media/libnbaio/PerformanceAnalysis.cpp - android_frameworks_av - Gitiles

 /*
  * Copyright (C) 2017 The Android Open Source Project
  *
  * Licensed under the Apache License, Version 2.0 (the "License");
  * you may not use this file except in compliance with the License.
  * You may obtain a copy of the License at
  *
  *      http://www.apache.org/licenses/LICENSE-2.0
  *
  * Unless required by applicable law or agreed to in writing, software
  * distributed under the License is distributed on an "AS IS" BASIS,
  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  * See the License for the specific language governing permissions and
  * limitations under the License.
  */


 #define LOG_TAG "PerformanceAnalysis"
 // #define LOG_NDEBUG 0

 #include <algorithm>
 #include <climits>
 #include <deque>
 #include <iostream>
 #include <math.h>
 #include <numeric>
 #include <vector>
 #include <stdarg.h>
 #include <stdint.h>
 #include <stdio.h>
 #include <string.h>
 #include <sys/prctl.h>
 #include <time.h>
 #include <new>
 #include <audio_utils/roundup.h>
 #include <media/nbaio/NBLog.h>
 #include <media/nbaio/PerformanceAnalysis.h>
 #include <media/nbaio/ReportPerformance.h>
 #include <utils/Log.h>
 #include <utils/String8.h>

 #include <queue>
 #include <utility>

 namespace android {

 namespace ReportPerformance {

 // Given a the most recent timestamp of a series of audio processing
 // wakeup timestamps,
 // buckets the time interval into a histogram, searches for
 // outliers, analyzes the outlier series for unexpectedly
 // small or large values and stores these as peaks
 void PerformanceAnalysis::logTsEntry(timestamp ts) {
     // after a state change, start a new series and do not
     // record time intervals in-between
     if (mBufferPeriod.mPrevTs == 0) {
         mBufferPeriod.mPrevTs = ts;
         return;
     }

     // calculate time interval between current and previous timestamp
     const msInterval diffMs = static_cast<msInterval>(
         deltaMs(mBufferPeriod.mPrevTs, ts));

     const int diffJiffy = deltaJiffy(mBufferPeriod.mPrevTs, ts);

     // old versus new weight ratio when updating the buffer period mean
     static constexpr double exponentialWeight = 0.999;
     // update buffer period mean with exponential weighting
     mBufferPeriod.mMean = (mBufferPeriod.mMean < 0) ? diffMs :
             exponentialWeight * mBufferPeriod.mMean + (1.0 - exponentialWeight) * diffMs;
     // set mOutlierFactor to a smaller value for the fastmixer thread
     const int kFastMixerMax = 10;
     // NormalMixer times vary much more than FastMixer times.
     // TODO: mOutlierFactor values are set empirically based on what appears to be
     // an outlier. Learn these values from the data.
     // TODO: the current settings are too high, change after next data collection is over
     mBufferPeriod.mOutlierFactor = mBufferPeriod.mMean < kFastMixerMax ? 1.8 : 2.0;
     // set outlier threshold
     mBufferPeriod.mOutlier = mBufferPeriod.mMean * mBufferPeriod.mOutlierFactor;

     // Check whether the time interval between the current timestamp
     // and the previous one is long enough to count as an outlier
     const bool isOutlier = detectAndStoreOutlier(diffMs);
     // If an outlier was found, check whether it was a peak
     if (isOutlier) {
         /*bool isPeak =*/ detectAndStorePeak(
             mOutlierData[0].first, mOutlierData[0].second);
         // TODO: decide whether to insert a new empty histogram if a peak
         // TODO: remove isPeak if unused to avoid "unused variable" error
         // occurred at the current timestamp
     }

