diff --git a/gcc/gimple-range.cc b/gcc/gimple-range.cc
index 01e62d3ff3901143bde33dc73c0debf41d0c0fdd..620fe32e85e5fe3847a933554fc656b2939cf02d 100644
--- a/gcc/gimple-range.cc
+++ b/gcc/gimple-range.cc
@@ -926,3 +926,53 @@ assume_query::dump (FILE *f)
     }
   fprintf (f, "------------------------------\n");
 }
+
+/* Return true if the operation "X CODE Y" in type does not overflow
+   underflow or wrap with value range info, otherwise return false.  */
+
+bool
+arith_without_overflow_p (tree_code code, tree x, tree y, tree type)
+{
+  gcc_assert (INTEGRAL_TYPE_P (type));
+
+  if (TYPE_OVERFLOW_UNDEFINED (type))
+    return true;
+
+  value_range vr0;
+  value_range vr1;
+  if (!(get_range (vr0, x) && get_range (vr1, y)))
+    return false;
+
+  switch (code)
+    {
+    case PLUS_EXPR:
+      return plus_without_overflow_p (vr0, vr1, type);
+    case MINUS_EXPR:
+      return minus_without_overflow_p (vr0, vr1, type);
+    case MULT_EXPR:
+      return mult_without_overflow_p (vr0, vr1, type);
+    default:
+      gcc_unreachable ();
+    }
+
+  return false;
+}
+
+/* Return true if "X" and "Y" have the same sign or zero.  */
+
+bool
+same_sign_p (tree x, tree y, tree type)
+{
+  gcc_assert (INTEGRAL_TYPE_P (type));
+
+  if (TYPE_UNSIGNED (type))
+    return true;
+
+  value_range vr0;
+  value_range vr1;
+  if (!(get_range (vr0, x) && get_range (vr1, y)))
+    return false;
+
+  return (vr0.nonnegative_p () && vr1.nonnegative_p ())
+	 || (vr0.nonpositive_p () && vr1.nonpositive_p ());
+}
diff --git a/gcc/gimple-range.h b/gcc/gimple-range.h
index 6587e4923ff44e10826a697ecced237a0ad23c88..84eac87392b642ed3305011415c804f5b319e09f 100644
--- a/gcc/gimple-range.h
+++ b/gcc/gimple-range.h
@@ -101,5 +101,7 @@ protected:
   gori_compute m_gori;
 };
 
+bool arith_without_overflow_p (tree_code code, tree x, tree y, tree type);
+bool same_sign_p (tree x, tree y, tree type);
 
 #endif // GCC_GIMPLE_RANGE_H
diff --git a/gcc/match.pd b/gcc/match.pd
index 8543f777a28e4f39b2b2a40d0702aed88786bbb3..87e990c5b1ebbd116d7d7efdba62347d3a967cdd 100644
--- a/gcc/match.pd
+++ b/gcc/match.pd
@@ -942,6 +942,70 @@ DEFINE_INT_AND_FLOAT_ROUND_FN (RINT)
 #endif
    ))))
 
