two version of R2R are here HEAD master

8 files changed, 885 insertions, 0 deletions

diff --git a/.venv/lib/python3.12/site-packages/opentelemetry/sdk/metrics/_internal/exponential_histogram/__init__.py b/.venv/lib/python3.12/site-packages/opentelemetry/sdk/metrics/_internal/exponential_histogram/__init__.py
new file mode 100644
index 00000000..e69de29b
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/opentelemetry/sdk/metrics/_internal/exponential_histogram/__init__.py
diff --git a/.venv/lib/python3.12/site-packages/opentelemetry/sdk/metrics/_internal/exponential_histogram/buckets.py b/.venv/lib/python3.12/site-packages/opentelemetry/sdk/metrics/_internal/exponential_histogram/buckets.py
new file mode 100644
index 00000000..e8a93326
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/opentelemetry/sdk/metrics/_internal/exponential_histogram/buckets.py
@@ -0,0 +1,190 @@
+# Copyright The OpenTelemetry Authors
+#
+# 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.
+
+from math import ceil, log2
+
+
+class Buckets:
+    # No method of this class is protected by locks because instances of this
+    # class are only used in methods that are protected by locks themselves.
+
+    def __init__(self):
+        self._counts = [0]
+
+        # The term index refers to the number of the exponential histogram bucket
+        # used to determine its boundaries. The lower boundary of a bucket is
+        # determined by base ** index and the upper boundary of a bucket is
+        # determined by base ** (index + 1). index values are signedto account
+        # for values less than or equal to 1.
+
+        # self._index_* will all have values equal to a certain index that is
+        # determined by the corresponding mapping _map_to_index function and
+        # the value of the index depends on the value passed to _map_to_index.
+
+        # Index of the 0th position in self._counts: self._counts[0] is the
+        # count in the bucket with index self.__index_base.
+        self.__index_base = 0
+
+        # self.__index_start is the smallest index value represented in
+        # self._counts.
+        self.__index_start = 0
+
+        # self.__index_start is the largest index value represented in
+        # self._counts.
+        self.__index_end = 0
+
+    @property
+    def index_start(self) -> int:
+        return self.__index_start
+
+    @index_start.setter
+    def index_start(self, value: int) -> None:
+        self.__index_start = value
+
+    @property
+    def index_end(self) -> int:
+        return self.__index_end
+
+    @index_end.setter
+    def index_end(self, value: int) -> None:
+        self.__index_end = value
+
+    @property
+    def index_base(self) -> int:
+        return self.__index_base
+
+    @index_base.setter
+    def index_base(self, value: int) -> None:
+        self.__index_base = value
+
+    @property
+    def counts(self):
+        return self._counts
+
+    def get_offset_counts(self):
+        bias = self.__index_base - self.__index_start
+        return self._counts[-bias:] + self._counts[:-bias]
+
+    def grow(self, needed: int, max_size: int) -> None:
+        size = len(self._counts)
+        bias = self.__index_base - self.__index_start
+        old_positive_limit = size - bias
+
+        # 2 ** ceil(log2(needed)) finds the smallest power of two that is larger
+        # or equal than needed:
+        # 2 ** ceil(log2(1)) == 1
+        # 2 ** ceil(log2(2)) == 2
+        # 2 ** ceil(log2(3)) == 4
+        # 2 ** ceil(log2(4)) == 4
+        # 2 ** ceil(log2(5)) == 8
+        # 2 ** ceil(log2(6)) == 8
+        # 2 ** ceil(log2(7)) == 8
+        # 2 ** ceil(log2(8)) == 8
+        new_size = min(2 ** ceil(log2(needed)), max_size)
+
+        new_positive_limit = new_size - bias
+
+        tmp = [0] * new_size
+        tmp[new_positive_limit:] = self._counts[old_positive_limit:]
+        tmp[0:old_positive_limit] = self._counts[0:old_positive_limit]
+        self._counts = tmp
+
+    @property
+    def offset(self) -> int:
+        return self.__index_start
+
+    def __len__(self) -> int:
+        if len(self._counts) == 0:
+            return 0
+
+        if self.__index_end == self.__index_start and self[0] == 0:
+            return 0
+
+        return self.__index_end - self.__index_start + 1
+
+    def __getitem__(self, key: int) -> int:
+        bias = self.__index_base - self.__index_start
+
+        if key < bias:
+            key += len(self._counts)
+
+        key -= bias
+
+        return self._counts[key]
+
+    def downscale(self, amount: int) -> None:
+        """
+        Rotates, then collapses 2 ** amount to 1 buckets.
