time-to-botec

Benchmark sampling in different programming languages
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ndarray.js (4191B)

      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 var abs = require( '@stdlib/math/base/special/abs' );
     26 
     27 
     28 // VARIABLES //
     29 
     30 // 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`.):
     31 var BLOCKSIZE = 128;
     32 
     33 
     34 // MAIN //
     35 
     36 /**
     37 * Computes the sum of absolute values (L1 norm) of single-precision floating-point strided array elements using pairwise summation.
     38 *
     39 * ## Method
     40 *
     41 * -   This implementation uses pairwise summation, which accrues rounding error `O(log2 N)` instead of `O(N)`. The recursion depth is also `O(log2 N)`.
     42 *
     43 * ## References
     44 *
     45 * -   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).
     46 *
     47 * @param {PositiveInteger} N - number of indexed elements
     48 * @param {Float32Array} x - input array
     49 * @param {integer} stride - stride length
     50 * @param {NonNegativeInteger} offset - starting index
     51 * @returns {number} sum
     52 *
     53 * @example
     54 * var Float32Array = require( '@stdlib/array/float32' );
     55 * var floor = require( '@stdlib/math/base/special/floor' );
     56 *
     57 * var x = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
     58 * var N = floor( x.length / 2 );
     59 *
     60 * var v = sasumpw( N, x, 2, 1 );
     61 * // returns 9.0
     62 */
     63 function sasumpw( N, x, stride, offset ) {
     64 	var ix;
     65 	var s0;
     66 	var s1;
     67 	var s2;
     68 	var s3;
     69 	var s4;
     70 	var s5;
     71 	var s6;
     72 	var s7;
     73 	var M;
     74 	var s;
     75 	var n;
     76 	var i;
     77 
     78 	if ( N <= 0 ) {
     79 		return 0.0;
     80 	}
     81 	if ( N === 1 || stride === 0 ) {
     82 		return abs( x[ offset ] );
     83 	}
     84 	ix = offset;
     85 	if ( N < 8 ) {
     86 		// Use simple summation...
     87 		s = 0.0;
     88 		for ( i = 0; i < N; i++ ) {
     89 			s = float64ToFloat32( s + abs( x[ ix ] ) );
     90 			ix += stride;
     91 		}
     92 		return s;
     93 	}
     94 	if ( N <= BLOCKSIZE ) {
     95 		// Sum a block with 8 accumulators (by loop unrolling, we lower the effective blocksize to 16)...
     96 		s0 = abs( x[ ix ] );
     97 		s1 = abs( x[ ix+stride ] );
     98 		s2 = abs( x[ ix+(2*stride) ] );
     99 		s3 = abs( x[ ix+(3*stride) ] );
    100 		s4 = abs( x[ ix+(4*stride) ] );
    101 		s5 = abs( x[ ix+(5*stride) ] );
    102 		s6 = abs( x[ ix+(6*stride) ] );
    103 		s7 = abs( x[ ix+(7*stride) ] );
    104 		ix += 8 * stride;
    105 
    106 		M = N % 8;
    107 		for ( i = 8; i < N-M; i += 8 ) {
    108 			s0 = float64ToFloat32( s0 + abs( x[ ix ] ) );
    109 			s1 = float64ToFloat32( s1 + abs( x[ ix+stride ] ) );
    110 			s2 = float64ToFloat32( s2 + abs( x[ ix+(2*stride) ] ) );
    111 			s3 = float64ToFloat32( s3 + abs( x[ ix+(3*stride) ] ) );
    112 			s4 = float64ToFloat32( s4 + abs( x[ ix+(4*stride) ] ) );
    113 			s5 = float64ToFloat32( s5 + abs( x[ ix+(5*stride) ] ) );
    114 			s6 = float64ToFloat32( s6 + abs( x[ ix+(6*stride) ] ) );
    115 			s7 = float64ToFloat32( s7 + abs( x[ ix+(7*stride) ] ) );
    116 			ix += 8 * stride;
    117 		}
    118 		// Pairwise sum the accumulators:
    119 		s = float64ToFloat32( float64ToFloat32( float64ToFloat32(s0+s1) + float64ToFloat32(s2+s3) ) + float64ToFloat32( float64ToFloat32(s4+s5) + float64ToFloat32(s6+s7) ) ); // eslint-disable-line max-len
    120 
    121 		// Clean-up loop...
    122 		for ( i; i < N; i++ ) {
    123 			s = float64ToFloat32( s + abs( x[ ix ] ) );
    124 			ix += stride;
    125 		}
    126 		return s;
    127 	}
    128 	// Recurse by dividing by two, but avoiding non-multiples of unroll factor...
    129 	n = floor( N/2 );
    130 	n -= n % 8;
    131 	return float64ToFloat32( sasumpw( n, x, stride, ix ) + sasumpw( N-n, x, stride, ix+(n*stride) ) ); // eslint-disable-line max-len
    132 }
    133 
    134 
    135 // EXPORTS //
    136 
    137 module.exports = sasumpw;