fix: fix floating point precision error

docs/PROJECT_OVERVIEW.md

@@ -89,6 +89,42 @@ Services from BPN API may lack complete data (especially prices). Always enrich
 ### Notification System
 Field handlers generate notifications (auto-changes) → collected by controller → sent via HX-Trigger → displayed as toasts.
 
+### Floating-Point Precision in Price Calculations
+**Critical**: All monetary comparisons must account for floating-point arithmetic accumulation errors.
+
+**The Problem:**
+- Prices are parsed from XML as German-formatted strings (e.g., `"1.812,70"`)
+- Multiple price additions (rooms + services + insurances) accumulate tiny precision errors (`~1e-15` per operation)
+- With bulk insurance and deep calculation chains, errors compound to `~1e-13` or larger
+- Example: API returns `1812.7`, calculation produces `1812.6999999999998`
+
+**The Solution:**
+- **Always round monetary values to 2 decimal places before comparison**
+- Use `round($price, 2)` for cent precision (standard for EUR currency)
+- Never use strict equality (`===` or `!==`) on unrounded float prices
+
+**Implementation Example (Step3Controller:93-94):**
+```php
+// CORRECT: Round to cent precision before comparison
+$apiTotal = round($inquiryResponse->totalPrice ?? 0.0, 2);
+$calculatedTotal = round($this->priceCalculator->calculateGrandTotal($bookingCreateDto), 2);
+
+if ($apiTotal !== $calculatedTotal) {
+    // Handle mismatch
+}
+
+// WRONG: Direct float comparison (will fail due to precision errors)
+if ($inquiryResponse->totalPrice !== $this->priceCalculator->calculateGrandTotal($bookingCreateDto)) {
+    // This comparison is unreliable!
+}
+```
+
+**Important Notes:**
+- Rounding eliminates precision errors smaller than 1 cent (€0.01)
+- The BPN API returns prices already rounded to cent precision
+- This is the industry-standard approach for financial calculations
+- Only affects comparison logic - does not alter actual price calculation flow
+
 ### Dirty State Detection (Edit Mode)
 Fingerprint-based change detection to warn users about unsaved modifications:
 - **BookingFingerprintService** generates SHA-256 hash of all mutable booking data
@@ -345,6 +381,7 @@ ddev exec "php -r 'opcache_reset()';"             # Clear opcache after code cha
 - **Edit mode service availability**: Services with `available <= 0` remain visible and editable for participants who already have them (prevents fingerprint false positives)
 - **Session cleanup on exit**: All exit paths from edit mode (save, discard, cancel) properly clear session to reset dirty state
 - **Participant naming convention**: Index 0 is "Anmelder:in", others are "Teilnehmer:in N" (1-based, not 0-based)
+- **Floating-point price comparisons**: ALWAYS use `round($price, 2)` before comparing monetary values to avoid precision errors (see "Floating-Point Precision in Price Calculations" section)
 
 ## References