     // Insert a histogram to mHists if it is empty, or
     // close the current histogram and insert a new empty one if
     // if the current histogram has spanned its maximum time interval.
     if (mHists.empty() ||
         deltaMs(mHists[0].first, ts) >= kMaxLength.HistTimespanMs) {
         mHists.emplace_front(ts, std::map<int, int>());
         // When memory is full, delete oldest histogram
         // TODO: use a circular buffer
         if (mHists.size() >= kMaxLength.Hists) {
             mHists.resize(kMaxLength.Hists);
         }
     }
     // add current time intervals to histogram
     ++mHists[0].second[diffJiffy];
     // update previous timestamp
     mBufferPeriod.mPrevTs = ts;
 }


 // forces short-term histogram storage to avoid adding idle audio time interval
 // to buffer period data
 void PerformanceAnalysis::handleStateChange() {
     mBufferPeriod.mPrevTs = 0;
     return;
 }


 // Checks whether the time interval between two outliers is far enough from
 // a typical delta to be considered a peak.
 // looks for changes in distribution (peaks), which can be either positive or negative.
 // The function sets the mean to the starting value and sigma to 0, and updates
 // them as long as no peak is detected. When a value is more than 'threshold'
 // standard deviations from the mean, a peak is detected and the mean and sigma
 // are set to the peak value and 0.
 bool PerformanceAnalysis::detectAndStorePeak(msInterval diff, timestamp ts) {
     bool isPeak = false;
     if (mOutlierData.empty()) {
         return false;
     }
     // Update mean of the distribution
     // TypicalDiff is used to check whether a value is unusually large
     // when we cannot use standard deviations from the mean because the sd is set to 0.
     mOutlierDistribution.mTypicalDiff = (mOutlierDistribution.mTypicalDiff *
             (mOutlierData.size() - 1) + diff) / mOutlierData.size();

     // Initialize short-term mean at start of program
     if (mOutlierDistribution.mMean == 0) {
         mOutlierDistribution.mMean = diff;
     }
     // Update length of current sequence of outliers
     mOutlierDistribution.mN++;

     // Check whether a large deviation from the mean occurred.
     // If the standard deviation has been reset to zero, the comparison is
     // instead to the mean of the full mOutlierInterval sequence.
     if ((fabs(diff - mOutlierDistribution.mMean) <
             mOutlierDistribution.kMaxDeviation * mOutlierDistribution.mSd) ||
             (mOutlierDistribution.mSd == 0 &&
             fabs(diff - mOutlierDistribution.mMean) <
             mOutlierDistribution.mTypicalDiff)) {
         // update the mean and sd using online algorithm
         // https://en.wikipedia.org/wiki/
         // Algorithms_for_calculating_variance#Online_algorithm
         mOutlierDistribution.mN++;
         const double kDelta = diff - mOutlierDistribution.mMean;
         mOutlierDistribution.mMean += kDelta / mOutlierDistribution.mN;
         const double kDelta2 = diff - mOutlierDistribution.mMean;
         mOutlierDistribution.mM2 += kDelta * kDelta2;
         mOutlierDistribution.mSd = (mOutlierDistribution.mN < 2) ? 0 :
                 sqrt(mOutlierDistribution.mM2 / (mOutlierDistribution.mN - 1));
     } else {
         // new value is far from the mean:
         // store peak timestamp and reset mean, sd, and short-term sequence
         isPeak = true;
         mPeakTimestamps.emplace_front(ts);
         // if mPeaks has reached capacity, delete oldest data
         // Note: this means that mOutlierDistribution values do not exactly
         // match the data we have in mPeakTimestamps, but this is not an issue
         // in practice for estimating future peaks.
         // TODO: turn this into a circular buffer
         if (mPeakTimestamps.size() >= kMaxLength.Peaks) {
             mPeakTimestamps.resize(kMaxLength.Peaks);
         }
         mOutlierDistribution.mMean = 0;
         mOutlierDistribution.mSd = 0;
         mOutlierDistribution.mN = 0;
         mOutlierDistribution.mM2 = 0;
     }
     return isPeak;
 }


