source: project/release/4/numbers/trunk/NOTES @ 31494

Last change on this file since 31494 was 31494, checked in by sjamaan, 6 years ago

Numbers: Clarify treatment of extnums by analogy with srfi-4 vectors

File size: 5.0 KB
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1Some quick notes while everything's still fresh in my mind.  These
2might also be useful when integrating this in core.
3
4=== Integration of the numeric tower into the type system
5
6The basic idea in this code is that there are two distinct types of
7numbers: "basic" and "extended".  The basic numbers are the
8fundamental ones that have always been known by CHICKEN core, with the
9new addition of bignums.  The extended numbers exist *ONLY* in Scheme,
10which means that to C they're just structure/record objects (much like
11the way SRFI 4 vectors are currently handled in core as second-class
12citizens).  This rule is broken in only a handful of places (eqv, assq)
13for performance reasons.
14
15In the CHICKEN 4 numbers egg, this is faked out because we can't truly
16extend the core number types, so bignums are structures as well.  But
17for integration into core, this is changed to a true type.
18
19In intermediate versions of the "numbers" egg, we had to pass a
20failure continuation, which meant creating an extra closure object
21upon every call to numeric operations.  But now, in order to avoid any
22performance impact, the Scheme procedures are invoked as an
23"exception", much like the way the error handler is invoked through
24barf() in cases of error.  This allows us to only pass the arguments
25to a numeric operation, pretending the implementation is native C.
26
27=== Performance impact
28
29I've tried very hard to keep the performance of basic numeric
30operations exactly the same as in core.  In particular, the various
31checks for number types are done in exactly the same order as
32everywhere in core:
33
34- Is it a fixnum?
35- Is it an immediate?  If so, barf.
36- Does the header have a flonum tag? (before, this was combined with the immediate check)
37- Does the header have a bignum tag? (normally, we'd have an "else barf()" at this point)
38- Look up the numeric operation's matching Scheme procedure for extended numeric types, and call it (or barf, if it's not defined for these)
39
40This means that "generic" numeric code should incur ZERO performance
41penalty for functions that are non-allocating and inlineable....
42
43Unfortunately, that's where the good part ends.  Any operation that
44results in a fresh number is no longer inlineable, because in case of
45bignums they will need to allocate an unknown quantity of memory,
46which may require a GC.  The upshot is that every "allocating inline"
47procedure will now need to be called in primitive CPS context.  This
48is fundamental limitation that we can't do much about.
49
50In addition, the comparison functions (=, <, >, <=, >=) are no longer
51inline.  This is due to the fact that in order to correctly compare
52flonums, they need to be converted to a bignum and then compared.  We
53*could* decide to rip this out, but that would result in unexpected
54things, like: (< 19000000000000000.0 19000000000000001) => #f or
55(= 19000000000000000.0 190000000000000001) => #t
56These are currently the case, too.  This is due to precision loss from
57the fix->flo conversion (which means we drop from 62 bits to 54 bits).
58Because we _are_ comparing inexact numbers (which could already have
59lost information before comparing them), we could decide to ignore
60these edge cases and keep them like they are.  For the "=" function
61that would mean it can remain inlined and non-allocating.  For < and >,
62however, this doesn't help: in the case of ratnums we must multiply the
63numerator of x with the denominator of y and vice versa, and compare
64the results.  This means we're stuck with an allocating, non-inlineable
65function.  Because of this, I decided to keep the comparison functions
66all non-inlineable.
67
68Finally, the C implementation of the comparison functions as well as
69+, -, * and / are no longer vararg functions.  Instead, the variadic
70part is handled in Scheme, and the C implementation only compares two
71numbers at a time.  This shouldn't be too much of a performance impact
72considering they already have to be in CPS context anyway.  Plus,
73calls with two operations can easily be rewritten to a direct call,
74which leads us to...
75
76==== Specializations
77
78There's some light at the end of the tunnel: In critical
79number-crunching code, you'll usually be working with either integers
80or flonums (or you'd already be using the old numbers egg and
81everything would be shit-slow anyway).  These two situations are
82catered to specifically by specialized versions.  This is where the
83specialization/scrutiny stuff really shines: if we know something is a
84whole integer, we can use unsafe operations that only need to check a
85single bit to distinguish whether a number is fixnum or bignum, just
86like in the old situation we could this to distinguish between fixnum
87and flonum.
88
89This case should be easy to infer.  There's one caveat: do not use the
90"/" division operator, because this may result in a ratnum.  Instead,
91in fast code where you know you're dealing with integers, it's best to
92use "quotient", instead.  And of course, if you use the trigonometric
93operations you may get a flonum, which will also result in the generic
94number functions being used.
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