fix: correct reprint threshold display and de-duplicate the formula

src/util/shards.ts

@@ -0,0 +1,8 @@
+// Banana Split's fixed threshold policy: reconstruction requires a majority of
+// the shards, i.e. floor(total / 2) + 1. This lives in one place so the
+// generator (Share.vue) and the reprint view (Print.vue) can never disagree —
+// they did once: Print.vue re-implemented the formula as floor(total/2)+2 and
+// displayed the wrong "you need N more" count on reprints (finding F5).
+export function defaultThreshold(totalShards: number): number {
+  return Math.floor(totalShards / 2) + 1;
+}

src/views/Print.vue

@@ -11,7 +11,7 @@
             <br>
             <input
               id="totalShards"
-              v-model.number="requiredShards"
+              v-model.number="totalShards"
               type="number"
               min="3"
               max="255"
@@ -36,7 +36,7 @@
           v-for="code in qrCodes"
           :key="code"
           :shard="code"
-          :required-shards="parseInt(requiredShards/2)+2"
+          :required-shards="threshold"
           :title="title"
         />
       </div>
@@ -64,6 +64,7 @@
 
 <script lang="ts">
 import crypto, { Shard } from "../util/crypto";
+import { defaultThreshold } from "../util/shards";
 import ShardInfo from "../components/ShardInfo.vue";
 
 import Vue from "vue";
@@ -73,7 +74,7 @@ type PrintData = {
   nonce: string;
   shards: Shard[];
   qrCodes: Set<string>;
-  requiredShards?: number;
+  totalShards?: number;
   numberEntered: boolean;
   PLACEHOLDER_QR_DATA: string;
 };
@@ -87,21 +88,24 @@ export default Vue.extend({
       nonce: "",
       shards: [],
       qrCodes: new Set(),
-      requiredShards: undefined,
+      totalShards: undefined,
       numberEntered: false,
       PLACEHOLDER_QR_DATA: ""
     };
   },
   computed: {
     needMoreShards(): boolean {
-      return this.requiredShards !== undefined && this.shards.length !== this.requiredShards;
+      return this.totalShards !== undefined && this.shards.length !== this.totalShards;
     },
     remainingCodes(): number {
-      if (!this.requiredShards) {
+      if (!this.totalShards) {
         return 0;
       } else {
-        return this.requiredShards - this.shards.length;
+        return this.totalShards - this.shards.length;
       }
+    },
+    threshold(): number {
+      return this.totalShards ? defaultThreshold(this.totalShards) : 0;
     }
   },
   mounted: function() {
@@ -144,7 +148,7 @@ export default Vue.extend({
       window.print();
     },
     handleShardsInput: function() {
-      if (this.requiredShards && this.requiredShards >= 3 && this.requiredShards <= 255) {
+      if (this.totalShards && this.totalShards >= 3 && this.totalShards <= 255) {
         this.numberEntered = true;
       } else {
         this.$eventHub.$emit("showError", "Please enter a valid number of shards between 3 and 255.");

src/views/Share.vue

@@ -91,6 +91,7 @@
 <script lang="ts">
 import passPhrase from "../util/passPhrase";
 import crypto from "../util/crypto";
+import { defaultThreshold } from "../util/shards";
 
 import ShardInfo from "../components/ShardInfo.vue";
 import CanvasText from "../components/CanvasText.vue";
@@ -121,7 +122,7 @@ export default Vue.extend({
       return this.secret.length > 1024;
     },
     requiredShards(): number {
-      return Math.floor(this.totalShards / 2) + 1;
+      return defaultThreshold(this.totalShards);
     },
     shards(): string[] {
       this.$eventHub.$emit("clearAlerts");

tests/unit/shards.spec.ts

@@ -0,0 +1,24 @@
+import { defaultThreshold } from "../../src/util/shards";
+
+describe("defaultThreshold", () => {
+  // The bug fixed in F5 was Print.vue computing floor(total/2)+2 instead of
+  // floor(total/2)+1 — e.g. total=5 showed "need 4" instead of the correct 3.
+  test.each([
+    [3, 2],
+    [4, 3],
+    [5, 3], // the exact case from finding F5
+    [6, 4],
+    [7, 4],
+    [10, 6],
+    [19, 10],
+    [255, 128]
+  ])("threshold for %i total shards is %i", (total, expected) => {
+    expect(defaultThreshold(total)).toBe(expected);
+  });
+
+  test("always requires a strict majority across the whole UI range", () => {
+    for (let n = 3; n <= 255; n++) {
+      expect(defaultThreshold(n)).toBeGreaterThan(n / 2);
+    }
+  });
+});