 // Determines whether the difference between a timestamp and the previous
 // one is beyond a threshold. If yes, stores the timestamp as an outlier
 // and writes to mOutlierdata in the following format:
 // Time elapsed since previous outlier: Timestamp of start of outlier
 // e.g. timestamps (ms) 1, 4, 5, 16, 18, 28 will produce pairs (4, 5), (13, 18).
 // TODO: learn what timestamp sequences correlate with glitches instead of
 // manually designing a heuristic.
 bool PerformanceAnalysis::detectAndStoreOutlier(const msInterval diffMs) {
     bool isOutlier = false;
     if (diffMs >= mBufferPeriod.mOutlier) {
         isOutlier = true;
         mOutlierData.emplace_front(
                 mOutlierDistribution.mElapsed, mBufferPeriod.mPrevTs);
         // Remove oldest value if the vector is full
         // TODO: turn this into a circular buffer
         // TODO: make sure kShortHistSize is large enough that that data will never be lost
         // before being written to file or to a FIFO
         if (mOutlierData.size() >= kMaxLength.Outliers) {
             mOutlierData.resize(kMaxLength.Outliers);
         }
         mOutlierDistribution.mElapsed = 0;
     }
     mOutlierDistribution.mElapsed += diffMs;
     return isOutlier;
 }

 static int widthOf(int x) {
     int width = 0;
     if (x < 0) {
         width++;
         x = x == INT_MIN ? INT_MAX : -x;
     }
     // assert (x >= 0)
     do {
         ++width;
         x /= 10;
     } while (x > 0);
     return width;
 }

 // computes the column width required for a specific histogram value
 inline int numberWidth(double number, int leftPadding) {
     // Added values account for whitespaces needed around numbers, and for the
     // dot and decimal digit not accounted for by widthOf
     return std::max(std::max(widthOf(static_cast<int>(number)) + 3, 2), leftPadding + 1);
 }

 // rounds value to precision based on log-distance from mean
 inline double logRound(double x, double mean) {
     // Larger values decrease range of high resolution and prevent overflow
     // of a histogram on the console.
     // The following formula adjusts kBase based on the buffer period length.
     // Different threads have buffer periods ranging from 2 to 40. The
     // formula below maps buffer period 2 to kBase = ~1, 4 to ~2, 20 to ~3, 40 to ~4.
     // TODO: tighten this for higher means, the data still overflows
     const double kBase = log(mean) / log(2.2);
     const double power = floor(
         log(abs(x - mean) / mean) / log(kBase)) + 2;
     // do not round values close to the mean
     if (power < 1) {
         return x;
     }
     const int factor = static_cast<int>(pow(10, power));
     return (static_cast<int>(x) * factor) / factor;
 }

 // TODO Make it return a std::string instead of modifying body
 // TODO: move this to ReportPerformance, probably make it a friend function
 // of PerformanceAnalysis
 void PerformanceAnalysis::reportPerformance(String8 *body, int author, log_hash_t hash,
                                             int maxHeight) {
     if (mHists.empty()) {
         return;
     }

     // ms of active audio in displayed histogram
     double elapsedMs = 0;
     // starting timestamp of histogram
     timestamp startingTs = mHists[0].first;

     // histogram which stores .1 precision ms counts instead of Jiffy multiple counts
     // TODO: when there is more data, print many histograms, possibly separated at peaks
     std::map<double, int> buckets;
     for (const auto &shortHist: mHists) {
         for (const auto &countPair : shortHist.second) {
             const double ms = static_cast<double>(countPair.first) / kJiffyPerMs;
             buckets[logRound(ms, mBufferPeriod.mMean)] += countPair.second;
             elapsedMs += ms * countPair.second;
         }
     }

