ARSC T3D Users' Newsletter 9, October 21, 1994

List of Differences Between T3D and Y-MP

The current list of differences between the T3D and the Y-MP is:

  1. Data type sizes are not the same (Newsletter #5)
  2. Uninitialized variables are different (Newsletter #6)
  3. The effect of the -a static compiler switch (Newsletter #7)
  4. There is no GETENV on the T3D (Newsletter #8)
  5. Missing routine SMACH on T3D (Newsletter #9)
  6. Different Arithmetics (Newsletter #9)
I encourage users to e-mail in differences that they have found, so we all can benefit from each other's experience.

Missing Routine SMACH on the T3D

While coding up some exercises for the T3D class, I found an old friend missing. The routine SMACH was added to the BLAS routines when LINPACK came out in 1978. The routine interrogates the machine it's running on and can return three constants that describe the machine's arithmetic: EPS, TINY, HUGE. From the smach.f documentation we have:

  c     assume the computer has
  c
  c        b = base of arithmetic
  c        t = number of base  b  digits
  c        l = smallest possible exponent
  c        u = largest possible exponent
  c
  c     then
  c
  c        eps = b**(1-t)
  c        tiny = 100.0*b**(-l+t)
  c        huge = 0.01*b**(u-t)
Basically we have:

EPS is this definition of the machine epsilon TINY is close to the smallest machine representable number HUGE is close to the largest machine representable number

The Fortran version of the routine is available from netlib (anonymous ftp site: netlib2.cs.utk.edu).

But there is a better replacement for SMACH of LINPACK and that is SLAMCH of LAPACK. This routine, SLAMCH, is part of the T3D libraries. LAPACK is meant to be a replacement for the older linear algebra libraries LINPACK and EISPACK. SLAMCH works similar to SMACH by computationally interrogating the machine it's running on and returns a machine arithmetic constant. From the slamch.f documentation we have:


  *  SLAMCH determines single precision machine parameters.
  *
  *  Arguments
  *  =========
  *
  *  CMACH   (input) CHARACTER*1
  *          Specifies the value to be returned by SLAMCH:
  *          = 'E' or 'e',   SLAMCH := eps
  *          = 'S' or 's ,   SLAMCH := sfmin
  *          = 'B' or 'b',   SLAMCH := base
  *          = 'P' or 'p',   SLAMCH := eps*base
  *          = 'N' or 'n',   SLAMCH := t
  *          = 'R' or 'r',   SLAMCH := rnd
  *          = 'M' or 'm',   SLAMCH := emin
  *          = 'U' or 'u',   SLAMCH := rmin
  *          = 'L' or 'l',   SLAMCH := emax
  *          = 'O' or 'o',   SLAMCH := rmax
  *
  *  where
  *
  *    eps   = relative machine precision
  *    sfmin = safe minimum, such that 1/sfmin does not overflow
  *    base  = base of the machine
  *    prec  = eps*base
  *    t     = number of (base) digits in the mantissa
  *    rnd   = 1.0 when rounding occurs in addition, 0.0 else
  *    emin  = minimum exponent before (gradual) underflow
  *    rmin  = underflow threshold - base**(emin-1)
  *    emax  = largest exponent before overflow
  *    rmax  = overflow threshold  - (base**emax)*(1-eps)
So all of the functionality of SMACH and more is available in SLAMCH, which is available in the T3D libraries.

Arithmetic Differences Between Y-MP and T3D

With the above description of SMACH and SLAMCH, now is a good opportunity to describe some of the differences in the machine arithmetic between the Y-MP and the T3D. The machine arithmetic for the Y-MP was determined more than 20 years ago during the design of the CRAY-1. Since then, a lot has happened in machine arithmetic, most notably the publication of the IEEE Floating Point Standard 754 in 1981 and its acceptance in 1985. The Dec Alpha chip is implemented according to this new standard.

