🚀 go-pugleaf

In article <632@loligo.cc.fsu.edu>, mccalpin@loligo.cc.fsu.edu (John McCalpin) writes:
> In article <1262@l.cc.purdue.edu> cik@l.cc.purdue.edu (Herman Rubin) writes:
> 
> >Another example is floating point arithmetic.  The RISCy CRAY, on problems
> >with rigid vectors, will run rings around the CYBER 205 in single precision
> >floating point (around 14 digits).  If we now change to double precision,
> >we not get a time factor of about 15 in favor of the CYBER.  Many problems
> >in which non-rigid vectors are appropriate also favor the CYBER.
> 
> >Herman Rubin, Dept. of Statistics,hrubin@l.cc.purdue.edu
> 
> (1) What is a "rigid vector"?

Rigid vector operations are those in which the position of an element
is essentially unchanged, except by scalar shifts.  Examples of non-
rigid vector operations are removing the elements of a vector corresponding
to 0's in a bit vector with subsequent shrinking of the length of the vector,
inserting the first elements for vector a in locations in vector b selected
by a bit vector, merging under control of a bit vector, etc.

> (2) On 64-bit vector operations with long vectors, the Crays do not
>     "run rings around" the Cyber 205.  The asymptotic speeds (MFLOPS) are:
> 		Cray-1		Cyber 205	Cray X/MP
> 		 160		   200		   235

Asymptotic speeds are much less often approximated on the CYBER, unfortunately.
The CYBER also can only do one vector operation at a time, but there is no
interference, in general, on the CYBER for vector and scalar.  I prefer the
CYBER myself, and I guess I took the most pessimistic view.  The actual
ratios depend on a lot of things.

> (3) Both the X/MP and 205 perform "double precision" (128-bit) arithmetic
>     in software, and experience a slow-down of close to a factor of 100
>     relative to 64-bit vector operations.

Double precision has 96 bits in the mantissa on the X/MP and 94 on the CYBER.*
If one is willing to lose 1-2 bit accuracy on the CYBER, the slow-down factor
can be reduced to around 5.  The CYBER has the direct capability of getting
both the most and least significant part of the sum or product, with two 
instruction calls, but no additional overhead, but the CRAYs only get the
most significant part; this is the biggest problem, and requires that half-
precision is used to get double precision.

*No flames, please.  There is disagreement on how the number of bits is to be
counted.  This is the number of significant bits in a sign-magnitude represent-
ation.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907
Phone: (317)494-6054
hrubin@l.cc.purdue.edu (Internet, bitnet, UUCP)