343343343343342, -3.303303303303302, -3.263263263263262, -3.223223223223222, -3.183183183183182, -3.143143143143142, -3.103103103103102, -3.063063063063062, -3.023023023023022, -2.982982982982982, -2.942942942942942, -2.902902902902902, -2.862862862862862, -2.822822822822822, -2.782782782782782, -2.7427427427427418, -2.7027027027027017, -2.6626626626626617, -2.6226226226226217, -2.5825825825825817, -2.5425425425425416, -2.5025025025025016, -2.4624624624624616, -2.4224224224224216, -2.3823823823823815, -2.3423423423423415, -2.3023023023023015, -2.2622622622622615, -2.2222222222222214, -2.1821821821821814, -2.1421421421421414, -2.1021021021021014, -2.0620620620620613, -2.0220220220220213, -1.9819819819819813, -1.9419419419419413, -1.9019019019019012, -1.8618618618618612, -1.8218218218218212, -1.7817817817817811, -1.7417417417417411, -1.701701701701701, -1.661661661661661, -1.621621621621621, -1.581581581581581, -1.541541541541541, -1.501501501501501, -1.461461461461461, -1.421421421421421, -1.381381381381381, -1.3413413413413409, -1.3013013013013008, -1.2612612612612608, -1.2212212212212208, -1.1811811811811808, -1.1411411411411407, -1.1011011011011007, -1.0610610610610607, -1.0210210210210207, -0.9809809809809806, -0.9409409409409406, -0.9009009009009006, -0.8608608608608606, -0.8208208208208205, -0.7807807807807805, -0.7407407407407405, -0.7007007007007005, -0.6606606606606604, -0.6206206206206204, -0.5805805805805804, -0.5405405405405403, -0.5005005005005003, -0.4604604604604603, -0.42042042042042027, -0.38038038038038025, -0.3403403403403402, -0.3003003003003002, -0.26026026026026017, -0.22022022022022014, -0.18018018018018012, -0.1401401401401401, -0.10010010010010006, -0.06006006006006004, -0.020020020020020013, 0.020020020020020013, 0.06006006006006004, 0.10010010010010006, 0.1401401401401401, 0.18018018018018012, 0.22022022022022014, 0.26026026026026017, 0.3003003003003002, 0.3403403403403402, 0.38038038038038025, 0.42042042042042027, 0.4604604604604603, 0.5005005005005003, 0.5405405405405403, 0.5805805805805804, 0.6206206206206204, 0.6606606606606604, 0.7007007007007005, 0.7407407407407405, 0.7807807807807805, 0.8208208208208205, 0.8608608608608606, 0.9009009009009006, 0.9409409409409406, 0.9809809809809806, 1.0210210210210207, 1.0610610610610607, 1.1011011011011007, 1.1411411411411407, 1.1811811811811808, 1.2212212212212208, 1.2612612612612608, 1.3013013013013008, 1.3413413413413409, 1.381381381381381, 1.421421421421421, 1.461461461461461, 1.501501501501501, 1.541541541541541, 1.581581581581581, 1.621621621621621, 1.661661661661661, 1.701701701701701, 1.7417417417417411, 1.7817817817817811, 1.8218218218218212, 1.8618618618618612, 1.9019019019019012, 1.9419419419419413, 1.9819819819819813, 2.0220220220220213, 2.0620620620620613, 2.1021021021021014, 2.1421421421421414, 2.1821821821821814, 2.2222222222222214, 2.2622622622622615, 2.3023023023023015, 2.3423423423423415, 2.3823823823823815, 2.4224224224224216, 2.4624624624624616, 2.5025025025025016, 2.5425425425425416, 2.5825825825825817, 2.6226226226226217, 2.6626626626626617, 2.7027027027027017, 2.7427427427427418, 2.782782782782782, 2.822822822822822, 2.862862862862862, 2.902902902902902, 2.942942942942942, 2.982982982982982, 3.023023023023022, 3.063063063063062, 3.103103103103102, 3.143143143143142, 3.183183183183182, 3.223223223223222, 3.263263263263262, 3.303303303303302, 3.343343343343342, 3.383383383383382, 3.423423423423422, 3.4634634634634622, 3.5035035035035023, 3.5435435435435423, 3.5835835835835823, 3.6236236236236223, 3.6636636636636624, 3.7037037037037024, 3.7437437437437424, 3.7837837837837824, 3.8238238238238225, 3.8638638638638625, 3.9039039039039025, 3.9439439439439425, 3.9839839839839826, 4.024024024024023, 4.064064064064063, 4.104104104104103, 4.144144144144143, 4.184184184184183, 4.224224224224223, 4.264264264264263, 4.304304304304303, 4.344344344344343, 4.384384384384383, 4.424424424424423, 4.464464464464463, 4.504504504504503, 4.544544544544543, 4.584584584584583, 4.624624624624623, 4.664664664664663, 4.704704704704703, 4.744744744744743, 4.784784784784783, 4.824824824824823, 4.864864864864863, 4.904904904904903, 4.944944944944943, 4.984984984984983, 5.025025025025023, 5.065065065065063, 5.105105105105103, 5.145145145145143, 5.185185185185183, 5.225225225225223, 5.265265265265263, 5.305305305305303, 5.3453453453453434, 5.3853853853853835, 5.4254254254254235, 5.4654654654654635, 5.5055055055055035, 5.545545545545544, 5.585585585585584, 5.625625625625624, 5.665665665665667, 5.705705705705707, 5.745745745745747, 5.785785785785787, 5.825825825825827, 5.865865865865867, 5.905905905905907, 5.945945945945947, 5.985985985985987, 6.026026026026027, 6.0660660660660675, 6.1061061061061075, 6.1461461461461475, 6.1861861861861875, 6.226226226226228, 6.266266266266268, 6.306306306306308, 6.346346346346348, 6.386386386386388, 6.426426426426428, 6.466466466466468, 6.506506506506508, 6.546546546546548, 6.586586586586588, 6.626626626626628, 6.666666666666668, 6.706706706706708, 6.746746746746748, 6.786786786786788, 6.826826826826828, 6.866866866866868, 6.906906906906908, 6.946946946946948, 6.986986986986988, 7.027027027027028, 7.067067067067068, 7.107107107107108, 7.147147147147148, 7.187187187187188, 7.227227227227228, 7.267267267267268, 7.307307307307308, 7.347347347347348, 7.387387387387388, 7.427427427427428, 7.467467467467468, 7.507507507507508, 7.547547547547548, 7.5875875875875884, 7.6276276276276285, 7.6676676676676685, 7.7077077077077085, 7.7477477477477485, 7.787787787787789, 7.827827827827829, 7.867867867867869, 7.907907907907909, 7.947947947947949, 7.987987987987989, 8.028028028028029, 8.068068068068069, 8.108108108108109, 8.148148148148149, 8.188188188188189, 8.228228228228229, 8.268268268268269, 8.308308308308309, 8.348348348348349, 8.388388388388389, 8.428428428428429, 8.468468468468469, 8.508508508508509, 8.548548548548549, 8.588588588588589, 8.62862862862863, 8.66866866866867, 8.70870870870871, 8.74874874874875, 8.78878878878879, 8.82882882882883, 8.86886886886887, 8.90890890890891, 8.94894894894895, 8.98898898898899, 9.02902902902903, 9.06906906906907, 9.10910910910911, 9.14914914914915, 9.18918918918919, 9.22922922922923, 9.26926926926927, 9.30930930930931, 9.34934934934935, 9.38938938938939, 9.42942942942943, 9.46946946946947, 9.50950950950951, 9.54954954954955, 9.58958958958959, 9.62962962962963, 9.66966966966967, 9.70970970970971, 9.74974974974975, 9.78978978978979, 9.82982982982983, 9.86986986986987, 9.90990990990991, 9.94994994994995, 9.98998998998999, 10.03003003003003, 10.07007007007007, 10.11011011011011, 10.15015015015015, 10.19019019019019, 10.23023023023023, 10.27027027027027, 10.31031031031031, 10.35035035035035, 10.39039039039039, 10.43043043043043, 10.47047047047047, 10.51051051051051, 10.55055055055055, 10.59059059059059, 10.63063063063063, 10.67067067067067, 10.71071071071071, 10.75075075075075, 10.79079079079079, 10.83083083083083, 10.87087087087087, 10.91091091091091, 10.95095095095095, 10.99099099099099, 11.03103103103103, 11.07107107107107, 11.11111111111111, 11.15115115115115, 11.19119119119119, 11.23123123123123, 11.27127127127127, 11.31131131131131, 11.35135135135135, 11.391391391391391, 11.431431431431431, 11.471471471471471, 11.511511511511511, 11.551551551551551, 11.591591591591591, 11.631631631631631, 11.671671671671671, 11.711711711711711, 11.751751751751751, 11.791791791791791, 11.831831831831831, 11.871871871871871, 11.911911911911911, 11.951951951951951, 11.991991991991991, 12.032032032032035, 12.072072072072075, 12.112112112112115, 12.152152152152155, 12.192192192192195, 12.232232232232235, 12.272272272272275, 12.312312312312315, 12.352352352352355, 12.392392392392395, 12.432432432432435, 12.472472472472475, 12.512512512512515, 12.552552552552555, 12.592592592592595, 12.632632632632635, 12.672672672672675, 12.712712712712715, 12.752752752752755, 12.792792792792795, 12.832832832832835, 12.872872872872875, 12.912912912912915, 12.952952952952955, 12.992992992992995, 13.033033033033036, 13.073073073073076, 13.113113113113116, 13.153153153153156, 13.193193193193196, 13.233233233233236, 13.273273273273276, 13.313313313313316, 13.353353353353356, 13.393393393393396, 13.433433433433436, 13.473473473473476, 13.513513513513516, 13.553553553553556, 13.593593593593596, 13.633633633633636, 13.673673673673676, 13.713713713713716, 13.753753753753756, 13.793793793793796, 13.833833833833836, 13.873873873873876, 13.913913913913916, 13.953953953953956, 13.993993993993996, 14.034034034034036, 14.074074074074076, 14.114114114114116, 14.154154154154156, 14.194194194194196, 14.234234234234236, 14.274274274274276, 14.314314314314316, 14.354354354354356, 14.394394394394396, 14.434434434434436, 14.474474474474476, 14.514514514514516, 14.554554554554556, 14.594594594594597, 14.634634634634637, 14.674674674674677, 14.714714714714717, 14.754754754754757, 14.794794794794797, 14.834834834834837, 14.874874874874877, 14.914914914914917, 14.954954954954957, 14.994994994994997, 15.035035035035037, 15.075075075075077, 15.115115115115117, 15.155155155155157, 15.195195195195197, 15.235235235235237, 15.275275275275277, 15.315315315315317, 15.355355355355357, 15.395395395395397, 15.435435435435437, 15.475475475475477, 15.515515515515517, 15.555555555555557, 15.595595595595597, 15.635635635635637, 15.675675675675677, 15.715715715715717, 15.755755755755757, 15.795795795795797, 15.835835835835837, 15.875875875875877, 15.915915915915917, 15.955955955955957, 15.995995995995997, 16.036036036036037, 16.076076076076077, 16.116116116116117, 16.156156156156158, 16.196196196196198, 16.236236236236238, 16.276276276276278, 16.316316316316318, 16.356356356356358, 16.396396396396398, 16.436436436436438, 16.476476476476478, 16.516516516516518, 16.556556556556558, 16.596596596596598, 16.636636636636638, 16.676676676676678, 16.716716716716718, 16.756756756756758, 16.796796796796798, 16.836836836836838, 16.876876876876878, 16.916916916916918, 16.956956956956958, 16.996996996996998, 17.037037037037038, 17.077077077077078, 17.117117117117118, 17.157157157157158, 17.197197197197198, 17.237237237237238, 17.27727727727728, 17.31731731731732, 17.35735735735736, 17.3973973973974, 17.43743743743744, 17.47747747747748, 17.51751751751752, 17.55755755755756, 17.5975975975976, 17.63763763763764, 17.67767767767768, 17.71771771771772, 17.75775775775776, 17.7977977977978, 17.83783783783784, 17.87787787787788, 17.91791791791792, 17.95795795795796, 17.997997997998, 18.03803803803804, 18.07807807807808, 18.11811811811812, 18.15815815815816, 18.1981981981982, 18.23823823823824, 18.27827827827828, 18.31831831831832, 18.35835835835836, 18.3983983983984, 18.43843843843844, 18.47847847847848, 18.51851851851852, 18.55855855855856, 18.5985985985986, 18.63863863863864, 18.67867867867868, 18.71871871871872, 18.75875875875876, 18.7987987987988, 18.83883883883884, 18.87887887887888, 18.91891891891892, 18.95895895895896, 18.998998998999, 19.03903903903904, 19.07907907907908, 19.11911911911912, 19.15915915915916, 19.1991991991992, 19.23923923923924, 19.27927927927928, 19.31931931931932, 19.35935935935936, 19.3993993993994, 19.43943943943944, 19.47947947947948, 19.51951951951952, 19.55955955955956, 19.5995995995996, 19.63963963963964, 19.67967967967968, 19.71971971971972, 19.75975975975976, 19.7997997997998, 19.83983983983984, 19.87987987987988, 19.91991991991992, 19.95995995995996, 20.0], "x": [-1.0, -0.997997997997998, -0.995995995995996, -0.993993993993994, -0.991991991991992, -0.98998998998999, -0.987987987987988, -0.985985985985986, -0.983983983983984, -0.9819819819819819, -0.97997997997998, -0.977977977977978, -0.975975975975976, -0.973973973973974, -0.9719719719719719, -0.96996996996997, -0.967967967967968, -0.965965965965966, -0.963963963963964, -0.9619619619619619, -0.95995995995996, -0.957957957957958, -0.955955955955956, -0.953953953953954, -0.9519519519519519, -0.94994994994995, -0.9479479479479479, -0.9459459459459459, -0.943943943943944, -0.9419419419419419, -0.93993993993994, -0.9379379379379379, -0.9359359359359359, -0.933933933933934, -0.9319319319319319, -0.92992992992993, -0.9279279279279279, -0.9259259259259259, -0.9239239239239239, -0.9219219219219219, -0.91991991991992, -0.9179179179179179, -0.9159159159159159, -0.9139139139139139, -0.9119119119119119, -0.9099099099099099, -0.9079079079079079, -0.9059059059059059, -0.9039039039039038, -0.9019019019019019, -0.8998998998998999, -0.8978978978978979, -0.8958958958958959, -0.8938938938938938, -0.8918918918918919, -0.8898898898898899, -0.8878878878878879, -0.8858858858858859, -0.8838838838838838, -0.8818818818818819, -0.8798798798798799, -0.8778778778778779, -0.8758758758758759, -0.8738738738738738, -0.8718718718718719, -0.8698698698698699, -0.8678678678678678, -0.8658658658658659, -0.8638638638638638, -0.8618618618618619, -0.8598598598598599, -0.8578578578578578, -0.8558558558558559, -0.8538538538538538, -0.8518518518518519, -0.8498498498498499, -0.8478478478478478, -0.8458458458458459, -0.8438438438438438, -0.8418418418418419, -0.8398398398398399, -0.8378378378378378, -0.8358358358358359, -0.8338338338338338, -0.8318318318318318, -0.8298298298298299, -0.8278278278278278, -0.8258258258258259, -0.8238238238238238, -0.8218218218218218, -0.8198198198198199, -0.8178178178178178, -0.8158158158158157, -0.8138138138138138, -0.8118118118118118, -0.8098098098098099, -0.8078078078078078, -0.8058058058058057, -0.8038038038038038, -0.8018018018018018, -0.7997997997997999, -0.7977977977977978, -0.7957957957957957, -0.7937937937937938, -0.7917917917917918, -0.7897897897897898, -0.7877877877877878, -0.7857857857857857, -0.7837837837837838, -0.7817817817817818, -0.7797797797797797, -0.7777777777777778, -0.7757757757757757, -0.7737737737737738, -0.7717717717717718, -0.7697697697697697, -0.7677677677677678, -0.7657657657657657, -0.7637637637637638, -0.7617617617617618, -0.7597597597597597, -0.7577577577577578, -0.7557557557557557, -0.7537537537537538, -0.7517517517517518, -0.7497497497497497, -0.7477477477477478, -0.7457457457457457, -0.7437437437437437, -0.7417417417417418, -0.7397397397397397, -0.7377377377377378, -0.7357357357357357, -0.7337337337337337, -0.7317317317317318, -0.7297297297297297, -0.7277277277277278, -0.7257257257257257, -0.7237237237237237, -0.7217217217217218, -0.7197197197197197, -0.7177177177177176, -0.7157157157157157, -0.7137137137137137, -0.7117117117117118, -0.7097097097097097, -0.7077077077077076, -0.7057057057057057, -0.7037037037037037, -0.7017017017017018, -0.6996996996996997, -0.6976976976976976, -0.6956956956956957, -0.6936936936936937, -0.6916916916916918, -0.6896896896896897, -0.6876876876876876, -0.6856856856856857, -0.6836836836836837, -0.6816816816816818, -0.6796796796796797, -0.6776776776776776, -0.6756756756756757, -0.6736736736736737, -0.6716716716716717, -0.6696696696696697, -0.6676676676676676, -0.6656656656656657, -0.6636636636636637, -0.6616616616616617, -0.6596596596596597, -0.6576576576576576, -0.6556556556556556, -0.6536536536536537, -0.6516516516516517, -0.6496496496496497, -0.6476476476476476, -0.6456456456456456, -0.6436436436436437, -0.6416416416416417, -0.6396396396396397, -0.6376376376376376, -0.6356356356356356, -0.6336336336336337, -0.6316316316316316, -0.6296296296296297, -0.6276276276276276, -0.6256256256256256, -0.6236236236236237, -0.6216216216216216, -0.6196196196196196, -0.6176176176176176, -0.6156156156156156, -0.6136136136136137, -0.6116116116116116, -0.6096096096096096, -0.6076076076076076, -0.6056056056056056, -0.6036036036036037, -0.6016016016016016, -0.5995995995995996, -0.5975975975975976, -0.5955955955955956, -0.5935935935935936, -0.5915915915915916, -0.5895895895895895, -0.5875875875875876, -0.5855855855855856, -0.5835835835835836, -0.5815815815815816, -0.5795795795795