magic numbers

RuiLoureiro · May 14, 2013, 01:15:09 AM

Hi,
When i read the code from Mikl__ i saw that
his magic number was

42949673 ;2^32/100

So we could get the magic for 10 = 2^32/10 = 429496730

The question was: is this correct ?

The answer is: NO !

So the next DivideREGby10 and DivideREGby100
are not correct.

. Well we may use DivideREGby10 if number is < 1073741829
. But we CANNOT use DivideREGby100 because it is wrong
at least for numbers 10 to 129 ... and much much more !

Thanks all of you :t

Please try it may be i have made something wrong.

Quote
; ¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤
DivideREGby10 MACRO ireg
; note: we may use it but ...
mov ecx, ireg
mov eax, 429496730 ; =2^32/10
mul ecx
; ---------------
; edx = quotient
; ---------------

imul eax, edx,10
; -------------
; ecx=remainder
; -------------
sub ecx, eax
ENDM
; ¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤
DivideREGby100 MACRO ireg
; note: this is wrong

mov ecx, ireg
mov eax, 42949673 ;2^32/100
mul ecx
; ---------------
; edx = quotient
; ---------------

imul eax, edx,100 ; here it was 10 but the result is the same
; -------------
; ecx=remainder
; -------------
sub ecx, eax
ENDM

we get this:

Division by 10
1073741829
40000005
*** STOP - NOT EQUAL --- E N D ---***
---------------------------------------------------