     // underscores and spaces length corresponds to maximum width of histogram
     static const int kLen = 200;
     std::string underscores(kLen, '_');
     std::string spaces(kLen, ' ');

     auto it = buckets.begin();
     double maxDelta = it->first;
     int maxCount = it->second;
     // Compute maximum values
     while (++it != buckets.end()) {
         if (it->first > maxDelta) {
             maxDelta = it->first;
         }
         if (it->second > maxCount) {
             maxCount = it->second;
         }
     }
     int height = log2(maxCount) + 1; // maxCount > 0, safe to call log2
     const int leftPadding = widthOf(1 << height);
     const int bucketWidth = numberWidth(maxDelta, leftPadding);
     int scalingFactor = 1;
     // scale data if it exceeds maximum height
     if (height > maxHeight) {
         scalingFactor = (height + maxHeight) / maxHeight;
         height /= scalingFactor;
     }
     body->appendFormat("\n%*s %3.2f %s", leftPadding + 11,
             "Occurrences in", (elapsedMs / kMsPerSec), "seconds of audio:");
     body->appendFormat("\n%*s%d, %lld, %lld\n", leftPadding + 11,
             "Thread, hash, starting timestamp: ", author,
             static_cast<long long int>(hash), static_cast<long long int>(startingTs));
     // write histogram label line with bucket values
     body->appendFormat("\n%s", " ");
     body->appendFormat("%*s", leftPadding, " ");
     for (auto const &x : buckets) {
         const int colWidth = numberWidth(x.first, leftPadding);
         body->appendFormat("%*d", colWidth, x.second);
     }
     // write histogram ascii art
     body->appendFormat("\n%s", " ");
     for (int row = height * scalingFactor; row >= 0; row -= scalingFactor) {
         const int value = 1 << row;
         body->appendFormat("%.*s", leftPadding, spaces.c_str());
         for (auto const &x : buckets) {
             const int colWidth = numberWidth(x.first, leftPadding);
             body->appendFormat("%.*s%s", colWidth - 1,
                                spaces.c_str(), x.second < value ? " " : "|");
         }
         body->appendFormat("\n%s", " ");
     }
     // print x-axis
     const int columns = static_cast<int>(buckets.size());
     body->appendFormat("%*c", leftPadding, ' ');
     body->appendFormat("%.*s", (columns + 1) * bucketWidth, underscores.c_str());
     body->appendFormat("\n%s", " ");

     // write footer with bucket labels
     body->appendFormat("%*s", leftPadding, " ");
     for (auto const &x : buckets) {
         const int colWidth = numberWidth(x.first, leftPadding);
         body->appendFormat("%*.*f", colWidth, 1, x.first);
     }
     body->appendFormat("%.*s%s", bucketWidth, spaces.c_str(), "ms\n");

     // Now report glitches
     body->appendFormat("\ntime elapsed between glitches and glitch timestamps:\n");
     for (const auto &outlier: mOutlierData) {
         body->appendFormat("%lld: %lld\n", static_cast<long long>(outlier.first),
                            static_cast<long long>(outlier.second));
     }
 }

 //------------------------------------------------------------------------------

 // writes summary of performance into specified file descriptor
 void dump(int fd, int indent, PerformanceAnalysisMap &threadPerformanceAnalysis) {
     String8 body;
     const char* const kDirectory = "/data/misc/audioserver/";
     for (auto & thread : threadPerformanceAnalysis) {
         for (auto & hash: thread.second) {
             PerformanceAnalysis& curr = hash.second;
             // write performance data to console
             curr.reportPerformance(&body, thread.first, hash.first);
             if (!body.isEmpty()) {
                 dumpLine(fd, indent, body);
                 body.clear();
             }
             // write to file
             writeToFile(curr.mHists, curr.mOutlierData, curr.mPeakTimestamps,
                         kDirectory, false, thread.first, hash.first);
         }
     }
 }


 // Writes a string into specified file descriptor
 void dumpLine(int fd, int indent, const String8 &body) {
     dprintf(fd, "%.*s%s \n", indent, "", body.string());
 }

