sapxsumkbn.c (1977B)
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/sapxsumkbn.h" 20 #include <stdint.h> 21 #include <math.h> 22 23 /** 24 * Adds a constant to each single-precision floating-point strided array element and computes the sum using an improved Kahan–Babuška algorithm. 25 * 26 * ## Method 27 * 28 * - This implementation uses an "improved Kahan–Babuška algorithm", as described by Neumaier (1974). 29 * 30 * ## References 31 * 32 * - Neumaier, Arnold. 1974. "Rounding Error Analysis of Some Methods for Summing Finite Sums." _Zeitschrift Für Angewandte Mathematik Und Mechanik_ 54 (1): 39–51. doi:[10.1002/zamm.19740540106](https://doi.org/10.1002/zamm.19740540106). 33 * 34 * @param N number of indexed elements 35 * @param alpha constant 36 * @param X input array 37 * @param stride stride length 38 * @return output value 39 */ 40 float stdlib_strided_sapxsumkbn( const int64_t N, const float alpha, const float *X, const int64_t stride ) { 41 int64_t ix; 42 int64_t i; 43 float sum; 44 float v; 45 float t; 46 float c; 47 48 if ( N <= 0 ) { 49 return 0.0f; 50 } 51 if ( N == 1 || stride == 0 ) { 52 return alpha + X[ 0 ]; 53 } 54 if ( stride < 0 ) { 55 ix = (1-N) * stride; 56 } else { 57 ix = 0; 58 } 59 sum = 0.0f; 60 c = 0.0f; 61 for ( i = 0; i < N; i++ ) { 62 v = alpha + X[ ix ]; 63 t = sum + v; 64 if ( fabsf( sum ) >= fabsf( v ) ) { 65 c += (sum-t) + v; 66 } else { 67 c += (v-t) + sum; 68 } 69 sum = t; 70 ix += stride; 71 } 72 return sum + c; 73 }