diff --git a/gcc/doc/invoke.texi b/gcc/doc/invoke.texi
index 80bc7fe41e05..050077389a59 100644
--- a/gcc/doc/invoke.texi
+++ b/gcc/doc/invoke.texi
@@ -3126,7 +3126,7 @@ errors if these functions are not inlined everywhere they are called.
 @itemx -fno-modules-ts
 @opindex fmodules-ts
 @opindex fno-modules-ts
-Enable support for C++20 modules (@xref{C++ Modules}).  The
+Enable support for C++20 modules (@pxref{C++ Modules}).  The
 @option{-fno-modules-ts} is usually not needed, as that is the
 default.  Even though this is a C++20 feature, it is not currently
 implicitly enabled by selecting that standard version.
@@ -33608,7 +33608,7 @@ version selected, although in pre-C++20 versions, it is of course an
 extension.
 
 No new source file suffixes are required or supported.  If you wish to
-use a non-standard suffix (@xref{Overall Options}), you also need
+use a non-standard suffix (@pxref{Overall Options}), you also need
 to provide a @option{-x c++} option too.@footnote{Some users like to
 distinguish module interface files with a new suffix, such as naming
 the source @code{module.cppm}, which involves
@@ -33670,8 +33670,8 @@ to be resolved at the end of compilation.  Without this, imported
 macros are only resolved when expanded or (re)defined.  This option
 detects conflicting import definitions for all macros.
 
-@xref{C++ Module Mapper} for details of the @option{-fmodule-mapper}
-family of options.
+For details of the @option{-fmodule-mapper} family of options,
+@pxref{C++ Module Mapper}.
 
 @menu
 * C++ Module Mapper::       Module Mapper
@@ -33888,8 +33888,8 @@ dialect used and imports of the module.@footnote{The precise contents
 of this output may change.} The timestamp is the same value as that
 provided by the @code{__DATE__} & @code{__TIME__} macros, and may be
 explicitly specified with the environment variable
-@code{SOURCE_DATE_EPOCH}.  @xref{Environment Variables} for further
-details.
+@code{SOURCE_DATE_EPOCH}.  For further details
+@pxref{Environment Variables}.
 
 A set of related CMIs may be copied, provided the relative pathnames
 are preserved.
diff --git a/gcc/doc/md.texi b/gcc/doc/md.texi
index 2b41cb7fb7bb..ed35b8f2e364 100644
--- a/gcc/doc/md.texi
+++ b/gcc/doc/md.texi
@@ -5776,11 +5776,13 @@ multiplication.
 @item @samp{smul@var{m}3_highpart}
 Perform a signed multiplication of operands 1 and 2, which have mode
 @var{m}, and store the most significant half of the product in operand 0.
-The least significant half of the product is discarded.
+The least significant half of the product is discarded.  This may be
+represented in RTL using a @code{smul_highpart} RTX expression.
 
 @cindex @code{umul@var{m}3_highpart} instruction pattern
 @item @samp{umul@var{m}3_highpart}
-Similar, but the multiplication is unsigned.
+Similar, but the multiplication is unsigned.  This may be represented
+in RTL using an @code{umul_highpart} RTX expression.
 
 @cindex @code{madd@var{m}@var{n}4} instruction pattern
 @item @samp{madd@var{m}@var{n}4}
diff --git a/gcc/doc/rtl.texi b/gcc/doc/rtl.texi
index e1e76a93a8b7..2058997f9e0d 100644
--- a/gcc/doc/rtl.texi
+++ b/gcc/doc/rtl.texi
@@ -2524,7 +2524,19 @@ not be the same.
 For unsigned widening multiplication, use the same idiom, but with
 @code{zero_extend} instead of @code{sign_extend}.
 
