From: Stephen Adams Date: Tue, 31 Oct 1995 02:14:12 +0000 (+0000) Subject: Added some effiency tips about flonums. X-Git-Tag: 20090517-FFI~5813 X-Git-Url: https://birchwood-abbey.net/git?a=commitdiff_plain;h=dcf7d2b29bc2bba59dbd2e6ae8360b7f0ed9f8b5;p=mit-scheme.git Added some effiency tips about flonums. --- diff --git a/v7/doc/user-manual/user.texinfo b/v7/doc/user-manual/user.texinfo index 387835c36..e1d4c08c9 100644 --- a/v7/doc/user-manual/user.texinfo +++ b/v7/doc/user-manual/user.texinfo @@ -2,7 +2,7 @@ @iftex @finalout @end iftex -@comment $Id: user.texinfo,v 1.31 1995/10/30 21:37:29 adams Exp $ +@comment $Id: user.texinfo,v 1.32 1995/10/31 02:14:12 adams Exp $ @comment %**start of header (This is for running Texinfo on a region.) @setfilename user.info @settitle MIT Scheme User's Manual @@ -209,6 +209,7 @@ Efficiency Tips * Coding style:: * Global variables:: +* Fixnum arithmetic:: * Flonum arithmetic:: * Miscellaneous:: @@ -4013,6 +4014,7 @@ explanations useful. @menu * Coding style:: * Global variables:: +* Fixnum arithmetic:: * Flonum arithmetic:: * Miscellaneous:: @end menu @@ -4062,7 +4064,8 @@ There are two things tha make internal procedures faster: First, the procedure call is compiled to a direct jump to a known location, which is mare efficeint that jumping `via' a global binding. Second, there is a knock-on effect: since the compiler can see the -internal procedure it can analyze it and possibly produce better code. +internal procedure it can analyze it and possibly produce better code +for other expressions in the body of the loop too. @lisp (define (map f original-lst) @@ -4076,7 +4079,7 @@ internal procedure it can analyze it and possibly produce better code. @end lisp -@node Global variables, Flonum arithmetic, Coding style, Efficiency Tips +@node Global variables, Fixnum arithmetic, Coding style, Efficiency Tips @subsection Global variables @cindex variable caches @@ -4165,9 +4168,191 @@ For example, to ignore reference traps on all the variables except @end deffn -@node Flonum arithmetic, Miscellaneous, Global variables, Efficiency Tips + +@node Fixnum arithmetic, Flonum arithmetic, Global variables, Efficiency Tips +@subsection Fixnum arithmetic + +The usual arithmetic operations like @code{+} and @code{<} are called +generic arithmetic operations because they work for all (appropriate) +kinds of number. + +@cindex fixnum (defn) +A @dfn{fixnum} is an exact integer that is small enough to fit in a +machine word. In MIT Scheme, fixnums are typically 24 or 26 bits, +depending on the machine; it is reasonable to assume that fixnums are at +least 24 bits. Fixnums are signed; they are encoded using 2's +complement. + +All exact integers that are small enough to be encoded as fixnums are +always encoded as fixnums --- in other words, any exact integer that is +not a fixnum is too big to be encoded as such. For this reason, small +constants such as @code{0} or @code{1} are guaranteed to be fixnums. In +addition, the lengths of and valid indexes into strings and vectors are +also always fixnums. + +If you know that a value is always a small fixnum, you can substitute +the equivalent fixnum operation for the generic operation. However, +care should be exercised: if used improperly, these operations can +return incorrect answers, or even malformed objects that confuse the +garbage collector. The Scheme Reference Manual lists all the fixnum +operations. + +A fruitful area for inserting fixnum operations is in the index +operations in tight loops. + +Adding fixnum operations yourself is not always effective because the +compiler sometimes can figure out that a value just has to be a fixnum +and replaces the generic operation with the fixnum one. For example, in +the following code, the compiler knows that the result of +@code{vector-length} is always a fixnum, and so replaces @code{-} with +@code{fix:-}. + +@example +(define (last-index v) (- (vector-length v))) +@end example + +In the following example the compiler replaces @code{+} with +@code{fix:+} because it knows that if @var{k} was not a fixnum then the +@code{vector-ref} was an error: + +@example +(define (ref-inc v k) + (display (vector-ref v k)) + (+ k 1)) +@end example + +Unfortunately there is no reasonable way to tell which +operations the compiler replaces. + + +@node Flonum arithmetic, Miscellaneous, Fixnum arithmetic, Efficiency Tips @subsection Flonum arithmetic +!INCOMPLETE + +Getting efficient flonum