Intel ARCHITECTURE IA-32 - Manual (Page 413)

64-bit Mode Coding Guidelines
8
8-5
IMUL RAX, RCX
The 64-bit version above is more efficient than using the following
32-bit version:
MOV EAX, DWORD PTR[X]
MOV ECX, DWORD PTR[Y]
IMUL ECX
In the 32-bit case above, EAX is required to be a source. The result ends
up in the EDX:EAX pair instead of in a single 64-bit register.
Assembly/Compiler Coding Rule
Use the 64-bit versions of multiply for 32-bit integer multiplies that require
a 64 bit result.
To add two 64-bit numbers in 32-bit legacy mode, the add instruction
followed by the addc instruction is used. For example, to add two 64-bit
variables (X and Y), the following four instructions could be used:
MOV EAX, DWORD PTR[X]
MOV EDX, DWORD PTR[X+4]
ADD EAX, DWORD PTR[Y]
ADC EDX, DWORD PTR[Y+4]
The result will end up in the two-register EDX:EAX.
In 64-bit mode, the above sequence can be reduced to the following:
MOV RAX, QWORD PTR[X]
ADD RAX, QWORD PTR[Y]
The result is stored in rax. One register is required instead of two.
Assembly/Compiler Coding Rule
Use the 64-bit versions of add for 64-bit adds.