+@findex smul_highpart
+@findex umul_highpart
+@cindex high-part multiplication
+@cindex multiplication high part
+@item (smul_highpart:@var{m} @var{x} @var{y})
+@itemx (umul_highpart:@var{m} @var{x} @var{y})
+Represents the high-part multiplication of @var{x} and @var{y} carried
+out in machine mode @var{m}.  @code{smul_highpart} returns the high part
+of a signed multiplication, @code{umul_highpart} returns the high part
+of an unsigned multiplication.
+
 @findex fma
+@cindex fused multiply-add
 @item (fma:@var{m} @var{x} @var{y} @var{z})
 Represents the @code{fma}, @code{fmaf}, and @code{fmal} builtin
 functions, which compute @samp{@var{x} * @var{y} + @var{z}}
diff --git a/gcc/dwarf2out.c b/gcc/dwarf2out.c
index 9876750e4f9f..20f2c5da023f 100644
--- a/gcc/dwarf2out.c
+++ b/gcc/dwarf2out.c
@@ -16809,6 +16809,8 @@ mem_loc_descriptor (rtx rtl, machine_mode mode,
     case CONST_FIXED:
     case CLRSB:
     case CLOBBER:
+    case SMUL_HIGHPART:
+    case UMUL_HIGHPART:
       break;
 
     case CONST_STRING:
diff --git a/gcc/rtl.def b/gcc/rtl.def
index c80144b11325..5710a2e34551 100644
--- a/gcc/rtl.def
+++ b/gcc/rtl.def
@@ -467,6 +467,11 @@ DEF_RTL_EXPR(SS_MULT, "ss_mult", "ee", RTX_COMM_ARITH)
 /* Multiplication with unsigned saturation */
 DEF_RTL_EXPR(US_MULT, "us_mult", "ee", RTX_COMM_ARITH)
 
+/* Signed high-part multiplication.  */
+DEF_RTL_EXPR(SMUL_HIGHPART, "smul_highpart", "ee", RTX_COMM_ARITH)
+/* Unsigned high-part multiplication.  */
+DEF_RTL_EXPR(UMUL_HIGHPART, "umul_highpart", "ee", RTX_COMM_ARITH)
+
 /* Operand 0 divided by operand 1.  */
 DEF_RTL_EXPR(DIV, "div", "ee", RTX_BIN_ARITH)
 /* Division with signed saturation */
diff --git a/gcc/simplify-rtx.c b/gcc/simplify-rtx.c
index 16286befd79e..e4fae0b3e57f 100644
--- a/gcc/simplify-rtx.c
+++ b/gcc/simplify-rtx.c
@@ -4142,11 +4142,36 @@ simplify_context::simplify_binary_operation_1 (rtx_code code,
     case US_PLUS:
     case SS_MINUS:
     case US_MINUS:
+      /* Simplify x +/- 0 to x, if possible.  */
+      if (trueop1 == CONST0_RTX (mode))
+	return op0;
+      return 0;
+
     case SS_MULT:
     case US_MULT:
+      /* Simplify x * 0 to 0, if possible.  */
+      if (trueop1 == CONST0_RTX (mode)
+	  && !side_effects_p (op0))
+	return op1;
+
+      /* Simplify x * 1 to x, if possible.  */
+      if (trueop1 == CONST1_RTX (mode))
+	return op0;
+      return 0;
+
+    case SMUL_HIGHPART:
+    case UMUL_HIGHPART:
+      /* Simplify x * 0 to 0, if possible.  */
+      if (trueop1 == CONST0_RTX (mode)
+	  && !side_effects_p (op0))
+	return op1;
+      return 0;
+
     case SS_DIV:
     case US_DIV:
-      /* ??? There are simplifications that can be done.  */
+      /* Simplify x / 1 to x, if possible.  */
+      if (trueop1 == CONST1_RTX (mode))
+	return op0;
       return 0;
 
