chore(profiling): add recursive test to benchmarking suite (#13628)

New benchmarking scenario to measure the performance impact of different
DD_PROFILING_STACK_V2_MAX_FRAMES values on applications with deep call
stacks.

For context, DD_PROFILING_STACK_V2_MAX_FRAMES controls the maximum
number of stack frames captured and sampled by the profiler. We want to
test the performance overhead of different stack frame upper limits (by
running a recursive function to create the stack frames) and we are
planning to increase this limit from 64 to 512 frames to provide users
with more complete stack traces.

The configurable parameters are
- max_depth: controls recursion depth (stack frame count)
- enable_sleep/sleep_duration: mixed CPU/idle workload patterns
- profiler_enabled: enable profiler for frame limit testing

## Checklist
- [x] PR author has checked that all the criteria below are met
- The PR description includes an overview of the change
- The PR description articulates the motivation for the change
- The change includes tests OR the PR description describes a testing
strategy
- The PR description notes risks associated with the change, if any
- Newly-added code is easy to change
- The change follows the [library release note
guidelines](https://ddtrace.readthedocs.io/en/stable/releasenotes.html)
- The change includes or references documentation updates if necessary
- Backport labels are set (if
[applicable](https://ddtrace.readthedocs.io/en/latest/contributing.html#backporting))

## Reviewer Checklist
- [x] Reviewer has checked that all the criteria below are met 
- Title is accurate
- All changes are related to the pull request's stated goal
- Avoids breaking
[API](https://ddtrace.readthedocs.io/en/stable/versioning.html#interfaces)
changes
- Testing strategy adequately addresses listed risks
- Newly-added code is easy to change
- Release note makes sense to a user of the library
- If necessary, author has acknowledged and discussed the performance
implications of this PR as reported in the benchmarks PR comment
- Backport labels are set in a manner that is consistent with the
[release branch maintenance
policy](https://ddtrace.readthedocs.io/en/latest/contributing.html#backporting)

---------

Co-authored-by: Taegyun Kim <taegyun.kim@datadoghq.com>

Author: alyshawang

.gitlab/benchmarks/microbenchmarks.yml

@@ -162,6 +162,7 @@ microbenchmarks:
         - "rate_limiter"
         - "packages_package_for_root_module_mapping"
         - "packages_update_imported_dependencies"
+        - "recursive_computation"
         - "telemetry_add_metric"
         - "startup"
 

benchmarks/recursive_computation/config.yaml

@@ -0,0 +1,18 @@
+shallow: &base
+  max_depth: 10
+  enable_sleep: false
+  sleep_duration: 0.1
+  profiler_enabled: false
+
+medium: 
+  <<: *base
+  max_depth: 50
+
+deep:
+  <<: *base
+  max_depth: 400
+
+deep-profiled:
+  <<: *base
+  max_depth: 400
+  profiler_enabled: true

benchmarks/recursive_computation/scenario.py

@@ -0,0 +1,75 @@
+import time
+from typing import Callable
+from typing import Generator
+
+import bm
+import bm.utils as utils
+
+from ddtrace.trace import tracer
+
+
+class RecursiveComputation(bm.Scenario):
+    name: str
+    max_depth: int
+    enable_sleep: bool
+    sleep_duration: float
+    profiler_enabled: bool
+
+    def cpu_intensive_computation(self, depth: int) -> int:
+        limit = 100 + (depth * 10)
+        primes = []
+
+        for num in range(2, limit):
+            is_prime = True
+            for i in range(2, int(num**0.5) + 1):
+                if num % i == 0:
+                    is_prime = False
+                    break
+
+            if is_prime:
+                primes.append(num)
+
+        return len(primes)
+
+    def recursive_traced_computation(self, depth: int = 0) -> int:
+        with tracer.trace(f"recursive_computation.depth_{depth}") as span:
+            span.set_tag("recursion.depth", depth)
+            span.set_tag("recursion.max_depth", self.max_depth)
+            span.set_tag("profiler.enabled", self.profiler_enabled)
+            span.set_tag("component", "recursive_computation")
+
+            if depth % 3 == 0:
+                start_time = time.time()
+                result = self.cpu_intensive_computation(depth)
+                compute_time = time.time() - start_time
+
+                span.set_metric("computation.time_ms", compute_time * 1000)
+                span.set_metric("computation.result", result)
+            else:
+                result = depth
+                span.set_metric("computation.time_ms", 0)
+                span.set_metric("computation.result", result)
+
+            if depth < self.max_depth:
+                child_result = self.recursive_traced_computation(depth + 1)
+                span.set_metric("child.result", child_result)
+                result += child_result
+            elif self.enable_sleep:
+                span.set_tag("action", "sleep_at_max_depth")
+                time.sleep(self.sleep_duration)
+
+            span.set_metric("final.result", result)
+            return result
+
+    def run(self) -> Generator[Callable[[int], None], None, None]:
+        if self.profiler_enabled:
+            import ddtrace.profiling.auto  # noqa: F401
+
+        utils.drop_traces(tracer)
+        utils.drop_telemetry_events()
+
+        def _(loops: int) -> None:
+            for _ in range(loops):
+                self.recursive_traced_computation()
+
+        yield _