machine number

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3 matching pages

1: 3.1 Arithmetics and Error Measures

… ► ►The set of machine numbers

\mathbb{R}_{{\rm fl}}

is the union of

0

and the set … ►The lower and upper bounds for the absolute values of the nonzero machine numbers are given by … ►

Rounding

… ►Interval arithmetic is intended for bounding the total effect of rounding errors of calculations with machine numbers. …

2: 27.15 Chinese Remainder Theorem

§27.15 Chinese Remainder Theorem

… ►This theorem is employed to increase efficiency in calculating with large numbers by making use of smaller numbers in most of the calculation. …Their product

m

has 20 digits, twice the number of digits in the data. … ►Even though the lengthy calculation is repeated four times, once for each modulus, most of it only uses five-digit integers and is accomplished quickly without overwhelming the machine’s memory. Details of a machine program describing the method together with typical numerical results can be found in Newman (1967). …

3: 27.16 Cryptography

§27.16 Cryptography

… ►The primes are kept secret but their product

n=pq

, an 800-digit number, is made public. …With the most efficient computer techniques devised to date (2010), factoring an 800-digit number may require billions of years on a single computer. For this reason, the codes are considered unbreakable, at least with the current state of knowledge on factoring large numbers. … ►If

p

and

q

are known,

s

and

y^{s}

can be determined (mod

n

) by straightforward calculations that require only a few minutes of machine time. …