[racket] Optimization; converting 'Float' to 'Fixnum' in Typed Racket

From: Robby Findler (robby at eecs.northwestern.edu)
Date: Sat Feb 18 23:14:05 EST 2012

What if his code used fx+ and friends instead of + and friends?


On Sat, Feb 18, 2012 at 10:04 PM, Vincent St-Amour <stamourv at ccs.neu.edu> wrote:
> At Sat, 18 Feb 2012 21:07:05 -0500,
> SF wrote:
>> I'm trying to optimize some code that processes a bunch of data,
>> basically image pixels, which currently takes on the order of several
>> seconds and seems like it should be much faster (important because
>> it's an interactive application). Coming from C++ I have a good idea
>> in my mind of how I'd write it with low-level operations. I read up on
>> Racket optimization. It is still somewhat unclear to me how Racket
>> deals with fixnums, flonums, unsafe operations, Typed Racket types,
>> and how it all fits together.
> Racket's unsafe operations do not perform any checks and guide the
> compiler's unboxing optimizations. Using them can lead to significant
> speedups.
> Typed Racket performs type-driven optimization when it can guarantee
> that doing so is safe. Most of its optimizations replace generic
> arithmetic with specialized unsafe operations. The performance
> benefits are equivalent to using unsafe operations manually. The
> advantage of using TR is that it won't introduce bugs by optimizing
> when it's not safe to do so.
> In practice, TR will optimize pretty much any floating-point
> computation. In the case of fixnum operations, it optimizes only when
> it can guarantee that no overflow will happen. This means that you may
> need to help it a bit if you want to get fixnum optimizations.
> To see how TR optimizes your code (for example, to make sure that you
> get all the optimizations you want), check out the "performance
> report" DrRacket tool.
>> I chose to optimize my program (partly
>> to learn how) incrementally, trying all the options, timing at every
>> step with debugging info turned off. This worked until I wanted to
>> convert Integers to Fixnums in Typed Racket (which has been giving me
>> much faster results than anything in untyped Racket).
> You don't need to convert between integers and fixnums. Fixnums are
> simply integers that are small enough to be represented as tagged
> machine integers. If an operation on fixnums would cause an overflow,
> the result is transparently promoted to a bignum instead.
> To use fixnums in TR, you can annotate your variables as being of
> `Fixnum' type. However, due to the promotion semantics, fixnums have
> pretty bad closure properties, which means that the result of, say,
> adding two fixnums is not guaranteed to be a fixnum itself and has to
> be given the `Integer' type.
> To help with this, TR provides an `Index' type which is for integers
> bounded by the length of the longest possible vector (smaller than a
> fixnum). Adding two of these is guaranteed to produce a `Fixnum'.
> The bottom line is that it's possible to get fixnum optimizations in
> TR, but since TR has to be conservative in order to be safe, sometimes
> you may have to use unsafe fixnum operations manually to get the
> performance you want.
>> The problem is that I can't find a way to convert a Float to a Fixnum,
>> only to an Integer. None of fl->fx, unsafe-fl->fx, or
>> fl->exact-integer work, as Type Checker tells me they're untyped
>> identifiers.
> That should work. I'll look into that.
> Vincent
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