amforth-devel — Development discussion and user support

Re: [Amforth-devel] printing floats

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

Leon, thanks! I am very happy that you publish the float updates!
Pito.

PS: Leon, is there any chance to name the .zip updates with e.g. a
date in it as it is uneasy to recognise and track the files based on
those codes like "..-float-9e1ace1.zip"
P.

> 
> PS I'm not sure if these type of updates are of
> general interest, but there's 
> been a lot of floating point stuff going around,
> so I'll keep sending them for 
> the moment.

[Amforth-devel] printing floats

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

I've finally added a function to output floats (in scientific notation):

> 355 s>f 113 s>f f/ fs.
3.1415927  ok
> 1 s>f f2/ f2/ f2/ f2/ fs.
6.25E-2  ok
> 12345 s>f fs.
1.23449993E4  ok

You can see from the second example that rounding problems do happen. That can 
be avoided... if you don't mind coding with decuple length integers (need to 
be able to store up to 2^154). See the pdf at:

http://portal.acm.org/citation.cfm?id=93559

So I'm going to stick with this simpler -- but less accurate -- method for the 
moment (also in the pdf) -- I'll work on input before spending more time with 
output (similar problems exist -- maybe there are easier solutions). As usual, 
the code is available at:

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

-Leon

PS I'm not sure if these type of updates are of general interest, but there's 
been a lot of floating point stuff going around, so I'll keep sending them for 
the moment.

Re: [Amforth-devel] Case sensitivity of amforth

[<an...@ki...>]

If I have to choose between "fast" or "ugly" then case sensitive being
fast and beautiful it is.

If I went with personal convenience and C# et al I would be running
windows and certainly wouldn't be contributing to Open Source.

Come up with a reasoned argument (other than personal convenience) that
shows where and how case insensitive is faster and better then case
sensitive (in real processing cycles, with proofs showing real
instructions) and I will agree with you.

Until then (to a computation scientist and experienced embedded
engineer) the discussion is a complete waste of text inches.

It takes two to tango.












On 03/09/10 20:28, pito wrote:
> So can we see light at the end of the tunnel? (hopefuly it's not the
> light of an incoming train..). Have a nice weekend! P.
>>
>> I want a smart solution, not a fast and ugly one.
>> And smart means
>> really smart. And I take the time for it... I've
>> got some ideas
>> already...
>>
>> Matthias
> 
> 
> 
> ------------------------------------------------------------------------------
> This SF.net Dev2Dev email is sponsored by:
> 
> Show off your parallel programming skills.
> Enter the Intel(R) Threading Challenge 2010.
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> 

Re: [Amforth-devel] TIMER and STOPWATCH, float time, for 1284P

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

The timer routine with automated tck_ms (float) calculation (I had
to test the tck_ms calculation a little bit..):
...
\ MEASURE TIME IN SECONDS (FLOAT)
decimal
2variable elapsed_ticks
\ tck_ms = 1 / f_cpu / timer2_overflow_count /
timer2_prescaler_ratio
\ tck_ms = 1 / f_cpu / 256 / 1024
f_cpu d>f 256 s>f f/ 1024 s>f f/ _1 fswap f/  fconstant tck_ms
: timer-start ( -- ) timer 2@ elapsed_ticks 2! ;
: timer-stop (  -- f ) timer 2@ d>f elapsed_ticks 2@ d>f f- tck_ms
f* ;
\ print elapsed time in ms e.g. 1234567 ms 
: prnt_elapsed_ms ( f -- ) _1e3 f* f>d d. ;

P.

Re: [Amforth-devel] Case sensitivity of amforth

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

So can we see light at the end of the tunnel? (hopefuly it's not the
light of an incoming train..). Have a nice weekend! P.
> 
> I want a smart solution, not a fast and ugly one.
> And smart means
> really smart. And I take the time for it... I've
> got some ideas
> already...
> 
> Matthias

Re: [Amforth-devel] Case sensitivity of amforth

[Matthias T. <mt...@we...>]

Pito,

> I do understand the issue with comparing words and not single chars
> in you implementation, but tell me please - what is the major reason
> for your hardcore position of not wanting to have a switch for case
> sensitivity/insensitivity?

I want a smart solution, not a fast and ugly one. And smart means
really smart. And I take the time for it... I've got some ideas
already...

