sys/matstat: Integer mathematical statistics library

sys/include/matstat.h

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+/*
+ * Copyright (C) 2018 Eistec AB
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser
+ * General Public License v2.1. See the file LICENSE in the top level
+ * directory for more details.
+ */
+
+/**
+ * @defgroup    sys_matstat Matstat - Integer mathematical statistics library
+ * @ingroup     sys
+ * @brief       Library for computing 1-pass statistics
+ *
+ * The Matstat library uses single pass algorithms to compute statistic measures
+ * such as mean and variance over many values. The values can be immediately
+ * discarded after processing, keeping the memory requirement constant
+ * regardless of how many values need to be processed.
+ *
+ * The design goal is to provide basic mathematical statistics operations on
+ * constrained devices with a "good enough" accuracy to be able to provide some
+ * descriptive measures of data. For more accurate measures of statistics, use a
+ * fancier library, or copy the data to a PC.
+ *
+ * It is important to know that using integer operations will result in lower
+ * precision in the computed measures because of truncation.
+ *
+ * @{
+ * @file
+ * @brief       Matstat library declarations
+ *
+ * @author      Joakim Nohlgård <joakim.nohlgard@eistec.se>
+ */
+
+#ifndef MATSTAT_H
+#define MATSTAT_H
+
+#include <stdint.h>
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/**
+ * @brief   Internal state for computing running statistics
+ */
+typedef struct {
+    int64_t sum;        /**< Sum of values added */
+    uint64_t sum_sq;    /**< Sum of squared differences */
+    uint32_t count;     /**< Number of values added */
+    int32_t mean;       /**< Mean value */
+    int32_t min;        /**< Minimum value seen */
+    int32_t max;        /**< Maximum value seen */
+} matstat_state_t;
+
+/**
+ * @brief   Empty state initializer
+ */
+#define MATSTAT_STATE_INIT (const matstat_state_t) { \
+        .sum = 0, \
+        .sum_sq = 0, \
+        .count = 0, \
+        .mean = 0, \
+        .min = INT32_MAX, \
+        .max = INT32_MIN, \
+    }
+
+/**
+ * @brief   Reset state
+ *
+ * @param[in]   state   State struct to clear
+ */
+void matstat_clear(matstat_state_t *state);
+
+/**
+ * @brief   Add a sample to state
+ *
+ * @param[in]   state   State struct to operate on
+ * @param[in]   value   Value to add to the state
+ */
+void matstat_add(matstat_state_t *state, int32_t value);
+
+/**
+ * @brief   Return the computed mean value of all samples so far
+ *
+ * @param[in]   state   State struct to operate on
+ *
+ * @return  arithmetic mean
+ */
+static inline int32_t matstat_mean(const matstat_state_t *state)
+{
+    return state->mean;
+}
+
+/**
+ * @brief   Compute the sample variance of all samples so far
+ *
+ * @param[in]   state   State struct to operate on
+ *
+ * @return  sample variance
+ */
+uint64_t matstat_variance(const matstat_state_t *state);
+
+/**
+ * @brief   Combine two states
+ *
+ * Add the sums and count of @p src and @p dest, take the maximum of the max
+ * values and minimum of the min values. The result is written to @p dest.
+ *
+ * @param[inout]    dest    destination state struct
+ * @param[out]      src     source state struct
+ */
+void matstat_merge(matstat_state_t *dest, const matstat_state_t *src);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* MATSTAT_H */
+
+/** @} */

sys/matstat/Makefile

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+include $(RIOTBASE)/Makefile.base

sys/matstat/matstat.c

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+/*
+ * Copyright (C) 2018 Eistec AB
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser
+ * General Public License v2.1. See the file LICENSE in the top level
+ * directory for more details.
+ */
+
+#include <stdint.h>
+#include "matstat.h"
+
+#define ENABLE_DEBUG    (0)
+#include "debug.h"
+
+void matstat_clear(matstat_state_t *state)
+{
+    *state = MATSTAT_STATE_INIT;
+}
+
+void matstat_add(matstat_state_t *state, int32_t value)
+{
+    if (value > state->max) {
+        state->max = value;
+    }
+    if (value < state->min) {
+        state->min = value;
+    }
+    state->sum += value;
+    /* Using Welford's algorithm for variance */
+    ++state->count;
+    if (state->count == 1) {
+        state->sum_sq = 0;
+        state->mean = value;
+    }
+    else {
+        int32_t new_mean = state->sum / state->count;
+        int64_t diff = (value - state->mean) * (value - new_mean);
+        if ((diff < 0) && ((uint64_t)(-diff) > state->sum_sq)) {
+            /* Handle corner cases where sum_sq becomes negative */
+            state->sum_sq = 0;
+        }
+        else {
+            state->sum_sq += diff;
+        }
+        state->mean = new_mean;
+    }
+}
+
+uint64_t matstat_variance(const matstat_state_t *state)
+{
+    if (state->count < 2) {
+        /* We don't have any way of returning an error */
+        return 0;
+    }
+    uint64_t variance = state->sum_sq / (state->count - 1);
+    DEBUG("Var: (%" PRIu64 " / (%" PRId32 " - 1)) = %" PRIu64 "\n",
+        state->sum_sq, state->count, variance);
+    return variance;
+}
+
+void matstat_merge(matstat_state_t *dest, const matstat_state_t *src)
+{
+    if (src->count == 0) {
+        /* src is empty, no-op */
+        return;
+    }
+    if (dest->count == 0) {
+        /* dest is empty, straight copy */
+        *dest = *src;
+        return;
+    }
+    /* Combining the variance of the two samples needs some extra
+     * handling if the means are different between the two states,
+     * source: https://stats.stackexchange.com/a/43183
+     * (using sum_sq = sigma2 * n, instead of sum_sq = sigma2 * (n-1) to simplify algorithm)
+     */
+    dest->sum_sq = (dest->sum_sq + dest->sum * dest->mean + src->sum_sq + src->sum * src->mean);
+    dest->count += src->count;
+    dest->sum += src->sum;
+    int32_t new_mean = dest->sum / dest->count;
+    int64_t diff = -new_mean * dest->sum;
+    if ((diff < 0) && ((uint64_t)(-diff) > dest->sum_sq)) {
+        /* Handle corner cases where sum_sq becomes negative */
+        dest->sum_sq = 0;
+    }
+    else {
+        dest->sum_sq += diff;
+    }
+    dest->mean = new_mean;
+    if (src->max > dest->max) {
+        dest->max = src->max;
+    }
+    if (src->min < dest->min) {
+        dest->min = src->min;
+    }
+}