time-to-botec

Benchmark sampling in different programming languages
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dnansumpw.js (4184B)

      1 /**
      2 * @license Apache-2.0
      3 *
      4 * Copyright (c) 2020 The Stdlib Authors.
      5 *
      6 * Licensed under the Apache License, Version 2.0 (the "License");
      7 * you may not use this file except in compliance with the License.
      8 * You may obtain a copy of the License at
      9 *
     10 *    http://www.apache.org/licenses/LICENSE-2.0
     11 *
     12 * Unless required by applicable law or agreed to in writing, software
     13 * distributed under the License is distributed on an "AS IS" BASIS,
     14 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
     15 * See the License for the specific language governing permissions and
     16 * limitations under the License.
     17 */
     18 
     19 'use strict';
     20 
     21 // MODULES //
     22 
     23 var floor = require( '@stdlib/math/base/special/floor' );
     24 
     25 
     26 // VARIABLES //
     27 
     28 // 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`.):
     29 var BLOCKSIZE = 128;
     30 
     31 
     32 // MAIN //
     33 
     34 /**
     35 * Computes the sum of a double-precision floating-point strided array elements, ignoring `NaN` values and using pairwise summation.
     36 *
     37 * ## Method
     38 *
     39 * -   This implementation uses pairwise summation, which accrues rounding error `O(log2 N)` instead of `O(N)`. The recursion depth is also `O(log2 N)`.
     40 *
     41 * ## References
     42 *
     43 * -   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).
     44 *
     45 * @private
     46 * @param {PositiveInteger} N - number of indexed elements
     47 * @param {NumericArray} out - two-element output array whose first element is the accumulated sum and whose second element is the accumulated number of summed values
     48 * @param {Float64Array} x - input array
     49 * @param {integer} stride - stride length
     50 * @param {NonNegativeInteger} offset - starting index
     51 * @returns {NumericArray} output array
     52 *
     53 * @example
     54 * var Float64Array = require( '@stdlib/array/float64' );
     55 * var floor = require( '@stdlib/math/base/special/floor' );
     56 *
     57 * var x = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0, NaN, NaN ] );
     58 * var N = floor( x.length / 2 );
     59 *
     60 * var out = [ 0.0, 0 ];
     61 * var v = dnansumpw( N, out, x, 2, 1 );
     62 * // returns [ 5.0, 4 ]
     63 */
     64 function dnansumpw( N, out, x, stride, offset ) {
     65 	var ix;
     66 	var s0;
     67 	var s1;
     68 	var s2;
     69 	var s3;
     70 	var s4;
     71 	var s5;
     72 	var s6;
     73 	var s7;
     74 	var M;
     75 	var s;
     76 	var n;
     77 	var v;
     78 	var i;
     79 
     80 	ix = offset;
     81 	if ( N < 8 ) {
     82 		// Use simple summation...
     83 		s = 0.0;
     84 		n = 0;
     85 		for ( i = 0; i < N; i++ ) {
     86 			v = x[ ix ];
     87 			if ( v === v ) {
     88 				s += v;
     89 				n += 1;
     90 			}
     91 			ix += stride;
     92 		}
     93 		out[ 0 ] += s;
     94 		out[ 1 ] += n;
     95 		return out;
     96 	}
     97 	if ( N <= BLOCKSIZE ) {
     98 		// Sum a block with 8 accumulators (by loop unrolling, we lower the effective blocksize to 16)...
     99 		s0 = 0.0;
    100 		s1 = 0.0;
    101 		s2 = 0.0;
    102 		s3 = 0.0;
    103 		s4 = 0.0;
    104 		s5 = 0.0;
    105 		s6 = 0.0;
    106 		s7 = 0.0;
    107 		n = 0;
    108 
    109 		M = N % 8;
    110 		for ( i = 0; i < N-M; i += 8 ) {
    111 			v = x[ ix ];
    112 			if ( v === v ) {
    113 				s0 += v;
    114 				n += 1;
    115 			}
    116 			ix += stride;
    117 			v = x[ ix ];
    118 			if ( v === v ) {
    119 				s1 += v;
    120 				n += 1;
    121 			}
    122 			ix += stride;
    123 			v = x[ ix ];
    124 			if ( v === v ) {
    125 				s2 += v;
    126 				n += 1;
    127 			}
    128 			ix += stride;
    129 			v = x[ ix ];
    130 			if ( v === v ) {
    131 				s3 += v;
    132 				n += 1;
    133 			}
    134 			ix += stride;
    135 			v = x[ ix ];
    136 			if ( v === v ) {
    137 				s4 += v;
    138 				n += 1;
    139 			}
    140 			ix += stride;
    141 			v = x[ ix ];
    142 			if ( v === v ) {
    143 				s5 += v;
    144 				n += 1;
    145 			}
    146 			ix += stride;
    147 			v = x[ ix ];
    148 			if ( v === v ) {
    149 				s6 += v;
    150 				n += 1;
    151 			}
    152 			ix += stride;
    153 			v = x[ ix ];
    154 			if ( v === v ) {
    155 				s7 += v;
    156 				n += 1;
    157 			}
    158 			ix += stride;
    159 		}
    160 		// Pairwise sum the accumulators:
    161 		s = ((s0+s1) + (s2+s3)) + ((s4+s5) + (s6+s7));
    162 
    163 		// Clean-up loop...
    164 		for ( i; i < N; i++ ) {
    165 			v = x[ ix ];
    166 			if ( v === v ) {
    167 				s += v;
    168 				n += 1;
    169 			}
    170 			ix += stride;
    171 		}
    172 		out[ 0 ] += s;
    173 		out[ 1 ] += n;
    174 		return out;
    175 	}
    176 	// Recurse by dividing by two, but avoiding non-multiples of unroll factor...
    177 	n = floor( N/2 );
    178 	n -= n % 8;
    179 	return dnansumpw( n, out, x, stride, ix ) + dnansumpw( N-n, out, x, stride, ix+(n*stride) ); // eslint-disable-line max-len
    180 }
    181 
    182 
    183 // EXPORTS //
    184 
    185 module.exports = dnansumpw;