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* @license Apache-2.0
*
* Copyright (c) 2024 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 FLOAT64_MAX = require( '@stdlib/constants/float64/max' );
var abs = require( '@stdlib/math/base/special/abs' );
var abs2 = require( '@stdlib/math/base/special/abs2' );
var sqrt = require( '@stdlib/math/base/special/sqrt' );
var reinterpret = require( '@stdlib/strided/base/reinterpret-complex128' );
// VARIABLES //
// Blue's scaling constants:
var tsml = 1.4916681462400413E-154;
var tbig = 1.9979190722022350E+146;
var ssml = 4.4989137945431964E+161;
var sbig = 1.1113793747425387E-162;
// MAIN //
/**
* Computes the L2-norm of a complex double-precision floating-point vector.
*
* @param {PositiveInteger} N - number of indexed elements
* @param {Complex128Array} x - input array
* @param {integer} strideX - `x` stride length
* @param {NonNegativeInteger} offsetX - starting index for `x`
* @returns {number} L2-norm
*
* @example
* var Complex128Array = require( '@stdlib/array/complex128' );
*
* var x = new Complex128Array( [ 0.3, 0.1, 0.5, 0.0, 0.0, 0.5, 0.0, 0.2, 2.0, 3.0 ] );
*
* var norm = dznrm2( 4, x, 1, 0 );
* // returns ~0.8
*/
function dznrm2( N, x, strideX, offsetX ) {
var notbig;
var sumsq;
var viewX;
var abig;
var amed;
var asml;
var ymax;
var ymin;
var scl;
var ax;
var ix;
var sx;
var i;
if ( N <= 0 ) {
return 0.0;
}
// Reinterpret the input array as a real-valued array comprised of interleaved real and imaginary components:
viewX = reinterpret( x, 0 );
sx = strideX * 2;
ix = offsetX * 2;
// Initialize loop values for accumulation:
notbig = true;
sumsq = 0.0;
abig = 0.0;
amed = 0.0;
asml = 0.0;
scl = 1.0;
// Compute the sum of squares using 3 accumulators--`abig` (sum of squares scaled down to avoid overflow), `asml` (sum of squares scaled up to avoid underflow), `amed` (sum of squares that do not require scaling)--and thresholds and multipliers--`tbig` (values bigger than this are scaled down by `sbig`) and `tsml` (values smaller than this are scaled up by `ssml`)...
for ( i = 0; i < N; i++ ) {
ax = abs( viewX[ ix ] );
if ( ax > tbig ) {
abig += abs2( ax * sbig );
notbig = false;
} else if ( ax < tsml ) {
if ( notbig ) {
asml += abs2( ax * ssml );
}
} else {
amed += ax * ax;
}
ax = abs( viewX[ ix + 1 ] );
if ( ax > tbig ) {
abig += abs2( ax * sbig );
notbig = false;
} else if ( ax < tsml ) {
if ( notbig ) {
asml += abs2( ax * ssml );
}
} else {
amed += ax * ax;
}
ix += sx;
}
// Combine `abig` and `amed` or `amed` and `asml` if more than one accumulator was used...
if ( abig > 0.0 ) {
// Combine `abig` and `amed` if `abig` > 0...
if ( amed > 0.0 || ( amed > FLOAT64_MAX ) || ( amed !== amed ) ) {
abig += ( amed * sbig ) * sbig;
}
scl = 1.0 / sbig;
sumsq = abig;
} else if ( asml > 0.0 ) {
// Combine `amed` and `asml` if `asml` > 0...
if ( amed > 0.0 || amed > FLOAT64_MAX || ( amed !== amed ) ) {
amed = sqrt( amed );
asml = sqrt( asml ) / ssml;
if ( asml > amed ) {
ymin = amed;
ymax = asml;
} else {
ymin = asml;
ymax = amed;
}
scl = 1.0;
sumsq = ( ymax * ymax ) * ( 1.0 + abs2( ymin / ymax ) );
} else {
scl = 1.0 / ssml;
sumsq = asml;
}
} else {
// All values are mid-range...
scl = 1.0;
sumsq = amed;
}
return sqrt( sumsq ) * scl;
}
// EXPORTS //
module.exports = dznrm2;
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