+#if GIMPLE
+(for div (trunc_div exact_div)
+ /* Simplify (t + M*N) / N -> t / N + M.  */
+ (simplify
+  (div (plus:c@4 @0 (mult:c@3 @1 @2)) @2)
+  (if (INTEGRAL_TYPE_P (type)
+       && arith_without_overflow_p (MULT_EXPR, @1, @2, type)
+       && arith_without_overflow_p (PLUS_EXPR, @0, @3, type)
+       && same_sign_p (@0, @4, type))
+  (plus (div @0 @2) @1)))
+
+ /* Simplify (t - M*N) / N -> t / N - M.  */
+ (simplify
+  (div (minus@4 @0 (mult:c@3 @1 @2)) @2)
+  (if (INTEGRAL_TYPE_P (type)
+       && arith_without_overflow_p (MULT_EXPR, @1, @2, type)
+       && arith_without_overflow_p (MINUS_EXPR, @0, @3, type)
+       && same_sign_p (@0, @4, type))
+  (minus (div @0 @2) @1))))
+
+/* Simplify
+   (t + C) / N -> t / N + C / N where C is multiple of N.
+   (t + C) >> N -> t >> N + C>>N if low N bits of C is 0.  */
+(for op (trunc_div exact_div rshift)
+ (simplify
+  (op (plus@3 @0 INTEGER_CST@1) INTEGER_CST@2)
+   (with
+    {
+      wide_int c = wi::to_wide (@1);
+      wide_int n = wi::to_wide (@2);
+      bool is_rshift = op == RSHIFT_EXPR;
+      bool neg_c = false;
+      bool ok = false;
+      if (INTEGRAL_TYPE_P (type))
+        {
+	  ok = is_rshift ? wi::ctz (c) >= n.to_shwi ()
+			 : wi::multiple_of_p (c, n, TYPE_SIGN (type));
+	  ok = ok && arith_without_overflow_p (PLUS_EXPR, @0, @1, type)
+	       && same_sign_p (@0, @3, type);
+
+	  /* Try check 'X + C' as 'X - -C' for unsigned.  */
+	  if (!ok && TYPE_UNSIGNED (type) && c.sign_mask () < 0)
+	    {
+	      neg_c = true;
+	      c = -c;
+	      ok = is_rshift ? wi::ctz (c) >= n.to_shwi ()
+			     : wi::multiple_of_p (c, n, UNSIGNED);
+	      value_range vr;
+	      ok = ok && get_range (vr, @0)
+		   && wi::geu_p (vr.lower_bound (), c);
+	    }
+	}
+    }
+   (if (ok)
+   (with
+    {
+      wide_int m;
+      m = is_rshift ? wi::rshift (c, n, TYPE_SIGN (type))
+		    : wi::div_trunc (c, n, TYPE_SIGN (type));
+      m = neg_c ? -m : m;
+    }
+   (plus (op @0 @2) { wide_int_to_tree(type, m); }))))))
+#endif
+
 (for op (negate abs)
  /* Simplify cos(-x) and cos(|x|) -> cos(x).  Similarly for cosh.  */
  (for coss (COS COSH)
diff --git a/gcc/range-op.cc b/gcc/range-op.cc
index cb584314f4cfc93aeec50c7f888829997a7dc8eb..487e781a0cdfa39416589983a246327957c14d54 100644
--- a/gcc/range-op.cc
+++ b/gcc/range-op.cc
@@ -4311,6 +4311,83 @@ range_op_table::initialize_integral_ops ()
 
 }
 
+bool
+plus_without_overflow_p (value_range &vr0, value_range &vr1, tree type)
+{
+  wi::overflow_type ovf;
+  signop sgn = TYPE_SIGN (type);
+  wide_int wmax0 = vr0.upper_bound ();
+  wide_int wmax1 = vr1.upper_bound ();
+  wi::add (wmax0, wmax1, sgn, &ovf);
+  if (ovf != wi::OVF_NONE)
+    return false;
+
+  if (TYPE_UNSIGNED (type))
+    return true;
+
+  wide_int wmin0 = vr0.lower_bound ();
+  wide_int wmin1 = vr1.lower_bound ();
+  wi::add (wmin0, wmin1, sgn, &ovf);
+  if (ovf != wi::OVF_NONE)
+    return false;
+
+  return true;
+}
+
+bool
+minus_without_overflow_p (value_range &vr0, value_range &vr1, tree type)
+{
+  wi::overflow_type ovf;
+  signop sgn = TYPE_SIGN (type);
+  wide_int wmin0 = vr0.lower_bound ();
+  wide_int wmax1 = vr1.upper_bound ();
+  wi::sub (wmin0, wmax1, sgn, &ovf);
+  if (ovf != wi::OVF_NONE)
+    return false;
+
+  if (TYPE_UNSIGNED (type))
+    return true;
+
+  wide_int wmax0 = vr0.upper_bound ();
+  wide_int wmin1 = vr1.lower_bound ();
+  wi::sub (wmax0, wmin1, sgn, &ovf);
+  if (ovf != wi::OVF_NONE)
+    return false;
+
+  return true;
+}
+
+bool
+mult_without_overflow_p (value_range &vr0, value_range &vr1, tree type)
+{
+  wi::overflow_type ovf;
+  signop sgn = TYPE_SIGN (type);
+  wide_int wmax0 = vr0.upper_bound ();
+  wide_int wmax1 = vr1.upper_bound ();
+  wi::mul (wmax0, wmax1, sgn, &ovf);
+  if (ovf != wi::OVF_NONE)
+    return false;
+
+  if (TYPE_UNSIGNED (type))
+    return true;
+
+  wide_int wmin0 = vr0.lower_bound ();
+  wide_int wmin1 = vr1.lower_bound ();
+  wi::mul (wmin0, wmin1, sgn, &ovf);
+  if (ovf != wi::OVF_NONE)
+    return false;
+
+  wi::mul (wmin0, wmax1, sgn, &ovf);
+  if (ovf != wi::OVF_NONE)
+    return false;
+
+  wi::mul (wmax0, wmin1, sgn, &ovf);
+  if (ovf != wi::OVF_NONE)
+    return false;
+
+  return true;
+}
+
 #if CHECKING_P
 #include "selftest.h"
 
