# What does this PR do?

Adds `_dd.p.ksr` (Knuth Sampling Rate) as a propagated tag set when
agent-based or rule-based sampling decisions are made. The tag is stored
in span `meta` (string type) with up to 6 significant digits and no
trailing zeros.

`format_sampling_rate` now returns `Option<String>` and guards against
invalid inputs (negative, >1.0, NaN, infinity), returning `None` instead
of producing garbage output.

# Motivation

To enable consistent sampling across tracers and backend retention
filters, the backend needs to know the sampling rate applied by the
tracer. Without transmitting the tracer's rate via `_dd.p.ksr`, backend
resampling cannot correctly compute effective rates in multi-stage
sampling scenarios.

See RFC: "Transmit Knuth sampling rate to backend"

# Additional Notes

Key files changed:
- `datadog-opentelemetry/src/core/constants.rs` — Added
`SAMPLING_KNUTH_RATE_TAG_KEY` constant
- `datadog-opentelemetry/src/sampling/datadog_sampler.rs` — Added
`format_sampling_rate()` helper (returns `Option<String>`, defensive
against invalid rates) and set ksr in agent/rule sampling paths
- Updated 2 snapshot JSON files

Related PRs across tracers:
- Java: DataDog/dd-trace-java#10802
- .NET: DataDog/dd-trace-dotnet#8287
- Ruby: DataDog/dd-trace-rb#5436
- Node.js: DataDog/dd-trace-js#7741
- PHP: DataDog/dd-trace-php#3701
- C++: DataDog/dd-trace-cpp#288
- System tests: DataDog/system-tests#6466

🤖 Generated with [Claude Code](https://claude.com/claude-code)

---------

Co-authored-by: Claude Opus 4.6 <noreply@anthropic.com>

## Summary of changes

Add `_dd.p.ksr` (Knuth Sampling Rate) propagated tag to spans when
sampling is applied via agent rates or trace sampling rules, per the
[Transmit Knuth Sampling Rate to Backend
RFC](https://docs.google.com/document/d/1Po3qtJb6PGheFeKFSUMv2pVY_y-HFAxTzNLuacCbCXY/edit).

## Reason for change

The backend needs to know the exact sampling rate applied by the tracer
to correctly compute effective rates during resampling (e.g., tracer 0.5
× backend 0.5 = effective 0.25). This tag enables that by propagating
the rate via `x-datadog-tags` and W3C `tracestate`.

## Implementation details

- Set `_dd.p.ksr` in `TraceContext.SetSamplingPriority()` for
`AgentRate`, `LocalTraceSamplingRule`, `RemoteAdaptiveSamplingRule`, and
`RemoteUserSamplingRule` mechanisms
- Use `TryAddTag` to preserve the original rate (consistent with
`AppliedSamplingRate ??= rate` semantics)
- Format with `"0.######"` (up to 6 decimal digits, no trailing zeros,
no scientific notation) per RFC spec
- Added `.IsOptional("_dd.p.ksr")` to `SpanTagAssertion.cs` so
integration test tag validators accept the new tag

## Test coverage

- Unit tests in `TraceContextTests_KnuthSamplingRate.cs`:
  - KSR set for agent rate sampling
- KSR set for trace sampling rules (local, remote adaptive, remote user)
- KSR NOT set for manual, AppSec, rate limiter, or single span
mechanisms
  - KSR preserved on subsequent sampling calls (TryAddTag semantics)
- Formatting with up to 6 decimal digits (boundary values including
small rates like 0.00001)
- System tests in [system-tests
#6466](DataDog/system-tests#6466)

## Other details

Related PRs across tracers:
- Java: DataDog/dd-trace-java#10802
- Ruby: DataDog/dd-trace-rb#5436
- Node.js: DataDog/dd-trace-js#7741
- PHP: DataDog/dd-trace-php#3701
- Rust: DataDog/dd-trace-rs#180
- C++: DataDog/dd-trace-cpp#288

🤖 Generated with [Claude Code](https://claude.com/claude-code)

---------

Co-authored-by: Claude Opus 4.6 <noreply@anthropic.com>