diff --git a/gcc/gimple-match-head.cc b/gcc/gimple-match-head.cc
index b08cd891a13..680a4cb2fc6 100644
--- a/gcc/gimple-match-head.cc
+++ b/gcc/gimple-match-head.cc
@@ -224,3 +224,57 @@ optimize_successive_divisions_p (tree divisor, tree inner_div)
     }
   return true;
 }
+
+/* Return true if "(X - N * M) / N + M" can be optimized into "X / N".
+   Otherwise return false.
+
+   For unsigned,
+   If sign bit of M is 0 (clz is 0), valid range is [N*M, MAX].
+   If sign bit of M is 1, valid range is [0, MAX - N*(-M)].
+
+   For signed,
+   If N*M > 0, valid range: [MIN+N*M, 0] + [N*M, MAX]
+   If N*M < 0, valid range: [MIN, -(-N*M)] + [0, MAX - (-N*M)].  */
+
+static bool
+optimize_x_minus_NM_div_N_plus_M (tree x, wide_int n, wide_int m, tree type)
+{
+  wide_int max = wi::max_value (type);
+  signop sgn = TYPE_SIGN (type);
+  wide_int nm;
+  wi::overflow_type ovf;
+  if (TYPE_UNSIGNED (type) && wi::clz (m) == 0)
+    nm = wi::mul (n, -m, sgn, &ovf);
+  else
+    nm = wi::mul (n, m, sgn, &ovf);
+
+  if (ovf != wi::OVF_NONE)
+    return false;
+
+  value_range vr0;
+  if (!get_range_query (cfun)->range_of_expr (vr0, x) || vr0.varying_p ()
+      || vr0.undefined_p ())
+    return false;
+
+  wide_int wmin0 = vr0.lower_bound ();
+  wide_int wmax0 = vr0.upper_bound ();
+  wide_int min = wi::min_value (type);
+
+  /* unsigned */
+  if ((TYPE_UNSIGNED (type)))
+    /* M > 0 (clz != 0): [N*M, MAX],  M < 0 : [0, MAX-N*(-M)]  */
+    return wi::clz (m) != 0 ? wi::ge_p (wmin0, nm, sgn)
+			    : wi::le_p (wmax0, max - nm, sgn);
+
+  /* signed, N*M > 0 */
+  else if (wi::gt_p (nm, 0, sgn))
+    /* [N*M, MAX] or [MIN+N*M, 0] */
+    return wi::ge_p (wmin0, nm, sgn)
+	   || (wi::ge_p (wmin0, min + nm, sgn) && wi::le_p (wmax0, 0, sgn));
+
+  /* signed, N*M < 0 */
+  /* [MIN, N*M] or [0, MAX + N*M]*/
+  else
+    return wi::le_p (wmax0, nm, sgn)
+	   || (wi::ge_p (wmin0, 0, sgn) && wi::le_p (wmax0, max - (-nm), sgn));
+}
diff --git a/gcc/match.pd b/gcc/match.pd
index ceae1c34abc..1aaa5530577 100644
--- a/gcc/match.pd
+++ b/gcc/match.pd
@@ -881,6 +881,28 @@ DEFINE_INT_AND_FLOAT_ROUND_FN (RINT)
 #endif
    ))))
 
+#if GIMPLE
+/* Simplify ((t + -N*M) / N + M) -> t / N.  */
+(for div (trunc_div exact_div)
+ (simplify
+  (plus (div (plus @0 INTEGER_CST@1) INTEGER_CST@2) INTEGER_CST@3)
+  (with {wide_int n = wi::to_wide (@2); wide_int m = wi::to_wide (@3);}
+    (if (INTEGRAL_TYPE_P (type)
+	 && n * m == -wi::to_wide (@1)
+	 && optimize_x_minus_NM_div_N_plus_M (@0, n, m, type))
+    (div @0 @2)))))
+
+/* Simplify ((t + -(M<<N)) >> N + M) -> t >> N.  */
+(simplify
+ (plus (rshift (plus @0 INTEGER_CST@1) INTEGER_CST@2) INTEGER_CST@3)
+ (with {wide_int n = wi::to_wide (@2); wide_int m = wi::to_wide (@3);}
+   (if (INTEGRAL_TYPE_P (type)
+	&& (m << n) == -wi::to_wide (@1)
+	&& optimize_x_minus_NM_div_N_plus_M (@0,
+	     wi::one (TYPE_PRECISION (type)) << n, m, type))
+    (rshift @0 @2))))
+#endif
+
 (for op (negate abs)
  /* Simplify cos(-x) and cos(|x|) -> cos(x).  Similarly for cosh.  */
  (for coss (COS COSH)
diff --git a/gcc/testsuite/gcc.dg/pr108757-1.c b/gcc/testsuite/gcc.dg/pr108757-1.c
new file mode 100644
index 00000000000..349318a7c82
--- /dev/null
+++ b/gcc/testsuite/gcc.dg/pr108757-1.c
@@ -0,0 +1,17 @@
+/* PR tree-optimization/108757 */
+/* { dg-do compile } */
+/* { dg-options "-O2 -fdump-tree-optimized" } */
+
+#include <limits.h>
+#define N 4
+#define M 3
+#define GAP 0
+typedef unsigned int UINT;
+typedef int INT;
+#define UMAX UINT_MAX
+#define IMAX INT_MAX
