Home |
Teaching |
Past papers index |
- See notes on applicability of these questions at bottom of this page.
- 1993 Paper 3 Question 10 $p$ and $e_{min/max}$ not explicitly defined in course, but good for supervision work.
- 1993 Paper 4 Question 10 `condition' and `stability' not defined in course, but can be used for supervisior work.
- 1994 Paper 3 Question 9 no longer covered.
- 1994 Paper 4 Question 9 `guard digit' and `two most common forms of rounding' not lectured in quite this detail, but possible for supervision work (use IEEE unbiased and round-toward-zero for rounding).
- 1995 Paper 3 Question 10 `denormal number' not covered but otherwise OK.
- 1995 Paper 4 Question 10 no longer on course, but near enough that supervisors could cover.
- 1996 Paper 3 Question 10 OK apart from denorms and NaNs no longer expected known, $e_{min/max}$ not mentioned explicitly.
- 1996 Paper 4 Question 9 OK
- 1997 Paper 3 Question 10 OK
- 1997 Paper 4 Question 9 OK except for `unit round off' not taught.
- 1998 Paper 3 Question 10 OK apart from `denormal number' and $e_{min/max}$ not taught explicitly.
- 1998 Paper 4 Question 9 no longer on course
- 1999 Paper 3 Question 10 Just about do-able,
beta=10,p=4 means 'decimal 4 sig fig'. Guard digit not taught.
- 1999 Paper 4 Question 9 no longer on course
- 2000 Paper 3 Question 10 OK, but denormal and
the p/beta/$e_{min/max}$ notation no longer taught explicitly.
- 2000 Paper 4 Question 9 OK
- 2001 Paper 3 Question 10 Some useful exercised but NaN propagation not covered and denorm details not taught.
- 2001 Paper 4 Question 9 no longer on course
- 2002 Paper 3 Question 7 no longer on course
- 2002 Paper 4 Question 7 OK, except "guard digits" no longer taught
- 2003 Paper 3 Question 6 OK, except IEEE parameters p/beta/$e_{min/max}$ no longer taught explicitly
- 2003 Paper 4 Question 7 no longer on course
- 2004 Paper 3 Question 6 OK, but denormal details no longer, neither is "x*" notation.
- 2004 Paper 4 Question 7 no longer on course
- 2005 Paper 3 Question 6 OK, but denormal and p/beta/emin/emax not taught explicitly, nor is infinity-propagation in part (b)
[but good for supervision purposes]
- 2005 Paper 4 Question 7 Fine.
- 2006 Paper 3 Question 6 Fine apart from
emin/emax not taught explicitly
- 2006 Paper 4 Question 7 no longer on course
- Notes: 1. the understanding of 'guard digits' asked for in the above
questions refers to a form of hardware (e.g. IBM360/370)
prior to IEEE. IEEE requires
the operations to be performed to logical infinite precision before
being rounded on conversion to 32/64 bits.
2. Although not directly explained in the course, knowing that
IEEE single precision has beta=2 (binary base to exponent),
p=24 (23 stored digitis) helps you do many of the questions above.
The symbols e_min and e_max were not specifically lectured
because the IEEE standard is a bit counter-intuitive on their defns.
It's easy to
learn that expt = 011..111 represents 2^0, i.e. 1.000, so the
normalised IEEE numbers with this mantissa are 2^{-126}..2^{+127}
[and that's all you need for this course].
*HOWEVER* IEEE *defines* e_min=-125 and e_max=128 [out-by-one] --
see the C standard library stdio.h:
#define FLT_MIN_EXP (-125)
#define FLT_MAX_EXP 128
because it (the IEEE standard) writes 0.xxxxx*2^e
(of course the first x is '1')
instead of the more logical-to-this-course 1.xxxxx*2^e.
Don't worry about it!
|