Division by 100

Code Select


 *** STOP - NOT EQUAL ---*** 10
0000000A
 *** STOP - NOT EQUAL ---*** 11
0000000B
 *** STOP - NOT EQUAL ---*** 12
0000000C
 *** STOP - NOT EQUAL ---*** 13
0000000D
 *** STOP - NOT EQUAL ---*** 14
0000000E
 *** STOP - NOT EQUAL ---*** 15
0000000F
 *** STOP - NOT EQUAL ---*** 16
00000010
 *** STOP - NOT EQUAL ---*** 17
00000011
 *** STOP - NOT EQUAL ---*** 18
00000012
 *** STOP - NOT EQUAL ---*** 19
00000013
 *** STOP - NOT EQUAL ---*** 20
00000014
 *** STOP - NOT EQUAL ---*** 21
00000015
 *** STOP - NOT EQUAL ---*** 22
00000016
 *** STOP - NOT EQUAL ---*** 23
00000017
 *** STOP - NOT EQUAL ---*** 24
00000018
 *** STOP - NOT EQUAL ---*** 25
00000019
 *** STOP - NOT EQUAL ---*** 26
0000001A
 *** STOP - NOT EQUAL ---*** 27
0000001B
 *** STOP - NOT EQUAL ---*** 28
0000001C
 *** STOP - NOT EQUAL ---*** 29
0000001D
 *** STOP - NOT EQUAL ---*** 30
0000001E
 *** STOP - NOT EQUAL ---*** 31
0000001F
 *** STOP - NOT EQUAL ---*** 32
00000020
 *** STOP - NOT EQUAL ---*** 33
00000021
 *** STOP - NOT EQUAL ---*** 34
00000022
 *** STOP - NOT EQUAL ---*** 35
00000023
 *** STOP - NOT EQUAL ---*** 36
00000024
 *** STOP - NOT EQUAL ---*** 37
00000025
 *** STOP - NOT EQUAL ---*** 38
00000026
 *** STOP - NOT EQUAL ---*** 39
00000027
 *** STOP - NOT EQUAL ---*** 40
00000028
 *** STOP - NOT EQUAL ---*** 41
00000029
 *** STOP - NOT EQUAL ---*** 42
0000002A
 *** STOP - NOT EQUAL ---*** 43
0000002B
 *** STOP - NOT EQUAL ---*** 44
0000002C
 *** STOP - NOT EQUAL ---*** 45
0000002D
 *** STOP - NOT EQUAL ---*** 46
0000002E
 *** STOP - NOT EQUAL ---*** 47
0000002F
 *** STOP - NOT EQUAL ---*** 48
00000030
 *** STOP - NOT EQUAL ---*** 49
00000031
 *** STOP - NOT EQUAL ---*** 50
00000032
 *** STOP - NOT EQUAL ---*** 51
00000033
 *** STOP - NOT EQUAL ---*** 52
00000034
 *** STOP - NOT EQUAL ---*** 53
00000035
 *** STOP - NOT EQUAL ---*** 54
00000036
 *** STOP - NOT EQUAL ---*** 55
00000037
 *** STOP - NOT EQUAL ---*** 56
00000038
 *** STOP - NOT EQUAL ---*** 57
00000039
 *** STOP - NOT EQUAL ---*** 58
0000003A
 *** STOP - NOT EQUAL ---*** 59
0000003B
 *** STOP - NOT EQUAL ---*** 60
0000003C
 *** STOP - NOT EQUAL ---*** 61
0000003D
 *** STOP - NOT EQUAL ---*** 62
0000003E
 *** STOP - NOT EQUAL ---*** 63
0000003F
 *** STOP - NOT EQUAL ---*** 64
00000040
 *** STOP - NOT EQUAL ---*** 65
00000041
 *** STOP - NOT EQUAL ---*** 66
00000042
 *** STOP - NOT EQUAL ---*** 67
00000043
 *** STOP - NOT EQUAL ---*** 68
00000044
 *** STOP - NOT EQUAL ---*** 69
00000045
 *** STOP - NOT EQUAL ---*** 70
00000046
 *** STOP - NOT EQUAL ---*** 71
00000047
 *** STOP - NOT EQUAL ---*** 72
00000048
 *** STOP - NOT EQUAL ---*** 73
00000049
 *** STOP - NOT EQUAL ---*** 74
0000004A
 *** STOP - NOT EQUAL ---*** 75
0000004B
 *** STOP - NOT EQUAL ---*** 76
0000004C
 *** STOP - NOT EQUAL ---*** 77
0000004D
 *** STOP - NOT EQUAL ---*** 78
0000004E
 *** STOP - NOT EQUAL ---*** 79
0000004F
 *** STOP - NOT EQUAL ---*** 80
00000050
 *** STOP - NOT EQUAL ---*** 81
00000051
 *** STOP - NOT EQUAL ---*** 82
00000052
 *** STOP - NOT EQUAL ---*** 83
00000053
 *** STOP - NOT EQUAL ---*** 84
00000054
 *** STOP - NOT EQUAL ---*** 85
00000055
 *** STOP - NOT EQUAL ---*** 86
00000056
 *** STOP - NOT EQUAL ---*** 87
00000057
 *** STOP - NOT EQUAL ---*** 88
00000058
 *** STOP - NOT EQUAL ---*** 89
00000059
 *** STOP - NOT EQUAL ---*** 90
0000005A
 *** STOP - NOT EQUAL ---*** 91
0000005B
 *** STOP - NOT EQUAL ---*** 92
0000005C
 *** STOP - NOT EQUAL ---*** 93
0000005D
 *** STOP - NOT EQUAL ---*** 94
0000005E
 *** STOP - NOT EQUAL ---*** 95
0000005F
 *** STOP - NOT EQUAL ---*** 96
00000060
 *** STOP - NOT EQUAL ---*** 97
00000061
 *** STOP - NOT EQUAL ---*** 98
00000062
 *** STOP - NOT EQUAL ---*** 99
00000063
 *** STOP - NOT EQUAL ---*** 100
00000064
 *** STOP - NOT EQUAL ---*** 101
00000065
 *** STOP - NOT EQUAL ---*** 102
00000066
 *** STOP - NOT EQUAL ---*** 103
00000067
 *** STOP - NOT EQUAL ---*** 104
00000068
 *** STOP - NOT EQUAL ---*** 105
00000069
 *** STOP - NOT EQUAL ---*** 106
0000006A
 *** STOP - NOT EQUAL ---*** 107
0000006B
 *** STOP - NOT EQUAL ---*** 108
0000006C
 *** STOP - NOT EQUAL ---*** 109
0000006D
 *** STOP - NOT EQUAL ---*** 110
0000006E
 *** STOP - NOT EQUAL ---*** 111
0000006F
 *** STOP - NOT EQUAL ---*** 112
00000070
 *** STOP - NOT EQUAL ---*** 113
00000071
 *** STOP - NOT EQUAL ---*** 114
00000072
 *** STOP - NOT EQUAL ---*** 115
00000073
 *** STOP - NOT EQUAL ---*** 116
00000074
 *** STOP - NOT EQUAL ---*** 117
00000075
 *** STOP - NOT EQUAL ---*** 118
00000076
 *** STOP - NOT EQUAL ---*** 119
00000077
 *** STOP - NOT EQUAL ---*** 120
00000078
 *** STOP - NOT EQUAL ---*** 121
00000079
 *** STOP - NOT EQUAL ---*** 122
0000007A
 *** STOP - NOT EQUAL ---*** 123
0000007B
 *** STOP - NOT EQUAL ---*** 124
0000007C
 *** STOP - NOT EQUAL ---*** 125
0000007D
 *** STOP - NOT EQUAL ---*** 126
0000007E
 *** STOP - NOT EQUAL ---*** 127
0000007F
 *** STOP - NOT EQUAL ---*** 128
00000080
 *** STOP - NOT EQUAL ---*** 129
00000081
 *** STOP - NOT EQUAL --- E N D ---***