+        """
+
+        bias = self.__index_base - self.__index_start
+
+        if bias != 0:
+            self.__index_base = self.__index_start
+
+            # [0, 1, 2, 3, 4] Original backing array
+
+            self._counts = self._counts[::-1]
+            # [4, 3, 2, 1, 0]
+
+            self._counts = (
+                self._counts[:bias][::-1] + self._counts[bias:][::-1]
+            )
+            # [3, 4, 0, 1, 2] This is a rotation of the backing array.
+
+        size = 1 + self.__index_end - self.__index_start
+        each = 1 << amount
+        inpos = 0
+        outpos = 0
+
+        pos = self.__index_start
+
+        while pos <= self.__index_end:
+            mod = pos % each
+            if mod < 0:
+                mod += each
+
+            index = mod
+
+            while index < each and inpos < size:
+                if outpos != inpos:
+                    self._counts[outpos] += self._counts[inpos]
+                    self._counts[inpos] = 0
+
+                inpos += 1
+                pos += 1
+                index += 1
+
+            outpos += 1
+
+        self.__index_start >>= amount
+        self.__index_end >>= amount
+        self.__index_base = self.__index_start
+
+    def increment_bucket(self, bucket_index: int, increment: int = 1) -> None:
+        self._counts[bucket_index] += increment
+
+    def copy_empty(self) -> "Buckets":
+        copy = Buckets()
+
+        # pylint: disable=no-member
+        # pylint: disable=protected-access
+        # pylint: disable=attribute-defined-outside-init
+        # pylint: disable=invalid-name
+        copy._Buckets__index_base = self._Buckets__index_base
+        copy._Buckets__index_start = self._Buckets__index_start
+        copy._Buckets__index_end = self._Buckets__index_end
+        copy._counts = [0 for _ in self._counts]
+
+        return copy
diff --git a/.venv/lib/python3.12/site-packages/opentelemetry/sdk/metrics/_internal/exponential_histogram/mapping/__init__.py b/.venv/lib/python3.12/site-packages/opentelemetry/sdk/metrics/_internal/exponential_histogram/mapping/__init__.py
new file mode 100644
index 00000000..387b1d14
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/opentelemetry/sdk/metrics/_internal/exponential_histogram/mapping/__init__.py
@@ -0,0 +1,98 @@
+# Copyright The OpenTelemetry Authors
+#
+# 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.
+
+from abc import ABC, abstractmethod
+
+
+class Mapping(ABC):
+    """
+    Parent class for `LogarithmMapping` and `ExponentialMapping`.
+    """
+
+    # pylint: disable=no-member
+    def __new__(cls, scale: int):
+        with cls._mappings_lock:
+            # cls._mappings and cls._mappings_lock are implemented in each of
+            # the child classes as a dictionary and a lock, respectively. They
+            # are not instantiated here because that would lead to both child
+            # classes having the same instance of cls._mappings and
+            # cls._mappings_lock.
+            if scale not in cls._mappings:
+                cls._mappings[scale] = super().__new__(cls)
+                cls._mappings[scale]._init(scale)
+
+        return cls._mappings[scale]
+
+    @abstractmethod
+    def _init(self, scale: int) -> None:
+        # pylint: disable=attribute-defined-outside-init
+
+        if scale > self._get_max_scale():
+            # pylint: disable=broad-exception-raised
+            raise Exception(f"scale is larger than {self._max_scale}")
+
+        if scale < self._get_min_scale():
+            # pylint: disable=broad-exception-raised
+            raise Exception(f"scale is smaller than {self._min_scale}")
+
+        # The size of the exponential histogram buckets is determined by a
+        # parameter known as scale, larger values of scale will produce smaller
+        # buckets. Bucket boundaries of the exponential histogram are located
+        # at integer powers of the base, where:
+        #
+        # base = 2 ** (2 ** (-scale))
+        # https://github.com/open-telemetry/opentelemetry-specification/blob/main/specification/metrics/data-model.md#all-scales-use-the-logarithm-function
+        self._scale = scale
+
+    @abstractmethod
+    def _get_min_scale(self) -> int:
+        """
+        Return the smallest possible value for the mapping scale
+        """
+
+    @abstractmethod
+    def _get_max_scale(self) -> int:
+        """
+        Return the largest possible value for the mapping scale
+        """
+
+    @abstractmethod
+    def map_to_index(self, value: float) -> int:
+        """
+        Maps positive floating point values to indexes corresponding to
+        `Mapping.scale`. Implementations are not expected to handle zeros,
+        +inf, NaN, or negative values.
