float$ macro and algo for testing

[jj2007]

The math.sdk file (vc++2008 translate) have some important constants value defined.

M_PI   equ   < 3.14159265358979323846>
jj2007                    PI = 3.14159265358979324

Better is to use this file .

ToutEnMasm,

you should at least try 1. to read posts properly and 2. to understand them.

[MichaelW]

AFAIK a REAL10 cannot represent 21 digits. Using TC 3.0, for which the CRT does support an 80-bit long double, this code:

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#include <math.h>
#include <stdio.h>
int main()
{
    long double pi10 = 3.14159265358979323846L;
    long double pif10;
    double pif8;
    asm {
        fldpi
        fstp pif10
        fldpi
        fstp pif8
    }
    printf( "3.14159265358979323846\n" );
    printf( "%.19Lf\n", (long double) pi10 );
    printf( "%.19Lf\n", (long double) pif10 );
    printf( "%.19f\n", (double) pif8 );
    getch();
    return 0;
}

Produces these results:

Code Select Expand


3.14159265358979323846
3.1415926535897932400
3.1415926535897932400
3.1415926535897931200


[jj2007]

AFAIK a REAL10 cannot represent 21 digits....
Produces these results:

Code Select Expand


3.14159265358979323846
3.1415926535897932400
3.1415926535897932400
3.1415926535897931200


Exactly. After a fldpi, Olly shows 3.1415926535897932380. The same identical value is obtained when pushing the value of 3.14159265358979323846 proposed by ToutEnMasm.

My new Str$ produces 3.14159265358979324, which is technically speaking more correct than the 32400 which wrongly pretends a higher precision, see here, point d.

[ToutEnMasm]

To jj2007,
Be cool , i was saying that the crt give all we need to use floating point.
atof,ftoa are very useful.
Add to this the strsafe librarie,and there is a lot of work to do with masm.
Useful comparisons can be made between the two.

[jj2007]

To jj2007,
Be cool , i was saying that the crt give all we need to use floating point.
atof,ftoa are very useful.
Add to this the strsafe librarie,and there is a lot of work to do with masm.
Useful comparisons can be made between the two.

I love useful comparisons. Please post some code showing the precision and the speed of your "alternatives". I suggest you use the value of 3.14159265358979323846 that you posted yourself.

[ToutEnMasm]

I am not microsoft,it's not my value.It's the value given by the math.h header file.

I this instant , the value can be put in a DT and is translate as this by a 32 bits

35 c2 68 21 a2 da 0f c9-00 40          ;dump of adress of the dt

view as follow by windbg

4000c90fdaa22168c235

fld accept the dt
After i need a viewer that can show 20 numbers after the virgul.
I will search

[jj2007]

After i need a viewer that can show 20 numbers after the virgul.

Hmmmm.... I thought you had already a "viewer":

the crt give all we need to use floating point.

[herge]

Hi JJ:

06:44 AM EST July 6 - Monday 2009
I thoght I saw a puddy Cat!

I like your avatar!

Regards herge

[sinsi]

Hah! so this is jj2007 vs ToutEnMasm! But we know who always wins between those two avatars... :lol

[ToutEnMasm]

Fan of titi ,see this one in french

http://video.google.com/videoplay?docid=2852273791155524323

[MichaelW]

Borland used the same value:

#define M_PI  3.14159265358979323846

As does MinGW:

#define M_PI  3.14159265358979323846

I think the idea was to exceed the ~19 digits that the FPU can handle and truncate the value at a point were the next digit was < 5.

3.1415926535897932384626433832795...

[dedndave]

i thought that, with MASM, you could define it to as many places as you like, and the assembler rounds it to fit the define type
i suppose that leaves a big spot for the assembler to make a mistake - lol
(we all know how perfect MASM is, right?)
i guess that also means that different assemblers might yield different results
to fix that, define it in raw float bytes ?

[jj2007]

Good point - what can the FPU handle, internally? A snippet for inspiration:

   fldpi      ; we push the exact PI
   fst MyPI8      ; a REAL8 for crt_printf
   fstp MyPI      ; a REAL10 for Str$
   fld MyPI      ; original value
   mov al, byte ptr MyPI
   dec eax
   mov byte ptr MyPI, al
   fld MyPI
   inc eax
   mov byte ptr MyPI, al
   fld MyPI
   inc eax
   mov byte ptr MyPI, al
   fld MyPI
   inc eax
   mov byte ptr MyPI, al
   fld MyPI
   inc eax
   mov byte ptr MyPI, al
   fld MyPI
   inc eax
   mov byte ptr MyPI, al
   fld MyPI
   inc eax
   mov byte ptr MyPI, al
   fld MyPI
   int 3

[ToutEnMasm]

Results  with  the fpu viewer , (libcmt )
Three value of PI    jj_PI ,SDK_PI, flpi_value

   ;35 c2 68 21 a2 da 0f c9-00 40  ;dump of memory
   ;4000c90fdaa22168c235           ; the DT show by windbg

jj_PI  dt  thevalue
SDK_PI dt  the value
the two show the same value in memory  ;dump of memory

Print of values loaded in the fpu registers,the three are the same

3.14159265358979310000       ;float print
54442D18h                             ;hexa print   

   

[MichaelW]

Using TC 3.0 again, this (16-bit DOS) code displays the values in the vicinity of pi that the REAL10 format can represent. The basis for this code is here.

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#include <math.h>
#include <stdio.h>
int main()
{
    long double pi10;
    int i=0;
    asm {
        fldpi
        fstp pi10
    }
    printf( "\t3.14159265358979323846\n" );
    asm {
        lea bx, pi10
        sub WORD PTR [bx], 10
        sbb WORD PTR [bx+2], 0
        sbb WORD PTR [bx+4], 0
        sbb WORD PTR [bx+6], 0
        sbb WORD PTR [bx+8], 0
    }
    printf( "%d\t%.19Lf\n", i-10, (long double) pi10 );
    for( i=1; i<60; i++ )
    {
        asm {
            lea bx, pi10
            add WORD PTR [bx], 1
            adc WORD PTR [bx+2], 0
            adc WORD PTR [bx+4], 0
            adc WORD PTR [bx+6], 0
            adc WORD PTR [bx+8], 0
        }
        if( i < 20 || i == 52 || i == 53 )
          printf( "%d\t%.19Lf\n", i-10, (long double) pi10 );
    }
    getch();
    return 0;
}

The representable values in the immediate vicinity of pi are so close together that the Borland CRT cannot display the differences. To see a difference, it was necessary to go 6 values down or 43 values up. Perhaps Olly can do better.

Code Select Expand


        3.14159265358979323846
-10     3.1415926535897932300
-9      3.1415926535897932300
-8      3.1415926535897932300
-7      3.1415926535897932300
-6      3.1415926535897932300
-5      3.1415926535897932400
-4      3.1415926535897932400
-3      3.1415926535897932400
-2      3.1415926535897932400
-1      3.1415926535897932400
0       3.1415926535897932400
1       3.1415926535897932400
2       3.1415926535897932400
3       3.1415926535897932400
4       3.1415926535897932400
5       3.1415926535897932400
6       3.1415926535897932400
7       3.1415926535897932400
8       3.1415926535897932400
9       3.1415926535897932400
42      3.1415926535897932400
43      3.1415926535897932500