diff --git a/gas/config/tc-i386.c b/gas/config/tc-i386.c
index d98950c7dfd..6d6fc65383e 100644
--- a/gas/config/tc-i386.c
+++ b/gas/config/tc-i386.c
@@ -7208,6 +7208,43 @@ check_EgprOperands (const insn_template *t)
   return 0;
 }
 
+/* Optimize APX NDD insns to legacy insns.  */
+static bool
+convert_NDD_to_REX2 (const insn_template *t)
+{
+  if (t->opcode_modifier.vexvvvv == VexVVVV_DST
+      && t->opcode_space == SPACE_EVEXMAP4
+      && !i.has_nf
+      && i.reg_operands >= 2)
+    {
+      unsigned int readonly_var = ~0;
+      unsigned int dest = i.operands - 1;
+      unsigned int src1 = i.operands - 2;
+      unsigned int src2 = (i.operands > 3) ? i.operands - 3 : 0;
+
+      if (i.types[src1].bitfield.class == Reg
+	  && i.op[src1].regs == i.op[dest].regs)
+	readonly_var = src2;
+      /* adcx, adox and imul can't support to swap the source operands.  */
+      else if (i.types[src2].bitfield.class == Reg
+	       && i.op[src2].regs == i.op[dest].regs
+	       && optimize > 1
+	       && t->opcode_modifier.commutative)
+	readonly_var = src1;
+      if (readonly_var != (unsigned int) ~0)
+	{
+	  if (readonly_var != src2)
+	    swap_2_operands (readonly_var, src2);
+
+	  --i.operands;
+	  --i.reg_operands;
+
+	  return true;
+	}
+    }
+  return false;
+}
+
 /* Helper function for the progress() macro in match_template().  */
 static INLINE enum i386_error progress (enum i386_error new,
 					enum i386_error last,
@@ -7728,6 +7765,21 @@ match_template (char mnem_suffix)
 	  i.memshift = memshift;
 	}
 
+      /* If we can optimize a NDD insn to non-NDD insn, like
+	 add %r16, %r8, %r8 -> add %r16, %r8,
+	 add  %r8, %r16, %r8 -> add %r16, %r8, then rematch template.  
+	 Note that the semantics have not been changed.  */
+      if (optimize
+	  && !i.no_optimize
+	  && i.vec_encoding != vex_encoding_evex
+	  && t + 1 < current_templates->end
+	  && !t[1].opcode_modifier.evex
+	  && convert_NDD_to_REX2 (t))
+	{
+	  specific_error = progress (internal_error);
+	  continue;
+	}
+
       /* We've found a match; break out of loop.  */
       break;
     }
diff --git a/gas/testsuite/gas/i386/x86-64-apx-ndd-optimize.d b/gas/testsuite/gas/i386/x86-64-apx-ndd-optimize.d
new file mode 100644
