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* @license Apache-2.0
*
* Copyright (c) 2026 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 min = require( '@stdlib/math/base/special/min' );
// MAIN //
/**
* Computes one dqds transform in ping-pong form.
*
* ## Notes
*
* - `Z` is a 1-D array of length >= `4*N0` storing interleaved q/e values.
* - `PP` is `0` for ping, `1` for pong.
*
* @private
* @param {integer} I0 - the first index
* @param {integer} N0 - the last index
* @param {Float64Array} Z - the QD array
* @param {integer} strideZ - stride length for `Z`
* @param {NonNegativeInteger} offsetZ - starting index for `Z`
* @param {integer} PP - ping-pong flag (0 or 1)
* @param {number} TAU - the shift
* @param {number} SIGMA - the accumulated shift
* @param {boolean} IEEE - IEEE arithmetic flag
* @param {number} EPS - epsilon used by the routine
* @param {Float64Array} out - output array containing `DMIN`, `DMIN1`, `DMIN2`, `DN`, `DNM1`, and `DNM2` respectively
* @param {integer} strideOut - stride length for `out`
* @param {NonNegativeInteger} offsetOut - starting index of `out`
* @returns {Float64Array} output array
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var out = new Float64Array( 6 );
* var Z = new Float64Array( [ 5, 0, 7, 0, 9, 0, 3, 0, 11, 0, 4, 0, 20, 0, 0, 0 ] );
*
* dlasq5( 0, 3, Z, 1, 0, 0, 0.1, 0.0, true, 2.220446049250313e-16, out, 1, 0 );
* // out => <Float64Array>[ ~3.606, ~3.606, ~3.606, ~11.823, ~5.904, ~3.606 ]
*/
function dlasq5( I0, N0, Z, strideZ, offsetZ, PP, TAU, SIGMA, IEEE, EPS, out, strideOut, offsetOut ) { // eslint-disable-line max-len, max-params
var dthresh;
var dmin1;
var dmin2;
var dnm1;
var dnm2;
var emin;
var dmin;
var temp;
var j4p2;
var idx;
var j4;
var dn;
var d;
// Quick return...
if ( ( N0 - I0 - 1 ) <= 0 ) {
return out;
}
dthresh = EPS * ( SIGMA + TAU );
if ( TAU < ( dthresh * 0.5 ) ) {
TAU = 0;
}
if ( TAU > 0 || TAU < 0 ) {
j4 = offsetZ + ( strideZ*( ( 4*I0 ) + PP ) );
emin = Z[ j4 + ( 4*strideZ ) ];
d = Z[ j4 ] - TAU;
dmin = d;
dmin1 = -Z[ j4 ];
if ( IEEE ) {
if ( PP === 0 ) {
j4 = offsetZ + ( strideZ * ( ( 4*I0 ) + 3 ) );
for ( idx = ( 4*I0 ) + 3; idx <= ( 4*N0 ) - 9; idx += 4 ) {
Z[ j4 - ( 2*strideZ ) ] = d + Z[ j4 - strideZ ];
temp = Z[ j4 + strideZ ] / Z[ j4 - ( 2*strideZ ) ];
d = ( d*temp ) - TAU;
dmin = min( dmin, d );
Z[ j4 ] = Z[ j4 - strideZ ]*temp;
emin = min( Z[ j4 ], emin );
j4 += 4*strideZ;
}
} else {
j4 = offsetZ + ( strideZ * ( ( 4*I0 ) + 3 ) );
for ( idx = ( 4*I0 ) + 3; idx <= ( 4*N0 ) - 9; idx += 4 ) {
Z[ j4 - ( 3*strideZ ) ] = d + Z[ j4 ];
temp = Z[ j4 + ( 2*strideZ ) ] / Z[ j4 - ( 3*strideZ ) ];
d = ( d*temp ) - TAU;
dmin = min( dmin, d );
Z[ j4 - strideZ ] = Z[ j4 ] * temp;
emin = min( Z[ j4 - strideZ ], emin );
j4 += 4*strideZ;
}
}
// Unroll last two steps.