test procedure:

Code Select


; File:     TestMagic10_1.asm
;    by     RuiLoureiro
;-----------------------------------
include \masm32\include\masm32rt.inc
.686
; ««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««
                            include  Macros10.inc
; «««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««« 
.data

; ««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««
.code
;==============================================================================
start:

jmp _stop
                print   "Division by 10", 13, 10            
                
                mov     esi, 0                
                jmp     _next

    _loop:
                DivideREGby10 esi           ; edx = quotient ecx=remainder
                push    ecx
                push    edx
                ;
                mov     eax, esi
                xor     edx, edx
                mov     ecx, 10
                div     ecx
                ;
                pop     ebx
                pop     ecx
                cmp     ebx, eax
                jne     _erro1
                cmp     ecx, edx
                jne     _erro1

    _next:      add     esi, 1
                or      esi, esi
                jns     _loop
                
                inkey " *** STOP - ALL EQUAL --- E N D ---*** " 
                jmp     _stop

    _erro1:     print   str$(esi),13,10
                print   hex$(esi),13,10        
                inkey " *** STOP - NOT EQUAL --- E N D ---*** " 

;------------------------------------------------------------------------------
    _stop:      xor     edi, edi            ; cases
                
                print   "Division by 100", 13, 10                            
                mov     esi, 0                
                jmp     _next1

    _loop1:
                DivideREGby100 esi           ; edx = quotient ecx=remainder
                push    ecx
                push    edx
                ;
                mov     eax, esi
                xor     edx, edx
                mov     ecx, 10
                div     ecx
                ;
                pop     ebx
                pop     ecx
                cmp     ebx, eax
                jne     _erro2
                cmp     ecx, edx
                jne     _erro2
                ;
    _next1:     add     esi, 1
                or      esi, esi
                jns     _loop1
                
                inkey " *** STOP - ALL EQUAL --- E N D ---*** " 
                jmp     _end

    _erro2:     print   " *** STOP - NOT EQUAL ---*** "   
                print   str$(esi),13,10
                print   hex$(esi),13,10        
                ;
                add     esi, 1
                add     edi, 1
                cmp     edi, 120
                jb      _loop1

                inkey " *** STOP - NOT EQUAL --- E N D ---*** "
                 
    _end:          
            exit
;*********************************************************************
end start

Tedd · May 14, 2013, 01:51:57 AM

http://www.masmforum.com/board/index.php?topic=17027.msg142029#msg142029

Quote
The simplified version...

For divide by 11, the magic reciprocal is 2³² / 11 = 390451572 (remainder 4)
and multiplying by this number gives 12345 * 390451572 = 4820124656340
which doesn't look right, until you realize what we actually did what multiply by 2³² and then divide by 11.
So, for the result, we can just divide by 2³² again - which would be the same as just dividing by 11 in the first place.
Luckily for us, the result of a mul is naturally split into edx and eax, where edx represents the upper part multiplied by 2³², so we just take edx directly as the result.