index 00000000000..d13daed38b5
--- /dev/null
+++ b/gas/testsuite/gas/i386/x86-64-apx-ndd-optimize.d
@@ -0,0 +1,126 @@
+#as: -Os
+#objdump: -drw
+#name: x86-64 APX NDD optimized encoding
+#source: x86-64-apx-ndd-optimize.s
+
+.*: +file format .*
+
+
+Disassembly of section .text:
+
+0+ <_start>:
+\s*[a-f0-9]+:\s*d5 19 ff c7          	inc    %r31
+\s*[a-f0-9]+:\s*d5 11 fe c7          	inc    %r31b
+\s*[a-f0-9]+:\s*d5 4d 01 f8          	add    %r31,%r8
+\s*[a-f0-9]+:\s*d5 45 00 f8          	add    %r31b,%r8b
+\s*[a-f0-9]+:\s*d5 4d 01 f8          	add    %r31,%r8
+\s*[a-f0-9]+:\s*d5 1d 03 c7          	add    %r31,%r8
+\s*[a-f0-9]+:\s*d5 4d 03 38          	add    \(%r8\),%r31
+\s*[a-f0-9]+:\s*d5 1d 03 07          	add    \(%r31\),%r8
+\s*[a-f0-9]+:\s*49 81 c7 33 44 34 12 	add    \$0x12344433,%r15
+\s*[a-f0-9]+:\s*49 81 c0 11 22 33 f4 	add    \$0xfffffffff4332211,%r8
+\s*[a-f0-9]+:\s*d5 18 ff c9          	dec    %r17
+\s*[a-f0-9]+:\s*d5 10 fe c9          	dec    %r17b
+\s*[a-f0-9]+:\s*d5 18 f7 d1          	not    %r17
+\s*[a-f0-9]+:\s*d5 10 f6 d1          	not    %r17b
+\s*[a-f0-9]+:\s*d5 18 f7 d9          	neg    %r17
+\s*[a-f0-9]+:\s*d5 10 f6 d9          	neg    %r17b
+\s*[a-f0-9]+:\s*d5 1c 29 f9          	sub    %r15,%r17
+\s*[a-f0-9]+:\s*d5 14 28 f9          	sub    %r15b,%r17b
+\s*[a-f0-9]+:\s*62 54 84 18 29 38    	sub    %r15,\(%r8\),%r15
+\s*[a-f0-9]+:\s*d5 49 2b 04 07       	sub    \(%r15,%rax,1\),%r16
+\s*[a-f0-9]+:\s*d5 19 81 ee 34 12 00 00 	sub    \$0x1234,%r30
+\s*[a-f0-9]+:\s*d5 1c 19 f9          	sbb    %r15,%r17
+\s*[a-f0-9]+:\s*d5 14 18 f9          	sbb    %r15b,%r17b
+\s*[a-f0-9]+:\s*62 54 84 18 19 38    	sbb    %r15,\(%r8\),%r15
+\s*[a-f0-9]+:\s*d5 49 1b 04 07       	sbb    \(%r15,%rax,1\),%r16
+\s*[a-f0-9]+:\s*d5 19 81 de 34 12 00 00 	sbb    \$0x1234,%r30
+\s*[a-f0-9]+:\s*d5 1c 11 f9          	adc    %r15,%r17
+\s*[a-f0-9]+:\s*d5 14 10 f9          	adc    %r15b,%r17b
+\s*[a-f0-9]+:\s*4d 13 38             	adc    \(%r8\),%r15
+\s*[a-f0-9]+:\s*d5 49 13 04 07       	adc    \(%r15,%rax,1\),%r16
+\s*[a-f0-9]+:\s*d5 19 81 d6 34 12 00 00 	adc    \$0x1234,%r30
+\s*[a-f0-9]+:\s*d5 1c 09 f9          	or     %r15,%r17
+\s*[a-f0-9]+:\s*d5 14 08 f9          	or     %r15b,%r17b
+\s*[a-f0-9]+:\s*4d 0b 38             	or     \(%r8\),%r15