Using the above two functions we can see some of the differences between the arithmetics on each machine:


  from SMACH                       Y-MP               T3D

  eps = b**(1-t)          7.105427357601E-15    2.22044604925031308E-16
  tiny = 100.0*b**(-l+t)  1.2902840147914E-2450 4.00833672001794556E-290
  huge = 0.01*b**(u-t)    7.7502316430824E+2449 2.49480038691839982E+289

  from SLAMCH

  eps  =            7.105427357601E-15    1.11022302462515654E-16
  sfmin=            3.6672077351097E-2466 2.22507385850720138E-308
  base =            2.                    2.
  prec =            1.4210854715202E-14   2.22044604925031308E-16
  t    =           48.                   53.
  rnd  =            0.                    1. 
  emin =        -8192                 -1021
  rmin =            0.                    2.22507385850720138E-308
  emax =         8190                  1024
  rmax =            R                     1.79769313486231571E+308
All of these numbers were gotten from the Fortran versions available from netlib and printed out with a Fortran statement like:

  print *, SMACH( 1 )
All of the results from the Fortran version agreed with the answers from libsci on both machines. This is just part of the story of the numerical differences between the Y-MP and the T3D. We will discuss these numerical differences more in future newsletters.

PVM Between T3D and Y-MP

Last week I requested experience from our users on using the PVM encoding PvmDataRaw between the Y-MP and T3D. I have tried several test programs and the experience I have on available encodings is:

  Between T3D and T3D:
    PvmDataDefault  - slowest, loses precision
    PvmDataRaw      - fast
    PvmDataInplace  - fastest, but user needs to synchronize
  Between T3D and Y-MP:
    PvmDataDefault  - the only one available
After I finish teaching the T3D class, I'll report some timings for each of the above encodings.

ARSC Course Announcement

Title: Applications Programming On The Cray T3D Dates: October 31, November 1,2 Time: 9:00 AM - 12:00 M, 1:00 - 5:00 PM Location: University of Alaska Fairbanks main campus, room TBA Instructor: Mike Ess, Parallel Applications Specialist (ARSC) Course Description: An introduction to parallel programming on CRAY T3D Massively Parallel Processor (MPP). Data-sharing, work-sharing, and message-passing programming techniques will be described. The primary goal is to provide practical experience in implementing techniques that enhance overall code performance. These include performance tools for bottleneck determination, debugging and code development tools, and parallel processing principles. This class will have directed lab sessions and users will have an opportunity to have their applications examined with the instructor. Intended Audience: Researchers who will be developing programs to run on the CRAY T3D Massively Parallel Processor (MPP). Prerequisites: Applicants should have a denali userid or be in the process of applying for a userid. Applicants should be familiar with programming in Fortran or C on a UNIX system.

Application Procedure

There is no charge for attendance, but enrollment will be limited to 15. In the event of greater demand, applicants will be selected by ARSC staff based on qualifications, need and order of application.

Send e-mail to consult@arsc.edu with the following information:

  • course name
  • your name
  • UA status (e.g., undergrad, grad, Asst. Prof.)
  • institution/dept.
  • phone
  • advisor (if you are a student)
  • denali userid
  • preferred e-mail address
  • describe programming experience
  • describe need for this class

Request for References

I received a request for references that describe the T3D hardware that were not from CRI. The only one I know is a good two page description in:

  Advanced Computer Architecture, Kai Hwang, McGraw-Hill Inc., 1993
If you know of any other good publications about the T3D, e-mail the reference on to me and I'll send it on.

Jokes

Ron Renfrew, the ARSC Analyst in Charge from CRI passed along this quote:

Quote of the week, due to David Clark of MIT: "There is an old network saying: Bandwidth problems can be cured with money. Latency problems are harder because the speed of light is fixed--you can't bribe God."

We can expand this list to include both networks and computers:


  Solved with money    To be solved by God
  -----------------    -------------------
  more bandwidth       latency beyond the speed of light
  more memory          infinite precision arithmetic
                       perfectly linear speedups
                       bug free code

Current Editors:
Ed Kornkven ARSC HPC Specialist ph: 907-450-8669
Kate Hedstrom ARSC Oceanographic Specialist ph: 907-450-8678
Arctic Region Supercomputing Center
University of Alaska Fairbanks
PO Box 756020
Fairbanks AK 99775-6020
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