Sure enough...

12345 / 11 = 1122.27
12345 * 390451572 = 4820124656340 = 1122 * 2³² + 1171350228 => 1122

That's the simplified version because we didn't take the 4 remainder into account, which leads to accumulated errors depending on what values you're dividing. As Dave said, it depends on the range you want to include.
To increase accuracy, you'd shift the magic value and add on a proportion of the remainder. Then shift the result back again to correct for the inherent shift in the magic value, which can effectively give you a few decimal places of accuracy (rounded, naturally.)

dedndave · May 14, 2013, 03:42:22 AM

here's a piece of code that was originally written by Drizz and modified by me to squeeze out a couple clock cycles
(one of my favorite pieces of "Drizz code")

Code Select

;EAX = 0 to 9999

        mov     edx,4294968          ;2^32/1000
        mov     ebx,10               ;per digit
        mul     edx                  ;extend first digit
        mov     ecx,edx              ;digit 1 in CL
        mul     ebx                  ;second digit
        mov     ch,dl                ;digit 2 in CH
        mul     ebx                  ;third digit
        bswap   ecx                  ;digits 1 & 2 up high
        mov     ch,dl                ;digit 3 in CH
        mul     ebx                  ;digit 4 in DL
        lea     ecx,[edx+ecx+'0000'] ;combine and make ASCII
        bswap   ecx                  ;re-order bytes

;ECX = "0000" to "9999"

this is a good example of what we are talking about because we use a "magic" number that works over a certain range
it works for dividends in the 0 to 9999 range, but will undoubtedly fail for larger dividends
the reason for using a multiplier that only works over a certain range is so that we do not have to shift the result

if we wanted to divide by 1000, and work over the full range of the dword in EAX....

Code Select

 mov eax,X
 mov edx,10624DD3h  ;2^38 / 1000
 mul edx
 shr edx,6
 ; edx = quotient

notice that the multiplier is 2^38 / 1000
the 32-bit register displacement of EDX:EAX takes care of 32 of the shifts
the SHR EDX,6 takes care of the remaining 6 shifts

i have, in the past, written loops to test divider constants over the desired range to verify they work :P
you perform the divide with the constant, and with DIV, and compare the results
i usually start at low dividends and work up, and write the loop to exit on first failure
that's ok for 32-bit code, but can't be done for 64-bit dividers (it would take 400 years to loop)

RuiLoureiro · May 14, 2013, 04:21:06 AM

Hey,
sometimes Dave has some good ideas
and he doesnt say anything

That code, Dave, is good ! ;)
What about your health ?
I hope fine !!! :t

qWord · May 14, 2013, 04:25:14 AM

I think the tricky part of this algorithm is to adjust the constant factor such it has the required precision for the whole input range. We can maximize the precision by calculating 2³²/x in arbitrary precision and then normalize the result to bit 2³¹ (of course correctly rounded). Due the normalization, these extra shifts come up.
For ¹/₁₀₀₀ this could be:
2³²/1000 << 9 = 2199023263

Remarks that the algorithm from AMD increase the precision only as far as needed to reduce the shift count (IIRC).

RuiLoureiro · May 14, 2013, 06:40:41 AM

Quote from: dedndave on May 14, 2013, 03:42:22 AM
here's a piece of code that was originally written by Drizz and modified by me to squeeze out a couple clock cycles
(one of my favorite pieces of "Drizz code")

Dave i tested your code, and
it is correct and we gain 130 cycles
more or less :t

dedndave · May 14, 2013, 09:18:21 AM

credit to Drizz on that one :t

Mikl__ · May 14, 2013, 04:57:02 PM

My programm division by 100

Code Select

; masm windows console #
include \masm32\include\masm32rt.inc
.686
.code
start:	mov esi,1000000000
	mov ebx,100
@@:	mov eax,42949673
	mul esi
	mov edi,edx
	xor edx,edx
	mov eax,esi
	div ebx
	cmp edi,eax
	jne error
	dec esi
	jnz @b
inkey " *** STOP - ALL EQUAL --- E N D ---*** " 
	exit
error:  print   str$(esi),13,10
        print   str$(edi),13,10
        print   str$(eax),13,10
inkey " *** STOP - NOT EQUAL --- E N D ---*** " 
            exit
end start

