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 do-able.
• 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 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/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 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 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 infinity-propagation 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 non-examinable 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 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 logical-to-this-course 1.xxxxx*2^e.