795, -0.5775775775775776, -0.5755755755755756, -0.5735735735735736, -0.5715715715715716, -0.5695695695695695, -0.5675675675675675, -0.5655655655655656, -0.5635635635635636, -0.5615615615615616, -0.5595595595595595, -0.5575575575575575, -0.5555555555555556, -0.5535535535535536, -0.5515515515515516, -0.5495495495495495, -0.5475475475475475, -0.5455455455455456, -0.5435435435435436, -0.5415415415415415, -0.5395395395395395, -0.5375375375375375, -0.5355355355355356, -0.5335335335335336, -0.5315315315315315, -0.5295295295295295, -0.5275275275275275, -0.5255255255255256, -0.5235235235235236, -0.5215215215215215, -0.5195195195195195, -0.5175175175175175, -0.5155155155155156, -0.5135135135135136, -0.5115115115115115, -0.5095095095095095, -0.5075075075075075, -0.5055055055055055, -0.5035035035035035, -0.5015015015015015, -0.49949949949949946, -0.4974974974974975, -0.49549549549549554, -0.4934934934934935, -0.4914914914914915, -0.48948948948948945, -0.4874874874874875, -0.48548548548548554, -0.48348348348348347, -0.4814814814814815, -0.47947947947947944, -0.4774774774774775, -0.47547547547547553, -0.47347347347347346, -0.4714714714714715, -0.46946946946946944, -0.4674674674674675, -0.4654654654654655, -0.46346346346346345, -0.4614614614614615, -0.45945945945945943, -0.4574574574574575, -0.4554554554554555, -0.45345345345345345, -0.4514514514514515, -0.4494494494494494, -0.44744744744744747, -0.4454454454454454, -0.44344344344344344, -0.4414414414414415, -0.4394394394394394, -0.43743743743743746, -0.4354354354354354, -0.43343343343343343, -0.4314314314314315, -0.4294294294294294, -0.42742742742742745, -0.4254254254254254, -0.42342342342342343, -0.42142142142142147, -0.4194194194194194, -0.41741741741741745, -0.4154154154154154, -0.4134134134134134, -0.41141141141141147, -0.4094094094094094, -0.40740740740740744, -0.4054054054054054, -0.4034034034034034, -0.40140140140140146, -0.3993993993993994, -0.39739739739739743, -0.39539539539539537, -0.3933933933933934, -0.39139139139139134, -0.3893893893893894, -0.3873873873873874, -0.38538538538538536, -0.3833833833833834, -0.38138138138138133, -0.3793793793793794, -0.3773773773773774, -0.37537537537537535, -0.3733733733733734, -0.37137137137137133, -0.36936936936936937, -0.3673673673673674, -0.36536536536536535, -0.3633633633633634, -0.3613613613613613, -0.35935935935935936, -0.3573573573573574, -0.35535535535535534, -0.3533533533533534, -0.3513513513513513, -0.34934934934934936, -0.3473473473473474, -0.34534534534534533, -0.3433433433433434, -0.3413413413413413, -0.33933933933933935, -0.3373373373373374, -0.3353353353353353, -0.33333333333333337, -0.3313313313313313, -0.32932932932932935, -0.3273273273273274, -0.3253253253253253, -0.32332332332332336, -0.3213213213213213, -0.31931931931931934, -0.31731731731731727, -0.3153153153153153, -0.31331331331331336, -0.3113113113113113, -0.30930930930930933, -0.30730730730730726, -0.3053053053053053, -0.30330330330330335, -0.3013013013013013, -0.2992992992992993, -0.29729729729729726, -0.2952952952952953, -0.29329329329329334, -0.2912912912912913, -0.2892892892892893, -0.28728728728728725, -0.2852852852852853, -0.28328328328328334, -0.28128128128128127, -0.2792792792792793, -0.27727727727727725, -0.2752752752752753, -0.27327327327327333, -0.27127127127127126, -0.2692692692692693, -0.26726726726726724, -0.2652652652652653, -0.2632632632632632, -0.26126126126126126, -0.2592592592592593, -0.25725725725725723, -0.2552552552552553, -0.2532532532532532, -0.25125125125125125, -0.2492492492492493, -0.24724724724724723, -0.24524524524524527, -0.2432432432432432, -0.24124124124124124, -0.2392392392392393, -0.23723723723723722, -0.23523523523523526, -0.2332332332332332, -0.23123123123123124, -0.22922922922922928, -0.2272272272272272, -0.22522522522522526, -0.2232232232232232, -0.22122122122122123, -0.21921921921921927, -0.2172172172172172, -0.21521521521521525, -0.21321321321321318, -0.21121121121121122, -0.20920920920920927, -0.2072072072072072, -0.20520520520520524, -0.20320320320320318, -0.20120120120120122, -0.19919919919919926, -0.1971971971971972, -0.19519519519519524, -0.19319319319319317, -0.1911911911911912, -0.18918918918918914, -0.1871871871871872, -0.18518518518518523, -0.18318318318318316, -0.1811811811811812, -0.17917917917917914, -0.17717717717717718, -0.17517517517517522, -0.17317317317317316, -0.1711711711711712, -0.16916916916916913, -0.16716716716716717, -0.16516516516516522, -0.16316316316316315, -0.1611611611611612, -0.15915915915915912, -0.15715715715715717, -0.1551551551551552, -0.15315315315315314, -0.1511511511511512, -0.14914914914914912, -0.14714714714714716, -0.1451451451451452, -0.14314314314314314, -0.14114114114114118, -0.1391391391391391, -0.13713713713713716, -0.1351351351351351, -0.13313313313313313, -0.13113113113113117, -0.1291291291291291, -0.12712712712712715, -0.12512512512512508, -0.12312312312312312, -0.12112112112112117, -0.1191191191191191, -0.11711711711711714, -0.11511511511511507, -0.11311311311311312, -0.11111111111111116, -0.10910910910910909, -0.10710710710710714, -0.10510510510510507, -0.10310310310310311, -0.10110110110110115, -0.09909909909909909, -0.09709709709709713, -0.09509509509509506, -0.0930930930930931, -0.09109109109109115, -0.08908908908908908, -0.08708708708708712, -0.08508508508508505, -0.0830830830830831, -0.08108108108108114, -0.07907907907907907, -0.07707707707707712, -0.07507507507507505, -0.07307307307307309, -0.07107107107107113, -0.06906906906906907, -0.06706706706706711, -0.06506506506506504, -0.06306306306306309, -0.06106106106106102, -0.05905905905905906, -0.0570570570570571, -0.055055055055055035, -0.05305305305305308, -0.05105105105105101, -0.049049049049049054, -0.0470470470470471, -0.04504504504504503, -0.04304304304304307, -0.041041041041041004, -0.03903903903903905, -0.03703703703703709, -0.03503503503503502, -0.033033033033033066, -0.031031031031030998, -0.02902902902902904, -0.027027027027027084, -0.025025025025025016, -0.02302302302302306, -0.02102102102102099, -0.019019019019019034, -0.017017017017017078, -0.01501501501501501, -0.013013013013013053, -0.011011011011010985, -0.009009009009009028, -0.00700700700700696, -0.005005005005005003, -0.0030030030030030463, -0.0010010010010009784, 0.0010010010010010895, 0.0030030030030030463, 0.005005005005005003, 0.00700700700700696, 0.009009009009008917, 0.011011011011011096, 0.013013013013013053, 0.01501501501501501, 0.017017017017016967, 0.019019019019018923, 0.021021021021021102, 0.02302302302302306, 0.025025025025025016, 0.027027027027026973, 0.02902902902902893, 0.03103103103103111, 0.033033033033033066, 0.03503503503503502, 0.03703703703703698, 0.039039039039038936, 0.041041041041041115, 0.04304304304304307, 0.04504504504504503, 0.047047047047046986, 0.04904904904904894, 0.05105105105105112, 0.05305305305305308, 0.055055055055055035, 0.05705705705705699, 0.05905905905905895, 0.06106106106106113, 0.06306306306306309, 0.06506506506506504, 0.067067067067067, 0.06906906906906896, 0.07107107107107113, 0.07307307307307309, 0.07507507507507505, 0.077077077077077, 0.07907907907907896, 0.08108108108108114, 0.0830830830830831, 0.08508508508508505, 0.08708708708708701, 0.08908908908908897, 0.09109109109109115, 0.0930930930930931, 0.09509509509509506, 0.09709709709709702, 0.0990990990990992, 0.10110110110110115, 0.10310310310310311, 0.10510510510510507, 0.10710710710710702, 0.1091091091091092, 0.11111111111111116, 0.11311311311311312, 0.11511511511511507, 0.11711711711711703, 0.11911911911911921, 0.12112112112112117, 0.12312312312312312, 0.12512512512512508, 0.12712712712712704, 0.12912912912912922, 0.13113113113113117, 0.13313313313313313, 0.1351351351351351, 0.13713713713713704, 0.13913913913913922, 0.14114114114114118, 0.14314314314314314, 0.1451451451451451, 0.14714714714714705, 0.14914914914914923, 0.1511511511511512, 0.15315315315315314, 0.1551551551551551, 0.15715715715715706, 0.15915915915915924, 0.1611611611611612, 0.16316316316316315, 0.1651651651651651, 0.16716716716716706, 0.16916916916916924, 0.1711711711711712, 0.17317317317317316, 0.1751751751751751, 0.17717717717717707, 0.17917917917917925, 0.1811811811811812, 0.18318318318318316, 0.18518518518518512, 0.18718718718718708, 0.18918918918918926, 0.1911911911911912, 0.19319319319319317, 0.19519519519519513, 0.19719719719719708, 0.19919919919919926, 0.20120120120120122, 0.20320320320320318, 0.20520520520520513, 0.2072072072072071, 0.20920920920920927, 0.21121121121121122, 0.21321321321321318, 0.21521521521521514, 0.21721721721721732, 0.21921921921921927, 0.22122122122122123, 0.2232232232232232, 0.22522522522522515, 0.22722722722722732, 0.22922922922922928, 0.23123123123123124, 0.2332332332332332, 0.23523523523523515, 0.23723723723723733, 0.2392392392392393, 0.24124124124124124, 0.2432432432432432, 0.24524524524524516, 0.24724724724724734, 0.2492492492492493, 0.25125125125125125, 0.2532532532532532, 0.25525525525525516, 0.25725725725725734, 0.2592592592592593, 0.26126126126126126, 0.2632632632632632, 0.26526526526526517, 0.26726726726726735, 0.2692692692692693, 0.27127127127127126, 0.2732732732732732, 0.2752752752752752, 0.27727727727727736, 0.2792792792792793, 0.28128128128128127, 0.2832832832832832, 0.2852852852852852, 0.28728728728728736, 0.2892892892892893, 0.2912912912912913, 0.29329329329329323, 0.2952952952952952, 0.29729729729729737, 0.2992992992992993, 0.3013013013013013, 0.30330330330330324, 0.3053053053053052, 0.3073073073073074, 0.30930930930930933, 0.3113113113113113, 0.31331331331331325, 0.3153153153153152, 0.3173173173173174, 0.31931931931931934, 0.3213213213213213, 0.32332332332332325, 0.3253253253253252, 0.3273273273273274, 0.32932932932932935, 0.3313313313313313, 0.33333333333333326, 0.3353353353353352, 0.3373373373373374, 0.33933933933933935, 0.3413413413413413, 0.34334334334334327, 0.3453453453453452, 0.3473473473473474, 0.34934934934934936, 0.3513513513513513, 0.35335335335335327, 0.35535535535535545, 0.3573573573573574, 0.35935935935935936, 0.3613613613613613, 0.3633633633633633, 0.36536536536536546, 0.3673673673673674, 0.36936936936936937, 0.37137137137137133, 0.3733733733733733, 0.37537537537537546, 0.3773773773773774, 0.3793793793793794, 0.38138138138138133, 0.3833833833833833, 0.38538538538538547, 0.3873873873873874, 0.3893893893893894, 0.39139139139139134, 0.3933933933933933, 0.3953953953953955, 0.39739739739739743, 0.3993993993993994, 0.40140140140140135, 0.4034034034034033, 0.4054054054054055, 0.40740740740740744, 0.4094094094094094, 0.41141141141141135, 0.4134134134134133, 0.4154154154154155, 0.41741741741741745, 0.4194194194194194, 0.42142142142142136, 0.4234234234234233, 0.4254254254254255, 0.42742742742742745, 0.4294294294294294, 0.43143143143143137, 0.4334334334334333, 0.4354354354354355, 0.43743743743743746, 0.4394394394394394, 0.4414414414414414, 0.44344344344344333, 0.4454454454454455, 0.44744744744744747, 0.4494494494494494, 0.4514514514514514, 0.45345345345345334, 0.4554554554554555, 0.4574574574574575, 0.45945945945945943, 0.4614614614614614, 0.46346346346346334, 0.4654654654654655, 0.4674674674674675, 0.46946946946946944, 0.4714714714714714, 0.47347347347347357, 0.47547547547547553, 0.4774774774774775, 0.47947947947947944, 0.4814814814814814, 0.4834834834834836, 0.48548548548548554, 0.4874874874874875, 0.48948948948948945, 0.4914914914914914, 0.4934934934934936, 0.49549549549549554, 0.4974974974974975, 0.49949949949949946, 0.5015015015015014, 0.5035035035035036, 0.5055055055055055, 0.5075075075075075, 0.5095095095095095, 0.5115115115115114, 0.5135135135135136, 0.5155155155155156, 0.5175175175175175, 0.5195195195195195, 0.5215215215215214, 0.5235235235235236, 0.5255255255255256, 0.5275275275275275, 0.5295295295295295, 0.5315315315315314, 0.5335335335335336, 0.5355355355355356, 0.5375375375375375, 0.5395395395395395, 0.5415415415415414, 0.5435435435435436, 0.5455455455455456, 0.5475475475475475, 0.5495495495495495, 0.5515515515515514, 0.5535535535535536, 0.5555555555555556, 0.5575575575575575, 0.5595595595595595, 0.5615615615615615, 0.5635635635635636, 0.5655655655655656, 0.5675675675675675, 0.5695695695695695, 0.5715715715715715, 0.5735735735735736, 0.5755755755755756, 0.5775775775775776, 0.5795795795795795, 0.5815815815815815, 0.5835835835835836, 0.5855855855855856, 0.5875875875875876, 0.5895895895895895, 0.5915915915915915, 0.5935935935935936, 0.5955955955955956, 0.5975975975975976, 0.5995995995995995, 0.6016016016016015, 0.6036036036036037, 0.6056056056056056, 0.6076076076076076, 0.6096096096096095, 0.6116116116116117, 0.6136136136136137, 0.6156156156156156, 0.6176176176176176, 0.6196196196196195, 0.6216216216216217, 0.6236236236236237, 0.6256256256256256, 0.6276276276276276, 0.6296296296296295, 0.6316316316316317, 0.6336336336336337, 0.6356356356356356, 0.6376376376376376, 0.6396396396396395, 0.6416416416416417, 0.6436436436436437, 0.6456456456456456, 0.6476476476476476, 0.6496496496496496, 0.6516516516516517, 0.6536536536536537, 0.6556556556556556, 0.6576576576576576, 0.6596596596596596, 0.6616616616616617, 0.6636636636636637, 0.6656656656656657, 0.6676676676676676, 0.6696696696696696, 0.6716716716716717, 0.6736736736736737, 0.6756756756756757, 0.6776776776776776, 0.6796796796796796, 0.6816816816816818, 0.6836836836836837, 0.6856856856856857, 0.6876876876876876, 0.6896896896896896, 0.6916916916916918, 0.6936936936936937, 0.6956956956956957, 0.6976976976976976, 0.6996996996996996, 0.7017017017017018, 0.7037037037037037, 0.7057057057057057, 0.7077077077077076, 0.7097097097097096, 0.7117117117117118, 0.7137137137137137, 0.7157157157157157, 0.7177177177177176, 0.7197197197197196, 0.7217217217217218, 0.7237237237237237, 0.7257257257257257, 0.7277277277277276, 0.7297297297297298, 0.7317317317317318, 0.7337337337337337, 0.7357357357357357, 0.7377377377377377, 0.7397397397397398, 0.7417417417417418, 0.7437437437437437, 0.7457457457457457, 0.7477477477477477, 0.7497497497497498, 0.7517517517517518, 0.7537537537537538, 0.7557557557557557, 0.7577577577577577, 0.7597597597597598, 0.7617617617617618, 0.7637637637637638, 0.7657657657657657, 0.7677677677677677, 0.7697697697697699, 0.7717717717717718, 0.7737737737737738, 0.7757757757757757, 0.7777777777777777, 0.7797797797797799, 0.7817817817817818, 0.7837837837837838, 0.7857857857857857, 0.7877877877877877, 0.7897897897897899, 0.7917917917917918, 0.7937937937937938, 0.7957957957957957, 0.7977977977977977, 0.7997997997997999, 0.8018018018018018, 0.8038038038038038, 0.8058058058058057, 0.8078078078078077, 0.8098098098098099, 0.8118118118118118, 0.8138138138138138, 0.8158158158158157, 0.8178178178178177, 0.8198198198198199, 0.8218218218218218, 0.8238238238238238, 0.8258258258258258, 0.8278278278278277, 0.8298298298298299, 0.8318318318318318, 0.8338338338338338, 0.8358358358358358, 0.8378378378378377, 0.8398398398398399, 0.8418418418418419, 0.8438438438438438, 0.8458458458458458, 0.8478478478478477, 0.8498498498498499, 0.8518518518518519, 0.8538538538538538, 0.8558558558558558, 0.8578578578578577, 0.8598598598598599, 0.8618618618618619, 0.8638638638638638, 0.8658658658658658, 0.867867867867868, 0.8698698698698699, 0.8718718718718719, 0.8738738738738738, 0.8758758758758758, 0.877877877877878, 0.8798798798798799, 0.8818818818818819, 0.8838838838838838, 0.8858858858858858, 0.887887887887888, 0.8898898898898899, 0.8918918918918919, 0.8938938938938938, 0.8958958958958958, 0.897897897897898, 0.8998998998998999, 0.9019019019019019, 0.9039039039039038, 0.9059059059059058, 0.907907907907908, 0.9099099099099099, 0.9119119119119119, 0.9139139139139139, 0.9159159159159158, 0.917917917917918, 0.91991991991992, 0.9219219219219219, 0.9239239239239239, 0.9259259259259258, 0.927927927927928, 0.92992992992993, 0.9319319319319319, 0.9339339339339339, 0.9359359359359358, 0.937937937937938, 0.93993993993994, 