diff --git a/packages/compiler/src/backend/llvm/emit-function.ts b/packages/compiler/src/backend/llvm/emit-function.ts
index 3be3d979f..427e439ad 100644
--- a/packages/compiler/src/backend/llvm/emit-function.ts
+++ b/packages/compiler/src/backend/llvm/emit-function.ts
@@ -31,6 +31,7 @@ import { findLocalStackUnions } from "./stack-unions.js";
 import { findLocalStackObjects, findReassignedStackObjects } from "./stack-objects.js";
 import { findLocalUnionStorage } from "./local-union-storage.js";
 import { INT32_RANGE, analyzeIntegerRangeFacts } from "../../ir/integer-ranges.js";
+import { beginLoopEntryVersions } from "./loop-entry-versions.js";
 import { findBytesBounds } from "./bytes-bounds.js";
 import { findInt32Locals } from "./int32-locals.js";
 import { findIntegerViews } from "./integer-views.js";
@@ -246,6 +247,7 @@ export function emitFunction(emitter: LlEmitter, fn: IrFunction): string {
   const rangeFacts = analyzeIntegerRangeFacts(numericFn, slotFacts);
   emitter.integerRanges = rangeFacts.ranges;
   emitter.integerLoopRanges = rangeFacts.loopRanges;
+  beginLoopEntryVersions(emitter, numericFn, slotFacts, rangeFacts);
   emitter.int32Elements = slotFacts.elements ?? null;
   emitter.integerOrNaNLocals = findIntegerOrNaNLocals(emitter, numericFn);
   emitter.bytesBounds = findBytesBounds(numericFn, emitter.integerRanges);
diff --git a/packages/compiler/src/backend/llvm/emit-statements.ts b/packages/compiler/src/backend/llvm/emit-statements.ts
index 1eeceff4a..74c84ae86 100644
--- a/packages/compiler/src/backend/llvm/emit-statements.ts
+++ b/packages/compiler/src/backend/llvm/emit-statements.ts
@@ -46,6 +46,7 @@ import { emitBorrowedInput } from "./borrowed-inputs.js";
 import { f64Lit, llvmCommentText, loadArrCount, SCR_ARR_FIELD, sizeToDouble } from "./common.js";
 import { planInt32KindLoop, type Int32KindLoopPlan } from "./int32-kind-loops.js";
 import { withinInt32 } from "../../ir/integer-ranges.js";
+import { emitLoopEntryVersion, loopEntryVersion } from "./loop-entry-versions.js";
 import { resultSlotStore } from "../result-slots.js";
 import {
   matchIntegerArrayForLoop,
@@ -2349,6 +2350,13 @@ export function emitLoopCopies(
   exit: string,
   emitCopy: (exit: string) => void,
 ): void {
+  const entry = allowed ? loopEntryVersion(emitter, loop) : null;
+  if (entry) {
+    emitLoopEntryVersion(emitter, loop, entry, () =>
+      emitLoopCopies(emitter, loop, allowed, exit, emitCopy),
+    );
+    return;
+  }
   const plan =
     allowed &&
     emitter.speculativeLoopsEnabled &&
diff --git a/packages/compiler/src/backend/llvm/emitter.ts b/packages/compiler/src/backend/llvm/emitter.ts
index 425c4f4d4..2d2ebfb8d 100644
--- a/packages/compiler/src/backend/llvm/emitter.ts
+++ b/packages/compiler/src/backend/llvm/emitter.ts
@@ -1,4 +1,5 @@
 import type { TargetCpu } from "../target-cpu.js";
+import { loopEntryInlines } from "./loop-entry-versions.js";
 import type { FunctionLayout } from "./function-layout.js";
 import { relieveHeapPressure } from "../../heap-pressure.js";
 import { wasmBoundsChecks } from "./wasm-modules.js";
@@ -4009,8 +4010,10 @@ export class LlEmitter {
   emitDirectCall(line: string, callee: string): boolean {
     const B = this.B;
     // A small leaf called only from loops inlines into each of them, past
-    // LLVM's cost threshold (loop-callees.ts). Debug builds keep the call.
-    if (this.debug === null && this.loopCallees.has(callee)) {
+    // LLVM's cost threshold (loop-callees.ts), and so does a function called
+    // only from a loop's entry-range version (loop-entry-versions.ts).
+    // Debug builds keep the call.