+        """
+
+    @abstractmethod
+    def get_lower_boundary(self, index: int) -> float:
+        """
+        Returns the lower boundary of a given bucket index. The index is
+        expected to map onto a range that is at least partially inside the
+        range of normal floating point values.  If the corresponding
+        bucket's upper boundary is less than or equal to 2 ** -1022,
+        :class:`~opentelemetry.sdk.metrics.MappingUnderflowError`
+        will be raised. If the corresponding bucket's lower boundary is greater
+        than ``sys.float_info.max``,
+        :class:`~opentelemetry.sdk.metrics.MappingOverflowError`
+        will be raised.
+        """
+
+    @property
+    def scale(self) -> int:
+        """
+        Returns the parameter that controls the resolution of this mapping.
+        See: https://github.com/open-telemetry/opentelemetry-specification/blob/main/specification/metrics/datamodel.md#exponential-scale
+        """
+        return self._scale
diff --git a/.venv/lib/python3.12/site-packages/opentelemetry/sdk/metrics/_internal/exponential_histogram/mapping/errors.py b/.venv/lib/python3.12/site-packages/opentelemetry/sdk/metrics/_internal/exponential_histogram/mapping/errors.py
new file mode 100644
index 00000000..477ed6f0
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/opentelemetry/sdk/metrics/_internal/exponential_histogram/mapping/errors.py
@@ -0,0 +1,26 @@
+# Copyright The OpenTelemetry Authors
+#
+# 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.
+
+
+class MappingUnderflowError(Exception):
+    """
+    Raised when computing the lower boundary of an index that maps into a
+    denormal floating point value.
+    """
+
+
+class MappingOverflowError(Exception):
+    """
+    Raised when computing the lower boundary of an index that maps into +inf.
+    """
diff --git a/.venv/lib/python3.12/site-packages/opentelemetry/sdk/metrics/_internal/exponential_histogram/mapping/exponent_mapping.py b/.venv/lib/python3.12/site-packages/opentelemetry/sdk/metrics/_internal/exponential_histogram/mapping/exponent_mapping.py
new file mode 100644
index 00000000..297bb7a4
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/opentelemetry/sdk/metrics/_internal/exponential_histogram/mapping/exponent_mapping.py
@@ -0,0 +1,141 @@
+# Copyright The OpenTelemetry Authors
+#
+# 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.
+
+from math import ldexp
+from threading import Lock
+
+from opentelemetry.sdk.metrics._internal.exponential_histogram.mapping import (
+    Mapping,
+)
+from opentelemetry.sdk.metrics._internal.exponential_histogram.mapping.errors import (
+    MappingOverflowError,
+    MappingUnderflowError,
+)
+from opentelemetry.sdk.metrics._internal.exponential_histogram.mapping.ieee_754 import (
+    MANTISSA_WIDTH,
+    MAX_NORMAL_EXPONENT,
+    MIN_NORMAL_EXPONENT,
+    MIN_NORMAL_VALUE,
+    get_ieee_754_exponent,
+    get_ieee_754_mantissa,
+)
+
+
+class ExponentMapping(Mapping):
+    # Reference implementation here:
+    # https://github.com/open-telemetry/opentelemetry-go/blob/0e6f9c29c10d6078e8131418e1d1d166c7195d61/sdk/metric/aggregator/exponential/mapping/exponent/exponent.go
+
+    _mappings = {}
+    _mappings_lock = Lock()
+
+    _min_scale = -10
+    _max_scale = 0
+
+    def _get_min_scale(self):
+        # _min_scale defines the point at which the exponential mapping
+        # function becomes useless for 64-bit floats. With scale -10, ignoring
+        # subnormal values, bucket indices range from -1 to 1.
+        return -10
+
+    def _get_max_scale(self):
+        # _max_scale is the largest scale supported by exponential mapping. Use
+        # a logarithm mapping for larger scales.
+        return 0
+
+    def _init(self, scale: int):
+        # pylint: disable=attribute-defined-outside-init
+
+        super()._init(scale)
+
+        # self._min_normal_lower_boundary_index is the largest index such that
+        # base ** index < MIN_NORMAL_VALUE and
+        # base ** (index + 1) >= MIN_NORMAL_VALUE. An exponential histogram
+        # bucket with this index covers the range
+        # (base ** index, base (index + 1)], including MIN_NORMAL_VALUE. This
+        # is the smallest valid index that contains at least one normal value.