 } // namespace ReportPerformance

 }   // namespace android
	/*
	* Copyright (C) 2017 The Android Open Source Project
	*
	* Licensed under the Apache License, Version 2.0 (the "License");
	* you may not use this file except in compliance with the License.
	* You may obtain a copy of the License at
	*
	* http://www.apache.org/licenses/LICENSE-2.0
	*
	* Unless required by applicable law or agreed to in writing, software
	* distributed under the License is distributed on an "AS IS" BASIS,
	* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
	* See the License for the specific language governing permissions and
	* limitations under the License.
	*/


	#define LOG_TAG "PerformanceAnalysis"
	// #define LOG_NDEBUG 0

	#include <algorithm>
	#include <climits>
	#include <deque>
	#include <iostream>
	#include <math.h>
	#include <numeric>
	#include <vector>
	#include <stdarg.h>
	#include <stdint.h>
	#include <stdio.h>
	#include <string.h>
	#include <sys/prctl.h>
	#include <time.h>
	#include <new>
	#include <audio_utils/roundup.h>
	#include <media/nbaio/NBLog.h>
	#include <media/nbaio/PerformanceAnalysis.h>
	#include <media/nbaio/ReportPerformance.h>
	#include <utils/Log.h>
	#include <utils/String8.h>

	#include <queue>
	#include <utility>

	namespace android {

	namespace ReportPerformance {

	// Given a the most recent timestamp of a series of audio processing
	// wakeup timestamps,
	// buckets the time interval into a histogram, searches for
	// outliers, analyzes the outlier series for unexpectedly
	// small or large values and stores these as peaks
	void PerformanceAnalysis::logTsEntry(timestamp ts) {
	// after a state change, start a new series and do not
	// record time intervals in-between
	if (mBufferPeriod.mPrevTs == 0) {
	mBufferPeriod.mPrevTs = ts;
	return;
	}

	// calculate time interval between current and previous timestamp
	const msInterval diffMs = static_cast<msInterval>(
	deltaMs(mBufferPeriod.mPrevTs, ts));

	const int diffJiffy = deltaJiffy(mBufferPeriod.mPrevTs, ts);

	// old versus new weight ratio when updating the buffer period mean
	static constexpr double exponentialWeight = 0.999;
	// update buffer period mean with exponential weighting
	mBufferPeriod.mMean = (mBufferPeriod.mMean < 0) ? diffMs :
	exponentialWeight * mBufferPeriod.mMean + (1.0 - exponentialWeight) * diffMs;
	// set mOutlierFactor to a smaller value for the fastmixer thread
	const int kFastMixerMax = 10;
	// NormalMixer times vary much more than FastMixer times.
	// TODO: mOutlierFactor values are set empirically based on what appears to be
	// an outlier. Learn these values from the data.
	// TODO: the current settings are too high, change after next data collection is over
	mBufferPeriod.mOutlierFactor = mBufferPeriod.mMean < kFastMixerMax ? 1.8 : 2.0;
	// set outlier threshold
	mBufferPeriod.mOutlier = mBufferPeriod.mMean * mBufferPeriod.mOutlierFactor;

	// Check whether the time interval between the current timestamp
	// and the previous one is long enough to count as an outlier
	const bool isOutlier = detectAndStoreOutlier(diffMs);
	// If an outlier was found, check whether it was a peak
	if (isOutlier) {
	/bool isPeak =/ detectAndStorePeak(
	mOutlierData[0].first, mOutlierData[0].second);
	// TODO: decide whether to insert a new empty histogram if a peak
	// TODO: remove isPeak if unused to avoid "unused variable" error
	// occurred at the current timestamp
	}