Matthias

Re: [Amforth-devel] Case sensitivity of amforth

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

Matthias,
yes, sometimes I never give up.. 
I do understand the issue with comparing words and not single chars
in you implementation, but tell me please - what is the major reason
for your hardcore position of not wanting to have a switch for case
sensitivity/insensitivity? Pito
...
(besides that I do
> not want it) 

Re: [Amforth-devel] Case sensitivity of amforth

[Matthias T. <mt...@we...>]

Pito,

you never give, yea?

> the 4th is using a constant "casesensitive" for switching case
> sensitivity on/off. I've found that only "compare.4th" is using this
> constant (compares two strings). In C sources there is "comp_4th.c"
> which does mention sensitivness, but not using the constant. Can
> this somehow be used for amforth as well?

The idea yes, but not the implementation. 

The most important issue (besides that I do
not want it) is that icompare works on two
characters at the same time. And that the
case is only significant for 7bit ASCII,
not more not less. 

Matthias

Re: [Amforth-devel] TIMER and STOPWATCH, float time, for 1284P

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

Hi, for experimenters - very quick test for floating point math with
elapsed time indication. Requires Leon's float lib, Pito's last
floatconstants and stopwatch. To see result uncomment print.
Benchmark (run on atmega1284P @25MHz):
> measure_doloop_with_operation
Elapsed 8996 msec ok
> Pito

\ Quick test of float
marker -quicktestfloat
fvariable tmp
: measure_doloop_with_operation 
timer-start 
100 0 do 
_pi _ln2 f* tmp f! 
tmp f@ _e**pi f/ tmp f!
tmp f@ _log3 f+ tmp f!
tmp f@ _e f- tmp f!
\ print result
\ i ." I= " . tmp f@ _1e9 f* f>d ." RESULT= " d. ." <<< precise
result = -2147058546.4206755 " cr
loop 
timer-stop ." Elapsed " prnt_elapsed_ms ." msec" ;

Re: [Amforth-devel] Some useful Float Constants

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

The last update:
-----------------------------
marker _floatconstants_

\ some float constants

355 s>f 113 s>f f/ fconstant 		_pi
355 s>f 226 s>f f/ fconstant 		_pi_half
355 s>f 452 s>f f/ fconstant 		_pi_quarter

8119 s>f 5741 s>f f/ fconstant 		_sqrt2
5741 s>f 8119 s>f f/ fconstant 		_sqrt2half
13755 s>f 7953 s>f f/ fconstant 	_sqrt3
27379 s>f 8658 s>f f/ fconstant 	_sqrt10

25946 s>f 9545 s>f f/ fconstant 	_e
4319 s>f 6231 s>f f/ fconstant 		_ln2
5225 s>f 4756 s>f f/ fconstant 		_ln3
12381 s>f 5377 s>f f/ fconstant 	_ln10
2718 s>f 9029 s>f f/ fconstant 		_log2
1074 s>f 2251 s>f f/ fconstant 		_log3
10691 s>f 462 s>f f/ fconstant 		_e**pi
26120 s>f 1163 s>f f/ fconstant 	_pi**e

1 s>f 2 s>f f/ fconstant 		_half
1 s>f 3 s>f f/ fconstant 		_third
5 s>f 127 s>f f/ fconstant 		_mm2inch

10 s>f fconstant			_10
100 s>f fconstant			_1e2
1000 s>f fconstant			_1e3
10000 s>f fconstant			_1e4
_1e3 _1e3 f* fconstant 			_1e6
_1e6  _1e3 f* fconstant 		_1e9
_1e9  _1e3 f* fconstant 		_1e12
_1e12  _1e3 f* fconstant 		_1e15
_1e15  _1e3 f* fconstant 		_1e18

1 s>f 10 s>f f/ fconstant 		_1e-1
_1e-1 _1e-1 f* fconstant 		_1e-2
_1e-2 _1e-1 f* fconstant 		_1e-3
_1e-3 _1e-1 f* fconstant 		_1e-4
_1e-3 _1e-3 f* fconstant 		_1e-6
_1e-6 _1e-3 f* fconstant 		_1e-9
_1e-9 _1e-3 f* fconstant 		_1e-12
_1e-12 _1e-3 f* fconstant 		_1e-15
_1e-15 _1e-3 f* fconstant 		_1e-18

