time-to-botec

Benchmark sampling in different programming languages
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ndarray.js (4277B)

      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 isnan = require( '@stdlib/math/base/assert/is-nan' );
     24 var floor = require( '@stdlib/math/base/special/floor' );
     25 
     26 
     27 // VARIABLES //
     28 
     29 // 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`.):
     30 var BLOCKSIZE = 128;
     31 
     32 
     33 // MAIN //
     34 
     35 /**
     36 * Computes the sum of double-precision floating-point strided array elements, ignoring `NaN` values and using pairwise summation.
     37 *
     38 * ## Method
     39 *
     40 * -   This implementation uses pairwise summation, which accrues rounding error `O(log2 N)` instead of `O(N)`. The recursion depth is also `O(log2 N)`.
     41 *
     42 * ## References
     43 *
     44 * -   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).
     45 *
     46 * @param {PositiveInteger} N - number of indexed elements
     47 * @param {Float64Array} x - input array
     48 * @param {integer} stride - stride length
     49 * @param {NonNegativeInteger} offset - starting index
     50 * @returns {number} sum
     51 *
     52 * @example
     53 * var Float64Array = require( '@stdlib/array/float64' );
     54 * var floor = require( '@stdlib/math/base/special/floor' );
     55 *
     56 * var x = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0, NaN, NaN ] );
     57 * var N = floor( x.length / 2 );
     58 *
     59 * var v = dnansumpw( N, x, 2, 1 );
     60 * // returns 5.0
     61 */
     62 function dnansumpw( N, x, stride, offset ) {
     63 	var ix;
     64 	var s0;
     65 	var s1;
     66 	var s2;
     67 	var s3;
     68 	var s4;
     69 	var s5;
     70 	var s6;
     71 	var s7;
     72 	var M;
     73 	var s;
     74 	var n;
     75 	var i;
     76 
     77 	if ( N <= 0 ) {
     78 		return 0.0;
     79 	}
     80 	if ( N === 1 || stride === 0 ) {
     81 		if ( isnan( x[ offset ] ) ) {
     82 			return 0.0;
     83 		}
     84 		return x[ offset ];
     85 	}
     86 	ix = offset;
     87 	if ( N < 8 ) {
     88 		// Use simple summation...
     89 		s = 0.0;
     90 		for ( i = 0; i < N; i++ ) {
     91 			if ( isnan( x[ ix ] ) === false ) {
     92 				s += x[ ix ];
     93 			}
     94 			ix += stride;
     95 		}
     96 		return s;
     97 	}
     98 	if ( N <= BLOCKSIZE ) {
     99 		// Sum a block with 8 accumulators (by loop unrolling, we lower the effective blocksize to 16)...
    100 		s0 = ( isnan( x[ ix ] ) ) ? 0.0 : x[ ix ];
    101 		ix += stride;
    102 		s1 = ( isnan( x[ ix ] ) ) ? 0.0 : x[ ix ];
    103 		ix += stride;
    104 		s2 = ( isnan( x[ ix ] ) ) ? 0.0 : x[ ix ];
    105 		ix += stride;
    106 		s3 = ( isnan( x[ ix ] ) ) ? 0.0 : x[ ix ];
    107 		ix += stride;
    108 		s4 = ( isnan( x[ ix ] ) ) ? 0.0 : x[ ix ];
    109 		ix += stride;
    110 		s5 = ( isnan( x[ ix ] ) ) ? 0.0 : x[ ix ];
    111 		ix += stride;
    112 		s6 = ( isnan( x[ ix ] ) ) ? 0.0 : x[ ix ];
    113 		ix += stride;
    114 		s7 = ( isnan( x[ ix ] ) ) ? 0.0 : x[ ix ];
    115 		ix += stride;
    116 
    117 		M = N % 8;
    118 		for ( i = 8; i < N-M; i += 8 ) {
    119 			s0 += ( isnan( x[ ix ] ) ) ? 0.0 : x[ ix ];
    120 			ix += stride;
    121 			s1 += ( isnan( x[ ix ] ) ) ? 0.0 : x[ ix ];
    122 			ix += stride;
    123 			s2 += ( isnan( x[ ix ] ) ) ? 0.0 : x[ ix ];
    124 			ix += stride;
    125 			s3 += ( isnan( x[ ix ] ) ) ? 0.0 : x[ ix ];
    126 			ix += stride;
    127 			s4 += ( isnan( x[ ix ] ) ) ? 0.0 : x[ ix ];
    128 			ix += stride;
    129 			s5 += ( isnan( x[ ix ] ) ) ? 0.0 : x[ ix ];
    130 			ix += stride;
    131 			s6 += ( isnan( x[ ix ] ) ) ? 0.0 : x[ ix ];
    132 			ix += stride;
    133 			s7 += ( isnan( x[ ix ] ) ) ? 0.0 : x[ ix ];
    134 			ix += stride;
    135 		}
    136 		// Pairwise sum the accumulators:
    137 		s = ((s0+s1) + (s2+s3)) + ((s4+s5) + (s6+s7));
    138 
    139 		// Clean-up loop...
    140 		for ( i; i < N; i++ ) {
    141 			if ( isnan( x[ ix ] ) === false ) {
    142 				s += x[ ix ];
    143 			}
    144 			ix += stride;
    145 		}
    146 		return s;
    147 	}
    148 	// Recurse by dividing by two, but avoiding non-multiples of unroll factor...
    149 	n = floor( N/2 );
    150 	n -= n % 8;
    151 	return dnansumpw( n, x, stride, ix ) + dnansumpw( N-n, x, stride, ix+(n*stride) ); // eslint-disable-line max-len
    152 }
    153 
    154 
    155 // EXPORTS //
    156 
    157 module.exports = dnansumpw;