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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.
*/
'use strict';
// MODULES //
var abs2 = require( '@stdlib/math/base/special/abs2' );
var sin = require( '@stdlib/math/base/special/sin' );
// MAIN //
/**
* Computes the versed sine.
*
* ## Method
*
* Evaluating the textbook formula
*
* ```tex
* \operatorname{versin}(x) = 1 - \cos(x)
* ```
*
* loses significant digits when \\(\cos(x)\\) is close to one (i.e., for `x` near multiples of 2π, including small `x`). Accordingly, we use the equivalent half-angle identity
*
* ```tex
* \operatorname{versin}(x) = 2 \sin^2\left(\tfrac{x}{2}\right)
* ```
*
* which does not suffer from cancellation.
*
* @param {number} x - input value (in radians)
* @returns {number} versed sine
*
* @example
* var v = versin( 0.0 );
* // returns 0.0
*
* @example
* var v = versin( 3.141592653589793/2.0 );
* // returns ~1.0
*
* @example
* var v = versin( -3.141592653589793/6.0 );
* // returns ~0.13397
*
* @example
* var v = versin( NaN );
* // returns NaN
*/
function versin( x ) {
return 2.0 * abs2( sin( x / 2.0 ) );
}
// EXPORTS //
module.exports = versin;
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