0 s>f fconstant _0
-1 s>f fconstant _-1
1 s>f fconstant _1

[Amforth-devel] Case sensitivity of amforth

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

Hi Matthias,
the 4th is using a constant "casesensitive" for switching case
sensitivity on/off. I've found that only "compare.4th" is using this
constant (compares two strings). In C sources there is "comp_4th.c"
which does mention sensitivness, but not using the constant. Can
this somehow be used for amforth as well? Pito

Re: [Amforth-devel] TIMER and STOPWATCH, float time, for 1284P

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

Hi,
another example:

\
: measure_doloop_empty 
timer-start 
10000 0 do 
\ here put the stuff to measure
loop 
timer-stop prnt_elapsed_ms ;

\
fvariable tmp
: measure_doloop_with_operation 
timer-start 
10000 0 do 
_pi _ln2 f* tmp f! 
loop 
timer-stop prnt_elapsed_ms ;

------------------
Example: results in ms
> measure_doloop_empty
47  ok
> measure_doloop_with_operation
109274  ok
>
So the operation "tmp = pi * ln2" takes (109.274sec -
0.047sec)/10000 = 10.92ms per operation. Not fast, however. Pito

[Amforth-devel] TIMER and STOPWATCH, float time, for 1284P

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

Hi,
here is a routine for time measurement. 
It measures time in float seconds. Requires Leon's float lib and
Pito's floatconstants lib. You may change the granularity by
changing the prescaler, and the constant tck_ms. Mind the f_cpu as
well.

\ 2010-09-02 PITO - FLOAT TIME MEASUREMENT ATMEGA 1284P
\ based on  2007-12-26 EW   w4_clock_tick.fs
\ words: timer    2variable
\        tick_isr  interupt service routine: increments timer
\        +ticks    register and enable interupt
\        -ticks    disable interupt

marker -timer

decimal 

2variable timer
1. 2constant _one
0. 2constant _zero

\ overflow2 interupt service routine
\ increment tick
: tick_isr
_one timer 2@ d+ timer 2!
;

hex
\ enable ticks
\ overflow:  every f_cpu/256/1024
: +ticks
7 TCCR2B c! ( 111b = f_cpu clock/1024 )
0 ASSR  c! ( source: internal clock f_cpu)
['] tick_isr TIMER2_OVFAddr int! ( register interrupt )
_zero timer 2!
TIMSK2 c@  01 or TIMSK2 c! ( enable timer2 interrupt )
;

\ disable ticks
: -ticks
TIMSK2 c@ fe and TIMSK2 c! ( clr timer2 interrupt )
;

\ MEASURE TIME IN SECONDS (FLOAT)
decimal
2variable elapsed_ticks
\ f_cpu = 11059200
\ tck_ms = f_cpu \ 256 \ 1024
23703703. d>f _1e-9 f* fconstant tck_ms

: timer-start ( -- ) timer 2@ elapsed_ticks 2! ;

: timer-stop (  -- f ) timer 2@ d>f elapsed_ticks 2@ d>f f- tck_ms
f* ;

\ print elapsed time in ms 12345 = 12.345sec 
: prnt_elapsed_ms ( f -- ) _1e3 f* f>d d. ;

------------------------------------------

Example:
> +ticks
ok
> timer-start
ok
> timer-stop prnt_elapsed_ms
16023  ok
> 
.......Elapsed time 16.023sec.
Pito

Re: [Amforth-devel] Float testing - simple integration

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

hmmm.. imagine 3 cell zen float:
2 cells with double number, 1 cell with exponent, the dynamic range
+/- 2.147483648E+/-9863
We may count all Higgs bosons in 10^119 multiverses (assuming the
other universes are the same size as ours is) (:-))). Pito

> zenfloat uses 2 cells for a float number:
> first - mantissa
> second - exponent
> so the math is done much easier than the ieee one
> (Leon does).
> To get the Leon's precision (23 bit mantissa) we
> need 3 cells with
> the zen however: (2 cells mantissa 1 cell
> exponent), if even doable
> with the zen libs..
> Pito
> 
> ..
> > > source library named
> > > "zen float" (e.g. 4th) that could be useful as
> > > well. At least to not do
> 
> 

Re: [Amforth-devel] Float testing - simple integration

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

zenfloat uses 2 cells for a float number:
first - mantissa
second - exponent
so the math is done much easier than the ieee one (Leon does).
To get the Leon's precision (23 bit mantissa) we need 3 cells with
the zen however: (2 cells mantissa 1 cell exponent), if even doable
with the zen libs..
Pito

..
> > source library named
> > "zen float" (e.g. 4th) that could be useful as
> > well. At least to not do

Re: [Amforth-devel] Float testing - simple integration

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

.. the zen float seems to be a different format than Leon's float.
Not sure zenfloat is IEEE 754 like stuff.. P.

