diff --git a/lib/node_modules/@stdlib/math/base/special/expm1rel/README.md b/lib/node_modules/@stdlib/math/base/special/expm1rel/README.md new file mode 100644 index 000000000000..8ac93383ebd0 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expm1rel/README.md @@ -0,0 +1,131 @@ + + +# expm1rel + +> Compute the relative error exponential. + + + +
+ +The relative error exponential is defined as + + + +
+ Equation for the relative error exponential. +
+
+ + + +
+ + + + + +
+ +## Usage + +```javascript +var expm1rel = require( '@stdlib/math/base/special/expm1rel' ); +``` + +#### expm1rel( x ) + +Computes the relative error exponential. + +```javascript +var v = expm1rel( 0.0 ); +// returns 1.0 + +v = expm1rel( 1.0 ); +// returns ~1.718 + +v = expm1rel( -1.0 ); +// returns ~0.632 + +v = expm1rel( NaN ); +// returns NaN +``` + +
+ + + + + +
+ +## Notes + +- When `x` is near zero, `exp(x)-1` can suffer catastrophic cancellation (i.e., a significant loss in precision). `expm1rel` avoids such a loss in precision. + +
+ + + + + +
+ +## Examples + + + +```javascript +var randu = require( '@stdlib/random/base/randu' ); +var expm1rel = require( '@stdlib/math/base/special/expm1rel' ); + +var x; +var y; +var a; +var i; + +for ( i = 0; i < 100; i++ ) { + x = (randu()*100.0) - 50.0; + a = x.toFixed( 3 ); + y = expm1rel( x ); + console.log( '(e^%d - 1)/%d = %d', a, a, y ); +} +``` + +
+ + + + + +
+ +
+ + + + + +
+ +
+ + diff --git a/lib/node_modules/@stdlib/math/base/special/expm1rel/benchmark/benchmark.js b/lib/node_modules/@stdlib/math/base/special/expm1rel/benchmark/benchmark.js new file mode 100644 index 000000000000..715ed5f02421 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expm1rel/benchmark/benchmark.js @@ -0,0 +1,51 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2018 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 randu = require( '@stdlib/random/base/randu' ); +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var pkg = require( './../package.json' ).name; +var expm1rel = require( './../lib' ); + + +// MAIN // + +bench( pkg, function benchmark( b ) { + var x; + var y; + var i; + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + x = ( randu()*10.0 ) - 5.0; + y = expm1rel( x ); + 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/expm1rel/benchmark/python/scipy/benchmark.py b/lib/node_modules/@stdlib/math/base/special/expm1rel/benchmark/python/scipy/benchmark.py new file mode 100755 index 000000000000..0123da4516fd --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expm1rel/benchmark/python/scipy/benchmark.py @@ -0,0 +1,116 @@ +#!/usr/bin/env python +# +# @license Apache-2.0 +# +# Copyright (c) 2018 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. + +"""Benchmark scipy.special.exprel.""" + +from __future__ import print_function +import timeit + +NAME = "expm1rel" +REPEATS = 3 +ITERATIONS = 1000000 +COUNT = [0] # use a list to allow modification within nested scopes + + +def print_version(): + """Print the TAP version.""" + print("TAP version 13") + + +def print_summary(total, passing): + """Print the benchmark summary. + + # Arguments + + * `total`: total number of tests + * `passing`: number of passing tests + + """ + print("#") + print("1.." + str(total)) # TAP plan + print("# total " + str(total)) + print("# pass " + str(passing)) + print("#") + print("# ok") + + +def print_results(iterations, elapsed): + """Print benchmark results. + + # Arguments + + * `iterations`: number of iterations + * `elapsed`: elapsed time (in seconds) + + # Examples + + ``` python + python> print_results(100000, 0.131009101868) + ``` + """ + rate = iterations / elapsed + + print(" ---") + print(" iterations: " + str(iterations)) + print(" elapsed: " + str(elapsed)) + print(" rate: " + str(rate)) + print(" ...") + + +def benchmark(name, setup, stmt, iterations): + """Run the benchmark and print benchmark results. + + # Arguments + + * `name`: benchmark name (suffix) + * `setup`: benchmark setup + * `stmt`: statement to benchmark + * `iterations`: number of iterations + + # Examples + + ``` python + python> benchmark("::random", "from random import random;", "y = random()", 1000000) + ``` + """ + t = timeit.Timer(stmt, setup=setup) + + i = 0 + while i < REPEATS: + print("# python::scipy::" + NAME + name) + COUNT[0] += 1 + elapsed = t.timeit(number=iterations) + print_results(iterations, elapsed) + print("ok " + str(COUNT[0]) + " benchmark finished") + i += 1 + + +def main(): + """Run the benchmarks.""" + print_version() + + name = "" + setup = "from scipy.special import exprel; from random import random;" + stmt = "y = exprel(random())" + benchmark(name, setup, stmt, ITERATIONS) + + print_summary(COUNT[0], COUNT[0]) + + +if __name__ == "__main__": + main() diff --git a/lib/node_modules/@stdlib/math/base/special/expm1rel/docs/img/equation_relative_error_exponential.svg b/lib/node_modules/@stdlib/math/base/special/expm1rel/docs/img/equation_relative_error_exponential.svg new file mode 100644 index 000000000000..fea4e8afdb69 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expm1rel/docs/img/equation_relative_error_exponential.svg @@ -0,0 +1,32 @@ + +f left-parenthesis x right-parenthesis equals StartFraction e Superscript x Baseline minus 1 Over x EndFraction + + + \ No newline at end of file diff --git a/lib/node_modules/@stdlib/math/base/special/expm1rel/docs/repl.txt b/lib/node_modules/@stdlib/math/base/special/expm1rel/docs/repl.txt new file mode 100644 index 000000000000..6654af483b09 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expm1rel/docs/repl.txt @@ -0,0 +1,35 @@ + +{{alias}}( x ) + Relative error exponential. + + When `x` is near zero, + + e^x - 1 + + can suffer catastrophic cancellation (i.e., significant loss of precision). + This function avoids the loss of precision when `x` is near zero. + + Parameters + ---------- + x: number + Input value. + + Returns + ------- + y: number + Function value. + + Examples + -------- + > var y = {{alias}}( 0.0 ) + 1.0 + > y = {{alias}}( 1.0 ) + ~1.718 + > y = {{alias}}( -1.0 ) + ~0.632 + > y = {{alias}}( NaN ) + NaN + + See Also + -------- + diff --git a/lib/node_modules/@stdlib/math/base/special/expm1rel/examples/index.js b/lib/node_modules/@stdlib/math/base/special/expm1rel/examples/index.js new file mode 100644 index 000000000000..a1913d69c8d1 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expm1rel/examples/index.js @@ -0,0 +1,34 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2018 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 randu = require( '@stdlib/random/base/randu' ); +var expm1rel = require( './../lib' ); + +var x; +var y; +var a; +var i; + +for ( i = 0; i < 100; i++ ) { + x = (randu()*100.0) - 50.0; + a = x.toFixed( 3 ); + y = expm1rel( x ); + console.log( '(e^%d - 1)/%d = %d', a, a, y ); +} diff --git a/lib/node_modules/@stdlib/math/base/special/expm1rel/lib/index.js b/lib/node_modules/@stdlib/math/base/special/expm1rel/lib/index.js new file mode 100644 index 000000000000..2aefe8a14a46 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expm1rel/lib/index.js @@ -0,0 +1,49 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2018 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'; + +/** +* Relative error exponential function. +* +* @module @stdlib/math/base/special/expm1rel +* +* @example +* var expm1rel = require( '@stdlib/math/base/special/expm1rel' ); +* +* var v = expm1rel( 0.0 ); +* // returns 1.0 +* +* v = expm1rel( 1.0 ); +* // returns ~1.718 +* +* v = expm1rel( -1.0 ); +* // returns ~0.632 +* +* v = expm1rel( NaN ); +* // returns NaN +*/ + +// MODULES // + +var expm1rel = require( './main.js' ); + + +// EXPORTS // + +module.exports = expm1rel; diff --git a/lib/node_modules/@stdlib/math/base/special/expm1rel/lib/main.js b/lib/node_modules/@stdlib/math/base/special/expm1rel/lib/main.js new file mode 100644 index 000000000000..5315fc75d734 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expm1rel/lib/main.js @@ -0,0 +1,71 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2018 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 expm1 = require( '@stdlib/math/base/special/expm1' ); +var abs = require( '@stdlib/math/base/special/abs' ); +var EPS = require( '@stdlib/constants/math/float64-eps' ); +var PINF = require( '@stdlib/constants/math/float64-pinf' ); + + +// VARIABLES // + +var OVERFLOW_THRESHOLD = 7.09782712893383973096e+02; // 0x40862E42 0xFEFA39EF + + +// MAIN // + +/** +* Computes the relative error exponential. +* +* @param {number} x - input value +* @returns {number} function value +* +* @example +* var v = expm1rel( 0.0 ); +* // returns 1.0 +* +* @example +* var v = expm1rel( 1.0 ); +* // returns ~1.718 +* +* @example +* var v = expm1rel( -1.0 ); +* // returns ~0.632 +* +* @example +* var v = expm1rel( NaN ); +* // returns NaN +*/ +function expm1rel( x ) { + if ( abs( x ) <= EPS ) { + return 1.0; // L'Hopital's Rule + } + if ( x >= OVERFLOW_THRESHOLD ) { + return PINF; // L'Hopital's Rule + } + return expm1( x ) / x; +} + + +// EXPORTS // + +module.exports = expm1rel; diff --git a/lib/node_modules/@stdlib/math/base/special/expm1rel/package.json b/lib/node_modules/@stdlib/math/base/special/expm1rel/package.json new file mode 100644 index 000000000000..1e0830a7f963 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expm1rel/package.json @@ -0,0 +1,69 @@ +{ + "name": "@stdlib/math/base/special/expm1rel", + "version": "0.0.0", + "description": "Relative error exponential.", + "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" + }, + "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", + "mathematics", + "math", + "math.expm1", + "expm1", + "power", + "natural", + "exp", + "relative", + "error", + "err", + "exponential", + "function", + "euler", + "number" + ], + "__stdlib__": {} +} diff --git a/lib/node_modules/@stdlib/math/base/special/expm1rel/test/fixtures/python/medium_negative.json b/lib/node_modules/@stdlib/math/base/special/expm1rel/test/fixtures/python/medium_negative.json new file mode 100644 index 000000000000..98cbc8c726c1 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expm1rel/test/fixtures/python/medium_negative.json @@ -0,0 +1 @@ +{"x": [-709.78, -709.0705105105105, -708.361021021021, -707.6515315315315, -706.942042042042, -706.2325525525525, -705.5230630630631, -704.8135735735735, -704.1040840840841, -703.3945945945945, -702.6851051051051, -701.9756156156155, -701.2661261261261, -700.5566366366367, -699.8471471471471, -699.1376576576577, -698.4281681681681, -697.7186786786787, -697.0091891891892, -696.2996996996997, -695.5902102102102, -694.8807207207207, -694.1712312312312, -693.4617417417417, -692.7522522522522, -692.0427627627628, -691.3332732732732, -690.6237837837838, -689.9142942942942, -689.2048048048048, -688.4953153153153, -687.7858258258258, -687.0763363363363, -686.3668468468468, -685.6573573573573, -684.9478678678679, -684.2383783783783, -683.5288888888889, -682.8193993993993, -682.1099099099099, -681.4004204204203, -680.6909309309309, -679.9814414414415, -679.2719519519519, -678.5624624624625, -677.8529729729729, -677.1434834834835, -676.433993993994, -675.7245045045045, -675.015015015015, -674.3055255255255, -673.596036036036, -672.8865465465465, -672.177057057057, -671.4675675675676, -670.758078078078, -670.0485885885886, -669.339099099099, -668.6296096096096, -667.9201201201201, -667.2106306306306, -666.5011411411411, -665.7916516516516, -665.0821621621621, -664.3726726726727, -663.6631831831832, -662.9536936936937, -662.2442042042042, -661.5347147147147, -660.8252252252252, -660.1157357357357, -659.4062462462463, -658.6967567567567, -657.9872672672673, -657.2777777777777, -656.5682882882883, -655.8587987987987, -655.1493093093093, -654.4398198198198, -653.7303303303303, -653.0208408408408, -652.3113513513513, -651.6018618618618, -650.8923723723724, -650.1828828828828, -649.4733933933934, -648.7639039039038, -648.0544144144144, -647.344924924925, -646.6354354354354, -645.925945945946, -645.2164564564564, -644.506966966967, -643.7974774774775, -643.087987987988, -642.3784984984985, -641.669009009009, -640.9595195195195, -640.25003003003, -639.5405405405405, -638.8310510510511, -638.1215615615615, -637.4120720720721, -636.7025825825825, -635.9930930930931, -635.2836036036035, -634.5741141141141, -633.8646246246246, -633.1551351351351, -632.4456456456456, -631.7361561561561, -631.0266666666666, -630.3171771771772, -629.6076876876876, -628.8981981981982, -628.1887087087086, -627.4792192192192, -626.7697297297298, -626.0602402402402, -625.3507507507508, -624.6412612612612, -623.9317717717718, -623.2222822822823, -622.5127927927928, -621.8033033033033, -621.0938138138138, -620.3843243243243, -619.6748348348348, -618.9653453453453, -618.2558558558559, -617.5463663663663, -616.8368768768769, -616.1273873873873, -615.4178978978979, -614.7084084084083, -613.9989189189189, -613.2894294294294, -612.5799399399399, -611.8704504504504, -611.1609609609609, -610.4514714714715, -609.741981981982, -609.0324924924925, -608.323003003003, -607.6135135135135, -606.904024024024, -606.1945345345346, -605.485045045045, -604.7755555555556, -604.066066066066, -603.3565765765766, -602.6470870870871, -601.9375975975976, -601.2281081081081, -600.5186186186186, -599.8091291291291, -599.0996396396396, -598.3901501501501, -597.6806606606607, -596.9711711711711, -596.2616816816817, -595.5521921921921, -594.8427027027027, -594.1332132132131, -593.4237237237237, -592.7142342342343, -592.0047447447447, -591.2952552552553, -590.5857657657657, -589.8762762762763, -589.1667867867868, -588.4572972972973, -587.7478078078078, -587.0383183183183, -586.3288288288288, -585.6193393393394, -584.9098498498498, -584.2003603603604, -583.4908708708708, -582.7813813813814, -582.0718918918919, -581.3624024024024, -580.6529129129129, -579.9434234234234, -579.2339339339339, -578.5244444444445, -577.8149549549549, -577.1054654654654, -576.395975975976, -575.6864864864865, -574.976996996997, -574.2675075075075, -573.558018018018, -572.8485285285285, -572.1390390390391, -571.4295495495495, -570.7200600600601, -570.0105705705705, -569.3010810810811, -568.5915915915916, -567.8821021021021, -567.1726126126126, -566.4631231231231, -565.7536336336336, -565.0441441441442, -564.3346546546546, -563.6251651651652, -562.9156756756756, -562.2061861861862, -561.4966966966967, -560.7872072072072, -560.0777177177177, -559.3682282282282, -558.6587387387387, -557.9492492492493, -557.2397597597597, -556.5302702702702, -555.8207807807808, -555.1112912912913, -554.4018018018018, -553.6923123123123, -552.9828228228228, -552.2733333333333, -551.5638438438439, -550.8543543543543, -550.1448648648649, -549.4353753753753, -548.7258858858859, -548.0163963963964, -547.3069069069069, -546.5974174174174, -545.8879279279279, -545.1784384384384, -544.468948948949, -543.7594594594594, -543.04996996997, -542.3404804804804, -541.630990990991, -540.9215015015016, -540.212012012012, -539.5025225225224, -538.793033033033, -538.0835435435436, -537.3740540540541, -536.6645645645646, -535.955075075075, -535.2455855855856, -534.5360960960961, -533.8266066066066, -533.1171171171171, -532.4076276276276, -531.6981381381381, -530.9886486486487, -530.2791591591591, -529.5696696696697, -528.8601801801801, -528.1506906906907, -527.4412012012012, -526.7317117117117, -526.0222222222222, -525.3127327327327, -524.6032432432432, -523.8937537537538, -523.1842642642642, -522.4747747747748, -521.7652852852852, -521.0557957957958, -520.3463063063064, -519.6368168168168, -518.9273273273272, -518.2178378378378, -517.5083483483484, -516.7988588588589, -516.0893693693694, -515.3798798798798, -514.6703903903904, -513.9609009009009, -513.2514114114114, -512.5419219219219, -511.8324324324324, -511.1229429429429, -510.4134534534535, -509.70396396396393, -508.9944744744745, -508.284984984985, -507.5754954954955, -506.866006006006, -506.1565165165165, -505.44702702702705, -504.7375375375375, -504.02804804804805, -503.31855855855855, -502.60906906906905, -501.8995795795796, -501.19009009009005, -500.4806006006006, -499.7711111111111, -499.0616216216216, -498.3521321321321, -497.6426426426426, -496.93315315315317, -496.2236636636636, -495.5141741741742, -494.8046846846847, -494.0951951951952, -493.38570570570573, -492.6762162162162, -491.96672672672673, -491.25723723723723, -490.54774774774774, -489.8382582582583, -489.12876876876874, -488.4192792792793, -487.7097897897898, -487.0003003003003, -486.2908108108108, -485.5813213213213, -484.87183183183186, -484.1623423423423, -483.45285285285286, -482.74336336336336, -482.03387387387386, -481.3243843843844, -480.61489489489486, -479.9054054054054, -479.1959159159159, -478.4864264264264, -477.7769369369369, -477.0674474474474, -476.357957957958, -475.6484684684684, -474.938978978979, -474.2294894894895, -473.52, -472.81051051051054, -472.101021021021, -471.39153153153154, -470.68204204204204, -469.97255255255254, -469.2630630630631, -468.55357357357354, -467.8440840840841, -467.1345945945946, -466.4251051051051, -465.7156156156156, -465.0061261261261, -464.29663663663666, -463.5871471471471, -462.87765765765766, -462.16816816816817, -461.45867867867867, -460.7491891891892, -460.03969969969967, -459.3302102102102, -458.6207207207207, -457.9112312312312, -457.2017417417417, -456.49225225225223, -455.7827627627628, -455.07327327327323, -454.3637837837838, -453.6542942942943, -452.9448048048048, -452.2353153153153, -451.52582582582585, -450.81633633633635, -450.10684684684685, -449.39735735735735, -448.68786786786785, -447.97837837837835, -447.2688888888889, -446.5593993993994, -445.8499099099099, -445.1404204204204, -444.4309309309309, -443.7214414414414, -443.01195195195197, -442.3024624624625, -441.592972972973, -440.8834834834835, -440.173993993994, -439.4645045045045, -438.75501501501503, -438.04552552552553, -437.33603603603603, -436.62654654654654, -435.91705705705704, -435.2075675675676, -434.4980780780781, -433.7885885885886, -433.0790990990991, -432.3696096096096, -431.6601201201201, -430.95063063063066, -430.24114114114116, -429.53165165165166, -428.82216216216216, -428.11267267267266, -427.40318318318316, -426.6936936936937, -425.9842042042042, -425.2747147147147, -424.5652252252252, -423.8557357357357, -423.1462462462462, -422.4367567567568, -421.7272672672673, -421.0177777777778, -420.3082882882883, -419.5987987987988, -418.8893093093093, -418.17981981981984, -417.47033033033034, -416.76084084084084, -416.05135135135134, -415.34186186186184, -414.6323723723724, -413.9228828828829, -413.2133933933934, -412.5039039039039, -411.7944144144144, -411.0849249249249, -410.37543543543546, -409.66594594594596, -408.95645645645646, -408.24696696696697, -407.53747747747747, -406.82798798798797, -406.1184984984985, -405.409009009009, -404.6995195195195, -403.99003003003, -403.2805405405405, -402.57105105105103, -401.8615615615616, -401.1520720720721, -400.4425825825826, -399.7330930930931, -399.0236036036036, -398.3141141141141, -397.60462462462465, -396.89513513513515, -396.18564564564565, -395.47615615615615, -394.76666666666665, -394.05717717717715, -393.3476876876877, -392.6381981981982, -391.9287087087087, -391.2192192192192, -390.5097297297297, -389.80024024024027, -389.0907507507508, -388.3812612612613, -387.6717717717718, -386.9622822822823, -386.2527927927928, -385.54330330330333, -384.83381381381383, -384.12432432432433, -383.41483483483483, -382.70534534534534, -381.99585585585584, -381.2863663663664, -380.5768768768769, -379.8673873873874, -379.1578978978979, -378.4484084084084, -377.7389189189189, -377.02942942942946, -376.31993993993996, -375.61045045045046, -374.90096096096096, -374.19147147147146, -373.48198198198196, -372.7724924924925, -372.063003003003, -371.3535135135135, -370.644024024024, -369.9345345345345, -369.225045045045, -368.5155555555556, -367.8060660660661, -367.0965765765766, -366.3870870870871, -365.6775975975976, -364.96810810810814, -364.25861861861864, -363.54912912912914, -362.83963963963964, -362.13015015015014, -361.42066066066064, -360.7111711711712, -360.0016816816817, -359.2921921921922, -358.5827027027027, -357.8732132132132, -357.1637237237237, -356.45423423423426, -355.74474474474476, -355.03525525525527, -354.32576576576577, -353.61627627627627, -352.90678678678677, -352.1972972972973, -351.4878078078078, -350.7783183183183, -350.0688288288288, -349.35933933933933, -348.64984984984983, -347.9403603603604, -347.2308708708709, -346.5213813813814, -345.8118918918919, -345.1024024024024, -344.39291291291295, -343.68342342342345, -342.97393393393395, -342.26444444444445, -341.55495495495495, -340.84546546546545, -340.135975975976, -339.4264864864865, -338.716996996997, -338.0075075075075, -337.298018018018, -336.5885285285285, -335.87903903903907, -335.1695495495496, -334.4600600600601, -333.7505705705706, -333.0410810810811, -332.3315915915916, -331.62210210210213, -330.91261261261263, -330.20312312312313, -329.49363363363364, -328.78414414414414, -328.07465465465464, -327.3651651651652, -326.6556756756757, -325.9461861861862, -325.2366966966967, -324.5272072072072, -323.81771771771776, -323.10822822822826, -322.39873873873876, -321.68924924924926, -320.97975975975976, -320.27027027027026, -319.5607807807808, -318.8512912912913, -318.1418018018018, -317.4323123123123, -316.7228228228228, -316.0133333333333, -315.3038438438439, -314.5943543543544, -313.8848648648649, -313.1753753753754, -312.4658858858859, -311.7563963963964, -311.04690690690694, -310.33741741741744, -309.62792792792794, -308.91843843843844, -308.20894894894894, -307.49945945945944, -306.78996996997, -306.0804804804805, -305.370990990991, -304.6615015015015, -303.952012012012, -303.2425225225225, -302.53303303303306, -301.82354354354356, -301.11405405405407, -300.40456456456457, -299.69507507507507, -298.9855855855856, -298.2760960960961, -297.5666066066066, -296.8571171171171, -296.1476276276276, -295.43813813813813, -294.7286486486487, -294.0191591591592, -293.3096696696697, -292.6001801801802, -291.8906906906907, -291.1812012012012, -290.47171171171175, -289.76222222222225, -289.05273273273275, -288.34324324324325, -287.63375375375375, -286.92426426426425, -286.2147747747748, -285.5052852852853, -284.7957957957958, -284.0863063063063, -283.3768168168168, -282.6673273273273, -281.95783783783787, -281.2483483483484, -280.5388588588589, -279.8293693693694, -279.1198798798799, -278.4103903903904, -277.70090090090093, -276.99141141141143, -276.28192192192193, -275.57243243243244, -274.86294294294294, -274.1534534534535, -273.443963963964, -272.7344744744745, -272.024984984985, -271.3154954954955, -270.606006006006, -269.89651651651656, -269.18702702702706, -268.47753753753756, -267.76804804804806, -267.05855855855856, -266.34906906906906, -265.6395795795796, -264.9300900900901, -264.2206006006006, -263.5111111111111, -262.8016216216216, -262.0921321321321, -261.3826426426427, -260.6731531531532, -259.9636636636637, -259.2541741741742, -258.5446846846847, -257.8351951951952, -257.12570570570574, -256.41621621621624, -255.70672672672674, -254.99723723723724, -254.28774774774774, -253.5782582582583, -252.8687687687688, -252.1592792792793, -251.4497897897898, -250.7403003003003, -250.0308108108108, -249.32132132132136, -248.61183183183186, -247.90234234234237, -247.19285285285287, -246.48336336336337, -245.77387387387387, -245.06438438438443, -244.35489489489493, -243.64540540540543, -242.93591591591593, -242.22642642642643, -241.51693693693693, -240.8074474474475, -240.097957957958, -239.3884684684685, -238.678978978979, -237.9694894894895, -237.26, -236.55051051051055, -235.84102102102105, -235.13153153153155, -234.42204204204205, -233.71255255255255, -233.0030630630631, -232.2935735735736, -231.5840840840841, -230.8745945945946, -230.1651051051051, -229.4556156156156, -228.74612612612617, -228.03663663663667, -227.32714714714717, -226.61765765765767, -225.90816816816817, -225.19867867867868, -224.48918918918923, -223.77969969969973, -223.07021021021023, -222.36072072072074, -221.65123123123124, -220.94174174174174, -220.2322522522523, -219.5227627627628, -218.8132732732733, -218.1037837837838, -217.3942942942943, -216.6848048048048, -215.97531531531536, -215.26582582582586, -214.55633633633636, -213.84684684684686, -213.13735735735736, -212.42786786786786, -211.71837837837842, -211.00888888888892, -210.29939939939942, -209.58990990990992, -208.88042042042042, -208.17093093093098, -207.46144144144148, -206.75195195195198, -206.04246246246248, -205.33297297297298, -204.62348348348348, -203.91399399399404, -203.20450450450454, -202.49501501501504, -201.78552552552554, -201.07603603603604, -200.36654654654654, -199.6570570570571, -198.9475675675676, -198.2380780780781, -197.5285885885886, -196.81909909909916, -196.1096096096096, -195.40012012012016, -194.6906306306306, -193.98114114114117, -193.27165165165172, -192.56216216216217, -191.85267267267272, -191.14318318318317, -190.43369369369373, -189.72420420420417, -189.01471471471473, -188.30522522522529, -187.59573573573573, -186.8862462462463, -186.17675675675673, -185.4672672672673, -184.75777777777785, -184.0482882882883, -183.33879879879885, -182.6293093093093, -181.91981981981985, -181.2103303303304, -180.50084084084085, -179.7913513513514, -179.08186186186185, -178.3723723723724, -177.66288288288285, -176.9533933933934, -176.24390390390397, -175.5344144144144, -174.82492492492497, -174.11543543543542, -173.40594594594597, -172.69645645645653, -171.98696696696697, -171.27747747747753, -170.56798798798798, -169.85849849849853, -169.14900900900898, -168.43951951951954, -167.7300300300301, -167.02054054054054, -166.3110510510511, -165.60156156156154, -164.8920720720721, -164.18258258258265, -163.4730930930931, -162.76360360360366, -162.0541141141141, -161.34462462462466, -160.63513513513522, -159.92564564564566, -159.21615615615622, -158.50666666666666, -157.79717717717722, -157.08768768768766, -156.37819819819822, -155.66870870870878, -154.95921921921922, -154.24972972972978, -153.54024024024022, -152.83075075075078, -152.12126