Add ExponentialHistogram to Metrics data model

specification/metrics/datamodel.md

@@ -398,6 +398,82 @@ denotes Delta temporality where accumulated event counts are reset to zero after
 and a new aggregation occurs. Cumulative, on the other hand, continues to
 aggregate events, resetting with the use of a new start time.
 
+### ExponentialHistogram
+
+[ExponentialHistogram](TBD_after_PR322_merges) data points are an
+alternate representation, like the [Histogram](#histogram) that convey
+a population of recorded measurements in a compressed format.
+ExponentialHistogram compresses bucket boundaries using an exponential
+formula, making it suitable for conveying high-resolution histogram
+data with a large number of buckets.
+
+Statements about `Histogram` that refer to aggregation temporality,
+attributes, timestamps, as well as the `sum`, `count`, `exemplars`
+fields are identical for `ExponentialHistogram`.
+
+The resolution of the ExponentialHistogram is characterized by a
+parameter known as `scale`, with larger values of `scale` offering
+greater precision.  Bucket boundaries of the ExponentialHistogram are
+located at integer powers of the `base`, where:
+
+```
+base = 2**(2**(-scale))
+```
+
+The symbol `**` in these formulas represents exponentiation, thus
+`2**x` is read "Two to the power of X", typically computed by an
+expression like `math.Pow(2.0, x)`.  Calculated `base` values for
+selected scales are shown below:
+
+| Scale | Base              | Expression  |
+| --    | --                | --          |
+| 10    | 1.000677130693066 | 2**(1/1024) |
+| 9     | 1.001354719892108 | 2**(1/512)  |
+| 8     | 1.002711275050203 | 2**(1/256)  |
+| 7     | 1.005429901112803 | 2**(1/128)  |
+| 6     | 1.010889286051700 | 2**(1/64)   |
+| 5     | 1.021897148654117 | 2**(1/32)   |
+| 4     | 1.044273782427414 | 2**(1/16)   |
+| 3     | 1.090507732665258 | 2**(1/8)    |
+| 2     | 1.189207115002721 | 2**(1/4)    |
+| 1     | 1.414213562373095 | 2**(1/2)    |
+| 0     | 2                 | 2**1        |
+| -1    | 4                 | 2**2        |
+| -2    | 16                | 2**4        |
+| -3    | 256               | 2**8        |
+| -4    | 65536             | 2**16       |
+
+The ExponentialHistogram bucket identified by `index`, a signed
+integer, represents values in the population that are greater than or
+equal to `base**index` and less than `base**(index+1)`.
+
+The positive and negative ranges of the histogram are expressed
+separately.  Negative values are mapped by their absolute value
+into the negative range using the same scale as the positive range.
+
+Each range of the ExponentialHistogram data point uses a dense
+representation of the buckets, where a range of buckets is expressed
+as a single `offset` value, a signed integer, and an array of count
+values, where array element `i` represents the bucket count for bucket
+index `offset+i`.
+
+For a given range, positive or negative:
+
+- The absolute value 1.0 has bucket index `0`
+- Bucket index `0` counts measurements greater than or equal to 1.0 and less than `base`
+- Negative indexes correspond with absolute values less than 1.0.
+
+The ExponentialHistogram contains a special `zero_count` field
+containing is the count of values that are either exactly zero or
+within the region considered zero by the instrumentation at the
+tolerated degree of precision.  This bucket stores values that cannot
+be expressed using the standard exponential formula as well as values
+that have been rounded to zero.
+
+#### Producers and consumer requirements
+
+TODO: Work-In-Progress.
+
 ### Summary (Legacy)
 
 [Summary](https://github.com/open-telemetry/opentelemetry-proto/blob/v0.9.0/opentelemetry/proto/metrics/v1/metrics.proto#L268)