Quote*** STOP - ALL EQUAL --- E N D ---***

to calculate the exponential of this range is enough

RuiLoureiro · May 14, 2013, 07:25:48 PM

This is my test program.
using DivideREGby100 or not
i get quotient NOT EQUAL

By the way, in my last test i did div by 10 not by 100. Sorry !

Code Select


; File:     TestMagic10_1x.asm
;    by     RuiLoureiro
;-----------------------------------
include \masm32\include\masm32rt.inc
.686
; ¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤
DivideREGby100  MACRO   ireg
                
                mov     ecx, ireg
                            ;42949673 Mikl
                mov     eax, 42949673       ;2^32/100 ----
	          mul     ecx
                ; ---------------
                ; edx = quotient
                ; ---------------
                
                ;imul    eax, edx,100                
                ; -------------
                ; ecx=remainder
                ; -------------
                ;sub     ecx, eax
ENDM
; «««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««« 
.code
;==============================================================================
start:

                xor     edi, edi            ; cases
                
                print   "Division by 100", 13, 10                            
                mov     esi, 0                
                jmp     _next1

    _loop1:

            mov eax,42949673    ; this is from 
	      mul esi             ;  Mikl__
            ;mov edi,edx        ;
            
                ;DivideREGby100 esi           ; edx = quotient ecx=remainder
                ;push    ecx
                push    edx
                    ; -------------------------
                    ; Divide EDX:EAX by 100=ecx
                    ; -------------------------
                    mov     eax, esi
                    xor     edx, edx
                    mov     ecx, 100
                    div     ecx             ; eax= quotient edx=remainder
                ;
                pop     ebx                 ; ebx = quotient ecx=remainder         
                ;pop     ecx
                
                cmp     ebx, eax    ; quotient
                jne     _erro2
                ;
                ;cmp     ecx, edx    ; remainder
                ;jne     _erro3
                ;
    _next1:     add     esi, 1
                jns     _loop1
                
                inkey " *** STOP - ALL EQUAL --- E N D ---*** " 
                jmp     _end

    _erro2:     print   " *** STOP - quotient NOT EQUAL ---*** "   
                print   str$(esi),13,10
                print   hex$(esi),13,10        
                ;
                add     esi, 1
                add     edi, 1
                cmp     edi, 120
                jb      _loop1

                inkey " *** STOP - NOT EQUAL --- E N D ---*** "
                jmp     _end

    _erro3:     print   " *** STOP - remainder NOT EQUAL ---*** "   
                print   str$(esi),13,10
                print   hex$(esi),13,10        
                ;
                add     esi, 1
                add     edi, 1
                cmp     edi, 120
                jb      _loop1

                inkey " *** STOP - NOT EQUAL --- E N D ---*** "
                jmp     _end                 
    _end:          
            exit
;***********************************************************************************************
end start