126126134, -151.41177177177178, -150.70228228228234, -149.99279279279278, -149.28330330330334, -148.57381381381379, -147.86432432432434, -147.1548348348349, -146.44534534534534, -145.7358558558559, -145.02636636636635, -144.3168768768769, -143.60738738738746, -142.8978978978979, -142.18840840840846, -141.4789189189189, -140.76942942942947, -140.05993993994002, -139.35045045045047, -138.64096096096102, -137.93147147147147, -137.22198198198203, -136.51249249249247, -135.80300300300303, -135.09351351351359, -134.38402402402403, -133.6745345345346, -132.96504504504503, -132.2555555555556, -131.54606606606615, -130.8365765765766, -130.12708708708715, -129.4175975975976, -128.70810810810815, -127.9986186186186, -127.28912912912915, -126.57963963963971, -125.87015015015015, -125.16066066066071, -124.45117117117115, -123.74168168168171, -123.03219219219227, -122.32270270270271, -121.61321321321327, -120.90372372372372, -120.19423423423427, -119.48474474474483, -118.77525525525527, -118.06576576576583, -117.35627627627628, -116.64678678678683, -115.93729729729728, -115.22780780780784, -114.51831831831839, -113.80882882882884, -113.0993393393394, -112.38984984984984, -111.6803603603604, -110.97087087087095, -110.2613813813814, -109.55189189189196, -108.8424024024024, -108.13291291291296, -107.4234234234234, -106.71393393393396, -106.00444444444452, -105.29495495495496, -104.58546546546552, -103.87597597597596, -103.16648648648652, -102.45699699699708, -101.74750750750752, -101.03801801801808, -100.32852852852852, -99.61903903903908, -98.90954954954952, -98.20006006006008, -97.49057057057064, -96.78108108108108, -96.07159159159164, -95.36210210210209, -94.65261261261264, -93.9431231231232, -93.23363363363364, -92.5241441441442, -91.81465465465465, -91.1051651651652, -90.39567567567576, -89.6861861861862, -88.97669669669676, -88.2672072072072, -87.55771771771776, -86.84822822822821, -86.13873873873877, -85.42924924924932, -84.71975975975977, -84.01027027027033, -83.30078078078077, -82.59129129129133, -81.88180180180188, -81.17231231231233, -80.46282282282289, -79.75333333333333, -79.04384384384389, -78.33435435435433, -77.62486486486489, -76.91537537537545, -76.20588588588589, -75.49639639639645, -74.78690690690689, -74.07741741741745, -73.36792792792801, -72.65843843843845, -71.94894894894901, -71.23945945945945, -70.52996996997001, -69.82048048048057, -69.11099099099101, -68.40150150150157, -67.69201201201201, -66.98252252252257, -66.27303303303302, -65.56354354354357, -64.85405405405413, -64.14456456456458, -63.43507507507513, -62.72558558558558, -62.016096096096135, -61.30660660660669, -60.597117117117136, -59.887627627627694, -59.17813813813814, -58.468648648648696, -57.75915915915914, -57.0496696696697, -56.340180180180255, -55.6306906906907, -54.92120120120126, -54.2117117117117, -53.50222222222226, -52.792732732732816, -52.08324324324326, -51.37375375375382, -50.66426426426426, -49.95477477477482, -49.24528528528538, -48.53579579579582, -47.82630630630638, -47.11681681681682, -46.40732732732738, -45.697837837837824, -44.98834834834838, -44.27885885885894, -43.56936936936938, -42.85987987987994, -42.150390390390385, -41.44090090090094, -40.7314114114115, -40.021921921921944, -39.3124324324325, -38.602942942942946, -37.8934534534535, -37.18396396396395, -36.474474474474505, -35.76498498498506, -35.05549549549551, -34.346006006006064, -33.63651651651651, -32.927027027027066, -32.21753753753762, -31.508048048048067, -30.798558558558625, -30.08906906906907, -29.379579579579627, -28.67009009009007, -27.96060060060063, -27.251111111111186, -26.54162162162163, -25.832132132132188, -25.12264264264263, -24.41315315315319, -23.703663663663747, -22.99417417417419, -22.28468468468475, -21.575195195195192, -20.86570570570575, -20.156216216216308, -19.44672672672675, -18.73723723723731, -18.027747747747753, -17.31825825825831, -16.608768768768755, -15.899279279279313, -15.18978978978987, -14.480300300300314, -13.770810810810872, -13.061321321321316, -12.351831831831873, -11.642342342342431, -10.932852852852875, -10.223363363363433, -9.513873873873877, -8.804384384384434, -8.094894894894878, -7.385405405405436, -6.6759159159159935, -5.9664264264264375, -5.256936936936995, -4.547447447447439, -3.8379579579579968, -3.1284684684685544, -2.4189789789789984, -1.709489489489556, -1.0], "expected": [0.0014088872608413875, 0.0014102969805922807, 0.0014117095242742394, 0.00141312490038106, 0.0014145431174406372, 0.0014159641840151337, 0.001417388108701154, 0.0014188149001299174, 0.0014202445669674315, 0.0014216771179146688, 0.001423112561707742, 0.0014245509071180832, 0.0014259921629526209, 0.001427436338053961, 0.0014288834413005672, 0.0014303334816069423, 0.0014317864679238125, 0.0014332424092383105, 0.0014347013145741612, 0.0014361631929918686, 0.0014376280535889025, 0.0014390959054998876, 0.0014405667578967934, 0.0014420406199891255, 0.0014435175010241172, 0.0014449974102869235, 0.0014464803571008157, 0.0014479663508273758, 0.001449455400866696, 0.0014509475166575748, 0.0014524427076777167, 0.0014539409834439347, 0.0014554423535123495, 0.0014569468274785947, 0.0014584544149780203, 0.0014599651256858987, 0.0014614789693176316, 0.0014629959556289583, 0.0014645160944161653, 0.0014660393955162967, 0.001467565868807368, 0.0014690955242085766, 0.0014706283716805202, 0.0014721644212254102, 0.0014737036828872908, 0.0014752461667522578, 0.0014767918829486771, 0.0014783408416474096, 0.0014798930530620321, 0.0014814485274490612, 0.0014830072751081816, 0.001484569306382471, 0.0014861346316586308, 0.0014877032613672145, 0.0014892752059828612, 0.0014908504760245277, 0.0014924290820557229, 0.001494011034684745, 0.0014955963445649177, 0.0014971850223948306, 0.0014987770789185798, 0.0015003725249260087, 0.0015019713712529537, 0.0015035736287814876, 0.0015051793084401685, 0.001506788421204287, 0.0015084009780961152, 0.0015100169901851618, 0.0015116364685884211, 0.0015132594244706321, 0.001514885869044531, 0.0015165158135711132, 0.0015181492693598908, 0.0015197862477691546, 0.001521426760206238, 0.001523070818127781, 0.0015247184330399984, 0.0015263696164989464, 0.0015280243801107942, 0.0015296827355320954, 0.0015313446944700613, 0.0015330102686828377, 0.00153467946997978, 0.0015363523102217347, 0.0015380288013213193, 0.0015397089552432036, 0.0015413927840043978, 0.0015430802996745352, 0.0015447715143761633, 0.0015464664402850329, 0.0015481650896303901, 0.001549867474695272, 0.0015515736078167998, 0.0015532835013864804, 0.0015549971678505037, 0.0015567146197100453, 0.0015584358695215714, 0.0015601609298971438, 0.001561889813504728, 0.0015636225330685036, 0.0015653591013691768, 0.001567099531244294, 0.001568843835588558, 0.0015705920273541478, 0.0015723441195510369, 0.0015741001252473183, 0.001575860057569528, 0.0015776239297029726, 0.0015793917548920593, 0.0015811635464406252, 0.0015829393177122736, 0.0015847190821307077, 0.0015865028531800711, 0.001588290644405287, 0.0015900824694124, 0.0015918783418689246, 0.0015936782755041885, 0.0015954822841096864, 0.0015972903815394293, 0.0015991025817103002, 0.0016009188986024123, 0.0016027393462594664, 0.001604563938789114, 0.0016063926903633226, 0.0016082256152187403, 0.0016100627276570678, 0.0016119040420454278, 0.0016137495728167424, 0.0016155993344701073, 0.0016174533415711737, 0.0016193116087525302, 0.0016211741507140857, 0.001623040982223461, 0.0016249121181163746, 0.0016267875732970394, 0.0016286673627385559, 0.0016305515014833122, 0.001632440004643385, 0.0016343328874009425, 0.001636230165008653, 0.0016381318527900928, 0.0016400379661401603, 0.0016419485205254906, 0.0016438635314848739, 0.0016457830146296766, 0.0016477069856442664, 0.001649635460286438, 0.0016515684543878455, 0.0016535059838544326, 0.0016554480646668722, 0.001657394712881003, 0.0016593459446282736, 0.0016613017761161878, 0.0016632622236287527, 0.0016652273035269315, 0.0016671970322490977, 0.0016691714263114953, 0.001671150502308697, 0.001673134276914073, 0.0016751227668802575, 0.001677115989039619, 0.0016791139603047377, 0.0016811166976688817, 0.0016831242182064913, 0.0016851365390736608, 0.0016871536775086302, 0.0016891756508322768, 0.0016912024764486088, 0.0016932341718452685, 0.0016952707545940312, 0.0016973122423513147, 0.0016993586528586888, 0.0017014100039433881, 0.0017034663135188316, 0.001705527599585142, 0.0017075938802296729, 0.0017096651736275368, 0.0017117414980421378, 0.0017138228718257093, 0.0017159093134198537, 0.0017180008413560876, 0.0017200974742563912, 0.0017221992308337586, 0.0017243061298927577, 0.001726418190330088, 0.0017285354311351482, 0.0017306578713906038, 0.0017327855302729602, 0.0017349184270531407, 0.0017370565810970685, 0.0017392000118662536, 0.001741348738918381, 0.0017435027819079074, 0.00174566216058666, 0.0017478268948044402, 0.0017499970045096321, 0.001752172509749814, 0.001754353430672378, 0.0017565397875251494, 0.0017587316006570156, 0.0017609288905185562, 0.0017631316776626782, 0.0017653399827452596, 0.0017675538265257919, 0.0017697732298680323, 0.0017719982137406596, 0.0017742287992179326, 0.0017764650074803582, 0.0017787068598153586, 0.0017809543776179492, 0.0017832075823914196, 0.001785466495748016, 0.0017877311394096365, 0.0017900015352085238, 0.0017922777050879695, 0.0017945596711030193, 0.001796847455421186, 0.001799141080323167, 0.0018014405682035676, 0.0018037459415716317, 0.001806057223051972, 0.0018083744353853154, 0.001810697601429244, 0.0018130267441589505, 0.0018153618866679933, 0.00181770305216906, 0.0018200502639947383, 0.0018224035455982881, 0.0018247629205544254, 0.0018271284125601088, 0.0018295000454353315, 0.0018318778431239229, 0.0018342618296943525, 0.0018366520293405437, 0.0018390484663826912, 0.0018414511652680853, 0.0018438601505719457, 0.0018462754469982556, 0.0018486970793806098, 0.0018511250726830641, 0.001853559452000993, 0.0018560002425619538, 0.0018584474697265604, 0.0018609011589893595, 0.0018633613359797167, 0.0018658280264627085, 0.0018683012563400214, 0.0018707810516508602, 0.0018732674385728606, 0.0018757604434230092, 0.0018782600926585753, 0.0018807664128780426, 0.0018832794308220565, 0.0018857991733743733, 0.001888325667562818, 0.0018908589405602532, 0.0018933990196855503, 0.001895945932404574, 0.0018984997063311716, 0.0019010603692281695, 0.0019036279490083816, 0.0019062024737356211, 0.0019087839716257255, 0.001911372471047586, 0.0019139680005241858, 0.00191657058873365, 0.0019191802645102994, 0.0019217970568457178, 0.0019244209948898244, 0.0019270521079519547, 0.0019296904255019544, 0.0019323359771712782, 0.0019349887927541001, 0.001937648902208431, 0.001940316335657246, 0.0019429911233896221, 0.0019456732958618857, 0.0019483628836987675, 0.0019510599176945666, 0.001953764428814329, 0.00195647644819503, 0.0019591960071467704, 0.0019619231371539813, 0.0019646578698766385, 0.001967400237151488, 0.0019701502709932824, 0.0019729080035960247, 0.0019756734673342267, 0.0019784466947641746, 0.0019812277186252066, 0.0019840165718410015, 0.0019868132875208795, 0.0019896178989611086, 0.0019924304396462303, 0.0019952509432503897, 0.001998079443638679, 0.002000915974868495, 0.002003760571190905, 0.002006613267052025, 0.002009474097094409, 0.002012343096158455, 0.0020152202992838163, 0.002018105741710828, 0.0020209994588819466, 0.002023901486443203, 0.0020268118602456615, 0.002029730616346902, 0.0020326577910125027, 0.0020355934207175485, 0.002038537542148141, 0.0020414901922029298, 0.0020444514079946525, 0.0020474212268516896, 0.002050399686319635, 0.002053386824162875, 0.0020563826783661873, 0.0020593872871363496, 0.002062400688903764, 0.002065422922324096, 0.0020684540262799257, 0.0020714940398824187, 0.0020745430024730047, 0.0020776009536250767, 0.0020806679331457027, 0.002083743981077352, 0.00208682913769964, 0.0020899234435310843, 0.00209302693933088, 0.002096139666100688, 0.0020992616650864415, 0.0021023929777801687, 0.002105533645921828, 0.0021086837115011662, 0.0021118432167595877, 0.002115012204192043, 0.0021181907165489346, 0.002121378796838037, 0.002124576488326441, 0.0021277838345425066, 0.0021310008792778403, 0.0021342276665892875, 0.0021374642408009442, 0.002140710646506187, 0.002143966928569718, 0.0021472331321296364, 0.00215050930259952, 0.0021537954856705333, 0.002157091727313549, 0.0021603980737812923, 0.002163714571610505, 0.00216704126762413, 0.0021703782089335113, 0.0021737254429406213, 0.0021770830173403026, 0.0021804509801225374, 0.0021838293795747293, 0.0021872182642840134, 0.0021906176831395854, 0.002194027685335053, 0.002197448320370808, 0.002200879638056421, 0.002204321688513061, 0.002207774522175935, 0.0022112381897967494, 0.0022147127424462, 0.0022181982315164803, 0.0022216947087238146, 0.0022252022261110174, 0.002228720836050075, 0.0022322505912447514, 0.0022357915447332203, 0.002239343749890723, 0.0022429072604322467, 0.0022464821304152365, 0.002250068414242325, 0.002253666166664095, 0.0022572754427818633, 0.0022608962980504963, 0.002264528788281247, 0.0022681729696446256, 0.002271828898673293, 0.0022754966322649844, 0.0022791762276854616, 0.0022828677425714935, 0.0022865712349338647, 0.002290286763160414, 0.002294014386019105, 0.002297754162661122, 0.0023015061526240003, 0.002305270415834785, 0.0023090470126132215, 0.0023128360036749783, 0.0023166374501349006, 0.0023204514135102953, 0.0023242779557242498, 0.002328117139108984, 0.0023319690264092343, 0.0023358336807856707, 0.0023397111658183516, 0.0023436015455102085, 0.0023475048842905677, 0.0023514212470187087, 0.002355350698987454, 0.0023592933059268, 0.002363249134007581, 0.002367218249845171, 0.0023712007205032243, 0.0023751966134974507, 0.002379205996799432, 0.002383228938840477, 0.0023872655085155126, 0.002391315775187018, 0.002395379808688999, 0.0023994576793309997, 0.002403549457902156, 0.002407655215675296, 0.002411775024411074, 0.002415908956362155, 0.002420057084277434, 0.0024242194814063094, 0.0024283962215029893, 0.0024325873788308503, 0.002436793028166839, 0.0024410132448059196, 0.0024452481045655647, 0.0024494976837902984, 0.0024537620593562833, 0.0024580413086759557, 0.002462335509702711, 0.0024666447409356362, 0.002470969081424293, 0.002475308610773554, 0.0024796634091484838, 0.002484033557279278, 0.0024884191364662506, 0.0024928202285848773, 0.0024972369160908897, 0.0025016692820254236, 0.0025061174100202252, 0.0025105813843029103, 0.0025150612897022816, 0.002519557211653701, 0.0025240692362045215, 0.002528597450019576, 0.0025331419403867264, 0.0025377027952224736, 0.0025422801030776246, 0.0025468739531430257, 0.0025514844352553545, 0.0025561116399029755, 0.0025607556582318606, 0.002565416582051575, 0.0025700945038413265, 0.0025747895167560807, 0.0025795017146327463, 0.0025842311919964263, 0.002588978044066739, 0.002593742366764206, 0.002598524256716717, 0.00260332381126606, 0.0026081411284745257, 0.002612976307131589, 0.00261782944676066, 0.0026227006476259125, 0.002627590010739189, 0.002632497637866984, 0.002637423631537504, 0.0026423680950478055, 0.002647331132471019, 0.0026523128486636485, 0.0026573133492729575, 0.002662332740744436, 0.0026673711303293554, 0.0026724286260924055, 0.0026775053369194218, 0.0026826013725251992, 0.002687716843461398, 0.002692851861124535, 0.0026980065377640704, 0.002703180986490589, 0.0027083753212840725, 0.002713589657002267, 0.0027188241093891526, 0.002724078795083504, 0.0027293538316275553, 0.002734649337475766, 0.0027399654320036846, 0.002745302235516923, 0.0027506598692602275, 0.0027560384554266644, 0.002761438117166907, 0.0027668589785986367, 0.0027723011648160515, 0.0027777648018994907, 0.002783250016925169, 0.002788756937975031, 0.0027942856941467185, 0.0027998364155636603, 0.0028054092333852794, 0.0028110042798173266, 0.0028166216881223317, 0.002822261592630185, 0.0028279241287488465, 0.0028336094329751813, 0.0028393176429059265, 0.002845048897248795, 0.0028508033358337075, 0.0028565810996241665, 0.002862382330728766, 0.002868207172412843, 0.0028740557691102698, 0.002879928266435396, 0.0028858248111951284, 0.002891745551401168, 0.0028976906362823936, 0.0029036602162973986, 0.0029096544431471867, 0.002915673469788019, 0.0029217174504444256, 0.002927786540622379, 0.0029338808971226295, 0.0029400006780542103, 0.0029461460428481107, 0.002952317152271121, 0.0029585141684398504, 0.0029647372548349256, 0.0029709865763153666, 0.0029772622991331424, 0.0029835645909479184, 0.002989893620841983, 0.0029962495593353687, 0.0030026325784011714, 0.0030090428514810545, 0.0030154805535009634, 0.0030219458608870364, 0.003028438951581718, 0.0030349600050600892, 0.0030415092023464013, 0.0030480867260308255, 0.0030546927602864253, 0.003061327490886345, 0.003067991105221223, 0.003074683792316836, 0.0030814057428519715, 0.0030881571491765372, 0.003094938205329911, 0.003101749107059525, 0.0031085900518397066, 0.0031154612388907613, 0.0031223628691983123, 0.003129295145532898, 0.0031362582724698304, 0.003143252456409318, 0.0031502779055968613, 0.0031573348301439197, 0.003164423442048859, 0.00317154395521818, 0.0031786965854880373, 0.003185881550646045, 0.003193099070453382, 0.0032003493666671987, 0.0032076326630633297, 0.0032149491854593154, 0.003222299161737742, 0.0032296828218698987, 0.0032371003979397655, 0.003244552124168328, 0.0032520382369382326, 0.003259558974818781, 0.003267114578591275, 0.00327470529127471, 0.0032823313581518327, 0.0032899930267955607, 0.0032976905470957748, 0.0033054241712864845, 0.003313194153973385, 0.003321000752161792, 0.003328844225284981, 0.0033367248352329285, 0.0033446428463814576, 0.003352598525621806, 0.00336059214239061, 0.0033686239687003242, 0.0033766942791700755, 0.0033848033510569635, 0.00339295146428781, 0.0034011389014913735, 0.0034093659480310245, 0.0034176328920379005, 0.003425940024444545, 0.0034342876390190354, 0.003442676032399613, 0.0034511055041298224, 0.0034595763566941658, 0.003468088895554285, 0.0034766434291856802, 0.003485240269114973, 0.0034938797299577207, 0.0035025621294567997, 0.0035112877885213577, 0.0035200570312663515, 0.003528870185052681, 0.0035377275805279227, 0.0035466295516676824, 0.0035555764358175743, 0.0035645685737358303, 0.0035736063096365673, 0.0035826899912337062, 0.0035918199697855674, 0.0036009966001401463, 0.0036102202407810907, 0.003619491253874377, 0.0036288100053157163, 0.0036381768647786895, 0.0036475922057636334, 0.0036570564056472854, 0.0036665698457332024, 0.0036761329113029714, 0.0036857459916682218, 0.003695409480223456, 0.0037051237744997133, 0.0037148892762190857, 0.0037247063913500907, 0.003734575530163931, 0.003744497107291649, 0.0037544715417821947, 0.0037644992571614225, 0.0037745806814920404, 0.003784716247434519, 0.0037949063923089898, 0.003805151558158142, 0.003815452191811146, 0.0038258087449486106, 0.003836221674168611, 0.0038466914410537852, 0.003857218512239545, 0.003867803359483401, 0.0038784464597354366, 0.003889148295209947, 0.0038999093534582705, 0.0039107301274428265, 0.003921611115612393, 0.003932552821978648, 0.003943555756193987, 0.003954620433630662, 0.0039657473754612415, 0.003976937108740448, 0.003988190166488376, 0.0039995070877751285, 0.004010888417806898, 0.004022334708013529, 0.0040338465161375665, 0.004045424406324857, 0.004057068949216706, 0.004068780722043627, 0.004080560308720733, 0.00409240829994477, 0.004104325293292866, 0.0041163118933229955, 0.0041283687116762165, 0.00414049636718071, 0.004152695485957653, 0.00416496670152898, 0.004177310654927043, 0.004189727994806247, 0.004202219377556666, 0.004214785467419708, 0.004227426936605861, 0.0042401444654145545, 0.004252938742356205, 0.004265810464276464, 0.0042787603364827405, 0.004291789072873031, 0.004304897396067107, 0.0043180860375401165, 0.004331355737758652, 0.004344707246319328, 0.004358141322089939, 0.0043716587333532345, 0.004385260257953386, 0.004398946683445191, 0.004412718807246081, 0.004426577436791, 0.0044405233896901986, 0.004454557493890032, 0.004468680587836814, 0.004482893520643792, 0.00449719715226132, 0.004511592353650311, 0.004526080006959018, 0.004540661005703233, 0.004555336254949994, 0.004570106671504849, 0.0045849731841027825, 0.004599936733602883, 0.004614998273186832, 0.0046301587685613045, 0.004645419198164375, 0.004660780553376014, 0.0046762438387327795, 0.004691810072146795, 0.004707480285129112, 0.004723255523017572, 0.004739136845209258, 0.004755125325397652, 0.004771222051814612, 0.0047874281274772786, 0.004803744670440034, 0.004820172814051628, 0.004836713707217596, 0.0048533685146681035, 0.004870138417231339, 0.0048870246121126, 0.004904028313179199, 0.004921150751251346, 0.0049383931743991315, 0.004955756848245795, 0.004973243056277397, 0.004990853100159078, 0.005008588300058056, 0.005026449994973549, 0.0050444395430737565, 0.005062558322040129, 0.005080807729419066, 0.005099189182981265, 0.005117704121088874, 0.005136354003070707, 0.005155140309605651, 0.005174064543114561, 0.005193128228160791, 0.005212332911859605, 0.005231680164296752, 0.0052511715789563315, 0.0052708087731583204, 0.005290593388505908, 0.005310527091342978, 0.005330611573221953, 0.005350848551382285, 0.005371239769239927, 0.005391786996887983, 0.005412492031608951, 0.005433356698398775, 0.005454382850503063, 0.005475572369965845, 0.005496927168191114, 0.005518449186517615, 0.005540140396807149, 0.005562002802046815, 0.005584038436965597, 0.005606249368665611, 0.0056286376972685395, 0.005651205556577561, 0.005673955114755314, 0.0056968885750182715, 0.0057200081763480225, 0.005743316194219982, 0.005766814941349932, 0.00579050676845902, 0.005814394065057657, 0.005838479260248896, 0.005862764823551907, 0.005887253265746015, 0.005911947139736062, 0.005936849041439562, 0.005961961610696437, 0.005987287532201898, 0.006012829536463205, 0.0060385904007810645, 0.006064572950256295, 0.006090780058822666, 0.006117214650306577, 0.006143879699514465, 0.006170778233348813, 0.006197913331953536, 0.006225288129889792, 0.006252905817343044, 0.006280769641362393, 0.0063088829071332436, 0.0063372489792842355, 0.006365871283229658, 0.006394753306548342, 0.006423898600400324, 0.006453310780982384, 0.00648299353102375, 0.006512950601323323, 0.00654318581232964, 0.006573703055765134, 0.006604506296296002, 0.006635599573249246, 0.006666987002378493, 0.006698672777680101, 0.0067306611732613686, 0.006762956545262456, 0.006795563333833984, 0.006828486065172055, 0.006861729353612729, 0.006895297903788025, 0.006929196512845439, 0.006963430072733337, 0.006998003572554376, 0.00703292210098938, 0.007068190848794205, 0.0071038151113720326, 0.007139800291423916, 0.0071761519016802534, 0.007212875567716119, 0.007249977030853551, 0.00728746215115378, 0.007325336910502862, 0.007363607415793941, 0.007402279902209877, 0.007441360736609796, 0.007480856421023495, 0.007520773596257772, 0.00756111904561875, 0.007601899698754745, 0.007643122635624112, 0.007684795090592884, 0.007726924456667269, 0.007769518289866026, 0.007812584313738373, 0.007856130424032869, 0.007900164693523426, 0.00794469537699846, 0.007989730916419734, 0.008035279946257733, 0.008081351299010482, 0.008127954010913421, 0.008175097327847916, 0.00822279071145659, 0.00827104384547405, 0.00831986664228171, 0.008369269249696262, 0.008419262058001382, 0.008469855707232948, 0.00852106109472861, 0.008572889382952767, 0.008625352007608961, 0.008678460686051862, 0.008732227426012068, 0.008786664534647163, 0.00884178462793345, 0.008897600640413492, 0.008954125835315069, 0.00901137381505846, 0.009069358532169258, 0.009128094300615277, 0.009187595807586912, 0.009247878125741146, 0.009308956725930897, 0.009370847490442015, 0.009433566726761974, 0.009497131181905141, 0.009561558057321106, 0.009626865024414078, 0.009693070240702508, 0.009760192366650265, 0.009828250583201895, 0.009897264610056685, 0.009967254724718193, 0.01003824178235765, 0.010110247236532425, 0.010183293160802454, 0.010257402271290725, 0.010332597950235974, 0.010408904270588994, 0.010486346021707053, 0.010564948736203696, 0.01064473871801543, 0.010725743071749744, 0.01080798973338344, 0.010891507502384358, 0.01097632607533385, 0.011062476081132788, 0.011149989117878486, 0.01123889779150595, 0.011329235756292829, 0.011421037757333467, 0.011514339675095074, 0.011609178572175619, 0.011705592742391881, 0.011803621762333898, 0.011903306545531749, 0.01200468939939061, 0.012107814085060115, 0.012212725880416497, 0.012319471646347552, 0.012428099896544456, 0.012538660871018976, 0.012651206613579715, 0.012765791053518953, 0.01288247009177889, 0.013001301691887098, 0.013122345975971526, 0.013245665326189416, 0.013371324491929825, 0.013499390703176364, 0.013629933790447735, 0.013763026311765195, 0.013898743687132172, 0.014037164341049981, 0.014178369853634933, 0.014322445120949375, 0.014469478525208173, 0.01461956211557794, 0.014772791800346383, 0.014929267551304215, 0.015089093621255597, 0.015252378775650784, 0.015419236539423219, 0.015589785460207655, 0.01576414938922204, 0.015942457781212033, 0.01612484601498399, 0.016311455736195246, 0.016502435224224975, 0.01669793978512307, 0.016898132172825774, 0.017103183041038382, 0.017313271428422886, 0.017528585279988875, 0.017749322007880035, 0.017975689095072498, 0.018207904745865748, 0.018446198587453264, 0.018690812427313495, 0.018942001071673546, 0.01920003321086825, 0.019465192378061946, 0.019737777988524826, 0.02001810646747146, 0.020306512475394323, 0.020603350240867385, 0.020908995011980257, 0.02122384463890783, 0.021548321301648, 0.02188287339870596, 0.022227977614490756, 0.022584141185470693, 0.022951904387742434, 0.023331843271670906, 0.02372457267271204, 0.024130749531515606, 0.0245510765610208, 0.024986306303602365, 0.02543724562754368, 0.025904760719358867, 0.026389782636949466, 0.026893313498505128, 0.027416433393709836, 0.02796030811755749, 0.02852619784331662, 0.029115466870445705, 0.029729594606176548, 0.030370187966838852, 0.031038995417786343, 0.03173792291020483, 0.03246905202068515, 0.033234660657145206, 0.03403724676492237, 0.03487955555275008, 0.03576461086382385, 0.03669575144738978, 0.03767667304782901, 0.038711477429695884, 0.0398047297098569, 0.04096152568665084, 0.04218757126064718, 0.04348927655857836, 