+        index = MIN_NORMAL_EXPONENT >> -self._scale
+
+        if -self._scale < 2:
+            # For scales -1 and 0, the maximum value 2 ** -1022 is a
+            # power-of-two multiple, meaning base ** index == MIN_NORMAL_VALUE.
+            # Subtracting 1 so that base ** (index + 1) == MIN_NORMAL_VALUE.
+            index -= 1
+
+        self._min_normal_lower_boundary_index = index
+
+        # self._max_normal_lower_boundary_index is the index such that
+        # base**index equals the greatest representable lower boundary. An
+        # exponential histogram bucket with this index covers the range
+        # ((2 ** 1024) / base, 2 ** 1024], which includes opentelemetry.sdk.
+        # metrics._internal.exponential_histogram.ieee_754.MAX_NORMAL_VALUE.
+        # This bucket is incomplete, since the upper boundary cannot be
+        # represented. One greater than this index corresponds with the bucket
+        # containing values > 2 ** 1024.
+        self._max_normal_lower_boundary_index = (
+            MAX_NORMAL_EXPONENT >> -self._scale
+        )
+
+    def map_to_index(self, value: float) -> int:
+        if value < MIN_NORMAL_VALUE:
+            return self._min_normal_lower_boundary_index
+
+        exponent = get_ieee_754_exponent(value)
+
+        # Positive integers are represented in binary as having an infinite
+        # amount of leading zeroes, for example 2 is represented as ...00010.
+
+        # A negative integer -x is represented in binary as the complement of
+        # (x - 1). For example, -4 is represented as the complement of 4 - 1
+        # == 3. 3 is represented as ...00011. Its compliment is ...11100, the
+        # binary representation of -4.
+
+        # get_ieee_754_mantissa(value) gets the positive integer made up
+        # from the rightmost MANTISSA_WIDTH bits (the mantissa) of the IEEE
+        # 754 representation of value. If value is an exact power of 2, all
+        # these MANTISSA_WIDTH bits would be all zeroes, and when 1 is
+        # subtracted the resulting value is -1. The binary representation of
+        # -1 is ...111, so when these bits are right shifted MANTISSA_WIDTH
+        # places, the resulting value for correction is -1. If value is not an
+        # exact power of 2, at least one of the rightmost MANTISSA_WIDTH
+        # bits would be 1 (even for values whose decimal part is 0, like 5.0
+        # since the IEEE 754 of such number is too the product of a power of 2
+        # (defined in the exponent part of the IEEE 754 representation) and the
+        # value defined in the mantissa). Having at least one of the rightmost
+        # MANTISSA_WIDTH bit being 1 means that get_ieee_754(value) will
+        # always be greater or equal to 1, and when 1 is subtracted, the
+        # result will be greater or equal to 0, whose representation in binary
+        # will be of at most MANTISSA_WIDTH ones that have an infinite
+        # amount of leading zeroes. When those MANTISSA_WIDTH bits are
+        # shifted to the right MANTISSA_WIDTH places, the resulting value
+        # will be 0.
+
+        # In summary, correction will be -1 if value is a power of 2, 0 if not.
+
+        # FIXME Document why we can assume value will not be 0, inf, or NaN.
+        correction = (get_ieee_754_mantissa(value) - 1) >> MANTISSA_WIDTH
+
+        return (exponent + correction) >> -self._scale
+
+    def get_lower_boundary(self, index: int) -> float:
+        if index < self._min_normal_lower_boundary_index:
+            raise MappingUnderflowError()
+
+        if index > self._max_normal_lower_boundary_index:
+            raise MappingOverflowError()
+
+        return ldexp(1, index << -self._scale)
+
+    @property
+    def scale(self) -> int:
+        return self._scale
diff --git a/.venv/lib/python3.12/site-packages/opentelemetry/sdk/metrics/_internal/exponential_histogram/mapping/ieee_754.md b/.venv/lib/python3.12/site-packages/opentelemetry/sdk/metrics/_internal/exponential_histogram/mapping/ieee_754.md
new file mode 100644
index 00000000..0cf5c8c5
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/opentelemetry/sdk/metrics/_internal/exponential_histogram/mapping/ieee_754.md
@@ -0,0 +1,175 @@
+# IEEE 754 Explained
+
+IEEE 754 is a standard that defines a way to represent certain mathematical
+objects using binary numbers.
