A High Dynamic Range (HDR) Histogram
HdrHistogram.NET is the official port of the Java HdrHistogram library. All official implementations of HdrHistogram can be found at https://github.com/HdrHistogram
You would use it to efficiently capture large number of response times measurements.
Often when measuring response times, one could make the common mistake of reporting on the mean value or the 90th percentile. Gil Tene (the original author of the Java HdrHistogram) illustrates in numerous presentations (such as here and here) on why this is a mistake. Instead you want to collect all of the data and then be able to report your measurements across the range of measurements.
The library is available as a package from Nuget as HdrHistogram
Generally you want to be able to record at the finest accuracy the response-time of a given function of your software. To do this code might look something like this
// A Histogram covering the range from ~466 nanoseconds to 1 hour (3,600,000,000,000 ns) with a resolution of 3 significant figures:
var histogram = new LongHistogram(TimeStamp.Hours(1), 3);Next you would record your measurements.
The System.Diagnostics.Stopwatch.GetTimestamp() method provides the most accurate way to record the elapsed time an action took to run.
By measuring the difference of the timestamp values before and after the action to measure, we can get the most accurate recording of elapsed
time available on the .NET platform.
long startTimestamp = Stopwatch.GetTimestamp();
//Execute some action to be measured
long elapsed = Stopwatch.GetTimestamp() - startTimestamp;
histogram.RecordValue(elapsed);Once you have recorded all of your data, you are able to present that data based on a highly dynamic range of buckets. We are not interested in all the values, but just enough of the values to get a picture of our system's performance. To do this we want to generate a percentile distribution, with exponentially increasing fidelity.
Here we show an example of writing to the Console.
var writer = new StringWriter();
var scalingRatio = OutputScalingFactor.TimeStampToMicroseconds;
histogram.OutputPercentileDistribution(
writer,
outputValueUnitScalingRatio: scalingRatio);
Console.WriteLine(writer.ToString());
//Or just simply write directly to the Console output stream
//histogram.OutputPercentileDistribution(
// Console.Out,
// outputValueUnitScalingRatio: scalingRatio);Would produce output similar to:
Value Percentile TotalCount 1/(1-Percentile)
0.285 0.000000000000 1 1.00
0.448 0.100000000000 3535 1.11
0.466 0.200000000000 7100 1.25
0.497 0.300000000000 10504 1.43
0.523 0.400000000000 14046 1.67
0.535 0.500000000000 17644 2.00
0.541 0.550000000000 19466 2.22
0.547 0.600000000000 21134 2.50
0.555 0.650000000000 22898 2.86
0.567 0.700000000000 24513 3.33
0.594 0.750000000000 26260 4.00
0.609 0.775000000000 27129 4.44
0.627 0.800000000000 28005 5.00
0.642 0.825000000000 28939 5.71
0.660 0.850000000000 29793 6.67
0.680 0.875000000000 30649 8.00
0.687 0.887500000000 31095 8.89
0.693 0.900000000000 31550 10.00
0.698 0.912500000000 31992 11.43
0.703 0.925000000000 32415 13.33
0.710 0.937500000000 32880 16.00
0.713 0.943750000000 33080 17.78
0.717 0.950000000000 33277 20.00
0.721 0.956250000000 33476 22.86
0.727 0.962500000000 33710 26.67
0.736 0.968750000000 33925 32.00
0.741 0.971875000000 34023 35.56
0.748 0.975000000000 34141 40.00
0.757 0.978125000000 34249 45.71
0.768 0.981250000000 34352 53.33
0.786 0.984375000000 34459 64.00
0.803 0.985937500000 34515 71.11
0.815 0.987500000000 34567 80.00
0.838 0.989062500000 34622 91.43