0.04487386803715542, 0.04634952270541262, 0.04792552972983364, 0.04961248616853053, 0.05142253554894814, 0.053369660641650996, 0.05547004535337704, 0.05774252554575575, 0.0602091553384132, 0.0628959249016385, 0.06583367912374075, 0.06905930573812695, 0.07261728942649547, 0.0765617696335492, 0.08095930156640957, 0.08589261374722872, 0.09146580053511144, 0.09781161565892843, 0.10510189568837577, 0.11356272996478306, 0.12349695953816668, 0.13531819933733455, 0.14960330468755945, 0.16717487876238815, 0.18923353452246894, 0.2175738805672719, 0.25494350737857946, 0.3056496192631225, 0.37660002556905986, 0.4791148790078885, 0.6321205588285577]} \ No newline at end of file diff --git a/lib/node_modules/@stdlib/math/base/special/expm1rel/test/fixtures/python/medium_positive.json b/lib/node_modules/@stdlib/math/base/special/expm1rel/test/fixtures/python/medium_positive.json new file mode 100644 index 000000000000..cf0b8b0bd66c --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expm1rel/test/fixtures/python/medium_positive.json @@ -0,0 +1 @@ +{"x": [1.0, 1.7094894894894894, 2.418978978978979, 3.1284684684684683, 3.8379579579579577, 4.547447447447447, 5.2569369369369365, 5.966426426426426, 6.675915915915915, 7.385405405405405, 8.094894894894894, 8.804384384384385, 9.513873873873873, 10.223363363363362, 10.932852852852852, 11.642342342342342, 12.35183183183183, 13.06132132132132, 13.77081081081081, 14.4803003003003, 15.189789789789788, 15.899279279279277, 16.60876876876877, 17.318258258258258, 18.027747747747746, 18.737237237237235, 19.446726726726723, 20.156216216216215, 20.865705705705704, 21.575195195195192, 22.284684684684684, 22.994174174174173, 23.70366366366366, 24.41315315315315, 25.12264264264264, 25.83213213213213, 26.54162162162162, 27.251111111111108, 27.9606006006006, 28.67009009009009, 29.379579579579577, 30.089069069069065, 30.798558558558554, 31.508048048048046, 32.21753753753754, 32.92702702702702, 33.636516516516515, 34.346006006006, 35.05549549549549, 35.764984984984984, 36.47447447447447, 37.18396396396396, 37.893453453453446, 38.60294294294294, 39.31243243243243, 40.021921921921916, 40.73141141141141, 41.4409009009009, 42.150390390390385, 42.85987987987988, 43.56936936936937, 44.278858858858854, 44.988348348348346, 45.69783783783783, 46.40732732732732, 47.116816816816815, 47.8263063063063, 48.53579579579579, 49.24528528528528, 49.95477477477477, 50.66426426426426, 51.373753753753746, 52.08324324324324, 52.79273273273273, 53.502222222222215, 54.21171171171171, 54.9212012012012, 55.630690690690685, 56.34018018018018, 57.04966966966966, 57.759159159159154, 58.468648648648646, 59.17813813813813, 59.88762762762762, 60.59711711711711, 61.3066066066066, 62.01609609609609, 62.72558558558558, 63.43507507507507, 64.14456456456456, 64.85405405405405, 65.56354354354353, 66.27303303303303, 66.98252252252252, 67.692012012012, 68.4015015015015, 69.11099099099098, 69.82048048048047, 70.52996996996997, 71.23945945945945, 71.94894894894894, 72.65843843843844, 73.36792792792792, 74.07741741741741, 74.78690690690689, 75.49639639639639, 76.20588588588588, 76.91537537537536, 77.62486486486486, 78.33435435435435, 79.04384384384383, 79.75333333333333, 80.46282282282282, 81.1723123123123, 81.8818018018018, 82.59129129129128, 83.30078078078077, 84.01027027027027, 84.71975975975975, 85.42924924924924, 86.13873873873874, 86.84822822822822, 87.55771771771771, 88.26720720720719, 88.97669669669669, 89.68618618618618, 90.39567567567566, 91.10516516516516, 91.81465465465465, 92.52414414414413, 93.23363363363363, 93.94312312312312, 94.6526126126126, 95.3621021021021, 96.07159159159158, 96.78108108108107, 97.49057057057055, 98.20006006006005, 98.90954954954954, 99.61903903903902, 100.32852852852852, 101.03801801801801, 101.74750750750749, 102.45699699699699, 103.16648648648648, 103.87597597597596, 104.58546546546546, 105.29495495495495, 106.00444444444443, 106.71393393393393, 107.42342342342342, 108.1329129129129, 108.8424024024024, 109.55189189189188, 110.26138138138137, 110.97087087087085, 111.68036036036035, 112.38984984984984, 113.09933933933932, 113.80882882882882, 114.51831831831831, 115.22780780780779, 115.93729729729729, 116.64678678678678, 117.35627627627626, 118.06576576576576, 118.77525525525525, 119.48474474474473, 120.19423423423422, 120.90372372372372, 121.6132132132132, 122.32270270270268, 123.03219219219218, 123.74168168168167, 124.45117117117115, 125.16066066066065, 125.87015015015014, 126.57963963963962, 127.28912912912912, 127.99861861861861, 128.7081081081081, 129.4175975975976, 130.12708708708706, 130.83657657657656, 131.54606606606606, 132.25555555555553, 132.96504504504503, 133.67453453453453, 134.384024024024, 135.0935135135135, 135.803003003003, 136.51249249249247, 137.22198198198197, 137.93147147147147, 138.64096096096094, 139.35045045045044, 140.05993993993994, 140.7694294294294, 141.4789189189189, 142.1884084084084, 142.89789789789788, 143.60738738738738, 144.31687687687688, 145.02636636636635, 145.73585585585585, 146.44534534534534, 147.15483483483482, 147.86432432432431, 148.57381381381379, 149.28330330330328, 149.99279279279278, 150.70228228228225, 151.41177177177175, 152.12126126126125, 152.83075075075072, 153.54024024024022, 154.24972972972972, 154.9592192192192, 155.6687087087087, 156.3781981981982, 157.08768768768766, 157.79717717717716, 158.50666666666666, 159.21615615615613, 159.92564564564563, 160.63513513513513, 161.3446246246246, 162.0541141141141, 162.7636036036036, 163.47309309309307, 164.18258258258257, 164.89207207207207, 165.60156156156154, 166.31105105105104, 167.02054054054054, 167.73003003003, 168.4395195195195, 169.149009009009, 169.85849849849848, 170.56798798798798, 171.27747747747748, 171.98696696696695, 172.69645645645645, 173.40594594594592, 174.11543543543542, 174.82492492492491, 175.53441441441439, 176.24390390390388, 176.95339339339338, 177.66288288288285, 178.37237237237235, 179.08186186186185, 179.79135135135132, 180.50084084084082, 181.21033033033032, 181.9198198198198, 182.6293093093093, 183.3387987987988, 184.04828828828826, 184.75777777777776, 185.46726726726726, 186.17675675675673, 186.88624624624623, 187.59573573573573, 188.3052252252252, 189.0147147147147, 189.7242042042042, 190.43369369369367, 191.14318318318317, 191.85267267267267, 192.56216216216214, 193.27165165165164, 193.9811411411411, 194.6906306306306, 195.4001201201201, 196.10960960960958, 196.81909909909908, 197.52858858858858, 198.23807807807805, 198.94756756756755, 199.65705705705705, 200.36654654654652, 201.07603603603602, 201.78552552552551, 202.49501501501499, 203.20450450450448, 203.91399399399398, 204.62348348348345, 205.33297297297295, 206.04246246246245, 206.75195195195192, 207.46144144144142, 208.17093093093092, 208.8804204204204, 209.5899099099099, 210.2993993993994, 211.00888888888886, 211.71837837837836, 212.42786786786786, 213.13735735735733, 213.84684684684683, 214.55633633633633, 215.2658258258258, 215.9753153153153, 216.6848048048048, 217.39429429429427, 218.10378378378377, 218.81327327327324, 219.52276276276274, 220.23225225225224, 220.9417417417417, 221.6512312312312, 222.3607207207207, 223.07021021021018, 223.77969969969968, 224.48918918918918, 225.19867867867865, 225.90816816816815, 226.61765765765765, 227.32714714714712, 228.03663663663662, 228.74612612612611, 229.45561561561559, 230.16510510510508, 230.87459459459458, 231.58408408408405, 232.29357357357355, 233.00306306306305, 233.71255255255252, 234.42204204204202, 235.13153153153152, 235.841021021021, 236.5505105105105, 237.26, 237.96948948948946, 238.67897897897896, 239.38846846846843, 240.09795795795793, 240.80744744744743, 241.5169369369369, 242.2264264264264, 242.9359159159159, 243.64540540540537, 244.35489489489487, 245.06438438438437, 245.77387387387384, 246.48336336336334, 247.19285285285284, 247.9023423423423, 248.6118318318318, 249.3213213213213, 250.03081081081078, 250.74030030030028, 251.44978978978978, 252.15927927927925, 252.86876876876875, 253.57825825825824, 254.28774774774772, 254.99723723723721, 255.7067267267267, 256.4162162162162, 257.1257057057057, 257.8351951951952, 258.5446846846847, 259.2541741741741, 259.9636636636636, 260.6731531531531, 261.3826426426426, 262.0921321321321, 262.8016216216216, 263.51111111111106, 264.22060060060056, 264.93009009009006, 265.63957957957956, 266.34906906906906, 267.05855855855856, 267.768048048048, 268.4775375375375, 269.187027027027, 269.8965165165165, 270.606006006006, 271.3154954954955, 272.02498498498494, 272.73447447447444, 273.44396396396394, 274.15345345345344, 274.86294294294294, 275.5724324324324, 276.2819219219219, 276.9914114114114, 277.7009009009009, 278.4103903903904, 279.1198798798799, 279.8293693693693, 280.5388588588588, 281.2483483483483, 281.9578378378378, 282.6673273273273, 283.3768168168168, 284.08630630630626, 284.79579579579575, 285.50528528528525, 286.21477477477475, 286.92426426426425, 287.63375375375375, 288.3432432432432, 289.0527327327327, 289.7622222222222, 290.4717117117117, 291.1812012012012, 291.8906906906907, 292.60018018018013, 293.30966966966963, 294.01915915915913, 294.72864864864863, 295.43813813813813, 296.14762762762757, 296.85711711711707, 297.56660660660657, 298.27609609609607, 298.98558558558557, 299.69507507507507, 300.4045645645645, 301.114054054054, 301.8235435435435, 302.533033033033, 303.2425225225225, 303.952012012012, 304.66150150150145, 305.37099099099095, 306.08048048048045, 306.78996996996995, 307.49945945945944, 308.20894894894894, 308.9184384384384, 309.6279279279279, 310.3374174174174, 311.0469069069069, 311.7563963963964, 312.4658858858859, 313.1753753753753, 313.8848648648648, 314.5943543543543, 315.3038438438438, 316.0133333333333, 316.7228228228228, 317.43231231231226, 318.14180180180176, 318.85129129129126, 319.56078078078076, 320.27027027027026, 320.9797597597597, 321.6892492492492, 322.3987387387387, 323.1082282282282, 323.8177177177177, 324.5272072072072, 325.23669669669664, 325.94618618618614, 326.65567567567564, 327.36516516516514, 328.07465465465464, 328.78414414414414, 329.4936336336336, 330.2031231231231, 330.9126126126126, 331.6221021021021, 332.3315915915916, 333.0410810810811, 333.7505705705705, 334.46006006006, 335.1695495495495, 335.879039039039, 336.5885285285285, 337.298018018018, 338.00750750750746, 338.71699699699695, 339.42648648648645, 340.13597597597595, 340.84546546546545, 341.55495495495495, 342.2644444444444, 342.9739339339339, 343.6834234234234, 344.3929129129129, 345.1024024024024, 345.81189189189183, 346.52138138138133, 347.23087087087083, 347.94036036036033, 348.64984984984983, 349.35933933933933, 350.06882882882877, 350.77831831831827, 351.48780780780777, 352.19729729729727, 352.90678678678677, 353.61627627627627, 354.3257657657657, 355.0352552552552, 355.7447447447447, 356.4542342342342, 357.1637237237237, 357.8732132132132, 358.58270270270265, 359.29219219219215, 360.00168168168165, 360.71117117117115, 361.42066066066064, 362.13015015015014, 362.8396396396396, 363.5491291291291, 364.2586186186186, 364.9681081081081, 365.6775975975976, 366.387087087087, 367.0965765765765, 367.806066066066, 368.5155555555555, 369.225045045045, 369.9345345345345, 370.64402402402396, 371.35351351351346, 372.06300300300296, 372.77249249249246, 373.48198198198196, 374.19147147147146, 374.9009609609609, 375.6104504504504, 376.3199399399399, 377.0294294294294, 377.7389189189189, 378.4484084084084, 379.15789789789784, 379.86738738738734, 380.57687687687684, 381.28636636636634, 381.99585585585584, 382.70534534534534, 383.4148348348348, 384.1243243243243, 384.8338138138138, 385.5433033033033, 386.2527927927928, 386.9622822822822, 387.6717717717717, 388.3812612612612, 389.0907507507507, 389.8002402402402, 390.5097297297297, 391.21921921921916, 391.92870870870865, 392.63819819819815, 393.34768768768765, 394.05717717717715, 394.76666666666665, 395.4761561561561, 396.1856456456456, 396.8951351351351, 397.6046246246246, 398.3141141141141, 399.0236036036036, 399.73309309309303, 400.44258258258253, 401.15207207207203, 401.86156156156153, 402.57105105105103, 403.2805405405405, 403.99003003002997, 404.69951951951947, 405.40900900900897, 406.11849849849847, 406.82798798798797, 407.53747747747747, 408.2469669669669, 408.9564564564564, 409.6659459459459, 410.3754354354354, 411.0849249249249, 411.79441441441435, 412.50390390390385, 413.21339339339335, 413.92288288288285, 414.63237237237234, 415.34186186186184, 416.0513513513513, 416.7608408408408, 417.4703303303303, 418.1798198198198, 418.8893093093093, 419.5987987987988, 420.3082882882882, 421.0177777777777, 421.7272672672672, 422.4367567567567, 423.1462462462462, 423.8557357357357, 424.56522522522516, 425.27471471471466, 425.98420420420416, 426.69369369369366, 427.40318318318316, 428.11267267267266, 428.8221621621621, 429.5316516516516, 430.2411411411411, 430.9506306306306, 431.6601201201201, 432.3696096096096, 433.07909909909904, 433.78858858858854, 434.49807807807804, 435.20756756756754, 435.91705705705704, 436.6265465465465, 437.336036036036, 438.0455255255255, 438.755015015015, 439.4645045045045, 440.173993993994, 440.8834834834834, 441.5929729729729, 442.3024624624624, 443.0119519519519, 443.7214414414414, 444.4309309309309, 445.14042042042036, 445.84990990990985, 446.55939939939935, 447.26888888888885, 447.97837837837835, 448.68786786786785, 449.3973573573573, 450.1068468468468, 450.8163363363363, 451.5258258258258, 452.2353153153153, 452.9448048048048, 453.65429429429423, 454.36378378378373, 455.07327327327323, 455.78276276276273, 456.49225225225223, 457.20174174174167, 457.91123123123117, 458.62072072072067, 459.33021021021017, 460.03969969969967, 460.74918918918917, 461.4586786786786, 462.1681681681681, 462.8776576576576, 463.5871471471471, 464.2966366366366, 465.0061261261261, 465.71561561561555, 466.42510510510505, 467.13459459459455, 467.84408408408405, 468.55357357357354, 469.26306306306304, 469.9725525525525, 470.682042042042, 471.3915315315315, 472.101021021021, 472.8105105105105, 473.52, 474.2294894894894, 474.9389789789789, 475.6484684684684, 476.3579579579579, 477.0674474474474, 477.77693693693686, 478.48642642642636, 479.19591591591586, 479.90540540540536, 480.61489489489486, 481.32438438438436, 482.0338738738738, 482.7433633633633, 483.4528528528528, 484.1623423423423, 484.8718318318318, 485.5813213213213, 486.29081081081074, 487.00030030030024, 487.70978978978974, 488.41927927927924, 489.12876876876874, 489.83825825825824, 490.5477477477477, 491.2572372372372, 491.9667267267267, 492.6762162162162, 493.3857057057057, 494.0951951951952, 494.8046846846846, 495.5141741741741, 496.2236636636636, 496.9331531531531, 497.6426426426426, 498.3521321321321, 499.06162162162155, 499.77111111111105, 500.48060060060055, 501.19009009009005, 501.89957957957955, 502.609069069069, 503.3185585585585, 504.028048048048, 504.7375375375375, 505.447027027027, 506.1565165165165, 506.86600600600593, 507.57549549549543, 508.28498498498493, 508.99447447447443, 509.70396396396393, 510.4134534534534, 511.12294294294287, 511.83243243243237, 512.5419219219218, 513.2514114114114, 513.9609009009008, 514.6703903903904, 515.3798798798798, 516.0893693693694, 516.7988588588588, 517.5083483483482, 518.2178378378378, 518.9273273273272, 519.6368168168168, 520.3463063063062, 521.0557957957958, 521.7652852852852, 522.4747747747747, 523.1842642642642, 523.8937537537537, 524.6032432432432, 525.3127327327327, 526.0222222222221, 526.7317117117117, 527.4412012012011, 528.1506906906907, 528.8601801801801, 529.5696696696696, 530.2791591591591, 530.9886486486486, 531.6981381381381, 532.4076276276276, 533.1171171171171, 533.8266066066066, 534.536096096096, 535.2455855855856, 535.955075075075, 536.6645645645646, 537.374054054054, 538.0835435435434, 538.793033033033, 539.5025225225224, 540.212012012012, 540.9215015015014, 541.630990990991, 542.3404804804804, 543.0499699699699, 543.7594594594594, 544.4689489489489, 545.1784384384384, 545.8879279279279, 546.5974174174173, 547.3069069069069, 548.0163963963963, 548.7258858858859, 549.4353753753753, 550.1448648648648, 550.8543543543543, 551.5638438438438, 552.2733333333333, 552.9828228228228, 553.6923123123123, 554.4018018018018, 555.1112912912912, 555.8207807807808, 556.5302702702702, 557.2397597597597, 557.9492492492492, 558.6587387387386, 559.3682282282282, 560.0777177177176, 560.7872072072072, 561.4966966966966, 562.2061861861862, 562.9156756756756, 563.6251651651651, 564.3346546546546, 565.0441441441441, 565.7536336336336, 566.4631231231231, 567.1726126126125, 567.8821021021021, 568.5915915915915, 569.3010810810811, 570.0105705705705, 570.72006006006, 571.4295495495495, 572.139039039039, 572.8485285285285, 573.558018018018, 574.2675075075075, 574.976996996997, 575.6864864864864, 576.395975975976, 577.1054654654654, 577.8149549549549, 578.5244444444444, 579.2339339339338, 579.9434234234234, 580.6529129129128, 581.3624024024024, 582.0718918918918, 582.7813813813814, 583.4908708708708, 584.2003603603603, 584.9098498498498, 585.6193393393393, 586.3288288288288, 587.0383183183183, 587.7478078078077, 588.4572972972973, 589.1667867867867, 589.8762762762763, 590.5857657657657, 591.2952552552551, 592.0047447447447, 592.7142342342341, 593.4237237237237, 594.1332132132131, 594.8427027027027, 595.5521921921921, 596.2616816816816, 596.9711711711711, 597.6806606606606, 598.3901501501501, 599.0996396396396, 599.809129129129, 600.5186186186186, 601.228108108108, 601.9375975975976, 602.647087087087, 603.3565765765766, 604.066066066066, 604.7755555555555, 605.485045045045, 606.1945345345345, 606.904024024024, 607.6135135135135, 608.3230030030029, 609.0324924924925, 609.7419819819819, 610.4514714714715, 611.1609609609609, 611.8704504504504, 612.5799399399399, 613.2894294294293, 613.9989189189189, 614.7084084084083, 615.4178978978979, 616.1273873873873, 616.8368768768768, 617.5463663663663, 618.2558558558558, 618.9653453453453, 619.6748348348348, 620.3843243243242, 621.0938138138138, 621.8033033033032, 622.5127927927928, 623.2222822822822, 623.9317717717718, 624.6412612612612, 625.3507507507506, 626.0602402402402, 626.7697297297296, 627.4792192192192, 628.1887087087086, 628.8981981981981, 629.6076876876876, 630.3171771771771, 631.0266666666666, 631.7361561561561, 632.4456456456456, 633.1551351351351, 633.8646246246245, 634.5741141141141, 635.2836036036035, 635.9930930930931, 636.7025825825825, 637.412072072072, 638.1215615615615, 638.831051051051, 639.5405405405405, 640.25003003003, 640.9595195195194, 641.669009009009, 642.3784984984984, 643.087987987988, 643.7974774774774, 644.506966966967, 645.2164564564564, 645.9259459459458, 646.6354354354354, 647.3449249249248, 648.0544144144144, 648.7639039039038, 649.4733933933933, 650.1828828828828, 650.8923723723723, 651.6018618618618, 652.3113513513513, 653.0208408408408, 653.7303303303303, 654.4398198198197, 655.1493093093093, 655.8587987987987, 656.5682882882883, 657.2777777777777, 657.9872672672672, 658.6967567567567, 659.4062462462462, 660.1157357357357, 660.8252252252252, 661.5347147147146, 662.2442042042042, 662.9536936936936, 663.6631831831832, 664.3726726726726, 665.0821621621621, 665.7916516516516, 666.501141141141, 667.2106306306306, 667.92012012012, 668.6296096096096, 669.339099099099, 670.0485885885885, 670.758078078078, 671.4675675675675, 672.177057057057, 672.8865465465465, 673.596036036036, 674.3055255255255, 675.0150150150149, 675.7245045045045, 676.4339939939939, 677.1434834834835, 677.8529729729729, 678.5624624624623, 679.2719519519519, 679.9814414414413, 680.6909309309309, 681.4004204204203, 682.1099099099099, 682.8193993993993, 683.5288888888888, 684.2383783783783, 684.9478678678678, 685.6573573573573, 686.3668468468468, 687.0763363363362, 687.7858258258258, 688.4953153153152, 689.2048048048048, 689.9142942942942, 690.6237837837837, 691.3332732732732, 692.0427627627627, 692.7522522522522, 693.4617417417417, 694.1712312312312, 694.8807207207207, 695.5902102102101, 696.2996996996997, 697.0091891891891, 697.7186786786787, 698.4281681681681, 699.1376576576575, 699.8471471471471, 700.5566366366365, 701.2661261261261, 701.9756156156155, 702.6851051051051, 703.3945945945945, 704.104084084084, 704.8135735735735, 705.523063063063, 706.2325525525525, 706.942042042042, 707.6515315315314, 708.361021021021, 709.0705105105104, 709.78], "expected": [1.718281828459045, 2.6476557082478576, 4.230868893396085, 6.980723748510936, 11.837170938488475, 20.537051439636784, 36.3125547604133, 65.21644037709466, 118.64641795194642, 218.17100099748814, 404.7850366746777, 756.7133202032614, 1423.749138414389, 2693.647289367933, 5120.783387196175, 9775.992380562964, 18732.647410669844, 36014.031433864926, 69442.79309569157, 134256.9339007535, 260189.64786763582, 505349.4125130667, 983465.5739327852, 1917431.125210051, 3744638.4209245373, 7324418.982917706, 14346950.357244441, 28140024.394652512, 55262149.18296776, 108650939.37971984, 213849921.89277434, 421332677.31738895, 830911660.781952, 1640113202.6686773, 3240109964.4553404, 6406077484.200628, 12675128108.352404, 25097066810.39851, 49726518677.914314, 98589999443.34665, 195588679808.93036, 388246823408.48914, 771105217230.6013, 1532321530084.8323, 3046536809845.073, 6060013939840.757, 12059866513105.924, 24010690091289.633, 47824687841469.67, 95296637557045.12, 189965157177774.1, 378821552295908.44, 755707179508000.2, 1508081076537367.8, 3010527226693921.5, 6011763751570945.0, 1.2008748700996608e+16, 2.3995256581789976e+16, 4.796013040267117e+16, 9.588670109343966e+16, 1.9175885294734464e+17, 3.8359032744042586e+17, 7.675229818462166e+17, 1.536112968538228e+18, 3.0751026725018675e+18, 6.15740338755965e+18, 1.2332015946990504e+19, 2.470393489769626e+19, 4.9498381823442936e+19, 9.919870991025724e+19, 1.9884224569729633e+20, 3.986543158978485e+20, 7.994054781918712e+20, 1.6033131968863032e+21, 3.216237118398245e+21, 6.45288805134677e+21, 1.2948951191989999e+22, 2.598887853898275e+22, 5.21688340000463e+22, 1.047378362868676e+23, 2.103116060602734e+23, 4.223654800679491e+23, 8.483548468877192e+23, 1.7042335219928642e+24, 3.4240620001676046e+24, 6.880399813122283e+24, 1.3827507405292588e+25, 2.7792714715493136e+25, 5.586934837293588e+25, 1.123234859109803e+26, 2.2585030195298444e+26, 4.541745106526101e+26, 9.134308986142927e+26, 1.8372929843768536e+27, 3.695982131348738e+27, 7.435822613652629e+27, 1.4961492039335172e+28, 3.010693627644753e+28, 6.0590295118281625e+28, 1.219504820893569e+29, 2.4547487822072595e+29, 4.9416595021658996e+29, 9.949012899621302e+29, 2.0032160216938613e+30, 4.0338097983429115e+30, 8.12348038599974e+30, 1.6360900848666266e+31, 3.295413641437458e+31, 6.638188982373732e+31, 1.3372899207360182e+32, 2.694245451179928e+32, 5.42854867627191e+32, 1.0938674158456636e+33, 2.2043441695090083e+33, 4.4424986050771025e+33, 8.953808565609438e+33, 1.8047637498986704e+34, 3.6380144497462424e+34, 7.333975524435353e+34, 1.4785804250878585e+35, 2.981126491656587e+35, 6.010980507959926e+35, 1.2121021459952261e+36, 2.444340127741947e+36, 4.9296049269993937e+36, 9.942376547222754e+36, 2.0053744553381284e+37, 4.045083625029609e+37, 8.159919406135492e+37, 1.6461528873854453e+38, 3.321085101637076e+38, 6.7006200263953416e+38, 1.3519939539634139e+39, 2.728091357947893e+39, 5.5051240585864e+39, 1.1109614699194032e+40, 2.2420961052296468e+40, 4.525144513506393e+40, 9.133418396710686e+40, 1.843557124051455e+41, 3.721361623956826e+41, 7.512229880645694e+41, 1.5165519043580923e+42, 3.0617294075783357e+42, 6.181546752794812e+42, 1.248096172683489e+43, 2.5201083036296605e+43, 5.088740985505152e+43, 1.0275931608294923e+44, 2.0751596751323066e+44, 4.190839526567771e+44, 8.4638798160741e+44, 1.709450939955365e+45, 3.452727062165713e+45, 6.974066301525168e+45, 1.4087303684823927e+46, 2.8456889982455687e+46, 5.74863216733554e+46, 1.1613387411842084e+47, 2.346228997711128e+47, 4.7402228628818865e+47, 9.577315473443615e+47, 1.9351083682206815e+48, 3.9100566827030156e+48, 7.900905777665977e+48, 1.5965649304576352e+49, 3.226353662239748e+49, 6.520078944085465e+49, 1.3176772555261199e+50, 2.6630564828620197e+50, 5.382284641509789e+50, 1.0878467712678801e+51, 2.1987882281474012e+51, 4.444403919082487e+51, 8.983755382419596e+51, 1.8160024470174432e+52, 3.6710381372763563e+52, 7.421217531371164e+52, 1.5002895070934251e+53, 3.0331121909506075e+53, 6.132184611136386e+53, 1.2398100833516458e+54, 2.5067334707614314e+54, 5.06843715955704e+54, 1.0248321558906944e+55, 2.0722590962771903e+55, 4.190326505774815e+55, 8.473523511030972e+55, 1.7135329027204832e+56, 3.465237159211913e+56, 7.007860636079471e+56, 1.4172608945570857e+57, 2.8663279778094284e+57, 5.797137101683188e+57, 1.1724997294395394e+58, 2.3715009581484474e+58, 4.7967282593487255e+58, 9.702375342048342e+58, 1.9625560076382378e+59, 3.969876253572219e+59, 8.03050196106735e+59, 1.6244977778883214e+60, 3.2862920128635974e+60, 6.648193900195978e+60, 1.344966904683975e+61, 2.721007954509684e+61, 5.505011347896617e+61, 1.113773091747887e+62, 2.2534359734920392e+62, 4.5593573089830255e+62, 9.225116165081707e+62, 1.866593615211176e+63, 3.776916070893518e+63, 7.64248206767497e+63, 1.5464681132545414e+64, 3.1293696814609483e+64, 6.332599830056146e+64, 1.2814934993435323e+65, 2.5933424816328226e+65, 5.24822399602593e+65, 1.0621204987253186e+66, 2.1495328080156107e+66, 4.350339446082938e+66, 8.804626015099274e+66, 1.7819983846002473e+67, 3.606718487652263e+67, 7.300047033518307e+67, 1.4775679710332067e+68, 2.9907327268356984e+68, 6.053631627377828e+68, 1.2253567780829956e+69, 2.480374369576969e+69, 5.020881286353305e+69, 1.016367203853456e+70, 2.0574497467652588e+70, 4.1650063394823454e+70, 8.431597528150275e+70, 1.7069145259277518e+71, 3.455582942327362e+71, 6.995817088370136e+71, 1.4163255332490593e+72, 2.8674455205398847e+72, 5.805433529437242e+72, 1.1753885846645687e+73, 2.3797730966107015e+73, 4.818333359349445e+73, 9.755853937030675e+73, 1.9753353255494665e+74, 3.99966308209066e+74, 8.098656333354906e+74, 1.639870135531369e+75, 3.320571335648124e+75, 6.72392699029714e+75, 1.361569852189982e+76, 2.757170189636298e+76, 