/* This is a generated file. Do not edit directly. */

/* harmony default export */

/* harmony import */

/*#__PURE__*/

/**
* @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.
*
*
* ## Notice
*
* The following copyright, license, and long comment were part of the original implementation available as part of [FreeBSD]{@link https://svnweb.freebsd.org/base/release/9.3.0/lib/msun/src/e_exp.c}. The implementation follows the original, but has been modified for JavaScript.
*
* ```text
* Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ```
*/

/**
* @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.
*/

/**
* @license Apache-2.0
*
* Copyright (c) 2019 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.
*/

/**
* A learning component illustrating the impact of a confounding variable when assessing a causal relationship between two variables and of randomization.
*
* @property {(string|node)} x - name of explanatory variable
* @property {(string|node)} y - name of response variable
* @property {(string|node)} z - name of confounding variable
*/

/**
* Computes \\(e^{r} 2^k\\) where \\(r = \mathrm{hi} - \mathrm{lo}\\) and \\(|r| \leq \ln(2)/2\\).
*
* @private
* @param {number} hi - upper bound
* @param {number} lo - lower bound
* @param {integer} k - power of 2
* @returns {number} function value
*/

/**
* Evaluate the natural exponential function.
*
* @module @stdlib/math/base/special/exp
*
* @example
* var exp = require( '@stdlib/math/base/special/exp' );
*
* var v = exp( 4.0 );
* // returns ~54.5982
*
* v = exp( -9.0 );
* // returns ~1.234e-4
*
* v = exp( 0.0 );
* // returns 1.0
*
* v = exp( NaN );
* // returns NaN
*/

/**
* Evaluate the standard logistic function.
*
* @module @stdlib/math/base/special/expit
*
* @example
* var expit = require( '@stdlib/math/base/special/expit' );
*
* var y = expit( 0.0 );
* // returns 0.5
*
* y = expit( 1.0 );
* // returns ~0.731
*
* y = expit( -1.0 );
* // returns ~0.269
*
* y = expit( Infinity );
* // returns 1.0
*
* y = expit( NaN );
* // returns NaN
*/

/**
* Evaluates a polynomial.
*
* ## Notes
*
* -   The implementation uses [Horner's rule][horners-method] for efficient computation.
*
* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method
*
*
* @private
* @param {number} x - value at which to evaluate the polynomial
* @returns {number} evaluated polynomial
*/

/**
* Evaluates the natural exponential function.
*
* ## Method
*
* 1.  We reduce \\( x \\) to an \\( r \\) so that \\( |r| \leq 0.5 \cdot \ln(2) \approx 0.34658 \\). Given \\( x \\), we find an \\( r \\) and integer \\( k \\) such that
*
*     ```tex
*     \begin{align*}
*     x &= k \cdot \ln(2) + r \\
*     |r| &\leq 0.5 \cdot \ln(2)
*     \end{align*}
*     ```
*
*     <!-- <note> -->
*
*     \\( r \\) can be represented as \\( r = \mathrm{hi} - \mathrm{lo} \\) for better accuracy.
*
*     <!-- </note> -->
*
* 2.  We approximate of \\( e^{r} \\) by a special rational function on the interval \\(\[0,0.34658]\\):
*
*     ```tex
*     \begin{align*}
*     R\left(r^2\right) &= r \cdot \frac{ e^{r}+1 }{ e^{r}-1 } \\
*     &= 2 + \frac{r^2}{6} - \frac{r^4}{360} + \ldots
*     \end{align*}
*     ```
*
*     We use a special Remes algorithm on \\(\[0,0.34658]\\) to generate a polynomial of degree \\(5\\) to approximate \\(R\\). The maximum error of this polynomial approximation is bounded by \\(2^{-59}\\). In other words,
*
*     ```tex
*     R(z) \sim 2 + P_1 z + P_2 z^2 + P_3 z^3 + P_4 z^4 + P_5 z^5
*     ```
*
*     where \\( z = r^2 \\) and
*
*     ```tex
*     \left|  2 + P_1 z + \ldots + P_5 z^5  - R(z) \right| \leq 2^{-59}
*     ```
*
*     <!-- <note> -->
*
*     The values of \\( P_1 \\) to \\( P_5 \\) are listed in the source code.
*
*     <!-- </note> -->
*
*     The computation of \\( e^{r} \\) thus becomes
*
*     ```tex
*     \begin{align*}
