The purpose of this assignment is to help you get acquainted with pure object-oriented programming. The assignment is divided into three parts.
You will find a uSmalltalk interpreter in
~cs152/bin/usmalltalk; useful sources are in
~cs152/software/bare/usmalltalk and are part of the textbook software distribution.
This interpreter treats the variable
&trace specially; by defining it, you can trace message sends and answers.
It is an invaluable aid to debugging.
The textbook software distribution also includes
copies of the initial basis, collection classes, financial history,
and other examples from the textbook.
These examples can also be found in
To solve all four problems, you shouldn't need to add or change more than 20 lines of code in total.
<cache-printing function>= fun printCacheStats hits misses = app print ["\n[CACHE STATISTICS: ", Int.toString hits, " hits; ", Int.toString misses, " misses (hit rate ", Real.fmt (StringCvt.FIX (SOME 1)) (100.0 * real hits / real (hits + misses)), "%)]\n"]
For part 35(b) create a file
cachetests.smt that includes:
Notes and hints:
refworks in ML. Every call to
refdynamically allocates a new cell. If you call
reftoo few times, you will share too much mutable state and your code will have bugs. If you call
reftoo many times, you will share too little mutable state and you won't get enough hits in the cache.
classIdto find out if you have hit in the cache.
To implement method caching in an earlier version of uSmalltalk, I had to add or change about 40 lines of ML code.
Natural class is over 100 lines of uSmalltalk code;
my large-integer classes are 22 lines apiece.
My modifications to predefined number classes are about 25 lines.
You will find bignums and the bignum algorithms discussed at some length in Dave Hanson's book and in the article by Per Brinch Hansen. Be aware that your assignment below differs significantly from the implementation in Hanson's book.
decimalmethod must return a list of decimal digits, even if base 10 is not what is used in the representation. Suppress leading zeroes unless the value of
Naturalis itself zero.
XP_adddoes add with carry.
XP_subdoes subtract with borrow.
z := z + x * y, which is useful, but is not what we want unless
zis zero initially. Moreover, Hanson has to pass all the lengths explicitly.
Naturalis an immutable type. Your methods must not mutate existing natural numbers; you can only mutate a newly allocated number that you are sure has not been seen by any client.
digit:method carefully, you'll only have to worry about sizes when you allocate new results.
SmallInteger. In order to make your solution work with an unmodified usmalltalk, you must use this technique.
<fact.smt>= (define factorial (n) (if (strictlyPositive n) [(* n (value factorial (- n 1)))] )) (class Factorial Object () (classMethod printUpto: (limit) (locals n nfac) (begin (set n 1) (set nfac 1) (while [(<= n limit)] [(print n) (print #!) (print space) (print #=) (print space) (println nfac) (set n (+ n 1)) (set nfac (* n nfac))]))))
You might find it useful to test your implementation with the following table of factorials:
1! = 1 2! = 2 3! = 6 4! = 24 5! = 120 6! = 720 7! = 5040 8! = 40320 9! = 362880 10! = 3628800 11! = 39916800 12! = 479001600 13! = 6227020800 14! = 87178291200 15! = 1307674368000 16! = 20922789888000 17! = 355687428096000 18! = 6402373705728000 19! = 121645100408832000 20! = 2432902008176640000 21! = 51090942171709440000 22! = 1124000727777607680000 23! = 25852016738884976640000 24! = 620448401733239439360000 25! = 15511210043330985984000000Be warned that this test by itself is inadequate. You will want other tests.
If you want to make comparisons with a working implementation of
bignums, the languages Scheme, Icon, and Haskell all provide such
(Be aware that the real Scheme
define syntax is slightly different
from what we use in uScheme.)
b = 2and sometimes
b = 10, but when we want bignums, the choice of
bis hard to make in the general case:
b= 10, then converting to decimal representation is trivial, but storing bignums requires lots of memory.
bis, the less memory is required, and the more efficient everything is.
bis a power of 10, converting to decimal is relatively easy and is very efficient. Otherwise it requires (possibly long) division.
(b-1) * (b-1)fits in a machine word, than you can implement multiplication in high-level languages without difficulty. (Serious implementations pick the largest
a[i]is guaranteed to fit in a machine word, e.g.,
2^32on modern machines. Unfortunately, to work with such large values of
brequires special machine instructions to support ``add with carry'' and 64-bit multiply, so serious implementations have to be written in assembly language.)
bis a power of 2, bit-shift can be very efficient, but conversion to decimal is expensive. Fast bit-shift can be important in cryptographic and communications applications.
b's-complement. Knuth volume 2 is pretty informative about these topics.
For extra credit,
try the following variations on your implementation of class
baseand not any other code.) Measure the time needed to compute the first 50 factorials. Note both your measurements and your argument in your README file.
Naturaland for large integers. If this changes your argument for the largest possible base, explain how.
Change the base to the largest reasonable base, not necessarily a
power of 10.
You will have to re-implement
decimal using long division.
Measure the time needed to compute and print the first 50 factorials.
Does the smaller number of digits recoup the higher cost of converting
Make sure comparisons work, even with mixed kinds of integers.
So for example, make sure comparisons such as
(< 5 (* 1000000 1000000)) produce sensible answers.
to keep track of the size of numbers, and measure the
space cost of the different bases.
Estimate the difference in garbage-collection overhead for computing
with the different bases, given a fixed-size heap.
Pi (hard). Use a power series to compute the first 100 digits of pi (the ratio of a circle's circumference to its diameter). Be sure to cite your sources for the proper series approximation and its convergence properties. Hint: I vaguely remember that there's a faster convergence for pi over 4. Check with a numerical analyst.
basis.smtshowing whatever changes you had to make to the initial basis to do Exercises 4, 7(a), 11 and 27. Please be sure to identify your solutions using conspicuous comments, e.g.,
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;; ;;;; solution to Exercise 4 (class Array ... )
finhist.smtshowing your solution to Exercise 14.
bignum.smtshowing your solutions to Exercises 9 and 10. This file must work with an unmodified
usmalltalkinterpreter. Therefore, if for example you use results from problems 4, 7(a), 11, or any other problem (e.g., the class method
Arrayclass), you will need to duplicate those results in
bignum.smtas well as in
bigtests.smtshowing your solutions to Exercise T.
usmall.smlshowing your solution to Exercise 35.
cachetests.smtshowing your tests for Exercise 35(b).
cache.pdfexplaining your results for Exercise 35, parts (b) and (c). If you choose to submit this file late, you can email it to the course staff. Please be sure your mailer uses the correct MIME type!
Submit code using the submit-small script on nice.