0.869 0.990625000000 34676 106.67
1.045 0.992187500000 34731 128.00
1.815 0.992968750000 34759 142.22
1.943 0.993750000000 34786 160.00
1.989 0.994531250000 34813 182.86
2.038 0.995312500000 34841 213.33
2.087 0.996093750000 34868 256.00
2.127 0.996484375000 34881 284.44
2.161 0.996875000000 34895 320.00
2.225 0.997265625000 34909 365.71
2.355 0.997656250000 34922 426.67
2.539 0.998046875000 34936 512.00
2.601 0.998242187500 34943 568.89
2.653 0.998437500000 34950 640.00
2.689 0.998632812500 34957 731.43
2.755 0.998828125000 34964 853.33
2.801 0.999023437500 34970 1024.00
2.827 0.999121093750 34974 1137.78
2.847 0.999218750000 34977 1280.00
2.889 0.999316406250 34982 1462.86
2.947 0.999414062500 34984 1706.67
2.979 0.999511718750 34987 2048.00
3.015 0.999560546875 34989 2275.56
3.131 0.999609375000 34991 2560.00
3.267 0.999658203125 34993 2925.71
3.397 0.999707031250 34994 3413.33
3.627 0.999755859375 34996 4096.00
3.845 0.999780273438 34997 4551.11
3.995 0.999804687500 34998 5120.00
4.299 0.999829101563 34999 5851.43
4.299 0.999853515625 34999 6826.67
4.839 0.999877929688 35000 8192.00
10.039 0.999890136719 35001 9102.22
10.039 0.999902343750 35001 10240.00
11.911 0.999914550781 35002 11702.86
11.911 0.999926757813 35002 13653.33
11.911 0.999938964844 35002 16384.00
15.367 0.999945068359 35003 18204.44
15.367 0.999951171875 35003 20480.00
15.367 0.999957275391 35003 23405.71
15.367 0.999963378906 35003 27306.67
15.367 0.999969482422 35003 32768.00
2543.615 0.999972534180 35004 36408.89
2543.615 1.000000000000 35004
#[Mean = 0.633, StdDeviation = 13.588]
#[Max = 2541.568, Total count = 35004]
#[Buckets = 21, SubBuckets = 2048]
Note that in the example above a value for the optional parameter outputValueUnitScalingRatio is provided.
If you record elapsed time using the suggested method with Stopwatch.GetTimestamp(), then you will have recorded values in a non-standard unit of time.
Instead of paying to cost of converting recorded values at the time of recording, record raw values.
Use the helper methods to convert recorded values to standard units at output time, when performance is less critical.
You can also have HdrHistogram output the results in a file format that can be charted. This is especially useful when comparing measurements.
First you will need to create the file to be used as an input for the chart.
using (var writer = new StreamWriter("HistogramResults.hgrm"))
{
histogram.OutputPercentileDistribution(writer);
}The data can then be plotter to visualize the percentile distribution of your results. Multiple files can be plotted in the same chart allowing effective visual comparison of your results. You can use either
- the online tool - http://hdrhistogram.github.io/HdrHistogram/plotFiles.html
- the local tool - .\GoogleChartsExample\plotFiles.html
If you use the local tool, there are example result files in the .\GoogleChartsExample directory. The tool also allows you to export to png.
- itself is low latency
- tiny foot print due to just storing a dynamic range of buckets and counts
- produces the reports you actually want
This code sample show a recording of the time taken to execute a ping request. We execute and record this in a loop.
// A Histogram covering the range from ~466 nanoseconds to 1 hour (3,600,000,000,000 ns) with a resolution of 3 significant figures:
var histogram = new LongHistogram(TimeStamp.Hours(1), 3);
using (var ping = new System.Net.NetworkInformation.Ping())
{
for (int i = 0; i < 100; i++)
{
long startTimestamp = Stopwatch.GetTimestamp();
//Execute our action we want to record.
