Computer LaboratoryComputer Science Past Papers: Use of Numerical Analysis I for Floating Point Computation purposes

 Home | Teaching | Past papers index | 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.

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