arithmetic is much more complicated and harder +than getting efficient fixnum arithmetic. + +@subsubsection{Flonum consing} +@cindex flonum consing +One of the main disadvantages of generic arithmetic is that not all +kinds of number fit in a machine register. +Flonums have to be @dfn{boxed} because a 64 bit IEEE floating point +number (the representation the MIT Scheme uses) does not fit in a +regular machine word. +Values are boxed by storing them in a small record in the heap. +Every floating point value that you see at the REPL is boxed. +Floating point values are only unboxed for short periods of time when +they are in the machine's floating point unit and actual floating point +operations are begin performed. + + +Numerical calculations that happen to be using floating point numbers +cause many temporary floating point numbers to be allocated. It is not +uncommon for numerical programs to spend over half of the time creating +and garbage collecting the flonums. + +Consider the following procedure for computing the distance of a point +@var{(x,y)} from the origin. + +@example +(define (distance x y) + (sqrt (+ (* x x) (* y y)))) +@end example + +The call @code{(distance 0.3 0.4)} returns a new, boxed flonum, 0.5. +The calculation also generates three intermediate boxed flonums. This +next version works only for flonum inputs, generates only one boxed +flonum (the result) and runs eight times faster: + +@example +(define (flo:distance x y) + (flo:sqrt (flo:+ (flo:* x x) (flo:* y y)))) +@end example + +Note that @code{flo:} operations are usually effective only within a +single arithmetic expression. If the expression contains conditionals +or calls to procedures then the values tend to get boxed anyway. + + +@subsubsection{Flonum vectors} + +Flonum vectors are vectors which contain only floating point values, in +much the same way as a string is a `vector' containing only character +values. + +Flonum vectors have the advantages of compact storage (about half of +that of a conventional vector of flonums) and judicious use of flonum +vectors can decrease flonum consing. + +The disadvantages are that flonum vectors are incompatible with ordinary +vectors, and if not used carefully, can increase flonum consing. Flonum +vectors are a pain to use because they require you to make a decision +about the representation and stick with that, and it might not be easy +to assertain whether the advantages in one part of the program outweigh +the disadvantages in another. + +@deffn {procedure+} flo:vector-cons n +Create a flonum vector of length @var{N}. +The contents of the vector are arbitrary and might not be valid floating +point numbers. +The contents should not be used until initialized. +@end deffn + +@deffn {procedure+} flo:vector-ref flonum-vector index +@deffnx {procedure+} flo:vector-set! flonum-vector index value +@defnnx {procedure+} flo:vector-length flonum-vector +These operations are analogous to the ordinary vector operations. +@end deffn + +This next operation causes no flonum consing because the flonum is +loaded directly from the flonum vector into a floating point machine +register, added, and stored again. There is no need for a temporary +boxed flonum. + +@example +(flo:vector-set v 0 (flo:+ (flo:vector-ref v 0) 1.2)) +@end example + +In this example, every time @code{g} is called, a new boxed flonum has +to be created so that a valid Scheme object can be returned. +If @code{g} is called more often than the elements of @var{v} are +changed then an ordinary vector might be more efficient. + +@example +(define (g i) + (flo:vector-ref v i)) +@end example + + + +@subsubsection{Common pitfalls} + +Pitfall 1: +Make sure that your literals are floating point constants: + +@example +(define (f1 a) (flo:+ a 1)) +(define (f2 a) (flo:+ a 1.)) +@end example + +@code{F1} will most likely cause a hardware error, and certainly give +the wrong answer. + + +Pitfall 2: +It is tempting to insert calls to @code{exact->inexact} to coerce values +into flonums. +This does not always work because complex numbers may be exact or inexact too. +In addition, the current implementation of @code{exact->inexact} is slow. + + +Pitfall 3: +A great deal of care has to be taken with the standard math procedures. +For example, when called with a flonum, both @code{sqrt} and @code{asin} +can return a complex number. + + @node Miscellaneous, , Flonum arithmetic, Efficiency Tips @subsection Miscellaneous