----- PŮVODNÍ ZPRÁVA -----
Od: "Matthias Trute" <mt...@we...>
Komu: "Everything around amforth"
<amf...@li...>
Předmět: Re: [Amforth-devel] Float testing - simple integration
Datum: 1.9.2010 - 20:35:31

> Hi,
> 
> just a side note: I was just pointed to a forth
> source library named
> "zen float" (e.g. 4th) that could be useful as
> well. At least to not do
> all the work again.
> 
> I highly appreciate your work, Leon (and Pito)
> 
> Matthias
> 
> 
> 
> ------------------------------------------------------------------------------
> > This SF.net Dev2Dev email is sponsored by:
> 
> Show off your parallel programming skills.
> Enter the Intel(R) Threading Challenge 2010.
> http://p.sf.net/sfu/intel-thread-sfd
> _______________________________________________
> Amforth-devel mailing list
> Amf...@li...
> https://lists.sourceforge.net/lists/listinfo/amforth-devel

Re: [Amforth-devel] Float testing - simple integration

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

Matthias,
I've downloaded ~8MB of the 4th stuff 2m ago. But, as I wrote, these
sources (and a tons of others) need a case insensitive amforth (e.g.
see fpout.4th)..
Pito

> 
> just a side note: I was just pointed to a forth
> source library named
> "zen float" (e.g. 4th) that could be useful as
> well. At least to not do
> all the work again.
> 
> I highly appreciate your work, Leon (and Pito)
> 
> Matthias
> 
> 
> 
> ------------------------------------------------------------------------------
> > This SF.net Dev2Dev email is sponsored by:
> 
> Show off your parallel programming skills.
> Enter the Intel(R) Threading Challenge 2010.
> http://p.sf.net/sfu/intel-thread-sfd
> _______________________________________________
> Amforth-devel mailing list
> Amf...@li...
> https://lists.sourceforge.net/lists/listinfo/amforth-devel

Re: [Amforth-devel] Float testing - simple integration

[Matthias T. <mt...@we...>]

Hi,

just a side note: I was just pointed to a forth source library named
"zen float" (e.g. 4th) that could be useful as well. At least to not do
all the work again.

I highly appreciate your work, Leon (and Pito)

Matthias

[Amforth-devel] Float testing - simple integration

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

Hi, here is a very simple integration (no special method applied)
for testing f+ and f*.
It integrates y=x^3 from A to B. Currently A=-B (e.g. -1 to +1) thus
the result shall be zero. Still thinking on N in the loop (:-)).
Pito

-------------------------
marker -testadd

\ very simple integration to test float add, sub

\ needs float constants

\ INTEGRAL from A to B of the function Y=X^3

\ A=-B, So the result shall be 0

-1 s>f fconstant _-1
0 s>f fconstant _0

\ FROM A TO B

-1 s>f fconstant A
A _-1 f* fconstant B

300 constant N

B A f- N s>f f/ fconstant delta

fvariable INTG
fvariable X
fvariable Y
variable NLoop

: p6 _1e6 f* f>d d. ." .1e-6 " ;
: p3 _1e3 f* f>d d. ." .1e-3 " ;

: Y=X^3 fdup fdup f* f* ;

: Y=X^2 fdup f* ;

: print_INTG INTG f@ p3 ; 

: INTEGRAL 
A X f!
_0 INTG f!
N 1 + NLoop !

NLoop @ 0 do

X f@ Y=X^3 Y f!

\ print X, Y
cr cr X f@ ." X=" p6 cr Y f@ ." Y=" p3 

Y f@ INTG f@ f+ INTG f! 
X f@ delta f+ X f!

\ print
cr INTG f@ ." INTG=" p3

loop

\ print
cr	cr ." RESULT=" print_INTG
;

-----------------
Ex:
.....
X=1000004 .1e-6 
Y=1000 .1e-3 
INTG=1 .1e-3 

RESULT=1 .1e-3  ok
> 

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
> 

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,
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...>]

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,
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

[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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