-------------------------------------------------
VFP 9.0 FIX - ROUND() Function
February 2017
-------------------------------------------------
CCB
1. BUG:
There is a test program from Mr. Christof Wollenhaupt:
*PROC testroundfunction
?ROUND(512.9250000000,2) && Displays 512.92
?ROUND(512.925000000,2) && Displays 512.93
WAIT
RETURN
* END OF PROC TESTROUNDFUNCTION.
We think they will display 512.93, but:
?ROUND(512.9250000000,2) && Displays 512.92
2. CAUSE:
Please refer to the head of the testroundfunction.fxp:
00000000: FE F2 FF 22-02 01 00 00-00 D8 00 00-00 A1 00 00
00000010: 00 37 00 00-00 00 00 00-00 00 00 00-00 00 00 00
00000020: 00 00 00 00-00 00 00 3F-27 00 00 00-00 25 00 00
00000030: 00 00 00 00-00 00 00 00-00 68 00 00-00 03 00 00
00000040: 00 62 00 00-00 8F 56 82-47 1C 00 00-00 85 00 00
00000050: 35 00 00 00-19 00 02 F8-03 01 FC 43-FA 0E 0A 66
00000060: 66 66 66 66-07 80 40 F8-01 02 54 FD-FE 19 00 02
00000070: F8 03 01 FC-43 FA 0D 09-66 66 66 66-66 07 80 40
00000080: F8 01 02 54-FD FE 03 00-55 00 00 91-01 91 01 31
00000090: 00 00 00 00-00 00 00 00-00 00 00 00-00 00 00 00
The p-code for the statement "?ROUND(512.9250000000,2)" from 0x00000054:
19 00 02 F8 03 01 FC 43 FA 0E 0A 66 66 66 66 66 07 80 40 F8 01 02 54 FD FE
The width of the floating-point number is 0x0E (dec: 14).
The number of decimal places is 0x0A (dec: 10).
The 64-bit floating-point number is 0x4080076666666666.
The p-code for the statement "?ROUND(512.925000000,2)" from 0x0000006D:
19 00 02 F8 03 01 FC 43 FA 0D 09 66 66 66 66 66 07 80 40 F8 01 02 54 FD FE
The width of the floating-point number is 0x0D (dec: 13).
The number of decimal places is 0x09 (dec: 9).
The 64-bit floating-point number is 0x4080076666666666.
They are the same 64-bit floating-point numbers:
512.9250000000 = 0x4080076666666666
512.925000000 = 0x4080076666666666
the difference is the width of the floating-point number and the number of decimal places.
For the details when VFP calculate ROUND(512.9250000000,2):
512. 9249 9999 9999 9546 0
+ 0. 0000 0000 0000 0500 0 (n=10, eps = 0.5*10^(-(n+3)) = 5.0000000000000001520E-14)
----------------------------
512. 9249 9999 9999 9546 0
512. 9249 9999 9999 9546 0
* 100. 0000 0000 0000 0000 0
----------------------------
51292. 4999 9999 9992 720
+ 0. 5000 0000 0000 0000 0
----------------------------
51292. 9999 9999 9992 720
floor(51292. 9999 9999 9992 720) = 51292.000000000000000
51292. 0000 0000 0000 0000 0
/ 100. 0000 0000 0000 0000 0
----------------------------
512. 9199 9999 9999 9590 0
+ 0. 0000 0500 0000 0000 0 (n=2, eps = 0.5*10^(-(n+3)) = 5.0000000000000004090E-06)
----------------------------
512. 9200 0499 9999 9464 0
So ROUND(512.9250000000,2) = 512.92.
For the details when VFP calculate ROUND(512.925000000,2):
512. 9249 9999 9999 9546 0
+ 0. 0000 0000 0000 4999 9 (n=9, eps = 0.5*10^(-(n+3)) = 4.9999999999999999000E-13)
----------------------------
512. 9250 0000 0000 4092 0
512. 9250 0000 0000 4092 0
* 100. 0000 0000 0000 0000 0
----------------------------
51292. 5000 0000 0043 660
+ 0. 5000 0000 0000 0000 0
----------------------------
51293. 0000 0000 0043 660
floor(51293. 0000 0000 0043 660) = 51293.000000000000000
51293. 0000 0000 0000 0000 0
/ 100. 0000 0000 0000 0000 0
----------------------------
512. 9299 9999 9999 9500 0
+ 0. 0000 0500 0000 0000 0 (n=2, eps = 0.5*10^(-(n+3)) = 5.0000000000000004090E-06)
----------------------------
512. 9300 0499 9999 9374 0
So ROUND(512.925000000,2) = 512.93.
If we set enable adjust the precision of the floating-point numbers in Visual FoxPro Advanced,
Visual FoxPro Advanced will set 15 valid digits for the following functions:
ROUND() Function,
INT() Function.
Visual FoxPro Advanced will adjust the floating-point numbers before call the floor() function:
51292. 9999 9999 9992 720
+00000. 0000 0000 005
--------------------------
51293. 0000 0000 0042 720
floor(51292. 9999 9999 9992 720 +00000. 0000 0000 005) = 51293.000000000000000
So ROUND(512.9250000000,2) = 512.93.
51293. 0000 0000 0043 660
+00000. 0000 0000 005
--------------------------
51293. 0000 0000 0093 660
floor(51293. 0000 0000 0043 660 +00000. 0000 0000 005) = 51293.000000000000000
So ROUND(512.925000000,2) = 512.93.
Visual FoxPro Advanced will also set 15 valid digits and round the value to integer when subtract two datetimes
to get the difference between them in seconds.
For the test program from Mr. Sergey Karimov:
lnsec= {^2000/01/01 01:01:00 AM}-{^2000/01/01 00:00:00 AM}
a1= lnsec%3600
a2= a1/60
?lnsec, a1, a2, FLOOR(a1)/60, FLOOR(a1/60)
Now it can run fine if we set enable adjust the precision of the floating-point numbers in Visual FoxPro Advanced.
3. RESOLUTION:
We can write some code to fix the BUG.
Label4aea26 ::
mov eax , dword ptr [ esp + 20 ] ;0x004aea26 : 8b442414
fld qword ptr [ 8 * ebp + offset Data922520 ] ;0x004aea2a : dd04ed20259200
sub esp , 08h ;0x004aea31 : 83ec08
fstp qword ptr [ esp + 40 ] ;0x004aea34 : dd5c2428
test eax , eax ;0x004aea38 : 85c0
jne Label591da6 ;0x004aea3a : 0f8566330e00
fld qword ptr [ esp + 40 ] ;0x004aea40 : dd442428
fmul st(0) , st(1) ;0x004aea44 : d8c9
;
; -------------------------------------------------
; VFP 9.0 FIX - ROUND() Function
; February 2017
; -------------------------------------------------
; CCB
;
; Sometimes the ROUND() function returns wrong result, for example,
; ?ROUND(512.9250000000,2) && Displays 512.92
; ?ROUND(512.925000000,2) && Displays 512.93
;
; 2017/2/26, by ccb
;
cmp dword ptr vfpa_sys9001_data,00h
je Label4aea46
fld st(0)
fabs
fldlg2
fxch st(1)
fyl2x
fld st(0)
fistp dword ptr [ esp ]
mov ecx,dword ptr [ esp ]
cmp ecx,80000000h
je Label4aea45
and ecx,80000000h
test ecx,ecx
jne Label4aea45
mov eax,0
fadd qword ptr [ 8 * eax + offset Data922438 ]
mov eax,10
fadd qword ptr [ 8 * eax + offset Data922438 ]
fistp dword ptr [ esp ]
mov eax,15
sub eax,dword ptr [ esp ]
cmp eax,0
jle Label4aea46
cmp eax,15
jge Label4aea46
fld st(0)
fistp dword ptr [ esp ]
mov ecx,dword ptr [ esp ]
cmp ecx,80000000h
je Label4aea46
and ecx,80000000h
test ecx,ecx
jne Label4aea44
fadd qword ptr [ 8 * eax + offset Data922438 ]
jmp Label4aea46
Label4aea44 ::
fsub qword ptr [ 8 * eax + offset Data922438 ]
jmp Label4aea46
Label4aea45 ::
fstp st(0)
jmp Label4aea46
Label4aea46 ::
fadd qword ptr [ Data9256b0 ] ;0x004aea46 : dc05b0569200
fstp qword ptr [ esp ] ;0x004aea4c : dd1c24
fstp st(0) ;0x004aea4f : ddd8
call floor ;0x004aea51 : ff15a0799100
fdiv qword ptr [ esp + 40 ] ;0x004aea57 : dc742428
Label4aea5b ::
add esp , 08h ;0x004aea5b : 83c408
test ebx , ebx ;0x004aea5e : 85db
jne Label591dc2 ;0x004aea60 : 0f855c330e00
Label4aea66 ::
mov eax , dword ptr [ esp + 24 ] ;0x004aea66 : 8b442418
fstp qword ptr [edi] ;0x004aea6a : dd1f
test eax , eax ;0x004aea6c : 85c0
jne Label591dc9 ;0x004aea6e : 0f8555330e00
mov eax , dword ptr [ esp + 20 ] ;0x004aea74 : 8b442414
test eax , eax ;0x004aea78 : 85c0
jne Label591e1c ;0x004aea7a : 0f859c330e00
mov eax , dword ptr [ esi + 8 ] ;0x004aea80 : 8b4608
cmp ebp , eax ;0x004aea83 : 3be8
ja Label591e28 ;0x004aea85 : 0f879d330e00
Label4aea8b ::
cmp ebp , 012h ;0x004aea8b : 83fd12
jnl Label591e42 ;0x004aea8e : 0f8dae330e00
Label4aea94 ::
mov dword ptr [ esi + 8 ] , ebp ;0x004aea94 : 896e08
Label4aea97 ::
mov eax , dword ptr [ esi + 4 ] ;0x004aea97 : 8b4604
cmp eax , 028h ;0x004aea9a : 83f828
jnl Label4aeaa3 ;0x004aea9d : 7d04
inc eax ;0x004aea9f : 40
mov dword ptr [ esi + 4 ] , eax ;0x004aeaa0 : 894604
Label4aeaa3 ::
mov eax , dword ptr [ esp + 28 ] ;0x004aeaa3 : 8b44241c
test eax , eax ;0x004aeaa7 : 85c0
jne Label591e4c ;0x004aeaa9 : 0f859d330e00
Label4aeaaf ::
pop edi ;0x004aeaaf : 5f
pop esi ;0x004aeab0 : 5e
pop ebp ;0x004aeab1 : 5d
pop ebx ;0x004aeab2 : 5b
mov esp , ebp ;0x004aeab3 : 8be5
pop ebp ;0x004aeab5 : 5d
ret ;0x004aeab6 : c3
4. APPLIES TO:
VFP 6.0.8167.0
VFP 6.0.8961.0 (SP5)
VFP 7.0.0.9262
VFP 7.0.0.9465 (SP1)
VFP 8.0.0.2521
VFP 8.0.0.3117 (SP1)
VFP 9.0.0.2412
VFP 9.0.0.3504 (SP1)
VFP 9.0.0.4611 (SP2)
VFP 9.0.0.5015 (SP2)
VFP 9.0.0.5411 (SP2)
VFP 9.0.0.5721 (SP2)
VFP 9.0.0.5815 (SP2)
VFP 9.0.0.6303 (SP2)
VFP 9.0.0.6602 (SP2)
VFP 9.0.0.7423 (SP2)
The bug has been fixed in VFP Advanced.
5. REFERENCE WEBSITES:
1, baiyujia.com:
http://www.baiyujia.com
2, microsoft.com:
https://social.msdn.microsoft.com/Forums/en-US/cee551be-35f8-4ddc-a07e-51d2d7f79345/rounding-bug-in-vfp8
https://social.msdn.microsoft.com/Forums/en-US/a8725753-5815-4d45-aa7b-bdead9277986/how-can-i-subract-datetime-values
3, foxite.com:
https://www.foxite.com/archives/round-problem-0000070917.htm
https://www.foxite.com/archives/interesting-behavior-of-inputmask-0000406050.htm
https://www.foxite.com/archives/round-0000223089.htm
https://www.foxite.com/archives/how-to-compute-the-elapsed-time-in-foxpro-0000058524.htm
https://www.foxite.com/archives/int-strange-behavior-0000445268.htm
4, tek-tips.org:
http://www.tek-tips.com/viewthread.cfm?qid=531793
http://www.tek-tips.com/viewthread.cfm?qid=1738764
5, foxpert.com:
http://www.foxpert.com/foxpro/knowlbits/files/knowlbits_201102_1.html
6, fox-id.org:
http://www.fox-id.org/smf/general-code-activex-com/hasil-perhitungan-vfp-kok-beda-sama-kalkulator/
6. OTHER:
For reference only, there is no guarantees.
Any questions or suggestions, please e-mail to ccb2000@163.com.
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