dnm2 = d;
dmin2 = dmin;
j4 = offsetZ + ( strideZ * ( ( 4*N0 ) - 5 - PP ) );
j4p2 = j4 + ( strideZ * ( ( 2*PP ) - 1 ) );
Z[ j4 - ( 2*strideZ ) ] = dnm2 + Z[ j4p2 ];
Z[ j4 ] = Z[ j4p2 + ( 2*strideZ ) ] * ( Z[ j4p2 ] / Z[ j4 - ( 2*strideZ ) ] );
dnm1 = ( Z[ j4p2 + ( 2*strideZ ) ]*( dnm2 / Z[ j4 - ( 2*strideZ ) ] ) ) - TAU;
dmin = min( dmin, dnm1 );
dmin1 = dmin;
j4 += 4*strideZ;
j4p2 = j4 + ( strideZ * ( ( 2*PP ) - 1 ) );
Z[ j4 - ( 2*strideZ ) ] = dnm1 + Z[ j4p2 ];
Z[ j4 ] = Z[ j4p2 + ( 2*strideZ ) ] * ( Z[ j4p2 ] / Z[ j4 - ( 2*strideZ ) ] );
dn = ( Z[ j4p2 + ( 2*strideZ ) ]*( dnm1 / Z[ j4 - ( 2*strideZ ) ] ) ) - TAU;
dmin = min( dmin, dn );
} else {
if ( PP === 0 ) {
j4 = offsetZ + ( strideZ * ( ( 4*I0 ) + 3 ) );
for ( idx = ( 4*I0 ) + 3; idx <= ( 4*N0 ) - 9; idx += 4 ) {
Z[ j4 - ( 2*strideZ ) ] = d + Z[ j4 - strideZ ];
if ( d < 0 ) {
return out;
}
Z[ j4 ] = Z[ j4 + strideZ ] * ( Z[ j4 - strideZ ] / Z[ j4 - ( 2*strideZ ) ] );
d = ( Z[ j4 + strideZ ]*( d / Z[ j4 - ( 2*strideZ ) ] ) ) - TAU;
dmin = min( dmin, d );
emin = min( emin, Z[ j4 ] );
j4 += 4*strideZ;
}
} else {
j4 = offsetZ + ( strideZ * ( ( 4*I0 ) + 3 ) );
for ( idx = ( 4*I0 ) + 3; idx <= ( 4*N0 ) - 9; idx += 4 ) {
Z[ j4 - ( 3*strideZ ) ] = d + Z[ j4 ];
if ( d < 0 ) {
return out;
}
Z[ j4 - strideZ ] = Z[ j4 + ( 2*strideZ ) ] * ( Z[ j4 ] / Z[ j4 - ( 3*strideZ ) ] );
d = ( Z[ j4 + ( 2*strideZ ) ]*( d / Z[ j4 - ( 3*strideZ ) ] ) ) - TAU;
dmin = min( dmin, d );
emin = min( emin, Z[ j4 - strideZ ] );
j4 += 4*strideZ;
}
}
// Unroll last two steps.