These are my results

Code Select



Division by 100
 *** STOP - quotient NOT EQUAL ---*** 1073741899
4000004B
 *** STOP - quotient NOT EQUAL ---*** 1073741999
400000AF
 *** STOP - quotient NOT EQUAL ---*** 1073742099
40000113
 *** STOP - quotient NOT EQUAL ---*** 1073742199
40000177
 *** STOP - quotient NOT EQUAL ---*** 1073742299
400001DB
 *** STOP - quotient NOT EQUAL ---*** 1073742399
4000023F
 *** STOP - quotient NOT EQUAL ---*** 1073742499
400002A3
 *** STOP - quotient NOT EQUAL ---*** 1073742599
40000307
 *** STOP - quotient NOT EQUAL ---*** 1073742699
4000036B
 *** STOP - quotient NOT EQUAL ---*** 1073742799
400003CF
 *** STOP - quotient NOT EQUAL ---*** 1073742899
40000433
 *** STOP - quotient NOT EQUAL ---*** 1073742999
40000497
 *** STOP - quotient NOT EQUAL ---*** 1073743099
400004FB
 *** STOP - quotient NOT EQUAL ---*** 1073743199
4000055F
 *** STOP - quotient NOT EQUAL ---*** 1073743299
400005C3
 *** STOP - quotient NOT EQUAL ---*** 1073743399
40000627
 *** STOP - quotient NOT EQUAL ---*** 1073743499
4000068B
 *** STOP - quotient NOT EQUAL ---*** 1073743599
400006EF
 *** STOP - quotient NOT EQUAL ---*** 1073743699
40000753
 *** STOP - quotient NOT EQUAL ---*** 1073743799
400007B7
 *** STOP - quotient NOT EQUAL ---*** 1073743899
4000081B
 *** STOP - quotient NOT EQUAL ---*** 1073743999
4000087F
 *** STOP - quotient NOT EQUAL ---*** 1073744099
400008E3
 *** STOP - quotient NOT EQUAL ---*** 1073744199
40000947
 *** STOP - quotient NOT EQUAL ---*** 1073744299
400009AB
 *** STOP - quotient NOT EQUAL ---*** 1073744399
40000A0F
 *** STOP - quotient NOT EQUAL ---*** 1073744499
40000A73
 *** STOP - quotient NOT EQUAL ---*** 1073744599
40000AD7
 *** STOP - quotient NOT EQUAL ---*** 1073744699
40000B3B
 *** STOP - quotient NOT EQUAL ---*** 1073744799
40000B9F
 *** STOP - quotient NOT EQUAL ---*** 1073744899
40000C03
 *** STOP - quotient NOT EQUAL ---*** 1073744999
40000C67
 *** STOP - quotient NOT EQUAL ---*** 1073745099
40000CCB
 *** STOP - quotient NOT EQUAL ---*** 1073745199
40000D2F
 *** STOP - quotient NOT EQUAL ---*** 1073745299
40000D93
 *** STOP - quotient NOT EQUAL ---*** 1073745399
40000DF7
 *** STOP - quotient NOT EQUAL ---*** 1073745499
40000E5B
 *** STOP - quotient NOT EQUAL ---*** 1073745599
40000EBF
 *** STOP - quotient NOT EQUAL ---*** 1073745699
40000F23
 *** STOP - quotient NOT EQUAL ---*** 1073745799
40000F87
 *** STOP - quotient NOT EQUAL ---*** 1073745899
40000FEB
 *** STOP - quotient NOT EQUAL ---*** 1073745999
4000104F
 *** STOP - quotient NOT EQUAL ---*** 1073746099
400010B3
 *** STOP - quotient NOT EQUAL ---*** 1073746199
40001117
 *** STOP - quotient NOT EQUAL ---*** 1073746299
4000117B
 *** STOP - quotient NOT EQUAL ---*** 1073746399
400011DF
 *** STOP - quotient NOT EQUAL ---*** 1073746499
40001243
 *** STOP - quotient NOT EQUAL ---*** 1073746599
400012A7
 *** STOP - quotient NOT EQUAL ---*** 1073746699
4000130B
 *** STOP - quotient NOT EQUAL ---*** 1073746799
4000136F
 *** STOP - quotient NOT EQUAL ---*** 1073746899
400013D3
 *** STOP - quotient NOT EQUAL ---*** 1073746999
40001437
 *** STOP - quotient NOT EQUAL ---*** 1073747099
4000149B
 *** STOP - quotient NOT EQUAL ---*** 1073747199
400014FF
 *** STOP - quotient NOT EQUAL ---*** 1073747299
40001563
 *** STOP - quotient NOT EQUAL ---*** 1073747399
400015C7
 *** STOP - quotient NOT EQUAL ---*** 1073747499
4000162B
 *** STOP - quotient NOT EQUAL ---*** 1073747599
4000168F
 *** STOP - quotient NOT EQUAL ---*** 1073747699
400016F3
 *** STOP - quotient NOT EQUAL ---*** 1073747799
40001757
