diff --git a/doc/specs.md b/doc/specs.md
index c977f84..9328273 100644
--- a/doc/specs.md
+++ b/doc/specs.md
@@ -519,7 +519,7 @@ This instructions adds the values of two registers (modulo 2<sup>64</sup>). The
 These instructions output the high 64 bits of the whole 128-bit multiplication result. The result differs for signed and unsigned multiplication (IMULH is unsigned, ISMULH is signed). The variants with a register source operand perform a squaring operation if `dst` equals `src`.
 
 #### 5.2.6 IMUL_RCP
-This instruction multiplies the destination register by a reciprocal of `imm32` (the immediate value is zero-extended and treated as unsigned). The reciprocal is calculated as <code>rcp = 2<sup>x</sup> / imm32</code> by choosing the largest integer `x` such that <code>rcp < 2<sup>64</sup></code>. If `imm32` equals 0, IMUL_RCP is a no-op.
+If `imm32` equals 0 or is a power of 2, IMUL_RCP is a no-op. In other cases, the instruction multiplies the destination register by a reciprocal of `imm32` (the immediate value is zero-extended and treated as unsigned). The reciprocal is calculated as <code>rcp = 2<sup>x</sup> / imm32</code> by choosing the largest integer `x` such that <code>rcp < 2<sup>64</sup></code>.
 
 #### 5.2.7 INEG_R
 Performs two's complement negation of the destination register.
@@ -607,7 +607,7 @@ This instruction performs a conditional jump in the Program Buffer. It uses an i
 A register is considered as modified by an instruction in the following cases:
 
 * It is the destination register of an integer instruction except IMUL_RCP and ISWAP_R.
-* It is the destination register of IMUL_RCP and `imm32` is not zero.
+* It is the destination register of IMUL_RCP and `imm32` is not zero or a power of 2.
 * It is the source or the destination register of ISWAP_R and the destination and source registers are distinct.
 * The CBRANCH instruction is considered to modify all integer registers.
 
diff --git a/src/assembly_generator_x86.cpp b/src/assembly_generator_x86.cpp
index 030ea60..4af5b73 100644
--- a/src/assembly_generator_x86.cpp
+++ b/src/assembly_generator_x86.cpp
@@ -428,9 +428,10 @@ namespace randomx {
 	}
 
 	void AssemblyGeneratorX86::h_IMUL_RCP(Instruction& instr, int i) {
-		if (instr.getImm32() != 0) {
+		uint64_t divisor = instr.getImm32();
+		if (!isPowerOf2(divisor)) {
 			registerUsage[instr.dst].lastUsed = i;
-			asmCode << "\tmov rax, " << randomx_reciprocal(instr.getImm32()) << std::endl;
+			asmCode << "\tmov rax, " << randomx_reciprocal(divisor) << std::endl;
 			asmCode << "\timul " << regR[instr.dst] << ", rax" << std::endl;
 			traceint(instr);
 		}
diff --git a/src/common.hpp b/src/common.hpp
index ccbd301..56023ce 100644
--- a/src/common.hpp
+++ b/src/common.hpp
@@ -126,6 +126,10 @@ namespace randomx {
 		return minIndex;
 	}
 
+	inline bool isPowerOf2(uint64_t x) {
+		return (x & (x - 1)) == 0;
+	}
+
 	constexpr int mantissaSize = 52;
 	constexpr int exponentSize = 11;
 	constexpr uint64_t mantissaMask = (1ULL << mantissaSize) - 1;
diff --git a/src/jit_compiler_x86.cpp b/src/jit_compiler_x86.cpp
index b8ae884..82a5503 100644
--- a/src/jit_compiler_x86.cpp
+++ b/src/jit_compiler_x86.cpp
@@ -266,8 +266,6 @@ namespace randomx {
 			SuperscalarProgram& prog = programs[j];
 			for (unsigned i = 0; i < prog.getSize(); ++i) {
 				Instruction& instr = prog(i);
-				instr.src %= RegistersCount;
-				instr.dst %= RegistersCount;
 				generateSuperscalarCode(instr, reciprocalCache);
 			}
 			emit(codeShhLoad, codeSshLoadSize);
@@ -614,10 +612,11 @@ namespace randomx {
 	}
 
 	void JitCompilerX86::h_IMUL_RCP(Instruction& instr, int i) {
-		if (instr.getImm32() != 0) {
+		uint64_t divisor = instr.getImm32();
+		if (!isPowerOf2(divisor)) {
 			registerUsage[instr.dst].lastUsed = i;
 			emit(MOV_RAX_I);
-			emit64(randomx_reciprocal(instr.getImm32()));
+			emit64(randomx_reciprocal(divisor));
 			emit(REX_IMUL_RM);
 			emitByte(0xc0 + 8 * instr.dst);
 		}
diff --git a/src/vm_interpreted.cpp b/src/vm_interpreted.cpp
index b24a275..ea85f60 100644
--- a/src/vm_interpreted.cpp
+++ b/src/vm_interpreted.cpp
@@ -435,8 +435,8 @@ namespace randomx {
 				} break;
 
 				CASE_REP(IMUL_RCP) {
-					uint32_t divisor = instr.getImm32();
-					if (divisor != 0) {
+					uint64_t divisor = instr.getImm32();
+					if (!isPowerOf2(divisor)) {
 						auto dst = instr.dst % RegistersCount;
 						ibc.type = InstructionType::IMUL_R;
 						ibc.idst = &r[dst];