+\s*[a-f0-9]+:\s*d5 49 0b 04 07       	or     \(%r15,%rax,1\),%r16
+\s*[a-f0-9]+:\s*d5 19 81 ce 34 12 00 00 	or     \$0x1234,%r30
+\s*[a-f0-9]+:\s*d5 1c 31 f9          	xor    %r15,%r17
+\s*[a-f0-9]+:\s*d5 14 30 f9          	xor    %r15b,%r17b
+\s*[a-f0-9]+:\s*4d 33 38             	xor    \(%r8\),%r15
+\s*[a-f0-9]+:\s*d5 49 33 04 07       	xor    \(%r15,%rax,1\),%r16
+\s*[a-f0-9]+:\s*d5 19 81 f6 34 12 00 00 	xor    \$0x1234,%r30
+\s*[a-f0-9]+:\s*d5 1c 21 f9          	and    %r15,%r17
+\s*[a-f0-9]+:\s*d5 14 20 f9          	and    %r15b,%r17b
+\s*[a-f0-9]+:\s*4d 23 38             	and    \(%r8\),%r15
+\s*[a-f0-9]+:\s*d5 49 23 04 07       	and    \(%r15,%rax,1\),%r16
+\s*[a-f0-9]+:\s*d5 11 81 e6 34 12 00 00 	and    \$0x1234,%r30d
+\s*[a-f0-9]+:\s*d5 19 d1 cf          	ror    %r31
+\s*[a-f0-9]+:\s*d5 11 d0 cf          	ror    %r31b
+\s*[a-f0-9]+:\s*49 c1 cc 02          	ror    \$0x2,%r12
+\s*[a-f0-9]+:\s*41 c0 cc 02          	ror    \$0x2,%r12b
+\s*[a-f0-9]+:\s*d5 19 d1 c7          	rol    %r31
+\s*[a-f0-9]+:\s*d5 11 d0 c7          	rol    %r31b
+\s*[a-f0-9]+:\s*49 c1 c4 02          	rol    \$0x2,%r12
+\s*[a-f0-9]+:\s*41 c0 c4 02          	rol    \$0x2,%r12b
+\s*[a-f0-9]+:\s*d5 19 d1 df          	rcr    %r31
+\s*[a-f0-9]+:\s*d5 11 d0 df          	rcr    %r31b
+\s*[a-f0-9]+:\s*49 c1 dc 02          	rcr    \$0x2,%r12
+\s*[a-f0-9]+:\s*41 c0 dc 02          	rcr    \$0x2,%r12b
+\s*[a-f0-9]+:\s*d5 19 d1 d7          	rcl    %r31
+\s*[a-f0-9]+:\s*d5 11 d0 d7          	rcl    %r31b
+\s*[a-f0-9]+:\s*49 c1 d4 02          	rcl    \$0x2,%r12
+\s*[a-f0-9]+:\s*41 c0 d4 02          	rcl    \$0x2,%r12b
+\s*[a-f0-9]+:\s*d5 19 d1 e7          	shl    %r31
+\s*[a-f0-9]+:\s*d5 11 d0 e7          	shl    %r31b
+\s*[a-f0-9]+:\s*49 c1 e4 02          	shl    \$0x2,%r12
+\s*[a-f0-9]+:\s*41 c0 e4 02          	shl    \$0x2,%r12b
+\s*[a-f0-9]+:\s*d5 19 d1 ff          	sar    %r31
+\s*[a-f0-9]+:\s*d5 11 d0 ff          	sar    %r31b
+\s*[a-f0-9]+:\s*49 c1 fc 02          	sar    \$0x2,%r12
+\s*[a-f0-9]+:\s*41 c0 fc 02          	sar    \$0x2,%r12b
+\s*[a-f0-9]+:\s*d5 19 d1 e7          	shl    %r31
+\s*[a-f0-9]+:\s*d5 11 d0 e7          	shl    %r31b
+\s*[a-f0-9]+:\s*49 c1 e4 02          	shl    \$0x2,%r12