+#define IMIN INT_MIN
+#include "pr108757.h"
+
+/* { dg-final { scan-tree-dump-not " = x_\[0-9\]\\(D\\) \\+ " "optimized" } } */
+/* { dg-final { scan-tree-dump-not " = b_\[0-9\] \\+ " "optimized" } } */
diff --git a/gcc/testsuite/gcc.dg/pr108757-2.c b/gcc/testsuite/gcc.dg/pr108757-2.c
new file mode 100644
index 00000000000..7302e9c606c
--- /dev/null
+++ b/gcc/testsuite/gcc.dg/pr108757-2.c
@@ -0,0 +1,18 @@
+/* PR tree-optimization/108757 */
+/* { dg-do compile } */
+/* { dg-options "-O2 -fdump-tree-optimized" } */
+
+#include <limits.h>
+#define N 4
+#define M 3
+#define GAP 2
+typedef unsigned int UINT;
+typedef int INT;
+#define UMAX UINT_MAX
+#define IMAX INT_MAX
+#define IMIN INT_MIN
+#include "pr108757.h"
+
+/* { dg-final { scan-tree-dump-times " = x_\[0-9\]\\(D\\) \\+ " 16 "optimized" } } */
+/* { dg-final { scan-tree-dump-times " = b_\[0-9\] \\+ " 16 "optimized" } } */
+
diff --git a/gcc/testsuite/gcc.dg/pr108757.h b/gcc/testsuite/gcc.dg/pr108757.h
new file mode 100644
index 00000000000..9e12d106aad
--- /dev/null
+++ b/gcc/testsuite/gcc.dg/pr108757.h
@@ -0,0 +1,160 @@
+#define NOINLINE __attribute__ ((noinline))
+UINT NOINLINE
+opt_u1 (UINT x)
+{
+  if (x < (M * N) - GAP)
+    return 0;
+  UINT a = x - (M * N);
+  UINT b = a / N;
+  return b + M;
+}
+
+UINT NOINLINE
+opt_u2 (UINT x)
+{
+  if (x > (UMAX - (M * N) + GAP))
+    return 0;
+  UINT a = x + (M * N);
+  UINT b = a / N;
+  return b - M;
+}
+
+INT NOINLINE
+opt_s1 (INT x)
+{
+  if (x < (M * N) - GAP)
+    return 0;
+  INT a = x - (M * N);
+  INT b = a / N;
+  return b + M;
+}
+
+INT NOINLINE
+opt_s2 (INT x)
+{
+  if (x < IMIN + (M * N) - GAP || x > 0)
+    return 0;
+  INT a = x - (M * N);
+  INT b = a / N;
+  return b + M;
+}
+
+INT NOINLINE
+opt_s3 (INT x)
+{
+  if (x < (M * N) - GAP)
+    return 0;
+  INT a = x - (M * N);
+  INT b = a / -N;
+  return b + -M;
+}
+
+INT NOINLINE
+opt_s4 (INT x)
+{
+  if (x < IMIN + (M * N) - GAP || x > 0)
+    return 0;
+  INT a = x - (M * N);
+  INT b = a / -N;
+  return b + -M;
+}
+
+INT NOINLINE
+opt_s5 (INT x)
+{
+  if (x > (-M * N) + GAP)
+    return 0;
+  INT a = x - (-M * N);
+  INT b = a / N;
+  return b + -M;
+}
+
+INT NOINLINE
+opt_s6 (INT x)
+{
+  if (x > IMAX - (M * N) + GAP || x < 0)
+    return 0;
+  INT a = x - (-M * N);
+  INT b = a / N;
+  return b + -M;
+}
+
+INT NOINLINE
+opt_s7 (INT x)
+{
+  if (x > (M * -N) + GAP)
+    return 0;
+  INT a = x - (M * -N);
+  INT b = a / -N;
+  return b + M;
+}
+
+INT NOINLINE
+opt_s8 (INT x)
+{
+  if (x > IMAX - (M * N) + GAP || x < 0)
+    return 0;
+  INT a = x - (M * -N);
+  INT b = a / -N;
+  return b + M;
+}
+
+UINT NOINLINE
+opt_u3 (UINT x)
+{
+  if (x < (M << N) - GAP)
+    return 0;
+  UINT a = x - (M << N);
+  UINT b = a >> N;
+  return b + M;
+}
+
+UINT NOINLINE
+opt_u4 (UINT x)
+{
+  if (x > (UMAX - (M << N)) + GAP)
+    return 0;
+  UINT a = x + (M << N);
+  UINT b = a >> N;
+  return b - M;
+}
+
+INT NOINLINE
+opt_s9 (INT x)
+{
+  if (x < (M << N) - GAP)
+    return 0;
+  INT a = x - (M << N);
+  INT b = a >> N;
+  return b + M;
+}
+
+INT NOINLINE
+opt_s10 (INT x)
+{
+  if (x < IMIN + (M << N) - GAP || x > 0)
+    return 0;
+  INT a = x - (M << N);
+  INT b = a >> N;
+  return b + M;
+}
+
+INT NOINLINE
+opt_s11 (INT x)
+{
+  if (x > (-M << N) + GAP)
+    return 0;
+  INT a = x - (-M << N);
+  INT b = a >> N;
+  return b + -M;
+}
+
+INT NOINLINE
+opt_s12 (INT x)
+{
+  if (x > IMAX - (M << N) + GAP || x < 0)
+    return 0;
+  INT a = x - (-M << N);
+  INT b = a >> N;
+  return b + -M;
+}
