[seqfan] Re: Can this sequence be defined well: 7, 16, 34, ... ?

Joseph Myers jsm at polyomino.org.uk
Wed Apr 29 01:41:24 CEST 2020

On Tue, 28 Apr 2020, Alex Meiburg wrote:

> There is says that, in addition to DECIMAL32, DECIMAL64, and DECIMAL128,
> there is a k-bit decimal format for any k that is a multiple of *32* and
> >=128. This format always uses 15*k/16 - 10 bits of precision, and so has
> 9*k/32-2 bits of precision. Since allowed values of k go {32,64,128,

The restriction to >= 128 is only for binary interchange formats; IEEE 754 
defines decimal{k} for all k >= 32 and a multiple of 32.

For binary formats, binary16 has 11 bits of precision, binary32 has 24 
bits of precision, binary64 has 53 bits of precision, binary128 has 113 
bits of precision and in general binary{k}, for k >= 128 and a multiple of 
32, has k - round(4*log2(k)) + 13 bits of precision, where round() rounds 
to the nearest integer.

Joseph S. Myers
jsm at polyomino.org.uk

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