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The mapping of characters to code-points and back can be implemented in a number of ways. The simplest approach (akin to the original Luhn algorithm) is to use ASCII code arithmetic. For example, given an input set of 0 to 9, the code-point can be calculated by subtracting the ASCII code for '0' from the ASCII code of the desired character. The ...
The Luhn algorithm or Luhn formula, also known as the "modulus 10" or "mod 10" algorithm, named after its creator, IBM scientist Hans Peter Luhn, is a simple check digit formula used to validate a variety of identification numbers.
Comparison of Java and .NET platforms ALGOL 58's influence on ALGOL 60; ALGOL 60: Comparisons with other languages; Comparison of ALGOL 68 and C++; ALGOL 68: Comparisons with other languages; Compatibility of C and C++; Comparison of Pascal and Borland Delphi; Comparison of Object Pascal and C; Comparison of Pascal and C; Comparison of Java and C++
dload_2 28 0010 1000 → value load a double from local variable 2 dload_3 29 0010 1001 → value load a double from local variable 3 dmul 6b 0110 1011 value1, value2 → result multiply two doubles dneg 77 0111 0111 value → result negate a double drem 73 0111 0011 value1, value2 → result get the remainder from a division between two doubles
Modulo operations might be implemented such that a division with a remainder is calculated each time. For special cases, on some hardware, faster alternatives exist. For example, the modulo of powers of 2 can alternatively be expressed as a bitwise AND operation (assuming x is a positive integer, or using a non-truncating definition):
In computer science and mathematical logic, satisfiability modulo theories (SMT) is the problem of determining whether a mathematical formula is satisfiable.It generalizes the Boolean satisfiability problem (SAT) to more complex formulas involving real numbers, integers, and/or various data structures such as lists, arrays, bit vectors, and strings.
This power of 2 is multiplied (arithmetic modulo 2 32) by the de Bruijn sequence, thus producing a 32-bit product in which the bit sequence of the 5 MSBs is unique for each power of 2. The 5 MSBs are shifted into the LSB positions to produce a hash code in the range [0, 31], which is then used as an index into hash table BitPositionLookup.
Thus, a 123-bit shift register can be advanced 8 bits per iteration using only two-input XOR gates, the fastest possible. Finally the intermediate remainder can be reduced modulo the standard polynomial in a second slower shift register (once per CRC, rather than once per input byte) to yield the CRC-32 remainder. [13]