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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 abs = require( '@stdlib/math/base/special/abs' );
var max = require( '@stdlib/math/base/special/max' );
var FLOAT64_BIGGEST = require( '@stdlib/constants/float64/max' );
var FLOAT64_SMALLEST = require( '@stdlib/constants/float64/smallest-normal' );
var EPS = require( '@stdlib/constants/float64/eps' );
var real = require( '@stdlib/complex/float64/real' );
var imag = require( '@stdlib/complex/float64/imag' );
var Complex128 = require( '@stdlib/complex/float64/ctor' );
var robustInternal = require( './robust_internal.js' );
// VARIABLES //
var LARGE_THRESHOLD = FLOAT64_BIGGEST * 0.5;
var SMALL_THRESHOLD = FLOAT64_SMALLEST * ( 2.0 / EPS );
var RECIP_EPS_SQR = 2.0 / ( EPS * EPS );
// MAIN //
/**
* Divides two double-precision complex floating-point numbers.
*
* ## References
*
* - Baudin, Michael, and Robert L. Smith. 2012. "A Robust Complex Division in Scilab." _arXiv_ abs/1210.4539 \[cs.MS\] (October): 1–25. <https://arxiv.org/abs/1210.4539>.
*
* @param {Complex128} z1 - complex number
* @param {Complex128} z2 - complex number
* @returns {Complex128} result
*
* @example
* var Complex128 = require( '@stdlib/complex/float64/ctor' );
* var real = require( '@stdlib/complex/float64/real' );
* var imag = require( '@stdlib/complex/float64/imag' );
*
* var z1 = new Complex128( -13.0, -1.0 );
* // returns <Complex128>
*
* var z2 = new Complex128( -2.0, 1.0 );
* // returns <Complex128>
*
* var out = cdiv( z1, z2 );
* // returns <Complex128>
*
* var re = real( out );
* // returns 5.0
*
* var im = imag( out );
* // returns 3.0
*/
function cdiv( z1, z2 ) {
var re1;
var re2;
var im1;
var im2;
var out;
var ab;
var cd;
var s;
re1 = real( z1 );
re2 = real( z2 );
im1 = imag( z1 );
im2 = imag( z2 );
ab = max( abs(re1), abs(im1) );
cd = max( abs(re2), abs(im2) );
s = 1.0;
if ( ab >= LARGE_THRESHOLD ) {
re1 *= 0.5;
im1 *= 0.5;
s *= 2.0;
} else if ( ab <= SMALL_THRESHOLD ) {
re1 *= RECIP_EPS_SQR;
im1 *= RECIP_EPS_SQR;
s /= RECIP_EPS_SQR;
}
if ( cd >= LARGE_THRESHOLD ) {
re2 *= 0.5;
im2 *= 0.5;
s *= 0.5;
} else if ( cd <= SMALL_THRESHOLD ) {
re2 *= RECIP_EPS_SQR;
im2 *= RECIP_EPS_SQR;
s *= RECIP_EPS_SQR;
}
if ( abs( im2 ) <= abs( re2 ) ) {
out = robustInternal( re1, im1, re2, im2 );
} else {
out = robustInternal( im1, re1, im2, re2 );
out[ 1 ] *= -1.0;
}
out[ 0 ] *= s;
out[ 1 ] *= s;
return new Complex128( out[ 0 ], out[ 1 ] );
}
// EXPORTS //
module.exports = cdiv;
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