       Re: Dependence of precision on execution speed of Inverse

• To: mathgroup at smc.vnet.net
• Subject: [mg81749] Re: Dependence of precision on execution speed of Inverse
• From: Urijah Kaplan <uak at sas.upenn.edu>
• Date: Wed, 3 Oct 2007 02:20:07 -0400 (EDT)
• Organization: University of Pennsylvania
• References: <fdt3li\$rut\$1@smc.vnet.net>

```There's an extended (i.e. greater than 80 bit) precision reference
implementation of BLAS at http://crd.lbl.gov/~xiaoye/XBLAS/

Unfortunately, it only accepts single and double precision inputs, though
it can calculate in higher precision than that (106 bits). It's also a few
years old, and not as optimized as regular BLAS.

--Urijah Kaplan

>
> Ah I see, thanks for your reply Daniel. So the arbitrary precision numbers
> in Mathematica are each something like a struct with {a pointer to the
> arbitrary precision mantissa data, the exponent, the length of the mantissa
> data}; and because each element in a matrix could in principle have a
> *different* arbitrary precision, there's no way to pack the array into a
> contiguous lump of memory. So there's no way around de-referencing a lot of
> pointers.
>
> But Daniel, would you agree that for (hypothetical) *fixed* precision
> (across the whole matrix) non-machine-precision matrices of numbers, it
> *would* be possible to create the analogue of packed arrays and therefore
> make optimised routines to run on them, analogous to the routines that
> currently operate on packed arrays of machine-precision numbers? I guess one
> can write a code (in C++ or such) that can invert non-machine-precision
> matrices (and do other operations for which Mathematica employs packed
> arrays only for machine precision numbers) tens of times faster than
> Mathematica can, by combining something like the GNU multiple precision
> library (http://gmplib.org) with BLAS-like linear algebra code.
>
> I don't know how whether the efficiency of linear algebra at
> higher-than-machine-precision affects many users, but it has come up in my
> application so I am quite interested in the possibilities!
>
>

```

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