     case VEC_SERIES:
@@ -5012,6 +5037,51 @@ simplify_const_binary_operation (enum rtx_code code, machine_mode mode,
 	      }
 	    break;
 	  }
+
+	case SS_PLUS:
+	  result = wi::add (pop0, pop1, SIGNED, &overflow);
+ clamp_signed_saturation:
+	  if (overflow == wi::OVF_OVERFLOW)
+	    result = wi::max_value (GET_MODE_PRECISION (int_mode), SIGNED);
+	  else if (overflow == wi::OVF_UNDERFLOW)
+	    result = wi::min_value (GET_MODE_PRECISION (int_mode), SIGNED);
+	  else if (overflow != wi::OVF_NONE)
+	    return NULL_RTX;
+	  break;
+
+	case US_PLUS:
+	  result = wi::add (pop0, pop1, UNSIGNED, &overflow);
+ clamp_unsigned_saturation: 
+	  if (overflow != wi::OVF_NONE)
+	    result = wi::max_value (GET_MODE_PRECISION (int_mode), UNSIGNED);
+	  break;
+
+	case SS_MINUS:
+	  result = wi::sub (pop0, pop1, SIGNED, &overflow);
+	  goto clamp_signed_saturation;
+
+	case US_MINUS:
+	  result = wi::sub (pop0, pop1, UNSIGNED, &overflow);
+	  if (overflow != wi::OVF_NONE)
+	    result = wi::min_value (GET_MODE_PRECISION (int_mode), UNSIGNED);
+	  break;
+
+	case SS_MULT:
+	  result = wi::mul (pop0, pop1, SIGNED, &overflow);
+	  goto clamp_signed_saturation;
+
+	case US_MULT:
+	  result = wi::mul (pop0, pop1, UNSIGNED, &overflow);
+	  goto clamp_unsigned_saturation;
+
+	case SMUL_HIGHPART:
+	  result = wi::mul_high (pop0, pop1, SIGNED);
+	  break;
+
+	case UMUL_HIGHPART:
+	  result = wi::mul_high (pop0, pop1, UNSIGNED);
+	  break;
+
 	default:
 	  return NULL_RTX;
 	}
diff --git a/gcc/testsuite/gcc.target/i386/sse2-mmx-paddsb-2.c b/gcc/testsuite/gcc.target/i386/sse2-mmx-paddsb-2.c
new file mode 100644
index 000000000000..c677884ac5eb
--- /dev/null
+++ b/gcc/testsuite/gcc.target/i386/sse2-mmx-paddsb-2.c
@@ -0,0 +1,33 @@
+/* { dg-do compile } */
+/* { dg-options "-O2 -msse2" } */
+
+typedef char v8qi __attribute__ ((vector_size (8)));
+
+char foo()
+{
+  v8qi tx = { 1, 0, 0, 0, 0, 0, 0, 0 };
+  v8qi ty = { 2, 0, 0, 0, 0, 0, 0, 0 };
+  v8qi t = __builtin_ia32_paddsb(tx, ty);
+  return t[0];
+}
+
+char bar()
+{
+  v8qi tx = { 100, 0, 0, 0, 0, 0, 0, 0 };
+  v8qi ty = { 100, 0, 0, 0, 0, 0, 0, 0 };
+  v8qi t = __builtin_ia32_paddsb(tx, ty);
+  return t[0];
+}
+
+char baz()
+{
+  v8qi tx = { -100, 0, 0, 0, 0, 0, 0, 0 };
+  v8qi ty = { -100, 0, 0, 0, 0, 0, 0, 0 };
+  v8qi t = __builtin_ia32_paddsb(tx, ty);
+  return t[0];
+}
+
+/* { dg-final { scan-assembler-times "movl\[ \\t\]+\\\$3," 1 } } */
+/* { dg-final { scan-assembler-times "movl\[ \\t\]+\\\$127," 1 } } */
+/* { dg-final { scan-assembler-times "movl\[ \\t\]+\\\$-128," 1 } } */
+/* { dg-final { scan-assembler-not "paddsb\[ \\t\]+%xmm\[0-9\]+" } } */
diff --git a/gcc/testsuite/gcc.target/i386/sse2-mmx-paddusb-2.c b/gcc/testsuite/gcc.target/i386/sse2-mmx-paddusb-2.c
new file mode 100644
index 000000000000..b20891cf6939
