Cambridge is an old, venerable university and has a whole series of famous graduates: Francis Bacon, Isaac Newton, James Clerk Maxwell or Ludwig Wittgenstein, to name but these. If you want
to study - lets say - Mathematics in Cambridge, you have to pass the Cambridge Test of Mathematics for University Admission (TMUA). It contains 20 different tasks. The time to solve is 75 minutes.
That means: For each problem 3 minutes and 45 seconds are available. That's not much time, because the questions are demanding.
I will present here one of the tasks and show how to solve it; it's about an exponential equation. This is demonstrated in detail in the file EXPO.PDF. I wrote this text with LaTex; the corresponding
source file EXPO.TEX is a portion of the archive. After the task is done, it must still be shown that we've really found the solutions of the exponential equation. That's not part of the Cambridge test
anymore, but we do it for completeness.
The program EXPO.EXE serves for this purpose. I used PowerBASIC for DOS to do that job. That's the little brother of the two 32 bit PB compilers. But this DOS compiler knows the data type REAL10
and can handle it correctly. The same cannot be said of MSVC, for example. Under PB the data type is called Extended. For the check, this is recommended; in both solutions the logarithm plays a role.
These values are usually irrational, if not transcendent. Therefore, the best available accuracy must be used for that calculation, to minimize rounding errors. The README.TXT file contains more details
about the sources and files of the archive.
The program itself is a real mode program and should run under quite all configurations. I have tested it under native DOS, the DOS emulations of 32 bit Windows, Linux, BSD and OS/2 Warp 4.
It also runs without problems under various virtual machines and inside DOSBox. That's tested, too.
A feedback from other members would be nice. I'm interested in: Were the text and the calculations comprehensible? Does the program run under other configurations?
Many thanks in advance.
Gunther,
It looks like nice clean code but with Win10 not having a 16 bit subsystem, I cannot run it. I have not had a 16 bit capable OS since XP that would still run DOS apps. Sorry I cannot be much use to you here.
Thank you for the reply, Steve.
Quote from: hutch-- on March 01, 2022, 08:59:35 PM
It looks like nice clean code but with Win10 not having a 16 bit subsystem, I cannot run it. I have not had a 16 bit capable OS since XP that would still run DOS apps. Sorry I cannot be much use to you here.
DOSBox will do the job. Even poorly written DOS programs cannot do any harm in this sandbox. I have installed version 0.74-3 on my Win 10 machine. This runs without problems.
Quote from: Gunther on March 01, 2022, 06:34:44 PM
A feedback from other members would be nice. I'm interested in: Were the text and the calculations comprehensible? Does the program run under other configurations?
Hi Gunther,
Text and calculations were quite clear and, for a quick read,
seemed comprehensible. I may have to read it again with more
care for some of the logarithmic transforms. And the program
runs with Windows 2000, but seems a bit spare compared to
the PDF.
Regards,
Steve N.
I Gunther!
Quote from: Gunther on March 01, 2022, 06:34:44 PM
I used PowerBASIC for DOS to do that job.
Fantastic, I was missing that piece of history. For sure Zale also worked in Turbo Pascal because is exactly same way to include assembly modules.
If you tested in DosBox then DosBox-X isn't working well.
Regards, HSE
Quote from: HSE on March 02, 2022, 01:52:13 AM
Fantastic, I don't know that piece of history. For sure Zale also worked in Turbo Pascal because is exactly same way to include assembly modules.
Anders Hejlsberg is behind Turbo Pascal, then Delphi, then C# and vb.Net
Quote from: TimoVJL on March 02, 2022, 02:43:10 AM
Anders Hejlsberg is behind Turbo Pascal
At same time that Zale was working in Turbo Basic?
Later:
I found that Zale left Borland in 1989, and Hejlsberg enter to Borland that year. But Borland have a license of Hejlsberg's Pascal before 1983, and worked together in direct or indirect way.