	// Insert a histogram to mHists if it is empty, or
	// close the current histogram and insert a new empty one if
	// if the current histogram has spanned its maximum time interval.
	if (mHists.empty() \|\|
	deltaMs(mHists[0].first, ts) >= kMaxLength.HistTimespanMs) {
	mHists.emplace_front(ts, std::map<int, int>());
	// When memory is full, delete oldest histogram
	// TODO: use a circular buffer
	if (mHists.size() >= kMaxLength.Hists) {
	mHists.resize(kMaxLength.Hists);
	}
	}
	// add current time intervals to histogram
	++mHists[0].second[diffJiffy];
	// update previous timestamp
	mBufferPeriod.mPrevTs = ts;
	}


	// forces short-term histogram storage to avoid adding idle audio time interval
	// to buffer period data
	void PerformanceAnalysis::handleStateChange() {
	mBufferPeriod.mPrevTs = 0;
	return;
	}


	// Checks whether the time interval between two outliers is far enough from
	// a typical delta to be considered a peak.
	// looks for changes in distribution (peaks), which can be either positive or negative.
	// The function sets the mean to the starting value and sigma to 0, and updates
	// them as long as no peak is detected. When a value is more than 'threshold'
	// standard deviations from the mean, a peak is detected and the mean and sigma
	// are set to the peak value and 0.
	bool PerformanceAnalysis::detectAndStorePeak(msInterval diff, timestamp ts) {
	bool isPeak = false;
	if (mOutlierData.empty()) {
	return false;
	}
	// Update mean of the distribution
	// TypicalDiff is used to check whether a value is unusually large
	// when we cannot use standard deviations from the mean because the sd is set to 0.
	mOutlierDistribution.mTypicalDiff = (mOutlierDistribution.mTypicalDiff *
	(mOutlierData.size() - 1) + diff) / mOutlierData.size();

	// Initialize short-term mean at start of program
	if (mOutlierDistribution.mMean == 0) {
	mOutlierDistribution.mMean = diff;
	}
	// Update length of current sequence of outliers
	mOutlierDistribution.mN++;

	// Check whether a large deviation from the mean occurred.
	// If the standard deviation has been reset to zero, the comparison is
	// instead to the mean of the full mOutlierInterval sequence.
	if ((fabs(diff - mOutlierDistribution.mMean) <
	mOutlierDistribution.kMaxDeviation * mOutlierDistribution.mSd) \|\|
	(mOutlierDistribution.mSd == 0 &&
	fabs(diff - mOutlierDistribution.mMean) <
	mOutlierDistribution.mTypicalDiff)) {
	// update the mean and sd using online algorithm
	// https://en.wikipedia.org/wiki/
	// Algorithms_for_calculating_variance#Online_algorithm
	mOutlierDistribution.mN++;
	const double kDelta = diff - mOutlierDistribution.mMean;
	mOutlierDistribution.mMean += kDelta / mOutlierDistribution.mN;
	const double kDelta2 = diff - mOutlierDistribution.mMean;
	mOutlierDistribution.mM2 += kDelta * kDelta2;
	mOutlierDistribution.mSd = (mOutlierDistribution.mN < 2) ? 0 :
	sqrt(mOutlierDistribution.mM2 / (mOutlierDistribution.mN - 1));
	} else {
	// new value is far from the mean:
	// store peak timestamp and reset mean, sd, and short-term sequence
	isPeak = true;
	mPeakTimestamps.emplace_front(ts);
	// if mPeaks has reached capacity, delete oldest data
	// Note: this means that mOutlierDistribution values do not exactly
	// match the data we have in mPeakTimestamps, but this is not an issue
	// in practice for estimating future peaks.
	// TODO: turn this into a circular buffer
	if (mPeakTimestamps.size() >= kMaxLength.Peaks) {
	mPeakTimestamps.resize(kMaxLength.Peaks);
	}
	mOutlierDistribution.mMean = 0;
	mOutlierDistribution.mSd = 0;
	mOutlierDistribution.mN = 0;
	mOutlierDistribution.mM2 = 0;
	}
	return isPeak;
	}


