fix(medications): count the whole cadence in the supply runway

The runway estimate read FREQ=MONTHLY as one dose every 30 days whatever
its INTERVAL, so a quarterly injection with two doses left showed about 60
days of supply instead of 180. FREQ=DAILY;INTERVAL=2 counted as daily, a
yearly rule ignored INTERVAL and BYMONTH, and a monthly rule ignored extra
BYMONTHDAY values. A CYCLIC schedule was counted as if it never paused,
and a PRN schedule as if it were due every day. The rate now honours
INTERVAL for every frequency, counts the listed days and months, scales a
cyclic schedule by on / (on + off) and leaves PRN out. The low-stock job
selects the schedule type and cycle lengths so it reads the same rate.

Whole-dose counts no longer lose one to binary floating point: 2.4 mL at
0.8 mL per dose is 2.9999999999999996 in IEEE 754 and used to read as two
doses. The stock summary, both runway estimators, the list and detail
routes, the GLP-1 route, the Coach snapshot and the inventory readout now
floor through one helper that treats anything within 1e-9 of the next whole
number as that number.

src/lib/ai/coach/glp1-snapshot.ts

@@ -24,6 +24,7 @@ import { readNote } from "@/lib/crypto/note-cipher";
 import { matchGlp1SideEffectTags } from "@/lib/medications/glp1-side-effect-tag-match";
 import type { Glp1SideEffectTag } from "@/lib/medications/glp1-side-effect-tags";
 import { isRecordOnly } from "@/lib/medications/intake-tracking";
+import { floorWhole } from "@/lib/medications/units-per-dose";
 
 /**
  * Recommended generic name for the canonical GLP-1 drug brand. The Coach
@@ -372,7 +373,7 @@ export async function buildGlp1SnapshotBlock(
         0,
       );
       pensRemaining = usable.length;
-      dosesRemaining = Math.floor(
+      dosesRemaining = floorWhole(
         unitsRemaining / (Number(med.unitsPerDose) || 1),
       );
       weeksOfSupplyApprox = Math.round(dosesRemaining / dosesPerWeek);

src/lib/jobs/medication-low-stock.ts

@@ -422,6 +422,11 @@ export async function runMedicationLowStockTick(
               rollingIntervalDays: true,
               // v1.37.19 — per-slot units feed the slot-aware burn rate.
               unitsPerDose: true,
+              // A PRN schedule consumes nothing on a cadence, a CYCLIC one
+              // only in its "on" weeks.
+              scheduleType: true,
+              cyclicOnWeeks: true,
+              cyclicOffWeeks: true,
             },
           },
         },

src/lib/medications/inventory/__tests__/summary.test.ts

@@ -195,3 +195,14 @@ describe("supply surfaces — server computes, the detail-page clients render th
     expect(src).toContain("medications.detail.bestand.expiredSuffix");
   });
 });
+
+describe("summariseSupply — whole doses survive binary floating point", () => {
+  it("2.4 mL at 0.8 mL per dose is three doses, not two", () => {
+    const summary = summariseSupply(
+      [{ state: "ACTIVE", unitsRemaining: 2.4, unitsTotal: 2.4 }] as never,
+      0.8,
+    );
+    expect(summary.dosesRemaining).toBe(3);
+    expect(summary.dosesTotal).toBe(3);
+  });
+});

src/lib/medications/inventory/summary.ts

@@ -30,6 +30,8 @@
  * the client detail surfaces that also render from it.
  */
 
+import { floorWhole } from "@/lib/medications/units-per-dose";
+
 export type SupplyItemState = "ACTIVE" | "IN_USE" | "EXPIRED" | "USED_UP";
 
 export interface SupplyItem {
@@ -102,8 +104,8 @@ export function summariseSupply(
   return {
     unitsRemaining,
     unitsTotal,
-    dosesRemaining: Math.floor(unitsRemaining / perDose),
-    dosesTotal: Math.floor(unitsTotal / perDose),
+    dosesRemaining: floorWhole(unitsRemaining / perDose),
+    dosesTotal: floorWhole(unitsTotal / perDose),
     expiredUnits,
   };
 }

src/lib/medications/list-read.ts

@@ -34,6 +34,7 @@ import {
   scheduleWireFields,
 } from "@/lib/medications/intake-tracking";
 import { liveEraStartsByMedication } from "@/lib/medications/scheduling/live-era";
+import { floorWhole } from "@/lib/medications/units-per-dose";
 
 export type MedicationsListResult = Array<Record<string, unknown>>;
 
@@ -272,7 +273,7 @@ export async function buildMedicationsList(
     const stockDosesRemaining =
       stockUnitsRemaining === null
         ? null
-        : Math.floor(
+        : floorWhole(
             stockUnitsRemaining /
               effectiveUnitsPerDose(schedulesDto, Number(m.unitsPerDose)),
           );

src/lib/medications/units-per-dose.ts

@@ -136,3 +136,16 @@ export function formatUnitsPerDose(value: number, locale?: string): string {
     useGrouping: false,
   }).format(rounded);
 }
+
+/**
+ * `Math.floor` for the supply arithmetic, tolerant of binary floating point.
+ * 2.4 / 0.8 is 2.9999999999999996 in IEEE 754, so a plain floor reports two
+ * doses left where there are three. Units and units per dose carry at most
+ * four decimals (per dose at most 100), so a quotient that is not a whole
+ * number sits at least 1e-6 below the next one; a rounding error sits
+ * orders of magnitude closer. Anything within 1e-9 of the next whole
+ * number is that number.
+ */
+export function floorWhole(value: number): number {
+  return Math.floor(value + 1e-9);
+}