Quote from: HSE on March 02, 2022, 01:52:13 AM
Fantastic, I was missing that piece of history. For sure Zale also worked in Turbo Pascal because is exactly same way to include assembly modules.
I had known Bob Zale and Dave Navarro since the late 80's from the CompuServe forum. Bob was an excellent programmer. He wrote both the compilers for TurboBASIC
and PowerBASIC completely in assembler. If you want to know more historical details you can find them here (http://masm32.com/board/index.php?topic=964.msg8681#msg8681) or here (https://en.wikipedia.org/wiki/PowerBASIC). Another good source is Hutch, who worked
very closely with Bob at times. Asking him costs nothing.
I'm not entirely sure, but I think Bob had little to do with TurboPASCAL. The fact that OBJ files are included in TurboBASIC and TurboPASCAL in the same way is probably
related to Borland's design specifications. Casually, Bob Zale was a member here on the forum until the very end.
Steve,
thank you for your answer. :thumbsup:
Quote from: FORTRANS on March 02, 2022, 12:44:00 AM
... And the program runs with Windows 2000 ...
Another configuration in which the program does its job. Windows 2000 was between Windows ME and Windows XP, if I remember correctly. That must be a pretty old machine running.
Quote from: FORTRANS on March 02, 2022, 12:44:00 AM
... but seems a bit spare compared to the PDF.
That is clear. In the PDF file the complete solution is explained in detail. The PowerBASIC program, on the other hand, only performs the following function: Once you have calculated the
solutions, they are substituted into the initial equation to verify that they are correct. This procedure is called inference or conclusion. The software does just that and only that.
Memories of Turbo Pascal version 1.0 - Anders Hejlsberg, United States - Community Blogs - Embarcadero Community (https://community.embarcadero.com/blogs/entry/memories-of-turbo-pascal-version-10--anders-hejlsberg-united-states-39215)
Quote from: TimoVJL on March 02, 2022, 06:00:08 PM
Memories of Turbo Pascal version 1.0 - Anders Hejlsberg, United States - Community Blogs - Embarcadero Community (https://community.embarcadero.com/blogs/entry/memories-of-turbo-pascal-version-10--anders-hejlsberg-united-states-39215)
Thank you for the link. This confirms what I already presumed in this post (http://masm32.com/board/index.php?topic=9897.msg108538#msg108538). However, this question is only a minor aspect. This thread is mainly about PowerBASIC and the
Cambridge Test - as it states in the title. TurboPASCAL doesn't play any role.
Thanks Timo and Gunther!
Quote from: Gunther on March 02, 2022, 10:12:00 PM
This thread is mainly about PowerBASIC and the Cambridge Test - as it states in the title. TurboPASCAL doesn't play any role.
:thumbsup:
Making the object with TASM or ML the binary is 1408 bytes bigger. That is with PB/DOS 3.5. I think you reported previously some size diferences using differents tools.
Hi Gunther,
Quote from: Gunther on March 02, 2022, 12:52:55 PM
Steve,
thank you for your answer. :thumbsup:
You are welcome.
QuoteQuote from: FORTRANS on March 02, 2022, 12:44:00 AM
... And the program runs with Windows 2000 ...
Another configuration in which the program does its job. Windows 2000 was between Windows ME and Windows XP, if I remember correctly.
IIRC; 95 => 98 => ME; NT => 2000 => XP:
QuoteThat must be a pretty old machine running.
Well yes, I suppose. I got it in late December 2000. P-III running
Windows 2000 and OS/2 Warp 4. And your program runs with OS/2
as well.
Cheers,
Steve
Quote from: HSE on March 03, 2022, 12:50:02 AM
Making the object with TASM or ML the binary is 1408 bytes bigger. That is with PB/DOS 3.5. I think you reported previously some size diferences using differents tools.
I have also used PB 3.5. The difference comes from the assembler. The OBJ file generated by JWASM has a size of 343 bytes. Other assemblers obviously insert a whole lot of junk.
