  Past exam papers: Use of Numerical Analysis I for Floating Point Computation purposes
 NB this is the 2007 version; the 2008/09 course has two more lectures so that more questions are now doable.
 See notes on applicability of these questions at bottom of this page.
 1993 Paper 3 Question 10 e_min/e_max no longer taught explicitly, 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 roundtowardzero 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/e_max deemed no longer part of mainstream course.
 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/e_max deemed no longer part of mainstream course.
 1998 Paper 4 Question 9 no longer on course
 1999 Paper 3 Question 10 Just about doable,
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 e_min/e_max deemed no longer part of mainstream course.
 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 e_min/e_max deemed no longer part of mainstream course.
 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 e_min/e_max not taught explicitly, nor is infinitypropagation in part (b)
[but good for supervision purposes]
 2005 Paper 4 Question 7 Fine.
 2006 Paper 3 Question 6 Fine apart from
e_min/e_max deemed no longer part of mainstream course.
 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. The IEEE definition of symbols e_min and e_max were listed as
nonexaminable
because the IEEE standard is a bit counterintuitive 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 [outbyone] 
see the C standard library float.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 logicaltothiscourse 1.xxxxx*2^e.
