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Re: [Axiom-developer] Comments are wanted on for i in 1..1 repeatprint(
From: |
William Sit |
Subject: |
Re: [Axiom-developer] Comments are wanted on for i in 1..1 repeatprint(sin(i) :: Complex Float) |
Date: |
Thu, 13 Jan 2005 09:30:26 -0500 |
Vladimir Bondarenko wrote:
> -> for i in 1..1 repeat print(sin(i) :: Complex Float)
> sin(1)
Hmm, we need to understand this a bit more:
for i in 1..1 repeat print(a:=sin(i)::Complex Float)
for i in 1..1 repeat print(a:=(sin(i)::Complex Float))
all give
0.8414709848 0789650665
At least that is a work-around.
But
for i in 1..1 repeat print((a:=sin(i))::Complex Float)
sin(1)
for i in 1..1 repeat (a:=sin(i); print(a::Complex Float))
sin(1)
print is from PrintPackage, which calls
print from OutputForm, which calls
mathprint$Lisp
but the problem lies in print inside a loop (any type, not just a for-loop). The
problem seems to be an interpreter problem in parsing. This is confirmed partly
by the following transcript. When trying to code this as a package for the
compiler, it is not easy to figure out the sequence of functions to use to
coerce sin(i) from EXPR INT to Complex Float. I finally found one way, but it
may not be what the interpreter is doing:
--%Printest
)abbrev package PRINTEST Printest
Printest: T==C where
EXPR ==> Expression
INT ==> Integer
CF ==> Complex Float
T == with
foo:PositiveInteger->Void
C == add
import EXPR INT
foo(k)==
for i in 1..k repeat
a:=sin(i::INT::Float::CF::EXPR CF)$(EXPR CF)
print(retract(a)$(EXPR CF)@CF::OutputForm)
Of course it makes no difference whether a:= is eliminated or not. And this
works correctly. So my tentative conclusion is that the interpreter is "lazy" in
(1) to try to figure out this rather involved coercion sequence (Hey, I got it
to EXPR INT and I have no idea how to go further to Complex Float, I think it is
good enough ...:-), but in (2), it is somehow forced to work harder (Now you
want to save the result and I have to type the variable a, ok, ...). Is it a
bug? Don't know. There are limitations to the interpreter.
Tim: Do you know if there is a system limitation on the level of coercion the
interpreter will try before quitting? Can this be reset?
This example shows why a large percent of time (my low estimate is 70% and my
high is 90%) writing compiled code is spent on coercion.
Now, there is still the question: why does this happen only inside a loop?
Can one tell more from the way the libraries are loaded (see attached
print.out)? Notice in print.out, even after foo(3) is executed, (2) still needs
to load another bunch of libraries. Why?
William
----
Start with a fresh session:
Note that neither Float nor Complex is loaded in (1), only in (2). More
surprisingly, UniversalSegment is also not loaded in (1). (it does not matter if
the segment is 1..1 or 1..3).
AXIOM Computer Algebra System
Version of Tuesday November 30, 2004 at 21:11:14
-----------------------------------------------------------------------------
Issue )copyright to view copyright notices.
Issue )summary for a summary of useful system commands.
Issue )quit to leave AXIOM and return to shell.
-----------------------------------------------------------------------------
(1) -> for i in 1..3 repeat print(sin(i)::Complex Float)
Loading j:/Program Files/axiom/mnt/windows/algebra/EXPR.o for domain
Expression
Loading j:/Program Files/axiom/mnt/windows/algebra/KERNEL.o for
domain Kernel
Loading j:/Program Files/axiom/mnt/windows/algebra/BOP.o for domain
BasicOperator
Loading j:/Program Files/axiom/mnt/windows/algebra/SCACHE.o for
package SortedCache
Loading j:/Program Files/axiom/mnt/windows/algebra/VOID.o for domain
Void
Loading j:/Program Files/axiom/mnt/windows/algebra/UPMP.o for
package UnivariatePolynomialMultiplicationPackage
Loading j:/Program Files/axiom/mnt/windows/algebra/AN.o for domain
AlgebraicNumber
Loading j:/Program Files/axiom/mnt/windows/algebra/IAN.o for domain
InnerAlgebraicNumber
Loading j:/Program Files/axiom/mnt/windows/algebra/ACFS-.o for
domain AlgebraicallyClosedFunctionSpace&
Loading j:/Program Files/axiom/mnt/windows/algebra/FS-.o for domain
FunctionSpace&
Loading j:/Program Files/axiom/mnt/windows/algebra/COMMONOP.o for
package CommonOperators
Loading j:/Program Files/axiom/mnt/windows/algebra/KDAGG-.o for
domain KeyedDictionary&
Loading j:/Program Files/axiom/mnt/windows/algebra/DIAGG-.o for
