quantiles: add support for quantile estimation
Add estimation of quantiles using the Frugal-2U streaming algorithm (https://arxiv.org/pdf/1407.1121v1.pdf). It does not need to save previous samples and adapts to changes in the distribution. Allow multiple estimates of the same quantile and select the median for better stability.
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Miroslav Lichvar
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3 changed files with 307 additions and 0 deletions
201
quantiles.c
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201
quantiles.c
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/*
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chronyd/chronyc - Programs for keeping computer clocks accurate.
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**********************************************************************
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* Copyright (C) Miroslav Lichvar 2022
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of version 2 of the GNU General Public License as
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* published by the Free Software Foundation.
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*
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* This program is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License along
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* with this program; if not, write to the Free Software Foundation, Inc.,
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* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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*
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**********************************************************************
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=======================================================================
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Estimation of quantiles using the Frugal-2U streaming algorithm
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(https://arxiv.org/pdf/1407.1121v1.pdf)
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*/
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#include "config.h"
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#include "logging.h"
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#include "memory.h"
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#include "quantiles.h"
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#include "regress.h"
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#include "util.h"
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/* Maximum number of repeated estimates for stabilisation */
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#define MAX_REPEAT 64
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struct Quantile {
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double est;
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double step;
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int sign;
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};
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struct QNT_Instance_Record {
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struct Quantile *quants;
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int n_quants;
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int repeat;
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int q;
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int min_k;
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double min_step;
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int n_set;
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};
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/* ================================================== */
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QNT_Instance
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QNT_CreateInstance(int min_k, int max_k, int q, int repeat, double min_step)
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{
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QNT_Instance inst;
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long seed;
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if (q < 2 || min_k > max_k || min_k < 1 || max_k >= q ||
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repeat < 1 || repeat > MAX_REPEAT || min_step <= 0.0)
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assert(0);
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inst = MallocNew(struct QNT_Instance_Record);
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inst->n_quants = (max_k - min_k + 1) * repeat;
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inst->quants = MallocArray(struct Quantile, inst->n_quants);
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inst->repeat = repeat;
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inst->q = q;
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inst->min_k = min_k;
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inst->min_step = min_step;
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QNT_Reset(inst);
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/* Seed the random number generator, which will not be isolated from
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other instances and other random() users */
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UTI_GetRandomBytes(&seed, sizeof (seed));
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srandom(seed);
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return inst;
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}
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/* ================================================== */
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void
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QNT_DestroyInstance(QNT_Instance inst)
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{
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Free(inst->quants);
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Free(inst);
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}
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/* ================================================== */
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void
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QNT_Reset(QNT_Instance inst)
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{
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int i;
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inst->n_set = 0;
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for (i = 0; i < inst->n_quants; i++) {
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inst->quants[i].est = 0.0;
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inst->quants[i].step = inst->min_step;
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inst->quants[i].sign = 1;
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}
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}
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/* ================================================== */
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static void
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insert_initial_value(QNT_Instance inst, double value)
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{
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int i, j, r = inst->repeat;
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if (inst->n_set * r >= inst->n_quants)
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assert(0);
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/* Keep the initial estimates repeated and ordered */
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for (i = inst->n_set; i > 0 && inst->quants[(i - 1) * r].est > value; i--) {
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for (j = 0; j < r; j++)
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inst->quants[i * r + j].est = inst->quants[(i - 1) * r].est;
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}
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for (j = 0; j < r; j++)
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inst->quants[i * r + j].est = value;
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inst->n_set++;
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/* Duplicate the largest value in unset quantiles */
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for (i = inst->n_set * r; i < inst->n_quants; i++)
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inst->quants[i].est = inst->quants[i - 1].est;
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}
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/* ================================================== */
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static void
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update_estimate(struct Quantile *quantile, double value, double p, double rand,
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double min_step)
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{
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if (value > quantile->est && rand > (1.0 - p)) {
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quantile->step += quantile->sign > 0 ? min_step : -min_step;
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quantile->est += quantile->step > 0.0 ? fabs(quantile->step) : min_step;
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if (quantile->est > value) {
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quantile->step += value - quantile->est;
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quantile->est = value;
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}
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if (quantile->sign < 0 && quantile->step > min_step)
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quantile->step = min_step;
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quantile->sign = 1;
