Limitations of ARM processor instruction immediate addressing

In the assembly language of the ARM processor, there is a provision for constant expressions in the instruction syntax format: "The constant must correspond to an 8-bit bitmap, that is, the constant is obtained by cyclically shifting an even number of bits of an 8-bit constant."

Given an immediate number, judging whether it is legal can be divided into three steps: first, write the given immediate number in 32-bit binary form; then see if an 8-bit binary number can be used to include all the parts containing 1, if not, it is illegal; finally, see if this 8-bit binary number can be cyclically right-shifted by an even number of bits to obtain the given immediate number, if not, it is illegal.

0xff=00000000  00000000  00000000  111111111: equivalent to the 8-bit binary 11111111 shifted right by 0 bits, which is legal;

0x104=00000000  00000000  00000001  00000100: equivalent to the 8-bit binary 01000001 shifted right 2 bits, legal;

0x101=00000000  00000000  00000001  00000001: The part containing all 1s is 100000001, which cannot be represented by an 8-bit binary number and is illegal.

0x102=00000000  00000000  00000001  00000010: The part containing all 1s is 10000001, but 10000001 can only be cyclically right-shifted by odd bits to get the given number, which is illegal;

0xfC000002  =11111100  00000000  00000000  00000010: equivalent to the 8-bit binary number 10111111 circularly shifted right by 6 bits, which is legal.

0x8000007E=10000000  00000000  00000000  01111110: The part containing all 1s is 11111101, but 10000001 can only be rotated right by odd bits to get the given number, which is illegal.

Summary: First, to determine whether a number conforms to the principle of 8-bit bitmap, first check whether the number of 1s does not exceed 8 after the number is converted into binary. If not, check whether these n 1s (n<=8) can be put into 8 binary bits at the same time. If they can be put in, check whether these eight binary bits can be cyclically right-shifted by even bits to get the value that was initially judged. If so, this value conforms to the principle of 8-bit bitmap, otherwise, it does not conform. Second, it is impossible to represent an arbitrary 32-bit number with a 12-bit code. Only part of the 32-bit number can be obtained by cyclically right-shifting the even bits of the eight-bit binary number. The rest of the 32-bit numbers that cannot be represented can only be obtained through other means. For example, 0xffffff00 can be obtained by bitwise inversion of 0x000000ff.