No wonder that large binary clumps are then created. JWASM, on the other hand, is fast and produces small binaries. This is one of the reasons why this assembler is my first choice.
Japheth has really written an excellent program. It's a very good tool to work with.
Steve,
Quote from: FORTRANS on March 03, 2022, 01:18:49 AM
And your program runs with OS/2 as well.
Yes, I've tested that. It works with the DOS emulation of Warp 3 and Warp 4.
Quote from: FORTRANS on March 03, 2022, 01:18:49 AM
IIRC; 95 => 98 => ME; NT => 2000 => XP:
I was already sitting in front of a machine with NT 3.5 in 1994. NT 4.0 was released at the end of July 1996, ahead of Windows 98. I know this pretty well because the university spent vast sums
of money on equipping the labs with software back then.
Quote from: FORTRANS on March 03, 2022, 01:18:49 AM
Well yes, I suppose. I got it in late December 2000. P-III running Windows 2000 and OS/2 Warp 4.
So the machine has been running for over 20 years. :cool: :thumbsup: That's impressive. At that time there were still floppy disk drives. Today's young people don't even know what that is anymore.
DELETED
Quote from: TimoVJL on March 03, 2022, 05:37:32 PM
OBJ file consist many parts, ...
I know that OBJ files consist of many parts, because I've read this book (https://www.amazon.de/Linkers-Kaufmann-Software-Engineering-Programming-ebook/dp/B008HNGAG0).
Quote from: TimoVJL on March 03, 2022, 05:37:32 PM
... so a bit funny comment :smiley:
By now I know that you have a very strange sense of humor. What's so funny about that? I have compiled the assembly language source with JWASM and TASM 4.0; both in 2 passes. With the command line
switch /q for TASM. This suppresses the parts that are not necessary for linking. The size of the OBJ JWASM file is 345 bytes and 375 bytes for TASM. And that with this ridiculously small source. I'm sorry,
but that' s not funny to me.
But once again: That's not the issue here. The thread is about PowerBASIC and the Cambridge test. There can be no doubt about this, because this topic is quite clearly named in the title.
Hi Gunther!
Quote from: Gunther on March 03, 2022, 04:49:36 PM
The OBJ file generated by JWASM has a size of 343 bytes. Other assemblers obviously insert a whole lot of junk.
Like Timo say different OBJ sizes result in same EXE size. In fact, the OBJ file generated by ML has a size of 335 bytes.
Just to play, I builded JwasmR, and produce the 343 bytes OBJ, and is the same.
A little intriguing, but not important to enter Cambridge :thumbsup:
Regards, HSE.
Hi,Gunther
i got another result.
x1+x2=2*log(3,20)= 5.453666055721684 ;real10
;----------------------------------------------------
2*log(3,20)=[2*log(2,20)]/[1*log(2,3)]
local @tmpIValue:QWORD
local ResultReal10:REAL10
invoke RtlZeroMemory,addr buff,sizeof buff
invoke RtlZeroMemory,ADDR OutBuf,sizeof OutBuf
finit
;int 3
mov @tmpIValue,2
fild @tmpIValue
mov @tmpIValue,20
fild @tmpIValue
fyl2x ;st0=20,st1=2 --> st0=2*log(2,20)
fld1
mov @tmpIValue,3
fild @tmpIValue
fyl2x ;st0=3,st1=1 --> st0=1*log(2,3)
fdiv st(1),st(0) ; -->[2*log(2,20)]/[1*log(2,3)]
fxch st(1) ; st1 <--> st0
lea rax,ResultReal10
fstp TBYTE PTR [rax] ;st0 --> addr ResultReal10
invoke FpuFLtoA64,addr ResultReal10,15,ADDR OutBuf,SRC2_DIMM or SRC1_REAL or STR_REG ;STR_SCI
what's wrong?
regard.