0.9419419419419419, 0.9439439439439439, 0.9459459459459458, 0.947947947947948, 0.94994994994995, 0.9519519519519519, 0.9539539539539539, 0.9559559559559558, 0.957957957957958, 0.95995995995996, 0.9619619619619619, 0.9639639639639639, 0.9659659659659658, 0.967967967967968, 0.96996996996997, 0.9719719719719719, 0.9739739739739739, 0.9759759759759759, 0.977977977977978, 0.97997997997998, 0.9819819819819819, 0.9839839839839839, 0.9859859859859861, 0.987987987987988, 0.98998998998999, 0.991991991991992, 0.9939939939939939, 0.9959959959959961, 0.997997997997998, 1.0], "expected": [-1.0000000000000002, -0.6191943061779397, -0.24883119614217752, 0.04990850399446775, 0.26390544278445893, 0.39394512768096424, 0.448201469950323, 0.43896516561396176, 0.3805288186449476, 0.28768754343496117, 0.17465353467665426, 0.05428711673326174, -0.06241519701927391, -0.16661953961844903, -0.2517772328265539, -0.31360403952305804, -0.3499464974871397, -0.36056336337051276, -0.3468477824958956, -0.3115131993676577, -0.25826323405295837, -0.19146282350731292, -0.11582493959562402, -0.03612422767933721, 0.04305396190576598, 0.11752338442071966, 0.18366227494982074, 0.23853323043176036, 0.2799584714918983, 0.3065529711026076, 0.3177192327092772, 0.3136084803206651, 0.295053699715661, 0.2634803632634076, 0.22080080662242194, 0.16929813383889045, 0.1115052410656103, 0.050084102806180565, -0.012290106837125616, -0.07303614774016468, -0.12976191252662134, -0.18034524934252533, -0.22299871637360036, -0.25631730115812934, -0.27930881897257187, -0.29140732498967525, -0.2924704215922739, -0.2827618059573263, -0.26292077810295056, -0.2339207136146255, -0.19701869879231032, -0.15369863217363414, -0.10561012069941413, -0.054505448443726574, -0.0021767795042653966, 0.04960441595820311, 0.09914394208141429, 0.14487594743633364, 0.1854072468139737, 0.21955394943173454, 0.24636974589586863, 0.26516549955947555, 0.2755200689612282, 0.27728254990275975, 0.27056636263456174, 0.2557358170151149, 0.23338596299045333, 0.20431667314397803, 0.16950200730658727, 0.13005597630424312, 0.0871958538062207, 0.04220418371156824, -0.0036094018688720034, -0.04894549911026047, -0.09255041278282711, -0.13324893417159914, -0.16997367092098947, -0.20179031545618384, -0.2279183785774933, -0.24774705829703628, -0.2608460571196836, -0.26697130019279525, -0.2660656388478601, -0.25825474623158695, -0.24383852159733485, -0.2232784155362548, -0.1971811685045511, -0.16627951854788411, -0.13141048062103508, -0.09349182929925207, -0.05349742935449969, -0.012432055320597499, 0.028693677140864914, 0.06888767720997917, 0.10719949539586883, 0.1427416981331638, 0.17470907099140706, 0.2023952905091582, 0.22520677881048315, 0.2426735319829329, 0.2544577043038578, 0.2603482344007326, 0.26029042283328196, 0.2543629709392201, 0.24272882073366212, 0.22574187083409833, 0.20382715913692817, 0.1775139561033317, 0.14745982839424057, 0.1142921228990621, 0.07881495178244997, 0.041806052021720067, 0.004068567165994149, -0.03361000687223927, -0.07042272072607425, -0.10560633775942245, -0.13844395948687918, -0.1682785677540565, -0.1945249563635297, -0.21668029779081627, -0.23433255972401085, -0.24716708388723893, -0.2549706601734647, -0.25763375351618856, -0.2551505388315185, -0.2476169564002216, -0.2352268821458531, -0.21826623447449053, -0.19710556786561467, -0.17219131661670664, -0.14403589213492418, -0.1132062421813934, -0.08031253319088284, -0.04599548043549787, -0.010913463330022456, 0.024269102040776914, 0.058895791863096375, 0.09232888719537755, 0.1239606132079778, 0.1532253104981465, 0.17960722467016368, 0.20264979979959502, 0.22196266386098648, 0.23722743582667177, 0.24820212001708042, 0.25472403882984745, 0.25671130642930307, 0.2541628465307389, 0.24715699647444633, 0.2358487676203403, 0.2204658363270441, 0.20130336950281325, 0.1787178178540809, 0.15311978856602632, 0.12496616384398525, 0.09475159900663918, 0.06299958215807253, 0.030253194391127333, -0.0029342609893170226, -0.0360085896778234, -0.06842386527921618, -0.09965125359122246, -0.12918737420880647, -0.15656206934353756, -0.18134550068296101, -0.2031544036333232, -0.22165750784011778, -0.2365799993533994, -0.2477069989356333, -0.25488602260661963, -0.25802841138694504, -0.2571097326464257, -0.25216917255608784, -0.24330795357599444, -0.23068682540014254, -0.21452268997212784, -0.19508443369472023, -0.17268804948241284, -0.14769113892496866, -0.12048689350788824, -0.0914976572001125, -0.06116817643782856, -0.029958646594871366, 0.0016623387164490038, 0.0332248274307195, 0.06426443548287927, 0.09432906149201968, 0.12298529590403363, 0.14982443855052213, 0.1744680482102248, 0.19657295273194922, 0.21583566237814877, 0.23199613589909773, 0.24484086093375299, 0.25420522068314394, 0.25997512964034747, 0.262087931925047, 0.26053256618775417, 0.25534901125086035, 0.24662703615123654, 0.2345042872696068, 0.21916375350210598, 0.2008306577889955, 0.17976882999338228, 0.15627662153682984, 0.13068242701713717, 0.1033398814715121, 0.07462280461241297, 0.04491996473953934, 0.014629735898985332, -0.01584527915886298, -0.04610358853573993, -0.07575004432055887, -0.10440090310485947, -0.13168865223367662, -0.1572665439031426, -0.1808127852915097, -0.20203433806282997, -0.2206702870248842, -0.2364947441519843, -0.24931926094160353, -0.2589947289597945, -0.26541275538605913, -0.2685065072686662, -0.2682510250017008, -0.26466301211579213, -0.25780011478959597, -0.2477597104457259, -0.23467723035570895, -0.2187240462630547, -0.20010495560521221, -0.17905530395003436, -0.15583778669412796, -0.13073897491382183, -0.10406561246473489, -0.07614073303857283, -0.047299646803403164, -0.017885846656418538, 0.01175311618130251, 0.041269738338800314, 0.0703206046790634, 0.09857031731647434, 0.12569527001356515, 0.15138722755045564, 0.17535667285824857, 0.1973358882563609, 0.21708174096693905, 0.23437814714878105, 0.24903819294320936, 0.26090589539896486, 0.2698575905945251, 0.27580294074417566, 0.27868555651285337, 0.27848323512662015, 0.2752078190953593, 0.26890468443413407, 0.2596518711213034, 0.24755887214584027, 0.23276510083050994, 0.21543805914570163, 0.1957712324328401, 0.17398173830626573, 0.15030775949648037, 0.12500579201709644, 0.09834774127204579, 0.0706178995864495, 0.042109839121251706, 0.013123254244712662, -0.016039212817166873, -0.04507512982683085, -0.07368538358146041, -0.10157720910184605, -0.12846710943303263, -0.1540836383166108, -0.17817002002218976, -0.20048658286204926, -0.2208129853294258, -0.23895021636669445, -0.25472235395417614, -0.26797806898375837, -0.27859186421109405, -0.2864650409379208, -0.29152638893148586, -0.29373259791224454, -0.2930683917079221, -0.28954638885535045, -0.2832066960075556, -0.27411624294929937, -0.2623678703216829, -0.24807918328557965, -0.23139118629958857, -0.21246671593830063, -0.19148869021878065, -0.16865819422951484, -0.1441924229600843, -0.11832250310777032, -0.09129121628749481, -0.06335064649470425, -0.03475977486973298, -0.005782044791703517, 0.02331707990315832, 0.05227254122130687, 0.08082207610366515, 0.10870854739721743, 0.13568219677762283, 0.16150280083294866, 0.1859417127980101, 0.20878377383283375, 0.22982907925108134, 0.24889458670793532, 0.2658155550349347, 0.2804468041443249, 0.2926637882002605, 0.30236347605234315, 0.30946503473083675, 0.31391031359779986, 0.3156641285173645, 0.31471434713799107, 0.3110717780549974, 0.30476986823056973, 0.29586421457858114, 0.28443189706218036, 0.2705706419934824, 0.2543978254583484, 0.236049327907745, 0.21567825195456528, 0.19345351628617174, 0.16955833934468245, 0.14418862703680305, 0.11755127921151638, 0.08986242998742663, 0.0613456372226333, 0.03223003650138475, 0.002748474966194313, -0.026864359844224882, -0.05637380127657379, -0.08554704048750805, -0.11415492503757306, -0.14197370578240698, -0.16878671938099338, -0.19438599451493652, -0.21857377076054207, -0.24116391996818634, -0.26198326097175084, -0.28087275946564233, -0.29768860593870755, -0.3123031656339764, -0.3246057956012548, -0.33450352501731984, -0.3419215960567531, -0.3468038636969846, -0.34911305392555825, -0.34883088087826736, -0.3459580244662812, -0.34051397104179265, -0.33253672059878725, -0.3220823649024448, -0.30922454178221587, -0.2940537716051403, -0.2766766826636015, -0.2572151328617852, -0.23580523566520348, -0.21259629878530042, -0.18774968450495458, -0.1614376009097276, -0.13384183357355794, -0.10515242745637422, -0.0755663289057852, -0.0452859977166093, -0.014517999192401813, 0.016528413925455423, 0.04764271994057527, 0.07861453758415915, 0.10923501705364562, 0.1392982037884503, 0.16860236644094334, 0.19695128092615147, 0.22415546290275334, 0.2500333415463162, 0.27441236801863983, 0.2971300526098378, 0.3180349251275968, 0.3369874137260602, 0.35386063800025863, 0.368541112816213, 0.3809293599971075, 0.3909404256377918, 0.39850430146893623, 0.4035662493341895, 0.40608702847475175, 0.406043025931958, 0.4034262909763204, 0.39824447504756283, 0.39052067924153416, 0.3802932119036272, 0.3676152593820012, 0.352554473455242, 0.3351924793761546, 0.31562430886453724, 0.29395776273562946, 0.27031270816644287, 0.24482031587852746, 0.2176222427523989, 0.18886976558569302, 0.15872287186398595, 0.12734931353057172, 0.09492362981973831, 0.06162614525796139, 0.027641948940026577, -0.006840138846651762, -0.04162860664472604, -0.07653029259379122, -0.11135142017216672, -0.14589862330776776, -0.17997995544373738, -0.21340587736179967, -0.24599021880755578, -0.2775511092247132, -0.307911873187508, -0.3369018864199315, -0.3643573886045527, -0.3901222495105008, -0.4140486853071055, -0.43599792227466333, -0.4558408054744727, -0.473458350294476, -0.4887422351424902, -0.5015952339139559, -0.5119315872134556, -0.5196773116570421, -0.5247704469238187, -0.5271612405586217, -0.5268122708513817, -0.5236985084313593, -0.5178073175145891, -0.5091383980292761, -0.4977036701154384, -0.48352710275085053, -0.4666444884943223, -0.4471031665589652, -0.4249616966315807, -0.40028948603926867, -0.3731663730303849, -0.34368216908380633, -0.31193616328797524, -0.2780365919393804, -0.2421000765990088, -0.20425103391511357, -0.16462106057166204, -0.12334829675435546, -0.08057677154071646, -0.036455733617861766, 0.008861029288138544, 0.05521587892325989, 0.10244801966014246, 0.15039419306549665, 0.19888937072918794, 0.24776744229653602, 0.2968618957499755, 0.3460064871019469, 0.395035896786652, 0.44378637017322, 0.4920963397658627, 0.5398070268067471, 0.5867630201536291, 0.6328128304657236, 0.6778094178969496, 0.7216106916645242, 0.764079980032017, 0.8050864694185192, 0.8445056115185439, 0.8822194974899471, 0.9181171984385931, 0.9520950715979891, 0.9840570317689136, 1.0139147877474513, 1.041588043629204, 1.0670046650321217, 1.0901008104298726, 1.110821027931415, 1.129118317979951, 1.144954162575398, 1.1582985217484052, 1.1691297981306612, 1.1774347705752188, 1.1832084978818869, 1.1864541937760393, 1.1871830743743128, 1.185414179447718, 1.1811741688613884, 1.1744970956306706, 1.165424157085549, 1.1540034256794944, 1.1402895610148969, 1.1243435046854269, 1.106232159556068, 1.0860280551145034, 1.0638090005330516, 1.0396577270789542, 1.0136615215024691, 0.9859118520175076, 0.9565039884685783, 0.9255366182509909, 0.8931114595189328, 0.8593328731785186, 0.8243074751205737, 0.7881437501011518, 0.7509516686268957, 0.7128423081478099, 0.6739274798020872, 0.6343193618967785, 0.5941301412446308, 0.5534716634117559, 0.5124550928632211, 0.47119058392463875, 0.42978696340759115, 0.38835142567570063, 0.3469892408566178, 0.3058034768334749, 0.2648947355777365, 0.2243609043141899, 0.18429692193828023, 0.14479456103642271, 0.10594222579151312, 0.06782476598888458, 0.03052330727258985, -0.005884902261636377, -0.04132662911190365, -0.07573277508870796, -0.10903848179803591, -0.14118321903515546, -0.1721108572872217, -0.2017697245921368, -0.23011264804769072, -0.2570969803087225, -0.282684611450903, -0.3068419666176451, -0.3295399899016173, -0.35075411494430814, -0.3704642227661185, -0.3886545873654794, -0.40531380964862407, -0.42043474027180355, -0.43401439199508063, -0.44605384216132865, -0.4565581259258186, -0.46553612087083934, -0.4730004236462456, -0.47896721928077834, -0.4834561438104723, -0.48649014086964654, -0.4880953128868699, -0.48830076752311175, -0.48713845998200495, -0.48464303181304363, -0.4808516468175478, -0.47580382465462606, -0.46954127273013446, -0.46210771693601216, -0.45354873179038113, -0.4439115705105981, -0.43324499553218876, -0.42159910996630473, -0.409025190467223, -0.39557552195954293, -0.38130323465218835, -0.36626214374328575, -0.35050659219650454, -0.33409129694562706, -0.31707119886007706, -0.2995013167799568, -0.2814366059049466, -0.26293182079719984, -0.24404138323435956, -0.22481925512494616, -0.20531881667480362, -0.1855927499700769, -0.1656929281193604, -0.1456703100753237, -0.1255748412343443, -0.10545535989137378, -0.08535950960672768, -0.065333657521512, -0.04542281863918438, -0.02567058607225937, -0.0061190672354466125, 0.013191174050410115, 0.03222116959532619, 0.050933593085105665, 0.06929280061563212, 0.08726486561150576, 0.10481760823670226, 0.12192061941677255, 0.13854527960303248, 0.15466477241931462, 0.17025409334106198, 0.18529005356493886, 0.19975127923465916, 0.2136182061954713, 0.2268730704556, 0.2394998945381007, 0.2514844699108667, 0.26281433568615553, 0.2734787537838134, 0.2834686807545415, 0.2927767364610119, 0.3013971698154334, 0.30932582177237017, 0.31656008577518663, 0.3230988658535126, 0.32894253256758715, 0.3340928769933192, 0.33855306293936477, 0.34232757758456733, 0.34542218072070574, 0.347843852781731, 0.34960074183651074, 0.350702109717639, 0.3511582774541055, 0.35098057017054474, 0.3501812616105181, 0.3487735184357547, 0.3467713444475856, 0.3441895248709415, 0.3410435708352685, 0.3373496641806188, 0.33312460271094496, 0.32838574601037135, 0.3231509619318805, 0.3174385738615059, 0.31126730885480514, 0.3046562467360044, 0.2976247702439497, 0.2901925163027244, 0.2823793284886133, 0.274205210759006, 0.26569028250279486, 0.2568547349659605, 0.24771878910022294, 0.23830265487702343, 0.22862649210357194, 0.21871037277234417, 0.20857424497024593, 0.19823789836857375, 0.18772093131011483, 0.17704271950499928, 0.1662223863424424, 0.15527877482121427, 0.14423042109753878, 0.1330955296452177, 0.12189195001903116, 0.11063715520894496, 0.099348221569311, 0.08804181030408761, 0.07673415048620343, 0.06544102358638076, 0.054177749484222035, 0.04295917393195194, 0.03179965743905062, 0.020713065543995976, 