domain Dictionary&
Loading j:/Program Files/axiom/mnt/windows/algebra/BOP1.o for
package BasicOperatorFunctions1
Loading j:/Program Files/axiom/mnt/windows/algebra/PRINT.o for
package PrintPackage
Loading j:/Program Files/axiom/mnt/windows/algebra/EF.o for package
ElementaryFunction
Loading j:/Program Files/axiom/mnt/windows/algebra/ACF-.o for domain
AlgebraicallyClosedField&
Loading j:/Program Files/axiom/mnt/windows/algebra/ES-.o for domain
ExpressionSpace&
Loading j:/Program Files/axiom/mnt/windows/algebra/BASTYPE-.o for
domain BasicType&
Loading j:/Program Files/axiom/mnt/windows/algebra/FRETRCT-.o for
domain FullyRetractableTo&
Loading j:/Program Files/axiom/mnt/windows/algebra/EVALAB-.o for
domain Evalable&
Loading j:/Program Files/axiom/mnt/windows/algebra/TRANFUN-.o for
domain TranscendentalFunctionCategory&
Loading j:/Program Files/axiom/mnt/windows/algebra/IEVALAB-.o for
domain InnerEvalable&
Loading j:/Program Files/axiom/mnt/windows/algebra/TRIGCAT-.o for
domain TrigonometricFunctionCategory&
Loading j:/Program Files/axiom/mnt/windows/algebra/ATRIG-.o for
domain ArcTrigonometricFunctionCategory&
Loading j:/Program Files/axiom/mnt/windows/algebra/HYPCAT-.o for
domain HyperbolicFunctionCategory&
Loading j:/Program Files/axiom/mnt/windows/algebra/ELEMFUN-.o for
domain ElementaryFunctionCategory&
Loading j:/Program Files/axiom/mnt/windows/algebra/RADCAT-.o for
domain RadicalCategory&
Loading j:/Program Files/axiom/mnt/windows/algebra/AF.o for package
AlgebraicFunction
Loading j:/Program Files/axiom/mnt/windows/algebra/POLYROOT.o for
package PolynomialRoots
Loading j:/Program Files/axiom/mnt/windows/algebra/INTFACT.o for
package IntegerFactorizationPackage
Loading j:/Program Files/axiom/mnt/windows/algebra/IROOT.o for
package IntegerRoots
Loading j:/Program Files/axiom/mnt/windows/algebra/FACTFUNC.o for
package FactoredFunctions
Loading j:/Program Files/axiom/mnt/windows/algebra/POLYCATQ.o for
package PolynomialCategoryQuotientFunctions
Loading j:/Program Files/axiom/mnt/windows/algebra/FSAGG-.o for
domain FiniteSetAggregate&
Loading j:/Program Files/axiom/mnt/windows/algebra/FLASORT.o for
package FiniteLinearAggregateSort
Loading j:/Program Files/axiom/mnt/windows/algebra/IDPOAMS.o for
domain IndexedDirectProductOrderedAbelianMonoidSup
Loading j:/Program Files/axiom/mnt/windows/algebra/IDPOAM.o for
domain IndexedDirectProductOrderedAbelianMonoid
Loading j:/Program Files/axiom/mnt/windows/algebra/PGCD.o for
package PolynomialGcdPackage
sin(1)
sin(2)
sin(3)
Type: Void
(2) -> for i in 1..3 repeat print(a:=sin(i)::Complex Float)
Loading j:/Program Files/axiom/mnt/windows/algebra/FLOAT.o for
domain Float
Loading j:/Program Files/axiom/mnt/windows/algebra/COMPLEX.o for
domain Complex
Loading j:/Program Files/axiom/mnt/windows/algebra/COMPCAT-.o for
domain ComplexCategory&
Loading j:/Program Files/axiom/mnt/windows/algebra/FPS-.o for domain
FloatingPointSystem&
Loading j:/Program Files/axiom/mnt/windows/algebra/RNS-.o for domain
RealNumberSystem&
Loading j:/Program Files/axiom/mnt/windows/algebra/DFLOAT.o for
domain DoubleFloat
Loading j:/Program Files/axiom/mnt/windows/algebra/NUMERIC.o for
package Numeric
Loading j:/Program Files/axiom/mnt/windows/algebra/EXPR2.o for
package ExpressionFunctions2
Loading j:/Program Files/axiom/mnt/windows/algebra/FS2.o for package
FunctionSpaceFunctions2
Loading j:/Program Files/axiom/mnt/windows/algebra/POLYLIFT.o for
package PolynomialCategoryLifting
Loading j:/Program Files/axiom/mnt/windows/algebra/ES2.o for package
ExpressionSpaceFunctions2
Loading j:/Program Files/axiom/mnt/windows/algebra/MONOGEN-.o for
domain MonogenicAlgebra&
Loading j:/Program Files/axiom/mnt/windows/algebra/FRAMALG-.o for
domain FramedAlgebra&
Loading j:/Program Files/axiom/mnt/windows/algebra/FINRALG-.o for
domain FiniteRankAlgebra&
Loading j:/Program Files/axiom/mnt/windows/algebra/FEVALAB-.o for
domain FullyEvalableOver&
Loading j:/Program Files/axiom/mnt/windows/algebra/UNISEG.o for
domain UniversalSegment
0.8414709848 0789650665
0.9092974268 256816954
0.1411200080 598672221 + 0.3388131789 0172013563 E -20 %i
Type: Void
(3) ->
--
William Sit
Department of Mathematics....Email: address@hidden
City College of New York................Tel: 212-650-5179
Convent Ave at West 138th Street........Fax: 212-862-0004
New York, NY 10031..Axiom, A Scientific Computation Sytem
USA............... http://www.nongnu.org/axiom/index.html