diff --git a/gcc/range-op.h b/gcc/range-op.h
index af94c2756a74f710aa50aec1ac3b3de5eeb43a8e..1697ce5464c0cc8fbfb86234137ba7cc23e10979 100644
--- a/gcc/range-op.h
+++ b/gcc/range-op.h
@@ -220,6 +220,10 @@ protected:
   range_operator *m_operator;
 };
 
+extern bool plus_without_overflow_p (value_range &, value_range &, tree);
+extern bool minus_without_overflow_p (value_range &, value_range &, tree);
+extern bool mult_without_overflow_p (value_range &, value_range &, tree);
+
 // Cast the range in R to TYPE if R supports TYPE.
 
 inline bool
diff --git a/gcc/value-query.h b/gcc/value-query.h
index d10c3eac1e2e6c477cbab026942a45b4fcc2ddce..cf488c7ea9bfc423fd3de9d2c743f71175804ae2 100644
--- a/gcc/value-query.h
+++ b/gcc/value-query.h
@@ -137,6 +137,16 @@ get_range_query (const struct function *fun)
   return (fun && fun->x_range_query) ? fun->x_range_query : &global_ranges;
 }
 
+/* Return true if there is range for "X" expression at "S" statement,
+   and the range is not varying and not undefined.   */
+
+inline bool
+get_range (vrange &r, tree x, gimple *s = NULL)
+{
+  return get_range_query (cfun)->range_of_expr (r, x, s) && !r.varying_p ()
+	 && !r.undefined_p ();
+}
+
 // Query the global range of NAME in function F.  Default to cfun.
 extern void gimple_range_global (vrange &v, tree name,
 				 struct function *f = cfun);
diff --git a/gcc/value-range.cc b/gcc/value-range.cc
index 011bdbdeae62845b5627a8dfa0d261370df7e5db..5ae4e044194326c24aab6babf8e0df3e4b313e98 100644
--- a/gcc/value-range.cc
+++ b/gcc/value-range.cc
@@ -313,6 +313,18 @@ add_vrange (const vrange &v, inchash::hash &hstate,
 
 } //namespace inchash
 
+bool
+irange::nonnegative_p () const
+{
+  return wi::ge_p (lower_bound (), 0, TYPE_SIGN (type ()));
+}
+
+bool
+irange::nonpositive_p () const
+{
+  return wi::le_p (upper_bound (), 0, TYPE_SIGN (type ()));
+}
+
 bool
 irange::supports_type_p (const_tree type) const
 {
diff --git a/gcc/value-range.h b/gcc/value-range.h
index 0170188201bc9b1c4e117661c9a62819dc1547c5..a12dea514e48cdd04a3cee5dc6304637e501d399 100644
--- a/gcc/value-range.h
+++ b/gcc/value-range.h
@@ -280,6 +280,8 @@ public:
   virtual bool singleton_p (tree *result = NULL) const override;
   bool singleton_p (wide_int &) const;
   bool contains_p (const wide_int &) const;
+  bool nonnegative_p () const;
+  bool nonpositive_p () const;
 