0.00971276043752572, -0.0011884060998282565, -0.011978098484642773, -0.022644501881964735, -0.03317632556227474, -0.0435628051062087, -0.05379370350001155, -0.06385931116534659, -0.07375044496769555, -0.08345844624791958, -0.09297517792185697, -0.10229302069297852, -0.11140486842315804, -0.12030412270650714, -0.12898468669105248, -0.13744095819274219, -0.1456678221458644, -0.15366064243348998, -0.1614152531410011, -0.16892794927510038, -0.176195476990012, -0.1832150233617765, -0.18998420575073177, -0.19650106079133312, -0.2027640330475629, -0.2087719633711396, -0.2145240769987344, -0.2200199714233062, -0.22525960407357623, -0.23024327983451792, -0.2349716384405933, -0.23944564177229105, -0.24366656108531345, -0.2476359642005959, -0.25135570268208984, -0.2548278990280657, -0.2580549339004547, -0.2610394334155458, -0.26378425651815074, -0.2662924824601448, -0.26856739840311383, -0.2706124871636459, -0.2724314151186683, -0.2740280202870754, -0.27540630060276095, -0.2765704023930961, -0.2775246090757761, -0.2782733300859419, -0.27882109004441474, -0.27917251817691574, -0.2793323379931375, -0.279305357233601, -0.2790964580913113, -0.27871058771433915, -0.2781527489945965, -0.2774279916472455, -0.27654140358438545, -0.27549810258592067, -0.2743032282697374, -0.27296193436266547, -0.2714793812730031, -0.2698607289647569, -0.26811113013315474, -0.26623572368039533, -0.26423962849008237, -0.26212793749825725, -0.2599057120584902, -0.257577976598002, -0.25514971356141264, -0.2526258586382837, -0.2500112962702733, -0.24731085543338338, -0.24452930569047493, -0.24167135350891664, -0.23874163883802002, -0.23574473194062118, -0.23268513047302072, -0.2295672568072411, -0.22639545558945873, -0.22317399152826597, -0.2199070474063367, -0.21659872230894583, -0.21325303006269788, -0.20987389787778313, -0.20646516518699812, -0.20303058267473637, -0.19957381148916956, -0.19609842263077992, -0.192607896510476, -0.18910562267048664, -0.18559489966130605, -0.18207893506799697, -0.17856084567920427, -0.17504365779231526, -0.1715303076482671, -0.16802364198959405, -0.16452641873540394, -0.1610413077670492, -0.15757089181840295, -0.15411766746473063, -0.15068404620427864, -0.14727235562682356, -0.1438848406635556, -0.14052366491278048, -0.13719091203609887, -0.13388858721980282, -0.13061861869640648, -0.1273828593213698, -0.12418308820017325, -0.12102101236109394, -0.11789826846913402, -0.11481642457672661, -0.11177698190693094, -0.10878137666507269, -0.10583098187476486, -0.10292710923456595, -0.10007101099148864, -0.0972638818278449, -0.09450686075796909, -0.09180103303149416, -0.08914743204000175, -0.08654704122398489, -0.0840007959771479, -0.08150958554523216, -0.07907425491661241, -0.07669560670206603, -0.0743744030011759, -0.072111367252936, -0.06990718606825765, -0.06776251104209619, -0.06567796054303934, -0.06365412147832723, -0.06169155103217534, -0.05979077837560021, -0.05795230634573377, -0.05617661309290005, -0.05446415369360363, -0.05281536172775369, -0.051230650818410675, -0.049710416132385034, -0.0482550358401083, -0.046864872533115595, -0.04554027459758844, -0.04428157754237014, -0.0430891052798868, -0.04196317135837508, -0.040904080143875074, -0.03991212795036831, -0.03898760411643678, -0.03813079202683218, -0.0373419700772623, -0.03662141258067979, -0.03596939061334195, -0.035386172798801206, -0.03487202602801616, -0.034427216113572086, -0.03405200837612308, -0.03374666816090547, -0.03351146128219641, -0.03334665439348551, -0.03325251528103846, -0.033229313078379646, -0.03327731839922652, -0.03339680338614376, -0.033588041672254196, -0.033851308253035665, -0.034186879265247265, -0.0345950316698432, -0.035076042835569, -0.03563019001984326, -0.0362577497433756, -0.03695899705478051, -0.03773420468135377, -0.03858364206198353, -0.039507574258015925, -0.040506260737758065, -0.04157995403010551, -0.042728898242665105, -0.0439533274395205, -0.045253463873693556, -0.04662951606914839, -0.04808167674703801, -0.049610120590776234, -0.051215001844289225, -0.05289645173774673, -0.05465457573490348, -0.05648945059600133, -0.058401121250187565, -0.06038959747117028, -0.062454850349840295, -0.06459680855747808, -0.06681535439308298, -0.06911031960841785, -0.07148148100424676, -0.07392855579133617, -0.07645119670983597, -0.07904898690068371, -0.08172143452287486, -0.08446796711055318, -0.08728792566408901, -0.0901805584695883, -0.09314501464159392, -0.0961803373840982, -0.0992854569654319, -0.10245918340312914, -0.10570019885543677, -0.10900704971686656, -0.11237813841588305, -0.11581171491378886, -0.11930586790482178, -0.12285851571852861, -0.12646739692690936, -0.13013006065990976, -0.13384385663467274, -0.1376059249054724, -0.14141318534317754, -0.14526232685516025, -0.1491497963587915, -0.15307178752420636, -0.1570242293046549, -0.16100277427577223, -0.1650027868082762, -0.1690193311021467, -0.17304715911409507, -0.1770806984143008, -0.18111404001279824, -0.18514092620076383, -0.18915473845710165, -0.19314848547634958, -0.19711479137993798, -0.20104588417928912, -0.20493358456615135, -0.20876929511305511, -0.21254398997456925, -0.2162482051886693, -0.21987202968637495, -0.22340509712757012, -0.22683657869096807, -0.23015517695711377, -0.23334912103469374, -0.23640616309252313, -0.2393135764723752, -0.24205815557121302, -0.2446262176954934, -0.24700360710499716, -0.24917570147910892, -0.2511274210545417, -0.25284324070032965, -0.25430720521315675, -0.2555029481341764, -0.25641371440681276, -0.25702238721399806, -0.25731151935262203, -0.25726336952247214, -0.25685994392673595, -0.25608304360082174, -0.25491431790588803, -0.25333532464264685, -0.2513275972597205, -0.24887271964850563, -0.24595240903318352, -0.24254860747951545, -0.23864358255914048, -0.23422003771675348, -0.22926123289510958, -0.2237511159768474, -0.21767446560171966, -0.21101704591228101, -0.20376577376948884, -0.19590889896084046, -0.18743619789660784, -0.17833918125291817, -0.16861131597259943, -0.15824826197372, -0.14724812384041736, -0.13561171767795946, -0.12334285320234666, -0.1104486310009745, -0.0969397547421785, -0.08283085792443143, -0.06814084453682787, -0.052893242747082944, -0.0371165704369362, -0.020844711062317417, -0.0041172979212657085, 0.013019895540357596, 0.03051456227354264, 0.04830746850156273, 0.06633206508066437, 0.08451410826740378, 0.10277129568366998, 0.12101292425576726, 0.13913957801778767, 0.1570428549272255, 0.17460514325867077, 0.19169945973769698, 0.20818936337236346, 0.22392896095590348, 0.23876302247666994, 0.2525272272069697, 0.26504856408201666, 0.2761459131567735, 0.2856308384797084, 0.2933086266882255, 0.29897961005735557, 0.3024408176696683, 0.3034880038761711, 0.30191810934563407, 0.29753221682006764, 0.29013907128120714, 0.27955924266762383, 0.26563001865497, 0.248211125420844, 0.22719138587045043, 0.20249643761919012, 0.17409764724585153, 0.14202237309059643, 0.1063657463353032, 0.06730415944743226, 0.02511067248431388, -0.01982742854145469, -0.06698866080978749, -0.11569467192383953, -0.16508454372370776, -0.21408571573826815, -0.2613811321644635, -0.3053721730005796, -0.3441368821848939, -0.3753829528469489, -0.39639487156531705, -0.40397455929182746, -0.39437477574254604, -0.3632244759073372, -0.30544522116042244, -0.215157652464453, -0.08557692846924699, 0.09110408405343452, 0.3238452070861012, 0.6229044151811987, 1.0]} diff --git a/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/test/fixtures/python/integer_n.json b/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/test/fixtures/python/integer_n.json new file mode 100644 index 000000000000..63ec06977837 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/test/fixtures/python/integer_n.json @@ -0,0 +1 @@ +{"n": [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 30], "x": [-1.0, -0.997997997997998, -0.995995995995996, -0.993993993993994, -0.991991991991992, -0.98998998998999, -0.987987987987988, -0.985985985985986, -0.983983983983984, -0.9819819819819819, -0.97997997997998, -0.977977977977978, -0.975975975975976, -0.973973973973974, -0.9719719719719719, -0.96996996996997, -0.967967967967968, -0.965965965965966, -0.963963963963964, -0.9619619619619619, -0.95995995995996, -0.957957957957958, -0.955955955955956, -0.953953953953954, -0.9519519519519519, -0.94994994994995, -0.9479479479479479, -0.9459459459459459, -0.943943943943944, -0.9419419419419419, -0.93993993993994, -0.9379379379379379, -0.9359359359359359, -0.933933933933934, -0.9319319319319319, -0.92992992992993, -0.9279279279279279, -0.9259259259259259, -0.9239239239239239, -0.9219219219219219, -0.91991991991992, -0.9179179179179179, -0.9159159159159159, -0.9139139139139139, -0.9119119119119119, -0.9099099099099099, -0.9079079079079079, -0.9059059059059059, -0.9039039039039038, -0.9019019019019019, -0.8998998998998999, -0.8978978978978979, -0.8958958958958959, -0.8938938938938938, -0.8918918918918919, -0.8898898898898899, -0.8878878878878879, -0.8858858858858859, -0.8838838838838838, -0.8818818818818819, -0.8798798798798799, -0.8778778778778779, -0.8758758758758759, -0.8738738738738738, -0.8718718718718719, -0.8698698698698699, -0.8678678678678678, -0.8658658658658659, -0.8638638638638638, -0.8618618618618619, -0.8598598598598599, -0.8578578578578578, -0.8558558558558559, -0.8538538538538538, -0.8518518518518519, -0.8498498498498499, -0.8478478478478478, -0.8458458458458459, -0.8438438438438438, -0.8418418418418419, -0.8398398398398399, -0.8378378378378378, -0.8358358358358359, -0.8338338338338338, -0.8318318318318318, -0.8298298298298299, -0.8278278278278278, -0.8258258258258259, -0.8238238238238238, -0.8218218218218218, -0.8198198198198199, -0.8178178178178178, -0.8158158158158157, -0.8138138138138138, -0.8118118118118118, -0.8098098098098099, -0.8078078078078078, -0.8058058058058057, -0.8038038038038038, -0.8018018018018018, -0.7997997997997999, -0.7977977977977978, -0.7957957957957957, -0.7937937937937938, -0.7917917917917918, -0.7897897897897898, -0.7877877877877878, -0.7857857857857857, -0.7837837837837838, -0.7817817817817818, -0.7797797797797797, -0.7777777777777778, -0.7757757757757757, -0.7737737737737738, -0.7717717717717718, -0.7697697697697697, -0.7677677677677678, -0.7657657657657657, -0.7637637637637638, -0.7617617617617618, -0.7597597597597597, -0.7577577577577578, -0.7557557557557557, -0.7537537537537538, -0.7517517517517518, -0.7497497497497497, -0.7477477477477478, -0.7457457457457457, -0.7437437437437437, -0.7417417417417418, -0.7397397397397397, -0.7377377377377378, -0.7357357357357357, -0.7337337337337337, -0.7317317317317318, -0.7297297297297297, -0.7277277277277278, -0.7257257257257257, -0.7237237237237237, -0.7217217217217218, -0.7197197197197197, -0.7177177177177176, -0.7157157157157157, -0.7137137137137137, -0.7117117117117118, -0.7097097097097097, -0.7077077077077076, -0.7057057057057057, -0.7037037037037037, -0.7017017017017018, -0.6996996996996997, -0.6976976976976976, -0.6956956956956957, -0.6936936936936937, -0.6916916916916918, -0.6896896896896897, -0.6876876876876876, -0.6856856856856857, -0.6836836836836837, -0.6816816816816818, -0.6796796796796797, -0.6776776776776776, -0.6756756756756757, -0.6736736736736737, -0.6716716716716717, -0.6696696696696697, -0.6676676676676676, -0.6656656656656657, -0.6636636636636637, -0.6616616616616617, -0.6596596596596597, -0.6576576576576576, -0.6556556556556556, -0.6536536536536537, -0.6516516516516517, -0.6496496496496497, -0.6476476476476476, -0.6456456456456456, -0.6436436436436437, -0.6416416416416417, -0.6396396396396397, -0.6376376376376376, -0.6356356356356356, -0.6336336336336337, -0.6316316316316316, -0.6296296296296297, -0.6276276276276276, -0.6256256256256256, -0.6236236236236237, -0.6216216216216216, -0.6196196196196196, -0.6176176176176176, -0.6156156156156156, -0.6136136136136137, -0.6116116116116116, -0.6096096096096096, -0.6076076076076076, -0.6056056056056056, -0.6036036036036037, -0.6016016016016016, -0.5995995995995996, -0.5975975975975976, -0.5955955955955956, -0.5935935935935936, -0.5915915915915916, -0.5895895895895895, -0.5875875875875876, -0.5855855855855856, -0.5835835835835836, -0.5815815815815816, -0.5795795795795795, -0.5775775775775776, -0.5755755755755756, -0.5735735735735736, -0.5715715715715716, -0.5695695695695695, -0.5675675675675675, -0.5655655655655656, -0.5635635635635636, -0.5615615615615616, -0.5595595595595595, -0.5575575575575575, -0.5555555555555556, -0.5535535535535536, -0.5515515515515516, -0.5495495495495495, -0.5475475475475475, -0.5455455455455456, -0.5435435435435436, -0.5415415415415415, -0.5395395395395395, -0.5375375375375375, -0.5355355355355356, -0.5335335335335336, -0.5315315315315315, -0.5295295295295295, -0.5275275275275275, -0.5255255255255256, -0.5235235235235236, -0.5215215215215215, -0.5195195195195195, -0.5175175175175175, -0.5155155155155156, -0.5135135135135136, -0.5115115115115115, -0.5095095095095095, -0.5075075075075075, -0.5055055055055055, -0.5035035035035035, -0.5015015015015015, -0.49949949949949946, -0.4974974974974975, -0.49549549549549554, -0.4934934934934935, -0.4914914914914915, -0.48948948948948945, -0.4874874874874875, -0.48548548548548554, -0.48348348348348347, -0.4814814814814815, -0.47947947947947944, -0.4774774774774775, -0.47547547547547553, -0.47347347347347346, -0.4714714714714715, -0.46946946946946944, -0.4674674674674675, -0.4654654654654655, -0.46346346346346345, -0.4614614614614615, -0.45945945945945943, -0.4574574574574575, -0.4554554554554555, -0.45345345345345345, -0.4514514514514515, -0.4494494494494494, -0.44744744744744747, -0.4454454454454454, -0.44344344344344344, -0.4414414414414415, -0.4394394394394394, -0.43743743743743746, -0.4354354354354354, -0.43343343343343343, -0.4314314314314315, -0.4294294294294294, -0.42742742742742745, -0.4254254254254254, -0.42342342342342343, -0.42142142142142147, -0.4194194194194194, -0.41741741741741745, -0.4154154154154154, -0.4134134134134134, -0.41141141141141147, -0.4094094094094094, -0.40740740740740744, -0.4054054054054054, -0.4034034034034034, -0.40140140140140146, -0.3993993993993994, -0.39739739739739743, -0.39539539539539537, -0.3933933933933934, -0.39139139139139134, -0.3893893893893894, -0.3873873873873874, -0.38538538538538536, -0.3833833833833834, -0.38138138138138133, -0.3793793793793794, -0.3773773773773774, -0.37537537537537535, -0.3733733733733734, -0.37137137137137133, -0.36936936936936937, -0.3673673673673674, -0.36536536536536535, -0.3633633633633634, -0.3613613613613613, -0.35935935935935936, -0.3573573573573574, -0.35535535535535534, -0.3533533533533534, -0.3513513513513513, -0.34934934934934936, -0.3473473473473474, -0.34534534534534533, -0.3433433433433434, -0.3413413413413413, -0.33933933933933935, -0.3373373373373374, -0.3353353353353353, -0.33333333333333337, -0.3313313313313313, -0.32932932932932935, -0.3273273273273274, -0.3253253253253253, -0.32332332332332336, -0.3213213213213213, -0.31931931931931934, -0.31731731731731727, -0.3153153153153153, -0.31331331331331336, -0.3113113113113113, -0.30930930930930933, -0.30730730730730726, -0.3053053053053053, -0.30330330330330335, -0.3013013013013013, -0.2992992992992993, -0.29729729729729726, -0.2952952952952953, -0.29329329329329334, -0.2912912912912913, -0.2892892892892893, -0.28728728728728725, -0.2852852852852853, -0.28328328328328334, -0.28128128128128127, -0.2792792792792793, -0.27727727727727725, -0.2752752752752753, -0.27327327327327333, -0.27127127127127126, -0.2692692692692693, -0.26726726726726724, -0.2652652652652653, -0.2632632632632632, -0.26126126126126126, -0.2592592592592593, -0.25725725725725723, -0.2552552552552553, -0.2532532532532532, -0.25125125125125125, -0.2492492492492493, -0.24724724724724723, -0.24524524524524527, -0.2432432432432432, -0.24124124124124124, -0.2392392392392393, -0.23723723723723722, -0.23523523523523526, -0.2332332332332332, -0.23123123123123124, -0.22922922922922928, -0.2272272272272272, -0.22522522522522526, -0.2232232232232232, -0.22122122122122123, -0.21921921921921927, -0.2172172172172172, -0.21521521521521525, -0.21321321321321318, -0.21121121121121122, -0.20920920920920927, -0.2072072072072072, -0.20520520520520524, -0.20320320320320318, -0.20120120120120122, -0.19919919919919926, -0.1971971971971972, -0.19519519519519524, -0.19319319319319317, -0.1911911911911912, -0.18918918918918914, -0.1871871871871872, -0.18518518518518523, -0.18318318318318316, -0.1811811811811812, -0.17917917917917914, -0.17717717717717718, -0.17517517517517522, -0.17317317317317316, -0.1711711711711712, -0.16916916916916913, -0.16716716716716717, -0.16516516516516522, -0.16316316316316315, -0.1611611611611612, -0.15915915915915912, -0.15715715715715717, -0.1551551551551552, -0.15315315315315314, -0.1511511511511512, -0.14914914914914912, -0.14714714714714716, -0.1451451451451452, -0.14314314314314314, -0.14114114114114118, -0.1391391391391391, -0.13713713713713716, -0.1351351351351351, -0.13313313313313313, -0.13113113113113117, -0.1291291291291291, -0.12712712712712715, -0.12512512512512508, -0.12312312312312312, -0.12112112112112117, -0.1191191191191191, -0.11711711711711714, -0.11511511511511507, -0.11311311311311312, -0.11111111111111116, -0.10910910910910909, -0.10710710710710714, -0.10510510510510507, -0.10310310310310311, -0.10110110110110115, -0.09909909909909909, -0.09709709709709713, -0.09509509509509506, -0.0930930930930931, -0.09109109109109115, -0.08908908908908908, -0.08708708708708712, -0.08508508508508505, -0.0830830830830831, -0.08108108108108114, -0.07907907907907907, -0.07707707707707712, -0.07507507507507505, -0.07307307307307309, -0.07107107107107113, -0.06906906906906907, -0.06706706706706711, -0.06506506506506504, -0.06306306306306309, -0.06106106106106102, -0.05905905905905906, -0.0570570570570571, -0.055055055055055035, -0.05305305305305308, -0.05105105105105101, -0.049049049049049054, -0.0470470470470471, -0.04504504504504503, -0.04304304304304307, -0.041041041041041004, -0.03903903903903905, -0.03703703703703709, -0.03503503503503502, -0.033033033033033066, -0.031031031031030998, -0.02902902902902904, -0.027027027027027084, -0.025025025025025016, -0.02302302302302306, -0.02102102102102099, -0.019019019019019034, -0.017017017017017078, -0.01501501501501501, -0.013013013013013053, -0.011011011011010985, -0.009009009009009028, -0.00700700700700696, -0.005005005005005003, -0.0030030030030030463, -0.0010010010010009784, 