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/**
* @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 original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_60_0/boost/math/special_functions/powm1.hpp}. The implementation follows the original, but has been modified for JavaScript.
*
* ```text
* (C) Copyright John Maddock 2006.
*
* Use, modification and distribution are subject to the
* Boost Software License, Version 1.0. (See accompanying file
* LICENSE or copy at http://www.boost.org/LICENSE_1_0.txt)
* ```
*/
'use strict';
// MODULES //
var isnan = require( './../../../../base/assert/is-nan' );
var abs = require( './../../../../base/special/abs' );
var expm1 = require( './../../../../base/special/expm1' );
var ln = require( './../../../../base/special/ln' );
var pow = require( './../../../../base/special/pow' );
var trunc = require( './../../../../base/special/trunc' );
// MAIN //
/**
* Evaluates `bˣ - 1`.
*
* @param {number} b - base
* @param {number} x - exponent
* @returns {number} function value
*
* @example
* var y = powm1( 2.0, 3.0 );
* // returns 7.0
*
* @example
* var y = powm1( 4.0, 0.5 );
* // returns 1.0
*
* @example
* var y = powm1( 0.0, 100.0 );
* // returns -1.0
*
* @example
* var y = powm1( 100.0, 0.0 );
* // returns 0.0
*
* @example
* var y = powm1( 0.0, 0.0 );
* // returns 0.0
*
* @example
* var y = powm1( 3.141592653589793, 5.0 );
* // returns ~305.0197
*
* @example
* var y = powm1( NaN, 3.0 );
* // returns NaN
*
* @example
* var y = powm1( 5.0, NaN );
* // returns NaN
*/
function powm1( b, x ) {
var y;
if (
isnan( b ) ||
isnan( x )
) {
return NaN;
}
if ( x === 0.0 ) {
// Any number raised to zero (including 0) is always 1 => b^0 - 1 = 0
return 0.0;
}
if ( b === 0.0 ) {
// Zero raised to any number (except 0) is always zero => 0^x - 1 = -1
return -1.0;
}
if ( b < 0.0 && x%2.0 === 0 ) {
// If `x` is even, recognize that `(-b)**x == (b)**x`...
b = -b;
}
if ( b > 0.0 ) {
if (
abs( x*(b-1.0) ) < 0.5 ||
abs( x ) < 0.2
) {
// No good/quick approximation for ln(b)*x, so we have to evaluate...
y = ln( b ) * x;
if ( y < 0.5 ) {
return expm1( y );
}
}
} else if ( trunc( x ) !== x ) {
// Exponentiation would yield a complex result...
return NaN;
}
return pow( b, x ) - 1.0;
}
// EXPORTS //
module.exports = powm1;
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