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How is relative RIP addressing compared to mov reg, imm64?

It is known that x86-64 instructions do not support 64-bit immediate values ​​(except mov). Therefore, when transferring code from 32 to 64 bits, this instruction:

    cmp rax, addr32

cannot be replaced by the following:

    cmp rax, addr64

Under these conditions, I consider two alternatives: (a) using a zero register to load a constant, or (b) using relative addressing. These two approaches are as follows:

    mov r11, addr64 ; scratch register
    cmp rax, r11

ptr64: dq addr64

...
     cmp rax, [rel ptr64]    ; encoded as cmp rax, [rip+offset]

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true:  dq 0xFFFF0000FFFF0000
false: dq 0xAAAABBBBAAAABBBB

main:
    or rax, 1  ; rax is odd and constant "true" is even
    mov rcx, 0x1
    shl rcx, 30
branch:
    mov r11, 0xFFFF0000FFFF0000 ; not present in (b)
    cmp rax, r11                ; vs cmp rax, [rel true]
    je next
    add rax, 2
    loop branch

next:
    mov rax, 0
    ret
+1
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