+    if (this.debug === null && (this.loopCallees.has(callee) || loopEntryInlines(this, callee))) {
       const comment = line.indexOf(" ; ");
       line =
         comment < 0
diff --git a/packages/compiler/src/backend/llvm/loop-entry-versions.ts b/packages/compiler/src/backend/llvm/loop-entry-versions.ts
new file mode 100644
index 000000000..2c448cae4
--- /dev/null
+++ b/packages/compiler/src/backend/llvm/loop-entry-versions.ts
@@ -0,0 +1,231 @@
+/* Loop-entry range versions (ir/loop-entry-ranges.ts): a while loop whose
+ * integer work depends on locals entering it without range facts runs as
+ * two copies. A test on entry checks that each such local holds an integer
+ * in its assumed range; the fast copy is emitted under the facts that hold
+ * then, and the other copy is the loop as it would be emitted otherwise. */
+import type { IrFunction, IrModule, IrStmt } from "../../ir/ir.js";
+import { everyStmt, everyStmtList } from "../../ir/traverse.js";
+import { exprFunctionReference, moduleFunctionReferences } from "../../ir/function-references.js";
+import type { IntegerRangeFacts, IntegerSlotFacts } from "../../ir/integer-ranges.js";
+import { findLoopEntryVersions, type LoopEntryVersion } from "../../ir/loop-entry-ranges.js";
+import { f64Lit } from "./common.js";
+import type { LlEmitter } from "./emitter.js";
+import { defineModuleState } from "./emitter-state.js";
+
+interface LoopEntryState {
+  fn: IrFunction | null;
+  facts: IntegerRangeFacts | null;
+  slots: IntegerSlotFacts;
+  /** Found on the first while loop the function emits. */
+  versions: Map<IrStmt, LoopEntryVersion> | null;
+  /** Loops whose copies are being emitted: a loop is versioned once. */
+  readonly versioning: Set<IrStmt>;
+  /** Direct calls per module function, or -1 for a function some value or
+   * the module's metadata references. */
+  calls: Map<string, number> | null;
+  /** The callees whose calls the fast copy being emitted inlines. */
+  inlined: ReadonlySet<string> | null;
+}
+
+const ENTRY_VERSIONS = defineModuleState<LoopEntryState>(() => ({
+  fn: null,
+  facts: null,
+  slots: {},
+  versions: null,
+  versioning: new Set<IrStmt>(),
+  calls: null,
+  inlined: null,
+}));
+
+/** The most IR nodes a callee may have for its call in a fast copy to be
+ * inlined (singleCallees). */
+const MAX_INLINED_NODES = 400;
+
+/** Sets the state for the function about to be emitted: `numericFn` and the
+ * facts emitFunction computed for it. Debug builds keep every loop as is. */
+export function beginLoopEntryVersions(
+  emitter: LlEmitter,
+  numericFn: IrFunction,
+  slots: IntegerSlotFacts,
+  facts: IntegerRangeFacts,
+): void {
+  const state = ENTRY_VERSIONS.of(emitter);
+  state.fn = emitter.debug === null ? numericFn : null;
+  state.slots = slots;
+  state.facts = facts;
+  state.versions = null;
+  state.versioning.clear();
+}
+
+/** The entry version of `loop`, when it has one and the emitter can test
+ * its locals: plain double slots of the current function, outside a
+ * speculative copy and a coroutine. */
+export function loopEntryVersion(emitter: LlEmitter, loop: IrStmt): LoopEntryVersion | null {
+  if (loop.kind !== "while") return null;
+  const state = ENTRY_VERSIONS.of(emitter);
+  if (state.fn === null || state.facts === null || state.versioning.has(loop)) return null;
+  if (
+    !emitter.speculativeLoopsEnabled ||
+    emitter.speculation !== null ||
+    emitter.speculationResume !== null ||
+    emitter.currentCoro !== null
+  )
+    return null;
+  state.versions ??= findLoopEntryVersions(state.fn, state.facts, state.slots);
+  const version = state.versions.get(loop);
+  if (!version) return null;
+  for (const id of version.entry.keys())
+    if (!emitter.currentLocals.has(id) || !emitter.speculativeLocal(id)) return null;
+  return version;
+}
+
+/** Emit the entry test and both copies of `loop`. `emitCopies` emits the
+ * loop as it would be emitted without the version; it runs once under the
+ * version's facts and once as is. */
+export function emitLoopEntryVersion(
+  emitter: LlEmitter,
+  loop: IrStmt,
+  version: LoopEntryVersion,
+  emitCopies: () => void,
+): void {
+  const B = emitter.B;
+  let ok: string | null = null;
+  for (const [id, range] of version.entry) {
+    // An integer in [min, max] other than -0: the ordered comparisons
+    // reject NaN, and the bits of the value and its round trip agree only
+    // for integers that are not -0. A local the loop writes before it reads
+    // may be unset on entry, and a conversion out of range is poison:
+    // `freeze` makes both an arbitrary fixed value.
+    const raw = B.tmp(),
+      value = B.tmp(),
+      low = B.tmp(),
+      high = B.tmp(),
+      converted = B.tmp(),
+      integer = B.tmp(),
+      back = B.tmp(),
+      bits = B.tmp(),
+      backBits = B.tmp(),
+      exact = B.tmp(),
+      inRange = B.tmp(),
+      passed = B.tmp();
+    B.line(`${raw} = load double, ptr ${emitter.binding(id).slot}`);
+    B.line(`${value} = freeze double ${raw}`);
+    B.line(`${low} = fcmp oge double ${value}, ${f64Lit(range.min)}`);
+    B.line(`${high} = fcmp ole double ${value}, ${f64Lit(range.max)}`);
+    B.line(`${converted} = fptosi double ${value} to i64`);
+    B.line(`${integer} = freeze i64 ${converted}`);
+    B.line(`${back} = sitofp i64 ${integer} to double`);
+    B.line(`${bits} = bitcast double ${value} to i64`);
+    B.line(`${backBits} = bitcast double ${back} to i64`);
+    B.line(`${exact} = icmp eq i64 ${bits}, ${backBits}`);
+    B.line(`${inRange} = and i1 ${low}, ${high}`);
+    B.line(`${passed} = and i1 ${inRange}, ${exact}`);
+    if (ok === null) ok = passed;
+    else {
+      const both = B.tmp();
+      B.line(`${both} = and i1 ${ok}, ${passed}`);
+      ok = both;
+    }
+  }
+  const fast = B.newLabel("entry.fast"),
+    slow = B.newLabel("entry.slow");
+  // The test is expected to pass, which keeps the ordinary copy's calls
+  // cold for the inliner.
