snansumpw.js (4725B)
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 float64ToFloat32 = require( '@stdlib/number/float64/base/to-float32' ); 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 a 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 * @private 47 * @param {PositiveInteger} N - number of indexed elements 48 * @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 49 * @param {Float32Array} x - input array 50 * @param {integer} stride - stride length 51 * @param {NonNegativeInteger} offset - starting index 52 * @returns {NumericArray} output array 53 * 54 * @example 55 * var Float32Array = require( '@stdlib/array/float32' ); 56 * var floor = require( '@stdlib/math/base/special/floor' ); 57 * 58 * var x = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0, NaN, NaN ] ); 59 * var N = floor( x.length / 2 ); 60 * 61 * var out = [ 0.0, 0 ]; 62 * var v = snansumpw( N, out, x, 2, 1 ); 63 * // returns [ 5.0, 4 ] 64 */ 65 function snansumpw( N, out, x, stride, offset ) { 66 var ix; 67 var s0; 68 var s1; 69 var s2; 70 var s3; 71 var s4; 72 var s5; 73 var s6; 74 var s7; 75 var M; 76 var s; 77 var n; 78 var v; 79 var i; 80 81 ix = offset; 82 if ( N < 8 ) { 83 // Use simple summation... 84 s = 0.0; 85 n = 0; 86 for ( i = 0; i < N; i++ ) { 87 v = x[ ix ]; 88 if ( v === v ) { 89 s = float64ToFloat32( s + v ); 90 n += 1; 91 } 92 ix += stride; 93 } 94 out[ 0 ] = float64ToFloat32( out[ 0 ] + s ); 95 out[ 1 ] += n; 96 return out; 97 } 98 if ( N <= BLOCKSIZE ) { 99 // Sum a block with 8 accumulators (by loop unrolling, we lower the effective blocksize to 16)... 100 s0 = 0.0; 101 s1 = 0.0; 102 s2 = 0.0; 103 s3 = 0.0; 104 s4 = 0.0; 105 s5 = 0.0; 106 s6 = 0.0; 107 s7 = 0.0; 108 n = 0; 109 110 M = N % 8; 111 for ( i = 0; i < N-M; i += 8 ) { 112 v = x[ ix ]; 113 if ( v === v ) { 114 s0 = float64ToFloat32( s0 + v ); 115 n += 1; 116 } 117 ix += stride; 118 v = x[ ix ]; 119 if ( v === v ) { 120 s1 = float64ToFloat32( s1 + v ); 121 n += 1; 122 } 123 ix += stride; 124 v = x[ ix ]; 125 if ( v === v ) { 126 s2 = float64ToFloat32( s2 + v ); 127 n += 1; 128 } 129 ix += stride; 130 v = x[ ix ]; 131 if ( v === v ) { 132 s3 = float64ToFloat32( s3 + v ); 133 n += 1; 134 } 135 ix += stride; 136 v = x[ ix ]; 137 if ( v === v ) { 138 s4 = float64ToFloat32( s4 + v ); 139 n += 1; 140 } 141 ix += stride; 142 v = x[ ix ]; 143 if ( v === v ) { 144 s5 = float64ToFloat32( s5 + v ); 145 n += 1; 146 } 147 ix += stride; 148 v = x[ ix ]; 149 if ( v === v ) { 150 s6 = float64ToFloat32( s6 + v ); 151 n += 1; 152 } 153 ix += stride; 154 v = x[ ix ]; 155 if ( v === v ) { 156 s7 = float64ToFloat32( s7 + v ); 157 n += 1; 158 } 159 ix += stride; 160 } 161 // Pairwise sum the accumulators: 162 s = float64ToFloat32( float64ToFloat32(float64ToFloat32(s0+s1) + float64ToFloat32(s2+s3)) + float64ToFloat32(float64ToFloat32(s4+s5) + float64ToFloat32(s6+s7)) ); // eslint-disable-line max-len 163 164 // Clean-up loop... 165 for ( i; i < N; i++ ) { 166 v = x[ ix ]; 167 if ( v === v ) { 168 s = float64ToFloat32( s + v ); 169 n += 1; 170 } 171 ix += stride; 172 } 173 out[ 0 ] = float64ToFloat32( out[ 0 ] + s ); 174 out[ 1 ] += n; 175 return out; 176 } 177 // Recurse by dividing by two, but avoiding non-multiples of unroll factor... 178 n = floor( N/2 ); 179 n -= n % 8; 180 return float64ToFloat32( snansumpw( n, out, x, stride, ix ) + snansumpw( N-n, out, x, stride, ix+(n*stride) ) ); // eslint-disable-line max-len 181 } 182 183 184 // EXPORTS // 185 186 module.exports = snansumpw;