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Human interface device report descriptor bytes use a byte-count bitfield of 2 bits to encode the size of the following integer of zero, one, two, or four bytes, always little endian. Signedness, i.e. whether to expand the shortened integer with sign or not, depends on the descriptor type.
In particular, multiplying or adding two integers may result in a value that is unexpectedly small, and subtracting from a small integer may cause a wrap to a large positive value (for example, 8-bit integer addition 255 + 2 results in 1, which is 257 mod 2 8, and similarly subtraction 0 − 1 results in 255, a two's complement representation ...
A variable-length quantity (VLQ) is a universal code that uses an arbitrary number of binary octets (eight-bit bytes) to represent an arbitrarily large integer. A VLQ is essentially a base-128 representation of an unsigned integer with the addition of the eighth bit to mark continuation of bytes. VLQ is identical to LEB128 except in endianness ...
If we can store a lookup table of the hamming function of every 16 bit integer, we can do the following to compute the Hamming weight of every 32 bit integer. static uint8_t wordbits [ 65536 ] = { /* bitcounts of integers 0 through 65535, inclusive */ }; //This algorithm uses 3 arithmetic operations and 2 memory reads. int popcount32e ( uint32 ...
A Nivenmorphic number or harshadmorphic number for a given number base is an integer t such that there exists some harshad number N whose digit sum is t, and t, written in that base, terminates N written in the same base. For example, 18 is a Nivenmorphic number for base 10: 16218 is a harshad number 16218 has 18 as digit sum 18 terminates 16218
The same carry bit is also generally used to indicate borrows in subtraction, though the bit's meaning is inverted due to the effects of two's complement arithmetic. Normally, a carry bit value of "1" signifies that an addition overflowed the ALU, and must be accounted for when adding data words of lengths greater than that of the CPU. For ...
In number theory and computer science, the partition problem, or number partitioning, [1] is the task of deciding whether a given multiset S of positive integers can be partitioned into two subsets S 1 and S 2 such that the sum of the numbers in S 1 equals the sum of the numbers in S 2.
A fixed-point representation of a fractional number is essentially an integer that is to be implicitly multiplied by a fixed scaling factor. For example, the value 1.23 can be stored in a variable as the integer value 1230 with implicit scaling factor of 1/1000 (meaning that the last 3 decimal digits are implicitly assumed to be a decimal fraction), and the value 1 230 000 can be represented ...