5.5833374823320215e+76, 1.1306567770195789e+77, 2.289677178435471e+77, 4.636862574383825e+77, 9.390325520710031e+77, 1.9017064297701495e+78, 3.8513470707835294e+78, 7.799884062434071e+78, 1.5796828254672773e+79, 3.199321301237321e+79, 6.479656505331111e+79, 1.312357717468767e+80, 2.658021860812974e+80, 5.383576586284977e+80, 1.0904084954540416e+81, 2.2085818389563745e+81, 4.473461073303571e+81, 9.061074079940771e+81, 1.8353610432736368e+82, 3.7176551750643495e+82, 7.530475961234946e+82, 1.5253918874382903e+83, 3.0899117909063255e+83, 6.259164042533174e+83, 1.2679208660885319e+84, 2.5684640273940843e+84, 5.2030776858611855e+84, 1.0540290445933783e+85, 2.135257487633213e+85, 4.325669134029088e+85, 8.763178807694517e+85, 1.775314676283499e+86, 3.5966176477730825e+86, 7.286490779896767e+86, 1.4762086765682586e+87, 2.9907646380222674e+87, 6.059291341731143e+87, 1.2276272261956521e+88, 2.487231637525793e+88, 5.0393087247497286e+88, 1.0210115955273046e+89, 2.068689577352362e+89, 4.191455776247785e+89, 8.492573757113854e+89, 1.7207532995491636e+90, 3.4866046657263454e+90, 7.064665173485147e+90, 1.4314797504392572e+91, 2.9005713436845766e+91, 5.877418043025327e+91, 1.1909520266794745e+92, 2.4132736974584445e+92, 4.890164706148787e+92, 9.909345258401931e+92, 2.0080335748829212e+93, 4.069129272304509e+93, 8.245869982058014e+93, 1.670997992049841e+94, 3.386256056156391e+94, 6.86227400093606e+94, 1.3906590949535356e+95, 2.8182378544319625e+95, 5.711351882080776e+95, 1.157455961832601e+96, 2.3457098474097423e+96, 4.753881328433477e+96, 9.634442417361411e+96, 1.952580791581245e+97, 3.9572691745947314e+97, 8.020220310242971e+97, 1.6254780366194036e+98, 3.2944277647042835e+98, 6.677023804202779e+98, 1.3532869267662758e+99, 2.7428423763299184e+99, 5.559244728905557e+99, 1.126768479686269e+100, 2.2837970963674343e+100, 4.628968765063795e+100, 9.382419949099461e+100, 1.9017321366083915e+101, 3.854674056414026e+101, 7.813215284855993e+101, 1.5837101984984896e+102, 3.2101505895267563e+102, 6.506970623682916e+102, 1.3189733244767042e+103, 2.6736027709289238e+103, 5.419527641738129e+103, 1.0985748441617983e+104, 2.2269040471280938e+104, 4.514160312178946e+104, 9.15073650789396e+104, 1.8549777293242932e+105, 3.760320885542712e+105, 7.62280220335045e+105, 1.545282590242585e+106, 3.132598023097299e+106, 6.350455901221588e+106, 1.287385452208177e+107, 2.6098510866112505e+107, 5.290860094612086e+107, 1.0726060128670571e+108, 2.174490715097846e+108, 4.4083721499261936e+108, 8.937216650165656e+108, 1.8118808996374774e+109, 3.6733331176532597e+109, 7.4472214856084014e+109, 1.509841980821092e+110, 3.0610609397482494e+110, 6.206055990753902e+110, 1.2582374882304202e+111, 2.551013467599088e+111, 5.172089896489394e+111, 1.0486306406703763e+112, 2.126092573991342e+112, 4.310671509102807e+112, 8.739987314577388e+112, 1.7720655126598288e+113, 3.592955401456253e+113, 7.284956193063475e+113, 1.4770837206465996e+114, 2.994927487030203e+114, 6.072542021428352e+114, 1.2312826132303912e+115, 2.49659416093167e+115, 5.062221264384251e+115, 1.02644870582291e+116, 2.081307830407319e+116, 4.2202512636505694e+116, 8.557427091099288e+116, 1.73520583882005e+117, 3.5185333505048843e+117, 7.134691633444749e+117, 1.4467436743491303e+118, 2.9336669741179814e+118, 5.948847718562194e+118, 1.206306583020825e+119, 2.446162678298947e+119, 4.960389178642346e+119, 1.0058863870938324e+120, 2.0397871897771716e+120, 4.1364094849568597e+120, 8.388125372531414e+120, 1.701018392377289e+121, 3.449497235896755e+121, 6.995282776050676e+121, 1.4185917095139198e+122, 2.8768168600706066e+122, 5.8340434005779026e+122, 1.1831225317824583e+123, 2.3993434097818833e+123, 4.8658386240293033e+123, 9.867919145317412e+123, 2.0012255626192e+124, 4.0585328631202745e+124, 8.230849213149619e+124, 1.6692553060937426e+125, 3.385348740954753e+125, 6.865727770687342e+125, 1.392426402164694e+126, 2.82397216775592e+126, 5.727314811907237e+126, 1.1615667394832662e+127, 2.355807160027915e+127, 4.777907664079972e+127, 9.690321845983673e+127, 1.9653552950659434e+128, 3.98608316799225e+128, 8.084516249693408e+128, 1.639698915003569e+129, 3.325650127484773e+129, 6.745146276783582e+129, 1.3680707017408232e+130, 2.774776811780166e+130, 5.627945774136491e+130, 1.1414951610343844e+131, 2.3152642041529046e+131, 4.696013547558402e+131, 9.524899802883576e+131, 1.931940606551244e+132, 3.918586119030548e+132, 7.948172429217074e+132, 1.612157299446303e+133, 3.2700153164423365e+133, 6.632761613273733e+133, 1.3453683586523665e+134, 2.7289164484970416e+134, 5.535303875308045e+134, 1.1227805619028329e+135, 2.277458554265904e+135, 4.619641231696714e+135, 9.370616737319996e+135, 1.900772990762938e+136, 3.855622178374567e+136, 7.820973576920341e+136, 1.5864605948393755e+137, 3.218102499631025e+137, 6.5278859657762155e+137, 1.3241809623699324e+138, 2.6861125452869324e+138, 5.448828594261936e+138, 1.1053101400542031e+139, 2.2421631973385313e+139, 4.548333845567683e+139, 9.226553163315823e+139, 1.8716673907062561e+140, 3.7968188902884236e+140, 7.702170053145259e+140, 1.5624579185936942e+141, 3.1696079843534014e+141, 6.429908057120799e+141, 1.3043854716897494e+142, 2.646117433238248e+142, 5.368021389965708e+142, 1.0889835405441835e+143, 2.209176117702768e+143, 4.481684721444732e+143, 9.091890422513751e+143, 1.8444590000119024e+144, 3.741844472218129e+144, 7.591093911931671e+144, 1.5400147970269556e+145, 3.12426103746997e+145, 6.338282815577286e+145, 1.2858721443321753e+146, 2.6087101581110046e+146, 5.2924373866902265e+146, 1.0737111891479935e+147, 2.1783169573873234e+147, 4.419330701400454e+147, 8.965897268777576e+147, 1.819000574047197e+148, 3.6904024252113034e+148, 7.487148097897104e+148, 1.5190109998740653e+149, 3.081819544541901e+149, 6.252522673094769e+149, 1.2685427925219514e+150, 2.5736929832423117e+150, 5.2216783630808174e+150, 1.0594128867787386e+151, 2.1494241980669687e+151, 4.3609464872432735e+151, 8.847918539756792e+151, 1.7951601584896268e+152, 3.642226979436122e+152, 7.389797313703616e+152, 1.4993387090047913e+153, 3.042066337591999e+153, 6.172190201223681e+153, 1.252309306201903e+154, 2.5408884279349296e+154, 5.1553868126507404e+154, 1.0460166182891771e+155, 2.1223527719918774e+155, 4.306239848860752e+155, 8.73736554622008e+155, 1.7728191616582374e+156, 3.597079227638147e+156, 7.298560264297455e+156, 1.4809009626839945e+157, 3.004806074340234e+157, 6.096891850805657e+157, 1.237092397172255e+158, 2.5101367480495735e+158, 5.093240889421062e+158, 1.0334575384559958e+159, 2.0969720275966697e+159, 4.25494754258232e+159, 8.63370788278123e+159, 1.751870711401235e+160, 3.554743828288192e+160, 7.213003041717217e+160, 1.463610328188579e+161, 2.9698625746586175e+161, 6.026272607134621e+161, 1.2228205265350601e+162, 2.481293783644282e+162, 5.034950088546655e+162, 1.0216771051432951e+163, 2.0731639898448703e+163, 4.206831819775895e+163, 8.53646642066121e+163, 1.7322182487128824e+164, 3.5150261828413054e+164, 7.132733459464077e+164, 1.4473877646121771e+165, 2.937076537957334e+165, 5.960011408120145e+165, 1.2094289849724155e+166, 2.4542291127531145e+166, 4.980251540187014e+166, 1.0106223353130887e+167, 2.0508218666664828e+167, 4.161677428448807e+167, 8.445207288124061e+167, 1.7137743192218637e+168, 3.477750009431043e+168, 7.057396181142597e+168, 1.4321616448072836e+169, 2.9063035794265697e+169, 5.8978172013385074e+169, 1.1968591010401397e+170, 2.4288244616842096e+170, 4.928906817402175e+170, 1.000245164040183e+171, 2.0298487618124114e+171, 4.1192890285076955e+171, 8.35953667989896e+171, 1.6964595308188334e+172, 3.4427552495288224e+172, 6.98666851643045e+172, 1.417866911077936e+173, 2.877412534352207e+173, 5.839425538398182e+173, 1.1850575571622351e+174, 2.4049723311967065e+174, 4.880699176777669e+174, 9.905018902704419e+174, 2.0101565615927036e+175, 4.0794889555941506e+175, 8.279096365400277e+175, 1.680201651373535e+176, 3.409896255455025e+176, 6.920256780113519e+176, 1.4044443437594291e+177, 2.8502839887661373e+177, 5.784595623102589e+177, 1.173975796612011e+178, 2.3825748051138857e+178, 4.835431164858603e+178, 9.81352695929162e+178, 1.991664968700119e+179, 4.0421152798654525e+179, 8.203559788396795e+179, 1.6649348250597785e+180, 3.379040215746536e+180, 6.857893128124128e+180, 1.3918399254623829e+181, 2.8248090019528322e+181, 5.733107744396688e+181, 1.163569507667457e+182, 2.3615425137227191e+182, 4.792922535037907e+182, 9.727612273004065e+182, 1.9743006609356764e+183, 4.007020115310249e+183, 8.132628669234219e+183, 1.6505988894882084e+184, 3.35006578274332e+184, 6.799332799244657e+184, 1.3800042866950752e+185, 2.800887992211082e+185, 5.684761036831596e+185, 1.1537981734723412e+186, 2.3417937289952866e+186, 4.753008428922934e+186, 9.64694229468579e+186, 1.9579965563976254e+187, 3.974068142675625e+187, 8.066030035652855e+187, 1.637138778838649e+188, 3.32286187273691e+188, 6.744351703065022e+188, 1.3688922209664847e+189, 2.778429762041265e+189, 5.639371520810922e+189, 1.144624678043853e+190, 2.3232535724846518e+190, 4.7155377838164806e+190, 9.571212261389738e+190, 1.9426911697420372e+191, 3.9431353151674314e+191, 8.003513620439624e+191, 1.6245040006159834e+192, 3.297326613886708e+192, 6.692744304531958e+192, 1.3584622594198477e+193, 2.7573506428196235e+193, 5.596770382682062e+193, 1.1360149604227207e+194, 2.3058533198576583e+194, 4.6803719341854697e+194, 9.500142383983838e+194, 1.9283280466128596e+195, 3.9141077210779706e+195, 7.944849574105707e+195, 1.6126481756494858e+196, 3.2733664211040518e+196, 6.644321763395671e+196, 1.3486762966409879e+197, 2.7375737422192826e+197, 5.556802461110885e+197, 1.1279377102408073e+198, 2.2895297885870745e+198, 4.6473833800969483e+198, 9.433475370019696e+198, 1.9148552653902338e+199, 3.886880581582645e+199, 7.88982644898895e+199, 1.6015286325951564e+200, 3.250895180379531e+200, 6.598910293438266e+200, 1.339499260602065e+201, 2.7190282802607844e+201, 5.519324911447796e+201, 1.1203640990338714e+202, 2.274224797428528e+202, 4.616454699826839e+202, 9.370974236144553e+202, 1.902224997090563e+203, 3.861357365333356e+203, 7.838249417931971e+203, 1.5911060495527353e+204, 3.229833527745857e+204, 6.556349711778912e+204, 1.3308988207843698e+205, 2.7016490020527294e+205, 5.484206024134842e+205, 1.1132675424968076e+206, 2.2598846880558063e+206, 4.587477587327319e+206, 9.31242037133511e+206, 1.8903931156537138e+207, 3.83744900427054e+207, 7.789938696309766e+207, 1.581344136534778e+208, 3.210108210309193e+208, 6.516492153061154e+208, 1.3228451294269206e+209, 2.6853756570827622e+209, 5.4513241768271145e+209, 1.1066234896042331e+210, 2.2464599006717418e+210, 4.5603519981465114e+210, 9.257611818039625e+210, 1.8793188520127433e+211, 3.815073197412932e+211, 7.744728140829331e+211, 1.5722093534560421e+212, 3.1916515186580375e+212, 6.479200927064289e+212, 1.3153105915959495e+213, 2.6701525364277955e+213, 5.420566902901229e+213, 1.100409235119978e+214, 2.2339045966233725e+214, 4.534985389806099e+214, 9.206361743150243e+214, 1.8689644863161863e+215, 3.794153791320704e+215, 7.702464002428233e+215, 1.5636706590943197e+216, 3.1744007815167945e+216, 6.444349501425872e+216, 1.3082696604004888e+217, 2.655928060503729e+217, 5.391830061548177e+217, 1.0946037525253415e+218, 2.2221763220572913e+218, 4.5112920446771586e+218, 9.15849707480386e+218, 1.8592950734820973e+219, 3.774620227562919e+219, 7.663003813862865e+219, 1.5556992871254477e+220, 3.1582979148283143e+220, 6.411820593775825e+220, 1.3016986542028714e+221, 2.6426544110341223e+221, 5.36501709676147e+221, 1.0891875448177547e+222, 2.2112357075046137e+222, 4.489192465086447e+222, 9.113857284401041e+222, 1.8502781979494265e+223, 3.7564070488840215e+223, 7.626215395316995e+223, 1.5482685458885524e+224, 3.1432890185475155e+224, 6.3815053598005686e+224, 1.2955755931182019e+225, 2.6302872017999154e+225, 5.340038374305296e+225, 1.0841425109910652e+226, 2.2010461989957085e+226, 4.468612831826772e+226, 9.072293296117583e+226, 1.8418837540654727e+227, 3.7394534569253266e+227, 7.591975963679796e+227, 1.5413536389994614e+228, 3.129324015357653e+228, 6.353302665622025e+228, 1.2898800524683393e+229, 2.6187851834919505e+229, 5.31681058726452e+229, 1.0794518263062574e+230, 2.1915738169131675e+230, 4.449484518448312e+230, 9.033666508613736e+230, 1.8340837490402554e+231, 3.723702915333165e+231, 7.560171333115111e+231, 1.534931504322577e+232, 3.116356326319184e+232, 6.327118434446827e+232, 1.284593031177548e+233, 2.608109978611184e+233, 5.295256222033747e+233, 1.0750998347223299e+234, 2.1827869392997177e+234, 4.43174365475206e+234, 8.997847915702226e+234, 1.826852125805558e+235, 3.709102792909217e+235, 7.530695196173876e+235, 1.5289806691500785e+236, 3.1043425791130435e+236, 6.302865058806164e+236, 1.2796968333601689e+237, 2.598225842911091e+237, 5.275303077711991e+237, 1.0710719520678968e+238, 2.174656106781668e+238, 4.415330733760154e+238, 8.964717314494137e+238, 1.8201646034772925e+239, 3.695604042172022e+239, 7.503448476166282e+239, 1.523481119714324e+240, 3.0932423451314004e+240, 6.280460870820639e+240, 1.275174961584766e+241, 2.5890994503372536e+241, 5.256883832761375e+241, 1.067354578726742e+242, 2.1671538466300456e+242, 4.400190257199897e+242, 8.93416259105369e+242, 1.8139985334092083e+243, 3.683160909302832e+243, 7.478338742672406e+243, 1.5184141834075003e+244, 3.0830179021362345e+244, 6.25982966392431e+244, 1.2710120204951968e+245, 2.5806996988023787e+245, 5.23993565361393e+245, 1.0639350207622613e+246, 2.1602545138074015e+246, 4.386270415176693e+246, 8.906079074834212e+246, 1.8083327690954552e+247, 3.671730671953432e+247, 7.45527968313587e+247, 1.5137624222904585e+248, 3.0736340196357423e+248, 6.24090026031886e+248, 1.2671936296332076e+249, 2.572997534488551e+249, 5.2243998405542065e+249, 1.0608014185459018e+250, 2.1539341471211047e+250, 4.373522796241198e+250, 8.880368954323311e+250, 1.8031475483886013e+251, 3.661273401847834e+251, 7.434190624373828e+251, 1.5095095366450874e+252, 3.065057764486336e+252, 6.2236061191287476e+252, 1.263706344455462e+253, 2.5659657926421336e+253, 5.210221506808361e+253, 1.0579426820713891e+254, 2.1481703388298803e+254, 4.3619021245543265e+254, 8.856940747214561e+254, 1.7984243866967735e+255, 3.651751749491091e+255, 7.414996098572043e+255, 1.5056402774876987e+256, 3.057258324527034e+256, 6.207884980866856e+256, 1.2605375846623622e+257, 2.559579053086742e+257, 5.19734928727102e+257, 1.0553484322339313e+258, 2.142942116265988e+258, 4.351366021232182e+258, 8.835708819273732e+258, 1.7941459799872163e+259, 3.6431307486126505e+259, 7.397625449040507e+259, 1.5021403670839554e+260, 3.050206848328693e+260, 6.193678544355244e+260, 1.257675569058372e+261, 2.5538135088949768e+261, 5.1857350737181676e+261, 1.0530089474438373e+262, 2.138229834196626e+262, 4.341874787321307e+262, 8.816592946771975e+262, 1.790296116557927e+263, 3.6353776382787607e+263, 7.382012471529314e+263, 1.498996426626574e+264, 3.043876299371115e+264, 6.1809321726835325e+264, 1.2551092562643522e+265, 2.5486468468383522e+265, 5.17533377374533e+265, 1.0509151150193746e+266, 2.134015076807975e+266, 4.333391206157825e+266, 8.799517917933526e+266, 1.7868595966728696e+267, 3.628461700831862e+267, 7.368095087428918e+267, 1.4961959103363949e+268, 3.0382413231486216e+268, 6.1695946252274116e+268, 1.2528282906751214e+269, 2.5440581384046926e+269, 5.166103090996034e+269, 1.0490583868648674e+270, 2.1302805683263127e+270, 4.325880363114606e+270, 8.784413169430844e+270, 1.783822159251522e+271, 3.622354114043409e+271, 7.35581504560866e+271, 1.4937270453278282e+272, 3.033278125897288e+272, 6.159617813059657e+272, 1.2508229531305438e+273, 2.5400277403132476e+273, 5.158003324507843e+273, 1.0474307390034485e+274, 2.1270100913983045e+274, 4.319309480983371e+274, 8.771212454365932e+274, 1.7811704149033468e+275, 3.617027816052337e+275, 7.345117649992365e+275, 1.4915787766642542e+276, 3.0289643637691263e+276, 6.150956575414476e+276, 1.249084115829456e+277, 2.536537203570355e+277, 5.150997185282151e+277, 1.0460246345768544e+278, 2.124188412458704e+278, 4.3136477694392714e+278, 8.759853538614073e+278, 1.7788917846783576e+279, 3.6124573818126916e+279, 7.335951510342405e+279, 1.4897407170852313e+280, 3.025279041422512e+280, 6.143568475130977e+280, 1.247603201064069e+281, 2.5335691902314887e+281, 5.1450496283668584e+281, 1.0448329899721037e+282, 2.121801213400894e+282, 4.308866287193079e+282, 8.750277922756385e+282, 1.7769744439701497e+283, 3.6086189099271507e+283, 7.328268313963066e+283, 1.4882031009506883e+284, 3.022202419113144e+284, 6.137413611209063e+284, 1.2463721434069037e+285, 2.531107397113335e+285, 5.140127698950014e+285, 1.0438491437727647e+286, 2.119835028933394e+286, 4.3049378156162456e+286, 8.742430587108567e+286, 1.775407271075102e+287, 3.605489918867857e+287, 7.322022616313357e+287, 1.486956741997388e+288, 3.0197159274616043e+288, 6.132454446852635e+288, 1.2453833550153735e+289, 2.529136485791815e+289, 5.136200391127643e+289, 1.043066828261568e+290, 2.1182771890855067e+290, 4.3018367427313045e+290, 8.736259757650023e+290, 1.7741797999659177e+291, 3.603049251680806e+291, 7.31717164873803e+291, 1.4859929945424901e+292, 3.0178020891716224e+292, 6.128655651515049e+292, 1.2446296937599752e+293, 2.5276420182940878e+293, 5.133238518133606e+293, 1.042480143236834e+294, 2.117115766370678e+294, 4.2995389565953115e+294, 8.731716690895745e+294, 1.7732821768783275e+295, 3.601276988388548e+295, 7.313675141696029e+295, 1.4853037178124472e+296, 3.0164444470515275e+296, 6.125983955643199e+296, 1.2441044339134643e+297, 2.5266103979460203e+297, 5.131214592979163e+297, 1.0420835319243277e+298, 2.116339527176246e+298, 4.298021747207806e+298, 8.728755475927608e+298, 1.7727051203629143e+299, 3.600154365367926e+299, 7.311495162058127e+299, 1.4848812431097936e+300, 3.0156274977481396e+300, 6.124408016954128e+300, 1.2438012391624045e+301, 2.5260288149083615e+301, 5.130102718530395e+301, 1.0418717587929655e+302, 2.115937886993775e+302, 4.297263716149366e+302, 8.727332852040496e+302, 1.7724398844799722e+303, 3.599663701068505e+303, 7.310595963196275e+303, 1.4847183435546851e+304, 3.0153366306819095e+304, 6.1238982971814895e+304, 1.243714137730863e+305, 2.525885195968491e+305]} \ No newline at end of file diff --git a/lib/node_modules/@stdlib/math/base/special/expm1rel/test/fixtures/python/runner.py b/lib/node_modules/@stdlib/math/base/special/expm1rel/test/fixtures/python/runner.py new file mode 100644 index 000000000000..b3c354c91d9e --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expm1rel/test/fixtures/python/runner.py @@ -0,0 +1,86 @@ +#!/usr/bin/env python +# +# @license Apache-2.0 +# +# Copyright (c) 2018 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 exprel + +# Get the file path: +FILE = os.path.realpath(__file__) + +# Extract the directory in which this file resides: +DIR = os.path.dirname(FILE) + + +def gen(x, name): + """Generate fixture data and write to file. + + # Arguments + + * `x`: domain + * `name::str`: output filename + + # Examples + + ``` python + python> x = linspace(-1000, 1000, 2001) + python> gen(x, './data.json') + ``` + """ + y = exprel(x) + data = { + "x": x.tolist(), + "expected": y.tolist() + } + + # 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") as outfile: + json.dump(data, outfile) + + +def main(): + """Generate fixture data.""" + # Medium negative values: + x = np.linspace(-709.78, -1.0, 1000) + gen(x, "medium_negative.json") + + # Medium positive values: + x = np.linspace(1.0, 709.78, 1000) + gen(x, "medium_positive.json") + + # Small negative values: + x = np.linspace(-1.0, -2.0**-54, 1000) + gen(x, "small_negative.json") + + # Small positive values: + x = np.linspace(2.0**-54, 1.0, 1000) + gen(x, "small_positive.json") + + # Tiny values: + x = np.linspace(-2.0**-54, 2.0**-54, 1000) + gen(x, "tiny.json") + + +if __name__ == "__main__": + main() diff --git a/lib/node_modules/@stdlib/math/base/special/expm1rel/test/fixtures/python/small_negative.json b/lib/node_modules/@stdlib/math/base/special/expm1rel/test/fixtures/python/small_negative.json new file mode 100644 index 000000000000..0d09a7c46b12 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expm1rel/test/fixtures/python/small_negative.json @@ -0,0 +1 @@ +{"x": [-1.0, -0.998998998998999, -0.997997997997998, -0.996996996996997, -0.995995995995996, -0.994994994994995, -0.993993993993994, -0.992992992992993, -0.991991991991992, -0.990990990990991, -0.98998998998999, -0.988988988988989, -0.987987987987988, -0.986986986986987, -0.985985985985986, -0.984984984984985, -0.983983983983984, -0.982982982982983, -0.9819819819819819, -0.980980980980981, -0.97997997997998, -0.978978978978979, -0.977977977977978, -0.9769769769769769, -0.975975975975976, -0.974974974974975, -0.973973973973974, -0.972972972972973, -0.9719719719719719, -0.970970970970971, -0.96996996996997, -0.968968968968969, -0.967967967967968, -0.9669669669669669, -0.965965965965966, -0.964964964964965, -0.963963963963964, -0.962962962962963, -0.9619619619619619, -0.960960960960961, -0.95995995995996, -0.958958958958959, -0.957957957957958, -0.9569569569569569, -0.955955955955956, -0.954954954954955, -0.953953953953954, -0.9529529529529529, -0.9519519519519519, -0.950950950950951, -0.94994994994995, -0.948948948948949, -0.9479479479479479, -0.9469469469469469, -0.9459459459459459, -0.944944944944945, -0.943943943943944, -0.9429429429429429, -0.9419419419419419, -0.9409409409409409, -0.93993993993994, -0.938938938938939, -0.9379379379379379, -0.9369369369369369, -0.9359359359359359, -0.934934934934935, -0.933933933933934, -0.9329329329329329, -0.9319319319319319, -0.9309309309309309, -0.92992992992993, -0.928928928928929, -0.9279279279279279, -0.9269269269269269, -0.9259259259259259, -0.924924924924925, -0.9239239239239239, -0.9229229229229229, -0.9219219219219219, -0.9209209209209209, -0.91991991991992, -0.9189189189189189, -0.9179179179179179, -0.9169169169169169, -0.9159159159159159, -0.914914914914915, -0.9139139139139139, -0.9129129129129129, -0.9119119119119119, -0.9109109109109109, -0.9099099099099099, -0.9089089089089089, -0.9079079079079079, -0.9069069069069069, -0.9059059059059059, -0.9049049049049049, -0.9039039039039038, -0.9029029029029029, -0.9019019019019019, -0.9009009009009009, -0.8998998998998999, -0.8988988988988988, -0.8978978978978979, -0.8968968968968969, -0.8958958958958959, -0.8948948948948949, -0.8938938938938938, -0.8928928928928929, -0.8918918918918919, -0.8908908908908909, -0.8898898898898899, -0.8888888888888888, -0.8878878878878879, -0.8868868868868869, -0.8858858858858859, -0.8848848848848849, -0.8838838838838838, -0.8828828828828829, -0.8818818818818819, -0.8808808808808809, -0.8798798798798799, -0.8788788788788788, -0.8778778778778779, -0.8768768768768769, -0.8758758758758759, -0.8748748748748749, -0.8738738738738738, -0.8728728728728729, -0.8718718718718719, -0.8708708708708709, -0.8698698698698699, -0.8688688688688688, -0.8678678678678678, -0.8668668668668669, -0.8658658658658659, -0.8648648648648649, -0.8638638638638638, -0.8628628628628628, -0.8618618618618619, -0.8608608608608609, -0.8598598598598599, -0.8588588588588588, -0.8578578578578578, -0.8568568568568569, -0.8558558558558559, -0.8548548548548549, -0.8538538538538538, -0.8528528528528528, -0.8518518518518519, -0.8508508508508509, -0.8498498498498499, -0.8488488488488488, -0.8478478478478478, -0.8468468468468469, -0.8458458458458459, -0.8448448448448449, -0.8438438438438438, -0.8428428428428428, -0.8418418418418419, -0.8408408408408409, -0.8398398398398399, -0.8388388388388388, -0.8378378378378378, -0.8368368368368369, -0.8358358358358359, -0.8348348348348349, -0.8338338338338338, -0.8328328328328328, -0.8318318318318318, -0.8308308308308309, -0.8298298298298299, -0.8288288288288288, -0.8278278278278278, -0.8268268268268268, -0.8258258258258259, -0.8248248248248249, -0.8238238238238238, -0.8228228228228228, -0.8218218218218218, -0.8208208208208209, -0.8198198198198199, -0.8188188188188188, -0.8178178178178178, -0.8168168168168168, -0.8158158158158157, -0.8148148148148149, -0.8138138138138138, -0.8128128128128128, -0.8118118118118118, -0.8108108108108107, -0.8098098098098099, -0.8088088088088088, -0.8078078078078078, -0.8068068068068068, -0.8058058058058057, -0.8048048048048049, -0.8038038038038038, -0.8028028028028028, -0.8018018018018018, -0.8008008008008007, -0.7997997997997999, -0.7987987987987988, -0.7977977977977978, -0.7967967967967968, -0.7957957957957957, -0.7947947947947948, -0.7937937937937938, -0.7927927927927928, -0.7917917917917918, -0.7907907907907907, -0.7897897897897898, -0.7887887887887888, -0.7877877877877878, -0.7867867867867868, -0.7857857857857857, -0.7847847847847848, -0.7837837837837838, -0.7827827827827828, -0.7817817817817818, -0.7807807807807807, -0.7797797797797797, -0.7787787787787788, -0.7777777777777778, -0.7767767767767768, -0.7757757757757757, -0.7747747747747747, -0.7737737737737738, -0.7727727727727728, -0.7717717717717718, -0.7707707707707707, -0.7697697697697697, -0.7687687687687688, -0.7677677677677678, -0.7667667667667668, -0.7657657657657657, -0.7647647647647647, -0.7637637637637638, -0.7627627627627628, -0.7617617617617618, -0.7607607607607607, -0.7597597597597597, -0.7587587587587588, -0.7577577577577578, -0.7567567567567568, -0.7557557557557557, -0.7547547547547547, -0.7537537537537538, -0.7527527527527528, -0.7517517517517518, -0.7507507507507507, -0.7497497497497497, -0.7487487487487487, -0.7477477477477478, -0.7467467467467468, -0.7457457457457457, -0.7447447447447447, -0.7437437437437437, -0.7427427427427428, -0.7417417417417418, -0.7407407407407407, -0.7397397397397397, -0.7387387387387387, -0.7377377377377378, -0.7367367367367368, -0.7357357357357357, -0.7347347347347347, -0.7337337337337337, -0.7327327327327328, -0.7317317317317318, -0.7307307307307307, -0.7297297297297297, -0.7287287287287287, -0.7277277277277278, -0.7267267267267268, -0.7257257257257257, -0.7247247247247247, -0.7237237237237237, -0.7227227227227226, -0.7217217217217218, -0.7207207207207207, -0.7197197197197197, -0.7187187187187187, -0.7177177177177176, -0.7167167167167168, -0.7157157157157157, -0.7147147147147147, -0.7137137137