amforth-devel

[Amforth-devel] Float testing - small/large numbers

[pito <pi...@vo...>]

Leon,
simple testing of the floats f*, f/. Some cases results are in
error. 
It seems division is sensitive. Not sure about the result's sign,
however the result shall be 31415 in all cases.
-------------------
\ test1 float small and large numbers
\ needs float constant _pi

marker _testfloat_

: test1 
10000 s>f fdup fdup fdup fdup fdup
f* f* f* f* f*
_pi  
fswap 
f/
10000 s>f fdup fdup fdup fdup fdup fdup 
f* f* f* f* f* f* f* 
f>s . ( the result shall be 31415 )
;

: test2
_pi 10000 s>f f/ 
10000 s>f f/ 

10000 s>f fdup fdup
f* f* f*
f>s . ( the result shall be 31415 )
;


: test3
_pi 10000 s>f f/ 
10000 s>f f/ 
10000 s>f f/ 

10000 s>f fdup fdup fdup
f* f* f* f*
f>s . ( the result shall be 31415 )
;

: test4 
-10000 s>f fdup fdup fdup fdup fdup
f* f* f* f* f*
_pi  
fswap 
f/
10000 s>f fdup fdup fdup fdup fdup fdup 
f* f* f* f* f* f* f* 
f>s . ( the result shall be 31415 )
;

: test5
_pi -10000 s>f f/ 
10000 s>f f/ 

-10000 s>f fdup fdup
f* f* f*
f>s . ( the result shall be 31415 )
;


: test6
_pi -10000 s>f f/ 
10000 s>f f/ 
10000 s>f f/ 

-10000 s>f fdup fdup fdup
f* f* f* f*
f>s . ( the result shall be -31415 )
;

------------
Pito

Re: [Amforth-devel] Float testing - small/large numbers

[Leon N M. <leo...@gm...>]

I don't have my device handy so I can't test your code. Could you be a little 
more clear about which ones failed, what the results are supposed to be, and 
what the results actually are? (When you write "the result shall be -31415", 
is that what it's supposed to be, what it actualy is, or something else?)

It looks like you're dividing and then multiplying by very large powers of 10. 
I wouldn't be surprised if you loose some significant figures by doing this.
-Leon

Re: [Amforth-devel] Float testing - small/large numbers

[pito <pi...@vo...>]

The test cases are designed specifically to se how it handles large
and small numbers. The cases 1-3 are the same as 4-6, the later have
only minus sign with those 10000 numbers. All the results shall be
by design the integer number 31415 (visualised by "10000 x Pi" - as
we do not have float format yet). The Pi is simply multiplied or/and
divided by large numbers (as we do not have float input yet, it is
done by several multiplication/division by 10000).
The results are:
> test1
31415  ok
> test2
31415  ok
> test3
|significand| > 16777215 

Here the sign is chabged only:
> test4
|significand| > 16777215 
> test5
31438  ok
> test6
|significand| > 16777215 
> 

My current understanding is the division is cousing issues. The lost
of significant figures shall not be the case - see the test 1:

tmp = pi / (10000^5)
pi = tmp * 10000^6   (correct result 31415).

The test 2:

tmp = pi / 10000 / 10000 
pi = tmp * 10000^3   (correct result 31415).

Te test 3:

tmp = pi / 10000 / 10000 /10000
pi = tmp * 10000^4   (error).

The test4-6 are same as the above one, but with minus sign at 10000.
So the result shall be 31415 (when ignoring the sign).

As you may see from previous test the f/ is sensitive to signs of
the operands and gives unpecise results - see  for example test5
result.

Pito.




----- PŮVODNÍ ZPRÁVA -----
Od: "Leon N Maurer" <leo...@gm...>
Komu: amf...@li...
Předmět: Re: [Amforth-devel] Float testing - small/large numbers
Datum: 29.8.2010 - 19:17:31

> I don't have my device handy so I can't test your
> code. Could you be a little 
> more clear about which ones failed, what the
> results are supposed to be, and 
> what the results actually are? (When you write
> "the result shall be -31415", 
> is that what it's supposed to be, what it actualy
> is, or something else?)
> 
> It looks like you're dividing and then multiplying
> by very large powers of 10. 
> I wouldn't be surprised if you loose some
> significant figures by doing this.
> -Leon
> 
> ------------------------------------------------------------------------------
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Re: [Amforth-devel] Float testing - small/large numbers

[pito <pi...@vo...>]

Leon, or, to make it simple:
Q: why the test1 gives a correct result (31415) and the test4 gives
an error (|significand| > 16777215).
The test1 is the same as the test4, the only difference is the test4
has minus10000 as the first multiplicand.
Pito

