feat(background-agent): add loop detector helpers

Ultraworked with [Sisyphus](https://github.com/code-yeongyu/oh-my-openagent)

Co-authored-by: Sisyphus <clio-agent@sisyphuslabs.ai>

src/features/background-agent/loop-detector.ts

@@ -0,0 +1,96 @@
+import type { BackgroundTaskConfig } from "../../config/schema"
+import {
+  DEFAULT_CIRCUIT_BREAKER_REPETITION_THRESHOLD_PERCENT,
+  DEFAULT_CIRCUIT_BREAKER_WINDOW_SIZE,
+  DEFAULT_MAX_TOOL_CALLS,
+} from "./constants"
+import type { ToolCallWindow } from "./types"
+
+export interface CircuitBreakerSettings {
+  maxToolCalls: number
+  windowSize: number
+  repetitionThresholdPercent: number
+}
+
+export interface ToolLoopDetectionResult {
+  triggered: boolean
+  toolName?: string
+  repeatedCount?: number
+  sampleSize?: number
+  thresholdPercent?: number
+}
+
+export function resolveCircuitBreakerSettings(
+  config?: BackgroundTaskConfig
+): CircuitBreakerSettings {
+  return {
+    maxToolCalls:
+      config?.circuitBreaker?.maxToolCalls ?? config?.maxToolCalls ?? DEFAULT_MAX_TOOL_CALLS,
+    windowSize: config?.circuitBreaker?.windowSize ?? DEFAULT_CIRCUIT_BREAKER_WINDOW_SIZE,
+    repetitionThresholdPercent:
+      config?.circuitBreaker?.repetitionThresholdPercent ??
+      DEFAULT_CIRCUIT_BREAKER_REPETITION_THRESHOLD_PERCENT,
+  }
+}
+
+export function recordToolCall(
+  window: ToolCallWindow | undefined,
+  toolName: string,
+  settings: CircuitBreakerSettings
+): ToolCallWindow {
+  const previous = window?.toolNames ?? []
+  const toolNames = [...previous, toolName].slice(-settings.windowSize)
+
+  return {
+    toolNames,
+    windowSize: settings.windowSize,
+    thresholdPercent: settings.repetitionThresholdPercent,
+  }
+}
+
+export function detectRepetitiveToolUse(
+  window: ToolCallWindow | undefined
+): ToolLoopDetectionResult {
+  if (!window || window.toolNames.length === 0) {
+    return { triggered: false }
+  }
+
+  const counts = new Map<string, number>()
+  for (const toolName of window.toolNames) {
+    counts.set(toolName, (counts.get(toolName) ?? 0) + 1)
+  }
+
+  let repeatedTool: string | undefined
+  let repeatedCount = 0
+
+  for (const [toolName, count] of counts.entries()) {
+    if (count > repeatedCount) {
+      repeatedTool = toolName
+      repeatedCount = count
+    }
+  }
+
+  const sampleSize = window.toolNames.length
+  const minimumSampleSize = Math.min(
+    window.windowSize,
+    Math.ceil((window.windowSize * window.thresholdPercent) / 100)
+  )
+
+  if (sampleSize < minimumSampleSize) {
+    return { triggered: false }
+  }
+
+  const thresholdCount = Math.ceil((sampleSize * window.thresholdPercent) / 100)
+
+  if (!repeatedTool || repeatedCount < thresholdCount) {
+    return { triggered: false }
+  }
+
+  return {
+    triggered: true,
+    toolName: repeatedTool,
+    repeatedCount,
+    sampleSize,
+    thresholdPercent: window.thresholdPercent,
+  }
+}