feat: implement tiered billing expression evaluation and related functionality

- Added support for tiered billing expressions in the billing system.
- Introduced new types and functions for handling billing expressions, including caching and execution.
- Updated existing billing logic to accommodate tiered billing scenarios.
- Enhanced request handling to support incoming billing expression requests.
- Added tests for tiered billing functionality to ensure correctness.

pkg/billingexpr/types.go

@@ -0,0 +1,59 @@
+package billingexpr
+
+import (
+	"crypto/sha256"
+	"fmt"
+)
+
+type RequestInput struct {
+	Headers map[string]string
+	Body    []byte
+}
+
+// TokenParams holds all token dimensions passed into an Expr evaluation.
+// Fields beyond P and C are optional — when absent they default to 0,
+// which means cache-unaware expressions keep working unchanged.
+type TokenParams struct {
+	P    float64 // prompt tokens
+	C    float64 // completion tokens
+	CR   float64 // cache read (hit) tokens
+	CC   float64 // cache creation tokens (5-min TTL for Claude, generic for others)
+	CC1h float64 // cache creation tokens — 1-hour TTL (Claude only)
+}
+
+// TraceResult holds side-channel info captured by the tier() function
+// during Expr execution. This replaces the old Breakdown mechanism —
+// the Expr itself is the single source of truth for billing logic.
+type TraceResult struct {
+	MatchedTier string  `json:"matched_tier"`
+	Cost        float64 `json:"cost"`
+}
+
+// BillingSnapshot captures the billing rule state frozen at pre-consume time.
+// It is fully serializable and contains no compiled program pointers.
+type BillingSnapshot struct {
+	BillingMode               string  `json:"billing_mode"`
+	ModelName                 string  `json:"model_name"`
+	ExprString                string  `json:"expr_string"`
+	ExprHash                  string  `json:"expr_hash"`
+	GroupRatio                float64 `json:"group_ratio"`
+	EstimatedPromptTokens     int     `json:"estimated_prompt_tokens"`
+	EstimatedCompletionTokens int     `json:"estimated_completion_tokens"`
+	EstimatedQuotaBeforeGroup float64 `json:"estimated_quota_before_group"`
+	EstimatedQuotaAfterGroup  int     `json:"estimated_quota_after_group"`
+	EstimatedTier             string  `json:"estimated_tier"`
+}
+
+// TieredResult holds everything needed after running tiered settlement.
+type TieredResult struct {
+	ActualQuotaBeforeGroup float64 `json:"actual_quota_before_group"`
+	ActualQuotaAfterGroup  int     `json:"actual_quota_after_group"`
+	MatchedTier            string  `json:"matched_tier"`
+	CrossedTier            bool    `json:"crossed_tier"`
+}
+
+// ExprHashString returns the SHA-256 hex digest of an expression string.
+func ExprHashString(expr string) string {
+	h := sha256.Sum256([]byte(expr))
+	return fmt.Sprintf("%x", h)
+}