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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 f32 = require( '@stdlib/number/float64/base/to-float32' );
var FLOAT32_MAX = require( '@stdlib/constants/float32/max' );
var absf = require( '@stdlib/math/base/special/absf' );
var abs2f = require( '@stdlib/math/base/special/abs2f' );
var sqrtf = require( '@stdlib/math/base/special/sqrtf' );
var reinterpret = require( '@stdlib/strided/base/reinterpret-complex64' );
// VARIABLES //
// Blue's scaling constants:
var tsml = 1.08420217E-19;
var tbig = 4.50359963E+15;
var ssml = 3.77789319E+22;
var sbig = 1.32348898E-23;
// MAIN //
/**
* Computes the L2-norm of a single-precision complex floating-point vector.
*
* @param {PositiveInteger} N - number of indexed elements
* @param {Complex64Array} x - input array
* @param {integer} strideX - `x` stride length
* @param {NonNegativeInteger} offsetX - starting index for `x`
* @returns {number} L2-norm
*
* @example
* var Complex64Array = require( '@stdlib/array/complex64' );
*
* var x = new Complex64Array( [ 0.3, 0.1, 0.5, 0.0, 0.0, 0.5, 0.0, 0.2, 2.0, 3.0 ] );
*
* var norm = scnrm2( 4, x, 1, 0 );
* // returns ~0.8
*/
function scnrm2( 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 = absf( viewX[ ix ] );
if ( ax > tbig ) {
abig = f32( abig + abs2f( ax * sbig ) );
notbig = false;
} else if ( ax < tsml ) {
if ( notbig ) {
asml = f32( asml + abs2f( ax * ssml ) );
}
} else {
amed = f32( amed + f32( ax * ax ) );
}
ax = absf( viewX[ ix + 1 ] );
if ( ax > tbig ) {
abig = f32( abig + abs2f( ax * sbig ) );
notbig = false;
} else if ( ax < tsml ) {
if ( notbig ) {
asml = f32( asml + abs2f( ax * ssml ) );
}
} else {
amed = f32( amed + f32( 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 > FLOAT32_MAX ) || ( amed !== amed ) ) {
abig = f32( abig + f32( f32( amed * sbig ) * sbig ) );
}
scl = f32( 1.0 / sbig );
sumsq = abig;
} else if ( asml > 0.0 ) {
// Combine `amed` and `asml` if `asml` > 0...
if ( amed > 0.0 || amed > FLOAT32_MAX || ( amed !== amed ) ) {
amed = sqrtf( amed );
asml = f32( sqrtf( asml ) / ssml );
if ( asml > amed ) {
ymin = amed;
ymax = asml;
} else {
ymin = asml;
ymax = amed;
}
scl = 1.0;
sumsq = f32( f32( ymax * ymax ) * f32( 1.0 + abs2f( ymin / ymax ) ) ); // eslint-disable-line max-len
} else {
scl = f32( 1.0 / ssml );
sumsq = asml;
}
} else {
// All values are mid-range...
scl = 1.0;
sumsq = amed;
}
return f32( sqrtf( sumsq ) * scl );
}
// EXPORTS //
module.exports = scnrm2;
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