   // In-place operators.
   virtual bool union_ (const vrange &) override;
diff --git a/gcc/testsuite/gcc.dg/pr108757-1.c b/gcc/testsuite/gcc.dg/pr108757-1.c
new file mode 100644
index 0000000000000000000000000000000000000000..7908f4bdcb8e225fe311b668efbe8f6db525b4d5
--- /dev/null
+++ b/gcc/testsuite/gcc.dg/pr108757-1.c
@@ -0,0 +1,18 @@
+/* PR tree-optimization/108757 */
+/* { dg-do compile } */
+/* { dg-options "-O2 -fdump-tree-optimized" } */
+
+#include <limits.h>
+#define N 5
+#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 " = 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 0000000000000000000000000000000000000000..82bebd09944f0be2e0690c604723bfe6182acec3
--- /dev/null
+++ b/gcc/testsuite/gcc.dg/pr108757-2.c
@@ -0,0 +1,19 @@
+/* PR tree-optimization/108757 */
+/* { dg-do compile } */
+/* { dg-options "-O2 -fdump-tree-optimized -fwrapv" } */
+
+#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 " = x_\[0-9\]+\\(D\\) \\- " 3 "optimized" } } */
+/* { dg-final { scan-tree-dump-times " \\+ x_\[0-9\]+\\(D\\)" 3 "optimized" } } */
+
diff --git a/gcc/testsuite/gcc.dg/pr108757.h b/gcc/testsuite/gcc.dg/pr108757.h
new file mode 100644
index 0000000000000000000000000000000000000000..5550199c1ef952f54eaa83087cec25e992057c34
--- /dev/null
+++ b/gcc/testsuite/gcc.dg/pr108757.h
@@ -0,0 +1,233 @@
+#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;
+}
+
+UINT NOINLINE
+opt_u5 (UINT x, UINT n, UINT m)
+{
+  if (n > N || m > M)
+    return 0;
+  if (x < (M*N) - GAP)
+    return 0;
+  UINT a = x - (m * n);
+  UINT b = a / n;
+  return b + m;
+}
+
+UINT NOINLINE
+opt_u6 (UINT x, UINT n, UINT m)
+{
+  if (n > N || m > M)
+    return 0;
+  if (x > (UMAX - M*N) + GAP)
+    return 0;
+  UINT a = x + (m * n);
+  UINT b = a / n;
+  return b - m;
+}
+
+INT NOINLINE
+opt_s13 (INT x, INT n, INT m)
+{
+  if (n > N || m > M || n < 0 || m < 0)
+    return 0;
+  if (x < (M*N) - GAP)
+    return 0;
+  INT a = x - (m * n);
+  INT b = a / n;
+  return b + m;
+}
+
+INT NOINLINE
+opt_s14 (INT x, INT n, INT m)
+{
+  if (n > N || m > M || n < 0 || m < 0)
+    return 0;
+  if (x > -M*N + GAP)
+    return 0;
+  INT a = x + (m * n);
+  INT b = a / n;
+  return b - m;
+}
+
+INT
+opt_s15 (INT x, INT n, INT m)
+{
+  if (n > 0 || m > 0 || n < -N || m < -M)
+    return 0;
+  if (x < (M*N) - GAP)
+    return 0;
+  INT a = x - (m * n);
+  INT b = a / n;
+  return b + m;
+}
+
+INT NOINLINE
+opt_s16 (INT x, INT n, INT m)
+{
+  if (n > 0 || m > 0 || n < -N || m < -M)
+    return 0;
+  if (x < 0 || x > (IMAX - M*N) + GAP)
+    return 0;
+  INT a = x + (m * n);
+  INT b = a / n;
+  return b - m;
+}
+
