The conversion is free, at least on x86-like platforms, because there are no separate 32-bit and 64-bit registers. Instead, there is a fixed shared set of regis

The conversion is free, at least on x86-like platforms, because there are no separate 32-bit and 64-bit registers. Instead, there is a fixed shared set of registers, and the instructions signal whether they operate on the 32-bit or 64-bit value on it. When assigning to a register in 32-bit mode the top 32 bits are cleared, so if x and n were loaded into 32-bit registers, a 64-bit multiplication can be applied to it directly, without any conversion instructions.