Tim Peters wrote: > [Kay Schluehr] > > I concur and I wonder why CAS like e.g. Maple that represent floating > > point numbers using two integers [1] are neither awkward to use nor > > inefficient. > > My guess is that it's because you never timed the difference in Maple > -- or, perhaps, that you did, but misinterpreted the results. You > don't give any data, so it's hard to guess which. > > BTW, why do you think Maple's developers added the UseHardwareFloats option?
For no good reason at least not as a public interface. But since the value of UseHardwareFloats is deduced from the accuracy ( Digits environment variable ) a programmer has seldom to deal explicitely with UseHardwareFloats. That means he pays for accuracy only, what is the essential numerical information. I guess an analogy is the use of integers in Python with the differerence that precision is replaced by the amount of absolute value. The solution is so nice that I wonder why floats and decimals could not be unified in a similar way? > > According to the Python numeric experts one has to pay a > > high tradeoff between speed and accuracy. But as it seems it just > > compares two Python implementations ( float / decimal ) and does not > > compare those to approaches in other scientific computing systems. > > It's easy to find papers comparing the speed of HW and SW floating > point in Maple. Have you done that, Kay? O.K. you are right here. > For example, read: > > "Symbolic and Numeric Scientific Computation in Maple" > K.O. Geddes, H.Q. Le > http://www.scg.uwaterloo.ca/~kogeddes/papers/ICAAA02.ps > > Keith Geddes is a key figure in Maple's history and development, and > can hardly be accused of being a Python apologist ;-) Note that > Example 1.5 there shows a _factor_ of 47 speed gain from using HW > instead of SW floats in Maple, when solving a reasonably large system > of linear equations. So I'll ask again ;-): why do you think Maple's > developers added the UseHardwareFloats option? > > While that paper mentions the facility only briefly, Geddes and Zheng > give detailed analyses of the tradeoffs in Maple here: > > "Exploiting Fast Hardware Floating Point in High Precision Computation" > http://www.scg.uwaterloo.ca/~kogeddes/papers/TR200241.ps > > If you're uncomfortable reading technical papers, one bottom line is > that they show that the time required by Maple to do a floating-point > multiplication in software "is at least 1000 times larger" than doing > the same with UseHardwareFloats set to true (and Digits:=15 in both > cases). No, it's perfect, Tim. Thanks for the links. > > By the way one can also learn from Maple how accuracy can be adjusted > > practically. I never heard users complaining about that. > > It's easy to change the number of digits of precision in Python's > decimal module. If I remember correctly it was Steve Holden who complained that explaining accuracy by means of the decimal module would be a non issue for beginners in Python. I have nothing to complain here ( o.k. nesting two levels deep to set prec is less nice than having Digits offered by the CAS immediately. But this is more cosmetic ). Kay -- http://mail.python.org/mailman/listinfo/python-list