----- PŮVODNÍ ZPRÁVA -----
Od: "pito" <pi...@vo...>
Komu: leo...@gm..., amf...@li...
Předmět: Re: [Amforth-devel] Float testing - small/large numbers
Datum: 29.8.2010 - 20:01:01

> The test cases are designed specifically to se how
> it handles large
> and small numbers. The cases 1-3 are the same as
> 4-6, the later have
> only minus sign with those 10000 numbers. All the
> results shall be
> by design the integer number 31415 (visualised by
> "10000 x Pi" - as
> we do not have float format yet). The Pi is simply
> multiplied or/and
> divided by large numbers (as we do not have float
> input yet, it is
> done by several multiplication/division by 10000).
> The results are:
> > test1
> 31415  ok
> > test2
> 31415  ok
> > test3
> |significand| > 16777215 
> 
> Here the sign is chabged only:
> > test4
> |significand| > 16777215 
> > test5
> 31438  ok
> > test6
> |significand| > 16777215 
> > 
> 
> My current understanding is the division is
> cousing issues. The lost
> of significant figures shall not be the case - see
> the test 1:
> 
> tmp = pi / (10000^5)
> pi = tmp * 10000^6   (correct result 31415).
> 
> The test 2:
> 
> tmp = pi / 10000 / 10000 
> pi = tmp * 10000^3   (correct result 31415).
> 
> Te test 3:
> 
> tmp = pi / 10000 / 10000 /10000
> pi = tmp * 10000^4   (error).
> 
> The test4-6 are same as the above one, but with
> minus sign at 10000.
> So the result shall be 31415 (when ignoring the
> sign).
> 
> As you may see from previous test the f/ is
> sensitive to signs of
> the operands and gives unpecise results - see  for
> example test5
> result.
> 
> Pito.
> 
> 
> 
> 
> ----- PŮVODNÍ ZPRÁVA -----
> Od: "Leon N Maurer" <leo...@gm...>
> Komu: amf...@li...
> Předmět: Re: [Amforth-devel] Float testing -
> small/large numbers
> Datum: 29.8.2010 - 19:17:31
> 
> > I don't have my device handy so I can't test
> > your
> > > code. Could you be a little 
> > more clear about which ones failed, what the
> > results are supposed to be, and 
> > what the results actually are? (When you write
> > "the result shall be -31415", 
> > is that what it's supposed to be, what it
> > actualy
> > > is, or something else?)
> > 
> > It looks like you're dividing and then
> > multiplying
> > > by very large powers of 10. 
> > I wouldn't be surprised if you loose some
> > significant figures by doing this.
> > -Leon
> > 
> > ------------------------------------------------------------------------------
> > > > > > Sell apps to millions through the Intel(R)
> > Atom(Tm) Developer Program
> > Be part of this innovative community and reach
> > millions of netbook users 
> > worldwide. Take advantage of special
> > opportunities
> > > to increase revenue and 
> > speed time-to-market. Join now, and jumpstart
> > your
> > > future.
> > http://p.sf.net/sfu/intel-atom-d2d
> > _______________________________________________
> > Amforth-devel mailing list
> > Amf...@li...
> > https://lists.sourceforge.net/lists/listinfo/amforth-devel
> > 
> 
> 
> ------------------------------------------------------------------------------
> > Sell apps to millions through the Intel(R)
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> Be part of this innovative community and reach
> millions of netbook users 
> worldwide. Take advantage of special opportunities
> to increase revenue and 
> speed time-to-market. Join now, and jumpstart your
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Re: [Amforth-devel] Float testing - small/large numbers

[Leon N M. <leo...@gm...>]

That's a good way to boil it down. It defintely shouldn't be doing that -- 
hopefully I'll be able to look in to it tomorrow.
-Leon

>Sunday 29 August 2010
>From: "pito" <pi...@vo...>
>Subject: Re: [Amforth-devel] Float testing - small/large numbers
> Leon, or, to make it simple:
> Q: why the test1 gives a correct result (31415) and the test4 gives
> an error (|significand| > 16777215).
> The test1 is the same as the test4, the only difference is the test4
> has minus10000 as the first multiplicand.
> Pito

Re: [Amforth-devel] Float testing - small/large numbers

[pito <pi...@vo...>]

Leon,
I uploaded in other post an update of useful float constnats (these
constants are useful till we will have input and output of float
numbers).
However it freezes when uploading (e.g. when compiling _third) so it
seems the f/ is cousing a problem. Try it plz.
Pito

> That's a good way to boil it down. It defintely
> shouldn't be doing that -- 
> hopefully I'll be able to look in to it tomorrow.
> -Leon

Re: [Amforth-devel] Float testing - small/large numbers

[pito <pi...@vo...>]

Some errors when compiling float constants:

> 1074 s>f 2251 s>f f/ fconstant   _log3
|significand| > 16777215 

> 10691 s>f 462 s>f f/ fconstant   _e**pi
|significand| > 16777215 

> _1e-6 1000 s>f f/ fconstant   _1e-9
|significand| > 16777215 

P.

