sapxsumkbn2.c (2239B)
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/sapxsumkbn2.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 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 alpha constant 36 * @param X input array 37 * @param stride stride length 38 * @return output value 39 */ 40 float stdlib_strided_sapxsumkbn2( 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 ccs; 45 float cs; 46 float cc; 47 float v; 48 float t; 49 float c; 50 51 if ( N <= 0 ) { 52 return 0.0f; 53 } 54 if ( N == 1 || stride == 0 ) { 55 return alpha + X[ 0 ]; 56 } 57 if ( stride < 0 ) { 58 ix = (1-N) * stride; 59 } else { 60 ix = 0; 61 } 62 sum = 0.0f; 63 ccs = 0.0f; // second order correction term for lost lower order bits 64 cs = 0.0f; // first order correction term for lost low order bits 65 for ( i = 0; i < N; i++ ) { 66 v = alpha + X[ ix ]; 67 t = sum + v; 68 if ( fabsf( sum ) >= fabsf( v ) ) { 69 c = (sum-t) + v; 70 } else { 71 c = (v-t) + sum; 72 } 73 sum = t; 74 t = cs + c; 75 if ( fabsf( cs ) >= fabsf( c ) ) { 76 cc = (cs-t) + c; 77 } else { 78 cc = (c-t) + cs; 79 } 80 cs = t; 81 ccs += cc; 82 ix += stride; 83 } 84 return sum + cs + ccs; 85 }