137137, -0.7127127127127126, -0.7117117117117118, -0.7107107107107107, -0.7097097097097097, -0.7087087087087087, -0.7077077077077076, -0.7067067067067068, -0.7057057057057057, -0.7047047047047047, -0.7037037037037037, -0.7027027027027026, -0.7017017017017018, -0.7007007007007007, -0.6996996996996997, -0.6986986986986987, -0.6976976976976976, -0.6966966966966968, -0.6956956956956957, -0.6946946946946947, -0.6936936936936937, -0.6926926926926926, -0.6916916916916918, -0.6906906906906907, -0.6896896896896897, -0.6886886886886887, -0.6876876876876876, -0.6866866866866868, -0.6856856856856857, -0.6846846846846847, -0.6836836836836837, -0.6826826826826826, -0.6816816816816818, -0.6806806806806807, -0.6796796796796797, -0.6786786786786787, -0.6776776776776776, -0.6766766766766767, -0.6756756756756757, -0.6746746746746747, -0.6736736736736737, -0.6726726726726726, -0.6716716716716717, -0.6706706706706707, -0.6696696696696697, -0.6686686686686687, -0.6676676676676676, -0.6666666666666667, -0.6656656656656657, -0.6646646646646647, -0.6636636636636637, -0.6626626626626626, -0.6616616616616617, -0.6606606606606606, -0.6596596596596597, -0.6586586586586587, -0.6576576576576576, -0.6566566566566567, -0.6556556556556556, -0.6546546546546547, -0.6536536536536537, -0.6526526526526526, -0.6516516516516517, -0.6506506506506506, -0.6496496496496497, -0.6486486486486487, -0.6476476476476476, -0.6466466466466467, -0.6456456456456456, -0.6446446446446447, -0.6436436436436437, -0.6426426426426426, -0.6416416416416417, -0.6406406406406406, -0.6396396396396397, -0.6386386386386387, -0.6376376376376376, -0.6366366366366367, -0.6356356356356356, -0.6346346346346347, -0.6336336336336337, -0.6326326326326326, -0.6316316316316316, -0.6306306306306306, -0.6296296296296297, -0.6286286286286287, -0.6276276276276276, -0.6266266266266266, -0.6256256256256256, -0.6246246246246246, -0.6236236236236237, -0.6226226226226226, -0.6216216216216216, -0.6206206206206206, -0.6196196196196196, -0.6186186186186187, -0.6176176176176176, -0.6166166166166166, -0.6156156156156156, -0.6146146146146146, -0.6136136136136137, -0.6126126126126126, -0.6116116116116116, -0.6106106106106106, -0.6096096096096096, -0.6086086086086087, -0.6076076076076076, -0.6066066066066066, -0.6056056056056056, -0.6046046046046046, -0.6036036036036037, -0.6026026026026026, -0.6016016016016016, -0.6006006006006006, -0.5995995995995996, -0.5985985985985987, -0.5975975975975976, -0.5965965965965966, -0.5955955955955956, -0.5945945945945945, -0.5935935935935936, -0.5925925925925926, -0.5915915915915916, -0.5905905905905906, -0.5895895895895895, -0.5885885885885886, -0.5875875875875876, -0.5865865865865866, -0.5855855855855856, -0.5845845845845845, -0.5835835835835836, -0.5825825825825826, -0.5815815815815816, -0.5805805805805806, -0.5795795795795795, -0.5785785785785786, -0.5775775775775776, -0.5765765765765766, -0.5755755755755756, -0.5745745745745745, -0.5735735735735736, -0.5725725725725725, -0.5715715715715716, -0.5705705705705706, -0.5695695695695695, -0.5685685685685686, -0.5675675675675675, -0.5665665665665666, -0.5655655655655656, -0.5645645645645645, -0.5635635635635636, -0.5625625625625625, -0.5615615615615616, -0.5605605605605606, -0.5595595595595595, -0.5585585585585586, -0.5575575575575575, -0.5565565565565566, -0.5555555555555556, -0.5545545545545545, -0.5535535535535536, -0.5525525525525525, -0.5515515515515516, -0.5505505505505506, -0.5495495495495495, -0.5485485485485486, -0.5475475475475475, -0.5465465465465466, -0.5455455455455456, -0.5445445445445445, -0.5435435435435436, -0.5425425425425425, -0.5415415415415415, -0.5405405405405406, -0.5395395395395395, -0.5385385385385386, -0.5375375375375375, -0.5365365365365365, -0.5355355355355356, -0.5345345345345345, -0.5335335335335336, -0.5325325325325325, -0.5315315315315315, -0.5305305305305306, -0.5295295295295295, -0.5285285285285286, -0.5275275275275275, -0.5265265265265265, -0.5255255255255256, -0.5245245245245245, -0.5235235235235236, -0.5225225225225225, -0.5215215215215215, -0.5205205205205206, -0.5195195195195195, -0.5185185185185186, -0.5175175175175175, -0.5165165165165165, -0.5155155155155156, -0.5145145145145145, -0.5135135135135136, -0.5125125125125125, -0.5115115115115115, -0.5105105105105106, -0.5095095095095095, -0.5085085085085086, -0.5075075075075075, -0.5065065065065065, -0.5055055055055055, -0.5045045045045045, -0.5035035035035035, -0.5025025025025025, -0.5015015015015015, -0.5005005005005005, -0.49949949949949946, -0.4984984984984985, -0.4974974974974975, -0.4964964964964965, -0.49549549549549554, -0.49449449449449445, -0.4934934934934935, -0.4924924924924925, -0.4914914914914915, -0.49049049049049054, -0.48948948948948945, -0.48848848848848847, -0.4874874874874875, -0.4864864864864865, -0.48548548548548554, -0.48448448448448445, -0.48348348348348347, -0.4824824824824825, -0.4814814814814815, -0.48048048048048053, -0.47947947947947944, -0.47847847847847846, -0.4774774774774775, -0.4764764764764765, -0.47547547547547553, -0.47447447447447444, -0.47347347347347346, -0.4724724724724725, -0.4714714714714715, -0.4704704704704705, -0.46946946946946944, -0.46846846846846846, -0.4674674674674675, -0.4664664664664665, -0.4654654654654655, -0.46446446446446443, -0.46346346346346345, -0.4624624624624625, -0.4614614614614615, -0.4604604604604605, -0.45945945945945943, -0.45845845845845845, -0.4574574574574575, -0.4564564564564565, -0.4554554554554555, -0.4544544544544544, -0.45345345345345345, -0.45245245245245247, -0.4514514514514515, -0.4504504504504504, -0.4494494494494494, -0.44844844844844844, -0.44744744744744747, -0.4464464464464465, -0.4454454454454454, -0.4444444444444444, -0.44344344344344344, -0.44244244244244246, -0.4414414414414415, -0.4404404404404404, -0.4394394394394394, -0.43843843843843844, -0.43743743743743746, -0.4364364364364365, -0.4354354354354354, -0.4344344344344344, -0.43343343343343343, -0.43243243243243246, -0.4314314314314315, -0.4304304304304304, -0.4294294294294294, -0.42842842842842843, -0.42742742742742745, -0.4264264264264265, -0.4254254254254254, -0.4244244244244244, -0.42342342342342343, -0.42242242242242245, -0.42142142142142147, -0.4204204204204204, -0.4194194194194194, -0.4184184184184184, -0.41741741741741745, -0.41641641641641647, -0.4154154154154154, -0.4144144144144144, -0.4134134134134134, -0.41241241241241244, -0.41141141141141147, -0.4104104104104104, -0.4094094094094094, -0.4084084084084084, -0.40740740740740744, -0.40640640640640646, -0.4054054054054054, -0.4044044044044044, -0.4034034034034034, -0.40240240240240244, -0.40140140140140146, -0.40040040040040037, -0.3993993993993994, -0.3983983983983984, -0.39739739739739743, -0.39639639639639646, -0.39539539539539537, -0.3943943943943944, -0.3933933933933934, -0.39239239239239243, -0.39139139139139134, -0.39039039039039036, -0.3893893893893894, -0.3883883883883884, -0.3873873873873874, -0.38638638638638634, -0.38538538538538536, -0.3843843843843844, -0.3833833833833834, -0.3823823823823824, -0.38138138138138133, -0.38038038038038036, -0.3793793793793794, -0.3783783783783784, -0.3773773773773774, -0.37637637637637633, -0.37537537537537535, -0.3743743743743744, -0.3733733733733734, -0.3723723723723724, -0.37137137137137133, -0.37037037037037035, -0.36936936936936937, -0.3683683683683684, -0.3673673673673674, -0.3663663663663663, -0.36536536536536535, -0.36436436436436437, -0.3633633633633634, -0.3623623623623624, -0.3613613613613613, -0.36036036036036034, -0.35935935935935936, -0.3583583583583584, -0.3573573573573574, -0.3563563563563563, -0.35535535535535534, -0.35435435435435436, -0.3533533533533534, -0.3523523523523524, -0.3513513513513513, -0.35035035035035034, -0.34934934934934936, -0.3483483483483484, -0.3473473473473474, -0.3463463463463463, -0.34534534534534533, -0.34434434434434436, -0.3433433433433434, -0.3423423423423424, -0.3413413413413413, -0.34034034034034033, -0.33933933933933935, -0.3383383383383384, -0.3373373373373374, -0.3363363363363363, -0.3353353353353353, -0.33433433433433435, -0.33333333333333337, -0.3323323323323324, -0.3313313313313313, -0.3303303303303303, -0.32932932932932935, -0.32832832832832837, -0.3273273273273274, -0.3263263263263263, -0.3253253253253253, -0.32432432432432434, -0.32332332332332336, -0.3223223223223223, -0.3213213213213213, -0.3203203203203203, -0.31931931931931934, -0.31831831831831836, -0.31731731731731727, -0.3163163163163163, -0.3153153153153153, -0.31431431431431434, -0.31331331331331336, -0.31231231231231227, -0.3113113113113113, -0.3103103103103103, -0.30930930930930933, -0.30830830830830835, -0.30730730730730726, -0.3063063063063063, -0.3053053053053053, -0.30430430430430433, -0.30330330330330335, -0.30230230230230226, -0.3013013013013013, -0.3003003003003003, -0.2992992992992993, -0.29829829829829835, -0.29729729729729726, -0.2962962962962963, -0.2952952952952953, -0.2942942942942943, -0.29329329329329334, -0.29229229229229226, -0.2912912912912913, -0.2902902902902903, -0.2892892892892893, -0.28828828828828834, -0.28728728728728725, -0.2862862862862863, -0.2852852852852853, -0.2842842842842843, -0.28328328328328334, -0.28228228228228225, -0.28128128128128127, -0.2802802802802803, -0.2792792792792793, -0.27827827827827833, -0.27727727727727725, -0.27627627627627627, -0.2752752752752753, -0.2742742742742743, -0.27327327327327333, -0.27227227227227224, -0.27127127127127126, -0.2702702702702703, -0.2692692692692693, -0.26826826826826833, -0.26726726726726724, -0.26626626626626626, -0.2652652652652653, -0.2642642642642643, -0.2632632632632632, -0.26226226226226224, -0.26126126126126126, -0.2602602602602603, -0.2592592592592593, -0.2582582582582582, -0.25725725725725723, -0.25625625625625625, -0.2552552552552553, -0.2542542542542543, -0.2532532532532532, -0.25225225225225223, -0.25125125125125125, -0.2502502502502503, -0.2492492492492493, -0.2482482482482482, -0.24724724724724723, -0.24624624624624625, -0.24524524524524527, -0.2442442442442443, -0.2432432432432432, -0.24224224224224222, -0.24124124124124124, -0.24024024024024027, -0.2392392392392393, -0.2382382382382382, -0.23723723723723722, -0.23623623623623624, -0.23523523523523526, -0.23423423423423428, -0.2332332332332332, -0.23223223223223222, -0.23123123123123124, -0.23023023023023026, -0.22922922922922928, -0.2282282282282282, -0.2272272272272272, -0.22622622622622623, -0.22522522522522526, -0.22422422422422428, -0.2232232232232232, -0.2222222222222222, -0.22122122122122123, -0.22022022022022025, -0.21921921921921927, -0.21821821821821819, -0.2172172172172172, -0.21621621621621623, -0.21521521521521525, -0.21421421421421427, -0.21321321321321318, -0.2122122122122122, -0.21121121121121122, -0.21021021021021025, -0.20920920920920927, -0.20820820820820818, -0.2072072072072072, -0.20620620620620622, -0.20520520520520524, -0.20420420420420426, -0.20320320320320318, -0.2022022022022022, -0.20120120120120122, -0.20020020020020024, -0.19919919919919926, -0.19819819819819817, -0.1971971971971972, -0.19619619619619622, -0.19519519519519524, -0.19419419419419415, -0.19319319319319317, -0.1921921921921922, -0.1911911911911912, -0.19019019019019023, -0.18918918918918914, -0.18818818818818817, -0.1871871871871872, -0.1861861861861862, -0.18518518518518523, -0.18418418418418414, -0.18318318318318316, -0.18218218218218218, -0.1811811811811812, -0.18018018018018023, -0.17917917917917914, -0.17817817817817816, -0.17717717717717718, -0.1761761761761762, -0.17517517517517522, -0.17417417417417413, -0.17317317317317316, -0.17217217217217218, -0.1711711711711712, -0.17017017017017022, -0.16916916916916913, -0.16816816816816815, -0.16716716716716717, -0.1661661661661662, -0.16516516516516522, -0.16416416416416413, -0.16316316316316315, -0.16216216216216217, -0.1611611611611612, -0.16016016016016021, -0.15915915915915912, -0.15815815815815815, -0.15715715715715717, -0.1561561561561562, -0.1551551551551552, -0.15415415415415412, -0.15315315315315314, -0.15215215215215216, -0.1511511511511512, -0.1501501501501502, -0.14914914914914912, -0.14814814814814814, -0.14714714714714716, -0.14614614614614618, -0.1451451451451452, -0.14414414414414412, -0.14314314314314314, -0.14214214214214216, -0.14114114114114118, -0.1401401401401402, -0.1391391391391391, -0.13813813813813813, -0.13713713713713716, -0.13613613613613618, -0.1351351351351351, -0.1341341341341341, -0.13313313313313313, -0.13213213213213215, -0.13113113113113117, -0.13013013013013008, -0.1291291291291291, -0.12812812812812813, -0.12712712712712715, -0.12612612612612617, -0.12512512512512508, -0.1241241241241241, -0.12312312312312312, -0.12212212212212215, -0.12112112112112117, -0.12012012012012008, -0.1191191191191191, -0.11811811811811812, -0.11711711711711714, -0.11611611611611616, -0.11511511511511507, -0.1141141141141141, -0.11311311311311312, -0.11211211211211214, -0.11111111111111116, -0.11011011011011007, -0.10910910910910909, -0.10810810810810811, -0.10710710710710714, -0.10610610610610616, -0.10510510510510507, -0.10410410410410409, -0.10310310310310311, -0.10210210210210213, -0.10110110110110115, -0.10010010010010006, -0.09909909909909909, -0.09809809809809811, -0.09709709709709713, -0.09609609609609615, -0.09509509509509506, -0.09409409409409408, -0.0930930930930931, -0.09209209209209213, -0.09109109109109115, -0.09009009009009006, -0.08908908908908908, -0.0880880880880881, -0.08708708708708712, -0.08608608608608614, -0.08508508508508505, -0.08408408408408408, -0.0830830830830831, -0.08208208208208212, -0.08108108108108114, -0.08008008008008005, -0.07907907907907907, -0.0780780780780781, -0.07707707707707712, -0.07607607607607614, -0.07507507507507505, -0.07407407407407407, -0.07307307307307309, -0.07207207207207211, -0.07107107107107113, -0.07007007007007005, -0.06906906906906907, -0.06806806806806809, -0.06706706706706711, -0.06606606606606602, -0.06506506506506504, -0.06406406406406406, -0.06306306306306309, -0.06206206206206211, -0.06106106106106102, -0.06006006006006004, -0.05905905905905906, -0.05805805805805808, -0.0570570570570571, -0.056056056056056014, -0.055055055055055035, -0.05405405405405406, -0.05305305305305308, -0.0520520520520521, -0.05105105105105101, -0.05005005005005003, -0.049049049049049054, -0.048048048048048075, -0.0470470470470471, -0.04604604604604601, -0.04504504504504503, -0.04404404404404405, -0.04304304304304307, -0.042042042042042094, -0.041041041041041004, -0.040040040040040026, -0.03903903903903905, -0.03803803803803807, -0.03703703703703709, -0.036036036036036, -0.03503503503503502, -0.034034034034034044, -0.033033033033033066, -0.03203203203203209, -0.031031031031030998, -0.03003003003003002, -0.02902902902902904, -0.028028028028028062, -0.027027027027027084, -0.026026026026025995, -0.025025025025025016, -0.024024024024024038, -0.02302302302302306, -0.02202202202202208, -0.02102102102102099, -0.020020020020020013, -0.019019019019019034, -0.018018018018018056, -0.017017017017017078, -0.016016016016015988, -0.01501501501501501, -0.014014014014014031, -0.013013013013013053, -0.012012012012012074, -0.011011011011010985, -0.010010010010010006, -0.009009009009009028, -0.00800800800800805, -0.00700700700700696, -0.006006006006005982, -0.005005005005005003, -0.004004004004004025, -0.0030030030030030463, -0.002002002002001957, -0.0010010010010009784, -5.551115123125783e-17], "expected": [0.6321205588285577, 0.6323851449331281, 0.6326498920765035, 0.6329148003730879, 0.6331798699373731, 0.6334451008839398, 0.633710493327457, 0.6339760473826822, 0.6342417631644617, 0.6345076407877301, 0.6347736803675114, 0.6350398820189175, 0.6353062458571501, 0.6355727719974997, 0.6358394605553455, 0.636106311646156, 0.636373325385489, 0.6366405018889914, 0.6369078412723996, 0.6371753436515394, 0.6374430091423258, 0.6377108378607639, 0.637978829922948, 0.6382469854450622, 0.6385153045433805, 0.6387837873342664, 0.6390524339341742, 0.6393212444596469, 0.6395902190273187, 0.6398593577539134, 0.6401286607562452, 0.6403981281512183, 0.6406677600558279, 0.6409375565871588, 0.641207517862387, 0.6414776439987787, 0.6417479351136909, 0.6420183913245715, 0.6422890127489588, 0.6425597995044824, 0.6428307517088625, 0.6431018694799105, 0.6433731529355289, 0.6436446021937117, 0.6439162173725435, 0.6441879985902006, 0.6444599459649507, 0.644732059615153, 0.6450043396592581, 0.6452767862158083, 0.6455493994034376, 0.6458221793408719, 0.6460951261469287, 0.6463682399405176, 0.6466415208406401, 0.6469149689663898, 0.6471885844369527, 0.6474623673716066, 0.6477363178897216, 0.6480104361107607, 0.6482847221542789, 0.6485591761399238, 0.6488337981874356, 0.6491085884166472, 0.6493835469474845, 0.6496586738999656, 0.649933969394202, 0.6502094335503982, 0.6504850664888515, 0.6507608683299525, 0.6510368391941849, 0.6513129792021255, 0.6515892884744451, 0.6518657671319071, 0.6521424152953693, 0.6524192330857821, 0.6526962206241902, 0.652973378031732, 0.6532507054296397, 0.653528202939239, 0.65380587068195, 0.6540837087792867, 0.6543617173528573, 0.654639896524364, 0.6549182464156036, 0.6551967671484668, 0.6554754588449389, 0.6557543216271, 0.6560333556171245, 0.6563125609372815, 0.6565919377099347, 0.656871486057543, 0.6571512061026595, 0.6574310979679333, 0.6577111617761074, 0.657991397650021, 0.6582718057126073, 0.6585523860868961, 0.6588331388960117, 0.6591140642631736, 0.6593951623116977, 0.6596764331649951, 0.6599578769465722, 0.6602394937800314, 0.6605212837890712, 0.6608032470974855, 0.6610853838291646, 0.6613676941080947, 0.661650178058358, 0.6619328358041329, 0.6622156674696947, 0.6624986731794141, 0.662781853057759, 0.6630652072292935, 0.6633487358186784, 0.6636324389506709, 0.6639163167501257, 0.6642003693419936, 0.6644845968513224, 0.6647689994032573, 0.6650535771230401, 0.6653383301360104, 0.6656232585676046, 0.6659083625433561, 0.6661936421888963, 0.666479097629954, 0.6667647289923552, 0.6670505364020236, 0.667336519984981, 0.6676226798673466, 0.6679090161753377, 0.6681955290352694, 0.6684822185735549, 0.6687690849167055, 0.6690561281913308, 0.6693433485241383, 0.6696307460419345, 0.6699183208716238, 0.6702060731402092, 0.6704940029747924, 0.670782110502574, 0.6710703958508528, 0.6713588591470266, 0.6716475005185929, 0.671936320093147, 0.6722253179983838, 0.672514494362098, 0.6728038493121823, 0.6730933829766296, 0.6733830954835319, 0.6736729869610808, 0.6739630575375675, 0.6742533073413824, 0.6745437365010165, 0.6748343451450597, 0.6751251334022023, 0.6754161014012345, 0.6757072492710464, 0.6759985771406284, 0.6762900851390712, 0.6765817733955652, 0.6768736420394024, 0.6771656911999736, 0.6774579210067716, 0.6777503315893894, 0.67804292307752, 0.6783356956009583, 0.6786286492895993, 0.6789217842734394, 0.6792151006825756, 0.6795085986472064, 0.6798022782976313, 0.6800961397642511, 0.6803901831775682, 0.6806844086681861, 0.6809788163668102, 0.6812734064042472, 0.6815681789114054, 0.6818631340192954, 0.6821582718590296, 0.6824535925618215, 0.6827490962589877, 0.6830447830819463, 0.6833406531622178, 0.6836367066314251, 0.6839329436212932, 0.6842293642636496, 0.6845259686904246, 0.6848227570336507, 0.6851197294254636, 0.6854168859981015, 0.6857142268839052, 0.686011752215319, 0.6863094621248897, 0.6866073567452678, 0.6869054362092066, 0.687203700649563, 0.6875021501992968, 0.6878007849914716, 0.6880996051592544, 0.688398610835916, 0.688697802154831, 0.6889971792494776, 0.6892967422534375, 0.6895964913003972, 0.6898964265241467, 0.6901965480585802, 0.6904968560376963, 0.6907973505955977, 0.6910980318664918, 0.6913988999846898, 0.6916999550846085, 0.6920011973007685, 0.6923026267677955, 0.69260424362042, 0.6929060479934773, 0.6932080400219077, 0.6935102198407567, 0.693812587585175, 0.6941151433904182, 0.6944178873918477, 0.69472081972493, 0.6950239405252372, 0.6953272499284472, 0.6956307480703431, 0.6959344350868143, 0.6962383111138558, 0.6965423762875684, 0.6968466307441594, 0.6971510746199414, 0.6974557080513343, 0.6977605311748634, 0.6980655441271606, 0.6983707470449646, 0.6986761400651201, 0.698981723324579, 0.6992874969603994, 0.6995934611097465, 0.6998996159098926, 0.7002059614982165, 0.7005124980122045, 0.7008192255894498, 0.7011261443676529, 0.7014332544846216, 0.7017405560782715, 0.702048049286625, 0.702355734247813, 0.7026636111000732, 0.7029716799817517, 0.7032799410313021, 0.7035883943872863, 0.7038970401883737, 0.7042058785733426, 0.7045149096810789, 0.7048241336505768, 0.7051335506209395, 0.705443160731378, 0.7057529641212122, 0.7060629609298706, 0.7063731512968907, 0.7066835353619185, 0.706994113264709, 0.707304885145126, 0.7076158511431432, 0.7079270113988425, 0.7082383660524159, 0.7085499152441642, 0.7088616591144982, 0.7091735978039376, 0.7094857314531124, 0.7097980602027618, 0.7101105841937354, 0.7104233035669919, 0.7107362184636009, 0.7110493290247416, 0.7113626353917036, 0.7116761377058862, 0.7119898361087998, 0.7123037307420651, 0.7126178217474128, 0.7129321092666854, 0.7132465934418346, 0.713561274414924, 0.7138761523281281, 0.7141912273237316, 0.7145064995441311, 0.7148219691318343, 0.7151376362294596, 0.7154535009797371, 0.7157695635255088, 0.7160858240097274, 0.7164022825754579, 0.7167189393658768, 0.7170357945242725, 0.717352848194045, 0.7176701005187067, 0.7179875516418821, 0.7183052017073075, 0.7186230508588317, 0.718941099240416, 0.7192593469961341, 0.7195777942701723, 0.7198964412068293, 0.7202152879505165, 0.7205343346457588, 0.7208535814371932, 0.7211730284695702, 0.7214926758877537, 0.7218125238367196, 0.7221325724615586, 0.722452821907474, 0.7227732723197822, 0.7230939238439141, 0.7234147766254139, 0.7237358308099392, 0.7240570865432618, 0.7243785439712674, 0.7247002032399561, 0.7250220644954413, 0.7253441278839513, 0.7256663935518286, 0.72598886164553, 0.7263115323116268, 0.7266344056968052, 0.7269574819478655, 0.7272807612117234, 0.7276042436354093, 0.7279279293660684, 0.7282518185509611, 0.7285759113374634, 0.7289002078730654, 0.7292247083053739, 0.7295494127821104, 0.7298743214511119, 0.7301994344603318, 0.730524751957838, 0.7308502740918155, 0.7311760010105643, 0.7315019328625011, 0.7318280697961582, 0.7321544119601843, 0.7324809595033445, 0.7328077125745204, 0.7331346713227095, 0.7334618358970268, 0.7337892064467032, 0.734116783121087, 0.7344445660696428, 0.7347725554419526, 0.7351007513877157, 0.7354291540567476, 0.7357577635989822, 0.7360865801644699, 0.7364156039033792, 0.736744834965996, 0.7370742735027231, 0.7374039196640825, 0.7377337736007125, 0.7380638354633706, 0.7383941054029316, 0.7387245835703886, 0.7390552701168531, 0.7393861651935549, 0.739717268951842, 0.7400485815431811, 0.7403801031191575, 0.7407118338314754, 0.7410437738319574, 0.7413759232725453, 0.7417082823053, 0.7420408510824011, 0.742373629756148, 0.7427066184789591, 0.743039817403372, 0.7433732266820441, 0.7437068464677521, 0.744040676913393, 0.7443747181719831, 0.7447089703966585, 0.7450434337406756, 0.7453781083574109, 0.7457129944003608, 0.7460480920231423, 0.7463834013794927, 0.7467189226232694, 0.7470546559084511, 0.747390601389137, 0.7477267592195465, 0.7480631295540204, 0.7483997125470203, 0.7487365083531292, 0.749073517127051, 0.7494107390236109, 0.7497481741977554, 0.7500858228045527, 0.7504236849991924, 0.7507617609369861, 0.7511000507733666, 0.7514385546638891, 0.7517772727642306, 0.7521162052301902, 0.7524553522176892, 0.752794713882771, 0.7531342903816016, 0.7534740818704696, 0.7538140885057858, 0.754154310444084, 0.7544947478420208, 0.7548354008563752, 0.7551762696440498, 0.7555173543620702, 0.7558586551675848, 0.7562001722178656, 0.7565419056703079, 0.7568838556824306, 0.757226022411876, 0.7575684060164102, 0.7579110066539234, 0.7582538244824291, 0.7585968596600652, 0.7589401123450938, 0.7592835826959009, 0.7596272708709968, 0.7599711770290167, 0.7603153013287195, 0.7606596439289898, 0.7610042049888357, 0.7613489846673911, 0.7616939831239145, 0.7620392005177891, 0.7623846370085237, 0.762730292755752, 0.7630761679192335, 0.7634222626588526, 0.7637685771346192, 0.7641151115066696, 0.7644618659352651, 0.7648088405807932, 0.7651560356037672, 0.7655034511648264, 0.7658510874247368, 0.76619894454439, 0.766547022684804, 0.7668953220071241, 0.767243842672621, 0.7675925848426929, 0.7679415486788645, 0.7682907343427877, 0.7686401419962408, 0.7689897718011297, 0.7693396239194875, 0.7696896985134744, 0.7700399957453776, 0.770390515777613, 0.7707412587727231, 0.7710922248933784, 0.7714434143023774, 0.7717948271626464, 0.7721464636372396, 0.7724983238893398, 0.7728504080822578, 0.7732027163794325, 0.7735552489444316, 0.7739080059409514, 0.7742609875328166, 0.774614193883981, 0.7749676251585271, 0.7753212815206664, 0.7756751631347395, 0.7760292701652162, 0.776383602776696, 0.7767381611339073, 0.7770929454017081, 0.7774479557450863, 0.7778031923291593, 0.7781586553191748, 0.7785143448805094, 0.7788702611786713, 0.7792264043792976, 0.779582774648156, 0.779939372151145, 0.7802961970542931, 0.7806532495237598, 0.781010529725835, 0.7813680378269395, 0.7817257739936252, 0.7820837383925745, 0.7824419311906019, 0.782800352554652, 0.7831590026518016, 0.7835178816492588, 0.7838769897143631, 0.7842363270145856, 0.7845958937175291, 0.7849556899909291, 0.7853157160026524, 0.7856759719206976, 0.7860364579131963, 0.7863971741484124, 0.7867581207947412, 0.787119298020712, 0.7874807059949855, 0.7878423448863564, 0.7882042148637508, 0.7885663160962292, 0.7889286487529844, 0.7892912130033425, 0.7896540090167632, 0.7900170369628392, 0.7903802970112975, 0.7907437893319975, 0.7911075140949337, 0.7914714714702334, 0.7918356616281587, 0.7922000847391052, 0.7925647409736032, 0.7929296305023166, 0.7932947534960444, 0.7936601101257196, 0.7940257005624108, 0.7943915249773201, 0.7947575835417853, 0.7951238764272788, 0.7954904038054083, 0.7958571658479162, 0.7962241627266814, 0.796591394613717, 0.7969588616811718, 0.7973265641013311, 0.7976945020466149, 0.7980626756895797, 0.7984310852029177, 0.7987997307594579, 0.7991686125321641, 0.7995377306941377, 0.799907085418616, 0.8002766768789729, 0.8006465052487189, 0.8010165707015016, 0.8013868734111046, 