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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.
The register width of a processor determines the range of values that can be represented in its registers. Though the vast majority of computers can perform multiple-precision arithmetic on operands in memory, allowing numbers to be arbitrarily long and overflow to be avoided, the register width limits the sizes of numbers that can be operated on (e.g., added or subtracted) using a single ...
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 server successfully processed the request, asks that the requester reset its document view, and is not returning any content. 206 Partial Content The server is delivering only part of the resource (byte serving) due to a range header sent by the client. The range header is used by HTTP clients to enable resuming of interrupted downloads, or ...
Arbitrary-precision arithmetic can also be used to avoid overflow, which is an inherent limitation of fixed-precision arithmetic. Similar to an automobile's odometer display which may change from 99999 to 00000, a fixed-precision integer may exhibit wraparound if numbers grow too large to represent at the fixed level of precision.
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If the 2 bits after the sign bit are "11", then the 8-bit exponent field is shifted 2 bits to the right (after both the sign bit and the "11" bits thereafter), and the represented significand is in the remaining 21 bits. In this case there is an implicit (that is, not stored) leading 3-bit sequence "100" in the true significand:
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