 *** STOP - quotient NOT EQUAL ---*** 1073747899
400017BB
 *** STOP - quotient NOT EQUAL ---*** 1073747999
4000181F
 *** STOP - quotient NOT EQUAL ---*** 1073748099
40001883
 *** STOP - quotient NOT EQUAL ---*** 1073748199
400018E7
 *** STOP - quotient NOT EQUAL ---*** 1073748299
4000194B
 *** STOP - quotient NOT EQUAL ---*** 1073748399
400019AF
 *** STOP - quotient NOT EQUAL ---*** 1073748499
40001A13
 *** STOP - quotient NOT EQUAL ---*** 1073748599
40001A77
 *** STOP - quotient NOT EQUAL ---*** 1073748699
40001ADB
 *** STOP - quotient NOT EQUAL ---*** 1073748799
40001B3F
 *** STOP - quotient NOT EQUAL ---*** 1073748899
40001BA3
 *** STOP - quotient NOT EQUAL ---*** 1073748999
40001C07
 *** STOP - quotient NOT EQUAL ---*** 1073749099
40001C6B
 *** STOP - quotient NOT EQUAL ---*** 1073749199
40001CCF
 *** STOP - quotient NOT EQUAL ---*** 1073749299
40001D33
 *** STOP - quotient NOT EQUAL ---*** 1073749399
40001D97
 *** STOP - quotient NOT EQUAL ---*** 1073749499
40001DFB
 *** STOP - quotient NOT EQUAL ---*** 1073749599
40001E5F
 *** STOP - quotient NOT EQUAL ---*** 1073749699
40001EC3
 *** STOP - quotient NOT EQUAL ---*** 1073749799
40001F27
 *** STOP - quotient NOT EQUAL ---*** 1073749899
40001F8B
 *** STOP - quotient NOT EQUAL ---*** 1073749999
40001FEF
 *** STOP - quotient NOT EQUAL ---*** 1073750099
40002053
 *** STOP - quotient NOT EQUAL ---*** 1073750199
400020B7
 *** STOP - quotient NOT EQUAL ---*** 1073750299
4000211B
 *** STOP - quotient NOT EQUAL ---*** 1073750399
4000217F
 *** STOP - quotient NOT EQUAL ---*** 1073750499
400021E3
 *** STOP - quotient NOT EQUAL ---*** 1073750599
40002247
 *** STOP - quotient NOT EQUAL ---*** 1073750699
400022AB
 *** STOP - quotient NOT EQUAL ---*** 1073750799
4000230F
 *** STOP - quotient NOT EQUAL ---*** 1073750899
40002373
 *** STOP - quotient NOT EQUAL ---*** 1073750999
400023D7
 *** STOP - quotient NOT EQUAL ---*** 1073751099
4000243B
 *** STOP - quotient NOT EQUAL ---*** 1073751199
4000249F
 *** STOP - quotient NOT EQUAL ---*** 1073751299
40002503
 *** STOP - quotient NOT EQUAL ---*** 1073751399
40002567
 *** STOP - quotient NOT EQUAL ---*** 1073751499
400025CB
 *** STOP - quotient NOT EQUAL ---*** 1073751599
4000262F
 *** STOP - quotient NOT EQUAL ---*** 1073751699
40002693
 *** STOP - quotient NOT EQUAL ---*** 1073751799
400026F7
 *** STOP - quotient NOT EQUAL ---*** 1073751899
4000275B
 *** STOP - quotient NOT EQUAL ---*** 1073751999
400027BF
 *** STOP - quotient NOT EQUAL ---*** 1073752099
40002823
 *** STOP - quotient NOT EQUAL ---*** 1073752199
40002887
 *** STOP - quotient NOT EQUAL ---*** 1073752299
400028EB
 *** STOP - quotient NOT EQUAL ---*** 1073752399
4000294F
 *** STOP - quotient NOT EQUAL ---*** 1073752499
400029B3
 *** STOP - quotient NOT EQUAL ---*** 1073752599
40002A17
 *** STOP - quotient NOT EQUAL ---*** 1073752699
40002A7B
 *** STOP - quotient NOT EQUAL ---*** 1073752799
40002ADF
 *** STOP - quotient NOT EQUAL ---*** 1073752899
40002B43
 *** STOP - quotient NOT EQUAL ---*** 1073752999
40002BA7
 *** STOP - quotient NOT EQUAL ---*** 1073753099
40002C0B
 *** STOP - quotient NOT EQUAL ---*** 1073753199
40002C6F
 *** STOP - quotient NOT EQUAL ---*** 1073753299
40002CD3
 *** STOP - quotient NOT EQUAL ---*** 1073753399
40002D37
 *** STOP - quotient NOT EQUAL ---*** 1073753499
40002D9B
 *** STOP - quotient NOT EQUAL ---*** 1073753599
40002DFF
 *** STOP - quotient NOT EQUAL ---*** 1073753699
40002E63
 *** STOP - quotient NOT EQUAL ---*** 1073753799
40002EC7
 *** STOP - NOT EQUAL --- E N D ---***

