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Integer overflow can be demonstrated through an odometer overflowing, a mechanical version of the phenomenon. All digits are set to the maximum 9 and the next increment of the white digit causes a cascade of carry-over additions setting all digits to 0, but there is no higher digit (1,000,000s digit) to change to a 1, so the counter resets to zero.
This 128-bit quadruple precision is designed not only for applications requiring results in higher than double precision, [1] but also, as a primary function, to allow the computation of double precision results more reliably and accurately by minimising overflow and round-off errors in intermediate calculations and scratch variables.
32, 64, or 128 bits see Jenkins hash function: CityHash [4] 32, 64, 128, or 256 bits FarmHash [5] 32, 64 or 128 bits MetroHash [6] 64 or 128 bits numeric hash (nhash) [7] variable division/modulo xxHash [8] 32, 64 or 128 bits product/rotation t1ha (Fast Positive Hash) [9] 64 or 128 bits product/rotation/XOR/add GxHash [10] 32, 64 or 128 bits ...
On 5 January 1975, the 12-bit field that had been used for dates in the TOPS-10 operating system for DEC PDP-10 computers overflowed, in a bug known as "DATE75". The field value was calculated by taking the number of years since 1964, multiplying by 12, adding the number of months since January, multiplying by 31, and adding the number of days since the start of the month; putting 2 12 − 1 ...
The existing 64- and 128-bit formats follow this rule, but the 16- and 32-bit formats have more exponent bits (5 and 8 respectively) than this formula would provide (3 and 7 respectively). As with IEEE 754-1985, the biased-exponent field is filled with all 1 bits to indicate either infinity (trailing significand field = 0) or a NaN (trailing ...
In the following table, "s" is the value of the sign bit (0 means positive, 1 means negative), "e" is the value of the exponent field interpreted as a positive integer, and "m" is the significand interpreted as a positive binary number, where the binary point is located between bits 63 and 62.
The binary interchange formats have the "half precision" (16-bit storage format) and "quad precision" (128-bit format) added, together with generalized formulae for some wider formats; the basic formats have 32-bit, 64-bit, and 128-bit encodings. Three new decimal formats are described, matching the lengths of the 32–128-bit binary formats.
The lookup3 function consumes input in 12 byte (96 bit) chunks. [9] It may be appropriate when speed is more important than simplicity. Note, though, that any speed improvement from the use of this hash is only likely to be useful for large keys, and that the increased complexity may also have speed consequences such as preventing an optimizing compiler from inlining the hash function.