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#289 Trouble with escapes or map? ←	↑	→ #290 Axiom failed to integrate elementary function

#29 for i in 1..1 repeat print(sin(i) :: Complex Float)

Edit detail for #29 for i in 1..1 repeat print(sin(i) :: Complex Float) revision 3 of 3

	1 2 3
Editor: test1 Time: 2014/05/13 16:31:33 GMT+0
Note:

added:

From test1 Tue May 13 16:31:33 +0000 2014
From: test1
Date: Tue, 13 May 2014 16:31:33 +0000
Subject: 
Message-ID: <20140513163133+0000@axiom-wiki.newsynthesis.org>

Status: open => closed

Vladimir Bondarenko wrote:

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(1) -> )set message autoload on

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for i in 1..1 repeat print(sin(i) :: Complex Float)

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   0.8414709848_0789650665

Type: Void

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).

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for i in 1..3 repeat print(sin(i)::Complex Float)

   0.8414709848_0789650665
   0.9092974268_256816954
   0.1411200080_598672221

Type: Void

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for i in 1..3 repeat print(a:=sin(i)::Complex Float)

   0.8414709848_0789650665
   0.9092974268_256816954
   0.1411200080_598672221

Type: Void

Hmm, we need to understand this a bit more:

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for i in 1..1 repeat print(a:=sin(i)::Complex Float)

   0.8414709848_0789650665

Type: Void

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for i in 1..1 repeat print(a:=(sin(i)::Complex Float))

   0.8414709848_0789650665

Type: Void

all give:

  0.8414709848 0789650665

At least that is a work-around.

But

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for i in 1..1 repeat print((a:=sin(i))::Complex Float)

   0.8414709848_0789650665

Type: Void

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for i in 1..1 repeat (a:=sin(i); print(a::Complex Float))

   0.8414709848_0789650665

Type: Void

Gives:

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

The comments below turned out to be in error:

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for i in 1..1 repeat print(sqrt(i) :: Complex Float)

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      for domain FramedModule& 
   1.0

Type: Void

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for i in 1..1 repeat print(exp(i) :: Complex Float)

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      for domain Matrix

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      for domain InnerIndexedTwoDimensionalArray

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      for domain MatrixCategory& 
   2.7182818284_590452354

Type: Void

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for i in 1..1 repeat print(log(i) :: Complex Float)

   0.0

Type: Void

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for i in 1..1 repeat print(atan(i) :: Complex Float)

   0.7853981633_9744830961

Type: Void

I'd say that it's a bug. A workaround (not a fix...) is to say

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for i in 1..1 repeat print(sqrt(i) @ Complex Float)

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Loading 
      /usr/local/lib/fricas/target/x86_64-linux-gnu/algebra/FEVALAB-.fasl
      for domain FullyEvalableOver& 
   1.0

Type: Void

It is quite clear that Axioms behaviour will be the same for all operators (defined in op.spad).

Tracing the call with

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)set message bottom on

   Your user access level is compiler and this set option is therefore 
      not available. See the )set userlevel command for more 
      information.
for i in 1..3 repeat print((sin(i))::Complex Float)

   0.8414709848_0789650665
   0.9092974268_256816954
   0.1411200080_598672221

Type: Void

which looks quite strange: Axiom is looking for a function print with argument of type Complex Float, but the thing it prints is not of this type...

... --kratt6, Fri, 28 Dec 2007 14:55:39 -0800 reply

Category: Axiom Mathematics => Axiom Interpreter Status: closed => open

the bug with sin is still open

... --kratt6, Fri, 28 Dec 2007 14:55:46 -0800 reply

Name: #29 for i in 1..1 repeatprint(sin(i) :: Complex Float) => #29 for i in 1..1 repeat print(sin(i) :: Complex Float)

... --test1, Tue, 13 May 2014 16:31:33 +0000 reply

Status: open => closed