ping.Send("www.github.com");
long elapsed = Stopwatch.GetTimestamp() - startTimestamp;
histogram.RecordValue(elapsed);
}
}
//Output the percentile distribution of our results to the Console with values presented in Milliseconds
histogram.OutputPercentileDistribution(
printStream: Console.Out,
percentileTicksPerHalfDistance: 3,
outputValueUnitScalingRatio: OutputScalingFactor.TimeStampToMilliseconds);output:
Value Percentile TotalCount 1/(1-Percentile)
79.360 0.000000000000 1 1.00
80.435 0.166666666667 17 1.20
80.896 0.333333333333 36 1.50
81.050 0.500000000000 52 2.00
81.152 0.583333333333 59 2.40
81.254 0.666666666667 70 3.00
81.357 0.750000000000 76 4.00
81.459 0.791666666667 86 4.80
81.459 0.833333333333 86 6.00
81.510 0.875000000000 93 8.00
81.510 0.895833333333 93 9.60
81.510 0.916666666667 93 12.00
81.562 0.937500000000 94 16.00
81.613 0.947916666667 98 19.20
81.613 0.958333333333 98 24.00
81.613 0.968750000000 98 32.00
81.613 0.973958333333 98 38.40
81.613 0.979166666667 98 48.00
81.664 0.984375000000 99 64.00
81.664 0.986979166667 99 76.80
81.664 0.989583333333 99 96.00
86.067 0.992187500000 100 128.00
86.067 1.000000000000 100
#[Mean = 80.964, StdDeviation = 0.746]
#[Max = 86.067, Total count = 100]
#[Buckets = 26, SubBuckets = 2048]
We welcome pull requests! If you do choose to contribute, please first raise an issue so we are not caught off guard by the pull request. Next can you please ensure that your PR (Pull Request) has a comment in it describing what it achieves and the issues that it closes. Ideally if it is fixing an issue or a bug, there would be a Unit Test proving the fix and a reference to the Issues in the PR comments.
An HdrHistogram supports the recording and analyzing of sampled data value counts across a configurable integer value range with configurable value precision within the range. Value precision is expressed as the number of significant digits in the value recording, and provides control over value quantization behavior across the value range and the subsequent value resolution at any given level.
For example, a Histogram could be configured to track the counts of observed integer values between 0 and 3,600,000,000 while maintaining a value precision of 3 significant digits across that range. Value quantization within the range will thus be no larger than 1/1,000th (or 0.1%) of any value. This example Histogram could be used to track and analyze the counts of observed response times ranging between 1 microsecond and 1 hour in magnitude. This Histogram would still maintain a value resolution of 1 microsecond up to 1 millisecond, a resolution of 1 millisecond (or better) up to one second, and a resolution of 1 second (or better) up to 1,000 seconds. At its maximum tracked value (1 hour), it would still maintain a resolution of 3.6 seconds (or better).
The HdrHistogram package includes the LongHistogram implementation, which tracks value counts in long fields, and is expected to be the commonly used Histogram form.
IntHistogram and ShortHistogram, which track value counts in int and short fields respectively, are provided for use cases where smaller count ranges are practical and smaller overall storage is beneficial.
Performance impacts should be measured prior to choosing one over the other in the name of optimization.
HdrHistogram is designed for recoding histograms of value measurements in latency and performance sensitive applications. Measurements show value recording times as low as 3-6 nanoseconds on modern (circa 2012) Intel CPUs. That is, 1,000,000,000 (1 billion) recordings can be made at a total cost of around 3 seconds on modern hardware. A Histogram's memory footprint is constant, with no allocation operations involved in recording data values or in iterating through them. The memory footprint is fixed regardless of the number of data value samples recorded, and depends solely on the dynamic range and precision chosen. The amount of work involved in recording a sample is constant, and directly computes storage index locations such that no iteration or searching is ever involved in recording data values.
A combination of high dynamic range and precision is useful for collection and accurate post-recording analysis of sampled value data distribution in various forms. Whether it's calculating or plotting arbitrary percentiles, iterating through and summarizing values in various ways, or deriving mean and standard deviation values, the fact that the recorded data information is kept in high resolution allows for accurate post-recording analysis with low [and ultimately configurable] loss in accuracy when compared to performing the same analysis directly on the potentially infinite series of sourced data values samples.