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} else if (value < quantile->est && rand > p) {
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quantile->step += quantile->sign < 0 ? min_step : -min_step;
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quantile->est -= quantile->step > 0.0 ? fabs(quantile->step) : min_step;
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if (quantile->est < value) {
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quantile->step += quantile->est - value;
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quantile->est = value;
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}
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if (quantile->sign > 0 && quantile->step > min_step)
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quantile->step = min_step;
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quantile->sign = -1;
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}
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}
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/* ================================================== */
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void
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QNT_Accumulate(QNT_Instance inst, double value)
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{
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double p, rand;
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int i;
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/* Initialise the estimates with first received values */
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if (inst->n_set * inst->repeat < inst->n_quants) {
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insert_initial_value(inst, value);
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return;
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}
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for (i = 0; i < inst->n_quants; i++) {
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p = (double)(i / inst->repeat + inst->min_k) / inst->q;
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rand = (double)random() / ((1U << 31) - 1);
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update_estimate(&inst->quants[i], value, p, rand, inst->min_step);
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}
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}
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/* ================================================== */
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double
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QNT_GetQuantile(QNT_Instance inst, int k)
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{
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double estimates[MAX_REPEAT];
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int i;
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if (k < inst->min_k || k - inst->min_k >= inst->n_quants)
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assert(0);
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for (i = 0; i < inst->repeat; i++)
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estimates[i] = inst->quants[(k - inst->min_k) * inst->repeat + i].est;
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return RGR_FindMedian(estimates, inst->repeat);
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}
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40
quantiles.h
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40
quantiles.h
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@ -0,0 +1,40 @@
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/*
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chronyd/chronyc - Programs for keeping computer clocks accurate.
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**********************************************************************
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* Copyright (C) Miroslav Lichvar 2022
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of version 2 of the GNU General Public License as
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* published by the Free Software Foundation.
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*
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* This program is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License along
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* with this program; if not, write to the Free Software Foundation, Inc.,
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* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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*
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**********************************************************************
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=======================================================================
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Header file for estimation of quantiles.
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*/
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#ifndef GOT_QUANTILES_H
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#define GOT_QUANTILES_H
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typedef struct QNT_Instance_Record *QNT_Instance;
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extern QNT_Instance QNT_CreateInstance(int min_k, int max_k, int q, int repeat, double min_step);
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extern void QNT_DestroyInstance(QNT_Instance inst);
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extern void QNT_Reset(QNT_Instance inst);
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extern void QNT_Accumulate(QNT_Instance inst, double value);
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extern double QNT_GetQuantile(QNT_Instance inst, int k);
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#endif
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66
test/unit/quantiles.c
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66
test/unit/quantiles.c
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/*
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**********************************************************************
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* Copyright (C) Miroslav Lichvar 2022
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of version 2 of the GNU General Public License as
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* published by the Free Software Foundation.
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*
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* This program is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License along
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* with this program; if not, write to the Free Software Foundation, Inc.,
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* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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*
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**********************************************************************
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*/
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#include <local.h>
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#include "test.h"
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#include <quantiles.c>
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void
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test_unit(void)
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{
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int i, j, k, min_k, max_k, q, r, in_order, out_order;
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QNT_Instance inst;
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double x;
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in_order = out_order = 0;
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for (i = 0; i < 100; i++) {
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r = random() % 10 + 1;
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q = random() % 20 + 2;
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do {
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min_k = random() % (q - 1) + 1;
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max_k = random() % (q - 1) + 1;
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} while (min_k > max_k);
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inst = QNT_CreateInstance(min_k, max_k, q, r, 1e-9);
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for (j = 0; j < 3000; j++) {
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x = TST_GetRandomDouble(0.0, 2e-6);
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QNT_Accumulate(inst, x);
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for (k = min_k; k < max_k; k++)
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if (j < max_k - min_k) {
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TEST_CHECK(QNT_GetQuantile(inst, k) <= QNT_GetQuantile(inst, k + 1));
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} else if (j > 1000) {
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if (QNT_GetQuantile(inst, k) <= QNT_GetQuantile(inst, k + 1))
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in_order++;
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else
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out_order++;
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}
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}
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QNT_Reset(inst);
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TEST_CHECK(inst->n_set == 0);
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QNT_DestroyInstance(inst);
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}
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TEST_CHECK(in_order > 100 * out_order);
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}
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