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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 log10 = require( '@stdlib/math/base/special/log10' );
var ln = require( '@stdlib/math/base/special/ln' );
var abs = require( '@stdlib/math/base/special/abs' );
var floor = require( '@stdlib/math/base/special/floor' );
var exponent = require( '@stdlib/number/float64/base/exponent' );
// MAIN //
/**
* Rounds a numeric value to the nearest number toward negative infinity with \\(N\\) significant figures.
*
* @param {number} x - input value
* @param {PositiveInteger} n - number of significant figures
* @param {PositiveInteger} b - base
* @returns {number} rounded value
*
* @example
* var v = floorsd( 3.141592653589793, 5, 10 );
* // returns 3.1415
*
* @example
* var v = floorsd( 3.141592653589793, 1, 10 );
* // returns 3.0
*
* @example
* var v = floorsd( 12368.0, 2, 10 );
* // returns 12000.0
*
* @example
* var v = floorsd( 0.0313, 2, 2 );
* // returns 0.03125
*/
function floorsd( x, n, b ) {
var exp;
var s;
var y;
if (
isnan( x ) ||
isnan( n ) ||
n < 1 ||
isInfinite( n ) ||
isnan( b ) ||
b <= 0 ||
isInfinite( b )
) {
return NaN;
}
if ( isInfinite( x ) || x === 0.0 ) {
return x;
}
if ( b === 10 ) {
exp = log10( abs( x ) );
}
else if ( b === 2 ) {
exp = exponent( abs( x ) );
}
else {
exp = ln( abs(x) ) / ln( b );
}
exp = floor( exp - n + 1.0 );
s = pow( b, abs( exp ) );
// Check for overflow:
if ( isInfinite( s ) ) {
return x;
}
// To avoid numerical stability issues due to floating-point rounding error (e.g., 3.55/0.1-35.5 = -7.105427357601e-15 and 3.55*10-35.5 = 0), we must treat positive and negative exponents separately.
if ( exp < 0 ) {
y = floor( x * s ) / s;
} else {
y = floor( x / s ) * s;
}
// Check for overflow:
if ( isInfinite( y ) ) {
return x;
}
return y;
}
// EXPORTS //
module.exports = floorsd;
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