An common use example of HdrHistogram would be to record response times in units of microseconds across a dynamic range stretching from 1 usec to over an hour, with a good enough resolution to support later performing post-recording analysis on the collected data. Analysis can include computing, examining, and reporting of distribution by percentiles, linear or logarithmic value buckets, mean and standard deviation, or by any other means that can can be easily added by using the various iteration techniques supported by the Histogram. In order to facilitate the accuracy needed for various post-recording analysis techniques, this example can maintain a resolution of ~1 usec or better for times ranging to ~2 msec in magnitude, while at the same time maintaining a resolution of ~1 msec or better for times ranging to ~2 sec, and a resolution of ~1 second or better for values up to 2,000 seconds. This sort of example resolution can be thought of as "always accurate to 3 decimal points." Such an example Histogram would simply be created with a highestTrackableValue of 3,600,000,000, and a numberOfSignificantValueDigits of 3, and would occupy a fixed, unchanging memory footprint of around 185KB (see "Footprint estimation" below).
The HdrHistogram package includes multiple implementations of the
HistogramBase class:
LongHistogram, which is the commonly used Histogram form and tracks value counts inlongfields.IntHistogramandShortHistogram, which track value counts inintandshortfields respectively, are provided for use cases where smaller count ranges are practical and smaller overall storage is beneficial (e.g. systems where tens of thousands of in-memory histogram are being tracked).SynchronizedHistogram(see 'Synchronization and concurrent access' below)
Internally, data in HdrHistogram variants is maintained using a concept somewhat similar to that of floating point number representation.
Using an exponent a (non-normalized) mantissa to support a wide dynamic range at a high but varying (by exponent value) resolution.
Histograms use exponentially increasing bucket value ranges (the parallel of the exponent portion of a floating point number) with each bucket containing a fixed number (per bucket) set of linear sub-buckets (the parallel of a non-normalized mantissa portion of a floating point number).
Both dynamic range and resolution are configurable, with highestTrackableValue controlling dynamic range, and numberOfSignificantValueDigits controlling resolution.
In the interest of keeping value recording cost to a minimum, the commonly used LongHistogram class and its IntHistogram and ShortHistogram variants are NOT internally synchronized, and do NOT use atomic variables.
Callers wishing to make potentially concurrent, multi-threaded updates or queries against Histogram objects should either take care to externally synchronize and/or order their access, or use the SynchronizedHistogram variant.
It is worth mentioning that since Histogram objects are additive, it is common practice to use per-thread, non-synchronized histograms for the recording fast path, and "flipping" the actively recorded-to histogram (usually with some non-locking variants on the fast path) and having a summary/reporting thread perform histogram aggregation math across time and/or threads.
Histograms supports multiple convenient forms of iterating through the histogram data set, including linear, logarithmic, and percentile iteration mechanisms, as well as means for iterating through each recorded value or each possible value level.
The iteration mechanisms are accessible through the HistogramData available through getHistogramData().
Iteration mechanisms all provide HistogramIterationValue data points along the histogram's iterated data set.
Recorded values are available as instance methods:
RecordedValues: AnIEnumerable<HistogramIterationValue>through the histogram using aRecordedValuesEnumerable`RecordedValuesEnumerator`AllValues: AnIEnumerable<HistogramIterationValue>through the histogram using aAllValueEnumerable`AllValuesEnumerator`
All others are available for the default (corrected) histogram data set via the following extension methods:
Percentiles: AnIEnumerable<HistogramIterationValue>through the histogram using aPercentileEnumerable/PercentileEnumeratorLinearBucketValues: AnIEnumerable<HistogramIterationValue>through the histogram using aLinearBucketEnumerable/LinearEnumeratorLogarithmicBucketValues: AnIEnumerable<HistogramIterationValue>through the histogram using aLogarithmicBucketEnumerable/LogarithmicEnumerator
Iteration is typically done with a for-each loop statement. E.g.:
foreach (var v in histogram.Percentiles(ticksPerHalfDistance))
{
...
}or
for (var v in histogram.LinearBucketValues(unitsPerBucket))
{
...
}These enumerators are optimised for fast forward readonly "hosepipe" usage. They are low allocation and may reuse objects internally to keep allocations low and thus reduce garbage collection/memory pressure.
