Criticism of a proposed floating point (cs)prng requested.
in [Cryptography]
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From: Phoenix on 7 Jun 2010 05:45 On 7 Jun, 09:44, Mok-Kong Shen <mok-kong.s...(a)t-online.de> wrote: > Any floating point implementation covers of course only a finitely > many values (an extremely small part) of R and these values are > not uniformly distributed in the range implemented. Integers > implemented cover similarly only a small part of Z or N, but > the values are uniformly distributed in the range implemented. Why integers are uniformly distributed and fp not?
From: Tom St Denis on 7 Jun 2010 06:54 On Jun 7, 5:45 am, Phoenix <ribeiroa...(a)gmail.com> wrote: > On 7 Jun, 09:44, Mok-Kong Shen <mok-kong.s...(a)t-online.de> wrote: > > > Any floating point implementation covers of course only a finitely > > many values (an extremely small part) of R and these values are > > not uniformly distributed in the range implemented. Integers > > implemented cover similarly only a small part of Z or N, but > > the values are uniformly distributed in the range implemented. > > Why integers are uniformly distributed and fp not? Because some fractions are not easily representable in 2-adic terms. Tom
From: Phoenix on 7 Jun 2010 07:29 On 7 Jun, 11:54, Tom St Denis <t...(a)iahu.ca> wrote: > > Why integers are uniformly distributed and fp not? > > Because some fractions are not easily representable in 2-adic terms. > > Tom Well, with that assumption, we never have uniformly distribution in (0;1).
From: Mok-Kong Shen on 7 Jun 2010 07:33 Phoenix wrote: > Mok-Kong Shen wrote: > >> Any floating point implementation covers of course only a finitely >> many values (an extremely small part) of R and these values are >> not uniformly distributed in the range implemented. Integers >> implemented cover similarly only a small part of Z or N, but >> the values are uniformly distributed in the range implemented. > > Why integers are uniformly distributed and fp not? For integers on computers, the difference between neighbours is 1. For floating points, which consist of mantissa and exponent, the difference between neighbours depends on the exponent; the larger the exponent the larger the distance between them (when considered on the line of R). M. K. Shen
From: Noob on 7 Jun 2010 07:34
Phoenix wrote: > The incompatibility between i.e. (Intel/SUN) communications, is for > all areas (Chemistry, Trigonometry, Biology, Geometry, etc) or only > for crypto? > If answer is only for crypto, what is the solution to pass accurate > and compatible values in R from one system to another? You might be interested in reading Goldberg's famous paper. What Every Computer Scientist Should Know About Floating-Point Arithmetic http://docs.sun.com/source/806-3568/ncg_goldberg.html Regards. |