*     e^{r} &= 1 + \frac{2r}{R-r} \\
*           &= 1 + r + \frac{r \cdot R_1(r)}{2 - R_1(r)}\ \text{for better accuracy}
*     \end{align*}
*     ```
*
*     where
*
*     ```tex
*     R_1(r) = r - P_1\ r^2 + P_2\ r^4 + \ldots + P_5\ r^{10}
*     ```
*
* 3.  We scale back to obtain \\( e^{x} \\). From step 1, we have
*
*     ```tex
*     e^{x} = 2^k e^{r}
*     ```
*
*
* ## Special Cases
*
* ```tex
* \begin{align*}
* e^\infty &= \infty \\
* e^{-\infty} &= 0 \\
* e^{\mathrm{NaN}} &= \mathrm{NaN} \\
* e^0 &= 1\ \mathrm{is\ exact\ for\ finite\ argument\ only}
* \end{align*}
* ```
*
* ## Notes
*
* -   According to an error analysis, the error is always less than \\(1\\) ulp (unit in the last place).
*
* -   For an IEEE double,
*
*     -   if \\(x > 7.09782712893383973096\mbox{e+}02\\), then \\(e^{x}\\) overflows
*     -   if \\(x < -7.45133219101941108420\mbox{e+}02\\), then \\(e^{x}\\) underflows
*
* -   The hexadecimal values included in the source code are the intended ones for the used constants. Decimal values may be used, provided that the compiler will convert from decimal to binary accurately enough to produce the intended hexadecimal values.
*
*
* @param {number} x - input value
* @returns {number} function value
*
* @example
* var v = exp( 4.0 );
* // returns ~54.5982
*
* @example
* var v = exp( -9.0 );
* // returns ~1.234e-4
*
* @example
* var v = exp( 0.0 );
* // returns 1.0
*
* @example
* var v = exp( NaN );
* // returns NaN
*/

/**
* Evaluates the standard logistic function.
*
* @param {number} x - input value
* @returns {number} function value
*
* @example
* var y = expit( 0.0 );
* // returns 0.5
*
* @example
* var y = expit( 1.0 );
* // returns ~0.731
*
* @example
* var y = expit( -1.0 );
* // returns ~0.269
*
* @example
* var y = expit( Infinity );
* // returns 1.0
*
* @example
* var y = expit( NaN );
* // returns NaN
*/

/**
* Round a double-precision floating-point number toward positive infinity.
*
* @module @stdlib/math/base/special/ceil
*
* @example
* var ceil = require( '@stdlib/math/base/special/ceil' );
*
* var v = ceil( -4.2 );
* // returns -4.0
*
* v = ceil( 9.99999 );
* // returns 10.0
*
* v = ceil( 0.0 );
* // returns 0.0
*
* v = ceil( NaN );
* // returns NaN
*/

/**
* Round a double-precision floating-point number toward zero.
*
* @module @stdlib/math/base/special/trunc
*
* @example
* var trunc = require( '@stdlib/math/base/special/trunc' );
*
* var v = trunc( -4.2 );
* // returns -4.0
*
* v = trunc( 9.99999 );
* // returns 9.0
*
* v = trunc( 0.0 );
* // returns 0.0
*
* v = trunc( -0.0 );
* // returns -0.0
*
* v = trunc( NaN );
* // returns NaN
*
* v = trunc( Infinity );
* // returns Infinity
*
* v = trunc( -Infinity );
* // returns -Infinity
*/

/**
* Rounds a double-precision floating-point number toward positive infinity.
*
* @param {number} x - input value
* @returns {number} rounded value
*
* @example
* var v = ceil( -4.2 );
* // returns -4.0
*
* @example
* var v = ceil( 9.99999 );
* // returns 10.0
*
* @example
* var v = ceil( 0.0 );
* // returns 0.0
*
* @example
* var v = ceil( NaN );
* // returns NaN
*/

/**
* Rounds a double-precision floating-point number toward zero.
*
* @param {number} x - input value
* @returns {number} rounded value
*
* @example
* var v = trunc( -4.2 );
* // returns -4.0
*
* @example
* var v = trunc( 9.99999 );
* // returns 9.0
*
* @example
* var v = trunc( 0.0 );
* // returns 0.0
*
* @example
* var v = trunc( -0.0 );
* // returns -0.0
*
* @example
* var v = trunc( NaN );
* // returns NaN
*
* @example
* var v = trunc( Infinity );
* // returns Infinity
*
* @example
* var v = trunc( -Infinity );
* // returns -Infinity
*/

/***/

// EXPORTS //

// MAIN //

// MODULES //

// PROPERTIES //

// Reduce and compute `r = hi - lo` for extra precision.

// TODO: implementation (?)

// eslint-disable-line stdlib/no-builtin-math
