time-to-botec

Benchmark sampling in different programming languages
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ssumpw.c (3276B)

      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/ssumpw.h"
     20 #include <stdint.h>
     21 
     22 /**
     23 * Computes the sum of single-precision floating-point strided array elements using pairwise summation.
     24 *
     25 * ## Method
     26 *
     27 * -   This implementation uses pairwise summation, which accrues rounding error `O(log2 N)` instead of `O(N)`. The recursion depth is also `O(log2 N)`.
     28 *
     29 * ## References
     30 *
     31 * -   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).
     32 *
     33 * @param N       number of indexed elements
     34 * @param X       input array
     35 * @param stride  stride length
     36 * @return        output value
     37 */
     38 float stdlib_strided_ssumpw( const int64_t N, const float *X, const int64_t stride ) {
     39 	float *xp1;
     40 	float *xp2;
     41 	int64_t ix;
     42 	int64_t M;
     43 	int64_t n;
     44 	int64_t i;
     45 	float sum;
     46 	float s0;
     47 	float s1;
     48 	float s2;
     49 	float s3;
     50 	float s4;
     51 	float s5;
     52 	float s6;
     53 	float s7;
     54 
     55 	if ( N <= 0 ) {
     56 		return 0.0f;
     57 	}
     58 	if ( N == 1 || stride == 0 ) {
     59 		return X[ 0 ];
     60 	}
     61 	if ( stride < 0 ) {
     62 		ix = (1-N) * stride;
     63 	} else {
     64 		ix = 0;
     65 	}
     66 	if ( N < 8 ) {
     67 		// Use simple summation...
     68 		sum = 0.0f;
     69 		for ( i = 0; i < N; i++ ) {
     70 			sum += X[ ix ];
     71 			ix += stride;
     72 		}
     73 		return sum;
     74 	}
     75 	// Blocksize for pairwise summation: 128 (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`.)
     76 	if ( N <= 128 ) {
     77 		// Sum a block with 8 accumulators (by loop unrolling, we lower the effective blocksize to 16)...
     78 		s0 = X[ ix ];
     79 		s1 = X[ ix+stride ];
     80 		s2 = X[ ix+(2*stride) ];
     81 		s3 = X[ ix+(3*stride) ];
     82 		s4 = X[ ix+(4*stride) ];
     83 		s5 = X[ ix+(5*stride) ];
     84 		s6 = X[ ix+(6*stride) ];
     85 		s7 = X[ ix+(7*stride) ];
     86 		ix += 8 * stride;
     87 
     88 		M = N % 8;
     89 		for ( i = 8; i < N-M; i += 8 ) {
     90 			s0 += X[ ix ];
     91 			s1 += X[ ix+stride ];
     92 			s2 += X[ ix+(2*stride) ];
     93 			s3 += X[ ix+(3*stride) ];
     94 			s4 += X[ ix+(4*stride) ];
     95 			s5 += X[ ix+(5*stride) ];
     96 			s6 += X[ ix+(6*stride) ];
     97 			s7 += X[ ix+(7*stride) ];
     98 			ix += 8 * stride;
     99 		}
    100 		// Pairwise sum the accumulators:
    101 		sum = ((s0+s1) + (s2+s3)) + ((s4+s5) + (s6+s7));
    102 
    103 		// Clean-up loop...
    104 		for (; i < N; i++ ) {
    105 			sum += X[ ix ];
    106 			ix += stride;
    107 		}
    108 		return sum;
    109 	}
    110 	// Recurse by dividing by two, but avoiding non-multiples of unroll factor...
    111 	n = N / 2;
    112 	n -= n % 8;
    113 	if ( stride < 0 ) {
    114 		xp1 = (float *)X + ( (n-N)*stride );
    115 		xp2 = (float *)X;
    116 	} else {
    117 		xp1 = (float *)X;
    118 		xp2 = (float *)X + ( n*stride );
    119 	}
    120 	return stdlib_strided_ssumpw( n, xp1, stride ) + stdlib_strided_ssumpw( N-n, xp2, stride );
    121 }