dnansumkbn2.c (2340B)
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/dnansumkbn2.h" 20 #include "stdlib/math/base/assert/is_nan.h" 21 #include <stdint.h> 22 #include <math.h> 23 24 /** 25 * Computes the sum of double-precision floating-point strided array elements, ignoring `NaN` values and using a second-order iterative Kahan–Babuška algorithm. 26 * 27 * ## Method 28 * 29 * - This implementation uses a second-order iterative Kahan–Babuška algorithm, as described by Klein (2005). 30 * 31 * ## References 32 * 33 * - 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). 34 * 35 * @param N number of indexed elements 36 * @param X input array 37 * @param stride stride length 38 * @return output value 39 */ 40 double stdlib_strided_dnansumkbn2( const int64_t N, const double *X, const int64_t stride ) { 41 double sum; 42 double ccs; 43 int64_t ix; 44 int64_t i; 45 double cs; 46 double cc; 47 double v; 48 double t; 49 double c; 50 51 if ( N <= 0 ) { 52 return 0.0; 53 } 54 if ( N == 1 || stride == 0 ) { 55 if ( stdlib_base_is_nan( X[ 0 ] ) ) { 56 return 0.0; 57 } 58 return X[ 0 ]; 59 } 60 if ( stride < 0 ) { 61 ix = (1-N) * stride; 62 } else { 63 ix = 0; 64 } 65 sum = 0.0; 66 ccs = 0.0; // second order correction term for lost lower order bits 67 cs = 0.0; // first order correction term for lost low order bits 68 for ( i = 0; i < N; i++ ) { 69 v = X[ ix ]; 70 if ( !stdlib_base_is_nan( v ) ) { 71 t = sum + v; 72 if ( fabs( sum ) >= fabs( v ) ) { 73 c = (sum-t) + v; 74 } else { 75 c = (v-t) + sum; 76 } 77 sum = 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 ix += stride; 88 } 89 return sum + cs + ccs; 90 }