fix(tracer): use fixed-point format for _dd.p.ksr tag

ddtrace/tracer/sampler.go

@@ -6,6 +6,7 @@
 package tracer
 
 import (
+	"bytes"
 	"encoding/json"
 	"io"
 	"math"
@@ -121,9 +122,24 @@ func sampledByRate(n uint64, rate float64) bool {
 	return n*knuthFactor <= uint64(rate*math.MaxUint64)
 }
 
-// formatKnuthSamplingRate formats a sampling rate as a string with up to 6 decimal digits
+// formatKnuthSamplingRate formats a sampling rate as a string with up to 6
+// decimal places, trimming trailing zeros. It uses AppendFloat with a
+// stack-allocated buffer to avoid heap allocations.
 func formatKnuthSamplingRate(rate float64) string {
-	return strconv.FormatFloat(rate, 'g', 6, 64)
+	var buf [24]byte
+	b := strconv.AppendFloat(buf[:0], rate, 'f', 6, 64)
+	// Trim trailing zeros after decimal point, then the dot itself if needed.
+	if i := bytes.IndexByte(b, '.'); i >= 0 {
+		end := len(b)
+		for end > i+1 && b[end-1] == '0' {
+			end--
+		}
+		if b[end-1] == '.' {
+			end--
+		}
+		b = b[:end]
+	}
+	return string(b)
 }
 
 // serviceEnvKey is used as a map key for per-service sampling rates,

ddtrace/tracer/sampler_test.go

@@ -2227,6 +2227,10 @@ func TestKnuthSamplingRateWithFloatRules(t *testing.T) {
 		{"six_decimals", 0.123456, "0.123456"},
 		{"seven_decimals_rounded", 0.1234567, "0.123457"},
 		{"trailing_zeros", 0.100000, "0.1"},
+		{"rate_1_strips_trailing_zeros", 1.0, "1"},
+		{"six_decimal_precision_boundary", 0.000001, "0.000001"},
+		{"below_precision_rounds_to_zero", 0.0000001, "0"},
+		{"rounds_up_to_one_millionth", 0.00000051, "0.000001"},
 	}
 
 	for _, tc := range testCases {
@@ -2260,6 +2264,14 @@ func TestKnuthSamplingRateWithFloatRules(t *testing.T) {
 	}
 }
 
+func BenchmarkFormatKnuthSamplingRate(b *testing.B) {
+	rates := []float64{1.0, 0.5, 0.000001, 0.0000001, 0.00000051, 0.7654321}
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		formatKnuthSamplingRate(rates[i%len(rates)])
+	}
+}
+
 func TestCappedRate(t *testing.T) {
 	tests := []struct {
 		name        string