Your test program do only one step esi=0FFFFFFFFh
then dec esi do esi=0FFFFFFFEh and it has SIGN
so EXIT. It is very very very FAST ! ;)

Quote
; masm windows console #
include \masm32\include\masm32rt.inc
.686
.code
start:   mov esi,0FFFFFFFFh
     mov ebx,100

@@:   mov eax,42949673
     mul esi
mov edi,edx
;
     xor edx,edx
     mov eax,esi
     div ebx
;
     cmp edi,eax
     jne error

     dec esi
     jns @b ;<---- your error is HERE

inkey " *** STOP - ALL EQUAL --- E N D ---*** "
     exit

error: print str$(esi),13,10
print str$(edi),13,10
print str$(eax),13,10
inkey " *** STOP - NOT EQUAL --- E N D ---*** "
exit
end start

Your result should be this:
-97
42949672
2
*** STOP - NOT EQUAL --- E N D ---***

Mikl__ · May 14, 2013, 07:32:26 PM

Hi, RuiLoureiro!

QuoteYour test program do only one step esi=0FFFFFFFFh

I've seen this error, thank you!
But in the rang from 1000000000 to 0 my test is working correctly!

RuiLoureiro · May 14, 2013, 08:20:36 PM

Quote from: Mikl__ on May 14, 2013, 07:32:26 PM
Hi, RuiLoureiro!
QuoteYour test program do only one step esi=0FFFFFFFFh
I've seen this error, thank you!
But in the rang from 1000000000 to 0 my test is working correctly!

you should use this:
mov eax,X
mov edx,051EB851Fh
mul edx
shr edx,05h <- more this instruction only
; edx = quotient
i think that i tested it in that range and it works well, yes.

RuiLoureiro · May 14, 2013, 10:57:49 PM

Quote from: dedndave on May 14, 2013, 09:18:21 AM
credit to Drizz on that one :t

credit to Dave, i say. I did it because Dave post it :t
well, Drizz takes a little one ;)
thank you Dave

RuiLoureiro · May 14, 2013, 11:12:15 PM

Quote from: Mikl__ on May 14, 2013, 04:57:02 PM
My programm division by 100
...
to calculate the exponential of this range is enough

Yes, very well, it is exactly correct.

I put the question to myself for all cases
because i wanted to save the procedure as a macro
for future use. And i found out that i can save it
but with some notes ! See my reply 15

dedndave · May 14, 2013, 11:14:51 PM

the original post
http://www.masmforum.com/board/index.php?topic=12234.msg93696#msg93696
Drizz writes some fast stuff :P

he used push/pop and shl 16
i replaced those with a couple bswap's and squeezed 2 clock cycles - lol

RuiLoureiro · May 14, 2013, 11:24:04 PM

Quote from: dedndave on May 14, 2013, 11:14:51 PM
the original post
http://www.masmforum.com/board/index.php?topic=12234.msg93696#msg93696
Drizz writes some fast stuff :P

he used push/pop and shl 16
i replaced those with a couple bswap's and squeezed 2 clock cycles - lol

well what bsawp does ? i dont know. Does it exchange the "e" part of eax with ax for instance ?

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