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@stdlib/blas-ext-base-ssumpw

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Calculate the sum of single-precision floating-point strided array elements using pairwise summation.

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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 float64ToFloat32 = require( '@stdlib/number-float64-base-to-float32' ); 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 single-precision floating-point strided array elements 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). * * @param {PositiveInteger} N - number of indexed elements * @param {Float32Array} x - input array * @param {integer} stride - stride length * @param {NonNegativeInteger} offset - starting index * @returns {number} sum * * @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 ] ); * * var v = ssumpw( 4, x, 2, 1 ); * // returns 5.0 */ function ssumpw( N, x, stride, offset ) { var ix; var s0; var s1; var s2; var s3; var s4; var s5; var s6; var s7; var M; var s; var n; var i; if ( N <= 0 ) { return 0.0; } if ( N === 1 || stride === 0 ) { return x[ offset ]; } ix = offset; if ( N < 8 ) { // Use simple summation... s = 0.0; for ( i = 0; i < N; i++ ) { s = float64ToFloat32( s + x[ ix ] ); ix += stride; } return s; } if ( N <= BLOCKSIZE ) { // Sum a block with 8 accumulators (by loop unrolling, we lower the effective blocksize to 16)... s0 = x[ ix ]; s1 = x[ ix+stride ]; s2 = x[ ix+(2*stride) ]; s3 = x[ ix+(3*stride) ]; s4 = x[ ix+(4*stride) ]; s5 = x[ ix+(5*stride) ]; s6 = x[ ix+(6*stride) ]; s7 = x[ ix+(7*stride) ]; ix += 8 * stride; M = N % 8; for ( i = 8; i < N-M; i += 8 ) { s0 = float64ToFloat32( s0 + x[ ix ] ); s1 = float64ToFloat32( s1 + x[ ix+stride ] ); s2 = float64ToFloat32( s2 + x[ ix+(2*stride) ] ); s3 = float64ToFloat32( s3 + x[ ix+(3*stride) ] ); s4 = float64ToFloat32( s4 + x[ ix+(4*stride) ] ); s5 = float64ToFloat32( s5 + x[ ix+(5*stride) ] ); s6 = float64ToFloat32( s6 + x[ ix+(6*stride) ] ); s7 = float64ToFloat32( s7 + x[ ix+(7*stride) ] ); ix += 8 * stride; } // Pairwise sum the accumulators: s = float64ToFloat32( float64ToFloat32( float64ToFloat32(s0+s1) + float64ToFloat32(s2+s3) ) + float64ToFloat32( float64ToFloat32(s4+s5) + float64ToFloat32(s6+s7) ) ); // eslint-disable-line max-len // Clean-up loop... for ( i; i < N; i++ ) { s = float64ToFloat32( s + x[ ix ] ); ix += stride; } return s; } // Recurse by dividing by two, but avoiding non-multiples of unroll factor... n = floor( N/2 ); n -= n % 8; return float64ToFloat32( ssumpw( n, x, stride, ix ) + ssumpw( N-n, x, stride, ix+(n*stride) ) ); // eslint-disable-line max-len } // EXPORTS // module.exports = ssumpw;