0.0010010010010010895, 0.0030030030030030463, 0.005005005005005003, 0.00700700700700696, 0.009009009009008917, 0.011011011011011096, 0.013013013013013053, 0.01501501501501501, 0.017017017017016967, 0.019019019019018923, 0.021021021021021102, 0.02302302302302306, 0.025025025025025016, 0.027027027027026973, 0.02902902902902893, 0.03103103103103111, 0.033033033033033066, 0.03503503503503502, 0.03703703703703698, 0.039039039039038936, 0.041041041041041115, 0.04304304304304307, 0.04504504504504503, 0.047047047047046986, 0.04904904904904894, 0.05105105105105112, 0.05305305305305308, 0.055055055055055035, 0.05705705705705699, 0.05905905905905895, 0.06106106106106113, 0.06306306306306309, 0.06506506506506504, 0.067067067067067, 0.06906906906906896, 0.07107107107107113, 0.07307307307307309, 0.07507507507507505, 0.077077077077077, 0.07907907907907896, 0.08108108108108114, 0.0830830830830831, 0.08508508508508505, 0.08708708708708701, 0.08908908908908897, 0.09109109109109115, 0.0930930930930931, 0.09509509509509506, 0.09709709709709702, 0.0990990990990992, 0.10110110110110115, 0.10310310310310311, 0.10510510510510507, 0.10710710710710702, 0.1091091091091092, 0.11111111111111116, 0.11311311311311312, 0.11511511511511507, 0.11711711711711703, 0.11911911911911921, 0.12112112112112117, 0.12312312312312312, 0.12512512512512508, 0.12712712712712704, 0.12912912912912922, 0.13113113113113117, 0.13313313313313313, 0.1351351351351351, 0.13713713713713704, 0.13913913913913922, 0.14114114114114118, 0.14314314314314314, 0.1451451451451451, 0.14714714714714705, 0.14914914914914923, 0.1511511511511512, 0.15315315315315314, 0.1551551551551551, 0.15715715715715706, 0.15915915915915924, 0.1611611611611612, 0.16316316316316315, 0.1651651651651651, 0.16716716716716706, 0.16916916916916924, 0.1711711711711712, 0.17317317317317316, 0.1751751751751751, 0.17717717717717707, 0.17917917917917925, 0.1811811811811812, 0.18318318318318316, 0.18518518518518512, 0.18718718718718708, 0.18918918918918926, 0.1911911911911912, 0.19319319319319317, 0.19519519519519513, 0.19719719719719708, 0.19919919919919926, 0.20120120120120122, 0.20320320320320318, 0.20520520520520513, 0.2072072072072071, 0.20920920920920927, 0.21121121121121122, 0.21321321321321318, 0.21521521521521514, 0.21721721721721732, 0.21921921921921927, 0.22122122122122123, 0.2232232232232232, 0.22522522522522515, 0.22722722722722732, 0.22922922922922928, 0.23123123123123124, 0.2332332332332332, 0.23523523523523515, 0.23723723723723733, 0.2392392392392393, 0.24124124124124124, 0.2432432432432432, 0.24524524524524516, 0.24724724724724734, 0.2492492492492493, 0.25125125125125125, 0.2532532532532532, 0.25525525525525516, 0.25725725725725734, 0.2592592592592593, 0.26126126126126126, 0.2632632632632632, 0.26526526526526517, 0.26726726726726735, 0.2692692692692693, 0.27127127127127126, 0.2732732732732732, 0.2752752752752752, 0.27727727727727736, 0.2792792792792793, 0.28128128128128127, 0.2832832832832832, 0.2852852852852852, 0.28728728728728736, 0.2892892892892893, 0.2912912912912913, 0.29329329329329323, 0.2952952952952952, 0.29729729729729737, 0.2992992992992993, 0.3013013013013013, 0.30330330330330324, 0.3053053053053052, 0.3073073073073074, 0.30930930930930933, 0.3113113113113113, 0.31331331331331325, 0.3153153153153152, 0.3173173173173174, 0.31931931931931934, 0.3213213213213213, 0.32332332332332325, 0.3253253253253252, 0.3273273273273274, 0.32932932932932935, 0.3313313313313313, 0.33333333333333326, 0.3353353353353352, 0.3373373373373374, 0.33933933933933935, 0.3413413413413413, 0.34334334334334327, 0.3453453453453452, 0.3473473473473474, 0.34934934934934936, 0.3513513513513513, 0.35335335335335327, 0.35535535535535545, 0.3573573573573574, 0.35935935935935936, 0.3613613613613613, 0.3633633633633633, 0.36536536536536546, 0.3673673673673674, 0.36936936936936937, 0.37137137137137133, 0.3733733733733733, 0.37537537537537546, 0.3773773773773774, 0.3793793793793794, 0.38138138138138133, 0.3833833833833833, 0.38538538538538547, 0.3873873873873874, 0.3893893893893894, 0.39139139139139134, 0.3933933933933933, 0.3953953953953955, 0.39739739739739743, 0.3993993993993994, 0.40140140140140135, 0.4034034034034033, 0.4054054054054055, 0.40740740740740744, 0.4094094094094094, 0.41141141141141135, 0.4134134134134133, 0.4154154154154155, 0.41741741741741745, 0.4194194194194194, 0.42142142142142136, 0.4234234234234233, 0.4254254254254255, 0.42742742742742745, 0.4294294294294294, 0.43143143143143137, 0.4334334334334333, 0.4354354354354355, 0.43743743743743746, 0.4394394394394394, 0.4414414414414414, 0.44344344344344333, 0.4454454454454455, 0.44744744744744747, 0.4494494494494494, 0.4514514514514514, 0.45345345345345334, 0.4554554554554555, 0.4574574574574575, 0.45945945945945943, 0.4614614614614614, 0.46346346346346334, 0.4654654654654655, 0.4674674674674675, 0.46946946946946944, 0.4714714714714714, 0.47347347347347357, 0.47547547547547553, 0.4774774774774775, 0.47947947947947944, 0.4814814814814814, 0.4834834834834836, 0.48548548548548554, 0.4874874874874875, 0.48948948948948945, 0.4914914914914914, 0.4934934934934936, 0.49549549549549554, 0.4974974974974975, 0.49949949949949946, 0.5015015015015014, 0.5035035035035036, 0.5055055055055055, 0.5075075075075075, 0.5095095095095095, 0.5115115115115114, 0.5135135135135136, 0.5155155155155156, 0.5175175175175175, 0.5195195195195195, 0.5215215215215214, 0.5235235235235236, 0.5255255255255256, 0.5275275275275275, 0.5295295295295295, 0.5315315315315314, 0.5335335335335336, 0.5355355355355356, 0.5375375375375375, 0.5395395395395395, 0.5415415415415414, 0.5435435435435436, 0.5455455455455456, 0.5475475475475475, 0.5495495495495495, 0.5515515515515514, 0.5535535535535536, 0.5555555555555556, 0.5575575575575575, 0.5595595595595595, 0.5615615615615615, 0.5635635635635636, 0.5655655655655656, 0.5675675675675675, 0.5695695695695695, 0.5715715715715715, 0.5735735735735736, 0.5755755755755756, 0.5775775775775776, 0.5795795795795795, 0.5815815815815815, 0.5835835835835836, 0.5855855855855856, 0.5875875875875876, 0.5895895895895895, 0.5915915915915915, 0.5935935935935936, 0.5955955955955956, 0.5975975975975976, 0.5995995995995995, 0.6016016016016015, 0.6036036036036037, 0.6056056056056056, 0.6076076076076076, 0.6096096096096095, 0.6116116116116117, 0.6136136136136137, 0.6156156156156156, 0.6176176176176176, 0.6196196196196195, 0.6216216216216217, 0.6236236236236237, 0.6256256256256256, 0.6276276276276276, 0.6296296296296295, 0.6316316316316317, 0.6336336336336337, 0.6356356356356356, 0.6376376376376376, 0.6396396396396395, 0.6416416416416417, 0.6436436436436437, 0.6456456456456456, 0.6476476476476476, 0.6496496496496496, 0.6516516516516517, 0.6536536536536537, 0.6556556556556556, 0.6576576576576576, 0.6596596596596596, 0.6616616616616617, 0.6636636636636637, 0.6656656656656657, 0.6676676676676676, 0.6696696696696696, 0.6716716716716717, 0.6736736736736737, 0.6756756756756757, 0.6776776776776776, 0.6796796796796796, 0.6816816816816818, 0.6836836836836837, 0.6856856856856857, 0.6876876876876876, 0.6896896896896896, 0.6916916916916918, 0.6936936936936937, 0.6956956956956957, 0.6976976976976976, 0.6996996996996996, 0.7017017017017018, 0.7037037037037037, 0.7057057057057057, 0.7077077077077076, 0.7097097097097096, 0.7117117117117118, 0.7137137137137137, 0.7157157157157157, 0.7177177177177176, 0.7197197197197196, 0.7217217217217218, 0.7237237237237237, 0.7257257257257257, 0.7277277277277276, 0.7297297297297298, 0.7317317317317318, 0.7337337337337337, 0.7357357357357357, 0.7377377377377377, 0.7397397397397398, 0.7417417417417418, 0.7437437437437437, 0.7457457457457457, 0.7477477477477477, 0.7497497497497498, 0.7517517517517518, 0.7537537537537538, 0.7557557557557557, 0.7577577577577577, 0.7597597597597598, 0.7617617617617618, 0.7637637637637638, 0.7657657657657657, 0.7677677677677677, 0.7697697697697699, 0.7717717717717718, 0.7737737737737738, 0.7757757757757757, 0.7777777777777777, 0.7797797797797799, 0.7817817817817818, 0.7837837837837838, 0.7857857857857857, 0.7877877877877877, 0.7897897897897899, 0.7917917917917918, 0.7937937937937938, 0.7957957957957957, 0.7977977977977977, 0.7997997997997999, 0.8018018018018018, 0.8038038038038038, 0.8058058058058057, 0.8078078078078077, 0.8098098098098099, 0.8118118118118118, 0.8138138138138138, 0.8158158158158157, 0.8178178178178177, 0.8198198198198199, 0.8218218218218218, 0.8238238238238238, 0.8258258258258258, 0.8278278278278277, 0.8298298298298299, 0.8318318318318318, 0.8338338338338338, 0.8358358358358358, 0.8378378378378377, 0.8398398398398399, 0.8418418418418419, 0.8438438438438438, 0.8458458458458458, 0.8478478478478477, 0.8498498498498499, 0.8518518518518519, 0.8538538538538538, 0.8558558558558558, 0.8578578578578577, 0.8598598598598599, 0.8618618618618619, 0.8638638638638638, 0.8658658658658658, 0.867867867867868, 0.8698698698698699, 0.8718718718718719, 0.8738738738738738, 0.8758758758758758, 0.877877877877878, 0.8798798798798799, 0.8818818818818819, 0.8838838838838838, 0.8858858858858858, 0.887887887887888, 0.8898898898898899, 0.8918918918918919, 0.8938938938938938, 0.8958958958958958, 0.897897897897898, 0.8998998998998999, 0.9019019019019019, 0.9039039039039038, 0.9059059059059058, 0.907907907907908, 0.9099099099099099, 0.9119119119119119, 0.9139139139139139, 0.9159159159159158, 0.917917917917918, 0.91991991991992, 0.9219219219219219, 0.9239239239239239, 0.9259259259259258, 0.927927927927928, 0.92992992992993, 0.9319319319319319, 0.9339339339339339, 0.9359359359359358, 0.937937937937938, 0.93993993993994, 0.9419419419419419, 0.9439439439439439, 0.9459459459459458, 0.947947947947948, 0.94994994994995, 0.9519519519519519, 0.9539539539539539, 0.9559559559559558, 0.957957957957958, 0.95995995995996, 0.9619619619619619, 0.9639639639639639, 0.9659659659659658, 0.967967967967968, 0.96996996996997, 0.9719719719719719, 0.9739739739739739, 0.9759759759759759, 0.977977977977978, 0.97997997997998, 0.9819819819819819, 0.9839839839839839, 0.9859859859859861, 0.987987987987988, 0.98998998998999, 0.991991991991992, 0.9939939939939939, 0.9959959959959961, 0.997997997997998, 1.0], "expected": [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, -0.9319319319319319, -0.92992992992993, -0.9279279279279279, -0.9259259259259259, -0.9239239239239239, -0.9219219219219219, -0.91991991991992, -0.9179179179179179, -0.9159159159159159, -0.9139139139139139, -0.9119119119119119, -0.9099099099099099, -0.9079079079079079, -0.9059059059059059, -0.9039039039039038, -0.9019019019019019, -0.8998998998998999, -0.8978978978978979, -0.8958958958958959, -0.8938938938938938, -0.8918918918918919, -0.8898898898898899, -0.8878878878878879, -0.8858858858858859, -0.8838838838838838, -0.8818818818818819, -0.8798798798798799, -0.8778778778778779, -0.8758758758758759, -0.8738738738738738, -0.8718718718718719, -0.8698698698698699, -0.8678678678678678, 0.6245855465074687, 0.6193911629347062, 0.6142088033979924, 0.6090384678973269, 0.6038801564327089, 0.5987338690041396, 0.5935996056116173, 0.5884773662551439, 0.5833671509347187, 0.5782689596503409, 0.573182792402012, 0.56810864918973, 0.563046530013497, 0.557996434873312, 0.5529583637691745, 0.5479323167010858, 0.5429182936690442, 0.5379162946730514, 0.5329263197131067, 0.5279483687892096, 0.5229824419013612, 0.5180285390495598, 0.5130866602338073, 0.5081568054541028, 0.5032389747104461, 0.49833316800283756, 0.49343938533127707, 0.48855762669576475, 0.4836878920963006, 0.47883018153288426, 0.47398449500551587, 0.46915083251419576, 0.4643291940589238, -0.07933957980000061, -0.07276180419994893, -0.06623199234729682, -0.05975002388132222, -0.05331577844130447, -0.04692913566652196, -0.040589975196253236, -0.034298176669777525, -0.028053619726373435, -0.02185618400532019, -0.015705749145896397, -0.00960219478737978, -0.0035454005690509494, 0.002464753869812819, 0.00842838888993147, 0.01434562485202695, 0.020216582116820703, 0.02604138104503345, 0.031820141997386586, 0.037552985334600775, 0.043240031417397795, 0.04888140060649904, 0.054477213262625335, 0.06002758974649791, 0.06553265041883788, 0.07099251564036652, 0.07640730577180532, 0.0817771411738753, 0.08710214220729748, 0.09238242923279294, 0.09761812261108344, 0.10280934270288997, 0.1079562098689334, 0.11305884446993528, -0.3786131375845869, -0.381311424151927, -0.38392772053012425, -0.38646264069138536, -0.3889167969211814, -0.3912907998182459, -0.39358525829457575, -0.3958007795754316, -0.39793796919933605, -0.3999974310180759, -0.4019797671967006, -0.40388557821352306, -0.40571546286011934, -0.40747001824132856, -0.4091498397752525, -0.4107555211932573, -0.4122876545399708, -0.4137468301732855, -0.4151336367643562, -0.41644866129760066, -0.41769248907070056, -0.41886570369459997, -0.41996888709350694, -0.4210026195048918, -0.42196747947948904, -0.4228640438812953, -0.4236928878875707, -0.42445458498883915, -0.42514970698888727, -0.4257788240047645, -0.426342504466784, -0.4268413151185218, -0.42727582101681705, 0.30353383204691, 0.2994559447644539, 0.29533318081522264, 0.29116678381052785, 0.28695798731724137, 0.2827080148881839, 0.2784180800925178, 0.274089386546138, 0.269723127942065, 0.26532048808083464, 0.26088264090089275, 0.25641075050898243, 0.25190597121054015, 0.24736944754008405, 0.24280231429160737, 0.23820569654897072, 0.23358070971629075, 0.22892845954833524, 0.22425004218091332, 0.2195465441612654, 0.21481904247845907, 0.21006860459377608, 0.20529628847110643, 0.20050314260734092, 0.19569020606275978, 0.19085850849142832, 0.1860090701715839, 0.18114290203603212, 0.17626100570253572, 0.17136437350420597, 0.16645398851989712, 0.16153082460459467, 0.15659584641980945, 0.17305530971696967, 0.1778136796907429, 0.18250789957982028, 0.18713727932280116, 0.19170115088606338, 0.1961988680649866, 0.20062980628584196, 0.20499336240835447, 0.20928895452893323, 0.21351602178456885, 0.21767402415740378, 0.2217624422799691, 0.22578077724109216, 0.22972855039247353, 0.2336053031559319, 0.23741059683131913, 0.2411440124051045, 0.2448051503596292, 0.24839363048302845, 0.25190909167982334, 0.2553511917821829, 0.25871960736185434, 0.26201403354276387, 0.2652341838142851, 0.2683797898451779, 0.2714506012981965, 0.27444638564536594, 0.2773669279839294, 0.2802120308529642, 0.28298151405066485, 0.2856752144522996, 0.28829298582883256, 0.29083469866621736, 