+  let likely = "true";
+  if (ok !== null) {
+    emitter.declare("declare i1 @llvm.expect.i1(i1, i1)");
+    likely = B.tmp();
+    B.line(`${likely} = call i1 @llvm.expect.i1(i1 ${ok}, i1 true)`);
+  }
+  B.condBr(likely, fast, slow);
+  const state = ENTRY_VERSIONS.of(emitter);
+  const originalRanges = emitter.integerRanges;
+  const originalLoopRanges = emitter.integerLoopRanges;
+  state.versioning.add(loop);
+  try {
+    B.startBlock(fast);
+    // An enclosing version may have narrowed a range already.
+    const ranges = new Map(originalRanges);
+    for (const [node, range] of version.ranges) {
+      const known = originalRanges.get(node);
+      ranges.set(
+        node,
+        known
+          ? { min: Math.max(known.min, range.min), max: Math.min(known.max, range.max) }
+          : range,
+      );
+    }
+    emitter.integerRanges = ranges;
+    state.inlined = singleCallees(emitter, state, loop);
+    if (version.loopRanges) {
+      const loopRanges = new Map(originalLoopRanges);
+      loopRanges.set(loop, version.loopRanges);
+      emitter.integerLoopRanges = loopRanges;
+    }
+    emitCopies();
+    state.inlined = null;
+    emitter.integerRanges = originalRanges;
+    emitter.integerLoopRanges = originalLoopRanges;
+    B.startBlock(slow);
+    emitCopies();
+  } finally {
+    emitter.integerRanges = originalRanges;
+    emitter.integerLoopRanges = originalLoopRanges;
+    state.versioning.delete(loop);
+    state.inlined = null;
+  }
+}
+
+/** Whether the fast copy being emitted inlines its calls of `callee`. */
+export function loopEntryInlines(emitter: LlEmitter, callee: string): boolean {
+  return ENTRY_VERSIONS.of(emitter).inlined?.has(callee) === true;
+}
+
+/** The functions the loop calls that have no other call or reference in
+ * the module and at most MAX_INLINED_NODES nodes. LLVM inlines a function's
+ * only call at almost any size; the two copies give each such function a
+ * second call, so the fast copy's call is marked to keep that inlining. */
+function singleCallees(emitter: LlEmitter, state: LoopEntryState, loop: IrStmt): Set<string> {
+  const callees = new Set<string>();
+  everyStmt(loop, {
+    expr: (e) => {
+      if (e.kind === "call") callees.add(e.callee);
+      return true;
+    },
+    stmt: () => true,
+  });
+  const result = new Set<string>();
+  if (callees.size === 0) return result;
+  state.calls ??= countCalls(emitter.mod);
+  for (const name of callees) {
+    if (state.calls.get(name) !== 1 || name === state.fn?.name) continue;
+    const fn = emitter.mod.functions.find((f) => f.name === name);
+    if (fn && !fn.async && !fn.generator && nodeCount(fn.body) <= MAX_INLINED_NODES)
+      result.add(name);
+  }
+  return result;
+}
+
+function countCalls(mod: IrModule): Map<string, number> {
+  const calls = new Map<string, number>();
+  const referenced = new Set(moduleFunctionReferences(mod));
+  for (const fn of mod.functions)
+    everyStmtList(fn.body, {
+      expr: (e) => {
+        if (e.kind === "call") calls.set(e.callee, (calls.get(e.callee) ?? 0) + 1);
+        const name = exprFunctionReference(e);
+        if (name !== undefined) referenced.add(name);
+        return true;
+      },
+      stmt: () => true,
+    });
+  for (const name of referenced) calls.set(name, -1);
+  return calls;
+}
+
+function nodeCount(body: IrStmt[]): number {
+  let count = 0;
+  const visit = (): boolean => ++count <= MAX_INLINED_NODES;
+  everyStmtList(body, { expr: visit, stmt: visit });
+  return count;
+}
diff --git a/packages/compiler/src/ir/integer-ranges.ts b/packages/compiler/src/ir/integer-ranges.ts
index 51c0a929b..23e2df90a 100644
--- a/packages/compiler/src/ir/integer-ranges.ts
+++ b/packages/compiler/src/ir/integer-ranges.ts
@@ -23,6 +23,11 @@ export interface IntegerRangeFacts {
   ranges: IntegerRanges;
   loopRanges: ReadonlyMap<IrStmt, ReadonlyMap<string, IntegerRange>>;
 }
+/** Ranges assumed for locals on entry to while loops (loop-entry-ranges.ts):
+ * the facts inside such a loop hold in a copy of it that runs only after a
+ * test proves every assumed local is an integer in its range. After the
+ * loop, its assumed locals and its writes carry no facts. */
+export type LoopEntryAssumptions = ReadonlyMap<IrStmt, ReadonlyMap<string, IntegerRange>>;
 const SIGNED: IntegerRange = { min: -2147483648, max: 2147483647 };
 const UNSIGNED: IntegerRange = { min: 0, max: 4294967295 };
 /** Int32 and uint32 at once: the bound under which `%` (modeled only for
@@ -309,6 +314,7 @@ export function analyzeIntegerRanges(fn: IrFunction, slots: IntegerSlotFacts = {
 export function analyzeIntegerRangeFacts(
   fn: IrFunction,
   slots: IntegerSlotFacts = {},
+  entries?: LoopEntryAssumptions,
 ): IntegerRangeFacts {
   const ranges = new Map<IrExpr, IntegerRange | null>();
   const loopRanges = new Map<IrStmt, Map<string, IntegerRange>>();
@@ -1074,6 +1080,8 @@ export function analyzeIntegerRangeFacts(
         }
         case "while":
         case "doWhile": {
+          const assumed = entries?.get(s);
+          if (assumed) for (const [id, range] of assumed) if (!facts.has(id)) set(facts, id, range);
           // Counters the condition bounds keep their range at every read
           // inside and after the loop.