dnm2 = d;
dmin2 = dmin;
j4 = offsetZ + ( strideZ * ( ( 4*N0 ) - 5 - PP ) );
j4p2 = j4 + ( strideZ * ( ( 2*PP ) - 1 ) );
Z[ j4 - ( 2*strideZ ) ] = dnm2 + Z[ j4p2 ];
if ( dnm2 < 0 ) {
return out;
}
Z[ j4 ] = Z[ j4p2 + ( 2*strideZ ) ] * ( Z[ j4p2 ] / Z[ j4 - ( 2*strideZ ) ] );
dnm1 = ( Z[ j4p2 + ( 2*strideZ ) ]*( dnm2 / Z[ j4 - ( 2*strideZ ) ] ) ) - TAU;
dmin = min( dmin, dnm1 );
dmin1 = dmin;
j4 += 4*strideZ;
j4p2 = j4 + ( strideZ * ( ( 2*PP ) - 1 ) );
Z[ j4 - ( 2*strideZ ) ] = dnm1 + Z[ j4p2 ];
if ( dnm1 < 0 ) {
return out;
}
Z[ j4 ] = Z[ j4p2 + ( 2*strideZ ) ] * ( Z[ j4p2 ] / Z[ j4 - ( 2*strideZ ) ] );
dn = ( Z[ j4p2 + ( 2*strideZ ) ]*( dnm1 / Z[ j4 - ( 2*strideZ ) ] ) ) - TAU;
dmin = min( dmin, dn );
}
} else {
// This is the version that sets d's to zero if they are small enough
j4 = offsetZ + ( strideZ * ( ( 4*I0 ) + PP ) );
emin = Z[ j4 + ( 4*strideZ ) ];
d = Z[ j4 ];
dmin = d;
dmin1 = -Z[ j4 ];
if ( IEEE ) {
if ( PP === 0 ) {
j4 = offsetZ + ( strideZ * ( ( 4*I0 ) + 3 ) );
for ( idx = ( 4*I0 ) + 3; idx <= ( 4*N0 ) - 9; idx += 4 ) {
Z[ j4 - ( 2*strideZ ) ] = d + Z[ j4 - strideZ ];
temp = Z[ j4 + strideZ ] / Z[ j4 - ( 2*strideZ ) ];
d = ( d*temp ) - TAU;
if ( d < dthresh ) {
d = 0;
}
dmin = min( dmin, d );
Z[ j4 ] = Z[ j4 - strideZ ] * temp;
emin = min( Z[ j4 ], emin );
j4 += 4*strideZ;
}
} else {
j4 = offsetZ + ( strideZ * ( ( 4*I0 ) + 3 ) );
for ( idx = ( 4*I0 ) + 3; idx <= ( 4*N0 ) - 9; idx += 4 ) {
Z[ j4 - ( 3*strideZ ) ] = d + Z[ j4 ];
temp = Z[ j4 + ( 2*strideZ ) ] / Z[ j4 - ( 3*strideZ ) ];
d = ( d*temp ) - TAU;
if ( d < dthresh ) {
d = 0;
}
dmin = min( dmin, d );
Z[ j4 - strideZ ] = Z[ j4 ] * temp;
emin = min( Z[ j4 - strideZ ], emin );
j4 += 4*strideZ;
}
}
// Unroll last two steps.
dnm2 = d;
dmin2 = dmin;
j4 = offsetZ + ( strideZ * ( ( 4*N0 ) - 5 - PP ) );
j4p2 = j4 + ( strideZ * ( ( 2*PP ) - 1 ) );
Z[ j4 - ( 2*strideZ ) ] = dnm2 + Z[ j4p2 ];
Z[ j4 ] = Z[ j4p2 + ( 2*strideZ ) ] * ( Z[ j4p2 ] / Z[ j4 - ( 2*strideZ ) ] );
dnm1 = ( Z[ j4p2 + ( 2*strideZ ) ]*( dnm2 / Z[ j4 - ( 2*strideZ ) ] ) ) - TAU;
dmin = min( dmin, dnm1 );
dmin1 = dmin;
j4 += 4*strideZ;
j4p2 = j4 + ( strideZ * ( ( 2*PP ) - 1 ) );
Z[ j4 - ( 2*strideZ ) ] = dnm1 + Z[ j4p2 ];