0.29330023998535903, -0.27753791840282066, -0.27460491539184995, -0.27159501744417514, -0.268509576124704, -0.26534995206812617, -0.26211751454364124, -0.25881364102425913, -0.25543971676065635, -0.25199713435956933, -0.2484872933667076, -0.244911599854171, -0.24127146601235072, -0.23756830974629994, -0.23380355427655342, -0.22997862774437983, -0.2260949628214528, -0.22215399632391708, -0.2181571688308359, -0.21410592430700465, -0.21000170973010523, -0.20584597472219507, -0.20164017118550326, -0.19738575294252148, -0.19308417538037093, -0.18873689509942937, -0.18434536956619813, -0.17991105677039532, -0.17543541488625225, -0.17091990193800255, -0.16636597546954124, -0.161775092218238, -0.15714870779288992, -0.1524882763557901, -0.16151534150504815, -0.16603884617257217, -0.17049072459029535, -0.17486972832064143, -0.1791746420944147, -0.18340428387098137, -0.1875575048890212, -0.19163318970797752, -0.19563025624031802, -0.19954765577472933, -0.20338437299036313, -0.20713942596224744, -0.2108118661579878, -0.21440077842586658, -0.21790528097446255, -0.2213245253439046, -0.224657696368873, -0.22790401213346656, -0.2310627239180436, -0.23413311613815782, -0.23711450627569633, -0.24000624480233368, -0.2428077150954164, -0.24551833334638454, -0.24813754846184669, -0.25066484195741473, -0.25309972784440915, -0.2554417525095469, -0.257690494587715, -0.2598455648279444, -0.26190660595268805, -0.26387329251051006, -0.26574533072229667, 0.18752800939552888, 0.18336260532465087, 0.17912659360294036, 0.17482200884427446, 0.1704509015284041, 0.16601533712645516, 0.16151739522957548, 0.15695916868095788, 0.15234276271144004, 0.14767029407887883, 0.14294389021151604, 0.13816568835551624, 0.1333378347268821, 0.12846248366793356, 0.12354179680853433, 0.11857794223226431, 0.11357309364769674, 0.10852942956497597, 0.10344913247786164, 0.0983343880514071, 0.09318738431545337, 0.08801031086408101, 0.08280535806120115, 0.07757471625243545, 0.07232057498343092, 0.06704512222478276, 0.061750543603688535, 0.056439021642495535, 0.05111273500428065, 0.04577385774559001, 0.04042455857649685, 0.03506700012808428, 0.02970333822750154, 0.23026638893122658, 0.23248427950899772, 0.2345838198971471, 0.236564342386036, 0.23842523774320612, 0.2401659551371602, 0.24178600203819672, 0.24328494409652468, 0.24466240499790787, 0.2459180662970783, 0.24705166722916827, 0.24806300449941768, 0.2489519320514082, 0.24971836081409224, 0.25036225842787563, 0.2508836489500274, 0.2512826125396864, 0.2515592851227424, 0.2517138580368698, 0.2517465776569979, 0.2516577450015035, 0.25144771531941323, 0.2511168976589111, 0.2506657544174432, 0.25009480087371827, 0.24940460470190662, 0.248595785468337, 0.24766901411100195, 0.24662501240217377, 0.24546455239444773, 0.2441884558505223, 0.24279759365702835, 0.24129288522273243, 0.23967529786142364, 0.012234389346627461, 0.017940672480202008, 0.02363030464700358, 0.029300143570675313, 0.034947068249927105, 0.04056798047013943, 0.04615980629564012, 0.05171949754214003, 0.05724403322880556, 0.0627304210094746, 0.06817569858252753, 0.07357693507893082, 0.07893123242799896, 0.0842357267004111, 0.08948758942804962, 0.09468402890022785, 0.09982229143589191, 0.10489966263139479, 0.10991346858344482, 0.11486107708685282, 0.11973989880670882, 0.12454738842463199, 0.12928104575875338, 0.13393841685709526, 0.13851709506403206, 0.14301472205952612, 0.14742898887084033, 0.15175763685645297, 0.15599845866189546, 0.16014929914726395, 0.164208056286154, 0.16817268203578886, 0.17204118317811895, -0.18375325693615568, -0.18021276477406467, -0.17655799696862517, -0.17279148421346247, -0.16891582079573716, -0.1649336628375304, -0.16084772650933704, -0.15666078621673207, -0.15237567276129887, -0.1479952714768814, -0.1435225203422623, -0.1389604080713529, -0.13431197218198732, -0.12958029704443697, -0.12476851191072977, -0.11987978892589979, -0.11491734112227275, -0.10988442039789315, -0.10478431548022754, -0.0996203498762403, -0.09439587980997302, -0.08911429214874678, -0.08377900231909191, -0.07839345221354865, -0.0729611080894281, -0.06748545846067128, -0.06197001198391397, -0.056418295339860314, -0.05083385111109681, -0.045220235657428776, -0.0395810169898593, -0.03391977264430729, -0.02824008755614718, -0.21215693030464763, -0.21342338937529176, -0.21453081657038905, -0.21547856813433228, -0.21626611577689397, -0.2168930467981561, -0.2173590641369346, -0.21766398634290085, -0.21780774747265028, -0.2177903969100059, -0.2176120991108928, -0.2172731332731529, -0.21677389293172108, -0.21611488547961422, -0.215296731615233, -0.21432016471651494, -0.21318603014251242, -0.21189528446301484, -0.2104489946168712, -0.20884833699970343, -0.207094596481748, -0.20518916535658943, -0.20313354222159596, -0.2009293307909012, -0.1985782386418048, -0.19608207589551457, -0.1934427538331719, -0.1906622834481475, -0.18774277393562516, -0.18468643112051666, -0.18149555582480292, -0.17817254217539943, -0.1747198758537046, -0.17114013228800024, -0.12288307729439066, -0.12776772091015653, -0.13254317835327725, -0.13720550880219617, -0.14175086713838156, -0.14617550691483597, -0.15047578324572022, -0.1546481556151309, -0.15868919060309575, -0.1625955645269267, -0.16636406599613457, -0.1699915983791476, -0.1734751821801711, -0.17681195732455673, -0.17999918535113196, -0.18303425151000421, -0.1859146667644065, -0.1886380696952369, -0.19120222830699302, -0.1936050417338816, -0.1958445418449518, -0.1979188947471573, -0.19982640218534173, -0.20156550283819447, -0.20313477350930328, -0.20453293021250318, -0.20575882915078278, -0.20681146758809466, -0.2076899846134778, -0.20839366179697735, -0.20892192373692317, -0.2092743384981929, -0.20945061794116965, -0.003145110069368795, -0.009432330289487617, -0.015710553494990204, -0.02197379081128628, -0.02821606705844293, -0.03443142621290737, -0.04061393685310069, -0.04675769758430434, -0.052856842438254864, -0.058905546242903034, -0.06489802995780425, -0.07082856597063006, -0.0766914833503327, -0.08248117305250742, -0.08819209307255008, -0.09381877354223547, -0.09935582176538808, -0.10479792718836378, -0.11013986630110154, -0.11537650746456442, -0.12050281566044047, -0.12551385715902705, -0.13040480410129707, -0.1351709389911881, -0.13980765909424084, -0.14431048073877822, -0.14867504351587782, -0.15289711437448936, -0.15697259160809954, -0.1608975087294498, -0.16466803822988707, -0.16828049522001137, -0.17173134094838544, 0.08778279028004271, 0.08191406798370293, 0.07595398143160587, 0.06990896197958468, 0.06378553754469768, 0.057590325875702175, 0.051330027722338745, 0.045011419909919526, 0.03864134832580737, 0.03222672082446423, 0.0257745000578542, 0.019291696238051353, 0.012785359838994259, 0.006262574244403463, -0.00026955165107167556, -0.006803890880319546, -0.01333330587466297, -0.019850655959933405, -0.02634880487044336, -0.03282062827352214, -0.039259021297266106, -0.04565690605412415, -0.052007239152916024, -0.05830301919188677, -0.06453729422537066, -0.07070316919666192, -0.07679381332968803, -0.08280246747209237, -0.08872245138237007, -0.09454717095370278, -0.10027012536719995, -0.10588491416727737, -0.11138524425195347, -0.11676493677091182, 0.13315327737955907, 0.12821595196326302, 0.12311557011707555, 0.11785828621124345, 0.11245045764309874, 0.10689863765291041, 0.10120956788962301, 0.09539017073401934, 0.08944754138713926, 0.0833889397320586, 0.07722178197743676, 0.07095363209148986, 0.06459219303532512, 0.058145297804829854, 0.051620900290543476, 0.045027065965204255, 0.03837196240887403, 0.03166384968177624, 0.024911070555199172, 0.018122040611006612, 0.011305238220514602, 0.004469194413655203, -0.0023775173504640423, -0.00922629150033566, -0.016068500744749137, -0.02289550652983688, -0.029698669548781198, -0.03646936029237102, -0.043198969628480605, -0.04987891939846689, -0.05650067301836981, -0.06305574607275322, -0.06953571688895135, 0.15385554050662809, 0.14973052638014717, 0.1453878636151588, 0.14083336049033923, 0.13607313842437113, 0.13111362458799253, 0.12596154407079788, 0.12062391161072683, 0.11510802289476837, 0.10942144544001015, 0.10357200906473935, 0.09756779595989942, 0.09141713037175928, 0.08512856790722761, 0.07871088447379693, 0.07217306486663191, 0.06552429101587307, 0.05877392990772279, 0.0519315211934015, 0.04500676450055763, 0.038009506462180265, 0.03094972747855665, 0.023837528228238453, 0.016683115944438748, 0.009496790473688288, 0.002288930133979211, -0.0049300226099747435, -0.012149575636389992, -0.01935920180264053, -0.02654835370940492, -0.03370647857377676, -0.040823033192075864, -0.04788749897285516, 0.1554085404122057, 0.1513298339822617, 0.1469977739923453, 0.14241885605613497, 0.1375999987575871, 0.13254853460113353, 0.12727220026093908, 0.12177912613903966, 0.11607782524330663, 0.11017718139724969, 0.10408643679477766, 0.09781517891411422, 0.09137332680612198, 0.08477111677337634, 0.07801908745734668, 0.07112806435210037, 0.06410914376395013, 0.056973676237461496, 0.04973324946923946, 0.04239967073184747, 0.03498494883117159, 0.027501275621451465, 0.01996100710308152, 0.012376644129173053, 0.0047608127476768125, -0.002873755793305982, -0.010514245348630463, -0.01814777545850149, -0.025761422180293037, -0.033342239139280055, -0.04087727876712122, -0.048353613696328235, -0.055758358278414494, 0.14045372029872186, 0.13536815301537636, 0.13001798959491956, 0.12441254595706265, 0.11856165971648466, 0.11247567516448725, 0.10616542721347327, 0.09964222432313262, 0.0929178304291793, 0.08600444589741844, 0.078914687527887, 0.07166156763570486, 0.06425847223719652, 0.056719138371696176, 0.04905763059133447, 0.041288316652889484, 0.033425842447595805, 0.025485106206554198, 0.017481232021073934, 0.009429542718983358, 0.001345532139529898, -0.006755163148922355, -0.0148567926426669, -0.022943521160738528, -0.030999458518703588, -0.03900868956825407, -0.046955304551417026, -0.05482342971698498, -0.06259725814566869, -0.07026108072939086, -0.07779931724919444, -0.08519654749533415, -0.09243754237231311, -0.09950729493092127, 0.09269568357161304, 0.08539223229364507, 0.07788568100232732, 0.07019181684641351, 0.06232693002353182, 0.05430778239091405, 0.04615157476106946, 0.0378759129351911, 0.029498772530382994, 0.021038462660019353, 0.012513588529765418, 0.003943013014858415, -0.0046541827127047075, -0.013258739435483974, -0.021851260946004064, -0.03041225582905932, -0.03892217989112054, -0.04736147915450711, -0.055710633331590126, -0.0639501996920442, -0.07206085723399833, -0.08002345106798447, -0.0878190369207206, -0.0954289256640902, -0.10283472777317212, -0.11001839761580137, -0.11696227747499374, -0.12364914120455844, -0.13006223741741987, -0.1361853321055647, -0.1420027505900973, -0.14749941869969066, -0.152660903075703, 0.008601604965233128, -0.0005184178390452432, -0.009659097849699594, -0.018796769412320558, -0.027907601735377013, -0.03696765830345394, -0.04595295728771637, -0.054839532818577674, -0.06360349698109341, -0.07222110238940993, -0.0806688051926739, -0.08892332836110911, -0.09696172509761443, -0.1047614422171311, -0.11230038333325738, -0.11955697168915555, -0.126510212467665, -0.13313975441380632, -0.13942595060145876, -0.14534991817498322, -0.15089359689595294, -0.15603980632490852, -0.16077230146826346, -0.1650758267210834, -0.16893616793749214, -0.17234020246194695, -0.17527594695651805, -0.17773260286169534, -0.17970059933105925, -0.18117163348343773, -0.18213870781992875, -0.18259616465737727, -0.18253971743459785, -0.11001439933350883, -0.11778656879534355, -0.12521628648990693, -0.13227841813139782, -0.13894873641636402, -0.1452040063963049, -0.15102206915362057, -0.15638192349993632, -0.16126380541549296, -0.16564926494878957, -0.1695212402969489, -0.17286412878939747, -0.17566385450044816, -0.17790793222019927, -0.17958552751791634, -0.18068751263768218, -0.18120651797263326, -0.18113697887155666, -0.18047517753998543, -0.1792192798072273, -0.17736936654098423, -0.17492745950235966, -0.17189754144612096, -0.16828557028406285, -0.16409948714320388, -0.15934921816532174, -0.15404666991000002, -0.14820571823985726, -0.14184219058400588, -0.1349738414939394, -0.1276203214250118, -0.11980313869638681, -0.11154561460275589, -0.10287283167226935, -0.17922560149336392, -0.17783074736427343, -0.17575675091499277, -0.1730062745863415, -0.16958456882348316, -0.1654994924279901, -0.1607615236028704, -0.1553837614313953, -0.14938191755795155, -0.14277429786818027, -0.1355817739963646, -0.12782774452033732, -0.11953808573799535, -0.11074109195486889, -0.10146740524890269, -0.09174993471670076, -0.08162376524482755, -0.0711260558902234, -0.06029592799539914, -0.04917434320654206, -0.037803971606043776, -0.02622905021502983, -0.014495232166095495, -0.0026494268915942254, 0.00926036828182486, 0.021185244696169447, 0.03307556660077182, 0.04488116253958771, 0.05655152331503384, 0.06803600591190047, 0.07928404272116434, 0.0902453553607865, 0.10087017234898521, -0.03688542243321255, -0.024520443811614057, -0.011979193244275765, 0.0006805894280896285, 0.013399748388787325, 0.026117962647204285, 0.03877400856139579, 0.05130603321991134, 0.0636518377415022, 0.07574916947225256, 0.08753602198185041, 0.09895094168472268, 0.10993333983786224, 0.12042380859590646, 0.13036443973581444, 0.1396991445987109, 0.1483739737357262, 0.15633743468827768, 0.16354080628178944, 0.16993844776579253, 0.1754881010931135, 0.1801511845970382, 0.18389307629829857, 0.18668338505402907, 0.18849620774892503, 0.18931037072515244, 0.1891096536526083, 0.18788299405530082, 0.18562467073337566, 0.18233446435402478, 0.1780177935285993, 0.17268582474802074, 0.16635555461440626, 0.1857369834585496, 0.1877416883419612, 0.1886045594752977, 0.1883054519333446, 0.18683100426437982, 0.18417489977460594, 0.18033809327881173, 0.1753290005489495, 0.16916364778587023, 0.16186577855397927, 0.15346691575467053, 0.14400637637266134, 0.13353123691017377, 0.12209624762772536, 0.1097636939373186, 0.0966032035441694, 0.08269149820689504, 0.0681120892830123, 0.05295491654654791, 0.037315930107009704, 0.021296615623289453, 0.005003463391602014, -0.011452617707876103, -0.027956939996397603, -0.04439172866265109, -0.060636862999927835, -0.07657066443273994, -0.09207072806706544, -0.10701479400450922, -0.12128165415975514, -0.13475208981561576, -0.1473098346437589, -0.15884255741544342, -0.16924285812881495, -0.08677822095757938, -0.10293212400154264, -0.11834869464743697, -0.13288095683737963, -0.1463855058846113, -0.15872389042913715, -0.16976401717071346, -0.1793815675409328, -0.1874614146350458, -0.1938990279160789, -0.19860185243865172, -0.20149064862799043, -0.20250077800196567, -0.20158341965218313, -0.19870670181633412, -0.19385673249089072, -0.18703851276395345, -0.17827671640627485, -0.1676163192581091, -0.15512306210488627, -0.1408837310602351, -0.12500623998508897, -0.10761950018117432, -0.08887306352030067, -0.06893652632177796, -0.04799868268248751, -0.026266417610478363, -0.003963332225638785, 0.018671904519403454, 0.041387480668771445, 0.06392064294336167, 0.08600017250118336, 0.10734912863399144, 0.023902767063381306, 0.048152182456999065, 0.07210245953917463, 0.09541863432073801, 0.1177595332364311, 0.13878212680287175, 0.1581462433990324, 0.17551961103825647, 0.19058318684267553, 0.20303672528011027, 0.21260452712696962, 0.21904130163967406, 0.2221380646286537, 0.22172798512774824, 0.21769208325272, 0.20996467178240352, 0.1985384241366418, 0.18346894195575447, 0.16487868662670527, 0.14296013110466985, 0.1179779815360327, 0.0902703128313755, 0.06024845884104643, 0.028395496577329357, -0.004736834514721483, -0.0385329323720809, -0.07231999657648072, -0.1053766890738046, -0.13694390467381845, -0.16623773980498918, -0.19246471606277948, -0.21483927504520184, -0.2326035116892179, -0.20780532492994544, -0.22831948394735657, -0.24295698299305285, -0.25091751493474884, -0.25152361308643767, -0.24425823762713283, -0.2288038567331019, -0.20508207756904728, -0.17329261387143685, -0.13395006520049133, -0.08791662288975514, -0.036428403644668275, 