+
+## Binary Number Fields
+
+The binary numbers used in IEEE 754 can have different lengths, the length that
+is interesting for the purposes of this project is 64 bits. These binary
+numbers are made up of 3 contiguous fields of bits, from left to right:
+
+1. 1 sign bit
+2. 11 exponent bits
+3. 52 mantissa bits
+
+Depending on the values these fields have, the represented mathematical object
+can be one of:
+
+* Floating point number
+* Zero
+* NaN
+* Infinite
+
+## Floating Point Numbers
+
+IEEE 754 represents a floating point number $f$ using an exponential
+notation with 4 components: $sign$, $mantissa$, $base$ and $exponent$:
+
+$$f = sign \times mantissa \times base ^ {exponent}$$
+
+There are two possible representations of floating point numbers:
+_normal_ and _denormal_, which have different valid values for
+their $mantissa$ and $exponent$ fields.
+
+### Binary Representation
+
+$sign$, $mantissa$, and $exponent$ are represented in binary, the
+representation of each component has certain details explained next.
+
+$base$ is always $2$ and it is not represented in binary.
+
+#### Sign
+
+$sign$ can have 2 values:
+
+1. $1$ if the `sign` bit is `0`
+2. $-1$ if the `sign` bit is `1`.
+
+#### Mantissa
+
+##### Normal Floating Point Numbers
+
+$mantissa$ is a positive fractional number whose integer part is $1$, for example
+$1.2345 \dots$. The `mantissa` bits represent only the fractional part and the
+$mantissa$ value can be calculated as:
+
+$$mantissa = 1 + \sum_{i=1}^{52} b_{i} \times 2^{-i} = 1 + \frac{b_{1}}{2^{1}} + \frac{b_{2}}{2^{2}} + \dots + \frac{b_{51}}{2^{51}} + \frac{b_{52}}{2^{52}}$$
+
+Where $b_{i}$ is:
+
+1. $0$ if the bit at the position `i - 1` is `0`.
+2. $1$ if the bit at the position `i - 1` is `1`.
+
+##### Denormal Floating Point Numbers
+
+$mantissa$ is a positive fractional number whose integer part is $0$, for example
+$0.12345 \dots$. The `mantissa` bits represent only the fractional part and the
+$mantissa$ value can be calculated as:
+
+$$mantissa = \sum_{i=1}^{52} b_{i} \times 2^{-i} = \frac{b_{1}}{2^{1}} + \frac{b_{2}}{2^{2}} + \dots + \frac{b_{51}}{2^{51}} + \frac{b_{52}}{2^{52}}$$
+
+Where $b_{i}$ is:
+
+1. $0$ if the bit at the position `i - 1` is `0`.
+2. $1$ if the bit at the position `i - 1` is `1`.
+
+#### Exponent
+
+##### Normal Floating Point Numbers
+
+Only the following bit sequences are allowed: `00000000001` to `11111111110`.
+That is, there must be at least one `0` and one `1` in the exponent bits.
+
+The actual value of the $exponent$ can be calculated as:
+
+$$exponent = v - bias$$
+
+where $v$ is the value of the binary number in the exponent bits and $bias$ is $1023$.
+Considering the restrictions above, the respective minimum and maximum values for the
+exponent are:
+
+1. `00000000001` = $1$, $1 - 1023 = -1022$
+2. `11111111110` = $2046$, $2046 - 1023 = 1023$
+
+So, $exponent$ is an integer in the range $\left[-1022, 1023\right]$.
+
+
+##### Denormal Floating Point Numbers
+
+$exponent$ is always $-1022$. Nevertheless, it is always represented as `00000000000`.
+
+### Normal and Denormal Floating Point Numbers
+
+The smallest absolute value a normal floating point number can have is calculated
+like this:
+
+$$1 \times 1.0\dots0 \times 2^{-1022} = 2.2250738585072014 \times 10^{-308}$$
+
+Since normal floating point numbers always have a $1$ as the integer part of the
+$mantissa$, then smaller values can be achieved by using the smallest possible exponent
+( $-1022$ ) and a $0$ in the integer part of the $mantissa$, but significant digits are lost.
+
+The smallest absolute value a denormal floating point number can have is calculated
+like this:
+
+$$1 \times 2^{-52} \times 2^{-1022} = 5 \times 10^{-324}$$
+
+## Zero
+
+Zero is represented like this:
+
+* Sign bit: `X`
+* Exponent bits: `00000000000`
+* Mantissa bits: `0000000000000000000000000000000000000000000000000000`
+
+where `X` means `0` or `1`.