+\s*[a-f0-9]+:\s*41 c0 e4 02          	shl    \$0x2,%r12b
+\s*[a-f0-9]+:\s*d5 19 d1 ef          	shr    %r31
+\s*[a-f0-9]+:\s*d5 11 d0 ef          	shr    %r31b
+\s*[a-f0-9]+:\s*49 c1 ec 02          	shr    \$0x2,%r12
+\s*[a-f0-9]+:\s*41 c0 ec 02          	shr    \$0x2,%r12b
+\s*[a-f0-9]+:\s*62 74 9c 18 24 20 01 	shld   \$0x1,%r12,\(%rax\),%r12
+\s*[a-f0-9]+:\s*4d 0f a4 c4 02       	shld   \$0x2,%r8,%r12
+\s*[a-f0-9]+:\s*62 54 bc 18 24 c4 02 	shld   \$0x2,%r8,%r12,%r8
+\s*[a-f0-9]+:\s*62 74 b4 18 a5 08    	shld   %cl,%r9,\(%rax\),%r9
+\s*[a-f0-9]+:\s*d5 9c a5 e0          	shld   %cl,%r12,%r16
+\s*[a-f0-9]+:\s*62 7c 9c 18 a5 e0    	shld   %cl,%r12,%r16,%r12
+\s*[a-f0-9]+:\s*62 74 9c 18 2c 20 01 	shrd   \$0x1,%r12,\(%rax\),%r12
+\s*[a-f0-9]+:\s*4d 0f ac ec 01       	shrd   \$0x1,%r13,%r12
+\s*[a-f0-9]+:\s*62 54 94 18 2c ec 01 	shrd   \$0x1,%r13,%r12,%r13
+\s*[a-f0-9]+:\s*62 74 b4 18 ad 08    	shrd   %cl,%r9,\(%rax\),%r9
+\s*[a-f0-9]+:\s*d5 9c ad e0          	shrd   %cl,%r12,%r16
+\s*[a-f0-9]+:\s*62 7c 9c 18 ad e0    	shrd   %cl,%r12,%r16,%r12
+\s*[a-f0-9]+:\s*62 54 bd 18 66 c7    	adcx   %r15,%r8,%r8
+\s*[a-f0-9]+:\s*62 14 b9 18 66 04 3f 	adcx   \(%r15,%r31,1\),%r8,%r8
+\s*[a-f0-9]+:\s*62 54 bd 18 66 c8    	adcx   %r8,%r9,%r8
+\s*[a-f0-9]+:\s*62 54 be 18 66 c7    	adox   %r15,%r8,%r8
+\s*[a-f0-9]+:\s*62 14 ba 18 66 04 3f 	adox   \(%r15,%r31,1\),%r8,%r8
+\s*[a-f0-9]+:\s*62 54 be 18 66 c8    	adox   %r8,%r9,%r8
+\s*[a-f0-9]+:\s*67 0f 40 90 90 90 90 90 	cmovo  -0x6f6f6f70\(%eax\),%edx
+\s*[a-f0-9]+:\s*67 0f 41 90 90 90 90 90 	cmovno -0x6f6f6f70\(%eax\),%edx
+\s*[a-f0-9]+:\s*67 0f 42 90 90 90 90 90 	cmovb  -0x6f6f6f70\(%eax\),%edx
+\s*[a-f0-9]+:\s*67 0f 43 90 90 90 90 90 	cmovae -0x6f6f6f70\(%eax\),%edx
+\s*[a-f0-9]+:\s*67 0f 44 90 90 90 90 90 	cmove  -0x6f6f6f70\(%eax\),%edx
+\s*[a-f0-9]+:\s*67 0f 45 90 90 90 90 90 	cmovne -0x6f6f6f70\(%eax\),%edx
+\s*[a-f0-9]+:\s*67 0f 46 90 90 90 90 90 	cmovbe -0x6f6f6f70\(%eax\),%edx
+\s*[a-f0-9]+:\s*67 0f 47 90 90 90 90 90 	cmova  -0x6f6f6f70\(%eax\),%edx
+\s*[a-f0-9]+:\s*67 0f 48 90 90 90 90 90 	cmovs  -0x6f6f6f70\(%eax\),%edx
+\s*[a-f0-9]+:\s*67 0f 49 90 90 90 90 90 	cmovns -0x6f6f6f70\(%eax\),%edx
+\s*[a-f0-9]+:\s*67 0f 4a 90 90 90 90 90 	cmovp  -0x6f6f6f70\(%eax\),%edx
