• Normalize to 0/1
• 0/1 to mask
• 0/1 to inverted mask
• Conditional bitwise not
• Conditional negate
• Conditional add/sub
• Conditional assign
• Absolute value
• Modulo with unsigned power of 2
• Modulo with signed power of 2
• Average without overflow
• Is an unsigned a power of 2

Bit tricks

A few bit trick for integer arithmetic, some are obvious but they are there because they are used as base for more complex stuff. Integers are assumed to be 32 bits, so you need to adujst some things for other sizes.

I got most of this stuff from The Multimedia Guru: http://guru.multimedia.cx

Normalize to 0/1

  r = !!a
  r = a != 0

0/1 to mask

  r = -a

0/1 to inverted mask

  r = a-1

Conditional bitwise not

  r = a ^ mask

Conditional negate

  r = (a+mask) ^ mask

Conditional add/sub

  r += a & mask

Conditional assign

  r = ((a ^ b) & mask) ^ b

Absolute value

  s = a >> 31
  r = (a+s) ^ s

Modulo with unsigned power of 2

  r = a & (b-1)

Modulo with signed power of 2

  s = a>>31
  r = ((((a+s) ^ s) & (b-1)) + s) ^ s

Average without overflow

  r = (a & b) + ((a ^ b) >> 1)

Is an unsigned a power of 2

  r = (a & (a-1)) == 0