0.8017574135514501, 0.8021281912965956, 0.8024992068207367, 0.8028704602982069, 0.8032419519034757, 0.8036136818111514, 0.8039856501959798, 0.8043578572328436, 0.8047303030967644, 0.8051029879629017, 0.8054759120065524, 0.8058490754031524, 0.8062224783282756, 0.8065961209576346, 0.8069700034670801, 0.8073441260326022, 0.8077184888303293, 0.8080930920365287, 0.8084679358276071, 0.8088430203801104, 0.8092183458707232, 0.8095939124762699, 0.8099697203737143, 0.8103457697401603, 0.8107220607528504, 0.8110985935891684, 0.8114753684266363, 0.8118523854429179, 0.8122296448158167, 0.8126071467232757, 0.8129848913433791, 0.8133628788543517, 0.8137411094345582, 0.8141195832625053, 0.8144983005168395, 0.8148772613763484, 0.8152564660199613, 0.8156359146267487, 0.8160156073759217, 0.8163955444468337, 0.8167757260189794, 0.8171561522719951, 0.8175368233856589, 0.817917739539891, 0.8182989009147538, 0.8186803076904515, 0.8190619600473308, 0.8194438581658808, 0.8198260022267332, 0.8202083924106619, 0.8205910288985844, 0.8209739118715603, 0.8213570415107928, 0.8217404179976276, 0.8221240415135542, 0.822507912240205, 0.8228920303593563, 0.8232763960529277, 0.8236610095029827, 0.8240458708917283, 0.8244309804015157, 0.8248163382148402, 0.8252019445143416, 0.825587799482803, 0.8259739033031529, 0.8263602561584639, 0.8267468582319534, 0.8271337097069835, 0.8275208107670614, 0.8279081615958389, 0.8282957623771136, 0.8286836132948274, 0.8290717145330687, 0.8294600662760707, 0.8298486687082124, 0.8302375220140182, 0.8306266263781591, 0.8310159819854515, 0.8314055890208579, 0.8317954476694875, 0.8321855581165954, 0.8325759205475834, 0.832966535148, 0.8333574021035397, 0.8337485216000448, 0.8341398938235036, 0.8345315189600524, 0.834923397195974, 0.8353155287176991, 0.8357079137118052, 0.8361005523650178, 0.8364934448642101, 0.8368865913964028, 0.8372799921487646, 0.8376736473086126, 0.8380675570634118, 0.8384617216007753, 0.838856141108465, 0.8392508157743911, 0.8396457457866124, 0.8400409313333367, 0.8404363726029207, 0.8408320697838704, 0.8412280230648401, 0.8416242326346339, 0.8420206986822052, 0.8424174213966577, 0.8428144009672434, 0.843211637583365, 0.8436091314345748, 0.8440068827105753, 0.8444048916012187, 0.844803158296508, 0.8452016829865963, 0.845600465861787, 0.845999507112535, 0.8463988069294454, 0.8467983655032734, 0.8471981830249269, 0.8475982596854632, 0.8479985956760925, 0.8483991911881754, 0.8488000464132235, 0.8492011615429019, 0.8496025367690256, 0.8500041722835627, 0.8504060682786323, 0.8508082249465063, 0.8512106424796095, 0.8516133210705171, 0.8520162609119593, 0.852419462196817, 0.8528229251181246, 0.8532266498690702, 0.8536306366429932, 0.8540348856333876, 0.8544393970339, 0.8548441710383307, 0.8552492078406336, 0.8556545076349154, 0.8560600706154382, 0.8564658969766165, 0.8568719869130196, 0.8572783406193709, 0.8576849582905478, 0.8580918401215826, 0.8584989863076621, 0.8589063970441269, 0.859314072526474, 0.8597220129503534, 0.8601302185115722, 0.860538689406091, 0.8609474258300269, 0.8613564279796521, 0.8617656960513935, 0.8621752302418351, 0.8625850307477161, 0.862995097765932, 0.8634054314935331, 0.8638160321277277, 0.8642268998658799, 0.8646380349055093, 0.8650494374442937, 0.8654611076800662, 0.8658730458108177, 0.8662852520346958, 0.8666977265500054, 0.8671104695552083, 0.8675234812489239, 0.8679367618299295, 0.8683503114971594, 0.8687641304497064, 0.86917821888682, 0.8695925770079095, 0.8700072050125409, 0.8704221031004392, 0.8708372714714877, 0.8712527103257285, 0.871668419863362, 0.8720844002847474, 0.8725006517904038, 0.872917174581008, 0.8733339688573972, 0.873751034820567, 0.8741683726716735, 0.8745859826120321, 0.8750038648431171, 0.8754220195665636, 0.8758404469841669, 0.8762591472978821, 0.8766781207098239, 0.8770973674222686, 0.8775168876376527, 0.8779366815585726, 0.878356749387787, 0.878777091328214, 0.8791977075829341, 0.8796185983551881, 0.8800397638483785, 0.8804612042660694, 0.8808829198119863, 0.8813049106900169, 0.8817271771042101, 0.8821497192587776, 0.8825725373580924, 0.8829956316066907, 0.8834190022092705, 0.8838426493706926, 0.8842665732959804, 0.8846907741903204, 0.8851152522590617, 0.8855400077077168, 0.885965040741961, 0.886390351567634, 0.8868159403907376, 0.8872418074174383, 0.8876679528540662, 0.888094376907115, 0.8885210797832426, 0.8889480616892711, 0.8893753228321871, 0.8898028634191415, 0.8902306836574497, 0.890658783754592, 0.8910871639182136, 0.8915158243561244, 0.8919447652763004, 0.8923739868868811, 0.8928034893961735, 0.8932332730126487, 0.8936633379449436, 0.8940936844018623, 0.8945243125923729, 0.8949552227256111, 0.8953864150108785, 0.895817889657642, 0.8962496468755369, 0.8966816868743637, 0.8971140098640904, 0.8975466160548519, 0.8979795056569494, 0.8984126788808527, 0.8988461359371979, 0.8992798770367885, 0.8997139023905965, 0.9001482122097612, 0.9005828067055895, 0.9010176860895563, 0.901452850573306, 0.90188830036865, 0.9023240356875681, 0.9027600567422099, 0.9031963637448925, 0.9036329569081025, 0.9040698364444953, 0.904507002566896, 0.9049444554882983, 0.9053821954218654, 0.9058202225809308, 0.9062585371789972, 0.906697139429737, 0.9071360295469932, 0.9075752077447785, 0.9080146742372761, 0.9084544292388393, 0.9088944729639925, 0.9093348056274307, 0.9097754274440192, 0.9102163386287951, 0.9106575393969659, 0.9110990299639116, 0.911540810545182, 0.9119828813564991, 0.9124252426137577, 0.912867894533023, 0.9133108373305332, 0.9137540712226976, 0.9141975964260988, 0.914641413157491, 0.9150855216338023, 0.9155299220721318, 0.9159746146897525, 0.9164195997041105, 0.9168648773328241, 0.9173104477936861, 0.9177563113046622, 0.9182024680838914, 0.9186489183496864, 0.9190956623205346, 0.9195427002150969, 0.9199900322522082, 0.9204376586508777, 0.9208855796302888, 0.9213337954098006, 0.921782306208946, 0.9222311122474327, 0.9226802137451442, 0.9231296109221385, 0.9235793039986488, 0.9240292931950841, 0.9244795787320296, 0.9249301608302455, 0.9253810397106675, 0.9258322155944084, 0.9262836887027569, 0.9267354592571773, 0.9271875274793112, 0.9276398935909768, 0.9280925578141684, 0.928545520371058, 0.9289987814839944, 0.9294523413755036, 0.9299062002682889, 0.930360358385231, 0.9308148159493889, 0.9312695731839987, 0.9317246303124745, 0.932179987558409, 0.9326356451455734, 0.933091603297916, 0.9335478622395647, 0.9340044221948265, 0.9344612833881855, 0.9349184460443069, 0.9353759103880335, 0.9358336766443881, 0.9362917450385732, 0.93675011579597, 0.9372087891421406, 0.9376677653028258, 0.9381270445039472, 0.9385866269716061, 0.9390465129320853, 0.9395067026118465, 0.9399671962375333, 0.9404279940359689, 0.940889096234159, 0.9413505030592887, 0.9418122147387258, 0.942274231500019, 0.9427365535708978, 0.9431991811792747, 0.9436621145532428, 0.9441253539210781, 0.9445888995112387, 0.9450527515523645, 0.9455169102732778, 0.9459813759029844, 0.946446148670672, 0.9469112288057114, 0.9473766165376571, 0.9478423120962457, 0.9483083157113981, 0.948774627613218, 0.9492412480319936, 0.9497081771981963, 0.9501754153424817, 0.9506429626956894, 0.9511108194888438, 0.9515789859531527, 0.9520474623200098, 0.9525162488209925, 0.9529853456878634, 0.9534547531525706, 0.9539244714472471, 0.954394500804211, 0.9548648414559661, 0.9553354936352016, 0.9558064575747934, 0.9562777335078035, 0.9567493216674777, 0.957221222287251, 0.957693435600743, 0.9581659618417611, 0.9586388012442981, 0.9591119540425356, 0.9595854204708398, 0.960059200763767, 0.960533295156058, 0.9610077038826437, 0.9614824271786401, 0.9619574652793539, 0.9624328184202776, 0.9629084868370928, 0.9633844707656696, 0.9638607704420656, 0.964337386102528, 0.9648143179834922, 0.9652915663215834, 0.9657691313536149, 0.9662470133165895, 0.9667252124476998, 0.9672037289843278, 0.9676825631640458, 0.9681617152246145, 0.9686411854039855, 0.9691209739403016, 0.969601081071894, 0.9700815070372866, 0.9705622520751922, 0.9710433164245152, 0.9715247003243511, 0.9720064040139859, 0.9724884277328976, 0.9729707717207559, 0.9734534362174213, 0.9739364214629471, 0.9744197276975773, 0.9749033551617492, 0.9753873040960918, 0.9758715747414265, 0.9763561673387674, 0.9768410821293223, 0.9773263193544899, 0.9778118792558635, 0.9782977620752296, 0.9787839680545678, 0.9792704974360505, 0.9797573504620455, 0.9802445273751129, 0.9807320284180082, 0.98121985383368, 0.9817080038652717, 0.9821964787561216, 0.9826852787497621, 0.9831744040899209, 0.9836638550205202, 0.9841536317856783, 0.984643734629708, 0.9851341637971179, 0.9856249195326124, 0.9861160020810913, 0.9866074116876511, 0.9870991485975843, 0.9875912130563793, 0.9880836053097211, 0.9885763256034915, 0.9890693741837693, 0.9895627512968299, 0.9900564571891463, 0.9905504921073885, 0.991044856298424, 0.991539550009318, 0.9920345734873335, 0.9925299269799317, 0.9930256107347711, 0.9935216249997101, 0.9940179700228037, 0.994514646052307, 0.9950116533366726, 0.9955089921245539, 0.9960066626648015, 0.9965046652064669, 0.9970029999987994, 0.9975016672912493, 0.9980006673334666, 0.9985000003752998, 0.9989996666668004, 0.9994996664582168, 1.0]} \ No newline at end of file diff --git a/lib/node_modules/@stdlib/math/base/special/expm1rel/test/fixtures/python/small_positive.json b/lib/node_modules/@stdlib/math/base/special/expm1rel/test/fixtures/python/small_positive.json new file mode 100644 index 000000000000..ff742c186934 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expm1rel/test/fixtures/python/small_positive.json @@ -0,0 +1 @@ +{"x": [5.551115123125783e-17, 0.0010010010010010565, 0.0020020020020020575, 0.0030030030030030585, 0.0040040040040040595, 0.0050050050050050605, 0.0060060060060060615, 0.0070070070070070625, 0.008008008008008063, 0.009009009009009064, 0.010010010010010065, 0.011011011011011066, 0.012012012012012067, 0.013013013013013068, 0.01401401401401407, 0.01501501501501507, 0.01601601601601607, 0.01701701701701707, 0.018018018018018073, 0.019019019019019076, 0.020020020020020075, 0.021021021021021075, 0.022022022022022077, 0.02302302302302308, 0.02402402402402408, 0.02502502502502508, 0.02602602602602608, 0.027027027027027084, 0.028028028028028083, 0.029029029029029083, 0.030030030030030085, 0.031031031031031088, 0.03203203203203209, 0.033033033033033087, 0.034034034034034086, 0.03503503503503509, 0.03603603603603609, 0.03703703703703709, 0.0380380380380381, 0.039039039039039096, 0.040040040040040095, 0.041041041041041094, 0.042042042042042094, 0.0430430430430431, 0.0440440440440441, 0.0450450450450451, 0.046046046046046105, 0.047047047047047104, 0.0480480480480481, 0.0490490490490491, 0.0500500500500501, 0.05105105105105111, 0.05205205205205211, 0.053053053053053106, 0.05405405405405411, 0.05505505505505511, 0.05605605605605611, 0.05705705705705711, 0.05805805805805811, 0.059059059059059116, 0.060060060060060115, 0.061061061061061114, 0.06206206206206212, 0.06306306306306311, 0.06406406406406412, 0.06506506506506513, 0.06606606606606612, 0.06706706706706712, 0.06806806806806812, 0.06906906906906912, 0.07007007007007013, 0.07107107107107112, 0.07207207207207213, 0.07307307307307313, 0.07407407407407413, 0.07507507507507513, 0.07607607607607614, 0.07707707707707713, 0.07807807807807814, 0.07907907907907913, 0.08008008008008013, 0.08108108108108114, 0.08208208208208213, 0.08308308308308314, 0.08408408408408413, 0.08508508508508514, 0.08608608608608614, 0.08708708708708714, 0.08808808808808814, 0.08908908908908915, 0.09009009009009014, 0.09109109109109115, 0.09209209209209215, 0.09309309309309315, 0.09409409409409415, 0.09509509509509514, 0.09609609609609615, 0.09709709709709716, 0.09809809809809815, 0.09909909909909916, 0.10010010010010015, 0.10110110110110115, 0.10210210210210216, 0.10310310310310315, 0.10410410410410416, 0.10510510510510516, 0.10610610610610616, 0.10710710710710716, 0.10810810810810817, 0.10910910910910916, 0.11011011011011017, 0.11111111111111116, 0.11211211211211217, 0.11311311311311317, 0.11411411411411417, 0.11511511511511517, 0.11611611611611616, 0.11711711711711717, 0.11811811811811818, 0.11911911911911917, 0.12012012012012017, 0.12112112112112118, 0.12212212212212217, 0.12312312312312318, 0.12412412412412419, 0.1251251251251252, 0.12612612612612617, 0.12712712712712718, 0.12812812812812818, 0.1291291291291292, 0.1301301301301302, 0.13113113113113117, 0.13213213213213218, 0.13313313313313319, 0.1341341341341342, 0.1351351351351352, 0.13613613613613618, 0.13713713713713718, 0.1381381381381382, 0.1391391391391392, 0.1401401401401402, 0.1411411411411412, 0.14214214214214219, 0.1431431431431432, 0.1441441441441442, 0.1451451451451452, 0.1461461461461462, 0.1471471471471472, 0.1481481481481482, 0.1491491491491492, 0.1501501501501502, 0.15115115115115121, 0.15215215215215222, 0.1531531531531532, 0.1541541541541542, 0.1551551551551552, 0.15615615615615622, 0.15715715715715722, 0.1581581581581582, 0.1591591591591592, 0.16016016016016021, 0.16116116116116122, 0.16216216216216223, 0.1631631631631632, 0.1641641641641642, 0.16516516516516522, 0.16616616616616622, 0.16716716716716723, 0.1681681681681682, 0.16916916916916921, 0.17017017017017022, 0.17117117117117123, 0.17217217217217223, 0.17317317317317324, 0.17417417417417422, 0.17517517517517522, 0.17617617617617623, 0.17717717717717724, 0.17817817817817824, 0.17917917917917922, 0.18018018018018023, 0.18118118118118123, 0.18218218218218224, 0.18318318318318325, 0.18418418418418425, 0.18518518518518523, 0.18618618618618624, 0.18718718718718724, 0.18818818818818825, 0.18918918918918926, 0.19019019019019023, 0.19119119119119124, 0.19219219219219225, 0.19319319319319325, 0.19419419419419426, 0.19519519519519524, 0.19619619619619624, 0.19719719719719725, 0.19819819819819826, 0.19919919919919926, 0.20020020020020024, 0.20120120120120125, 0.20220220220220225, 0.20320320320320326, 0.20420420420420426, 0.20520520520520527, 0.20620620620620625, 0.20720720720720726, 0.20820820820820826, 0.20920920920920927, 0.21021021021021027, 0.21121121121121125, 0.21221221221221226, 0.21321321321321327, 0.21421421421421427, 0.21521521521521528, 0.21621621621621628, 0.21721721721721726, 0.21821821821821827, 0.21921921921921927, 0.22022022022022028, 0.2212212212212213, 0.22222222222222227, 0.22322322322322327, 0.22422422422422428, 0.22522522522522528, 0.2262262262262263, 0.22722722722722727, 0.22822822822822827, 0.22922922922922928, 0.2302302302302303, 0.2312312312312313, 0.23223223223223227, 0.23323323323323328, 0.23423423423423428, 0.2352352352352353, 0.2362362362362363, 0.2372372372372373, 0.23823823823823828, 0.2392392392392393, 0.2402402402402403, 0.2412412412412413, 0.2422422422422423, 0.24324324324324328, 0.2442442442442443, 0.2452452452452453, 0.2462462462462463, 0.2472472472472473, 0.24824824824824832, 0.2492492492492493, 0.25025025025025033, 0.2512512512512513, 0.2522522522522523, 0.2532532532532533, 0.2542542542542543, 0.25525525525525533, 0.2562562562562563, 0.2572572572572573, 0.2582582582582583, 0.2592592592592593, 0.26026026026026033, 0.2612612612612613, 0.2622622622622623, 0.2632632632632633, 0.2642642642642643, 0.26526526526526534, 0.2662662662662663, 0.2672672672672673, 0.26826826826826833, 0.2692692692692693, 0.27027027027027034, 0.2712712712712713, 0.2722722722722723, 0.27327327327327333, 0.2742742742742743, 0.27527527527527534, 0.2762762762762763, 0.27727727727727736, 0.27827827827827833, 0.2792792792792793, 0.28028028028028035, 0.2812812812812813, 0.28228228228228236, 0.28328328328328334, 0.2842842842842843, 0.28528528528528535, 0.28628628628628633, 0.28728728728728736, 0.28828828828828834, 0.2892892892892893, 0.29029029029029035, 0.29129129129129133, 0.29229229229229237, 0.29329329329329334, 0.2942942942942943, 0.29529529529529536, 0.29629629629629634, 0.29729729729729737, 0.29829829829829835, 0.2992992992992993, 0.30030030030030036, 0.30130130130130134, 0.3023023023023024, 0.30330330330330335, 0.3043043043043044, 0.30530530530530536, 0.30630630630630634, 0.3073073073073074, 0.30830830830830835, 0.3093093093093094, 0.31031031031031037, 0.31131131131131135, 0.3123123123123124, 0.31331331331331336, 0.3143143143143144, 0.31531531531531537, 0.31631631631631635, 0.3173173173173174, 0.31831831831831836, 0.3193193193193194, 0.3203203203203204, 0.32132132132132135, 0.3223223223223224, 0.32332332332332336, 0.3243243243243244, 0.3253253253253254, 0.32632632632632635, 0.3273273273273274, 0.32832832832832837, 0.3293293293293294, 0.3303303303303304, 0.33133133133133136, 0.3323323323323324, 0.33333333333333337, 0.3343343343343344, 0.3353353353353354, 0.33633633633633636, 0.3373373373373374, 0.3383383383383384, 0.3393393393393394, 0.3403403403403404, 0.3413413413413414, 0.3423423423423424, 0.3433433433433434, 0.3443443443443444, 0.3453453453453454, 0.3463463463463464, 0.3473473473473474, 0.3483483483483484, 0.3493493493493494, 0.3503503503503504, 0.3513513513513514, 0.3523523523523524, 0.3533533533533534, 0.3543543543543544, 0.3553553553553554, 0.35635635635635643, 0.3573573573573574, 0.3583583583583584, 0.3593593593593594, 0.3603603603603604, 0.36136136136136143, 0.3623623623623624, 0.3633633633633634, 0.3643643643643644, 0.3653653653653654, 0.36636636636636644, 0.3673673673673674, 0.36836836836836845, 0.3693693693693694, 0.3703703703703704, 0.37137137137137144, 0.3723723723723724, 0.37337337337337345, 0.37437437437437443, 0.3753753753753754, 0.37637637637637644, 0.3773773773773774, 0.37837837837837845, 0.37937937937937943, 0.3803803803803804, 0.38138138138138145, 0.3823823823823824, 0.38338338338338346, 0.38438438438438444, 0.3853853853853854, 0.38638638638638645, 0.3873873873873874, 0.38838838838838846, 0.38938938938938944, 0.3903903903903904, 0.39139139139139145, 0.39239239239239243, 0.39339339339339346, 0.39439439439439444, 0.3953953953953954, 0.39639639639639646, 0.39739739739739743, 0.39839839839839847, 0.39939939939939945, 0.4004004004004004, 0.40140140140140146, 0.40240240240240244, 0.40340340340340347, 0.40440440440440445, 0.4054054054054055, 0.40640640640640646, 0.40740740740740744, 0.4084084084084085, 0.40940940940940945, 0.4104104104104105, 0.41141141141141147, 0.41241241241241244, 0.4134134134134135, 0.41441441441441446, 0.4154154154154155, 0.41641641641641647, 0.41741741741741745, 0.4184184184184185, 0.41941941941941946, 0.4204204204204205, 0.42142142142142147, 0.42242242242242245, 0.4234234234234235, 0.42442442442442446, 0.4254254254254255, 0.4264264264264265, 0.42742742742742745, 0.4284284284284285, 0.42942942942942947, 0.4304304304304305, 0.4314314314314315, 0.4324324324324325, 0.4334334334334335, 0.43443443443443447, 0.4354354354354355, 0.4364364364364365, 0.4374374374374375, 0.4384384384384385, 0.43943943943943947, 0.4404404404404405, 0.4414414414414415, 0.4424424424424425, 0.4434434434434435, 0.4444444444444445, 0.4454454454454455, 0.4464464464464465, 0.4474474474474475, 0.4484484484484485, 0.4494494494494495, 0.4504504504504505, 0.4514514514514515, 0.4524524524524525, 0.4534534534534535, 0.4544544544544545, 0.4554554554554555, 0.4564564564564565, 0.45745745745745753, 0.4584584584584585, 0.4594594594594595, 0.4604604604604605, 0.4614614614614615, 0.46246246246246253, 0.4634634634634635, 0.4644644644644645, 0.4654654654654655, 0.4664664664664665, 0.46746746746746753, 0.4684684684684685, 0.46946946946946955, 0.4704704704704705, 0.4714714714714715, 0.47247247247247254, 0.4734734734734735, 0.47447447447447455, 0.47547547547547553, 0.4764764764764765, 0.47747747747747754, 0.4784784784784785, 0.47947947947947955, 0.48048048048048053, 0.4814814814814815, 0.48248248248248254, 0.4834834834834835, 0.48448448448448456, 0.48548548548548554, 0.4864864864864865, 0.48748748748748755, 0.4884884884884885, 0.48948948948948956, 0.49049049049049054, 0.4914914914914915, 0.49249249249249255, 0.49349349349349353, 0.49449449449449456, 0.49549549549549554, 0.4964964964964966, 0.49749749749749755, 0.49849849849849853, 0.49949949949949957, 0.5005005005005005, 0.5015015015015016, 0.5025025025025025, 0.5035035035035036, 0.5045045045045045, 0.5055055055055055, 0.5065065065065066, 0.5075075075075075, 0.5085085085085086, 0.5095095095095095, 0.5105105105105106, 0.5115115115115116, 0.5125125125125125, 0.5135135135135136, 0.5145145145145145, 0.5155155155155156, 0.5165165165165166, 0.5175175175175175, 0.5185185185185186, 0.5195195195195195, 0.5205205205205206, 0.5215215215215216, 0.5225225225225225, 0.5235235235235236, 0.5245245245245245, 0.5255255255255256, 0.5265265265265267, 0.5275275275275275, 0.5285285285285286, 0.5295295295295295, 0.5305305305305306, 0.5315315315315317, 0.5325325325325325, 0.5335335335335336, 0.5345345345345345, 0.5355355355355356, 0.5365365365365367, 0.5375375375375375, 0.5385385385385386, 0.5395395395395395, 0.5405405405405406, 0.5415415415415417, 0.5425425425425425, 0.5435435435435436, 0.5445445445445445, 0.5455455455455456, 0.5465465465465467, 0.5475475475475475, 0.5485485485485486, 0.5495495495495497, 0.5505505505505506, 0.5515515515515517, 0.5525525525525525, 0.5535535535535536, 0.5545545545545547, 0.5555555555555556, 0.5565565565565567, 0.5575575575575575, 0.5585585585585586, 0.5595595595595597, 0.5605605605605606, 0.5615615615615617, 0.5625625625625625, 0.5635635635635636, 0.5645645645645647, 0.5655655655655656, 0.5665665665665667, 0.5675675675675675, 0.5685685685685686, 0.5695695695695697, 0.5705705705705706, 0.5715715715715717, 0.5725725725725725, 0.5735735735735736, 0.5745745745745747, 0.5755755755755756, 0.5765765765765767, 0.5775775775775776, 0.5785785785785786, 0.5795795795795797, 0.5805805805805806, 0.5815815815815817, 0.5825825825825826, 0.5835835835835836, 0.5845845845845847, 0.5855855855855856, 0.5865865865865867, 0.5875875875875876, 0.5885885885885886, 0.5895895895895897, 0.5905905905905906, 0.5915915915915917, 0.5925925925925926, 0.5935935935935936, 0.5945945945945947, 0.5955955955955956, 0.5965965965965967, 0.5975975975975976, 0.5985985985985987, 0.5995995995995997, 0.6006006006006006, 0.6016016016016017, 0.6026026026026026, 0.6036036036036037, 0.6046046046046047, 0.6056056056056056, 0.6066066066066067, 0.6076076076076076, 0.6086086086086087, 0.6096096096096097, 0.6106106106106106, 0.6116116116116117, 0.6126126126126126, 0.6136136136136137, 0.6146146146146148, 0.6156156156156156, 0.6166166166166167, 0.6176176176176176, 0.6186186186186187, 0.6196196196196198, 0.6206206206206206, 0.6216216216216217, 0.6226226226226226, 0.6236236236236237, 0.6246246246246248, 0.6256256256256256, 0.6266266266266267, 0.6276276276276276, 0.6286286286286287, 0.6296296296296298, 0.6306306306306306, 0.6316316316316317, 0.6326326326326326, 0.6336336336336337, 0.6346346346346348, 0.6356356356356356, 0.6366366366366367, 0.6376376376376376, 0.6386386386386387, 0.6396396396396398, 0.6406406406406406, 0.6416416416416417, 0.6426426426426426, 0.6436436436436437, 0.6446446446446448, 0.6456456456456456, 0.6466466466466467, 0.6476476476476476, 0.6486486486486487, 0.6496496496496498, 0.6506506506506506, 0.6516516516516517, 0.6526526526526526, 0.6536536536536537, 0.6546546546546548, 0.6556556556556556, 0.6566566566566567, 0.6576576576576576, 0.6586586586586587, 0.6596596596596598, 0.6606606606606606, 0.6616616616616617, 0.6626626626626626, 0.6636636636636637, 0.6646646646646648, 0.6656656656656657, 0.6666666666666667, 0.6676676676676676, 0.6686686686686687, 0.6696696696696698, 0.6706706706706707, 0.6716716716716717, 0.6726726726726726, 0.6736736736736737, 0.6746746746746748, 0.6756756756756757, 0.6766766766766767, 0.6776776776776778, 0.6786786786786787, 0.6796796796796798, 0.6806806806806807, 0.6816816816816818, 0.6826826826826828, 0.6836836836836837, 0.6846846846846848, 0.6856856856856857, 0.6866866866866868, 0.6876876876876878, 0.6886886886886887, 0.6896896896896898, 0.6906906906906907, 0.6916916916916918, 0.6926926926926928, 0.6936936936936937, 0.6946946946946948, 0.6956956956956957, 0.6966966966966968, 0.6976976976976978, 0.6986986986986987, 0.6996996996996998, 0.7007007007007007, 0.7017017017017018, 0.7027027027027029, 0.7037037037037037, 0.7047047047047048, 0.7057057057057057, 0.7067067067067068, 0.7077077077077079, 0.7087087087087087, 0.7097097097097098, 0.7107107107107107, 0.7117117117117118, 0.7127127127127129, 0.7137137137137137, 0.7147147147147148, 0.7157157157157157, 0.7167167167167168, 0.7177177177177179, 0.7187187187187187, 0.7197197197197198, 0.7207207207207207, 0.7217217217217218, 0.7227227227227229, 0.7237237237237237, 0.7247247247247248, 0.7257257257257257, 0.7267267267267268, 0.7277277277277279, 0.7287287287287287, 0.7297297297297298, 0.7307307307307307, 0.7317317317317318, 0.7327327327327329, 0.7337337337337337, 0.7347347347347348, 0.7357357357357357, 0.7367367367367368, 0.7377377377377379, 0.7387387387387387, 0.7397397397397398, 0.7407407407407407, 0.7417417417417418, 0.7427427427427429, 0.7437437437437437, 0.7447447447447448, 0.7457457457457457, 0.7467467467467468, 0.7477477477477479, 0.7487487487487487, 0.7497497497497498, 0.7507507507507507, 0.7517517517517518, 0.7527527527527529, 0.7537537537537538, 0.7547547547547548, 0.7557557557557557, 0.7567567567567568, 0.7577577577577579, 0.7587587587587588, 0.7597597597597598, 0.7607607607607607, 0.7617617617617618, 0.7627627627627629, 0.7637637637637638, 0.7647647647647648, 0.7657657657657657, 0.7667667667667668, 0.7677677677677679, 0.7687687687687688, 0.7697697697697699, 0.7707707707707707, 0.7717717717717718, 0.7727727727727729, 0.7737737737737738, 0.7747747747747749, 0.7757757757757757, 0.7767767767767768, 0.7777777777777779, 0.7787787787787788, 0.7797797797797799, 0.7807807807807807, 0.7817817817817818, 0.7827827827827829, 0.7837837837837838, 0.7847847847847849, 0.7857857857857857, 0.7867867867867868, 0.7877877877877879, 0.7887887887887888, 0.7897897897897899, 0.7907907907907907, 0.7917917917917918, 0.7927927927927929, 0.7937937937937938, 0.7947947947947949, 0.7957957957957957, 0.7967967967967968, 0.7977977977977979, 0.7987987987987988, 0.7997997997997999, 0.8008008008008007, 0.8018018018018018, 0.8028028028028029, 0.8038038038038038, 0.8048048048048049, 0.805805805805806, 0.8068068068068068, 0.8078078078078079, 0.8088088088088088, 