hao对《高效程序的奥秘》的笔记(1)

第10页 逻辑加减运算的恒等式

逻辑加减运算的恒等式
-x = ~x + 1 = ~(x - 1)
~x = -x - 1
-(~x) = x + 1
~(-x) = x - 1
x + y = x - (~y)  - 1 = (x ^ y) + 2*(x & y) = (x | y) + (x & y) = 2*(x | y) - (x ^ y)
x - y = x + ~y + 1 = (x ^ y) - 2*(~x & y) = (x & ~y) - (~x & y) = 2*(x & ~y) - (x ^ y)
x ^ y = (x | y) - (x & y)
x & ~y = (x | y) - y = x - (x & y)
~(x - y) = y - x - 1 = ~x + y
x 恒等于 y = (x & y) - (x | y) - 1 = (x & y) + ~(x | y) 
x | y = (x & ~y) + y
x & y = (~x | y) - ~x