Add exponent and logarithm mappings

Fixes #2957

CHANGELOG.md

@@ -7,6 +7,8 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 ## [Unreleased](https://github.com/open-telemetry/opentelemetry-python/compare/v1.13.0...HEAD)
 
+- Add logarithm and exponent mappings
+  ([#2960](https://github.com/open-telemetry/opentelemetry-python/pull/2960))
 - Update explicit histogram bucket boundaries
   ([#2947](https://github.com/open-telemetry/opentelemetry-python/pull/2947))
 - `exporter-otlp-proto-http`: add user agent string

opentelemetry-sdk/src/opentelemetry/sdk/metrics/_internal/exponential_histogram/mapping/__init__.py

@@ -0,0 +1,85 @@
+# 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):
+
+    # pylint: disable=no-member
+    def __new__(cls, scale: int):
+
+        with cls._mappings_lock:
+            if scale not in cls._mappings:
+                cls._mappings[scale] = super().__new__(cls)
+
+        return cls._mappings[scale]
+
+    def __init__(self, scale: int) -> None:
+
+        if scale > self._max_scale:
+            raise Exception(f"scale is larger than {self._max_scale}")
+
+        if scale < self._min_scale:
+            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))
+        self._scale = scale
+
+    @property
+    @abstractmethod
+    def _min_scale(self) -> int:
+        """
+        Return the smallest possible value for the mapping scale
+        """
+
+    @property
+    @abstractmethod
+    def _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 normalized floating point values.  If the corresponding
+        bucket's upper boundary is less than or equal to 2 ** -1022,
+        `UnderflowError` will be raised. If the corresponding bucket's lower
+        boundary is greater than `sys.float_info.max`, `OverflowError` will be
+        raised.
+        """
+
+    @property
+    @abstractmethod
+    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
+        """

opentelemetry-sdk/src/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
+    denormalized floating point value.
+    """
+
+
+class MappingOverflowError(Exception):
+    """
+    Raised when computing the lower boundary of an index that maps into +inf.
+    """

opentelemetry-sdk/src/opentelemetry/sdk/metrics/_internal/exponential_histogram/mapping/exponent_mapping.py

@@ -0,0 +1,125 @@
+# 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 (
+    MAX_NORMAL_EXPONENT,
+    MIN_NORMAL_EXPONENT,
+    MIN_NORMAL_VALUE,
+    SIGNIFICAND_WIDTH,
+    get_ieee_754_exponent,
+    get_ieee_754_significand,
+)
+
+
+class ExponentMapping(Mapping):
+
+    _mappings = {}
+    _mappings_lock = Lock()
+    # _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.
+    _min_scale = -10
+    # _max_scale is the largest scale supported by exponential mapping. Use
+    # a logarithm mapping for larger scales.
+    _max_scale = 0
+
+    def __init__(self, scale: int):
+        super().__init__(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 (base ** index, base (index + 1)],
+        # including MIN_NORMAL_VALUE.
+        index = MIN_NORMAL_EXPONENT >> -self._scale
+
+        if -self._scale < 2:
+            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_significand(value) gets the positive integer made up
+        # from the rightmost SIGNIFICAND_WIDTH bits (the mantissa) of the IEEE
+        # 754 representation of value. If value is an exact power of 2, all
+        # these SIGNIFICAND_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 SIGNIFICAND_WIDTH
+        # places, the resulting value for correction is -1. If value is not an
+        # exact power of 2, at least one of the rightmost SIGNIFICAND_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
+        # SIGNIFICAND_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 SIGNIFICAND_WIDTH ones that have an infinite
+        # amount of leading zeroes. When those SIGNIFICAND_WIDTH bits are
+        # shifted to the right SIGNIFICAND_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_significand(value) - 1) >> SIGNIFICAND_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