Re: [Amforth-devel] Float testing - small/large numbers

[Leon N. M. <leo...@gm...>]

Ok, that bug should be fixed -- the new version of the code is up on

http://github.com/lnmaurer/amforth-float

Below are some of Pito's examples -- now working. Thanks again for catching 
this.

In answer to an earlier question -- I think double length floats would be 
trickier to do because there aren't words around to manipulate them. My 
priority is defiantly getting the other words from the floating point wordset 
done, followed by some from the floating point extended wordset (including 
functions like sine, cos, etc.)

-Leon

-Leon

> 355 s>f 113 s>f f/ fconstant _pi
 ok
> _pi 10000 s>f f/ 10000 s>f f/ 10000 s>f f/ 10000 s>f fdup fdup fdup f* f* f* 
f* f>s .
31415  ok
> 1074 s>f 2251 s>f f/ fconstant   _log3
 ok
> _log3 1000 s>f f* f>s .
477  ok
> 10691 s>f 462 s>f f/ fconstant   _e**pi
 ok
> _e**pi 1000 s>f f* f>s .
23140  ok

Re: [Amforth-devel] Float testing - small/large numbers

[pito <pi...@vo...>]

Leon,
Thanks! The results of the test1-6 (all results shall be equal
31415, ignoring sign):
> test1
31415  ok
> test2
31415  ok
> test3
31415  ok
> test4
31396  ok
> test5
31438  ok
> test6
-31434  ok
> 
The test4-6 are done with negative koef. You may see an error.
One important thing - in order to load float lib you have to add
the word d= into your compilation.
Pito

----- PŮVODNÍ ZPRÁVA -----
Od: "Leon Nathaniel Maurer" <leo...@gm...>
Komu: amf...@li...
Předmět: Re: [Amforth-devel] Float testing - small/large numbers
Datum: 30.8.2010 - 19:42:28

> Ok, that bug should be fixed -- the new version of
> the code is up on
> 
> http://github.com/lnmaurer/amforth-float
> 
> Below are some of Pito's examples -- now working.
> Thanks again for catching 
> this.
> 
> In answer to an earlier question -- I think double
> length floats would be 
> trickier to do because there aren't words around
> to manipulate them. My 
> priority is defiantly getting the other words from
> the floating point wordset 
> done, followed by some from the floating point
> extended wordset (including 
> functions like sine, cos, etc.)
> 
> -Leon
> 
> -Leon
> 
> > 355 s>f 113 s>f f/ fconstant _pi
> ok
> > _pi 10000 s>f f/ 10000 s>f f/ 10000 s>f f/ 10000
> > s>f fdup fdup fdup f* f* f* 
> > f* f>s .
> 31415  ok
> > 1074 s>f 2251 s>f f/ fconstant   _log3
> ok
> > _log3 1000 s>f f* f>s .
> 477  ok
> > 10691 s>f 462 s>f f/ fconstant   _e**pi
> ok
> > _e**pi 1000 s>f f* f>s .
> 23140  ok
> 
> ------------------------------------------------------------------------------
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> 
> Show off your parallel programming skills.
> Enter the Intel(R) Threading Challenge 2010.
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> https://lists.sourceforge.net/lists/listinfo/amforth-devel

Re: [Amforth-devel] Float testing - small/large numbers

[pito <pi...@vo...>]

Leon,
I think there is an issue with negative numbers:

> -1 s>f fconstant _-1    >>>> define 1.0
ok
> 1 s>f fconstant _1      >>>> define -1.0
ok

> _1 _pi f* _1e4 f* f>s .    >>>> 1.0 * pi * 1.0E4 = 31415
31415  ok

> _-1 _pi f* _1e4 f* f>s .   >>>>> -1.0 * pi * 1.0E4 = -31426
-31426  ok
>

It cannot be caused by of a rounding error accumulating or loosing a
valid digits. Some minor bug somewhere..
P.


> > Ok, that bug should be fixed -- the new version
> > of
> > > the code is up on
> > 
> > http://github.com/lnmaurer/amforth-float
> > 
> > Below are some of Pito's examples -- now
> > working.

Re: [Amforth-devel] Float testing - small/large numbers

[Leon N. M. <leo...@gm...>]

On Monday, August 30, 2010 04:19:55 pm pito wrote:
> The test4-6 are done with negative koef. You may see an error.
> One important thing - in order to load float lib you have to add
> the word d= into your compilation.
> Pito

I think 4-6 are getting the right results. test4 has (-1)^6=1, test5 has 
(-1)^4=1, and test6 has (-1)^5=-1.

