Newsletter No. 68

CUHK Newsletter No. 68 19th April 1995 3 HOW TO PATCH UP A BUGGIN PROBLE Microsoft Corp. is having problems wi th its long-awaited Windows 95 operating system. But such hiccups are not new to the computer world. For instance, Intel, the wo r l d 's largest microprocessor chip company, has had problems with the Pentium— its flagship for the future. Prof. Nicely of Virginia, USA, discovered a discrepancy in the results given by the Pentium when dividing 4,195,835 by 3,145,727. Intel stated that the probability of encountering a wrong d i v i s i on is extremely low 一 only once in 27,000 years for an average user, and the problem has been fixed for Pentium chips produced since the discovery of the bug. While 'probability' can be controversial, it is proven mathematically that even in the worst case, roughly the first five significant decimal digits of the computed quotient can still be trusted. To put things in perspective, before the problem was discovered, the first 16 or so significant digits produced by the Pentium could always be trusted. Intel has had a number of people in- volved in helping it rectify the problem, both within and without the company. Included in the latter category is Dr. Peter Tang of the Department of Mathematics at CUHK, whose current research interests focus on numerical analysis, including computer arithmetic, signal and image processing, and wavelets. Dr. Tang joined the University in August 1994 as a visiting lecturer. He is a researcher at Argonne National Laboratory, a US Department of Energy supported institution in Chicago. Bom in Hong Kong, he went to the University of Hawaii for undergraduate studies in computer science and obtained his Ph.D. from the University of California in Berkeley. As a graduate student, through his work, publications and adviser, he met people at Intel who were, to quote Dr. Tang, 'interested in improving some of their technology using more up-to-date research .' Dr. Tang has subsequently been consulted by Intel for various projects, the latest being a solution to the Pentium problem. This July Dr. Tang and a collaborator, Tim Cole, who is a computer chip design engineer in California, will present a paper detailing their findings (the 'fast patch formula' ) vis- à -vis the Pentium problem at the IEEE International Symposium on Computer Arithmetic in Bath, England. Dr. Tang so explains their finding: on the screen of a scientific calculator, numbers in scientific format always look like X . XXXX . .. times an exponent of ten to the power of something. The first X is non-zero, that is, in the range 1 to 9 while the other Xs range from 0 to 9. On the Pentium, numbers are represented in base 2, and the binary digits (bits) can only be 0 or 1. So a number looks like ' l . XXXX . . .' because the first digit being non-zero forces it to be '1' always. Not all numerator-denominator pairs would yield wrong results on the Pentium. If you take the first five bits of the denominator in the form 'l.XXXX ...', you can find 16 possible patterns because each X can have two possibilities (0 or 1 ), two such Xs together give four possibilites and so on. Out of these 16 possible patterns, only five particular patterns can ever, if indeed they do, cause the division to fail. Consequently, if the denominator belongs to the other 11 patterns, it is safe to use the Pentium division. For denominators belonging to one of those five 'dangerous' patterns, one can prove that 15/16 times that denominator produces a number belonging to one of the 11 safe patterns. Consequently, dividing 15/16 times the numerator by 15/16 times the denominator is a safe act. On an average of five times out of 16,therefore, you use this alternative division to get round the bug. Is this the best we can do? Well, not quite. 'Wh i le the above "patch" is workable, it is too conservative,' Dr. Tang continues. It is like always avoiding the Lion Rock Tunnel when travelling from CUHK to Kowloon Tong during office hours because the Tunnel may have a traffic jam. Just as the alternative to the Lion Rock Tunnel is very slow if there is no jam in the first place, the alternative division described above is also very slow (for technical reasons related to the operating systems) if there is no problem in the first place. 