Quote from: HSE on March 03, 2022, 11:19:19 PM
Like Timo say different OBJ sizes result in same EXE size. In fact, the OBJ file generated by ML has a size of 335 bytes.
Just to play, I builded JwasmR, and produce the 343 bytes OBJ, and is the same.
This is certainly correct for such small OBJ files. Otherwise, there may already be a difference.
Quote from: HSE on March 03, 2022, 11:19:19 PM
A little intriguing, but not important to enter Cambridge :thumbsup:
Of course. But wait a bit: in a few days I'll post on the Oxford test, which is equally quite challenging. I don't want anyone to be able to say that I'm taking sides unilaterally with Cambridge.
Dear six_L,
Quote from: six_L on March 04, 2022, 12:27:52 AM
Hi,Gunther
i got another result.
x1+x2=2*log(3,20)= 5.453666055721684 ;real10
;----------------------------------------------------
2*log(3,20)=[2*log(2,20)]/[1*log(2,3)]
At first glance, I would say that there is something wrong with the calculation. For example, I think that 1*log(2,3) = log(2,3). If you want, send me a PM with your email address. I'll then send you a PDF file with
the correct derivation of a formula with which you can calculate any logarithms to any bases. If others are interested in it too, I can also publish it here in the forum.
But I think that there is no great general interest in that. Therefore, let's do it individually between both of us. :cool:
Quote from: six_L on March 04, 2022, 12:27:52 AM
i got another result.
x1+x2=2*log(3,20)= 5.453666055721684 ;real10
what's wrong?
Nothing wrong! It's that.
Using qWord's algorithm in BASIC :icon_idea:
Note for Gunther: perhaps is more clear to say "result using x1 is ..."
updated files.
DELETED
HSE,
Quote from: HSE on March 04, 2022, 03:48:13 AM
Nothing wrong! It's that.
Using qWord's algorithm in BASIC :icon_idea:
right. It's the result for x1 + x2. But in principle, it doesn't matter at all. All we have to show is that 9*(SQR(3))^x - 3^x = 20. That's exactly what my program does - nothing more, nothing less.
But it's good that you've clarified the question. However, I had trouble because you did not change the old comment function header of GetSolution. And why is the new function called logbx? Is it
just a name or does it have a deeper meaning?
Quote from: HSE on March 04, 2022, 03:48:13 AM
Note for Gunther: perhaps is more clear to say "result using x1 is ..."
That' s a matter of taste, see my remark about what we just need to show.
Quote from: TimoVJL on March 04, 2022, 05:12:34 AM
Sure i do that, before that, i had to make a funny gmail address for that :smiley:
What's with all your blather? Are you bored?
Quote from: Gunther on March 04, 2022, 06:19:58 AM
However, I had trouble because you did not change the old comment function header of GetSolution.
I don't even noted that :thumbsup:
Quote from: Gunther on March 04, 2022, 06:19:58 AM
And why is the new function called logbx? Is it just a name or does it have a deeper meaning?
Means "logarithm of base x". It's the name in use in SmplMath from years (2011, I think).
Take me a while to find how to extract results:
**************************************
* Result x1 = 2.92994704143585433 *
* Result x2 = 2.52371901428582975 *
* Result x1+x2 = 5.45366605572168408 *
**************************************
2 * logbx(3,20) = 5.45366605572168408
HSE,
Quote from: HSE on March 04, 2022, 06:50:54 AM
Means "logarithm of base x". It's the name in use in SmplMath from years (2011, I think).
ah, qword's material. Since I'm not a big fan of macros, I didn't look into it. Are you the current package maintainer?
Quote from: HSE on March 04, 2022, 06:50:54 AM
Take me a while to find how to extract results:
Why? The approach is quite simple after all. Correctly combine the function with its inverse function and logarithmize this expression. That's all. The rest is just a matter of skills.
Gunther,
Quote from: Gunther on March 04, 2022, 08:00:19 AM
Are you the current package maintainer?