Commented out code for d= has been in the float.fth file in case it wasn't 
already installed.

-Leon

Re: [Amforth-devel] Float testing - small/large numbers

[pito <pi...@vo...>]

Leon,
the results of tests 4-6 are from what I see quite different (+/-
19) against the correct result =31415:
> test1
31415  ok
> test2
31415  ok
> test3
31415  ok
> test4
31396  ok
> test5
31438  ok
> test6
-31434  ok
>
I think the difference is too big for a single precision float..P.

----- PŮVODNÍ ZPRÁVA -----
Od: "Leon Nathaniel Maurer" <leo...@gm...>
Komu: "pito" <pi...@vo...>
Předmět: Re: [Amforth-devel] Float testing - small/large numbers
Datum: 30.8.2010 - 23:48:51

> On Monday, August 30, 2010 04:19:55 pm pito wrote:
> > The test4-6 are done with negative koef. You may
> > see an error.
> > > One important thing - in order to load float lib
> > you have to add
> > > the word d= into your compilation.
> > Pito
> 
> I think 4-6 are getting the right results. test4
> has (-1)^6=1, test5 has 
> (-1)^4=1, and test6 has (-1)^5=-1.
> 
> Commented out code for d= has been in the
> float.fth file in case it wasn't 
> already installed.
> 
> -Leon

Re: [Amforth-devel] Float testing - small/large numbers

[Leon N. M. <leo...@gm...>]

This should now be fixed:

> 1 s>f _pi f* 1000000. d>f f* f>d d.
3141592  ok
> -1 s>f _pi f* 1000000. d>f f* f>d d.
-3141593  ok

the discrepency in the smallest digit is due to the way the fractional part 
gets truncated (it rounds down). If you look directly at the float (take out 
the f>d and convert to binary) they are now idenetical except for the sign 
bit:

01001010001111111011111101100010
11001010001111111011111101100010

It turns out the root cause was something like this:

> -13176795. d2/ d.
-6588398  ok
> 13176795. d2/ d.
6588397  ok

Which is how it should work if you think of division by 2 as shifting right, 
but isn't something I had taken in to account -- a good lesson in how negative 
numbers are represented.

My reposititory has been updated -- keep the tests coming.

-Leon

On Monday, August 30, 2010 04:46:37 pm you wrote:
> Leon,
> 
> I think there is an issue with negative numbers:
> > -1 s>f fconstant _-1    >>>> define 1.0
> 
> ok
> 
> > 1 s>f fconstant _1      >>>> define -1.0
> 
> ok
> 
> > _1 _pi f* _1e4 f* f>s .    >>>> 1.0 * pi * 1.0E4 = 31415
> 
> 31415  ok
> 
> > _-1 _pi f* _1e4 f* f>s .   >>>>> -1.0 * pi * 1.0E4 = -31426
> 
> -31426  ok
> 
> 
> It cannot be caused by of a rounding error accumulating or loosing a
> valid digits. Some minor bug somewhere..
> P.

Re: [Amforth-devel] Float testing - small/large numbers

[pito <pi...@vo...>]

Leon, great! See the test:

\ test float small and large numbers f* f/
\ needs float constants

marker _tstflt_

314159265. d>f 100000000. d>f f/ fconstant _pi
-314159265. d>f 100000000. d>f f/ fconstant _-pi

: prntpi _1e6 _100 f* f* f>d d. ;

\ +pi f* f/

: test1 
_1e6 fdup fdup fdup fdup
f* f* f* f*
_pi  
fswap 
f/
_1e6 fdup fdup fdup fdup
f* f* f* f* f*

prntpi ( the result shall be 314159265 )
;

: test2
_pi _1e6 f/ _1e6 f/ _1e6 f/ _1e6 f/ _1e6 f/ 
_1e6 fdup fdup fdup fdup
f* f* f* f* f*
prntpi ( the result shall be 314159265 )
;

\ -pi f* f/

: test3 
_1e6 fdup fdup fdup fdup
f* f* f* f*
_-pi  
fswap 
f/
_1e6 fdup fdup fdup fdup
f* f* f* f* f*

prntpi ( the result shall be 314159265 )
;

: test4
_-pi _1e6 f/ _1e6 f/ _1e6 f/ _1e6 f/ _1e6 f/ 
_1e6 fdup fdup fdup fdup
f* f* f* f* f*
prntpi ( the result shall be 314159265 )
;

> test1
314159200  ok
> test2
314159136  ok
> test3
-314159200  ok
> test4
-314159136  ok
> 

The magnitude errors caused by single precision (let us hope so..).
The next step is to test add and sub.
Pito




.
> 
> My reposititory has been updated -- keep the tests
> coming.
> 
> -Leon
>