'That the denominator belongs to one of those five dangerous zones does not mean that you will definitely have aproblem; just as the Lion Rock Tunnel is not always jammed during office hours.' Dr. Tang and Tim Cole have proved that, in order for the Pentium division to fail, the denominators have to be more special than just belong to one of those five zones — the six bits following the leading five must all be '1'. This means that you only need to use the alternative division on an average of five out of 1,024 times — an improvement of 64 times on the original solution. It is this finding that Dr. Tang and Cole will present in Bath this July. 'If you incorporate the 64 times improvement, the performance penalty is almost unnoticeable,' he said, the 'penalty' referring to the fact that the alternative division is a fair bit slower than a straightforward division. Dr. Tang feels that it is only 'eternal vigilance' which can help stave off such bugs in the future. Losses that companies like Intel and various users face through bugs like this are inestimable, for, 'the damage of confidence.. .of customers and potential customers...cannot be calculated on paper.' In this day and age, as society's dependence on sophisticated software and hardware in fields as divergent as medicine and financial markets continues to but increase, the emphasis on more foolproof control and testing mechanisms and systems cannot be overemphasize nor can be the importance of research, which adds many dimensions to the creation, implementation and usage of such mechanisms and systems. Shalini Bahadur O n the foggy spring evening of 29th March, Chinese and English poets and poetry enthusiasts gathered for three hours of poetry in the Shaw College lecture theatre. The occasion was the third annual Tolo Lights. It was Prof. Andrew Parkin of the English Department who came up with the idea of having regular poetry readings in the University. When he first arrived in Hong Kong, he was invited by some local English-speaking poets to contribute his works to an anthology of English poetry from Hong Kong they were compiling. According to Prof. Parkin, Vs. — 12 H.K. Poets was the first anthology of English poetry from the territory, or at least the first for many years. The compilers of the anthology also held a series of poetry readings entitled Tost 97 一 Partners in Rhyme' in Lan Kwai Fong in which Prof. Parkin took part. These activities inspired him to plan something similar in the University, especially since he discovered, to his pleasant surprise, that there were quite a number of poets among the CUHK staff. It would be an opportunity for them to read their material and perhaps bring poetry to the uninitiated corners of the University. He said, 'I thought since we're bilingual at CUHK, we should get Chinese and English writers together. Shaw College had just built a new lecture theatre, so I requested to use the theatre for a bilingual poetry evening.' Mr. K.F. Chor of the Dean of Students' Office at Shaw College came up with an apt name for the occasion. Hence, the first Tolo Lights on 1st March 1993. Prof. Parkin said the criterion for invitation is that the poets' works have to be published in one form or another, and in the case of student participants, to have 'gainedsome kind of recognition such as winning a prize at a poetry competition.' This year 18 poets read. With the exception of Dr. Wong Wai-leung who read a Shakespearean sonnet in English and Dr. P. K. Leung who read 'Bird Street', an English translation of one of his Chinese poems, all the English poets were expatriates living or working in Hong Kong. The Chinese part featured local writers and as visiting poet of the evening, renowned Taiwanese poet Shang Qin (商禽). The forms used varied from free verse to the strictly metrical. The subjects addressed were also diverse, often creating interesting juxtapositions ： an imagist poem describing awater-lily by Dr. Michele Chase of the ELT Unit side by side with a poem by a student who waxed lyrical about dracula. The event was rounded off by 'SongCycle for a Bereaved Mother' written in English by Wu Ningkun ( 巫寧坤), a Chinese teaching in America who read at last year's Tolo Lights, set to music and performed by a singer and pianist. At the end of the evening, the fog seemed to have lifted. As poets and audience left the theatre, the lights of Tolo Harbour were seen, distant yet distinct. The poets were, in order of appearance ： Madeleine Slavick Wong Leung-wo (王良和） Kwan Mung-Nan (關夢南） Robert Allinson Lau Chun-wai (劉俊偉） Li Yuen-mei (李婉薇） Barbara Baker Tu Chia-chi (杜家祁） Wong Wai-leung (黃維樑） Andrew Parkin P. K. Leung (梁秉鈞） Maureen Corner Lee Ching-yeung (李淸揚） John Dent-Young Gloria Chan (陳中熹） Michele Chase Lawrence Wong (王國彬） Shang Qin (商禽） Piera Chen