0.018887362535412275, 0.07600760465695816, 0.1325250733225303, 0.18568102153407906, 0.23242432056024598, 0.269503317235757, 0.2935977395111661, 0.3014990796889628, 0.2903491417580871, 0.25794784379098956, 0.2031429328127309, 0.12631601338790507, 0.02998122915862453, -0.08048491318091108, -0.1959617059111962, -0.3025268817441993, -0.3801973174360031, -0.40143817135508286, -0.3294072892431328, -0.11589781977545299, 0.3010622967440444, 1.0]} diff --git a/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/test/fixtures/python/large_n.json b/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/test/fixtures/python/large_n.json new file mode 100644 index 000000000000..02443cc69689 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/test/fixtures/python/large_n.json @@ -0,0 +1 @@ +{"n": [30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 60], "x": [-1.0, -0.9959919839679359, -0.9919839679358717, -0.9879759519038076, -0.9839679358717435, -0.9799599198396793, -0.9759519038076152, -0.9719438877755511, -0.9679358717434869, -0.9639278557114228, -0.9599198396793587, -0.9559118236472945, -0.9519038076152304, -0.9478957915831663, -0.9438877755511023, -0.9398797595190381, -0.935871743486974, -0.9318637274549099, -0.9278557114228457, -0.9238476953907816, -0.9198396793587175, -0.9158316633266533, -0.9118236472945892, -0.9078156312625251, -0.9038076152304609, -0.8997995991983968, -0.8957915831663327, -0.8917835671342685, -0.8877755511022044, -0.8837675350701403, -0.8797595190380761, -0.875751503006012, -0.8717434869739479, -0.8677354709418837, -0.8637274549098196, -0.8597194388777555, -0.8557114228456915, -0.8517034068136273, -0.8476953907815632, -0.8436873747494991, -0.8396793587174349, -0.8356713426853708, -0.8316633266533067, -0.8276553106212425, -0.8236472945891784, -0.8196392785571143, -0.8156312625250501, -0.811623246492986, -0.8076152304609219, -0.8036072144288577, -0.7995991983967936, -0.7955911823647295, -0.7915831663326653, -0.7875751503006012, -0.7835671342685371, -0.779559118236473, -0.7755511022044088, -0.7715430861723447, -0.7675350701402806, -0.7635270541082164, -0.7595190380761523, -0.7555110220440882, -0.751503006012024, -0.7474949899799599, -0.7434869739478958, -0.7394789579158316, -0.7354709418837675, -0.7314629258517034, -0.7274549098196392, -0.7234468937875751, -0.719438877755511, -0.7154308617234469, -0.7114228456913828, -0.7074148296593187, -0.7034068136272545, -0.6993987975951904, -0.6953907815631263, -0.6913827655310621, -0.687374749498998, -0.6833667334669339, -0.6793587174348698, -0.6753507014028056, -0.6713426853707415, -0.6673346693386774, -0.6633266533066133, -0.6593186372745492, -0.6553106212424851, -0.6513026052104209, -0.6472945891783568, -0.6432865731462927, -0.6392785571142285, -0.6352705410821644, -0.6312625250501003, -0.6272545090180361, -0.623246492985972, -0.6192384769539079, -0.6152304609218437, -0.6112224448897796, -0.6072144288577155, -0.6032064128256514, -0.5991983967935872, -0.5951903807615231, -0.591182364729459, -0.5871743486973948, -0.5831663326653307, -0.5791583166332666, -0.5751503006012024, -0.5711422845691383, -0.5671342685370742, -0.56312625250501, -0.5591182364729459, -0.5551102204408818, -0.5511022044088176, -0.5470941883767535, -0.5430861723446894, -0.5390781563126252, -0.5350701402805611, -0.531062124248497, -0.5270541082164328, -0.5230460921843687, -0.5190380761523046, -0.5150300601202404, -0.5110220440881764, -0.5070140280561123, -0.5030060120240482, -0.498997995991984, -0.4949899799599199, -0.49098196392785576, -0.4869739478957916, -0.4829659318637275, -0.47895791583166336, -0.47494989979959923, -0.4709418837675351, -0.46693386773547096, -0.46292585170340683, -0.4589178356713427, -0.45490981963927857, -0.45090180360721444, -0.4468937875751503, -0.44288577154308617, -0.43887775551102204, -0.434869739478958, -0.4308617234468939, -0.42685370741482975, -0.4228456913827656, -0.4188376753507015, -0.41482965931863736, -0.4108216432865732, -0.4068136272545091, -0.40280561122244496, -0.3987975951903808, -0.3947895791583167, -0.39078156312625256, -0.38677354709418843, -0.3827655310621243, -0.37875751503006017, -0.37474949899799603, -0.3707414829659319, -0.36673346693386777, -0.36272545090180364, -0.3587174348697395, -0.35470941883767537, -0.35070140280561124, -0.3466933867735471, -0.342685370741483, -0.33867735470941884, -0.3346693386773547, -0.3306613226452907, -0.32665330661322656, -0.3226452905811624, -0.3186372745490983, -0.31462925851703416, -0.31062124248497003, -0.3066132264529059, -0.30260521042084176, -0.29859719438877763, -0.2945891783567135, -0.29058116232464937, -0.28657314629258523, -0.2825651302605211, -0.27855711422845697, -0.27454909819639284, -0.2705410821643287, -0.2665330661322646, -0.26252505010020044, -0.2585170340681363, -0.2545090180360722, -0.25050100200400804, -0.2464929859719439, -0.24248496993987978, -0.23847695390781565, -0.23446893787575152, -0.2304609218436875, -0.22645290581162336, -0.22244488977955923, -0.2184368737474951, -0.21442885771543096, -0.21042084168336683, -0.2064128256513027, -0.20240480961923857, -0.19839679358717444, -0.1943887775551103, -0.19038076152304617, -0.18637274549098204, -0.1823647294589179, -0.17835671342685377, -0.17434869739478964, -0.1703406813627255, -0.16633266533066138, -0.16232464929859725, -0.1583166332665331, -0.15430861723446898, -0.15030060120240485, -0.14629258517034072, -0.14228456913827658, -0.13827655310621245, -0.13426853707414832, -0.1302605210420842, -0.12625250501002017, -0.12224448897795603, -0.1182364729458919, -0.11422845691382777, -0.11022044088176364, -0.1062124248496995, -0.10220440881763537, -0.09819639278557124, -0.09418837675350711, -0.09018036072144298, -0.08617234468937884, -0.08216432865731471, -0.07815631262525058, -0.07414829659318645, -0.07014028056112231, -0.06613226452905818, -0.06212424849699405, -0.05811623246492992, -0.054108216432865786, -0.05010020040080165, -0.04609218436873752, -0.04208416833667339, -0.038076152304609256, -0.034068136272545124, -0.030060120240480992, -0.02605210420841686, -0.02204408817635284, -0.018036072144288706, -0.014028056112224574, -0.010020040080160442, -0.006012024048096309, -0.002004008016032177, 0.002004008016031955, 0.006012024048096087, 0.01002004008016022, 0.014028056112224352, 0.018036072144288484, 0.022044088176352616, 0.02605210420841675, 0.03006012024048088, 0.03406813627254501, 0.038076152304609145, 0.04208416833667328, 0.04609218436873741, 0.05010020040080154, 0.054108216432865675, 0.05811623246492981, 0.06212424849699394, 0.06613226452905807, 0.0701402805611222, 0.07414829659318634, 0.07815631262525047, 0.0821643286573146, 0.08617234468937873, 0.09018036072144286, 0.094188376753507, 0.09819639278557113, 0.10220440881763526, 0.1062124248496994, 0.11022044088176353, 0.11422845691382766, 0.11823647294589179, 0.12224448897795592, 0.12625250501002006, 0.13026052104208397, 0.1342685370741481, 0.13827655310621223, 0.14228456913827636, 0.1462925851703405, 0.15030060120240463, 0.15430861723446876, 0.1583166332665329, 0.16232464929859702, 0.16633266533066116, 0.1703406813627253, 0.17434869739478942, 0.17835671342685355, 0.18236472945891768, 0.18637274549098182, 0.19038076152304595, 0.19438877755511008, 0.1983967935871742, 0.20240480961923835, 0.20641282565130248, 0.2104208416833666, 0.21442885771543074, 0.21843687374749488, 0.222444889779559, 0.22645290581162314, 0.23046092184368727, 0.2344689378757514, 0.23847695390781554, 0.24248496993987967, 0.2464929859719438, 0.25050100200400793, 0.25450901803607207, 0.2585170340681362, 0.26252505010020033, 0.26653306613226446, 0.2705410821643286, 0.2745490981963927, 0.27855711422845686, 0.282565130260521, 0.2865731462925851, 0.29058116232464926, 0.2945891783567134, 0.2985971943887775, 0.30260521042084165, 0.3066132264529058, 0.3106212424849699, 0.31462925851703405, 0.3186372745490982, 0.3226452905811623, 0.32665330661322645, 0.3306613226452906, 0.3346693386773545, 0.3386773547094186, 0.34268537074148275, 0.3466933867735469, 0.350701402805611, 0.35470941883767515, 0.3587174348697393, 0.3627254509018034, 0.36673346693386755, 0.3707414829659317, 0.3747494989979958, 0.37875751503005994, 0.3827655310621241, 0.3867735470941882, 0.39078156312625234, 0.3947895791583165, 0.3987975951903806, 0.40280561122244474, 0.40681362725450887, 0.410821643286573, 0.41482965931863713, 0.41883767535070127, 0.4228456913827654, 0.42685370741482953, 0.43086172344689366, 0.4348697394789578, 0.4388777555110219, 0.44288577154308606, 0.4468937875751502, 0.4509018036072143, 0.45490981963927846, 0.4589178356713426, 0.4629258517034067, 0.46693386773547085, 0.470941883767535, 0.4749498997995991, 0.47895791583166325, 0.4829659318637274, 0.4869739478957915, 0.49098196392785565, 0.4949899799599198, 0.4989979959919839, 0.503006012024048, 0.5070140280561122, 0.5110220440881763, 0.5150300601202404, 0.5190380761523046, 0.5230460921843687, 0.5270541082164328, 0.531062124248497, 0.5350701402805611, 0.539078156312625, 0.5430861723446891, 0.5470941883767533, 0.5511022044088174, 0.5551102204408815, 0.5591182364729457, 0.5631262525050098, 0.5671342685370739, 0.5711422845691381, 0.5751503006012022, 0.5791583166332663, 0.5831663326653305, 0.5871743486973946, 0.5911823647294587, 0.5951903807615229, 0.599198396793587, 0.6032064128256511, 0.6072144288577153, 0.6112224448897794, 0.6152304609218435, 0.6192384769539077, 0.6232464929859718, 0.6272545090180359, 0.6312625250501, 0.6352705410821642, 0.6392785571142283, 0.6432865731462925, 0.6472945891783566, 0.6513026052104207, 0.6553106212424848, 0.659318637274549, 0.6633266533066131, 0.6673346693386772, 0.6713426853707414, 0.6753507014028055, 0.6793587174348696, 0.6833667334669338, 0.6873747494989979, 0.691382765531062, 0.6953907815631262, 0.6993987975951903, 0.7034068136272544, 0.7074148296593186, 0.7114228456913827, 0.7154308617234468, 0.719438877755511, 0.7234468937875751, 0.7274549098196392, 0.7314629258517034, 0.7354709418837675, 0.7394789579158316, 0.7434869739478958, 0.7474949899799597, 0.7515030060120238, 0.7555110220440879, 0.7595190380761521, 0.7635270541082162, 0.7675350701402803, 0.7715430861723445, 0.7755511022044086, 0.7795591182364727, 0.7835671342685369, 0.787575150300601, 0.7915831663326651, 0.7955911823647293, 0.7995991983967934, 0.8036072144288575, 0.8076152304609217, 0.8116232464929858, 0.8156312625250499, 0.819639278557114, 0.8236472945891782, 0.8276553106212423, 0.8316633266533064, 0.8356713426853706, 0.8396793587174347, 0.8436873747494988, 0.847695390781563, 0.8517034068136271, 0.8557114228456912, 0.8597194388777554, 0.8637274549098195, 0.8677354709418836, 0.8717434869739478, 0.8757515030060119, 0.879759519038076, 0.8837675350701402, 0.8877755511022043, 0.8917835671342684, 0.8957915831663326, 0.8997995991983967, 0.9038076152304608, 0.907815631262525, 0.9118236472945891, 0.9158316633266532, 0.9198396793587174, 0.9238476953907815, 0.9278557114228456, 0.9318637274549098, 0.9358717434869739, 0.939879759519038, 0.9438877755511021, 0.9478957915831663, 0.9519038076152302, 0.9559118236472943, 0.9599198396793585, 0.9639278557114226, 0.9679358717434867, 0.9719438877755509, 0.975951903807615, 0.9799599198396791, 0.9839679358717432, 0.9879759519038074, 0.9919839679358715, 0.9959919839679356, 1.0], "expected": [0.9999999999999969, -0.15642788998765786, -0.4030812848420975, -0.26003410538477495, -0.017487030891760694, 0.18212541529408532, 0.28647208377118616, 0.2939052931933759, 0.22744492130459582, 0.11842775235526143, -0.003034233401627548, -0.11294031032348958, -0.19523098306766892, -0.24172610196607003, -0.2509996243159388, -0.22676254035493482, -0.17613185830899247, 0.022566683112931196, -0.057049318393487966, -0.12628197913683958, -0.1788719066232224, -0.21109366879498015, -0.22165895658500817, -0.2114207604137843, -0.18295245142143213, -0.14006562814371082, -0.08731864618804344, -0.029555387479786283, 0.028497949723249212, 0.082560820829025, 0.12904284809034652, 0.1652039627304816, 0.18923487030466116, 0.20026655244001987, -0.1550090694389842, -0.11819936713303036, -0.07479236583914953, -0.027816805438498654, 0.01970581555510055, 0.0649376539465645, 0.10536995793110682, 0.13893374623460367, 0.1640743863614535, 0.17979081029523541, 0.18564179967646854, 0.181723067593145, 0.16861977131869807, 0.14733963592020188, 0.11923209011094643, 0.08589875775196432, 0.0641421872288309, 0.09875846866635182, 0.1279942424525618, 0.15063875733461352, 0.1658486141309342, 0.1731624813425786, 0.17249759706617518, 0.16412991580702035, 0.14866025260704457, 0.12696911417192394, 0.10016309478810212, 0.06951576585519073, 0.03640591742570323, 0.002255836237800471, -0.03152795328472761, -0.063609380869611, -0.09277121788580908, 0.1643811907045964, 0.16170188573724165, 0.15255162998219451, 0.13744958385358572, 0.11712890203344184, 0.09249852540372183, 0.06460055180010502, 0.03456506453506353, 0.003564241683076119, -0.02723254633062644, -0.05670110840092065, -0.08380093554514571, -0.10760872958242676, -0.1273461034065825, -0.14240085766072139, -0.1523414966046474, -0.15692489456961328, 0.08955302911817958, 0.0639857675025379, 0.03638129671412685, 0.0077473316192047115, -0.020900010808099737, -0.04857131974569318, -0.0743365463441748, -0.09735425215011381, -0.11689666390543595, -0.13236993081113102, -0.1433291695118965, -0.14948807170345046, -0.15072303351944993, -0.14707193949150132, -0.13872789239960914, -0.1260283200491821, -0.015930995624510086, -0.042205043305841114, -0.0668971704434265, -0.08922444456776597, -0.10849720096523596, -0.12413841515319768, -0.13569884334097926, -0.14286763734836722, -0.14547829297688178, -0.1435099392606932, -0.13708411623840688, -0.12645731727205312, -0.1120096854610303, -0.09423034994328802, -0.07369996507477042, -0.05107107251039117, -0.02704694258913598, -0.11868103091786938, -0.13022191936558614, -0.1376456474039437, -0.1407703592155933, -0.13954893643183405, -0.13406738111328512, -0.12453925354544315, -0.1112964607915719, -0.09477678705349524, -0.07550863661994672, -0.054093523027677254, -0.0311868830660261, -0.007477821007703389, 0.01633160294473711, 0.03954693494698834, 0.06150116092785739, 0.08157327202833688, -0.1297246958236691, -0.12023682857320822, -0.10718408340070512, -0.09098863620948197, -0.07215998939126375, -0.05127843160206344, -0.028976808912178742, -0.005921176479125517, 0.017209085831578416, 0.03974111301216267, 0.061027787469130325, 0.08046583602390449, 0.09751230995198039, 0.11169902549945779, 0.12264461083561125, 0.13006388139125613, -0.06314967955960857, -0.04216719240994371, -0.0200164135123658, 0.0026425113804881134, 0.025141841216508587, 0.046825723666413424, 0.06706898621542731, 0.08529471408263445, 0.1009901417808084, 0.1137204440177676, 0.12314008037711206, 0.1290014246191214, 0.13116049119714235, 0.12957965631069557, 0.12432735613276852, 0.11557482843634789, 0.1035900435056639, 0.060440751305933946, 0.07899457771518802, 0.09517372414605232, 0.10851856106861184, 0.11865589702299525, 0.1253087876738972, 0.12830344504046884, 0.1275730989419073, 0.1231587513685872, 0.11520685286434654, 0.103964015666172, 0.08976895901016613, 0.07304195559009144, 0.0542721128053994, 0.03400287660492421, 0.012816188186941246, 0.12359575721660337, 0.12602791849374714, 0.12472372944387122, 0.1197383117942325, 0.1112345453962921, 0.09947736935743326, 0.08482518419897948, 0.0677186397412342, 0.048667163741339364, 0.028233645433337645, 0.007017734601661746, -0.014361750402212062, -0.03528479387933742, -0.05514801763134587, -0.07338187451695494, -0.0894667204174261, -0.10294732195256881, 0.0733084476065113, 0.05497577518317186, 0.03502050657801205, 