--- /dev/null
+++ b/gcc/testsuite/gcc.target/i386/sse2-mmx-paddusb-2.c
@@ -0,0 +1,25 @@
+/* { dg-do compile } */
+/* { dg-options "-O2 -msse2" } */
+
+typedef char v8qi __attribute__ ((vector_size (8)));
+
+char foo()
+{
+  v8qi tx = { 1, 0, 0, 0, 0, 0, 0, 0 };
+  v8qi ty = { 2, 0, 0, 0, 0, 0, 0, 0 };
+  v8qi t = __builtin_ia32_paddusb(tx, ty);
+  return t[0];
+}
+
+char bar()
+{
+  v8qi tx = { 200, 0, 0, 0, 0, 0, 0, 0 };
+  v8qi ty = { 200, 0, 0, 0, 0, 0, 0, 0 };
+  v8qi t = __builtin_ia32_paddusb(tx, ty);
+  return t[0];
+}
+
+/* { dg-final { scan-assembler-times "movl\[ \\t\]+\\\$3," 1 } } */
+/* { dg-final { scan-assembler-times "movl\[ \\t\]+\\\$-1," 1 } } */
+/* { dg-final { scan-assembler-not "paddusb\[ \\t\]+%xmm\[0-9\]+" } } */
+
diff --git a/gcc/testsuite/gcc.target/i386/sse2-mmx-psubsb-2.c b/gcc/testsuite/gcc.target/i386/sse2-mmx-psubsb-2.c
new file mode 100644
index 000000000000..4fc292079d13
--- /dev/null
+++ b/gcc/testsuite/gcc.target/i386/sse2-mmx-psubsb-2.c
@@ -0,0 +1,33 @@
+/* { dg-do compile } */
+/* { dg-options "-O2 -msse2" } */
+
+typedef char v8qi __attribute__ ((vector_size (8)));
+
+char foo()
+{
+  v8qi tx = { 5, 0, 0, 0, 0, 0, 0, 0 };
+  v8qi ty = { 2, 0, 0, 0, 0, 0, 0, 0 };
+  v8qi t = __builtin_ia32_psubsb(tx, ty);
+  return t[0];
+}
+
+char bar()
+{
+  v8qi tx = { -100, 0, 0, 0, 0, 0, 0, 0 };
+  v8qi ty = { 100, 0, 0, 0, 0, 0, 0, 0 };
+  v8qi t = __builtin_ia32_psubsb(tx, ty);
+  return t[0];
+}
+
+char baz()
+{
+  v8qi tx = { 100, 0, 0, 0, 0, 0, 0, 0 };
+  v8qi ty = { -100, 0, 0, 0, 0, 0, 0, 0 };
+  v8qi t = __builtin_ia32_psubsb(tx, ty);
+  return t[0];
+}
+
+/* { dg-final { scan-assembler-times "movl\[ \\t\]+\\\$3," 1 } } */
+/* { dg-final { scan-assembler-times "movl\[ \\t\]+\\\$-128," 1 } } */
+/* { dg-final { scan-assembler-times "movl\[ \\t\]+\\\$127," 1 } } */
+/* { dg-final { scan-assembler-not "paddsb\[ \\t\]+%xmm\[0-9\]+" } } */
diff --git a/gcc/testsuite/gcc.target/i386/sse2-mmx-psubusb-2.c b/gcc/testsuite/gcc.target/i386/sse2-mmx-psubusb-2.c
new file mode 100644
index 000000000000..5fc58ef40ff4
--- /dev/null
+++ b/gcc/testsuite/gcc.target/i386/sse2-mmx-psubusb-2.c
@@ -0,0 +1,25 @@
+/* { dg-do compile } */
+/* { dg-options "-O2 -msse2" } */
+
+typedef char v8qi __attribute__ ((vector_size (8)));
+
+char foo()
+{
+  v8qi tx = { 5, 0, 0, 0, 0, 0, 0, 0 };
+  v8qi ty = { 2, 0, 0, 0, 0, 0, 0, 0 };
+  v8qi t = __builtin_ia32_psubusb(tx, ty);
+  return t[0];
+}
+
+char bar()
+{
+  v8qi tx = { 100, 0, 0, 0, 0, 0, 0, 0 };
+  v8qi ty = { 200, 0, 0, 0, 0, 0, 0, 0 };
+  v8qi t = __builtin_ia32_psubusb(tx, ty);
+  return t[0];
+}
+
+/* { dg-final { scan-assembler-times "movl\[ \\t\]+\\\$3," 1 } } */
+/* { dg-final { scan-assembler-times "xorl\[ \\t\]+" 1 } } */
+/* { dg-final { scan-assembler-not "psubusb\[ \\t\]+%xmm\[0-9\]+" } } */
+