+
+## NaN
+
+There are 2 kinds of NaNs that are represented:
+
+1. QNaNs (Quiet NaNs): represent the result of indeterminate operations.
+2. SNaNs (Signalling NaNs): represent the result of invalid operations.
+
+### QNaNs
+
+QNaNs are represented like this:
+
+* Sign bit: `X`
+* Exponent bits: `11111111111`
+* Mantissa bits: `1XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX`
+
+where `X` means `0` or `1`.
+
+### SNaNs
+
+SNaNs are represented like this:
+
+* Sign bit: `X`
+* Exponent bits: `11111111111`
+* Mantissa bits: `0XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX1`
+
+where `X` means `0` or `1`.
+
+## Infinite
+
+### Positive Infinite
+
+Positive infinite is represented like this:
+
+* Sign bit: `0`
+* Exponent bits: `11111111111`
+* Mantissa bits: `0000000000000000000000000000000000000000000000000000`
+
+where `X` means `0` or `1`.
+
+### Negative Infinite
+
+Negative infinite is represented like this:
+
+* Sign bit: `1`
+* Exponent bits: `11111111111`
+* Mantissa bits: `0000000000000000000000000000000000000000000000000000`
+
+where `X` means `0` or `1`.
diff --git a/.venv/lib/python3.12/site-packages/opentelemetry/sdk/metrics/_internal/exponential_histogram/mapping/ieee_754.py b/.venv/lib/python3.12/site-packages/opentelemetry/sdk/metrics/_internal/exponential_histogram/mapping/ieee_754.py
new file mode 100644
index 00000000..d4b7e861
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/opentelemetry/sdk/metrics/_internal/exponential_histogram/mapping/ieee_754.py
@@ -0,0 +1,117 @@
+# Copyright The OpenTelemetry Authors
+#
+# 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.
+
+from ctypes import c_double, c_uint64
+from sys import float_info
+
+# IEEE 754 64-bit floating point numbers use 11 bits for the exponent and 52
+# bits for the mantissa.
+MANTISSA_WIDTH = 52
+EXPONENT_WIDTH = 11
+
+# This mask is equivalent to 52 "1" bits (there are 13 hexadecimal 4-bit "f"s
+# in the mantissa mask, 13 * 4 == 52) or 0xfffffffffffff in hexadecimal.
+MANTISSA_MASK = (1 << MANTISSA_WIDTH) - 1
+
+# There are 11 bits for the exponent, but the exponent values 0 (11 "0"
+# bits) and 2047 (11 "1" bits) have special meanings so the exponent range is
+# from 1 to 2046. To calculate the exponent value, 1023 (the bias) is
+# subtracted from the exponent, so the exponent value range is from -1022 to
+# +1023.
+EXPONENT_BIAS = (2 ** (EXPONENT_WIDTH - 1)) - 1
+
+# All the exponent mask bits are set to 1 for the 11 exponent bits.
+EXPONENT_MASK = ((1 << EXPONENT_WIDTH) - 1) << MANTISSA_WIDTH
+
+# The sign mask has the first bit set to 1 and the rest to 0.
+SIGN_MASK = 1 << (EXPONENT_WIDTH + MANTISSA_WIDTH)
+
+# For normal floating point numbers, the exponent can have a value in the
+# range [-1022, 1023].
+MIN_NORMAL_EXPONENT = -EXPONENT_BIAS + 1
+MAX_NORMAL_EXPONENT = EXPONENT_BIAS
+
+# The smallest possible normal value is 2.2250738585072014e-308.
+# This value is the result of using the smallest possible number in the
+# mantissa, 1.0000000000000000000000000000000000000000000000000000 (52 "0"s in
+# the fractional part) and a single "1" in the exponent.
+# Finally 1 * (2 ** -1022) = 2.2250738585072014e-308.
+MIN_NORMAL_VALUE = float_info.min
+
+# Greatest possible normal value (1.7976931348623157e+308)
+# The binary representation of a float in scientific notation uses (for the
+# mantissa) one bit for the integer part (which is implicit) and 52 bits for
+# the fractional part. Consider a float binary 1.111. It is equal to 1 + 1/2 +
+# 1/4 + 1/8. The greatest possible value in the 52-bit binary mantissa would be
+# then 1.1111111111111111111111111111111111111111111111111111 (52 "1"s in the
+# fractional part) whose decimal value is 1.9999999999999998. Finally,
+# 1.9999999999999998 * (2 ** 1023) = 1.7976931348623157e+308.