           const guarded =
@@ -1102,6 +1110,10 @@ export function analyzeIntegerRangeFacts(
           } else body(s.body, new Map(loop));
           havocWith(facts, [s], facts, guarded);
           for (const [id, range] of guarded) set(facts, id, range);
+          if (assumed) {
+            invalidate(facts, [s]);
+            for (const id of assumed.keys()) facts.delete(id);
+          }
           break;
         }
         case "forOf": {
diff --git a/packages/compiler/src/ir/loop-entry-ranges.test.ts b/packages/compiler/src/ir/loop-entry-ranges.test.ts
new file mode 100644
index 000000000..ad1b78ef6
--- /dev/null
+++ b/packages/compiler/src/ir/loop-entry-ranges.test.ts
@@ -0,0 +1,143 @@
+import { expect, test } from "vitest";
+import { analyzeIntegerRangeFacts } from "./integer-ranges.js";
+import { findLoopEntryVersions, LOOP_ENTRY_RANGE } from "./loop-entry-ranges.js";
+import { BOOL, F64, type IrExpr, type IrFunction, type IrStmt } from "./ir.js";
+
+const loc = { file: "test.ts", start: 0, end: 0 };
+const num = (value: number): IrExpr => ({ loc, kind: "numLit", value, type: F64 });
+const ref = (localId: string): IrExpr => ({ loc, kind: "varRef", localId, type: F64 });
+const bin = (op: "+" | "-" | "*" | "%", left: IrExpr, right: IrExpr): IrExpr => ({
+  loc,
+  kind: "bin",
+  op,
+  left,
+  right,
+  type: F64,
+});
+const condition = (op: "<" | "===", left: IrExpr, right: IrExpr): IrExpr => ({
+  loc,
+  kind: "bin",
+  op,
+  left,
+  right,
+  type: BOOL,
+});
+const set = (localId: string, value: IrExpr): IrStmt => ({ loc, kind: "assign", localId, value });
+const bump = (localId: string): IrStmt => ({
+  loc,
+  kind: "exprStmt",
+  expr: { loc, kind: "incDec", op: "+", prefix: false, localId, type: F64 },
+});
+const observe = (value: IrExpr): IrStmt => ({ loc, kind: "exprStmt", expr: value });
+const fn = (body: IrStmt[], locals: string[]): IrFunction => ({
+  loc,
+  name: "f",
+  params: [],
+  returnType: F64,
+  locals: locals.map((id) => ({ id, name: id, type: F64, mutable: true })),
+  body,
+});
+
+/** base = unknown; breaks = unknown; count = 0; i = 0;
+ * while (i < 300) { ...extra; i++; count++; last = (count + base - breaks) % 8;
+ *   if (last === 0) breaks++; }
+ * observe(base) */
+function lineBreaks(extra: IrStmt[] = [], locals: string[] = []) {
+  const remainder = bin("%", bin("-", bin("+", ref("count"), ref("base")), ref("breaks")), num(8));
+  const after = ref("base");
+  const loop: IrStmt = {
+    loc,
+    kind: "while",
+    cond: condition("<", ref("i"), num(300)),
+    body: [
+      ...extra,
+      bump("i"),
+      bump("count"),
+      set("last", remainder),
+      {
+        loc,
+        kind: "if",
+        cond: condition("===", ref("last"), num(0)),
+        then: [bump("breaks")],
+        else_: null,
+      },
+    ],
+  };
+  const f = fn(
+    [
+      set("base", ref("unknown")),
+      set("breaks", ref("unknown")),
+      set("count", num(0)),
+      set("i", num(0)),
+      set("last", num(1)),
+      loop,
+      observe(after),
+    ],
+    ["base", "breaks", "count", "i", "last", ...locals],
+  );
+  return { f, loop, remainder, after };
+}
+
+test("versions a while loop whose remainder reads locals without entry facts", () => {
+  const { f, loop, remainder } = lineBreaks();
+  const facts = analyzeIntegerRangeFacts(f);
+  expect(facts.ranges.get(remainder)).toBeFalsy();
+  const version = findLoopEntryVersions(f, facts).get(loop);
+  expect(version).toBeDefined();
+  expect([...version!.entry]).toEqual([
+    ["base", LOOP_ENTRY_RANGE],
+    ["breaks", LOOP_ENTRY_RANGE],
+  ]);
+  // The dividend is an exact integer; `%` itself is modeled only for
+  // non-negative dividends.
+  const dividend = (remainder as Extract<IrExpr, { kind: "bin" }>).left;
+  expect(version!.ranges.get(dividend)).toBeDefined();
+  // The loop's counters, `breaks` among them, are bounded in the copy.