	// Determines whether the difference between a timestamp and the previous
	// one is beyond a threshold. If yes, stores the timestamp as an outlier
	// and writes to mOutlierdata in the following format:
	// Time elapsed since previous outlier: Timestamp of start of outlier
	// e.g. timestamps (ms) 1, 4, 5, 16, 18, 28 will produce pairs (4, 5), (13, 18).
	// TODO: learn what timestamp sequences correlate with glitches instead of
	// manually designing a heuristic.
	bool PerformanceAnalysis::detectAndStoreOutlier(const msInterval diffMs) {
	bool isOutlier = false;
	if (diffMs >= mBufferPeriod.mOutlier) {
	isOutlier = true;
	mOutlierData.emplace_front(
	mOutlierDistribution.mElapsed, mBufferPeriod.mPrevTs);
	// Remove oldest value if the vector is full
	// TODO: turn this into a circular buffer
	// TODO: make sure kShortHistSize is large enough that that data will never be lost
	// before being written to file or to a FIFO
	if (mOutlierData.size() >= kMaxLength.Outliers) {
	mOutlierData.resize(kMaxLength.Outliers);
	}
	mOutlierDistribution.mElapsed = 0;
	}
	mOutlierDistribution.mElapsed += diffMs;
	return isOutlier;
	}

	static int widthOf(int x) {
	int width = 0;
	if (x < 0) {
	width++;
	x = x == INT_MIN ? INT_MAX : -x;
	}
	// assert (x >= 0)
	do {
	++width;
	x /= 10;
	} while (x > 0);
	return width;
	}

	// computes the column width required for a specific histogram value
	inline int numberWidth(double number, int leftPadding) {
	// Added values account for whitespaces needed around numbers, and for the
	// dot and decimal digit not accounted for by widthOf
	return std::max(std::max(widthOf(static_cast<int>(number)) + 3, 2), leftPadding + 1);
	}

	// rounds value to precision based on log-distance from mean
	inline double logRound(double x, double mean) {
	// Larger values decrease range of high resolution and prevent overflow
	// of a histogram on the console.
	// The following formula adjusts kBase based on the buffer period length.
	// Different threads have buffer periods ranging from 2 to 40. The
	// formula below maps buffer period 2 to kBase = ~1, 4 to ~2, 20 to ~3, 40 to ~4.
	// TODO: tighten this for higher means, the data still overflows
	const double kBase = log(mean) / log(2.2);
	const double power = floor(
	log(abs(x - mean) / mean) / log(kBase)) + 2;
	// do not round values close to the mean
	if (power < 1) {
	return x;
	}
	const int factor = static_cast<int>(pow(10, power));
	return (static_cast<int>(x) * factor) / factor;
	}

	// TODO Make it return a std::string instead of modifying body
	// TODO: move this to ReportPerformance, probably make it a friend function
	// of PerformanceAnalysis
	void PerformanceAnalysis::reportPerformance(String8 *body, int author, log_hash_t hash,
	int maxHeight) {
	if (mHists.empty()) {
	return;
	}

	// ms of active audio in displayed histogram
	double elapsedMs = 0;
	// starting timestamp of histogram
	timestamp startingTs = mHists[0].first;

	// histogram which stores .1 precision ms counts instead of Jiffy multiple counts
	// TODO: when there is more data, print many histograms, possibly separated at peaks
	std::map<double, int> buckets;
	for (const auto &shortHist: mHists) {
	for (const auto &countPair : shortHist.second) {
	const double ms = static_cast<double>(countPair.first) / kJiffyPerMs;
	buckets[logRound(ms, mBufferPeriod.mMean)] += countPair.second;
	elapsedMs += ms * countPair.second;
	}
	}

