Index: lib/Analysis/ScalarEvolution.cpp
===================================================================
--- lib/Analysis/ScalarEvolution.cpp
+++ lib/Analysis/ScalarEvolution.cpp
@@ -6306,8 +6306,35 @@
     // also returns true if StepV is maximally negative (eg, INT_MIN), but that
     // case is not handled as this code is guarded by !CountDown.
     if (StepV.isPowerOf2() &&
-        GetMinTrailingZeros(Distance) >= StepV.countTrailingZeros())
-      return getUDivExactExpr(Distance, Step);
+        GetMinTrailingZeros(Distance) >= StepV.countTrailingZeros()) {
+      // Here we've constrained the equation to be of the form
+      //
+      //   2^(N + k) * Distance' = (StepV == 2^N) * X (mod 2^W)  ... (0)
+      //
+      // where we're operating on a W bit wide integer domain and k is
+      // non-negative.  The smallest unsigned solution for X is the trip count.
+      //
+      // (0) is equivalent to:
+      //
+      //      2^(N + k) * Distance' - 2^N * X = L * 2^W
+      // <=>  2^N(2^k * Distance' - X) = L * 2^(W - N) * 2^N
+      // <=>  2^k * Distance' - X = L * 2^(W - N)
+      // <=>  2^k * Distance'     = L * 2^(W - N) + X    ... (1)
+      //
+      // The smallest X satisfying (1) is unsigned remainder of dividing the LHS
+      // by 2^(W - N).
+
+      const auto *ModuloResult = getUDivExactExpr(Distance, Step);
+
+      // Since SCEV does not have a URem instruction, we mask out the lower bits
+      // by a truncate followed by a zero extend to compute the remainder.
+
+      unsigned NarrowWidth = StepV.getBitWidth() - StepV.countTrailingZeros();
+      auto *NarrowTy = IntegerType::get(getContext(), NarrowWidth);
+      auto *WideTy = Distance->getType();
+
+      return getZeroExtendExpr(getTruncateExpr(ModuloResult, NarrowTy), WideTy);
+    }
   }
 
   // If the condition controls loop exit (the loop exits only if the expression
Index: test/Analysis/ScalarEvolution/pr24757.ll
===================================================================
--- /dev/null
+++ test/Analysis/ScalarEvolution/pr24757.ll
@@ -0,0 +1,35 @@
+; RUN: opt -analyze -scalar-evolution < %s | FileCheck %s
+
+; CHECK: Loop %bb1: backedge-taken count is (zext i7 (trunc i8 %a.promoted to i7) to i8)
+
+target datalayout = "e-m:o-i64:64-f80:128-n8:16:32:64-S128"
+target triple = "x86_64-apple-macosx10.10.0"
+
+@a = global i8 -127, align 1
+@b = common global i32 0, align 4
+
+declare void @use(i32)
+
+define i32 @main() {
+bb:
+  %a.promoted = load i8, i8* @a
+  br label %bb1
+
+bb1:                                              ; preds = %bb1, %bb
+  %tmp = phi i8 [ %tmp2, %bb1 ], [ %a.promoted, %bb ]
+  %tmp2 = add i8 %tmp, -1
+  %tmp3 = sext i8 %tmp to i32
+  %tmp4 = xor i32 %tmp3, -1
+  %tmp5 = sext i8 %tmp2 to i32
+  %tmpf = sub nsw i32 %tmp4, %tmp5
+  %tmp6 = trunc i32 %tmpf to i8
+  %tmp7 = icmp eq i8 %tmp6, 0
+  br i1 %tmp7, label %bb8, label %bb1
+
+bb8:                                              ; preds = %bb1
+  store i8 %tmp2, i8* @a
+  store i32 %tmp4, i32* @b
+  %tmp9 = sext i8 %tmp2 to i32
+  call void @use(i32 %tmp9)
+  ret i32 0
+}