README.md (5184B)
1 <!-- 2 3 @license Apache-2.0 4 5 Copyright (c) 2020 The Stdlib Authors. 6 7 Licensed under the Apache License, Version 2.0 (the "License"); 8 you may not use this file except in compliance with the License. 9 You may obtain a copy of the License at 10 11 http://www.apache.org/licenses/LICENSE-2.0 12 13 Unless required by applicable law or agreed to in writing, software 14 distributed under the License is distributed on an "AS IS" BASIS, 15 WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 16 See the License for the specific language governing permissions and 17 limitations under the License. 18 19 --> 20 21 # dsumpw 22 23 > Calculate the sum of double-precision floating-point strided array elements using pairwise summation. 24 25 <section class="intro"> 26 27 </section> 28 29 <!-- /.intro --> 30 31 <section class="usage"> 32 33 ## Usage 34 35 ```javascript 36 var dsumpw = require( '@stdlib/blas/ext/base/dsumpw' ); 37 ``` 38 39 #### dsumpw( N, x, stride ) 40 41 Computes the sum of double-precision floating-point strided array elements using pairwise summation. 42 43 ```javascript 44 var Float64Array = require( '@stdlib/array/float64' ); 45 46 var x = new Float64Array( [ 1.0, -2.0, 2.0 ] ); 47 var N = x.length; 48 49 var v = dsumpw( N, x, 1 ); 50 // returns 1.0 51 ``` 52 53 The function has the following parameters: 54 55 - **N**: number of indexed elements. 56 - **x**: input [`Float64Array`][@stdlib/array/float64]. 57 - **stride**: index increment for `x`. 58 59 The `N` and `stride` parameters determine which elements in `x` are accessed at runtime. For example, to compute the sum of every other element in `x`, 60 61 ```javascript 62 var Float64Array = require( '@stdlib/array/float64' ); 63 var floor = require( '@stdlib/math/base/special/floor' ); 64 65 var x = new Float64Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] ); 66 var N = floor( x.length / 2 ); 67 68 var v = dsumpw( N, x, 2 ); 69 // returns 5.0 70 ``` 71 72 Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views. 73 74 <!-- eslint-disable stdlib/capitalized-comments --> 75 76 ```javascript 77 var Float64Array = require( '@stdlib/array/float64' ); 78 var floor = require( '@stdlib/math/base/special/floor' ); 79 80 var x0 = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] ); 81 var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element 82 83 var N = floor( x0.length / 2 ); 84 85 var v = dsumpw( N, x1, 2 ); 86 // returns 5.0 87 ``` 88 89 #### dsumpw.ndarray( N, x, stride, offset ) 90 91 Computes the sum of double-precision floating-point strided array elements using pairwise summation and alternative indexing semantics. 92 93 ```javascript 94 var Float64Array = require( '@stdlib/array/float64' ); 95 96 var x = new Float64Array( [ 1.0, -2.0, 2.0 ] ); 97 var N = x.length; 98 99 var v = dsumpw.ndarray( N, x, 1, 0 ); 100 // returns 1.0 101 ``` 102 103 The function has the following additional parameters: 104 105 - **offset**: starting index for `x`. 106 107 While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying `buffer`, the `offset` parameter supports indexing semantics based on a starting index. For example, to calculate the sum of every other value in `x` starting from the second value 108 109 ```javascript 110 var Float64Array = require( '@stdlib/array/float64' ); 111 var floor = require( '@stdlib/math/base/special/floor' ); 112 113 var x = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] ); 114 var N = floor( x.length / 2 ); 115 116 var v = dsumpw.ndarray( N, x, 2, 1 ); 117 // returns 5.0 118 ``` 119 120 </section> 121 122 <!-- /.usage --> 123 124 <section class="notes"> 125 126 ## Notes 127 128 - If `N <= 0`, both functions return `0.0`. 129 - In general, pairwise summation is more numerically stable than ordinary recursive summation (i.e., "simple" summation), with slightly worse performance. While not the most numerically stable summation technique (e.g., compensated summation techniques such as the Kahan–Babuška-Neumaier algorithm are generally more numerically stable), pairwise summation strikes a reasonable balance between numerical stability and performance. If either numerical stability or performance is more desirable for your use case, consider alternative summation techniques. 130 131 </section> 132 133 <!-- /.notes --> 134 135 <section class="examples"> 136 137 ## Examples 138 139 <!-- eslint no-undef: "error" --> 140 141 ```javascript 142 var randu = require( '@stdlib/random/base/randu' ); 143 var round = require( '@stdlib/math/base/special/round' ); 144 var Float64Array = require( '@stdlib/array/float64' ); 145 var dsumpw = require( '@stdlib/blas/ext/base/dsumpw' ); 146 147 var x; 148 var i; 149 150 x = new Float64Array( 10 ); 151 for ( i = 0; i < x.length; i++ ) { 152 x[ i ] = round( randu()*100.0 ); 153 } 154 console.log( x ); 155 156 var v = dsumpw( x.length, x, 1 ); 157 console.log( v ); 158 ``` 159 160 </section> 161 162 <!-- /.examples --> 163 164 * * * 165 166 <section class="references"> 167 168 ## References 169 170 - Higham, Nicholas J. 1993. "The Accuracy of Floating Point Summation." _SIAM Journal on Scientific Computing_ 14 (4): 783–99. doi:[10.1137/0914050][@higham:1993a]. 171 172 </section> 173 174 <!-- /.references --> 175 176 <section class="links"> 177 178 [@stdlib/array/float64]: https://www.npmjs.com/package/@stdlib/array-float64 179 180 [mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray 181 182 [@higham:1993a]: https://doi.org/10.1137/0914050 183 184 </section> 185 186 <!-- /.links -->