	// underscores and spaces length corresponds to maximum width of histogram
	static const int kLen = 200;
	std::string underscores(kLen, '_');
	std::string spaces(kLen, ' ');

	auto it = buckets.begin();
	double maxDelta = it->first;
	int maxCount = it->second;
	// Compute maximum values
	while (++it != buckets.end()) {
	if (it->first > maxDelta) {
	maxDelta = it->first;
	}
	if (it->second > maxCount) {
	maxCount = it->second;
	}
	}
	int height = log2(maxCount) + 1; // maxCount > 0, safe to call log2
	const int leftPadding = widthOf(1 << height);
	const int bucketWidth = numberWidth(maxDelta, leftPadding);
	int scalingFactor = 1;
	// scale data if it exceeds maximum height
	if (height > maxHeight) {
	scalingFactor = (height + maxHeight) / maxHeight;
	height /= scalingFactor;
	}
	body->appendFormat("\n%*s %3.2f %s", leftPadding + 11,
	"Occurrences in", (elapsedMs / kMsPerSec), "seconds of audio:");
	body->appendFormat("\n%*s%d, %lld, %lld\n", leftPadding + 11,
	"Thread, hash, starting timestamp: ", author,
	static_cast<long long int>(hash), static_cast<long long int>(startingTs));
	// write histogram label line with bucket values
	body->appendFormat("\n%s", " ");
	body->appendFormat("%*s", leftPadding, " ");
	for (auto const &x : buckets) {
	const int colWidth = numberWidth(x.first, leftPadding);
	body->appendFormat("%*d", colWidth, x.second);
	}
	// write histogram ascii art
	body->appendFormat("\n%s", " ");
	for (int row = height * scalingFactor; row >= 0; row -= scalingFactor) {
	const int value = 1 << row;
	body->appendFormat("%.*s", leftPadding, spaces.c_str());
	for (auto const &x : buckets) {
	const int colWidth = numberWidth(x.first, leftPadding);
	body->appendFormat("%.*s%s", colWidth - 1,
	spaces.c_str(), x.second < value ? " " : "\|");
	}
	body->appendFormat("\n%s", " ");
	}
	// print x-axis
	const int columns = static_cast<int>(buckets.size());
	body->appendFormat("%*c", leftPadding, ' ');
	body->appendFormat("%.s", (columns + 1) bucketWidth, underscores.c_str());
	body->appendFormat("\n%s", " ");

	// write footer with bucket labels
	body->appendFormat("%*s", leftPadding, " ");
	for (auto const &x : buckets) {
	const int colWidth = numberWidth(x.first, leftPadding);
	body->appendFormat("%.f", colWidth, 1, x.first);
	}
	body->appendFormat("%.*s%s", bucketWidth, spaces.c_str(), "ms\n");

	// Now report glitches
	body->appendFormat("\ntime elapsed between glitches and glitch timestamps:\n");
	for (const auto &outlier: mOutlierData) {
	body->appendFormat("%lld: %lld\n", static_cast<long long>(outlier.first),
	static_cast<long long>(outlier.second));
	}
	}

	//------------------------------------------------------------------------------

	// writes summary of performance into specified file descriptor
	void dump(int fd, int indent, PerformanceAnalysisMap &threadPerformanceAnalysis) {
	String8 body;
	const char* const kDirectory = "/data/misc/audioserver/";
	for (auto & thread : threadPerformanceAnalysis) {
	for (auto & hash: thread.second) {
	PerformanceAnalysis& curr = hash.second;
	// write performance data to console
	curr.reportPerformance(&body, thread.first, hash.first);
	if (!body.isEmpty()) {
	dumpLine(fd, indent, body);
	body.clear();
	}
	// write to file
	writeToFile(curr.mHists, curr.mOutlierData, curr.mPeakTimestamps,
	kDirectory, false, thread.first, hash.first);
	}
	}
	}


	// Writes a string into specified file descriptor
	void dumpLine(int fd, int indent, const String8 &body) {
	dprintf(fd, "%.*s%s \n", indent, "", body.string());
	}

	} // namespace ReportPerformance

	} // namespace android