• Contents
  • About the operation counting methodology
  • Compute the sign of an integer
  • Detect if two integers have opposite signs
  • Compute the integer absolute value (abs) without branching
  • Compute the minimum (min) or maximum (max) of two integers without branching
  • Determining if an integer is a power of 2
  • Sign extending
    • Sign extending from a constant bit-width
    • Sign extending from a variable bit-width
    • Sign extending from a variable bit-width in 3 operations
  • Conditionally set or clear bits without branching
  • Conditionally negate a value without branching
  • Merge bits from two values according to a mask
  • Counting bits set
    • Counting bits set, naive way
    • Counting bits set by lookup table
    • Counting bits set, Brian Kernighan’s way
    • Counting bits set in 14, 24, or 32-bit words using 64-bit instructions
    • Counting bits set, in parallel
    • Count bits set (rank) from the most-significant bit upto a given position
    • Select the bit position (from the most-significant bit) with the given count (rank)
  • Computing parity (1 if an odd number of bits set, 0 otherwise)
    • Compute parity of a word the naive way
    • Compute parity by lookup table
    • Compute parity of a byte using 64-bit multiply and modulus division
    • Compute parity of word with a multiply
    • Compute parity in parallel
  • Swapping Values
    • Swapping values with subtraction and addition
    • Swapping values with XOR
    • Swapping individual bits with XOR
  • Reversing bit sequences
    • Reverse bits the obvious way
    • Reverse bits in word by lookup table
    • Reverse the bits in a byte with 3 operations (64-bit multiply and modulus division)
    • Reverse the bits in a byte with 4 operations (64-bit multiply, no division)
    • Reverse the bits in a byte with 7 operations (no 64-bit, only 32)
    • Reverse an N-bit quantity in parallel with 5 * lg(N) operations
  • Modulus division (aka computing remainders)
    • Computing modulus division by 1 << s without a division operation (obvious)
    • Computing modulus division by (1 << s) - 1 without a division operation
    • Computing modulus division by (1 << s) - 1 in parallel without a division operation
  • Finding integer log base 2 of an integer (aka the position of the highest bit set)
    • Find the log base 2 of an integer with the MSB N set in O(N) operations (the obvious way)
    • Find the integer log base 2 of an integer with an 64-bit IEEE float
    • Find the log base 2 of an integer with a lookup table
    • Find the log base 2 of an N-bit integer in O(lg(N)) operations
    • Find the log base 2 of an N-bit integer in O(lg(N)) operations with multiply and lookup
  • Find integer log base 10 of an integer
  • Find integer log base 10 of an integer the obvious way
  • Find integer log base 2 of a 32-bit IEEE float
  • Find integer log base 2 of the pow(2, r)-root of a 32-bit IEEE float (for unsigned integer r)
  • Counting consecutive trailing zero bits (or finding bit indices)
    • Count the consecutive zero bits (trailing) on the right linearly
    • Count the consecutive zero bits (trailing) on the right in parallel
    • Count the consecutive zero bits (trailing) on the right by binary search
    • Count the consecutive zero bits (trailing) on the right by casting to a float
    • Count the consecutive zero bits (trailing) on the right with modulus division and lookup
    • Count the consecutive zero bits (trailing) on the right with multiply and lookup
  • Round up to the next highest power of 2 by float casting
  • Round up to the next highest power of 2
  • Interleaving bits (aka computing Morton Numbers)
    • Interleave bits the obvious way
    • Interleave bits by table lookup
    • Interleave bits with 64-bit multiply
    • Interleave bits by Binary Magic Numbers
  • Testing for ranges of bytes in a word (and counting occurances found)
    • Determine if a word has a zero byte
    • Determine if a word has a byte equal to n
    • Determine if a word has byte less than n
    • Determine if a word has a byte greater than n
    • Determine if a word has a byte between m and n
  • Compute the lexicographically next bit permutation