![]() Portable algorithms that don't need (or benefit from) any HW supportĪ pre-populated table lookup method can be very fast if your CPU has a large cache and you are doing lots of these operations in a tight loop. C) might not expose any portable function that could use a CPU-specific popcount when there is one. But your compiler's choice of fallback for target CPUs that don't have hardware popcnt might not be optimal for your use-case. C++20 std::popcount(), or C++ std::bitset::count(), as a portable way to access builtin / intrinsic functions (see another answer on this question). Your compiler may know how to do something that's good for the specific CPU you're compiling for, e.g. The 'best' algorithm really depends on which CPU you are on and what your usage pattern is. ![]() Some other architectures may have a slow instruction implemented with a microcoded loop that tests a bit per cycle ( citation needed - hardware popcount is normally fast if it exists at all.). Instructions like x86's popcnt (on CPUs where it's supported) will almost certainly be fastest for a single integer. Some CPUs have a single built-in instruction to do it and others have parallel instructions which act on bit vectors. Simply multiple and divide the value as you encode and decode it.This is known as the ' Hamming Weight', 'popcount' or 'sideways addition'. What if you need more precision? The answer very similar to how we indexed or rounded big numbers. So far we have only dealt with rounded numbers. If you don’t expect negative numbers and need a bigger range, explicitly use unsigned int or unsigned long. The data types we used so far are all signed, which means all of the tricks work just as well for negative values. This does mean that for example in a word only 15 of the 16 bits are available for the actual number, limiting the range from 65536 to 32768. These set the highest (left-most) bit to 1 to indicate it’s a negative number. To tell the difference between -100 and 100 you will need a signed data type. myVal = (( long )( bytes ) << 24 ) + (( long )( bytes ) << 16 ) + (( long )( bytes ) << 8 ) + (( long )( bytes )) How to send negative numbers? # To indicate that you mean 11 in hex and not two bits or the number eleven, you prefix it with the 0x formatter. The above example translated to the decimal system and padded for readability would be: 255 240 015 017 The advantage is that it is shorter and explicit about the maximum value (257 is not an option). Wasn’t a byte a group of 8 0s and 1s? □ You’re totally right, but just like we already saw 11111111 translates to 255 in the good old decimal system, we can also translate it to FF in the hexadecimal system where each position has 16 (0-9 A-F) possible values. ![]() Often, you’ll see a group of bytes displayed as: FF F0 0F 11 See the pattern? The number of choices per position (n) to the power of the number of positions (r) is the number of permutations: n r. If we have a group of 3 bytes, this could either represent 3 values between 0 and 255, but also one single value between 7216 (256 3). Like a byte is a group of 8 bits, a buffer is a group of a pre-defined number of bytes. Think of buffer as just another word for an array, list, whatever resonates with your programming experience. Learn more on How Stuff Works: How Bits and Bytes Work and the Arduino Bit Math Tutorial to learn more about it. Puzzled? Remember that 3 decimal numbers also don’t just stand for 3 values between 0 and 9, but 1000 (10 3) permutations from 0(00) to 999. Thus, one byte can represent a decimal number between 0(00) and 255. A byte is not just 8 values between 0 and 1, but 256 (2 8) different combinations (rather permutations) ranging from 00000000 via e.g. A bit is the most basic unit and can be either 1 or 0. Even a single bit 1 would do! What is a byte? #Ī byte is a group of 8 bits. Fortunately, you don’t need a picture of that smart garage bin that needs to emptied. The unprecedented range of the LoRaWAN technology we build on comes at the cost of low bandwidth and limited airtime (the number times size of packages you send). This guide will help you encode different types of data in as little bytes possible. To send data back and forth over The Things Network you’ll need to use bytes.
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