Z[ j4 ] = Z[ j4p2 + ( 2*strideZ ) ] * ( Z[ j4p2 ] / Z[ j4 - ( 2*strideZ ) ] );
dn = ( Z[ j4p2 + ( 2*strideZ ) ]*( dnm1 / Z[ j4 - ( 2*strideZ ) ] ) ) - TAU;
dmin = min( dmin, dn );
} else {
if ( PP === 0 ) {
j4 = offsetZ + ( strideZ * ( ( 4*I0 ) + 3 ) );
for ( idx = ( 4*I0 ) + 3; idx <= ( 4*N0 ) - 9; idx += 4 ) {
Z[ j4 - ( 2*strideZ ) ] = d + Z[ j4 - strideZ ];
if ( d < 0 ) {
return out;
}
Z[ j4 ] = Z[ j4 + strideZ ] * ( Z[ j4 - strideZ ] / Z[ j4 - ( 2*strideZ ) ] );
d = ( Z[ j4 + strideZ ]*( d / Z[ j4 - ( 2*strideZ ) ] ) ) - TAU;
if ( d < dthresh ) {
d = 0;
}
dmin = min( dmin, d );
emin = min( emin, Z[ j4 ] );
j4 += 4*strideZ;
}
} else {
j4 = offsetZ + ( strideZ * ( ( 4*I0 ) + 3 ) );
for ( idx = ( 4*I0 ) + 3; idx <= ( 4*N0 ) - 9; idx += 4 ) {
Z[ j4 - ( 3*strideZ ) ] = d + Z[ j4 ];
if ( d < 0 ) {
return out;
}
Z[ j4 - strideZ ] = Z[ j4 + ( 2*strideZ ) ] * ( Z[ j4 ] / Z[ j4 - ( 3*strideZ ) ] );
d = ( Z[ j4 + ( 2*strideZ ) ]*( d / Z[ j4 - ( 3*strideZ ) ] ) ) - TAU;
if ( d < dthresh ) {
d = 0;
}
dmin = min( dmin, d );
emin = min( emin, Z[ j4 - strideZ ] );
j4 += 4*strideZ;
}
}
// Unroll last two steps.
dnm2 = d;
dmin2 = dmin;
j4 = offsetZ + ( strideZ * ( ( 4*N0 ) - 5 - PP ) );
j4p2 = j4 + ( strideZ * ( ( 2*PP ) - 1 ) );
Z[ j4 - ( 2*strideZ ) ] = dnm2 + Z[ j4p2 ];
if ( dnm2 < 0 ) {
return out;
}
Z[ j4 ] = Z[ j4p2 + ( 2*strideZ ) ] * ( Z[ j4p2 ] / Z[ j4 - ( 2*strideZ ) ] );
dnm1 = ( Z[ j4p2 + ( 2*strideZ ) ]*( dnm2 / Z[ j4 - ( 2*strideZ ) ] ) ) - TAU;
dmin = min( dmin, dnm1 );
dmin1 = dmin;
j4 += 4*strideZ;
j4p2 = j4 + ( strideZ * ( ( 2*PP ) - 1 ) );
Z[ j4 - ( 2*strideZ ) ] = dnm1 + Z[ j4p2 ];
if ( dnm1 < 0 ) {
return out;
}
Z[ j4 ] = Z[ j4p2 + ( 2*strideZ ) ] * ( Z[ j4p2 ] / Z[ j4 - ( 2*strideZ ) ] );
dn = ( Z[ j4p2 + ( 2*strideZ ) ]*( dnm1 / Z[ j4 - ( 2*strideZ ) ] ) ) - TAU;
dmin = min( dmin, dn );
}
}
Z[ j4 + ( 2*strideZ ) ] = dn;
Z[ offsetZ + ( strideZ * ( ( 4*N0 ) + 3 - PP ) ) ] = emin;
idx = offsetOut;
out[ idx ] = dmin;
idx += strideOut;
out[ idx ] = dmin1;
idx += strideOut;
out[ idx ] = dmin2;
idx += strideOut;
out[ idx ] = dn;
idx += strideOut;
out[ idx ] = dnm1;
idx += strideOut;
out[ idx ] = dnm2;
return out;
}
// EXPORTS //
module.exports = dlasq5;
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