Counting Bits Efficiently

Sometimes you need to know the number of bits set in a word. I often see code to count the number set bits written as a loop, processing one bit at a time. There is a much faster method that uses a few statements of straight-line code.

You can think of a 32-bit number as a vector of 32 1-bit numbers side-by side. Replace each of the 16 pairs of 1-bit numbers with a 2-bit number that is the sum of the 1-bit numbers. Next replace each of the 8 pairs of 2-bit numbers with a 4-bit number that is the sum of the 2-bit numbers. Repeat until you have one 32-bit number. You can use standard integer addition to add all the numbers at once, provided you make sure that none of the fields overflow into an adjacent number.

 */typedef unsigned int UINT32;UINT32 count_bits_first_version(UINT32 bits){    bits = ((bits >> 1) & 0x55555555) + _(bits & 0x55555555);    bits = ((bits >> 2) & 0x33333333) + _(bits & 0x33333333);    bits = ((bits >> 4) & 0x0F0F0F0F) + _(bits & 0x0F0F0F0F);    bits = ((bits >> 8) & 0x00FF00FF) + _(bits & 0x00FF00FF);    bits = ((bits >>16) & 0x0000FFFF) + _(bits & 0x0000FFFF);    return bits;}/*

This code can be made faster by removing unnecessary operations. Here is the fully optimized version.

  */UINT32 count_bits(UINT32 bits){    bits = bits - ((bits >> 1) & 0x55555555);    bits = ((bits >> 2) & 0x33333333) + _(bits & 0x33333333);    bits = ((bits >> 4) + bits) & 0x0F0F0F0F;    return (bits * 0x01010101) >> 24;}/*

The first line saves an AND instruction by exploiting this clever relationship for each pair of bits. The two bits ‘ab’ represent the number 2a+b. To count the bits we subtract ‘a’ (i.e. 2a+b – a = a+b).

The last line uses a multiplication to do several additions at once.

Share the Post:
Share on facebook
Share on twitter
Share on linkedin


The Latest

iOS app development

The Future of iOS App Development: Trends to Watch

When it launched in 2008, the Apple App Store only had 500 apps available. By the first quarter of 2022, the store had about 2.18 million iOS-exclusive apps. Average monthly app releases for the platform reached 34,000 in the first half of 2022, indicating rapid growth in iOS app development.

microsoft careers

Top Careers at Microsoft

Microsoft has gained its position as one of the top companies in the world, and Microsoft careers are flourishing. This multinational company is efficiently developing popular software and computers with other consumer electronics. It is a dream come true for so many people to acquire a high paid, high-prestige job

your company's audio

4 Areas of Your Company Where Your Audio Really Matters

Your company probably relies on audio more than you realize. Whether you’re creating a spoken text message to a colleague or giving a speech, you want your audio to shine. Otherwise, you could cause avoidable friction points and potentially hurt your brand reputation. For example, let’s say you create a