+  expect(version!.loopRanges?.get("breaks")).toEqual({
+    min: LOOP_ENTRY_RANGE.min,
+    max: LOOP_ENTRY_RANGE.max + 300,
+  });
+});
+
+test("the entry test covers only the locals the remainder depends on", () => {
+  // acc = acc + scale reads two more locals without facts.
+  const { f, loop } = lineBreaks(
+    [set("acc", bin("+", ref("acc"), ref("scale")))],
+    ["acc", "scale"],
+  );
+  f.body.unshift(set("acc", ref("unknown")), set("scale", ref("unknown")));
+  const version = findLoopEntryVersions(f, analyzeIntegerRangeFacts(f)).get(loop);
+  expect([...version!.entry.keys()]).toEqual(["base", "breaks"]);
+});
+
+test("assumed facts do not leave the loop", () => {
+  const { f, loop, after } = lineBreaks();
+  const assumed = new Map([[loop, new Map([["base", LOOP_ENTRY_RANGE]])]]);
+  expect(analyzeIntegerRangeFacts(f, {}, assumed).ranges.get(after)).toBeFalsy();
+});
+
+test("loops without a remainder the assumption proves keep one copy", () => {
+  // A local the loop makes fractional, a product without a remainder, and a
+  // remainder the function already proves.
+  const fractional = lineBreaks([set("base", bin("+", ref("base"), num(0.5)))]);
+  expect(findLoopEntryVersions(fractional.f, analyzeIntegerRangeFacts(fractional.f)).size).toBe(0);
+  const product: IrStmt = {
+    loc,
+    kind: "while",
+    cond: condition("<", ref("i"), num(300)),
+    body: [set("acc", bin("*", ref("acc"), ref("scale"))), bump("i")],
+  };
+  const products = fn(
+    [set("acc", ref("unknown")), set("scale", ref("unknown")), set("i", num(0)), product],
+    ["acc", "scale", "i"],
+  );
+  expect(findLoopEntryVersions(products, analyzeIntegerRangeFacts(products)).size).toBe(0);
+  const proven: IrStmt = {
+    loc,
+    kind: "while",
+    cond: condition("<", ref("i"), num(300)),
+    body: [set("acc", bin("%", ref("i"), num(7))), bump("i")],
+  };
+  const known = fn([set("acc", ref("unknown")), set("i", num(0)), proven], ["acc", "i"]);
+  expect(findLoopEntryVersions(known, analyzeIntegerRangeFacts(known)).size).toBe(0);
+});
diff --git a/packages/compiler/src/ir/loop-entry-ranges.ts b/packages/compiler/src/ir/loop-entry-ranges.ts
new file mode 100644
index 000000000..a5b7628be
--- /dev/null
+++ b/packages/compiler/src/ir/loop-entry-ranges.ts
@@ -0,0 +1,218 @@
+import type { IrExpr, IrFunction, IrStmt } from "./ir.js";
+import { everyExpr, everyStmt, everyStmtList } from "./traverse.js";
+import {
+  analyzeIntegerRangeFacts,
+  type IntegerRange,
+  type IntegerRangeFacts,
+  type IntegerSlotFacts,
+  type LoopEntryAssumptions,
+} from "./integer-ranges.js";
+
+type WhileLoop = Extract<IrStmt, { kind: "while" }>;
+
+/** The range a versioned loop requires of each assumed local on entry. A
+ * loop's counters stay below a typed array or string length (at most 2^48),
+ * so sums of a few such values and assumed locals stay exact integers. */
+export const LOOP_ENTRY_RANGE: IntegerRange = { min: -(2 ** 48), max: 2 ** 48 };
+
+/** A copy of a while loop that runs when every local in `entry` holds an
+ * integer in its range on entry (never -0). `ranges` are the facts that
+ * hold for the loop's expressions in that copy and that the function's own
+ * analysis does not prove; `loopRanges` are the loop's bounded bindings
+ * there. */
+export interface LoopEntryVersion {
+  entry: ReadonlyMap<string, IntegerRange>;
+  ranges: ReadonlyMap<IrExpr, IntegerRange>;
+  loopRanges: ReadonlyMap<string, IntegerRange> | undefined;
+}
+
+/** Versions of innermost while loops whose integer work depends on locals
+ * that enter the loop without range facts: copies of module globals,
+ * parameters, fields or call results (`const base = offset;` before a loop
+ * that computes `(count + base) % 60`).
+ *
+ * The function is analyzed again with each number local the loop reads
+ * without a fact assumed in LOOP_ENTRY_RANGE at the loop's entry. A loop is
+ * versioned when that analysis proves both operands of a remainder that the
+ * function's own analysis leaves unproven. Only remainders qualify: the
+ * operands of a product or a sum of such locals are as often fractional,
+ * and a loop whose test fails runs the ordinary copy in a larger function.