+MAX_NORMAL_VALUE = float_info.max
+
+
+def get_ieee_754_exponent(value: float) -> int:
+    """
+    Gets the exponent of the IEEE 754 representation of a float.
+    """
+
+    return (
+        (
+            # This step gives the integer that corresponds to the IEEE 754
+            # representation of a float. For example, consider
+            # -MAX_NORMAL_VALUE for an example. We choose this value because
+            # of its binary representation which makes easy to understand the
+            # subsequent operations.
+            #
+            # c_uint64.from_buffer(c_double(-MAX_NORMAL_VALUE)).value == 18442240474082181119
+            # bin(18442240474082181119) == '0b1111111111101111111111111111111111111111111111111111111111111111'
+            #
+            # The first bit of the previous binary number is the sign bit: 1 (1 means negative, 0 means positive)
+            # The next 11 bits are the exponent bits: 11111111110
+            # The next 52 bits are the mantissa bits: 1111111111111111111111111111111111111111111111111111
+            #
+            # This step isolates the exponent bits, turning every bit outside
+            # of the exponent field (sign and mantissa bits) to 0.
+            c_uint64.from_buffer(c_double(value)).value & EXPONENT_MASK
+            # For the example this means:
+            # 18442240474082181119 & EXPONENT_MASK == 9214364837600034816
+            # bin(9214364837600034816) == '0b111111111100000000000000000000000000000000000000000000000000000'
+            # Notice that the previous binary representation does not include
+            # leading zeroes, so the sign bit is not included since it is a
+            # zero.
+        )
+        # This step moves the exponent bits to the right, removing the
+        # mantissa bits that were set to 0 by the previous step. This
+        # leaves the IEEE 754 exponent value, ready for the next step.
+        >> MANTISSA_WIDTH
+        # For the example this means:
+        # 9214364837600034816 >> MANTISSA_WIDTH == 2046
+        # bin(2046) == '0b11111111110'
+        # As shown above, these are the original 11 bits that correspond to the
+        # exponent.
+        # This step subtracts the exponent bias from the IEEE 754 value,
+        # leaving the actual exponent value.
+    ) - EXPONENT_BIAS
+    # For the example this means:
+    # 2046 - EXPONENT_BIAS == 1023
+    # As mentioned in a comment above, the largest value for the exponent is
+
+
+def get_ieee_754_mantissa(value: float) -> int:
+    return (
+        c_uint64.from_buffer(c_double(value)).value
+        # This step isolates the mantissa bits. There is no need to do any
+        # bit shifting as the mantissa bits are already the rightmost field
+        # in an IEEE 754 representation.
+        & MANTISSA_MASK
+    )
diff --git a/.venv/lib/python3.12/site-packages/opentelemetry/sdk/metrics/_internal/exponential_histogram/mapping/logarithm_mapping.py b/.venv/lib/python3.12/site-packages/opentelemetry/sdk/metrics/_internal/exponential_histogram/mapping/logarithm_mapping.py
new file mode 100644
index 00000000..e73f3a81
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/opentelemetry/sdk/metrics/_internal/exponential_histogram/mapping/logarithm_mapping.py
@@ -0,0 +1,138 @@
+# Copyright The OpenTelemetry Authors
+#
+# 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.
+
+from math import exp, floor, ldexp, log
+from threading import Lock
+
+from opentelemetry.sdk.metrics._internal.exponential_histogram.mapping import (
+    Mapping,
+)
+from opentelemetry.sdk.metrics._internal.exponential_histogram.mapping.errors import (
+    MappingOverflowError,
+    MappingUnderflowError,
+)
+from opentelemetry.sdk.metrics._internal.exponential_histogram.mapping.ieee_754 import (
+    MAX_NORMAL_EXPONENT,
+    MIN_NORMAL_EXPONENT,
+    MIN_NORMAL_VALUE,
+    get_ieee_754_exponent,
+    get_ieee_754_mantissa,
+)
+
+
+class LogarithmMapping(Mapping):
+    # Reference implementation here:
+    # https://github.com/open-telemetry/opentelemetry-go/blob/0e6f9c29c10d6078e8131418e1d1d166c7195d61/sdk/metric/aggregator/exponential/mapping/logarithm/logarithm.go
+
+    _mappings = {}
+    _mappings_lock = Lock()
+
+    _min_scale = 1
+    _max_scale = 20
+
+    def _get_min_scale(self):
+        # _min_scale ensures that ExponentMapping is used for zero and negative
+        # scale values.
