this is the simple program made in C for understanding how does multiplication work; booth algorithm
and this is a working half multiply in x86 assembly
multiply.half: /* multiplicand, multiplier */
cmp rax, 0
jz multiply.half.done
xor rcx, rcx /* initiate previous_number, ZERO */
mov rdx, rdi /* cast next_number, multiplier */
multiply.half.repeat:
mov rsi, rax /* cast argument_3, multiplicand */
and rsi, 1 /* and argument_2, LOWEST_BIT */
jz multiply.half.zero
add rcx, rdx /* ahead previous_number, next_number */
multiply.half.zero:
shl rdx, 1
shr rax, 1
jnz multiply.half.repeat
mov rax, rcx /* cast return_value, half_product */
multiply.half.done:
jmp r11 /* return */and this is a working full multiply in x86 assembly
multiply.full: /* multiplicand, multiplier */
xor rdx, rdx /* initiate return_value.high, 0 */
cmp rax, 0 /* compare multiplicand, 0 */
jz multiply.full.done
xor rsi, rsi /* initiate previous_number.low, 0 */
mov r9, rdi /* cast next_number.low, multiplier */
mov r10, rdi /* cast next_number.high, multiplier */
shr r10, 0x3F /* shift next_number.high, 0x3F --arithmaticly */
mov rcx, 0x3F /* initiate next_position.high, 0x3F */
multiply.full.repeat:
mov r8, rax /* cast argument_5, multiplicand */
and r8, 1 /* and argument_5, LOWEST_BIT */
jz multiply.full.zero
add rsi, r9 /* ahead previous_number.low, next_number.low */
adc rdx, r10 /* ahead previous_number.high, next_number.high --carry */
multiply.full.zero:
shl r9, 1 /* shift next_number.low, NEXT_POSITION --left */
mov r10, rdi /* cast next_number.high, multiplier */
shr r10, cl /* shift next_number.high, next_position.high --arithmaticly */
add rcx, -1 /* back next_position.high, 1 */
shr rax, 1 /* shift unsign_multipliicand, NEXT_BIT --right */
jnz multiply.full.repeat
mov rax, rsi /* cast return_value.low, previous_number.low */
multiply.full.done:
jmp r11 /* return */and this is a working full multiply unsign sign in x86 assembly
multiply.unsign_sign: /* unsign_multiplicand, sign_multiplier */
xor rdx, rdx /* initiate return_value.high, 0 */
cmp rax, 0 /* compare unsign_multiplicand, 0 */
jz multiply.unsign_sign.done
xor rsi, rsi /* initiate previous_number.low, 0 */
mov r9, rdi /* cast next_number.low, sign_multiplier */
mov r10, rdi /* cast next_number.high, sign_multiplier */
sar r10, 0x3F /* shift next_number.high, 0x3F --arithmaticly */
mov rcx, 0x3F /* initiate next_position.high, 0x3F */
multiply.unsign_sign.repeat:
mov r8, rax /* cast argument_5, unsign_multiplicand */
and r8, 1 /* and argument_5, LOWEST_BIT */
jz multiply.unsign_sign.zero
add rsi, r9 /* ahead previous_number.low, next_number.low */
adc rdx, r10 /* ahead previous_number.high, next_number.high --carry */
multiply.unsign_sign.zero:
shl r9, 1 /* shift next_number.low, NEXT_POSITION --left */
mov r10, rdi /* cast next_number.high, sign_multiplier */
sar r10, cl /* shift next_number.high, next_position.high --arithmaticly */
add rcx, -1 /* back next_position.high, 1 */
shr rax, 1 /* shift unsign_multipliicand, NEXT_BIT --right */
jnz multiply.unsign_sign.repeat
mov rax, rsi /* cast return_value.low, previous_number.low */
multiply.unsign_sign.done:
jmp r11 /* return */base on multiply unsign sign, we can do multiply both sign
multiply.sign: /* sign_multiplicand, sign_multiplier */
lea rsi, multiply.sign.both_sign[rip]
lea rcx, multiply.unsign_sign[rip]
mov -8[rsp], rcx /* write stack(table.jump_address.0), jump_address.unsign_sign */
mov -0x10[rsp], rsi /* write stack(table.jump_address.1), jump_address.sign_sign */
mov r10, rsp /* cast pointer.jump_address, stack_pointer */
mov rsi, rax /* cast sign_checker, sign_multiplicand */
sar rsi, 0x3F /* shift sign_checker, 0x3F --arithmatically */
shl rsi, 3 /* shift jump_offset, 3 --left */
add r10, rsi /* ahead pointer.jump_address, jump_offset */
mov r10, -8[r10] /* fetch jump_address, pointer.jump_address(-8) */
jmp r10 /* go jump_address */
multiply.sign.both_sign:
mov -8[rsp], r11 /* write stack(BACKUP), return_address */
add rsp, -8 /* ahead stack_pointer, -8 */
lea r11, multiply.sign.return_point.0[rip]
jmp multiply.unsign_sign /* go multiply.unsign_sign */
multiply.sign.return_point.0:
mov r9, rdi /* cast next_sign_high, sign_multiplier */
multiply.sign.repeat_high:
add rdx, r9 /* ahead sign_high, next_sigh_high */
shl r9, 1 /* shift next_sign_high, 1 --left */
jnz multiply.sign.repeat_high
mov r11, 0[rsp] /* read return_address, stack(BACKUP) */
add rsp, 8 /* ahead stack_pointer, 8 */
jmp r11 /* return */