+ * The entry test covers only the assumed locals that such an operation reads, directly,
+ * through the loop's writes of other locals, or through the loop condition;
+ * when that drops any, the function is analyzed once more with the smaller
+ * sets, so the facts never rest on a local the test does not check. No
+ * fact leaves an assumed loop, so the loops' assumptions are independent. */
+export function findLoopEntryVersions(
+  fn: IrFunction,
+  facts: IntegerRangeFacts,
+  slots: IntegerSlotFacts = {},
+): Map<IrStmt, LoopEntryVersion> {
+  const result = new Map<IrStmt, LoopEntryVersion>();
+  if (fn.async || fn.generator) return result;
+  const captures = new Set(
+    [...(fn.captures ?? []), ...(fn.classCaptures ?? [])].map((c) => c.localId),
+  );
+  const eligible = new Set(
+    fn.locals
+      .filter((l) => l.type.kind === "f64" && !l.boxed && !l.tdz && !captures.has(l.id))
+      .map((l) => l.id),
+  );
+  const known = (e: IrExpr): boolean => !!facts.ranges.get(e);
+  let candidates = new Map<WhileLoop, ReadonlyMap<string, IntegerRange>>();
+  everyStmtList(fn.body, {
+    expr: () => true,
+    stmt: (s) => {
+      if (s.kind !== "while" || containsLoop(s.body)) return true;
+      const assumed = entryCandidates(s, eligible, known);
+      if (assumed.size > 0) candidates.set(s, assumed);
+      return true;
+    },
+  });
+  if (candidates.size === 0) return result;
+  let versioned = analyzeIntegerRangeFacts(fn, slots, assumptionsOf(candidates));
+  const pruned = new Map<WhileLoop, ReadonlyMap<string, IntegerRange>>();
+  let dropped = false;
+  for (const [loop, entry] of candidates) {
+    const roots = gainedOperands(loop, known, versioned);
+    if (roots.length === 0) continue;
+    const relevant = relevantLocals(loop, roots);
+    const kept = new Map<string, IntegerRange>();
+    for (const [id, range] of entry) if (relevant.has(id)) kept.set(id, range);
+    if (kept.size < entry.size) dropped = true;
+    if (kept.size > 0) pruned.set(loop, kept);
+  }
+  if (dropped) {
+    candidates = pruned;
+    if (candidates.size === 0) return result;
+    versioned = analyzeIntegerRangeFacts(fn, slots, assumptionsOf(candidates));
+  }
+  for (const [loop, entry] of candidates) {
+    if (gainedOperands(loop, known, versioned).length === 0) continue;
+    const ranges = new Map<IrExpr, IntegerRange>();
+    const visit = (e: IrExpr): boolean => {
+      const range = versioned.ranges.get(e);
+      const prior = facts.ranges.get(e);
+      if (range && !prior) ranges.set(e, range);
+      else if (range && prior && (range.min > prior.min || range.max < prior.max))
+        ranges.set(e, { min: Math.max(range.min, prior.min), max: Math.min(range.max, prior.max) });
+      return true;
+    };
+    everyStmt(loop, { expr: visit, stmt: () => true });
+    result.set(loop, { entry, ranges, loopRanges: versioned.loopRanges.get(loop) });
+  }
+  return result;
+}
+
+function assumptionsOf(
+  candidates: ReadonlyMap<WhileLoop, ReadonlyMap<string, IntegerRange>>,
+): LoopEntryAssumptions {
+  const result = new Map<IrStmt, ReadonlyMap<string, IntegerRange>>();
+  for (const [loop, entry] of candidates) result.set(loop, entry);
+  return result;
+}
+
+/** Number locals the loop reads without a range fact and does not declare,
+ * when the loop has a remainder without one. */
+function entryCandidates(
+  loop: WhileLoop,
+  eligible: ReadonlySet<string>,
+  known: (e: IrExpr) => boolean,
+): Map<string, IntegerRange> {
+  const read = new Set<string>();
+  const declared = new Set<string>();
+  let integerWork = false;
+  everyStmt(loop, {
+    expr: (e) => {
+      if (e.kind === "varRef" && eligible.has(e.localId) && !known(e)) read.add(e.localId);
+      else if (e.kind === "bin" && e.op === "%" && !known(e)) integerWork = true;
+      return true;
+    },
+    stmt: (s) => {
+      if (s.kind === "varDecl") declared.add(s.localId);
+      return true;
+    },
+  });
+  const result = new Map<string, IntegerRange>();
+  if (!integerWork) return result;
+  for (const id of read) if (!declared.has(id)) result.set(id, LOOP_ENTRY_RANGE);
+  return result;
+}
+
+/** Operands of the loop's remainders that the versioned analysis proves
+ * where the function's own analysis does not prove both. */
+function gainedOperands(
+  loop: WhileLoop,
+  known: (e: IrExpr) => boolean,
+  versioned: IntegerRangeFacts,
+): IrExpr[] {
+  const operands: IrExpr[] = [];
+  everyStmt(loop, {
+    expr: (e) => {
+      if (
+        e.kind === "bin" &&
+        e.op === "%" &&
+        !(known(e.left) && known(e.right)) &&
+        !!versioned.ranges.get(e.left) &&
+        !!versioned.ranges.get(e.right)
+      )
+        operands.push(e.left, e.right);
+      return true;
+    },
+    stmt: () => true,
+  });
+  return operands;
+}
+
+/** The locals `roots` read, closed over the loop's writes (a local written
+ * from others reads them) and over its condition (a local the condition
+ * reads makes every local of the condition relevant). */
+function relevantLocals(loop: WhileLoop, roots: readonly IrExpr[]): Set<string> {