+        return self._min_scale
+
+    def _get_max_scale(self):
+        # FIXME The Go implementation uses a value of 20 here, find out the
+        # right value for this implementation, more information here:
+        # https://github.com/lightstep/otel-launcher-go/blob/c9ca8483be067a39ab306b09060446e7fda65f35/lightstep/sdk/metric/aggregator/histogram/structure/README.md#mapping-function
+        # https://github.com/open-telemetry/opentelemetry-go/blob/0e6f9c29c10d6078e8131418e1d1d166c7195d61/sdk/metric/aggregator/exponential/mapping/logarithm/logarithm.go#L32-L45
+        return self._max_scale
+
+    def _init(self, scale: int):
+        # pylint: disable=attribute-defined-outside-init
+
+        super()._init(scale)
+
+        # self._scale_factor is defined as a multiplier because multiplication
+        # is faster than division. self._scale_factor is defined as:
+        # index = log(value) * self._scale_factor
+        # Where:
+        # index = log(value) / log(base)
+        # index = log(value) / log(2 ** (2 ** -scale))
+        # index = log(value) / ((2 ** -scale) * log(2))
+        # index = log(value) * ((1 / log(2)) * (2 ** scale))
+        # self._scale_factor = ((1 / log(2)) * (2 ** scale))
+        # self._scale_factor = (1 /log(2)) * (2 ** scale)
+        # self._scale_factor = ldexp(1 / log(2), scale)
+        # This implementation was copied from a Java prototype. See:
+        # https://github.com/newrelic-experimental/newrelic-sketch-java/blob/1ce245713603d61ba3a4510f6df930a5479cd3f6/src/main/java/com/newrelic/nrsketch/indexer/LogIndexer.java
+        # for the equations used here.
+        self._scale_factor = ldexp(1 / log(2), scale)
+
+        # self._min_normal_lower_boundary_index is the index such that
+        # base ** index == MIN_NORMAL_VALUE. An exponential histogram bucket
+        # with this index covers the range
+        # (MIN_NORMAL_VALUE, MIN_NORMAL_VALUE * base]. One less than this index
+        # corresponds with the bucket containing values <= MIN_NORMAL_VALUE.
+        self._min_normal_lower_boundary_index = (
+            MIN_NORMAL_EXPONENT << self._scale
+        )
+
+        # self._max_normal_lower_boundary_index is the index such that
+        # base ** index equals the greatest representable lower boundary. An
+        # exponential histogram bucket with this index covers the range
+        # ((2 ** 1024) / base, 2 ** 1024], which includes opentelemetry.sdk.
+        # metrics._internal.exponential_histogram.ieee_754.MAX_NORMAL_VALUE.
+        # This bucket is incomplete, since the upper boundary cannot be
+        # represented. One greater than this index corresponds with the bucket
+        # containing values > 2 ** 1024.
+        self._max_normal_lower_boundary_index = (
+            (MAX_NORMAL_EXPONENT + 1) << self._scale
+        ) - 1
+
+    def map_to_index(self, value: float) -> int:
+        """
+        Maps positive floating point values to indexes corresponding to scale.
+        """
+
+        # value is subnormal
+        if value <= MIN_NORMAL_VALUE:
+            return self._min_normal_lower_boundary_index - 1
+
+        # value is an exact power of two.
+        if get_ieee_754_mantissa(value) == 0:
+            exponent = get_ieee_754_exponent(value)
+            return (exponent << self._scale) - 1
+
+        return min(
+            floor(log(value) * self._scale_factor),
+            self._max_normal_lower_boundary_index,
+        )
+
+    def get_lower_boundary(self, index: int) -> float:
+        if index >= self._max_normal_lower_boundary_index:
+            if index == self._max_normal_lower_boundary_index:
+                return 2 * exp(
+                    (index - (1 << self._scale)) / self._scale_factor
+                )
+            raise MappingOverflowError()
+
+        if index <= self._min_normal_lower_boundary_index:
+            if index == self._min_normal_lower_boundary_index:
+                return MIN_NORMAL_VALUE
+            if index == self._min_normal_lower_boundary_index - 1:
+                return (
+                    exp((index + (1 << self._scale)) / self._scale_factor) / 2
+                )
+            raise MappingUnderflowError()
+
+        return exp(index / self._scale_factor)
+
+    @property
+    def scale(self) -> int:
+        return self._scale