@stdlib/math-base-special-sinpi/lib/main.js

Compute sin(πx).

/**
* @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 isnan = require( '@stdlib/math-base-assert-is-nan' );
var isInfinite = require( '@stdlib/math-base-assert-is-infinite' );
var cos = require( '@stdlib/math-base-special-cos' );
var sin = require( '@stdlib/math-base-special-sin' );
var abs = require( '@stdlib/math-base-special-abs' );
var copysign = require( '@stdlib/math-base-special-copysign' );
var PI = require( '@stdlib/constants-float64-pi' );


// MAIN //

/**
* Computes the value of `sin(πx)`.
*
* ## Notes
*
* -   `sin(-x) = -sin(x)`
* -   `sin(+n) = +0`, where `n` is a positive integer
* -   `sin(-n) = -sin(+n) = -0`, where `n` is a positive integer
* -   `cos(-x) = cos(x)`
*
* @param {number} x - input value
* @returns {number} function value
*
* @example
* var y = sinpi( 0.0 );
* // returns 0.0
*
* @example
* var y = sinpi( 0.5 );
* // returns 1.0
*
* @example
* var y = sinpi( 0.9 );
* // returns ~0.309
*
* @example
* var y = sinpi( NaN );
* // returns NaN
*/
function sinpi( x ) {
	var ar;
	var r;
	if ( isnan( x ) ) {
		return NaN;
	}
	if ( isInfinite( x ) ) {
		return NaN;
	}
	// Argument reduction (reduce to [0,2))...
	r = x % 2.0; // sign preserving
	ar = abs( r );

	// If `x` is an integer, the mod is an integer...
	if ( ar === 0.0 || ar === 1.0 ) {
		return copysign( 0.0, r );
	}
	if ( ar < 0.25 ) {
		return sin( PI*r );
	}
	// In each of the following, we further reduce to [-π/4,π/4)...
	if ( ar < 0.75 ) {
		ar = 0.5 - ar;
		return copysign( cos( PI*ar ), r );
	}
	if ( ar < 1.25 ) {
		r = copysign( 1.0, r ) - r;
		return sin( PI*r );
	}
	if ( ar < 1.75 ) {
		ar -= 1.5;
		return -copysign( cos( PI*ar ), r );
	}
	r -= copysign( 2.0, r );
	return sin( PI*r );
}


// EXPORTS //

module.exports = sinpi;