Due to the finite (and configurable) resolution of the histogram, multiple adjacent integer data values can be "equivalent". Two values are considered "equivalent" if samples recorded for both are always counted in a common total count due to the histogram's resolution level. HdrHistogram provides methods for
- determining the lowest and highest equivalent values for any given value,
- determining whether two values are equivalent,
- finding the next non-equivalent value for a given value (useful when looping through values, in order to avoid a double-counting count).
In order to support a common use case needed when histogram values are used to track response time distribution, Histogram provides for the recording of corrected histogram value by supporting a RecordValueWithExpectedInterval(long, long) variant is provided.
This value recording form is useful in [common latency measurement] scenarios where response times may exceed the expected interval between issuing requests, leading to "dropped" response time measurements that would typically correlate with "bad" results.
When a value recorded in the histogram exceeds the expectedIntervalBetweenValueSamples parameter, recorded histogram data will reflect an appropriate number of additional values, linearly decreasing in steps of expectedIntervalBetweenValueSamples, down to the last value that would still be higher than expectedIntervalBetweenValueSamples.
To illustrate why this corrective behavior is critically needed in order to accurately represent value distribution when large value measurements may lead to missed samples, imagine a system for which response times samples are taken once every 10 msec to characterize response time distribution.
The hypothetical system behaves "perfectly" for 100 seconds (10,000 recorded samples), with each sample showing a 1 msec response time value.
At each sample for 100 seconds (10,000 logged samples at 1 msec each).
The hypothetical system then encounters a 100 sec pause during which only a single sample is recorded (with a 100 second value).
The raw data histogram collected for such a hypothetical system (over the 200 second scenario above) would show ~99.99% of results at 1 msec or below, which is obviously "not right".
The same histogram, corrected with the knowledge of an expectedIntervalBetweenValueSamples of 10msec will correctly represent the response time distribution.
Only ~50% of results will be at 1 msec or below, with the remaining 50% coming from the auto-generated value records covering the missing increments spread between 10msec and 100 sec.
Data sets recorded with and without an expectedIntervalBetweenValueSamples parameter will differ only if at least one value recorded with the RecordValue(..) method was greater than its associated expectedIntervalBetweenValueSamples parameter.
Data sets recorded with an expectedIntervalBetweenValueSamples parameter will be identical to ones recorded without it if all values recorded via the RecordValue(..) calls were smaller than their associated (and optional) expectedIntervalBetweenValueSamples parameters.
When used for response time characterization, the recording with the optional expectedIntervalBetweenValueSamples parameter will tend to produce data sets that would much more accurately reflect the response time distribution that a random, uncoordinated request would have experienced.
Due to it's dynamic range representation, Histogram is relatively efficient in memory space requirements given the accuracy and dynamic range it covers.
Still, it is useful to be able to estimate the memory footprint involved for a given highestTrackableValue and numberOfSignificantValueDigits combination.
Beyond a relatively small fixed-size footprint used for internal fields and stats (which can be estimated as "fixed at well less than 1KB"), the bulk of a Histogram's storage is taken up by it's data value recording counts array.
The total footprint can be conservatively estimated by:
largestValueWithSingleUnitResolution = 2 * (10 ^ numberOfSignificantValueDigits);
subBucketSize = RoundedUpToNearestPowerOf2(largestValueWithSingleUnitResolution);
expectedHistogramFootprintInBytes = 512 +
({primitive type size} / 2) *
(Log2RoundedUp((highestTrackableValue) / subBucketSize) + 2) *
subBucketSize;A conservative (high) estimate of a Histogram's footprint in bytes is available via the GetEstimatedFootprintInBytes() method.
- Latency : The time that something is latent i.e. not being processed. This maybe due to being in a queue.
- Service Time : The time taken to actually service a request.
- Response time : The sum of the latency and the service time. e.g. the time your request was queued, plus the time it took to process.
References (see also):
- How NOT to Measure Latency Gil Tene - qCon 2013
- Understanding Latency Gil Tene - React San Francisco 2014
- Designing for Performance Martin Thompson - GOTO Chicago 2015
- https://en.wikipedia.org/wiki/Response_time_(technology)