+  const relevant = new Set<string>();
+  const readsOf = (e: IrExpr): string[] => {
+    const ids: string[] = [];
+    everyExpr(e, {
+      expr: (x) => {
+        if (x.kind === "varRef") ids.push(x.localId);
+        return true;
+      },
+      stmt: () => true,
+    });
+    return ids;
+  };
+  const written = new Map<string, IrExpr[]>();
+  everyStmt(loop, {
+    expr: (e) => {
+      if (e.kind === "assignExpr")
+        written.set(e.localId, [...(written.get(e.localId) ?? []), e.value]);
+      return true;
+    },
+    stmt: (s) => {
+      const value = s.kind === "assign" ? s.value : s.kind === "varDecl" ? s.init : undefined;
+      if (value && (s.kind === "assign" || s.kind === "varDecl"))
+        written.set(s.localId, [...(written.get(s.localId) ?? []), value]);
+      return true;
+    },
+  });
+  const condition = readsOf(loop.cond);
+  const pending: string[] = [];
+  const add = (id: string): void => {
+    if (relevant.has(id)) return;
+    relevant.add(id);
+    pending.push(id);
+  };
+  for (const root of roots) for (const id of readsOf(root)) add(id);
+  while (pending.length > 0) {
+    const id = pending.pop()!;
+    for (const value of written.get(id) ?? []) for (const other of readsOf(value)) add(other);
+    if (condition.includes(id)) for (const other of condition) add(other);
+  }
+  return relevant;
+}
+
+function containsLoop(body: IrStmt[]): boolean {
+  return !everyStmtList(body, {
+    expr: () => true,
+    stmt: (s) =>
+      s.kind !== "while" && s.kind !== "doWhile" && s.kind !== "for" && s.kind !== "forOf",
+  });
+}
diff --git a/packages/compiler/test/loop-entry-versions.test.ts b/packages/compiler/test/loop-entry-versions.test.ts
new file mode 100644
index 000000000..22e41e3e7
--- /dev/null
+++ b/packages/compiler/test/loop-entry-versions.test.ts
@@ -0,0 +1,45 @@
+import { mkdtemp, readFile, rm } from "node:fs/promises";
+import { tmpdir } from "node:os";
+import { join } from "node:path";
+import { expect, test } from "vitest";
+import { compile, deserializeModule } from "../src/index.js";
+import { emitLlvmModule } from "../src/backend/llvm/emitter.js";
+
+test("while loops test their entry values and run integer remainders in the fast copy", async () => {
+  const dir = await mkdtemp(join(tmpdir(), "scriptc-entry-versions-"));
+  try {
+    const entry = join(import.meta.dirname, "../../../tests/corpus/while-entry-range-versions.ts");
+    const outPath = join(dir, "versions.ir.json");
+    const result = await compile(entry, { outPath, outDir: dir, outputKind: "ir" });
+    if (!result.ok) throw new Error(result.diagnostics.map((d) => d.message).join("\n"));
+    const mod = deserializeModule(await readFile(outPath, "utf8"));
+    const ll = emitLlvmModule(mod, { pointerBits: 64 });
+    const body = (name: string): string =>
+      ll.match(
+        new RegExp(`define internal [^\\n]+ @sc_bf_${name}\\([^\\n]*\\{([\\s\\S]*?)\\n\\}`),
+      )![1]!;
+    for (const name of ["wrap", "ring", "_x25_Cursor_stripes"]) {
+      const fn = body(name);
+      const fast = fn.slice(fn.indexOf("\nentry.fast"), fn.indexOf("\nentry.slow"));
+      const slow = fn.slice(fn.indexOf("\nentry.slow"));
+      // The fast copy adds the dividend's integers; the ordinary copy adds
+      // doubles and tests the sum before its integer remainder.
+      const adds = (text: string): number => text.split("fadd double").length - 1;
+      expect(fast, name).toContain("srem i64");
+      expect(adds(fast), name).toBeLessThan(adds(slow));
+    }
+    // `complement` has no other caller: the fast copy's call keeps it inlined.
+    const wrap = body("wrap");
+    const fast = wrap.slice(wrap.indexOf("\nentry.fast"), wrap.indexOf("\nentry.slow"));
+    expect(fast).toMatch(/call i32 @sc_f_complement\.i32\([^)]*\) alwaysinline/);
+    expect(wrap.slice(wrap.indexOf("\nentry.slow"))).not.toContain("alwaysinline");
+    // Debug builds keep one copy.
+    const debug = emitLlvmModule(mod, {
+      pointerBits: 64,
+      debugSources: new Map([[entry, await readFile(entry, "utf8")]]),
+    });
+    expect(debug).not.toContain("entry.fast");
+  } finally {
+    await rm(dir, { recursive: true, force: true });
+  }
+});
diff --git a/packages/compiler/test/ts7/baselines/order-parity/tests/corpus/while-entry-range-versions.ts.json b/packages/compiler/test/ts7/baselines/order-parity/tests/corpus/while-entry-range-versions.ts.json
new file mode 100644
index 000000000..ec9e8eeae
--- /dev/null
+++ b/packages/compiler/test/ts7/baselines/order-parity/tests/corpus/while-entry-range-versions.ts.json
@@ -0,0 +1,6 @@
+{
+ "order": [
+  "<repo>/tests/corpus/while-entry-range-versions.ts"
+ ],
+ "diags": []
+}
diff --git a/tests/corpus/while-entry-range-versions.ts b/tests/corpus/while-entry-range-versions.ts
new file mode 100644
index 000000000..7d96c243a
--- /dev/null
+++ b/tests/corpus/while-entry-range-versions.ts
@@ -0,0 +1,160 @@
+// While loops whose remainder reads locals copied from module globals,
+// parameters and fields. Entry values cover integers inside and outside
+// [-2^48, 2^48], fractions, -0, NaN and infinities.