+\s*[a-f0-9]+:\s*67 0f 4b 90 90 90 90 90 	cmovnp -0x6f6f6f70\(%eax\),%edx
+\s*[a-f0-9]+:\s*67 0f 4c 90 90 90 90 90 	cmovl  -0x6f6f6f70\(%eax\),%edx
+\s*[a-f0-9]+:\s*67 0f 4d 90 90 90 90 90 	cmovge -0x6f6f6f70\(%eax\),%edx
+\s*[a-f0-9]+:\s*67 0f 4e 90 90 90 90 90 	cmovle -0x6f6f6f70\(%eax\),%edx
+\s*[a-f0-9]+:\s*67 0f 4f 90 90 90 90 90 	cmovg  -0x6f6f6f70\(%eax\),%edx
+\s*[a-f0-9]+:\s*67 0f af 90 09 09 09 00 	imul   0x90909\(%eax\),%edx
+\s*[a-f0-9]+:\s*d5 aa af 94 f8 09 09 00 00 	imul   0x909\(%rax,%r31,8\),%rdx
+\s*[a-f0-9]+:\s*48 0f af d0          	imul   %rax,%rdx
diff --git a/gas/testsuite/gas/i386/x86-64-apx-ndd-optimize.s b/gas/testsuite/gas/i386/x86-64-apx-ndd-optimize.s
new file mode 100644
index 00000000000..80c39059143
--- /dev/null
+++ b/gas/testsuite/gas/i386/x86-64-apx-ndd-optimize.s
@@ -0,0 +1,119 @@
+# Check 64bit APX NDD instructions with optimized encoding
+
+	.text
+_start:
+inc    %r31,%r31
+incb   %r31b,%r31b
+add    %r31,%r8,%r8
+addb   %r31b,%r8b,%r8b
+{store} add    %r31,%r8,%r8
+{load}  add    %r31,%r8,%r8
+add    %r31,(%r8),%r31
+add    (%r31),%r8,%r8
+add    $0x12344433,%r15,%r15
+add    $0xfffffffff4332211,%r8,%r8
+dec    %r17,%r17
+decb   %r17b,%r17b
+not    %r17,%r17
+notb   %r17b,%r17b
+neg    %r17,%r17
+negb   %r17b,%r17b
+sub    %r15,%r17,%r17
+subb   %r15b,%r17b,%r17b
+sub    %r15,(%r8),%r15
+sub    (%r15,%rax,1),%r16,%r16
+sub    $0x1234,%r30,%r30
+sbb    %r15,%r17,%r17
+sbbb   %r15b,%r17b,%r17b
+sbb    %r15,(%r8),%r15
+sbb    (%r15,%rax,1),%r16,%r16
+sbb    $0x1234,%r30,%r30
+adc    %r15,%r17,%r17
+adcb   %r15b,%r17b,%r17b
+adc    %r15,(%r8),%r15
+adc    (%r15,%rax,1),%r16,%r16
+adc    $0x1234,%r30,%r30
+or     %r15,%r17,%r17
+orb    %r15b,%r17b,%r17b
+or     %r15,(%r8),%r15
+or     (%r15,%rax,1),%r16,%r16
+or     $0x1234,%r30,%r30
+xor    %r15,%r17,%r17
+xorb   %r15b,%r17b,%r17b
+xor    %r15,(%r8),%r15
+xor    (%r15,%rax,1),%r16,%r16
+xor    $0x1234,%r30,%r30
+and    %r15,%r17,%r17
+andb   %r15b,%r17b,%r17b
+and    %r15,(%r8),%r15
+and    (%r15,%rax,1),%r16,%r16
+and    $0x1234,%r30,%r30
+ror    %r31,%r31
+rorb   %r31b,%r31b
+ror    $0x2,%r12,%r12
+rorb   $0x2,%r12b,%r12b
+rol    %r31,%r31
+rolb   %r31b,%r31b
+rol    $0x2,%r12,%r12
+rolb   $0x2,%r12b,%r12b