0.8098098098098099, 0.810810810810811, 0.8118118118118118, 0.8128128128128129, 0.8138138138138138, 0.8148148148148149, 0.815815815815816, 0.8168168168168168, 0.8178178178178179, 0.8188188188188188, 0.8198198198198199, 0.820820820820821, 0.8218218218218218, 0.8228228228228229, 0.8238238238238238, 0.8248248248248249, 0.825825825825826, 0.8268268268268268, 0.8278278278278279, 0.8288288288288288, 0.8298298298298299, 0.830830830830831, 0.8318318318318318, 0.8328328328328329, 0.8338338338338338, 0.8348348348348349, 0.835835835835836, 0.8368368368368369, 0.8378378378378379, 0.8388388388388388, 0.8398398398398399, 0.840840840840841, 0.8418418418418419, 0.8428428428428429, 0.8438438438438438, 0.8448448448448449, 0.845845845845846, 0.8468468468468469, 0.847847847847848, 0.8488488488488488, 0.8498498498498499, 0.850850850850851, 0.8518518518518519, 0.852852852852853, 0.8538538538538538, 0.8548548548548549, 0.855855855855856, 0.8568568568568569, 0.857857857857858, 0.8588588588588588, 0.8598598598598599, 0.860860860860861, 0.8618618618618619, 0.862862862862863, 0.8638638638638638, 0.8648648648648649, 0.865865865865866, 0.8668668668668669, 0.867867867867868, 0.8688688688688688, 0.8698698698698699, 0.870870870870871, 0.8718718718718719, 0.872872872872873, 0.8738738738738738, 0.8748748748748749, 0.875875875875876, 0.8768768768768769, 0.877877877877878, 0.8788788788788788, 0.8798798798798799, 0.880880880880881, 0.8818818818818819, 0.882882882882883, 0.8838838838838838, 0.8848848848848849, 0.885885885885886, 0.8868868868868869, 0.887887887887888, 0.8888888888888888, 0.8898898898898899, 0.890890890890891, 0.8918918918918919, 0.892892892892893, 0.8938938938938938, 0.8948948948948949, 0.895895895895896, 0.8968968968968969, 0.897897897897898, 0.8988988988988988, 0.8998998998998999, 0.900900900900901, 0.9019019019019019, 0.902902902902903, 0.9039039039039038, 0.9049049049049049, 0.905905905905906, 0.9069069069069069, 0.907907907907908, 0.9089089089089089, 0.9099099099099099, 0.910910910910911, 0.9119119119119119, 0.912912912912913, 0.9139139139139139, 0.914914914914915, 0.915915915915916, 0.9169169169169169, 0.917917917917918, 0.9189189189189189, 0.91991991991992, 0.920920920920921, 0.9219219219219219, 0.922922922922923, 0.9239239239239239, 0.924924924924925, 0.925925925925926, 0.9269269269269269, 0.927927927927928, 0.9289289289289289, 0.92992992992993, 0.930930930930931, 0.9319319319319319, 0.932932932932933, 0.9339339339339341, 0.934934934934935, 0.935935935935936, 0.9369369369369369, 0.937937937937938, 0.9389389389389391, 0.93993993993994, 0.940940940940941, 0.9419419419419419, 0.942942942942943, 0.9439439439439441, 0.944944944944945, 0.945945945945946, 0.9469469469469469, 0.947947947947948, 0.9489489489489491, 0.94994994994995, 0.9509509509509511, 0.9519519519519519, 0.952952952952953, 0.9539539539539541, 0.954954954954955, 0.9559559559559561, 0.9569569569569569, 0.957957957957958, 0.9589589589589591, 0.95995995995996, 0.9609609609609611, 0.9619619619619619, 0.962962962962963, 0.9639639639639641, 0.964964964964965, 0.9659659659659661, 0.9669669669669669, 0.967967967967968, 0.9689689689689691, 0.96996996996997, 0.9709709709709711, 0.9719719719719719, 0.972972972972973, 0.9739739739739741, 0.974974974974975, 0.9759759759759761, 0.9769769769769769, 0.977977977977978, 0.9789789789789791, 0.97997997997998, 0.9809809809809811, 0.9819819819819819, 0.982982982982983, 0.9839839839839841, 0.984984984984985, 0.9859859859859861, 0.986986986986987, 0.987987987987988, 0.9889889889889891, 0.98998998998999, 0.9909909909909911, 0.991991991991992, 0.992992992992993, 0.9939939939939941, 0.994994994994995, 0.9959959959959961, 0.996996996996997, 0.997997997997998, 0.9989989989989991, 1.0], "expected": [1.0, 1.0005006675428016, 1.001001669337473, 1.0015030056350673, 1.002004676686839, 1.0025066827442424, 1.0030090240589353, 1.0035117008827759, 1.0040147134678241, 1.0045180620663432, 1.0050217469307958, 1.0055257683138508, 1.0060301264683758, 1.0065348216474432, 1.0070398541043275, 1.007545224092507, 1.0080509318656616, 1.0085569776776762, 1.0090633617826381, 1.0095700844348388, 1.0100771458887732, 1.010584546399141, 1.0110922862208451, 1.0116003656089936, 1.012108784818898, 1.0126175441060763, 1.0131266437262494, 1.0136360839353447, 1.0141458649894939, 1.0146559871450351, 1.01516645065851, 1.0156772557866685, 1.0161884027864643, 1.0166998919150587, 1.0172117234298181, 1.0177238975883163, 1.0182364146483325, 1.0187492748678537, 1.0192624785050737, 1.019776025818393, 1.0202899170664188, 1.0208041525079679, 1.0213187324020616, 1.0218336570079323, 1.0223489265850174, 1.0228645413929647, 1.0233805016916289, 1.0238968077410742, 1.0244134598015715, 1.024930458133604, 1.0254478029978609, 1.0259654946552412, 1.0264835333668543, 1.027001919394018, 1.0275206529982608, 1.02803973444132, 1.028559163985144, 1.0290789418918904, 1.0295990684239282, 1.0301195438438362, 1.0306403684144048, 1.0311615423986344, 1.0316830660597374, 1.032204939661137, 1.0327271634664674, 1.0332497377395757, 1.0337726627445196, 1.0342959387455692, 1.0348195660072075, 1.0353435447941288, 1.0358678753712403, 1.0363925580036621, 1.036917592956727, 1.0374429804959808, 1.037968720887183, 1.038494814396306, 1.039021261289536, 1.0395480618332729, 1.0400752162941307, 1.0406027249389371, 1.0411305880347357, 1.0416588058487815, 1.0421873786485474, 1.0427163067017189, 1.0432455902761983, 1.0437752296401017, 1.0443052250617615, 1.0448355768097246, 1.0453662851527552, 1.045897350359832, 1.0464287727001504, 1.046960552443122, 1.0474926898583756, 1.0480251852157556, 1.0485580387853235, 1.0490912508373584, 1.0496248216423556, 1.0501587514710287, 1.0506930405943087, 1.051227689283344, 1.0517626978095007, 1.0522980664443642, 1.0528337954597367, 1.0533698851276398, 1.0539063357203136, 1.054443147510217, 1.0549803207700277, 1.0555178557726428, 1.056055752791179, 1.056594012098972, 1.0571326339695781, 1.0576716186767727, 1.058210966494552, 1.058750677697132, 1.0592907525589492, 1.0598311913546612, 1.0603719943591465, 1.0609131618475038, 1.061454694095054, 1.0619965913773388, 1.062538853970122, 1.0630814821493888, 1.0636244761913463, 1.0641678363724243, 1.064711562969274, 1.0652556562587707, 1.0658001165180107, 1.066344944024314, 1.0668901390552241, 1.0674357018885072, 1.0679816328021527, 1.068527932074374, 1.069074599983609, 1.0696216368085187, 1.0701690428279884, 1.0707168183211286, 1.0712649635672735, 1.0718134788459819, 1.0723623644370388, 1.072911620620453, 1.07346124767646, 1.0740112458855193, 1.0745616155283173, 1.075112356885766, 1.0756634702390035, 1.0762149558693936, 1.0767668140585271, 1.0773190450882224, 1.077871649240523, 1.0784246267977, 1.0789779780422528, 1.079531703256907, 1.0800858027246156, 1.080640276728561, 1.0811951255521526, 1.0817503494790273, 1.0823059487930518, 1.08286192377832, 1.083418274719156, 1.0839750019001118, 1.0845321056059685, 1.0850895861217378, 1.085647443732659, 1.0862056787242023, 1.086764291382068, 1.0873232819921865, 1.0878826508407176, 1.0884423982140519, 1.089002524398812, 1.089563029681849, 1.0901239143502472, 1.0906851786913216, 1.0912468229926178, 1.0918088475419143, 1.09237125262722, 1.0929340385367776, 1.0934972055590606, 1.0940607539827754, 1.0946246840968612, 1.0951889961904901, 1.0957536905530667, 1.0963187674742287, 1.096884227243849, 1.097450070152032, 1.0980162964891165, 1.0985829065456747, 1.0991499006125154, 1.0997172789806788, 1.100285041941442, 1.1008531897863147, 1.1014217228070438, 1.10199064129561, 1.1025599455442294, 1.1031296358453542, 1.1036997124916723, 1.104270175776107, 1.1048410259918189, 1.105412263432203, 1.1059838883908935, 1.106555901161759, 1.1071283020389064, 1.1077010913166792, 1.108274269289658, 1.1088478362526624, 1.1094217925007477, 1.1099961383292085, 1.1105708740335773, 1.1111459999096247, 1.1117215162533602, 1.1122974233610319, 1.1128737215291267, 1.1134504110543701, 1.1140274922337285, 1.1146049653644075, 1.11518283074385, 1.115761088669742, 1.116339739440008, 1.116918783352814, 1.1174982207065651, 1.118078051799908, 1.1186582769317306, 1.1192388964011608, 1.1198199105075697, 1.1204013195505682, 1.1209831238300099, 1.1215653236459908, 1.1221479192988473, 1.1227309110891603, 1.1233142993177518, 1.123898084285687, 1.1244822662942748, 1.1250668456450665, 1.1256518226398562, 1.1262371975806837, 1.1268229707698303, 1.1274091425098227, 1.1279957131034313, 1.1285826828536714, 1.129170052063802, 1.1297578210373278, 1.1303459900779984, 1.1309345594898081, 1.1315235295769972, 1.1321129006440516, 1.1327026729957028, 1.1332928469369286, 1.133883422772953, 1.1344744008092464, 1.1350657813515261, 1.1356575647057556, 1.1362497511781464, 1.136842341075157, 1.137435334703494, 1.13802873237011, 1.1386225343822067, 1.1392167410472347, 1.1398113526728915, 1.1404063695671238, 1.1410017920381272, 1.141597620394346, 1.142193854944474, 1.1427904959974535, 1.143387543862478, 1.1439849988489892, 1.1445828612666797, 1.1451811314254923, 1.1457798096356202, 1.1463788962075068, 1.1469783914518468, 1.1475782956795857, 1.1481786092019206, 1.1487793323303, 1.1493804653764241, 1.1499820086522452, 1.1505839624699672, 1.1511863271420455, 1.1517891029811915, 1.1523922903003654, 1.1529958894127827, 1.153599900631911, 1.1542043242714721, 1.1548091606454407, 1.1554144100680455, 1.1560200728537702, 1.156626149317351, 1.15723263977378, 1.1578395445383038, 1.1584468639264232, 1.1590545982538945, 1.1596627478367296, 1.1602713129911952, 1.160880294033814, 1.1614896912813661, 1.1620995050508856, 1.162709735659664, 1.1633203834252497, 1.1639314486654477, 1.1645429316983196, 1.1651548328421846, 1.1657671524156195, 1.1663798907374587, 1.166993048126795, 1.1676066249029782, 1.1682206213856166, 1.1688350378945787, 1.16944987474999, 1.1700651322722353, 1.1706808107819593, 1.1712969106000657, 1.1719134320477183, 1.1725303754463394, 1.173147741117613, 1.1737655293834823, 1.1743837405661521, 1.1750023749880871, 1.175621432972013, 1.176240914840917, 1.1768608209180476, 1.1774811515269141, 1.1781019069912897, 1.178723087635207, 1.1793446937829637, 1.1799667257591173, 1.18058918388849, 1.1812120684961664, 1.181835379907493, 1.1824591184480817, 1.1830832844438066, 1.183707878220807, 1.184332900105484, 1.1849583504245054, 1.185584229504802, 1.186210537673569, 1.1868372752582688, 1.187464442586626, 1.188092039986633, 1.1887200677865462, 1.1893485263148886, 1.1899774159004497, 1.1906067368722837, 1.1912364895597127, 1.1918666742923256, 1.192497291399977, 1.1931283412127898, 1.1937598240611542, 1.1943917402757267, 1.1950240901874343, 1.1956568741274693, 1.196290092427294, 1.1969237454186383, 1.1975578334335015, 1.1981923568041517, 1.1988273158631264, 1.1994627109432316, 1.2000985423775443, 1.2007348104994107, 1.2013715156424465, 1.202008658140539, 1.2026462383278447, 1.2032842565387927, 1.2039227131080812, 1.2045616083706812, 1.2052009426618342, 1.2058407163170533, 1.2064809296721242, 1.2071215830631044, 1.207762676826324, 1.2084042112983862, 1.2090461868161655, 1.2096886037168104, 1.2103314623377437, 1.2109747630166603, 1.2116185060915292, 1.2122626919005939, 1.212907320782371, 1.2135523930756538, 1.2141979091195076, 1.2148438692532741, 1.2154902738165707, 1.2161371231492886, 1.2167844175915958, 1.2174321574839355, 1.2180803431670286, 1.218728974981869, 1.2193780532697305, 1.2200275783721615, 1.220677550630989, 1.2213279703883164, 1.2219788379865244, 1.2226301537682722, 1.2232819180764953, 1.2239341312544099, 1.2245867936455086, 1.2252399055935634, 1.2258934674426252, 1.2265474795370233, 1.2272019422213676, 1.2278568558405474, 1.22851222073973, 1.2291680372643659, 1.2298243057601828, 1.2304810265731907, 1.2311382000496804, 1.231795826536222, 1.2324539063796704, 1.2331124399271571, 1.2337714275261, 1.2344308695241957, 1.2350907662694246, 1.235751118110049, 1.2364119253946138, 1.2370731884719472, 1.2377349076911606, 1.2383970834016476, 1.2390597159530876, 1.2397228056954412, 1.2403863529789558, 1.2410503581541608, 1.241714821571872, 1.2423797435831887, 1.2430451245394962, 1.243710964792464, 1.2443772646940492, 1.2450440245964918, 1.24571124485232, 1.2463789258143476, 1.247047067835675, 1.2477156712696886, 1.2483847364700635, 1.249054263790761, 1.2497242535860282, 1.250394706210403, 1.2510656220187093, 1.2517370013660598, 1.252408844607856, 1.2530811520997864, 1.2537539241978315, 1.2544271612582572, 1.255100863637622, 1.2557750316927725, 1.256449665780845, 1.2571247662592673, 1.2578003334857557, 1.2584763678183197, 1.2591528696152565, 1.2598298392351572, 1.2605072770369028, 1.2611851833796661, 1.261863558622912, 1.262542403126398, 1.2632217172501727, 1.2639015013545782, 1.2645817558002495, 1.2652624809481146, 1.265943677159394, 1.2666253447956028, 1.26730748421855, 1.267990095790338, 1.2686731798733637, 1.2693567368303187, 1.2700407670241898, 1.270725270818259, 1.2714102485761025, 1.2720957006615923, 1.272781627438897, 1.273468029272482, 1.2741549065271067, 1.2748422595678288, 1.275530088760002, 1.2762183944692786, 1.2769071770616056, 1.2775964369032302, 1.2782861743606952, 1.2789763898008444, 1.2796670835908157, 1.280358256098049, 1.2810499076902828, 1.2817420387355534, 1.2824346496021963, 1.2831277406588482, 1.2838213122744437, 1.2845153648182193, 1.2852098986597111, 1.2859049141687542, 1.2866004117154883, 1.2872963916703506, 1.2879928544040815, 1.2886898002877218, 1.2893872296926163, 1.2900851429904092, 1.29078354055305, 1.2914824227527877, 1.292181789962177, 1.292881642554074, 1.293581980901639, 1.2942828053783353, 1.294984116357931, 1.2956859142144974, 1.2963881993224116, 1.2970909720563535, 1.29779423279131, 1.298497981902571, 1.299202219765734, 1.2999069467567013, 1.3006121632516805, 1.301317869627186, 1.3020240662600395, 1.3027307535273684, 1.3034379318066074, 1.3041456014754977, 1.3048537629120907, 1.3055624164947421, 1.3062715626021177, 1.306981201613191, 1.3076913339072447, 1.3084019598638699, 1.3091130798629662, 1.3098246942847434, 1.310536803509721, 1.311249407918727, 1.3119625078929014, 1.3126761038136938, 1.3133901960628636, 1.314104785022483, 1.3148198710749333, 1.3155354546029085, 1.316251535989415, 1.3169681156177686, 1.3176851938716, 1.3184027711348512, 1.319120847791777, 1.3198394242269458, 1.3205585008252385, 1.32127807797185, 1.3219981560522884, 1.3227187354523773, 1.3234398165582535, 1.3241613997563682, 1.3248834854334883, 1.3256060739766957, 1.3263291657733876, 1.3270527612112766, 1.3277768606783915, 1.3285014645630773, 1.3292265732539956, 1.3299521871401248, 1.3306783066107597, 1.3314049320555128, 1.3321320638643146, 1.332859702427413, 1.3335878481353733, 1.334316501379081, 1.3350456625497382, 1.335775332038867, 1.336505510238309, 1.337236197540224, 1.3379673943370927, 1.3386991010217146, 1.3394313179872113, 1.3401640456270227, 1.3408972843349105, 1.3416310345049585, 1.3423652965315698, 1.3431000708094707, 1.3438353577337088, 1.3445711576996537, 1.3453074711029978, 1.3460442983397554, 1.346781639806265, 1.3475194958991878, 1.3482578670155076, 1.348996753552533, 1.349736155907897, 1.3504760744795559, 1.351216509665791, 1.351957461865209, 1.3526989314767413, 1.3534409188996437, 1.3541834245335, 1.3549264487782182, 1.3556699920340332, 1.3564140547015058, 1.357158637181525, 1.3579037398753058, 1.3586493631843903, 1.3593955075106487, 1.3601421732562797, 1.3608893608238093, 1.3616370706160923, 1.3623853030363122, 1.3631340584879814, 1.3638833373749422, 1.3646331401013656, 1.3653834670717535, 1.366134318690937, 1.3668856953640776, 1.3676375974966684, 1.368390025494533, 1.3691429797638255, 1.369896460711033, 1.3706504687429732, 1.371405004266797, 1.3721600676899863, 1.3729156594203569, 1.373671779866057, 1.3744284294355675, 1.3751856085377043, 1.3759433175816156, 1.376701556976784, 1.3774603271330272, 1.3782196284604973, 1.3789794613696806, 1.3797398262713987, 1.3805007235768096, 1.3812621536974066, 1.3820241170450187, 1.3827866140318115, 1.383549645070287, 1.3843132105732854, 1.385077310953982, 1.3858419466258907, 1.3866071180028634, 1.3873728254990896, 1.3881390695290974, 1.3889058505077536, 1.3896731688502628, 1.3904410249721706, 1.3912094192893607, 1.3919783522180575, 1.3927478241748248, 1.3935178355765667, 1.394288386840529, 1.3950594783842962, 1.3958311106257968, 1.3966032839832991, 1.3973759988754126, 1.398149255721091, 1.3989230549396283, 1.3996973969506628, 1.4004722821741744, 1.4012477110304868, 1.4020236839402673, 1.4028002013245273, 1.4035772636046218, 1.4043548712022502, 1.4051330245394564, 1.4059117240386305, 1.4066909701225068, 1.4074707632141648, 1.408251103737031, 1.409031992114877, 1.4098134287718223, 1.4105954141323316, 1.4113779486212168, 1.4121610326636385, 1.412944666685103, 1.4137288511114665, 1.4145135863689313, 1.4152988728840505, 1.416084711083724, 1.416871101395202, 1.417658044246084, 1.4184455400643181, 1.4192335892782035, 1.4200221923163898, 1.4208113496078763, 1.4216010615820138, 1.422391328668504, 1.4231821512974006, 1.4239735298991079, 1.4247654649043833, 1.425557956744337, 1.4263510058504298, 1.4271446126544778, 1.4279387775886492, 1.4287335010854654, 1.4295287835778028, 1.430324625498891, 1.4311210272823145, 1.4319179893620124, 1.4327155121722785, 1.4335135961477632, 1.4343122417234713, 1.4351114493347639, 1.4359112194173587, 1.4367115524073295, 1.437512448741107, 1.43831390885548, 1.4391159331875933, 1.4399185221749506, 1.4407216762554131, 1.441525395867201, 1.4423296814488924, 1.4431345334394243, 1.4439399522780947, 1.4447459384045591, 1.4455524922588339, 1.4463596142812951, 1.4471673049126805, 1.4479755645940873, 1.4487843937669744, 1.4495937928731635, 1.450403762354835, 1.451214302654533, 1.4520254142151656, 1.452837097480001, 1.4536493528926708, 1.4544621808971716, 1.455275581937862, 1.4560895564594643, 1.4569041049070657, 1.4577192277261177, 1.4585349253624378, 1.4593511982622058, 1.4601680468719702, 1.460985471638643, 1.461803473009503, 1.4626220514321957, 1.4634412073547325, 1.4642609412254919, 1.465081253493221, 1.4659021446070326, 1.4667236150164087, 1.4675456651711987, 1.4683682955216222, 1.4691915065182648, 1.4700152986120842, 1.4708396722544061, 1.471664627896926, 1.4724901659917098, 1.473316286991194, 1.4741429913481854, 1.4749702795158615, 1.4757981519477725, 1.4766266090978397, 1.4774556514203554, 1.4782852793699859, 1.4791154934017687, 1.4799462939711143, 1.480777681533808, 1.481609656546007, 1.4824422194642437, 1.4832753707454231, 1.4841091108468267, 1.484943440226109, 1.485778359341301, 1.4866138686508086, 1.4874499686134142, 1.4882866596882742, 1.489123942334924, 1.489961817013275, 1.490800284183615, 1.4916393443066092, 1.4924789978433017, 1.4933192452551134, 1.494160087003844, 1.4950015235516727, 1.495843555361156, 1.496686182895231, 1.497529406617214, 1.4983732269908017, 1.4992176444800704, 1.5000626595494782, 1.5009082726638616, 1.5017544842884418, 1.5026012948888188, 1.5034487049309762, 1.5042967148812794, 1.5051453252064757, 1.5059945363736957, 1.506844348850453, 1.5076947631046465, 1.508545779604556, 1.509397398818847, 1.5102496212165704, 1.51110244726716, 1.5119558774404362, 1.5128099122066048, 1.5136645520362568, 1.514519797400369, 1.5153756487703065, 1.5162321066178193, 1.5170891714150454, 1.5179468436345094, 1.5188051237491256, 1.5196640122321945, 1.5205235095574057, 1.5213836161988374, 1.5222443326309583, 1.5231056593286239, 1.5239675967670816, 1.5248301454219686, 1.5256933057693114, 1.5265570782855284, 1.5274214634474288, 1.5282864617322132, 1.5291520736174737, 1.5300182995811953, 1.5308851401017536, 1.5317525956579192, 1.5326206667288544, 1.5334893537941157, 1.5343586573336525, 1.5352285778278083, 1.536099115757323, 1.5369702716033282, 1.5378420458473527, 1.5387144389713208, 1.5395874514575507, 1.540461083788759, 1.541335336448058, 1.5422102099189547, 1.5430857046853568, 1.5439618212315669, 1.544838560042286, 1.5457159216026144, 1.5465939063980483, 1.547472514914485, 1.5483517476382203, 1.5492316050559496, 1.5501120876547676, 1.5509931959221688, 1.5518749303460502, 1.5527572914147074, 1.5536402796168387, 1.5545238954415428, 1.5554081393783208, 1.5562930119170768, 1.5571785135481155, 1.558064644762147, 1.558951406050282, 1.5598387979040367, 1.5607268208153309, 1.5616154752764873, 1.562504761780235, 1.5633946808197074, 1.5642852328884433, 1.5651764184803865, 1.566068238089887, 1.5669606922117016, 1.5678537813409945, 1.5687475059733342, 1.5696418666046996, 1.5705368637314754, 1.571432497850456, 1.5723287694588424, 1.5732256790542447, 1.5741232271346839, 1.5750214141985874, 1.575920240744796, 1.5768197072725578, 1.577719814281532, 1.57862056227179, 1.5795219517438128, 1.5804239831984934, 1.5813266571371372, 1.5822299740614612, 1.5831339344735955, 1.5840385388760827, 1.5849437877718795, 1.5858496816643548, 1.5867562210572932, 1.587663406454892, 1.5885712383617645, 1.5894797172829385, 1.5903888437238576, 1.59129861819038, 1.5922090411887824, 1.5931201132257542, 1.594031834808406, 1.5949442064442625, 1.5958572286412667, 1.59677090190778, 1.5976852267525812, 1.598600203684869, 1.5995158332142605, 1.6004321158507904, 1.6013490521049156, 1.6022666424875118, 1.6031848875098758, 1.6041037876837234, 1.6050233435211938, 1.605943555534846, 1.6068644242376613, 1.6077859501430436, 1.6087081337648192, 1.6096309756172362, 1.6105544762149675, 1.6114786360731088, 1.6124034557071802, 1.6133289356331257, 1.6142550763673136, 1.6151818784265384, 1.6161093423280195, 1.6170374685894016, 1.6179662577287566, 1.6188957102645813, 1.619825826715801, 1.6207566076017677, 1.6216880534422606, 1.622620164757487, 1.6235529420680825, 1.6244863858951126, 1.6254204967600694, 1.6263552751848764, 1.6272907216918866, 1.6282268368038824, 1.6291636210440774, 1.630101074936116, 1.6310391990040736, 1.6319779937724566, 1.632917459766205, 1.6338575975106897, 1.6347984075317155, 1.6357398903555194, 1.6366820465087715, 1.6376248765185772, 1.6385683809124743, 1.6395125602184373, 1.6404574149648739, 1.6414029456806274, 1.642349152894977, 1.6432960371376384, 1.6442435989387625, 1.645191838828939, 1.6461407573391929, 1.6470903550009868, 1.648040632346223, 1.6489915899072394, 1.6499432282168154, 1.6508955478081675, 1.6518485492149522, 1.6528022329712655, 1.6537565996116437, 1.6547116496710639, 1.6556673836849438, 1.6566238021891424, 1.6575809057199613, 1.658538694814142, 1.65949717000887, 1.6604563318417742, 1.661416180850924, 1.6623767175748356, 1.6633379425524666, 1.66429985632322, 1.6652624594269432, 1.6662257524039288, 1.6671897357949155, 1.668154410141086, 1.6691197759840706, 1.6700858338659463, 1.671052584329236, 1.6720200279169108, 1.6729881651723895, 1.673956996639538, 1.6749265228626715, 1.6758967443865547, 1.6768676617563998, 1.6778392755178706, 1.6788115862170787, 1.6797845944005882, 1.6807583006154128, 1.6817327054090174, 1.682707809329319, 1.6836836129246857, 1.684660116743939, 1.6856373213363516, 1.6866152272516515, 1.6875938350400173, 1.6885731452520838, 1.6895531584389392, 1.6905338751521257, 1.6915152959436424, 1.6924974213659414, 1.693480251971932, 1.6944637883149798, 1.695448030948906, 1.6964329804279896, 1.6974186373069675, 1.6984050021410322, 1.6993920754858363, 1.7003798578974898, 1.701368349932563, 1.7023575521480838, 1.7033474651015408, 1.7043380893508828, 1.705329425454518, 1.7063214739713164, 1.70731423546061, 1.7083077104821898, 1.7093018995963118, 1.7102968033636925, 1.7112924223455124, 1.7122887571034149, 1.7132858081995064, 1.7142835761963577, 1.7152820616570046, 1.716281265144947, 1.7172811872241505, 1.718281828459045]} \ No newline at end of file diff --git a/lib/node_modules/@stdlib/math/base/special/expm1rel/test/fixtures/python/tiny.json b/lib/node_modules/@stdlib/math/base/special/expm1rel/test/fixtures/python/tiny.json new file mode 100644 index 000000000000..298c112fdcea --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expm1rel/test/fixtures/python/tiny.json @@ -0,0 +1 @@ +{"x": [-5.551115123125783e-17, -5.5400017795359415e-17, -5.5288884359461e-17, -5.5177750923562586e-17, -5.506661748766417e-17, -5.4955484051765757e-17, -5.4844350615867345e-17, -5.473321717996893e-17, -5.4622083744070516e-17, -5.45109503081721e-17, -5.4399816872273687e-17, -5.4288683436375275e-17, -5.417755000047686e-17, -5.4066416564578446e-17, -5.395528312868003e-17, -5.3844149692781617e-17, -5.3733016256883205e-17, -5.362188282098479e-17, -5.3510749385086376e-17, -5.339961594918796e-17, -5.3288482513289546e-17, -5.3177349077391135e-17, -5.306621564149272e-17, -5.2955082205594306e-17, -5.284394876969589e-17, -5.2732815333797476e-17, -5.262168189789906e-17, -5.251054846200065e-17, -5.2399415026102235e-17, -5.228828159020382e-17, -5.2177148154305406e-17, -5.206601471840699e-17, -5.1954881282508577e-17, -5.1843747846610165e-17, -5.173261441071175e-17, -5.1621480974813336e-17, -5.151034753891492e-17, -5.1399214103016507e-17, -5.128808066711809e-17, -5.117694723121968e-17, -5.1065813795321266e-17, -5.095468035942285e-17, -5.0843546923524437e-17, -5.073241348762602e-17, -5.062128005172761e-17, -5.0510146615829196e-17, -5.039901317993078e-17, -5.0287879744032366e-17, -5.017674630813395e-17, -5.006561287223554e-17, -4.9954479436337126e-17, -4.984334600043871e-17, -4.9732212564540296e-17, -4.962107912864188e-17, -4.950994569274347e-17, -4.9398812256845055e-17, -4.928767882094664e-17, -4.9176545385048226e-17, -4.906541194914981e-17, -4.8954278513251397e-17, -4.8843145077352985e-17, -4.873201164145457e-17, -4.8620878205556156e-17, -4.850974476965774e-17, -4.8398611333759327e-17, -4.8287477897860915e-17, -4.81763444619625e-17, -4.8065211026064086e-17, -4.795407759016567e-17, -4.7842944154267257e-17, -4.7731810718368845e-17, -4.762067728247043e-17, -4.7509543846572016e-17, -4.73984104106736e-17, -4.7287276974775186e-17, -4.7176143538876775e-17, -4.706501010297836e-17, -4.6953876667079946e-17, -4.684274323118153e-17, -4.6731609795283116e-17, -4.6620476359384705e-17, -4.650934292348629e-17, -4.6398209487587875e-17, -4.628707605168946e-17, -4.6175942615791046e-17, -4.6064809179892635e-17, -4.5953675743994217e-17, -4.5842542308095805e-17, -4.573140887219739e-17, -4.5620275436298976e-17, -4.5509142000400564e-17, -4.5398008564502147e-17, -4.528687512860373e-17, -4.517574169270532e-17, -4.5064608256806906e-17, -4.4953474820908494e-17, -4.4842341385010077e-17, -4.473120794911166e-17, -4.462007451321325e-17, -4.4508941077314836e-17, -4.4397807641416424e-17, -4.4286674205518006e-17, -4.417554076961959e-17, -4.406440733372118e-17, -4.3953273897822766e-17, -4.384214046192435e-17, -4.3731007026025936e-17, -4.361987359012752e-17, -4.350874015422911e-17, -4.3397606718330695e-17, -4.328647328243228e-17, -4.3175339846533866e-17, -4.306420641063545e-17, -4.2953072974737037e-17, -4.2841939538838625e-17, -4.273080610294021e-17, -4.2619672667041796e-17, -4.250853923114338e-17, -4.2397405795244967e-17, -4.2286272359346555e-17, -4.217513892344814e-17, -4.2064005487549726e-17, -4.195287205165131e-17, -4.1841738615752897e-17, -4.1730605179854485e-17, -4.161947174395607e-17, -4.1508338308057656e-17, -4.139720487215924e-17, -4.1286071436260826e-17, -4.1174938000362415e-17, -4.1063804564464e-17, -4.0952671128565586e-17, -4.084153769266717e-17, -4.0730404256768756e-17, -4.0619270820870345e-17, -4.050813738497193e-17, -4.0397003949073515e-17, -4.02858705131751e-17, -4.0174737077276686e-17, -4.0063603641378275e-17, -3.9952470205479857e-17, -3.984133676958144e-17, -3.973020333368303e-17, -3.9619069897784616e-17, -3.9507936461886204e-17, -3.9396803025987787e-17, -3.928566959008937e-17, -3.917453615419096e-17, -3.9063402718292546e-17, -3.8952269282394134e-17, -3.8841135846495717e-17, -3.87300024105973e-17, -3.861886897469889e-17, -3.8507735538800476e-17, -3.8396602102902064e-17, -3.8285468667003646e-17, -3.817433523110523e-17, -3.806320179520682e-17, -3.7952068359308406e-17, -3.7840934923409994e-17, -3.7729801487511576e-17, -3.761866805161316e-17, -3.750753461571475e-17, -3.7396401179816335e-17, -3.7285267743917924e-17, -3.7174134308019506e-17, -3.706300087212109e-17, -3.6951867436222677e-17, -3.6840734000324265e-17, -3.6729600564425854e-17, -3.6618467128527436e-17, -3.650733369262902e-17, -3.6396200256730607e-17, -3.6285066820832195e-17, -3.6173933384933784e-17, -3.6062799949035366e-17, -3.595166651313695e-17, -3.5840533077238537e-17, -3.5729399641340125e-17, -3.5618266205441713e-17, -3.5507132769543296e-17, -3.539599933364488e-17, -3.5284865897746466e-17, -3.5173732461848055e-17, -3.506259902594964e-17, -3.4951465590051226e-17, -3.484033215415281e-17, -3.4729198718254396e-17, -3.4618065282355985e-17, -3.450693184645757e-17, -3.4395798410559155e-17, -3.428466497466074e-17, -3.4173531538762326e-17, -3.4062398102863915e-17, -3.3951264666965497e-17, -3.3840131231067085e-17, -3.372899779516867e-17, -3.3617864359270256e-17, -3.3506730923371844e-17, -3.3395597487473427e-17, -3.3284464051575015e-17, -3.31733306156766e-17, -3.3062197179778186e-17, -3.2951063743879774e-17, -3.2839930307981357e-17, -3.272879687208294e-17, -3.261766343618453e-17, -3.2506530000286116e-17, -3.2395396564387704e-17, -3.2284263128489286e-17, -3.217312969259087e-17, -3.206199625669246e-17, -3.1950862820794046e-17, -3.1839729384895634e-17, -3.1728595948997216e-17, -3.16174625130988e-17, -3.150632907720039e-17, -3.1395195641301975e-17, -3.1284062205403564e-17, -3.1172928769505146e-17, -3.106179533360673e-17, -3.0950661897708317e-17, -3.0839528461809905e-17, -3.0728395025911494e-17, -3.0617261590013076e-17, -3.050612815411466e-17, -3.0394994718216247e-17, -3.0283861282317835e-17, -3.0172727846419424e-17, -3.0061594410521006e-17, -2.995046097462259e-17, -2.9839327538724177e-17, -2.9728194102825765e-17, -2.9617060666927353e-17, -2.9505927231028936e-17, -2.939479379513052e-17, -2.9283660359232106e-17, -2.9172526923333695e-17, -2.9061393487435283e-17, -2.8950260051536866e-17, -2.883912661563845e-17, -2.8727993179740036e-17, -2.8616859743841625e-17, -2.8505726307943213e-17, -2.8394592872044795e-17, -2.828345943614638e-17, -2.8172326000247966e-17, -2.8061192564349555e-17, -2.7950059128451137e-17, -2.7838925692552725e-17, -2.7727792256654308e-17, -2.7616658820755896e-17, -2.7505525384857484e-17, -2.7394391948959067e-17, -2.7283258513060655e-17, -2.7172125077162237e-17, -2.7060991641263826e-17, -2.6949858205365414e-17, -2.6838724769466997e-17, -2.6727591333568585e-17, -2.6616457897670167e-17, -2.6505324461771756e-17, -2.6394191025873344e-17, -2.6283057589974926e-17, -2.6171924154076515e-17, -2.6060790718178097e-17, -2.5949657282279686e-17, -2.5838523846381274e-17, -2.5727390410482856e-17, -2.5616256974584445e-17, -2.5505123538686027e-17, -2.5393990102787615e-17, -2.5282856666889204e-17, -2.5171723230990786e-17, -2.5060589795092375e-17, -2.4949456359193957e-17, -2.4838322923295545e-17, -2.4727189487397128e-17, -2.4616056051498716e-17, -2.4504922615600304e-17, -2.4393789179701887e-17, -2.4282655743803475e-17, -2.4171522307905057e-17, -2.4060388872006646e-17, -2.3949255436108234e-17, -2.3838122000209817e-17, -2.3726988564311405e-17, -2.3615855128412987e-17, -2.3504721692514576e-17, -2.3393588256616164e-17, -2.3282454820717746e-17, -2.3171321384819335e-17, -2.3060187948920917e-17, -2.2949054513022506e-17, -2.2837921077124094e-17, -2.2726787641225676e-17, -2.2615654205327265e-17, -2.2504520769428847e-17, -2.2393387333530435e-17, -2.2282253897632024e-17, -2.2171120461733606e-17, -2.2059987025835195e-17, -2.1948853589936777e-17, -2.1837720154038365e-17, -2.1726586718139948e-17, -2.1615453282241536e-17, -2.1504319846343124e-17, -2.1393186410444707e-17, -2.1282052974546295e-17, -2.1170919538647877e-17, -2.1059786102749466e-17, -2.0948652666851054e-17, -2.0837519230952637e-17, -2.0726385795054225e-17, -2.0615252359155807e-17, -2.0504118923257396e-17, -2.0392985487358984e-17, -2.0281852051460566e-17, -2.0170718615562155e-17, -2.0059585179663737e-17, -1.9948451743765326e-17, -1.9837318307866914e-17, -1.9726184871968496e-17, -1.9615051436070085e-17, -1.9503918000171667e-17, -1.9392784564273255e-17, -1.9281651128374844e-17, -1.9170517692476426e-17, -1.9059384256578015e-17, -1.8948250820679597e-17, -1.8837117384781185e-17, -1.8725983948882774e-17, -1.8614850512984356e-17, -1.8503717077085944e-17, -1.8392583641187527e-17, -1.8281450205289115e-17, -1.8170316769390704e-17, -1.8059183333492286e-17, -1.7948049897593874e-17, -1.7836916461695457e-17, -1.7725783025797045e-17, -1.7614649589898627e-17, -1.7503516154000216e-17, -1.7392382718101804e-17, -1.7281249282203386e-17, -1.7170115846304975e-17, -1.7058982410406557e-17, -1.6947848974508146e-17, -1.6836715538609734e-17, -1.6725582102711316e-17, -1.6614448666812905e-17, -1.6503315230914487e-17, -1.6392181795016075e-17, -1.6281048359117664e-17, -1.6169914923219246e-17, -1.6058781487320835e-17, -1.5947648051422417e-17, -1.5836514615524005e-17, -1.5725381179625594e-17, -1.5614247743727176e-17, -1.5503114307828764e-17, -1.5391980871930347e-17, -1.5280847436031935e-17, -1.5169714000133524e-17, -1.5058580564235106e-17, -1.4947447128336694e-17, -1.4836313692438277e-17, -1.4725180256539865e-17, -1.4614046820641447e-17, -1.4502913384743036e-17, -1.4391779948844624e-17, -1.4280646512946206e-17, -1.4169513077047795e-17, -1.4058379641149377e-17, -1.3947246205250966e-17, -1.3836112769352554e-17, -1.3724979333454136e-17, -1.3613845897555725e-17, -1.3502712461657307e-17, -1.3391579025758895e-17, -1.3280445589860484e-17, -1.3169312153962066e-17, -1.3058178718063655e-17, -1.2947045282165237e-17, -1.2835911846266825e-17, -1.2724778410368414e-17, -1.2613644974469996e-17, -1.2502511538571584e-17, -1.2391378102673167e-17, -1.2280244666774755e-17, -1.2169111230876344e-17, -1.2057977794977926e-17, -1.1946844359079514e-17, -1.1835710923181097e-17, -1.1724577487282685e-17, -1.1613444051384273e-17, -1.1502310615485856e-17, -1.1391177179587444e-17, -1.1280043743689026e-17, -1.1168910307790615e-17, -1.1057776871892203e-17, -1.0946643435993786e-17, -1.0835510000095374e-17, -1.0724376564196956e-17, -1.0613243128298545e-17, -1.0502109692400127e-17, -1.0390976256501715e-17, -1.0279842820603304e-17, -1.0168709384704886e-17, -1.0057575948806475e-17, -9.946442512908057e-18, -9.835309077009645e-18, -9.724175641111234e-18, -9.613042205212816e-18, -9.501908769314404e-18, -9.390775333415987e-18, -9.279641897517575e-18, -9.168508461619164e-18, -9.057375025720746e-18, -8.946241589822334e-18, -8.835108153923917e-18, -8.723974718025505e-18, -8.612841282127093e-18, -8.501707846228676e-18, -8.390574410330264e-18, -8.279440974431846e-18, -8.168307538533435e-18, -8.057174102635023e-18, -7.946040666736606e-18, -7.834907230838194e-18, -7.723773794939776e-18, -7.612640359041365e-18, -7.501506923142947e-18, -7.390373487244535e-18, -7.279240051346124e-18, -7.168106615447706e-18, -7.056973179549295e-18, -6.945839743650877e-18, -6.834706307752465e-18, -6.723572871854054e-18, -6.612439435955636e-18, -6.501306000057224e-18, -6.390172564158807e-18, -6.279039128260395e-18, -6.1679056923619835e-18, -6.056772256463566e-18, -5.945638820565154e-18, -5.8345053846667365e-18, -5.723371948768325e-18, -5.612238512869913e-18, -5.501105076971496e-18, -5.389971641073084e-18, -5.278838205174666e-18, -5.167704769276255e-18, -5.056571333377843e-18, -4.9454378974794255e-18, -4.834304461581014e-18, -4.723171025682596e-18, -4.612037589784185e-18, -4.500904153885773e-18, -4.389770717987355e-18, -4.278637282088944e-18, -4.167503846190526e-18, -4.0563704102921145e-18, -3.945236974393703e-18, -3.834103538495285e-18, -3.722970102596874e-18, -3.611836666698456e-18, -3.500703230800044e-18, -3.3895697949016266e-18, -3.278436359003215e-18, -3.1673029231048035e-18, -3.0561694872063858e-18, -2.9450360513079742e-18, -2.8339026154095565e-18, -2.722769179511145e-18, -2.6116357436127334e-18, -2.5005023077143156e-18, -2.389368871815904e-18, -2.2782354359174864e-18, -2.1671020000190748e-18, -2.0559685641206632e-18, -1.9448351282222455e-18, -1.833701692323834e-18, -1.7225682564254162e-18, -1.6114348205270046e-18, -1.500301384628593e-18, -1.3891679487301754e-18, -1.2780345128317638e-18, -1.166901076933346e-18, -1.0557676410349345e-18, -9.44634205136523e-19, -8.335007692381052e-19, -7.2236733333969365e-19, -6.112338974412759e-19, -5.001004615428644e-19, -3.8896702564444664e-19, -2.7783358974603507e-19, -1.667001538476235e-19, -5.556671794920578e-20, 5.556671794921194e-20, 1.667001538476235e-19, 2.7783358974603507e-19, 3.8896702564444664e-19, 5.001004615428582e-19, 6.112338974412821e-19, 7.2236733333969365e-19, 8.335007692381052e-19, 9.446342051365168e-19, 1.0557676410349283e-18, 1.1669010769333522e-18, 1.2780345128317638e-18, 1.3891679487301754e-18, 1.500301384628587e-18, 1.6114348205269985e-18, 1.7225682564254224e-18, 1.833701692323834e-18, 1.9448351282222455e-18, 2.055968564120657e-18, 2.1671020000190686e-18, 2.2782354359174925e-18, 2.389368871815904e-18, 2.5005023077143156e-18, 2.6116357436127272e-18, 2.7227691795111388e-18, 2.8339026154095627e-18, 2.9450360513079742e-18, 3.0561694872063858e-18, 3.1673029231047974e-18, 3.278436359003209e-18, 3.3895697949016328e-18, 3.500703230800044e-18, 3.611836666698456e-18, 3.7229701025968675e-18, 3.834103538495279e-18, 3.945236974393703e-18, 4.0563704102921145e-18, 4.167503846190526e-18, 4.278637282088938e-18, 4.389770717987349e-18, 4.500904153885773e-18, 4.612037589784185e-18, 4.723171025682596e-18, 4.834304461581008e-18, 4.945437897479419e-18, 5.056571333377843e-18, 5.167704769276255e-18, 5.278838205174666e-18, 5.389971641073078e-18, 5.501105076971502e-18, 5.612238512869913e-18, 5.723371948768325e-18, 5.8345053846667365e-18, 5.945638820565148e-18, 6.056772256463572e-18, 6.1679056923619835e-18, 6.279039128260395e-18, 6.390172564158807e-18, 6.501306000057218e-18, 6.612439435955642e-18, 6.723572871854054e-18, 6.834706307752465e-18, 6.945839743650877e-18, 7.056973179549288e-18, 7.168106615447712e-18, 7.279240051346124e-18, 7.390373487244535e-18, 7.501506923142947e-18, 7.612640359041358e-18, 7.723773794939782e-18, 7.834907230838194e-18, 7.946040666736606e-18, 8.057174102635017e-18, 8.168307538533429e-18, 8.279440974431853e-18, 8.390574410330264e-18, 8.501707846228676e-18, 8.612841282127087e-18, 8.723974718025499e-18, 8.835108153923923e-18, 8.946241589822334e-18, 9.057375025720746e-18, 9.168508461619157e-18, 9.279641897517569e-18, 9.390775333415993e-18, 9.501908769314404e-18, 9.613042205212816e-18, 9.724175641111228e-18, 9.835309077009639e-18, 9.946442512908063e-18, 1.0057575948806475e-17, 1.0168709384704886e-17, 1.0279842820603298e-17, 1.0390976256501709e-17, 1.0502109692400133e-17, 1.0613243128298545e-17, 1.0724376564196956e-17, 1.0835510000095368e-17, 1.094664343599378e-17, 1.1057776871892203e-17, 1.1168910307790615e-17, 1.1280043743689026e-17, 1.1391177179587438e-17, 1.150231061548585e-17, 1.1613444051384273e-17, 1.1724577487282685e-17, 1.1835710923181097e-17, 1.1946844359079508e-17, 1.2057977794977932e-17, 1.2169111230876344e-17, 1.2280244666774755e-17, 1.2391378102673167e-17, 1.2502511538571578e-17, 1.2613644974470002e-17, 1.2724778410368414e-17, 1.2835911846266825e-17, 1.2947045282165237e-17, 1.3058178718063648e-17, 1.3169312153962072e-17, 1.3280445589860484e-17, 1.3391579025758895e-17, 1.3502712461657307e-17, 1.3613845897555719e-17, 1.3724979333454142e-17, 1.3836112769352554e-17, 1.3947246205250966e-17, 1.4058379641149377e-17, 1.416951307704779e-17, 1.4280646512946213e-17, 1.4391779948844624e-17, 1.4502913384743036e-17, 1.4614046820641447e-17, 1.472518025653986e-17, 1.4836313692438283e-17, 1.4947447128336694e-17, 1.5058580564235106e-17, 1.5169714000133517e-17, 1.528084743603193e-17, 1.5391980871930353e-17, 1.5503114307828764e-17, 1.5614247743727176e-17, 1.5725381179625588e-17, 1.5836514615524e-17, 1.5947648051422423e-17, 1.6058781487320835e-17, 1.6169914923219246e-17, 1.6281048359117658e-17, 1.639218179501607e-17, 1.6503315230914493e-17, 1.6614448666812905e-17, 1.6725582102711316e-17, 1.6836715538609728e-17, 1.694784897450814e-17, 1.7058982410406563e-17, 1.7170115846304975e-17, 1.7281249282203386e-17, 1.7392382718101798e-17, 1.750351615400021e-17, 1.7614649589898633e-17, 1.7725783025797045e-17, 1.7836916461695457e-17, 1.7948049897593868e-17, 1.805918333349228e-17, 1.8170316769390704e-17, 1.8281450205289115e-17, 1.8392583641187527e-17, 1.8503717077085938e-17, 1.861485051298435e-17, 1.8725983948882774e-17, 1.8837117384781185e-17, 1.8948250820679597e-17, 1.9059384256578008e-17, 1.917051769247642e-17, 1.9281651128374844e-17, 1.9392784564273255e-17, 1.9503918000171667e-17, 1.961505143607008e-17, 1.9726184871968502e-17, 1.9837318307866914e-17, 1.9948451743765326e-17, 2.0059585179663737e-17, 2.017071861556215e-17, 2.0281852051460573e-17, 2.0392985487358984e-17, 2.0504118923257396e-17, 2.0615252359155807e-17, 2.072638579505422e-17, 2.0837519230952643e-17, 2.0948652666851054e-17, 2.1059786102749466e-17, 2.1170919538647877e-17, 2.128205297454629e-17, 2.1393186410444713e-17, 2.1504319846343124e-17, 2.1615453282241536e-17, 2.1726586718139948e-17, 2.183772015403836e-17, 2.1948853589936783e-17, 2.2059987025835195e-17, 2.2171120461733606e-17, 2.2282253897632018e-17, 2.239338733353043e-17, 2.2504520769428853e-17, 2.2615654205327265e-17, 2.2726787641225676e-17, 2.2837921077124088e-17, 2.29490545130225e-17, 2.3060187948920923e-17, 2.3171321384819335e-17, 2.3282454820717746e-17, 2.3393588256616158e-17, 2.350472169251457e-17, 2.3615855128412993e-17, 2.3726988564311405e-17, 2.3838122000209817e-17, 2.3949255436108228e-17, 2.406038887200664e-17, 2.4171522307905064e-17, 2.4282655743803475e-17, 2.4393789179701887e-17, 2.4504922615600298e-17, 2.461605605149871e-17, 2.4727189487397134e-17, 2.4838322923295545e-17, 2.4949456359193957e-17, 2.5060589795092368e-17, 2.517172323099078e-17, 2.5282856666889204e-17, 2.5393990102787615e-17, 2.5505123538686027e-17, 2.561625697458444e-17, 2.572739041048285e-17, 2.5838523846381274e-17, 2.5949657282279686e-17, 2.6060790718178097e-17, 2.617192415407651e-17, 2.6283057589974933e-17, 2.6394191025873344e-17, 2.6505324461771756e-17, 2.6616457897670167e-17, 2.672759133356858e-17, 2.6838724769467003e-17, 2.6949858205365414e-17, 2.7060991641263826e-17, 2.7172125077162237e-17, 2.728325851306065e-17, 2.7394391948959073e-17, 2.7505525384857484e-17, 2.7616658820755896e-17, 2.7727792256654308e-17, 2.783892569255272e-17, 2.795005912845114e-17, 2.8061192564349555e-17, 2.8172326000247966e-17, 2.828345943614638e-17, 2.839459287204479e-17, 2.8505726307943213e-17, 2.8616859743841625e-17, 2.8727993179740036e-17, 2.883912661563845e-17, 2.895026005153686e-17, 2.9061393487435283e-17, 2.9172526923333695e-17, 2.9283660359232106e-17, 2.939479379513052e-17, 2.950592723102893e-17, 2.9617060666927353e-17, 2.9728194102825765e-17, 2.9839327538724177e-17, 2.995046097462259e-17, 3.0061594410521e-17, 3.0172727846419424e-17, 3.0283861282317835e-17, 3.0394994718216247e-17, 3.050612815411466e-17, 3.061726159001307e-17, 3.0728395025911494e-17, 3.0839528461809905e-17, 3.0950661897708317e-17, 3.106179533360673e-17, 3.117292876950514e-17, 3.1284062205403564e-17, 3.1395195641301975e-17, 3.150632907720039e-17, 3.16174625130988e-17, 3.172859594899721e-17, 3.1839729384895634e-17, 3.1950862820794046e-17, 3.206199625669246e-17, 3.217312969259087e-17, 3.228426312848928e-17, 3.2395396564387704e-17, 3.2506530000286116e-17, 3.261766343618453e-17, 3.272879687208294e-17, 3.283993030798135e-17, 3.2951063743879774e-17, 3.3062197179778186e-17, 3.31733306156766e-17, 3.328446405157501e-17, 3.339559748747342e-17, 3.3506730923371844e-17, 3.3617864359270256e-17, 3.372899779516867e-17, 3.384013123106708e-17, 3.39512646669655e-17, 3.4062398102863915e-17, 3.4173531538762326e-17, 3.428466497466074e-17, 3.439579841055915e-17, 3.4506931846457573e-17, 3.4618065282355985e-17, 3.4729198718254396e-17, 3.484033215415281e-17, 3.495146559005122e-17, 3.5062599025949643e-17, 3.5173732461848055e-17, 3.5284865897746466e-17, 3.539599933364488e-17, 3.550713276954329e-17, 3.5618266205441713e-17, 3.5729399641340125e-17, 3.5840533077238537e-17, 3.595166651313695e-17, 3.606279994903536e-17, 3.6173933384933784e-17, 3.6285066820832195e-17, 3.6396200256730607e-17, 3.650733369262902e-17, 3.661846712852743e-17, 3.6729600564425854e-17, 3.6840734000324265e-17, 3.6951867436222677e-17, 3.706300087212109e-17, 3.71741343080195e-17, 3.7285267743917924e-17, 3.7396401179816335e-17, 3.750753461571475e-17, 3.761866805161316e-17, 3.772980148751157e-17, 3.7840934923409994e-17, 3.7952068359308406e-17, 3.806320179520682e-17, 3.817433523110523e-17, 3.828546866700364e-17, 3.8396602102902064e-17, 3.8507735538800476e-17, 3.861886897469889e-17, 3.87300024105973e-17, 3.884113584649571e-17, 3.8952269282394134e-17, 3.9063402718292546e-17, 3.917453615419096e-17, 3.928566959008937e-17, 3.939680302598778e-17, 3.9507936461886204e-17, 3.9619069897784616e-17, 3.973020333368303e-17, 3.984133676958144e-17, 3.995247020547985e-17, 4.0063603641378275e-17, 4.0174737077276686e-17, 4.02858705131751e-17, 4.039700394907351e-17, 4.0508137384971933e-17, 4.0619270820870345e-17, 4.0730404256768756e-17, 4.084153769266717e-17, 4.095267112856558e-17, 4.1063804564464003e-17, 4.1174938000362415e-17, 4.1286071436260826e-17, 4.139720487215924e-17, 4.150833830805765e-17, 4.1619471743956073e-17, 4.1730605179854485e-17, 4.1841738615752897e-17, 4.195287205165131e-17, 4.206400548754972e-17, 4.2175138923448144e-17, 4.2286272359346555e-17, 4.2397405795244967e-17, 4.250853923114338e-17, 4.261967266704179e-17, 4.2730806102940214e-17, 4.2841939538838625e-17, 4.2953072974737037e-17, 4.306420641063545e-17, 4.317533984653386e-17, 4.3286473282432284e-17, 4.3397606718330695e-17, 4.350874015422911e-17, 4.361987359012752e-17, 4.373100702602593e-17, 4.3842140461924354e-17, 4.3953273897822766e-17, 4.406440733372118e-17, 4.417554076961959e-17, 4.4286674205518e-17, 4.4397807641416424e-17, 4.4508941077314836e-17, 4.462007451321325e-17, 4.473120794911166e-17, 4.484234138501007e-17, 4.4953474820908494e-17, 4.5064608256806906e-17, 4.517574169270532e-17, 4.528687512860373e-17, 4.539800856450214e-17, 4.5509142000400564e-17, 4.5620275436298976e-17, 4.573140887219739e-17, 4.58425423080958e-17, 4.595367574399421e-17, 4.6064809179892635e-17, 4.6175942615791046e-17, 4.628707605168946e-17, 4.639820948758787e-17, 4.650934292348628e-17, 4.6620476359384705e-17, 4.6731609795283116e-17, 4.684274323118153e-17, 4.695387666707994e-17, 4.706501010297835e-17, 4.7176143538876775e-17, 4.7287276974775186e-17, 4.73984104106736e-17, 4.750954384657201e-17, 4.762067728247042e-17, 4.7731810718368845e-17, 4.7842944154267257e-17, 4.795407759016567e-17, 4.806521102606408e-17, 4.8176344461962504e-17, 4.8287477897860915e-17, 4.8398611333759327e-17, 4.850974476965774e-17, 4.862087820555615e-17, 4.8732011641454574e-17, 4.8843145077352985e-17, 4.8954278513251397e-17, 4.906541194914981e-17, 4.917654538504822e-17, 4.9287678820946644e-17, 4.9398812256845055e-17, 4.950994569274347e-17, 4.962107912864188e-17, 4.973221256454029e-17, 4.9843346000438714e-17, 4.9954479436337126e-17, 5.006561287223554e-17, 5.017674630813395e-17, 5.028787974403236e-17, 5.0399013179930784e-17, 5.0510146615829196e-17, 5.062128005172761e-17, 5.073241348762602e-17, 5.084354692352443e-17, 5.0954680359422854e-17, 5.1065813795321266e-17, 5.117694723121968e-17, 5.128808066711809e-17, 5.13992141030165e-17, 5.1510347538914924e-17, 5.1621480974813336e-17, 5.173261441071175e-17, 5.184374784661016e-17, 5.195488128250857e-17, 5.2066014718406995e-17, 5.2177148154305406e-17, 5.228828159020382e-17, 5.239941502610223e-17, 5.251054846200064e-17, 5.2621681897899065e-17, 5.2732815333797476e-17, 5.284394876969589e-17, 5.29550822055943e-17, 5.306621564149271e-17, 5.3177349077391135e-17, 5.3288482513289546e-17, 5.339961594918796e-17, 5.351074938508637e-17, 5.362188282098478e-17, 5.3733016256883205e-17, 5.3844149692781617e-17, 5.395528312868003e-17, 5.406641656457844e-17, 5.417755000047685e-17, 5.4288683436375275e-17, 5.4399816872273687e-17, 5.45109503081721e-17, 5.462208374407051e-17, 5.4733217179968934e-17, 5.4844350615867345e-17, 5.4955484051765757e-17, 5.506661748766417e-17, 5.517775092356258e-17, 5.5288884359461004e-17, 5.5400017795359415e-17, 5.551115123125783e-17], "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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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]} \ No newline at end of file diff --git a/lib/node_modules/@stdlib/math/base/special/expm1rel/test/test.js b/lib/node_modules/@stdlib/math/base/special/expm1rel/test/test.js new file mode 100644 index 000000000000..e6b7d06a9df5 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/expm1rel/test/test.js @@ -0,0 +1,170 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2018 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 EPS = require( '@stdlib/constants/math/float64-eps' ); +var PINF = require( '@stdlib/constants/math/float64-pinf' ); +var NINF = require( '@stdlib/constants/math/float64-ninf' ); +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var expm1rel = require( './../lib' ); + + +// FIXTURES // + +var mediumNegative = require( './fixtures/python/medium_negative.json' ); +var mediumPositive = require( './fixtures/python/medium_positive.json' ); +var smallNegative = require( './fixtures/python/small_negative.json' ); +var smallPositive = require( './fixtures/python/small_positive.json' ); +var tiny = require( './fixtures/python/tiny.json' ); + + +// TESTS // + +tape( 'main export is a function', function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof expm1rel, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function accurately computes `(exp(x)-1)/x` for negative medium numbers', function test( t ) { + var expected; + var delta; + var tol; + var x; + var v; + var i; + + x = mediumNegative.x; + expected = mediumNegative.expected; + + for ( i = 0; i < x.length; i++ ) { + v = expm1rel( x[ i ] ); + delta = abs( v - expected[ i ] ); + tol = 3.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + t.end(); +}); + +tape( 'the function accurately computes `(exp(x)-1)/x` for positive medium numbers', function test( t ) { + var expected; + var delta; + var tol; + var x; + var v; + var i; + + x = mediumPositive.x; + expected = mediumPositive.expected; + + for ( i = 0; i < x.length; i++ ) { + v = expm1rel( x[ i ] ); + delta = abs( v - expected[ i ] ); + tol = 3.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + t.end(); +}); + +tape( 'the function accurately computes `(exp(x)-1)/x` for negative small numbers', function test( t ) { + var expected; + var delta; + var tol; + var x; + var v; + var i; + + x = smallNegative.x; + expected = smallNegative.expected; + + for ( i = 0; i < x.length; i++ ) { + v = expm1rel( x[ i ] ); + delta = abs( v - expected[ i ] ); + tol = 3.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + t.end(); +}); + +tape( 'the function accurately computes `(exp(x)-1)/x` for positive small numbers', function test( t ) { + var expected; + var delta; + var tol; + var x; + var v; + var i; + + x = smallPositive.x; + expected = smallPositive.expected; + + for ( i = 0; i < x.length; i++ ) { + v = expm1rel( x[ i ] ); + delta = abs( v - expected[ i ] ); + tol = 3.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + t.end(); +}); + +tape( 'the function accurately computes `(exp(x)-1)/x` for very small `x`', function test( t ) { + var expected; + var delta; + var tol; + var x; + var v; + var i; + + x = tiny.x; + expected = tiny.expected; + + for ( i = 0; i < x.length; i++ ) { + v = expm1rel( x[ i ] ); + delta = abs( v - expected[ i ] ); + tol = 3.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + expected[ i ] + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' ); + } + t.end(); +}); + +tape( 'the function returns `1.0` near `0.0`', function test( t ) { + t.equal( expm1rel( 0 ), 1.0, 'equals 1.0' ); + t.equal( expm1rel( EPS ), 1.0, 'equals 1.0'); + t.equal( expm1rel( -EPS ), 1.0, 'equals 1.0'); + t.end(); +}); + +tape( 'the function returns `NaN` when evaulated at `NaN`', function test( t ) { + var y = expm1rel( NaN ); + t.equal( isnan( y ), true, 'equals NaN'); + t.end(); +}); + +tape('the function returns `+infinity` at `+infinity`', function test( t ) { + t.equal( expm1rel( PINF ), PINF, 'equals +infinity'); + t.end(); +}); + +tape('the function returns `0` at `-infinity`', function test( t ) { + t.equal( expm1rel( NINF ), 0.0, 'equals 0'); + t.end(); +});