+
+let column = 0;
+let lines = 0;
+
+// A switch with more cases than a small leaf function has statements.
+function complement(code: number): number {
+  switch (code) {
+    case 65:
+      return 84;
+    case 67:
+      return 71;
+    case 71:
+      return 67;
+    case 84:
+      return 65;
+    case 97:
+      return 116;
+    case 99:
+      return 103;
+    case 103:
+      return 99;
+    case 116:
+      return 97;
+    case 85:
+      return 65;
+    case 117:
+      return 97;
+    case 82:
+      return 89;
+    case 89:
+      return 82;
+    case 75:
+      return 77;
+    case 77:
+      return 75;
+  }
+  return 78;
+}
+
+// Copies bytes in reverse, complemented, with a newline after every 8
+// columns counted from the module-level column and line counters.
+function wrap(input: Uint8Array, out: Uint8Array): number {
+  const base = column;
+  let breaks = lines;
+  let count = 0;
+  let o = 0;
+  let i = 0;
+  const len = input.length;
+  let last = 1;
+  let negativeZeros = 0;
+  while (i < len) {
+    out[o] = complement(input[len - 1 - i]!);
+    i++;
+    o++;
+    count++;
+    last = (count + base - breaks) % 8;
+    if (Object.is(last, -0)) negativeZeros++;
+    if (last === 0) {
+      out[o] = 10;
+      o++;
+      count++;
+      breaks++;
+    }
+  }
+  column = base + count;
+  lines = breaks;
+  console.log(`  last ${Object.is(last, -0) ? "-0" : last}, ${negativeZeros} of them -0`);
+  return o;
+}
+
+function text(out: Uint8Array, n: number): string {
+  let s = "";
+  for (let i = 0; i < n; i++) s += out[i] === 10 ? "|" : String.fromCharCode(out[i]!);
+  return s;
+}
+
+const input = new Uint8Array(29);
+const bases = "ACGTTGCAAGCTTCGA";
+for (let i = 0; i < input.length; i++) input[i] = bases.charCodeAt((i * 7) % bases.length);
+const out = new Uint8Array(64);
+
+const starts: [number, number][] = [
+  [0, 0],
+  [5, 2],
+  [-13, 0],
+  [-16, 0],
+  [2 ** 48, 3],
+  [-(2 ** 48), 0],
+  [2 ** 48 + 1, 0],
+  [2 ** 50, 1],
+  [2 ** 53 - 5, 0],
+  [2 ** 53, 0],
+  [2 ** 53 + 2, 1],
+  [0.5, 0],
+  [3, 0.25],
+  [3, 2 ** 49],
+  [-0, 0],
+  [0, -0],
+  [NaN, 0],
+  [Infinity, 0],
+  [-Infinity, 0],
+  [1e300, 0],
+];
+for (const [c, l] of starts) {
+  column = c;
+  lines = l;
+  console.log(`start column ${c} lines ${l}`);
+  const n = wrap(input, out);
+  console.log(`  ${text(out, n)}`);
+  console.log(`  column ${column} lines ${lines}`);
+}
+
+// Two calls in a row: the second starts from the first one's counters.
+column = 3;
+lines = 0;
+wrap(input, out);
+const n = wrap(input, out);
+console.log(`again ${text(out, n)} column ${column} lines ${lines}`);
+
+// A parameter and a field as the loop's entry values.
+function ring(values: Int32Array, offset: number, size: number): number {
+  let sum = 0;
+  let i = 0;
+  while (i < values.length) {
+    sum += values[(i + offset) % size]!;
+    i++;
+  }
+  return sum;
+}
+const values = new Int32Array([3, 1, 4, 1, 5, 9, 2, 6]);
+for (const offset of [0, 3, 7, 2 ** 40, 2 ** 49, 1.5, -0, -2]) {
+  const sum = ring(values, offset, values.length);
+  console.log(`ring ${offset} ${Number.isNaN(sum) ? "NaN" : sum}`);
+}
+
+class Cursor {
+  position: number;
+  constructor(position: number) {
+    this.position = position;
+  }
+  stripes(bytes: Uint8Array): string {
+    const start = this.position;
+    let i = 0;
+    let marks = "";
+    while (i < bytes.length) {
+      const r = (start + i) % 3;
+      marks += Object.is(r, -0) ? "z" : String(r);
+      i++;
+    }
+    this.position = start + i;
+    return marks;
+  }
+}
+for (const position of [0, 4, -5, 2 ** 48 + 7, 0.75, 2 ** 60]) {
+  const cursor = new Cursor(position);
+  console.log(`stripes ${position} ${cursor.stripes(input.subarray(0, 7))} ${cursor.position}`);
+}
diff --git a/tests/harness/corpus-costs/while-entry-range-versions.ts.json b/tests/harness/corpus-costs/while-entry-range-versions.ts.json
new file mode 100644
index 000000000..2a685047e
--- /dev/null
+++ b/tests/harness/corpus-costs/while-entry-range-versions.ts.json
@@ -0,0 +1 @@
+{ "plain": 3600, "san": 3000 }