That is qWord suggestion, but everyone can make a fork.
Quote from: Gunther on March 04, 2022, 08:00:19 AM
Why? The approach is quite simple after all.
Sorry, I was talking about the program itself. The program look like a console program using
print. After years using
print in console assembly programs take me a lot of effort to realize that PowerBasic
print is a graphic function :biggrin:
The instruction for console output is
stdout and work exactly like
print if console output is not captured.
PRINT
PRINT" **************************************"
PRINT" * Result x1 ="; STR$(x1, 18);" *"
PRINT" * Result x2 ="; STR$(x2, 18);" *"
PRINT" * Result x1+x2 ="; STR$(x1x2, 18); " *"
PRINT" **************************************"
PRINT
PRINT" 2 * logbx(3,20) = "; STR$(x3,18)
PRINT
STDOUT" **************************************"
STDOUT" * Result x1 =";
STDOUT STR$(x1, 18);
STDOUT " *"
STDOUT" * Result x2 =";
STDOUT STR$(x2, 18);
STDOUT" *"
STDOUT" * Result x1+x2 =";
STDOUT STR$(x1x2, 18);
STDOUT" *"
STDOUT" **************************************"
STDOUT
STDOUT" 2 * logbx(3,20) = ";
STDOUT STR$(x3,18)
STDOUT
Hi,HSE
QuoteNothing wrong! It's that.
thanks your confirm.
Hi,Gunther
Quoteright. It's the result for x1 + x2. But in principle, it doesn't matter at all. All we have to show is that 9*(SQR(3))^x - 3^x = 20. That's exactly what my program does - nothing more, nothing less.
i can't run the codes becauseof no 16bit system. At first glance, the paper " expo.pdf " is so remarkable, written
carefully / perfectly / earnestly / attractively . it Leads me to calculate again. You are always admirable while done everything
regard.
HSE,
Quote from: HSE on March 04, 2022, 09:22:14 AM
Sorry, I was talking about the program itself. The program look like a console program using print. After years using print in console assembly programs take me a lot of effort to realize that PowerBasic print is a graphic function :biggrin:
The instruction for console output is stdout and work exactly like print if console output is not captured.
that's remarkable. Can you give a simple working example for PB 3.5 and PBCC respectively? Steve aka Hutch and I would be very interested in this.
Quote from: six_L on March 04, 2022, 05:03:15 PM
i can't run the codes becauseof no 16bit system.
You should try DOSBox (https://www.dosbox.com/download.php?main=1). The DOS programs run under the direction of a solid Windows program and just "play" in a sandbox, so to speak. No damage can occur this way, even if
the DOS application is lousy written. It's really rock solid and easy to install.
Quote from: six_L on March 04, 2022, 05:03:15 PM
At first glance, the paper " expo.pdf " is so remarkable, written carefully / perfectly / earnestly / attractively . it Leads me to calculate again. You are always admirable while done everything
Thank you for the flowers. Well, I have made an effort. After all, the whole world can in theory read along. One shouldn't write nonsense there. Sure, some write garbage only to delete it
afterwards. This is a recent fashion in the forum, you know what I mean. I am not one of those people, because I think before I write something. That's my trick, which I have revealed herewith.
At the moment I am still going to prepare the post on the Oxford test. But this weekend I'll finish your paper on logarithms and mail it to you. I've not forgotten that.
Hi,Gunther
QuoteBut this weekend I'll finish your paper on logarithms and mail it to you. I've not forgotten that.
thanks you for the respone.
that will waste your times and disturbing your rest.
i'v remembered that you have researched video compression and transmission technology. i'm interesting more than it. if you have some spare times and irrelevant with your country military secrets. i hope you would write an A4 page about this.
best regard.
six_L,
Quote from: six_L on March 04, 2022, 06:11:37 PM
thanks you for the respone.
that will waste your times and disturbing your rest.
no, not really. For me, it's always an intellectual challenge to answer mathematical questions as simply as possible. I enjoy that and I like doing it. Hopefully others will also like my way of
explaining certain aspects of Mathematics.
