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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 isnan = require( '@stdlib/math/base/assert/is-nan' );
var isInfinite = require( '@stdlib/math/base/assert/is-infinite' );
var pow = require( '@stdlib/math/base/special/pow' );
var floor = require( '@stdlib/math/base/special/floor' );
var ceil = require( '@stdlib/math/base/special/ceil' );
var log2 = require( '@stdlib/math/base/special/log2' );
var MAX_EXP = require( '@stdlib/constants/float64/max-base2-exponent' );
var MIN_EXP_SUBNORMAL = require( '@stdlib/constants/float64/min-base2-exponent-subnormal' );
var PINF = require( '@stdlib/constants/float64/pinf' );
// VARIABLES //
// 2^1023:
var HUGE = pow( 2.0, MAX_EXP );
var HALF_HUGE = HUGE / 2.0;
// MAIN //
/**
* Rounds a numeric value to the nearest power of two on a linear scale.
*
* @param {number} x - input value
* @returns {number} rounded value
*
* @example
* var v = round2( 3.141592653589793 );
* // returns 4.0
*
* @example
* var v = round2( 13.0 );
* // returns 16.0
*
* @example
* var v = round2( -0.314 );
* // returns -0.25
*/
function round2( x ) {
var sign;
var half;
var p1;
var p2;
var y1;
var y2;
var p;
if (
isnan( x ) ||
isInfinite( x ) ||
x === 0.0
) {
return x;
}
if ( x < 0 ) {
x = -x;
sign = -1.0;
} else {
sign = 1.0;
}
// Solve the equation `2^p = x` for `p`:
p = log2( x );
// If provided the smallest subnormal, no rounding possible:
if ( p === MIN_EXP_SUBNORMAL ) {
return x;
}
// Find the previous and next integer powers:
p1 = floor( p );
p2 = ceil( p );
// Handle overflow:
if ( p1 === MAX_EXP ) {
if ( x - HUGE >= HALF_HUGE ) {
return sign * PINF; // sign-preserving
}
return sign * HUGE;
}
// Compute previous and next powers of two:
y1 = pow( 2.0, p1 );
y2 = pow( 2.0, p2 );
// Find the closest power of two:
half = ( y2 - y1 ) / 2.0;
if ( y1 + half > x ) {
return sign * y1;
}
return sign * y2;
}
// EXPORTS //
module.exports = round2;
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