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* @license Apache-2.0
*
* Copyright (c) 2025 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 float64ToFloat32 = require( '@stdlib/number/float64/base/to-float32' );
var isnanf = require( '@stdlib/math/base/assert/is-nanf' );
var floor = require( '@stdlib/math/base/special/floor' );
// VARIABLES //
// Blocksize for pairwise summation (NOTE: decreasing the blocksize decreases rounding error as more pairs are summed, but also decreases performance. Because the inner loop is unrolled eight times, the blocksize is effectively `16`.):
var BLOCKSIZE = 128;
// MAIN //
/**
* Computes the sum of a single-precision floating-point strided array elements, ignoring `NaN` values and using pairwise summation.
*
* ## Method
*
* - This implementation uses pairwise summation, which accrues rounding error `O(log2 N)` instead of `O(N)`. The recursion depth is also `O(log2 N)`.
*
* ## References
*
* - Higham, Nicholas J. 1993. "The Accuracy of Floating Point Summation." _SIAM Journal on Scientific Computing_ 14 (4): 783–99. doi:[10.1137/0914050](https://doi.org/10.1137/0914050).
*
* @private
* @param {PositiveInteger} N - number of indexed elements
* @param {Float32Array} x - input array
* @param {integer} strideX - stride length for `x`
* @param {NonNegativeInteger} offsetX - starting index for `x`
* @param {Float32Array} out - two-element output array whose first element is the accumulated sum and whose second element is the accumulated number of summed values
* @param {integer} strideOut - stride length for `out`
* @param {NonNegativeInteger} offsetOut - starting index for `out`
* @returns {Float32Array} output array
*
* @example
* var Float32Array = require( '@stdlib/array/float32' );
*
* var x = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0, NaN, NaN ] );
* var out = new Float32Array( [ 0.0, 0 ] );
*
* var v = sumpw( 5.0, x, 2, 1, out, 1, 0 );
* // returns <Float32Array>[ 5.0, 4 ]
*/
function sumpw( N, x, strideX, offsetX, out, strideOut, offsetOut ) { // eslint-disable-line max-statements
var ix;
var io;
var s0;
var s1;
var s2;
var s3;
var s4;
var s5;
var s6;
var s7;
var t0;
var t1;
var t2;
var t3;
var M;
var s;
var n;
var v;
var i;
if ( N <= 0 ) {
return out;
}
io = offsetOut;
ix = offsetX;
if ( strideX === 0 ) {
if ( isnanf( x[ ix ] ) ) {
return out;
}
out[ io ] += float64ToFloat32( float64ToFloat32( x[ ix ] ) * N );
out[ io+strideOut ] += N;
return out;
}
// Find the first non-NaN element...
for ( i = 0; i < N; i++ ) {
v = x[ ix ];
if ( isnanf( v ) === false ) {
break;
}
ix += strideX;
}
// If every element was NaN, we are done...
if ( i === N ) {
return out;
}
n = 1;
s = float64ToFloat32( v );
ix += strideX;
i += 1;
// In order to preserve the sign of zero which can be lost during pairwise summation below, find the first non-zero element...
if ( s === 0.0 ) {
for ( ; i < N; i++ ) {
v = x[ ix ];
if ( isnanf( v ) === false ) {
if ( v !== 0.0 ) {
break;
}
s += float64ToFloat32( v );
n += 1;
}
ix += strideX;
}
}
// If every subsequent element was either NaN or zero, we are done...
if ( i === N ) {
out[ io ] += float64ToFloat32( s );
out[ io+strideOut ] += n;
return out;
}
// If we are here, then we found a non-zero element and we no longer have to be concerned about preserving zero's sign...
if ( (N-i) < 8 ) {
// Use simple summation...
for ( ; i < N; i++ ) {
v = x[ ix ];
if ( isnanf( v ) === false ) {
s += float64ToFloat32( v );
n += 1;
}
ix += strideX;
}
out[ io ] += float64ToFloat32( s );
out[ io+strideOut ] += n;
return out;
}
if ( (N-i) <= BLOCKSIZE ) {
// Sum a block with 8 accumulators (by loop unrolling, we lower the effective blocksize to 16)...
s0 = -0.0; // note: negative zero in order to ensure sign preservation if all elements are negative zero
s1 = -0.0;
s2 = -0.0;
s3 = -0.0;
s4 = -0.0;
s5 = -0.0;
s6 = -0.0;
s7 = -0.0;
M = (N-i) % 8;
for ( ; i < N-M; i += 8 ) {
v = x[ ix ];
if ( isnanf( v ) === false ) {
s0 += float64ToFloat32( v );
n += 1;
}
ix += strideX;
v = x[ ix ];
if ( isnanf( v ) === false ) {
s1 += float64ToFloat32( v );
n += 1;
}
ix += strideX;
v = x[ ix ];
if ( isnanf( v ) === false ) {
s2 += float64ToFloat32( v );
n += 1;
}
ix += strideX;
v = x[ ix ];
if ( isnanf( v ) === false ) {
s3 += float64ToFloat32( v );
n += 1;
}
ix += strideX;
v = x[ ix ];
if ( isnanf( v ) === false ) {
s4 += float64ToFloat32( v );
n += 1;
}
ix += strideX;
v = x[ ix ];
if ( isnanf( v ) === false ) {
s5 += float64ToFloat32( v );
n += 1;
}
ix += strideX;
v = x[ ix ];
if ( isnanf( v ) === false ) {
s6 += float64ToFloat32( v );
n += 1;
}
ix += strideX;
v = x[ ix ];
if ( isnanf( v ) === false ) {
s7 += float64ToFloat32( v );
n += 1;
}
ix += strideX;
}
// Pairwise sum the accumulators:
t0 = float64ToFloat32( s0 ) + float64ToFloat32( s1 );
t1 = float64ToFloat32( s2 ) + float64ToFloat32( s3 );
t2 = float64ToFloat32( s4 ) + float64ToFloat32( s5 );
t3 = float64ToFloat32( s6 ) + float64ToFloat32( s7 );
s += float64ToFloat32( float64ToFloat32( t0 + t1 ) + float64ToFloat32( t2 + t3 ) ); // eslint-disable-line max-len
// Clean-up loop...
for ( ; i < N; i++ ) {
v = float64ToFloat32( x[ ix ] );
if ( isnanf( v ) === false ) {
s += float64ToFloat32( v );
n += 1;
}
ix += strideX;
}
out[ io ] += float64ToFloat32( s );
out[ io+strideOut ] += n;
return out;
}
out[ io ] += float64ToFloat32( s );
out[ io+strideOut ] += n;
// Recurse by dividing by two, but avoiding non-multiples of unroll factor...
n = floor( (N-i)/2 );
n -= n % 8;
sumpw( n, x, strideX, ix, out, strideOut, io );
sumpw( N-i-n, x, strideX, ix+(n*strideX), out, strideOut, io );
return out;
}
// EXPORTS //
module.exports = sumpw;
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