0.01404589158966825, -0.007317233301761733, -0.02842936147122778, -0.048661343380797646, -0.06741296541469767, -0.08413054014084828, -0.09832300208306322, -0.10957605151401348, -0.11756394980881871, -0.12205864163846475, -0.1229359595618273, -0.12017875301486926, -0.11387687377381424, -0.10422404109422688, -0.06863098465518581, -0.08508484266137287, -0.09890203963664662, -0.10966331097329794, -0.11704425107589002, -0.12082484110409539, -0.1208957629145919, -0.11726132686336753, -0.11003894363724553, -0.0994551741219985, -0.08583849341923866, -0.06960900250756193, -0.051265410880098644, -0.03136969319717718, -0.010529890300603625, 0.01061842204767205, -0.11743410103530566, -0.11139551466132522, -0.10181334173908005, -0.08899562084885672, -0.07335256915135334, -0.05538343425374059, -0.03566057330687583, -0.014811264483788722, 0.006502174925541879, 0.027603338415875145, 0.04782309106301105, 0.0665206727476263, 0.0831038846149586, 0.0970477291609779, 0.10791092327613844, 0.11534977034416831, 0.11912896001614057, 0.010771024262515805, 0.03195623363010615, 0.05208269090775444, 0.07048339475241434, 0.08654826035518293, 0.09974426325729979, 0.10963306226790615, 0.11588552316083804, 0.11829266503653185, 0.1167726670186253, 0.11137370062576131, 0.10227248864535407, 0.08976863030785835, 0.07427487056565649, 0.05630362388615753, 0.036450185897874215, 0.015373175497924843, 0.11626624636276715, 0.11159236833915974, 0.10302873765644227, 0.09086879535696121, 0.075531616422953, 0.05754768893731188, 0.03754079086817494, 0.016206573265172747, -0.005711425405435316, -0.0274475171752028, -0.04824047356698778, -0.06736008963954826, -0.08413278329494162, -0.09796533775677785, -0.10836595358274519, -0.11496186404749048, -0.013257312863382845, -0.03509071024629433, -0.05565538603012618, -0.07419032618717421, -0.09000664772365466, -0.10251328338775295, -0.11123922977116874, -0.11585151969533115, -0.11616822833552412, -0.11216599762547709, -0.10398175909347891, -0.09190854458861916, -0.07638548996077049, -0.05798235093212216, -0.037379055356848434, -0.015341004244892847, 0.007309001743505628, -0.10370159361898841, -0.09154856282393481, -0.07577047906484176, -0.05697645291124789, -0.03589766847565461, -0.013359459697354414, 0.009750566964636817, 0.03251715628961481, 0.05403344439979656, 0.0734370121009959, 0.08994452897758315, 0.10288360170415337, 0.11172053087413358, 0.11608282382330723, 0.11577550180956156, 0.11079047191575911, 0.10130849884761693, 0.09694983933901041, 0.1078430436229959, 0.11418240554926408, 0.11567649117757342, 0.11223800831965253, 0.10398951692677484, 0.09126028315021616, 0.07457427833982218, 0.05462969948394976, 0.03227075455245301, 0.008452799253997723, -0.01579778417309549, -0.039427324144639675, -0.06140038420209437, -0.08074513360336971, -0.09659659125311242, 0.0051495121849631925, -0.019631144501186262, -0.04358107566048282, -0.06558697764483172, -0.0846152503299541, -0.09976093951292743, -0.11029148743263437, -0.11568316368155968, -0.11564833951725417, -0.11015215174444495, -0.0994175630148262, -0.08391834462109074, -0.06436006335083794, -0.041649720983735025, -0.01685524743882451, 0.008843439954368579, 0.03420965346730091, -0.0693265314799904, -0.04673628601700905, -0.02167790214990649, 0.00458759876438021, 0.030722370085186607, 0.055379163375636496, 0.07727059571607639, 0.09523674626942033, 0.10830755221168137, 0.11575663945728862, 0.11714356789308755, 0.11234198321284594, 0.10155182794943692, 0.08529454446529261, 0.06439106656346105, 0.03992330214130184, 0.10900012850404943, 0.09593793641149229, 0.07736754762849307, 0.05429371843560933, 0.027993618693325187, -5.101108475799587e-05, -0.028235163954484666, -0.054921060353751175, -0.07853287742556565, -0.09765033470371476, -0.11109562580022353, -0.11800836994649855, -0.11790376135575603, -0.1107099045062415, -0.09678140704488548, -0.076887608634346, -0.05217528722827841, -0.11098859334162639, -0.09699933457542606, -0.07665389718037904, -0.051197127759425504, -0.02223087456800729, 0.008382166412591457, 0.038634815818677753, 0.06650507586105925, 0.09009099383130793, 0.10774190483374324, 0.11817706791617254, 0.12058313825462547, 0.11468294895084294, 0.10076967671033665, 0.0797025626633194, 0.05286284027365726, 0.022071239609309776, 0.0898705475476554, 0.06467039214322155, 0.03440214010339031, 0.0012854252151477952, -0.03219016524139358, -0.06344792862624052, -0.0900209641436979, -0.10974855949565451, -0.12095663759771941, -0.12260720752715071, -0.11440333040494925, -0.0968388596565625, -0.07118601869277116, -0.039418514395546875, -0.004073041569509203, 0.031942669297668036, -0.03537259015882534, 0.0012919994517524014, 0.03819602750800222, 0.07199811088145178, 0.0995403370225679, 0.11814694668019293, 0.12589355606521757, 0.12181987052202167, 0.10606216736536299, 0.07988768643591591, 0.04562115197623194, 0.006463399859120214, -0.03378728300376921, -0.0710899440805692, -0.1015612957266686, -0.12188380763201556, -0.12967976593383407, -0.11710073313988201, -0.12876458456435907, -0.12605217785288597, -0.1088942589006989, -0.07888942719352345, -0.03920815754041951, 0.005695923301973119, 0.05054929007765431, 0.08985513606139889, 0.11856158073085667, 0.13272429303081199, 0.13007880180553838, 0.11044012040399528, 0.07586068740639859, 0.030501868240061195, -0.019792249928457864, -0.0681904545153027, -0.035381292063456804, -0.08307905366254326, -0.11900736455634844, -0.1371550718271705, -0.13396928424534307, -0.10912027142954774, -0.065816424019716, -0.010560987230546257, 0.04767917963884992, 0.09882524658866271, 0.13338811136885442, 0.14425891017615539, 0.12826732816508435, 0.08717612066496515, 0.027831988588115156, -0.038688812685478094, -0.03003296821979251, -0.09365599062688751, -0.13774243289995194, -0.1507934708894887, -0.12775021594531386, -0.07207259673084326, 0.0040259702059663866, 0.08162905144797297, 0.1393784336121081, 0.15922488767585824, 0.13231234505169553, 0.06321419203706201, -0.029260231726171287, -0.115877145974423, -0.16536489005527702, -0.15563132337749197, -0.0843310804648324, -0.03681730762864323, 0.08088922377282536, 0.16672690732165182, 0.17215814454032669, 0.08260412396691522, -0.0631376311550797, -0.17975039608417165, -0.17862094999983244, -0.0364163879744442, 0.15349662501171768, 0.21247016890728326, 0.03247132176007274, -0.220757630064557, -0.1448262265787844, 0.2612433271904704, -0.0658058851285777, 1.0]} diff --git a/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/test/fixtures/python/outliers.json b/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/test/fixtures/python/outliers.json new file mode 100644 index 000000000000..a42cd0f1eb97 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/test/fixtures/python/outliers.json @@ -0,0 +1 @@ +{"n": [-1.5, 0.5, 2.5, 3.5, -4.5, -20.5, 50.5], "x": [2.0, -2.0, 10.0, -10.0, 100.0, 0.0, 1.0], "expected": [1.3291381621853577, "PINF", 604.5227763804005, "PINF", 32923453.01577544, 0.12613694630859365, 1.0]} diff --git a/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/test/fixtures/python/runner.py b/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/test/fixtures/python/runner.py new file mode 100644 index 000000000000..4ec2ec241289 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/test/fixtures/python/runner.py @@ -0,0 +1,99 @@ +#!/usr/bin/env python +# +# @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. + +"""Generate fixtures.""" + +import os +import json +import numpy as np +from scipy.special import eval_legendre + +# Get the file path: +FILE = os.path.realpath(__file__) + +# Extract the directory in which this file resides: +DIR = os.path.dirname(FILE) + + +def gen(n, x, name): + """Generate fixture data and write to file. + + # Arguments + + * `n`: degrees + * `x`: evaluation points + * `name::str`: output filename + + # Examples + + ``` python + python> n = np.arange(0, 30) + python> x = np.linspace(-1.0, 1.0, 30) + python> gen(n, x, './data.json') + ``` + """ + y = eval_legendre(n, x) + y = ["PINF" if np.isposinf(val) else "NINF" if np.isneginf(val) else val for val in y] + data = { + "n": n.tolist(), + "x": x.tolist(), + "expected": y, + } + + # Based on the script directory, create an output filepath: + filepath = os.path.join(DIR, name) + + # Write the data to the output filepath as JSON: + with open(filepath, "w", encoding="utf-8") as outfile: + json.dump(data, outfile) + outfile.write("\n") + + +def main(): + """Generate fixture data.""" + # Integer degrees, x in [-1, 1]: + n = 1000 + n_vals = np.linspace(0, 30, n, dtype=int) + x = np.linspace(-1.0, 1.0, n) + gen(n_vals, x, "integer_n.json") + + # Non-integer degrees, x in [-1, 1]: + n = 1000 + n_vals = np.linspace(-20.0, 20.0, n) + x = np.linspace(-1.0, 1.0, n) + gen(n_vals, x, "decimals.json") + + # Large integer degrees, x in [-1, 1]: + n = 500 + n_vals = np.linspace(30, 60, n, dtype=int) + x = np.linspace(-1.0, 1.0, n) + gen(n_vals, x, "large_n.json") + + # Outliers: x outside [-1, 1], mixed signs and large magnitudes: + n_vals = np.array([-1.5, 0.5, 2.5, 3.5, -4.5, -20.5, 50.5]) + x = np.array([2.0, -2.0, 10.0, -10.0, 100.0, 0.0, 1.0]) + gen(n_vals, x, "outliers.json") + + # Small x branch (integer n): + n_vals = np.array([2, 3, 4, 5, 10, 2, 3, 4, 5, 10], dtype=int) + x = np.array([0.0, 0.0, 0.0, 0.0, 0.0, 1e-10, -1e-10, 5e-6, -5e-6, 1e-7]) + gen(n_vals, x, "small_x.json") + + +if __name__ == "__main__": + main() diff --git a/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/test/fixtures/python/small_x.json b/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/test/fixtures/python/small_x.json new file mode 100644 index 000000000000..54c6d4f5d19f --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/test/fixtures/python/small_x.json @@ -0,0 +1 @@ +{"n": [2, 3, 4, 5, 10, 2, 3, 4, 5, 10], "x": [0.0, 0.0, 0.0, 0.0, 0.0, 1e-10, -1e-10, 5e-06, -5e-06, 1e-07], "expected": [-0.5000000000000001, 0.0, 0.375, 0.0, -0.24609375, -0.5000000000000001, 1.5000000000000002e-10, 0.37499999990625, -9.374999998906253e-06, -0.24609374999986464]} diff --git a/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/test/test.js b/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/test/test.js new file mode 100644 index 000000000000..1ff7684e7fbe --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/legendre-polynomial/test/test.js @@ -0,0 +1,238 @@ +/** +* @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. +*/ + +'use strict'; + +// MODULES // + +var tape = require( 'tape' ); +var abs = require( '@stdlib/math/base/special/abs' ); +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var EPS = require( '@stdlib/constants/float64/eps' ); +var PINF = require( '@stdlib/constants/float64/pinf' ); +var NINF = require( '@stdlib/constants/float64/ninf' ); +var legendrepoly = require( './../lib' ); + + +// FIXTURES // + +var integerN = require( './fixtures/python/integer_n.json' ); +var smallX = require( './fixtures/python/small_x.json' ); +var decimals = require( './fixtures/python/decimals.json' ); +var largeN = require( './fixtures/python/large_n.json' ); +var outliers = require( './fixtures/python/outliers.json' ); + + +// TESTS // + +tape( 'main export is a function', function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof legendrepoly, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function returns `NaN` if provided `NaN`', function test( t ) { + var v; + + v = legendrepoly( NaN, 0.5 ); + t.strictEqual( isnan( v ), true, 'returns expected value' ); + + v = legendrepoly( 1.0, NaN ); + t.strictEqual( isnan( v ), true, 'returns expected value' ); + + v = legendrepoly( NaN, NaN ); + t.strictEqual( isnan( v ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function returns `1` if `n` is 0', function test( t ) { + var v; + + v = legendrepoly( 0.0, 0.5 ); + t.strictEqual( v, 1.0, 'returns expected value' ); + + v = legendrepoly( 0.0, 0.0 ); + t.strictEqual( v, 1.0, 'returns expected value' ); + + v = legendrepoly( 0.0, -0.5 ); + t.strictEqual( v, 1.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function returns `x` if `n` is 1', function test( t ) { + var v; + + v = legendrepoly( 1.0, 0.5 ); + t.strictEqual( v, 0.5, 'returns expected value' ); + + v = legendrepoly( 1.0, -0.2 ); + t.strictEqual( v, -0.2, 'returns expected value' ); + + v = legendrepoly( 1.0, 2.0 ); + t.strictEqual( v, 2.0, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function correctly evaluates the Legendre polynomial for integer values of n', function test( t ) { + var expected; + var delta; + var tol; + var n; + var x; + var v; + var i; + + n = integerN.n; + x = integerN.x; + expected = integerN.expected; + + for ( i = 0; i < x.length; i++ ) { + v = legendrepoly( n[ i ], x[ i ] ); + if ( expected[ i ] === 'PINF' ) { + t.strictEqual( v, PINF, 'returns expected value' ); + continue; + } + if ( expected[ i ] === 'NINF' ) { + t.strictEqual( v, NINF, 'returns expected value' ); + continue; + } + delta = abs( v - expected[ i ] ); + tol = 470.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. n: ' + n[ i ] + ' x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + t.end(); +}); + +tape( 'the function correctly evaluates the Legendre polynomial for small values of x', function test( t ) { + var expected; + var delta; + var tol; + var n; + var x; + var v; + var i; + + n = smallX.n; + x = smallX.x; + expected = smallX.expected; + + for ( i = 0; i < x.length; i++ ) { + v = legendrepoly( n[ i ], x[ i ] ); + delta = abs( v - expected[ i ] ); + tol = EPS * abs( expected[ i ] ); + if ( expected[ i ] === 0.0 ) { + tol = EPS; + } + t.ok( delta <= tol, 'within tolerance. n: ' + n[ i ] + ' x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + t.end(); +}); + +// Large tolerance is set due to th loss of precision in hyp2f1 for non-integer values of n +tape( 'the function correctly evaluates the Legendre polynomial for non-integer values of n', function test( t ) { + var expected; + var delta; + var tol; + var n; + var x; + var v; + var i; + + n = decimals.n; + x = decimals.x; + expected = decimals.expected; + + for ( i = 0; i < x.length; i++ ) { + v = legendrepoly( n[ i ], x[ i ] ); + if ( expected[ i ] === 'PINF' ) { + t.strictEqual( v, PINF, 'returns expected value' ); + continue; + } + if ( expected[ i ] === 'NINF' ) { + t.strictEqual( v, NINF, 'returns expected value' ); + continue; + } + delta = abs( v - expected[ i ] ); + tol = 1e13 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. n: ' + n[ i ] + ' x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + t.end(); +}); + +tape( 'the function correctly evaluates the Legendre polynomial for large values of n', function test( t ) { + var expected; + var delta; + var tol; + var n; + var x; + var v; + var i; + + n = largeN.n; + x = largeN.x; + expected = largeN.expected; + + for ( i = 0; i < x.length; i++ ) { + v = legendrepoly( n[ i ], x[ i ] ); + if ( expected[ i ] === 'PINF' ) { + t.strictEqual( v, PINF, 'returns expected value' ); + continue; + } + if ( expected[ i ] === 'NINF' ) { + t.strictEqual( v, NINF, 'returns expected value' ); + continue; + } + delta = abs( v - expected[ i ] ); + tol = 3700.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. n: ' + n[ i ] + ' x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + t.end(); +}); + +tape( 'the function correctly evaluates the Legendre polynomial for outlier cases', function test( t ) { + var expected; + var delta; + var tol; + var n; + var x; + var v; + var i; + + n = outliers.n; + x = outliers.x; + expected = outliers.expected; + + for ( i = 0; i < x.length; i++ ) { + v = legendrepoly( n[ i ], x[ i ] ); + if ( expected[ i ] === 'PINF' ) { + t.strictEqual( v, PINF, 'returns expected value' ); + continue; + } + if ( expected[ i ] === 'NINF' ) { + t.strictEqual( v, NINF, 'returns expected value' ); + continue; + } + delta = abs( v - expected[ i ] ); + tol = 4200.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. n: ' + n[ i ] + ' x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + t.end(); +});