dcusumkbn2.c (2329B)
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 #include "stdlib/blas/ext/base/dcusumkbn2.h" 20 #include <stdint.h> 21 #include <math.h> 22 23 /** 24 * Computes the cumulative sum of double-precision floating-point strided array elements using a second-order iterative Kahan–Babuška algorithm. 25 * 26 * ## Method 27 * 28 * - This implementation uses a second-order iterative Kahan–Babuška algorithm, as described by Klein (2005). 29 * 30 * ## References 31 * 32 * - Klein, Andreas. 2005. "A Generalized Kahan-Babuška-Summation-Algorithm." _Computing_ 76 (3): 279–93. doi:[10.1007/s00607-005-0139-x](https://doi.org/10.1007/s00607-005-0139-x). 33 * 34 * @param N number of indexed elements 35 * @param sum initial sum 36 * @param X input array 37 * @param strideX X stride length 38 * @param Y output array 39 * @param strideY Y stride length 40 */ 41 void stdlib_strided_dcusumkbn2( const int64_t N, const double sum, const double *X, const int64_t strideX, double *Y, const int64_t strideY ) { 42 double ccs; 43 int64_t ix; 44 int64_t iy; 45 int64_t i; 46 double cs; 47 double cc; 48 double v; 49 double t; 50 double c; 51 double s; 52 53 if ( N <= 0 ) { 54 return; 55 } 56 if ( strideX < 0 ) { 57 ix = (1-N) * strideX; 58 } else { 59 ix = 0; 60 } 61 if ( strideY < 0 ) { 62 iy = (1-N) * strideY; 63 } else { 64 iy = 0; 65 } 66 s = sum; 67 ccs = 0.0; // second order correction term for lost lower order bits 68 cs = 0.0; // first order correction term for lost low order bits 69 for ( i = 0; i < N; i++ ) { 70 v = X[ ix ]; 71 t = s + v; 72 if ( fabs( s ) >= fabs( v ) ) { 73 c = (s-t) + v; 74 } else { 75 c = (v-t) + s; 76 } 77 s = t; 78 t = cs + c; 79 if ( fabs( cs ) >= fabs( c ) ) { 80 cc = (cs-t) + c; 81 } else { 82 cc = (c-t) + cs; 83 } 84 cs = t; 85 ccs += cc; 86 87 Y[ iy ] = s + cs + ccs; 88 ix += strideX; 89 iy += strideY; 90 } 91 return; 92 }