+rcr    %r31,%r31
+rcrb   %r31b,%r31b
+rcr    $0x2,%r12,%r12
+rcrb   $0x2,%r12b,%r12b
+rcl    %r31,%r31
+rclb   %r31b,%r31b
+rcl    $0x2,%r12,%r12
+rclb   $0x2,%r12b,%r12b
+sal    %r31,%r31
+salb   %r31b,%r31b
+sal    $0x2,%r12,%r12
+salb   $0x2,%r12b,%r12b
+sar    %r31,%r31
+sarb   %r31b,%r31b
+sar    $0x2,%r12,%r12
+sarb   $0x2,%r12b,%r12b
+shl    %r31,%r31
+shlb   %r31b,%r31b
+shl    $0x2,%r12,%r12
+shlb   $0x2,%r12b,%r12b
+shr    %r31,%r31
+shrb   %r31b,%r31b
+shr    $0x2,%r12,%r12
+shrb   $0x2,%r12b,%r12b
+shld   $0x1,%r12,(%rax),%r12
+shld   $0x2,%r8,%r12,%r12
+shld   $0x2,%r8,%r12,%r8
+shld   %cl,%r9,(%rax),%r9
+shld   %cl,%r12,%r16,%r16
+shld   %cl,%r12,%r16,%r12
+shrd   $0x1,%r12,(%rax),%r12
+shrd   $0x1,%r13,%r12,%r12
+shrd   $0x1,%r13,%r12,%r13
+shrd   %cl,%r9,(%rax),%r9
+shrd   %cl,%r12,%r16,%r16
+shrd   %cl,%r12,%r16,%r12
+adcx   %r15,%r8,%r8
+adcx   (%r15,%r31,1),%r8,%r8
+adcx   %r8,%r9,%r8
+adox   %r15,%r8,%r8
+adox   (%r15,%r31,1),%r8,%r8
+adox   %r8,%r9,%r8
+cmovo  0x90909090(%eax),%edx,%edx
+cmovno 0x90909090(%eax),%edx,%edx
+cmovb  0x90909090(%eax),%edx,%edx
+cmovae 0x90909090(%eax),%edx,%edx
+cmove  0x90909090(%eax),%edx,%edx
+cmovne 0x90909090(%eax),%edx,%edx
+cmovbe 0x90909090(%eax),%edx,%edx
+cmova  0x90909090(%eax),%edx,%edx
+cmovs  0x90909090(%eax),%edx,%edx
+cmovns 0x90909090(%eax),%edx,%edx
+cmovp  0x90909090(%eax),%edx,%edx
+cmovnp 0x90909090(%eax),%edx,%edx
+cmovl  0x90909090(%eax),%edx,%edx
+cmovge 0x90909090(%eax),%edx,%edx
+cmovle 0x90909090(%eax),%edx,%edx
+cmovg  0x90909090(%eax),%edx,%edx
+imul   0x90909(%eax),%edx,%edx
+imul   0x909(%rax,%r31,8),%rdx,%rdx
+imul   %rdx,%rax,%rdx
diff --git a/gas/testsuite/gas/i386/x86-64.exp b/gas/testsuite/gas/i386/x86-64.exp
index 668b366a212..eab99f9e52b 100644
--- a/gas/testsuite/gas/i386/x86-64.exp
+++ b/gas/testsuite/gas/i386/x86-64.exp
@@ -552,6 +552,7 @@ run_dump_test "x86-64-optimize-6"
 run_list_test "x86-64-optimize-7a" "-I${srcdir}/$subdir -march=+noavx -al"
 run_dump_test "x86-64-optimize-7b"
 run_list_test "x86-64-optimize-8" "-I${srcdir}/$subdir -march=+noavx2 -al"
+run_dump_test "x86-64-apx-ndd-optimize"
 run_dump_test "x86-64-align-branch-1a"
 run_dump_test "x86-64-align-branch-1b"
 run_dump_test "x86-64-align-branch-1c"