Gunther,
Quote from: Gunther on March 04, 2022, 05:09:23 PM
Can you give a simple working example for PB 3.5 and PBCC respectively?
Executing program from commandline "Hello_CC" show print and stdout functions in the screen.
Redirecting console "Hello_CC > out.txt" show print function in screen and stdout in the file.
HSE,
thank you for both programs. If I had read correctly on p. 259 in the Reference Manual of PB 3.5, I would know that. Maybe I even read that and just unfortunately forgot because I'm getting
old and senile, who knows? In any case, thanks for this refresher and reminder. :thumbsup:
Gunther,
:thumbsup: It's a good exercise.
Quote from: Gunther on March 05, 2022, 12:00:55 AM
in the Reference Manual of
That is the last resource, when every other things have failed :biggrin:
Regards, HSE.
HSE,
Quote from: HSE on March 05, 2022, 12:43:44 AM
That is the last resource, when every other things have failed :biggrin:
yes unfortunately. But especially the Reference Manual should always be at hand when it comes to programs.
six_L,
Quote from: six_L on March 04, 2022, 06:11:37 PM
i'v remembered that you have researched video compression and transmission technology. i'm interesting more than it. if you have some spare times and irrelevant with your country military secrets. i hope you would write an A4 page about this.
I'm afraid that won't work. The background of these things is pretty hard mathematics. We are not talking here about the 18th and 19th century mathematics of Euler, Lagrange or Laplace.
It's about the mathematics of the 20th century, founded by Stefan Banach and David Hilbert. It is still quite fresh and wet, so to speak. Much of this isn't yet in the textbooks. That can' t be
described on one page.
But I have been thinking about your question. Here is a book (https://www.google.de/books/edition/Chaos_and_Fractals/rZTkBwAAQBAJ?hl=de&gbpv=1&dq=isbn:1475747403&printsec=frontcover) I can recommend to you. It contains a short contribution by Yuval Fisher entitled:
A discussion of Fractal Image Compression.
You can use that as a starting point. Could I help you with that?
Hi Gunther,
Quote from: Gunther on March 04, 2022, 01:28:26 AM
I'll then send you a PDF file with
the correct derivation of a formula with which you can calculate any logarithms to any bases. If others are interested in it too, I can also publish it here in the forum.
Well I would like to take a look at it. If just to see if it is
interesting. Sort of depends on how useful I would find it.
Or if it is interesting in its own right.
Regards,
Steve N.
Steve,
Quote from: FORTRANS on March 05, 2022, 03:58:59 AM
Well I would like to take a look at it. If just to see if it is
interesting. Sort of depends on how useful I would find it.
Or if it is interesting in its own right.
why not? Please send me your mail address via a PM and you will also get a copy of the file. If you and six_L think it's good enough, I can post it on the forum afterwards.
But as I have already written here (http://masm32.com/board/index.php?topic=9897.msg108599#msg108599), there is nothing special about it:
Quote
The approach is quite simple after all. Correctly combine the function with its inverse function and logarithmize this expression. That's all.
I only want to say: Don't expect miracles or sensational revelations. It's really not complicated.
An important correction is necessary.
In another thread (http://masm32.com/board/index.php?topic=9909.msg108681#msg108681) FORTRANS pointed me to inaccuracies in the function GetFpu inside the assembly language file.
These errors are anything but harmless. I took another close look at the code for that reason. It was lucky that the
application ran properly. In other configurations, a crash could have occurred. I have therefore fixed the code of the
GetFpu function in the EXPO.ASM file accordingly. The right archive with the corrected file is EXPO1.ZIP and is below
the first post of this thread.
Once again, many thanks to FORTRANS. :thumbsup: